Land-Ocean Interactions in the Coastal Zone (LOICZ)
CORE PROJECT OF THE
INTERNATIONAL GEOSPHERE-BIOSPHERE PROGRAMME: A STUDY OF GLOBAL CHANGE
(IGBP)
OF THE INTERNATIONAL COUNCIL OF SCENTIFIC UNIONS
DOPP 0
DIPP 0 µM;
µM;
VPDIPP 0.
V DOP
VRDIPR = - 119
DIPQ = 0.4µM
DIP2 = 0.3 µM
DIP1
1.5 µM
VQDIPQ = 48
VX(DIP2 - DIP1) = -1,228
VRDOPR = - 59
DOP
VQDOPQ = 84
1
DOP2 = 0.3 µM
0.6
µM
DOPQ = 0.7 µM
VX(DOP2 - DOP1)= -307
DIP = + 1,299
DOP = + 282
LOICZ BIOGEOCHEMICAL Modelling Guidelines
D.C. GORDON, JR., P.R. BOUDREAU, K.H. MANN, J.-E. ONG, W.L. SILVERT, S.V. SMITH, G.
WATTAYAKORN,
F. WULFF AND T. YANAGI
LOICZ REPORTS & STUDIES NO. 5
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LOICZ BIOGEOCHEMICAL Modelling Guidelines
D.C. GORDON, JR.
BEDFORD INSTITUTE OF OCEANOGRAPHY, DARTMOUTH, CANADA.
P.R. BOUDREAU
LOICZ CORE PROJECT OFFICE, TEXEL, THE NETHERLANDS.
K.H. MANN
BEDFORD INSTITUTE OF OCEANOGRAPHY, DARTMOUTH, CANADA.
J.-E. ONG
UNIVERSITI SAINS MALAYSIA, PENANG, MALAYSIA.
W.L. SILVERT
BEDFORD INSTITUTE OF OCEANOGRAPHY, DARTMOUTH, CANADA.
S.V. SMITH
UNIVERSITY OF HAWAII, HONOLULU, UNITED STATES.
G. WATTAYAKORN
CHULALONGKORN UNIVERSITY, BANGKOK, THAILAND.
F. WULFF
STOCKHOLM UNIVERSITY, STOCKHOLM, SWEDEN.
T. YANAGI
EHIME UNIVERSITY, MATSUYAMA, JAPAN.
LOICZ REPORTS & STUDIES No. 5
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PUBLISHED IN THE NETHERLANDS, 1996 BY:
LOICZ CORE PROJECT
NETHERLANDS INSTITUTE FOR SEA RESEARCH
P.O. BOX 59
1790 AB DEN BURG - TEXEL
THE NETHERLANDS
THE LAND-OCEAN INTERACTIONS IN THE COASTAL ZONE PROJECT IS A CORE PROJECT
OF THE "INTERNATIONAL GEOSPHERE-BIOSPHERE PROGRAMME: A STUDY OF GLOBAL
CHANGE", OF THE INTERNATIONAL COUNCIL OF SCIENTIFIC UNIONS.
THE LOICZ CORE PROJECT IS FINANCIALLY SUPPORTED THROUGH THE NETHERLANDS
ORGANISATION FOR SCIENTIFIC RESEARCH BY: THE MINISTRY OF EDUCATION, CULTURE
AND SCIENCE; THE MINISTRY OF TRANSPORT, PUBLIC WORKS AND WATER
MANAGEMENT; THE MINISTRY OF HOUSING, PLANNING AND ENVIRONMENT; AND THE
MINISTRY OF AGRICULTURE, NATURE MANAGEMENT AND FISHERIES OF THE
NETHERLANDS, AS WELL AS THE ROYAL NETHERLANDS ACADEMY OF SCIENCES, AND
THE NETHERLANDS INSTITUTE FOR SEA RESEARCH.
Copyright © 1996, LAND-OCEAN INTERACTIONS IN THE COASTAL ZONE CORE PROJECT OF
THE IGBP.
SECOND EDITION.
REPRODUCTION OF THIS PUBLICATION FOR EDUCATIONAL OR OTHER,
NON-COMMERCIAL PURPOSES IS AUTHORISED WITHOUT PRIOR
PERMISSION FROM THE COPYRIGHT HOLDER.
REPRODUCTION FOR RESALE OR OTHER PURPOSES IS PROHIBITED
WITHOUT THE PRIOR, WRITTEN PERMISSION OF THE COPYRIGHT HOLDER.
CITATION:
D.C. GORDON, JR., P.R. BOUDREAU, K.H. MANN, J.-E. ONG, W.L. SILVERT,
S.V. SMITH, G. WATTAYAKORN, F. WULFF AND T. YANAGI. 1996. LOICZ
BIOGEOCHEMICAL MODELLING GUIDELINES. LOICZ/R&S/95-5, VI +96 PP.
LOICZ, TEXEL, THE NETHERLANDS.
ISSN:
1383-4304
COVER:
PHOSPORUS BUDGET FOR KLONG LAD KHAO KHAO, THAILAND.
DISCLAIMER: THE DESIGNATIONS EMPLOYED AND THE PRESENTATION OF THE
MATERIAL CONTAINED IN THIS REPORT DO NOT IMPLY THE EXPRESSION
OF ANY OPINION WHATSOEVER ON THE PART OF LOICZ OR THE IGBP
CONCERNING THE LEGAL STATUS OF ANY STATE, TERRITORY, CITY OR
AREA, OR CONCERNING THE DELIMITATION'S OF THEIR FRONTIERS OR
BOUNDARIES. THIS REPORT CONTAINS THE VIEWS EXPRESSED BY THE
AUTHORS AND MAY NOT NECESSARILY REFLECT THE VIEWS OF THE IGBP.
THE LOICZ REPORTS AND STUDIES SERIES IS PUBLISHED AND DISTRIBUTED FREE OF CHARGE TO SCIENTISTS
INVOLVED IN GLOBAL CHANGE RESEARCH IN COASTAL AREAS.
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TABLE OF CONTENTS
PAGE
PREFACE
v
1. EXECUTIVE SUMMARY
1
2. INTRODUCTION
3
2.1 The LOICZ Biogeochemical Modelling Strategy
3
2.2 Spatial and Temporal Scope of LOICZ Modelling
5
2.3 Recommended Modelling Approach
5
2.4 Integration of Biogeochemical and Socio-Economic Modelling within
6
LOICZ
2.5 Potential Benefits for Managers
6
2.6 Objectives of Guidelines
6
3. GENERAL CONSIDERATION IN CONSTRUCTING COASTAL MODELS
7
3.1 Why Build Models?
7
3.2 Some Basic Modelling Principles
7
3.3 The LOICZ Classification of Modelling Approaches
10
3.4 Budget Models
11
3.5 Process Models
11
3.6 System Models
11
3.7 Prognostic Models
12
3.8 Historical Perspective
12
3.9 Modelling Requirements of LOICZ
14
3.10 Importance of Scaling in Modelling
16
4. THE MERBOK MANGROVE EXPERIENCE
17
4.1 Single Cross-section Hydrodynamic Budgeting
17
4.2 3-D Numerical Hydrodynamic Flow Modelling
18
4.3 Modelling The Mangrove-Atmosphere Interface
18
4.4 A Mass Balance Carbon And Nutrient Budget in a Mangrove Ecosystem
18
4.5 Mangrove Modelling with STELLA
19
5. RESPONSE TO FIRST LOICZ MODELLING REQUIREMENT- QUANTIFY FLUX
23
5.1 Describing Physical/Biological Systems and Defining Natural Boundaries 23
5.2 Defining the Questions to be Addressed
23
5.3 General Methodological Background
24
5.4 Mathematical Structure of the Budgeting Procedure
29
5.5 Preparation for the Case-Study Calculations
40
5.6 Case Studies
43
5.7 Summary of Case Studies
74
6. RESPONSE TO SECOND LOICZ MODELLING REQUIREMENT - PREDICTION
75
6.1 The Development of a Dynamic Simulation Model -
78
a Simple Demonstration
7. MEETING THE GLOBAL BIOGEOCHEMICAL MODELLING OBJECTIVES OF LOICZ 85
8. ACKNOWLEDGEMENTS
87
9. REFERENCES
88
ANNEX 1 REVIEW OF SELECTED MODELLING SOFTWARE PACKAGES
94
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PAGE
TEXT BOXES
TEXT BOX 1.ACTIVITIES RELATED TO THE DEVELOPMENT OF GLOBAL SYNTHESES AND
MODELS
4
of carbon, nitrogen and phosphorous in the coastal ocean envisaged
under LOICZ. See LOICZ Implementation Plan
(Pernetta and Milliman, 1995) for details.
Text Box 2. Equations generated by STELLA software to implement mangrove model.
20
Text Box 3. Summary of sequential steps in budgetary modelling analysis.
24
Text Box 4. Summary of requirements for budget modelling analysis.
41
Text Box 5. The STELLA presentation of differential equations and processes
81
of the Model Bay.
Text Box 6. Basic advice for carrying out general system modelling.
84
TABLES
Table 1.
Factors relating to the definition of the coastal zone areas for the
15
development of coastal budget models.
Table 2.
Nonconservative dissolved inorganic P and N fluxes
46
in Bahia San Quintín Bay.
Table 3.
Average nutrient concentrations (µmol) for components of the
48
Klong Lad Khao Khao system.
Table 4.
Stream flow (VQ) , precipitation (P), and evaporation (E) data for Tomales Bay, 53
July 1987-July 1991, at the two-month increments.
Table 5.
Water circulation (residual flow and water exchange rate) as calculated from
54
the water and salt budgets for Tomales Bay, July 1987-July 1991.
Table 6.
Nonconservative flux calculations for DIP in Tomales Bay, July 1987-July 1991. 55
Notation as in previous table; VP=0.20.
Table 7.
Average nonconservative fluxes for dissolved carbon, nitrogen, and
56
phosphorous in Tomales Bay, July 1987-July 1991.
Table 8.
Average stoichiometric fluxes in Tomales Bay, July 1987-July 1991,
57
calculated from data in Table 7.
Table 9.
Nonconservative nitrogen and phosphorous fluxes and stoichiometric
65
calculations for sub-basins of the Baltic-Kattegat system
(fluxes in mmol m-2 yr-1).
Table 10. Nonconservative carbon, nitrogen and phosphorous fluxes and
71
stoichiometric calculations for sub-basins of Spencer Gulf
(fluxes in mmol m-2 d-1, except TA, which is in meq m-2 d-1 ).
FIGURES
Figure 1. Data and understanding requirements for modelling, from Holling (1978).
8
Figure 2.
Detailed model for Merbok mangrove developed using STELLA software.
20
Figure 3. Complex system model of the Merbok Mangrove system generated using
21
STELLA software.
Figure 4. Generalised box diagram illustrating the water budget for a coastal water body.
25
Figure 5. Generalized box diagram illustrating the salt budget for a coastal water body.
26
Figure 6. Generalized box diagram illustrating the budget for a nonconservative
27
material, Y, in a coastal water body.
Figure 7. Generalized box diagram illustrating the budget for a nonconservative
28
material, Y, with an active gas phase in a coastal water body.
Figure 8. Location of Bahia San Quintín, Mexico.
44
Figure 9. Steady-state water and salt budgets for Bahia San Quintín, Mexico.
45
Figure 10. Steady-state DIP and DIN budgets for Bahia San Quintín, Mexico.
46
Figure 11. Location of Klong Lad Khao Khao, Thailand.
48
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Figure 12. Steady-state water and salt budgets for Klong Lad Khao Khao.
49
Figure 13. Steady-state dissolved phosphorous and nitrogen budgets
50
for Klong Lad Khao Khao.
Figure 14. Location of Tomales Bay, California, United States.
52
Figure 15. Time series of daily water exchange volume (VX) between the inner
54
and outer portions of Tomales Bay.
Figure 16. Time series of net nonconservative flux of DIP (DIP) in Tomales Bay.
55
Figure 17. Location of the Baltic-Kattegat system.
57
Figure 18. Monthly variations in freshwater inputs, water level, and water exchange
58
in Bothnian Bay (solid) and Bothnian Sea (dashed).
Figure 19. Monthly variations in the nonconservative fluxes of materials in
59
Bothnian Bay (solid) and the Bothnian Sea (dashed).
Figure 20. Annual budgets of phosphorous and nitrogen in the Gulf of Bothnia 1991.
60
Figure 21. Steady-state water and salt budgets for the Baltic-Kattegat system
62
to illustrate horizontal and vertical linkages between compartments.
Figure 22. Steady-state dissolved inorganic phosphorous budget
63
for the Baltic-Kattegat system.
Figure 23. Steady-state dissolved inorganic nitrogen budget for the Baltic-Kattegat system. 64
Figure 24. Location of Spencer Gulf, Australia.
66
Figure 25. Distribution of DI P as a function of salinity in Spencer Gulf.
66
Figure 26. Steady-state water and salt budgets for Spencer Gulf.
67
Figure 27. Steady-state dissolved phosphorous budgets for Spencer Gulf.
68
Figure 28. Steady-state dissolved nitrogen budgets for Spencer Gulf.
69
Figure 29. Steady-state fluxes of total alkalinity, dissolved inorganic carbon, and
70
dissolved organic carbon in Spencer Gulf.
Figure 30. Calculated residual flow in the upper layers of Tokyo Bay
72
in the summer and winter.
Figure 31. Estimated exchange flow (VX) at the mouth of Tokyo Bay on the basis of
72
calculated tidal currents and residual flow.
Figure 32. Calculated residual flow in the upper and lower layers of the
73
East China Sea and the Yellow Sea in the summer and winter.
Figure 33. The basic flow structure that is resolved in most oceanic model of nutrient fluxes. 76
Figure 34. A simplified conceptual flow diagram of nutrient cycles in a coastal ecosystem.
76
Figure 35. A schematic illustration of spatial and temporal scales of coastanl and
78
marine systems. Processes that occur on large scales will be treated
as external forcing functions, those on a lower scale will be parameterised.
Figure 36. The graphical flow diagram of nutrient dynamic in the `Model Bay'
79
using STELLA software.
Figure 37. The change in concentration of nitrogen (µmol l-1 ) of the four state variables
82
in the model when there are no inputs, water exchange nor internal losses
through sediment burial or denitrification.
Figure 38. Variations with time in concentration of dissolved inorganic nitrogen, DIN,
83
with different levels of water exchange, from 0 to 1.2 % per day of the water
in the bay.
Figure 39. The percentage of inputs that are exported from the bay when the water
83
residence time is changed.
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PREFACE
One of the central concerns of the "International Geosphere-Biosphere Program: A Study of Global
Change" (IGBP) is an improved understanding of the global carbon cycle and the likely changes
which might occur as a consequence of global changes, both systemic and cumulative. The Land
Ocean Interactions in the Coastal Zone (LOICZ) Core Project of the IGBP, established in 1993, is
concerned with understanding the role of the coastal sub-system in the functioning of the total Earth
system, including the role of the coastal zone in the disturbed and undisturbed cycles of carbon,
nitrogen and phosphorus.
To achieve such an understanding will require the compilation of the results from local and site-
specific research, together with regional and wider scale approaches to understanding the flux of
materials and energy in coastal systems. Modelling of carbon, nitrogen and phosphorus in such
systems is therefore a necessary requirement for meeting the overall goals and objectives of LOICZ.
To ensure comparability and compatibility of the results of local and national research and to allow
the up-scaling required to develop regional and global scenarios of change in coastal areas will
require the adoption of similar approaches to the collection of empirical data and to the estimation of
budgets and fluxes in the world's coastal areas. As presented in the LOICZ Implementation Plan
(Pernetta and Milliman, 1995), the framework activities of LOICZ, co-ordinated through the Core
Project Office located in the Netherlands, include the development of a strong modelling component
within the LOICZ research agenda and the provision of methods, standards and protocols for the
conduct of LOICZ research.
The biogeochemical modelling guidelines presented in this document represent the consensus views
of the LOICZ Scientific Steering Committee concerning the best available approaches which can be
adopted to provide estimates of the role of coastal areas as sources and/or sinks of carbon, nitrogen
and phosphorus. This document has been developed from an initial consideration of alternative
modelling approaches conducted during a one day workshop held in conjunction with the
"International Symposium on Global Fluxes of Carbon and its Related Substances in the Coastal
Sea-Ocean-Atmosphere System" in Sapporo, Japan, during November 1994. This workshop (LOICZ,
1994) helped to identify the overall approach which could be used in the framework of LOICZ
biogeochemical modelling. This framework was presented at the second LOICZ Open Science
Meeting, held in Manila, The Philippines, during April 1995, for initial review and discussion (LOICZ,
1995a) and the proposal for developing guidelines for biogeochemical modelling within LOICZ was
well supported.
Accordingly, during the summer of 1995 members of the LOICZ Scientific Steering Committee,
assisted by other experts, contributed ideas and text which were compiled into an initial draft. This
draft was presented to a small workshop convened by Dr. D. Gordon on behalf of LOICZ and hosted
by the Bedford Institute of Oceanography in Dartmouth, Canada, in September 1995. During this
workshop (LOICZ, 1995b), the draft document was reviewed and extensively rewritten. In October
1995, the revised document was despatched to selected experts for critical review and comments. At
the same time, it was also sent to scientists participating in the SARCS/WOTRO/LOICZ Core Project
being conducted in Southeast Asia. During early December 1995, the draft guidelines were
thoroughly reviewed and tested at the SARCS/WOTRO/LOICZ Workshop on Biogeochemical
Modelling which was held at the Centre for Marine and Coastal Studies, Universiti Sains Malaysia,
Malaysia (LOICZ, 1995c). Participating scientists came from Australia, Brunei, Canada, Indonesia,
Malaysia, The Netherlands, Philippines, Singapore, Sweden, Taiwan Thailand, Vietnam and United
States.
All feedback on the draft guidelines received before the end of December 1995 was considered and
used by the LOICZ Scientific Steering Committee and Core Project Office to prepare the final draft in
early in 1996. It is hoped that through the application of the approaches outlined in this document to a
wide enough spectrum of coastal sites and regions, our understanding of the role of the coastal
system in global biogeochemical cycling will be improved.
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EXECUTIVE SUMMARY
One of the long term objectives of LOICZ is to develop improved numerical models that describe the
dynamics of biogeochemically important elements in the coastal zone at regional and global scales.
To do so requires the development of common and consistent modelling approaches that can
produce outputs at the local scale that can be integrated into larger-scale regional and global
syntheses. These modelling guidelines have been developed by LOICZ for use by participating
scientists in planning and conducting their research on a local scale in support of the broader regional
and global syntheses.
This document presents recommended guidelines for initiating the development of carbon, nitrogen
and phosphorus (CNP) models of the coastal zone. They have been developed as a LOICZ
framework activity through a series of international workshops and represent the consensus of
participating scientists. These guidelines can be used to develop models for specific coastal areas
using either existing data, or data that will be collected as part of new field programmes. The
guidelines are purposefully written so as to provide the information needed by scientists who wish to
participate in LOICZ biogeochemical modelling but who have no or limited previous modelling
experience. General background information is provided on the philosophy of modelling and different
kinds of models are briefly reviewed. Numerous references provide an entry into the scientific
literature on numerical modelling. In addition, the recommended procedures are described in
considerable detail and illustrated by numerous case studies from representative coastal systems
around the world.
From a LOICZ perspective, CNP models must consider both the current fluxes of these
biogeochemically important elements in the world's coastal zone and how these fluxes might change
in the future due to environmental change. In general, potential approaches for modelling the
dynamics of carbon, nitrogen and phosphorus in the coastal zone range, from relatively simple
budgets of boundary fluxes for specific elements, to detailed system simulation models which contain
a large number of variables and processes. The data and resource requirements vary markedly along
this gradient. Simple budgets require a relatively small amount of data and can be constructed in a
short time period, while large systems models require several years to develop by large scientific
teams.
The initial focus of LOICZ identified in these guidelines is on stoichimetrically linked CNP budget
models. Even though they are very simple and require relatively little data, these kinds of budgets
can provide a very good description and understanding of nutrient dynamics by identifying and
quantifying the important fluxes, in and out of the coastal zone. Not only does it make sound
scientific sense to start at the simplest end of the modelling spectrum, but this will allow for the
potential development, in a short time, of local models of value to LOICZ for a large number of
coastal areas around the world. The procedures and examples presented in this document cover a
wide range of situations with varying amounts of available data. Although the methodology appears
to be very robust, certain limitations in the application of these methods are identified and discussed
in detail in the text. In general, the techniques presented here are most readily applied to marine
systems which have a measurable salinity gradient.
While it is essential to generate budget models for the world's coastal zones, it is recognised that
dynamic simulation models will also play a very valuable role in reaching the long-term objectives of
LOICZ, especially in understanding how the dynamics of carbon, nitrogen and phosphorus in coastal
systems may change under different environmental conditions. Once robust budget models of
important CNP fluxes are developed, they can be used as the basis for developing dynamic
simulation models, that can be used to explore the effects of changing environmental conditions on
important biogeochemical fluxes in the coastal zone.
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These recommended modelling approaches require site specific data. Therefore, modelling activities
and field work should be conducted together, in an interdisciplinary manner, with the results from
both activities being compared on a routine basis. The data requirements of linked carbon, nitrogen
and phosphorus (CNP) budgets should be taken into account when designing new field programmes
or modifying existing ones. The most important data requirements for linked biogeochemical budget
modelling are water circulation and various forms of carbon, nitrogen and phosphorus. The simplest
way to obtain information on water circulation is by way of water and salinity budgets; this information
can also be extracted from physical oceanographic models where these are available.
If followed, these guidelines should lead to the development of models for a large number of coastal
systems around the word. It is anticipated that the development of most of these models will be
funded at the local or national level. By developing understanding of local physical oceanographic
and biogeochemical processes, these models will be able to contribute to the management of local
resources and understanding the socio-economic implications of global change. In addition, it is
important that the local models produced using these guidelines in different coastal areas be
compared and the results integrated to provide the regional and global syntheses required by LOICZ.
Such a comparison and integration will be guided by the LOICZ coastal typology exercise.
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2. INTRODUCTION
All countries with a coastline have an interest in the sound management of their coastal space and
resources. The problems associated with coastal management are expected to become more difficult
under the influence of global changes. The Land Ocean Interactions in the Coastal Zone (LOICZ)
Core Project of the IGBP focuses on the role of the world's coastal zones in the functioning of the
Earth system; the way in which global changes will influence that role; and the way in which such
changes will affect the use of coastal space and resources by humanity.
The general goals of LOICZ, as stated in the Science Plan (Holligan and de Boois, 1993) and
Implementation Plan (Pernetta and Milliman, 1995), are as follows:
To determine at global and regional scales:
a) the fluxes of materials between land, sea and atmosphere through the coastal zone
b) the capacity of coastal systems to transform and store particulate and dissolved matter
c) the effects of changes in external forcing conditions on the structure and functioning of
coastal ecosystems.
To determine how changes in land use, climate, sea level and human activities alter the fluxes
and retention of particulate matter in the coastal zone, and affect coastal morphodynamics.
To determine how changes in coastal systems, including responses to varying terrestrial and
oceanic inputs of organic matter and nutrients, will affect the global carbon cycle and the trace
gas composition of the atmosphere.
To assess how responses of coastal systems to global change will affect the habitation and usage
by humans of coastal environments, and to develop further the scientific and socio-economic
bases for the integrated management of the coastal environment.
Understanding the interactions between the coastal zone and global changes cannot be achieved by
observational studies alone. Modelling of key environmental processes is a vital tool that must be
used if LOICZ is to achieve its overall goals and objectives, particularly in view of the fact that many
of the uncertainties in global carbon flow models may represent unquantified processes occurring
within the coastal zone. This document is intended as a guide for those wishing to contribute to the
objective of elucidating the dynamics of carbon, nitrogen and phosphorus in the coastal ocean within
the framework of LOICZ.
2.1 The LOICZ Biogeochemical Modelling Strategy
The general LOICZ biogeochemical modelling strategy, as laid out in the LOICZ Implementation
Plan, consists of six components (Text Box 1). The first three are framework activities and will be led
by the LOICZ Core Project Office (LOICZ-CPO) with input from the proposed modelling nodes.
These include the development of a coastal typology, the development of a modelling network and
the development of improved upscaling methodology. The fourth and fifth components involve the
development of new local and regional biogeochemical models as well as their evaluation and
validation. It is anticipated that this work will be done primarily as part of national and regional
programmes with LOICZ co-ordination. The sixth component involves the development of global
biogeochemical models of the coastal zone which can provide data that can be used within models of
the entire Earth system such as those being developed by the IGBP Framework Activity Global
Analysis, Interpretation and Modelling (GAIM). This is seen as an integrative activity that would be
led by the LOICZ-CPO but also requires strong input from the entire LOICZ community.
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LOICZ BIOGEOCHEMICAL MODELLING
Carbon flow models of the world's coastal zone will be developed under LOICZ. These
models will be aquatic models that will include water, sediment and nutrients as well as
various forms of carbon. They will include internal dynamics as well as important
exchanges across landward and seaward boundaries. The tasks (in parentheses)
indicate where each activity is located in the LOICZ Implementation Plan.
Development of a system for formulating LOICZ global coastal typologies
(Task F.2.1)
The typology will be used to determine regions for which models and model output are needed,
and for developing global syntheses and models. This Task will be undertaken by the LOICZ-
CPO.
Development of a strong, centralised framework for LOICZ modelling activities
(Task F.5.1)
This Task will provide the overall framework for co-ordination and communication and provide
guidelines for model development. This Task will be led by the LOICZ-CPO with strong inputs
from the modelling nodes when established.
Develop improved methods for assimilating fine scale models into large scale models
(Task F.5.2)
This Task links hydrodynamic models to biogeochemical models, and involves scaling up from
local to regional models and from regional to global models. This Task will be led by the
LOICZ-CPO with strong inputs from the modelling nodes when established.
The development of new local and regional ecosystems models
(Task 1.4.1)
Building on existing data this Task involves constructing new budget and system models
following recommended guidelines. Budget models will be developed first followed by system
models for sites and regions identified through the typology exercise. An on-going activity that
will continue as new data become available, this activity will primarily be undertaken as part of
national and regional programmes with LOICZ co-ordination.
Evaluation and validation of budget and system models
(Task 3.1.4)
Under this Task models of similar coastal units and contrasting coastal units will be compared
and generic sub-models of key biogeochemical processes will be developed which have wider
applicability. New models will be validated using new field data. Where possible models will be
used to explore the effects of different scenarios on regional carbon flows. Undertaken
primarily as part of national and regional programmes this will require strong LOICZ
co-ordination.
The role of coastal Seas in the global carbon cycle
(Integrative Activities - Core Research)
This activity is dependent upon all the above activities, especially the typology exercise and
scaling up techniques. Using available regional models, develop carbon flow models for the
world's entire coastal zone. Feed the results of coastal carbon flow models into Earth system
models. Where possible, models will be used to explore the effects of different scenarios on
global carbon flows. Led by the LOICZ-CPO this Task will require strong input from the
modelling nodes and regional research networks when established.
TEXT BOX 1. ACTIVITIES RELATED TO THE DEVELOPMENT OF GLOBAL SYNTHESES AND
MODELS OF CARBON, NITROGEN AND PHOSPHORUS IN THE COASTAL OCEAN
ENVISAGED UNDER LOICZ. SEE LOICZ IMPLEMENTATION PLAN (PERNETTA
AND MILLIMAN, 1995) FOR DETAILS.
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The LOICZ approach is to encourage researchers around the world to develop models of the fluxes
of carbon, nitrogen and phosphorus for their local geographic areas of interest. If constructed in a
similar manner, these models would provide estimates which can be aggregated at regional and
global scales. For any group of scientists wishing to investigate and model a particular local coastal
system for subsequent up-scaling into larger models or wider regional estimates, there are two types
of information required:
estimations of biogeochemical fluxes in the system as it is now, for eventual incorporation into
global estimates of flux through the coastal zone; and,
dynamic simulations of processes in the coastal system which can be used to explore the
consequences of environmental change, and produce forecasts of future fluxes.
The LOICZ Implementation Plan calls for the development of guidelines of recommended modelling
techniques under Task F.5.1 and this document provides such guidelines for the LOICZ research
community.
2.2 Spatial and Temporal Scope of LOICZ Modelling
Numerical modelling can be carried out at quite different spatial and temporal scales. Three spatial
scales, defined in terms of linear coastline length, have been identified in the Implementation Plan as
being of primary interest to LOICZ. They are:
Local/Site (~1-100 km): These would address specific habitats such as saltmarshes, mangrove
forests, deltas, coral reefs, estuaries, bays and fishing banks. Modelling on this scale would be
generic in nature, for example, mangrove forests can be modelled in a way that allows application
of the models to other sites with similar conditions.
Regional (~100-10,000 km): These would incorporate a variety of near-shore and off-shore
habitats, in some cases out to the 200 m isobath. Modelling on this scale would be geographic in
nature and would be carried out for a particular region of the world such as the North Sea, South
China Sea, etc.
Global: These would incorporate several regional models representing either the entire world's
coastal zone or a substantial proportion, based on representative regions, the results from which
are up-scaled to the global scale.
Models can also have different temporal scales depending on their particular purpose, but the
prognostic, global scale models ultimately required by LOICZ and the IGBP must have a temporal
scale on the order of 10-100 years such that they can be used to resolve variability on inter-annual
time scales such as El Nino Southern Oscillation (ENSO) events, or multi-year scales such as the
effects of population growth, for example. They will also require relatively fine resolution to
incorporate episodic events.
In order to study multi-year phenomena it will be necessary for LOICZ models to resolve seasonal
cycles, annual cycles and directional changes over the next few decades.
2.3 Recommended Modelling Approach
The initial LOICZ priority is on the estimation of the present fluxes of carbon, nitrogen and
phosphorus in particular coastal systems on the local scale. Following the initial identification and
description of the system to be studied, possibly using simple budgets of water, nutrients and other
materials, we recommend that the first approach to any system not previously studied should be to
produce biogeochemical flux budgets of the system, integrating over annual or multi-annual scales.
By comparing fluxes through systems that differ in certain environmental parameters, it should be
possible to make tentative predictions of the consequences of environmental change. For example,
Nixon et al. (in press) have shown that the rate of denitrification in North Atlantic estuaries is a
function of residence time of the water. Changes in the amount of precipitation resulting from
environmental change would interact with concurrent changes in population density and water use.
The combined result might be a significant change in both runoff and denitrification.
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LOICZ recognises that for more elaborate predictions it will be essential to identify key processes
within representative coastal systems and produce dynamic simulation models based on coupled
process models. At present there are limitations and difficulties with this approach but an important
part of LOICZ is the working towards a solution of these problems. However, this is beyond the scope
of the present document.
2.4 Integration of Biogeochemical and Socio-Economic Modelling within LOICZ
Economic and social impacts of global change in coastal systems are an integral part of LOICZ and
the wide spectrum of proposed research activities is presented in the Implementation Plan. In a
separate but parallel exercise, guidelines for the assessment of coastal zone resources have been
developed (Turner and Adger, 1996). In order to meet the long term goals of LOICZ, it will be
necessary to integrate the biogeochemical and socio-economic modelling approaches. This will be a
difficult task because of limited collaboration between natural and social scientists in the past but a
concrete start has already been made within the SARCS/WOTRO/LOICZ project in Southeast Asia.
This collaborative project, which has been approved as a Core Research Project of LOICZ, involves
initially natural and social scientists from Indonesia, Malaysia, Philippines and Vietnam. The research
objectives are primarily focused on social and economic impacts of global change but also involve
the quantification of land-ocean fluxes and the integration of socio-economic and biogeochemical
modelling has a high priority.
2.5 Potential Benefits for Managers
While the primary aims of LOICZ and the IGBP are to carry out scientific research relevant to the
study of environmental and socio-economic change in the coastal zone, the results of LOICZ
research must also be applicable to management questions. The linkages between biogeochemical
modelling and socio-economic and management issues can be seen in a wide variety of existing
applied studies including fisheries management, eutrophication, effects of habitat alteration, and fate
and effects of contaminants. The LOICZ biogeochemical modelling guidelines presented in this
document will help scientists summarise existing and new data in consistent and rigorous formats
that will be more useful to coastal zone managers. It is also hoped that they will assist in the
development of more applied models that could be used by managers in the decision-making
process.
There is now a consensus in the scientific community that cumulative changes, driven by direct
human use of coastal space and resources, may result in changes to the Earth system which in turn
will impact future human use of coastal space and resources. LOICZ is a project designed to improve
our scientific understanding of this global feedback loop and hence provide a sound scientific basis
for the management of the world's coastal areas.
2.6 Objectives of the Guidelines
The objectives of these guidelines are to provide an introduction and overview of biogeochemical
modelling methodologies that will:
improve our quantitative evaluation of the role of the coastal zone in carbon, nitrogen and
phosphorus cycling through provision of a common, widely usable analytical framework of
modelling; and,
lay out this framework in sufficient detail to be followed by coastal zone researchers world-wide.
The guidelines can be used to help analyse existing data sets where they exist as well as to assist in
the design and conduct of new research programmes that will provide additional data for modelling.
In this manner, LOICZ modelling activities will increase the number of sites within and between
typologically similar units that can be compared and studied and so contribute to our overall
understanding of the role of the coastal zone in global carbon, nitrogen and phosphorus cycling.
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3. GENERAL CONSIDERATION IN CONSTRUCTING COASTAL MODELS
3.1 Why Build Models?
What is a model? By definition it is any simplified description or abstraction of a system or a process.
In science, models are tools that help us to conceptualise, integrate and generalise scientific
knowledge. Even in science the perception of models is vastly different depending on the scientific
field, the problem studied or the tools commonly used in that particular field. For this document, a
"model" may be considered to be any simplified representation of some aspect of the real world and
a "mathematical model" presents this simplification in the form of a series of mathematical equations.
In general, by simplifying reality, mathematical models allow system responses to perturbation, to be
tested computationally. It is also important to note that modelling is an iterative process, with no fixed
starting or end points and with varying goals, depending on the interests of the modellers.
There are two major benefits of modelling: the process and the product.
The process of building models is a valuable learning exercise for those involved. That is, it:
forces interaction among participating scientists from different scientific disciplines;
identifies critical information gaps; and,
helps to identify research priorities.
The benefits gained by undertaking the process alone, often more than justify the effort expended in
model development.
The products of modelling can be very diverse, ranging from a single estimate of a quantity of
material or energy, to the temporal description of a single process, to the mathematical description of
complex interactions among ecosystem components, such as internal dynamics. Assuming that the
process produces a usable product that describes and/or predicts the behaviour of the system with
sufficient accuracy, the models constructed can serve numerous purposes. For example:
for the scientist, the model provides a tool for hypothesis testing and prediction and it can also be
exchanged with other scientists and be used as the basis for developing better models;
for the manager, models provide a quantitative tool that can be used for decision making; and,
for the general public and politicians, models can serve as a means of visualising in graphical
fashion, our understanding of the ways in which complex systems function.
3.2 Some Basic Modelling Principles
The most important consideration in modelling, is to determine at the outset, what kinds of questions
are to be addressed. Most models can provide answers to only a limited range of questions, and
asking the wrong questions of a model may lead to unsatisfactory answers. Building a model without
a clear idea of what is expected from it, is like planning an experiment without a hypothesis to test, or
designing a cargo vessel without knowing the nature of the cargo. This definition of the question is a
critical first step in the development of any model.
Each type of model has advantages and disadvantages. Highly aggregated budget models of nutrient
or material fluxes can provide good overviews of the inputs and outputs of a particular system. But
these models cannot provide the kind of detailed process information required for many resource
management decisions. In contrast, very detailed numerical simulation models are valuable tools for
exploring the dynamic behaviour of systems on short time scales, but they seldom provide reliable
estimates of long-term net fluxes. This is because small errors in the very detailed descriptions
accumulate over time and often make the integrated results unreliable.
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A second important consideration in modelling is the balance between the availability of suitable data
and the understanding of the system to be modelled. Sufficient quantities of both are required to
carry out successful modelling activities. Holling (1978) provides a useful classification that puts
modelling into the overall context of in science (Figure 1). The horizontal axis in Figure 1 represents
the degree of scientific understanding of the system, or process being studied, while the vertical axis
describes the amount of data that are available for the system. The diagram is split into four
domains.
1
3
Data
4
2
Understanding
Figure 1. Data and understanding requirements for modelling, from Holling (1978).
Domain 3 is where we want to be; a good understanding supported by a wealth of good data. We are
rarely in this domain in coastal and marine science. It is a more common situation however within the
disciplines of engineering and physics where processes are limited and often well understood, and
data are relatively easy to obtain. Here, highly accurate numerical models have been developed that
are used routinely in everyday life. For instance, tides around the world can be predicted with a high
degree of accuracy and speed. Models of the global water cycle are also reaching this domain.
Domain 1 includes those systems for which we have lots of data but little understanding. This is
sometimes the case in marine science where there is a large amount of monitoring data, or data from
various scientific cruises. These data are usually scattered among various government archives and
department files, or if we are lucky in publications, and have been collected for many different
purposes. For instance, fishery scientists often collect data on hydrography, chemistry, biology and
economics in addition to data on fish. Hydrologists may provide data on fresh water and even
nutrient inputs to the coastal region. Harbour authorities provide additional data on bathymetry, sea
level variations and sediments. In such a case, compiling and structuring of the data may be
sufficient to generate useful levels of understanding. There is a danger associated with collecting
data without an identified purpose, although it may well be useful, it is generally inefficient.
Nevertheless, putting available data into a common framework (for example a database) to describe
the basic spatial and temporal characteristics of a system is a natural first step in any study of an
ecosystem. Here statistical techniques are useful to find relationships and to develop hypothesis.
Geographic information system (GIS) methods are becoming more useful for graphically describing
the spatial patterns in observations.
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Domain 4 is the usual domain of biogeochemical research in coastal environments, in that there are
few data and little understanding. Sometimes we have a good conceptual idea of how a system
operates, based upon studies done on similar systems elsewhere, but little data to support our
hypotheses as in Domain 2. It is in these two domains, 2 and 4, where modelling is most useful.
In modelling, it is best to start simply and to gradually build more complicated models as needs
dictate. How far to proceed along the modelling path depends very much upon the particular
scientific objectives, as well as the availability of data and understanding. In some instances, quite
simple models are sufficient for the task at hand. Since there are many possible paths to follow, it is
important that objectives are clearly stated and defined at the outcome. A sound rule which should be
followed in modelling, is to start with the simplest route possible and add complexity only when it is
clearly justified. It should also be recognised that the field of environmental numerical modelling is
evolving rapidly and that techniques in common practice today, will probably be superseded by better
ones in just a few years.
The development of coastal zone biogeochemical models is not a simple procedure. There is no
such thing as a standard approach that will work in all cases. Each coastal system must be evaluated
from the viewpoint of both its inherent characteristics and in terms of the kind of information that the
model will be expected to provide. It is also important to assess the data and conceptual
understanding on which the model will be based, considering both the availability of existing data and
the extent to which it is possible to collect new data. In all cases, modelling activities should be well
integrated at the very beginning with field and experiment studies in an overall strategy to address
the desired product.
The best overall modelling strategy is to begin by generating a basic description of the particular
coastal system being studied and comparing it to similar systems that may already be well described
and understood. This includes the critical step of defining system boundaries. Such an initial
typological approach will identify the considerations that are most likely to be of importance for such
a system, and help develop models that are most likely to provide the desired information. In many
cases, the ultimate uses of the model may not be well-defined since several different parties, with
varying interests, may be involved in model development. It is therefore necessary to proceed in an
iterative fashion, alternating between the development of the models and evaluating their utility from
different points of view. This of course means that the initial stages of modelling should focus on
simple models which can be constructed rapidly and evaluated easily. In many cases the first step in
the development of a model for a new area or system is simply to apply and refine an existing model,
rather than to start designing a completely new one.
The initial description of a system can be useful to identify what modelling approach(es) should be
taken to reach a desired goal. For example:
in systems dominated by water transport, physical exchange processes are more important than
internal cycling;
in relatively homogeneous systems, or systems which can be highly aggregated, process-based
nutrient budgets can answer many questions; and,
in high-diversity systems with complex trophic interactions, network analysis may be useful after
the trophic pathways and steady-state fluxes have been determined.


As understanding of a particular system increases, the models applied to the system frequently tend
to evolve from simple, highly aggregated, to more complex models. In many cases this development
proceeds by the progressive disaggregation of the existing model to add greater detail and
descriptive power. This means starting with very general models that contain only a few components
or levels, and subdividing these levels into finer levels with more detail only as it becomes
necessary. There is however, a tendency to disaggregate unnecessarily, simply because the
information to do so is available and often because specialists feel that the model cannot work unless
all of their expertise is incorporated in it.



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Therefore the following questions should always be asked before proceeding with disaggregating or
refining any models:

will this disaggregation improve the performance of the model in relation to the objectives of the
study?
will weaknesses in other parts of the model limit this improvement?
do we have enough data to calibrate a more detailed submodel?
It is important to maintain a sense of balance in model development and starting from a highly
aggregated model can help with this. If a flux consists of two components, and one of the
components is highly variable, there may be little value to refining the modelling of the other
component.
Another caution concerning the progression from simple aggregated models to more detailed
complex modelling activities is the fact that, although the response of complex mathematical models
may tend to mimic system response to some perturbations more closely than simple models, the
observation that model response does mimic system response under controlled conditions does not
guarantee that the model is actually an accurate description of real-world behaviour. One
consequence is that complex mathematical models, which may be difficult in themselves to
"understand," may give very false views of how the real world works once they are run under
uncontrolled, non-test conditions. Simple mathematical models which are robust with respect to
specific aspects of a system may actually give more insight into those specific aspects of system
function than more complex models.
In the short term, where data and understanding are limited, which is the usual situation for most of
the world's coastal zone (for example, Domain 4 in Figure 1) budgets and other empirical models are
likely to provide greater predictive value for different management strategies than the development
of detailed numerical models. Unfortunately, the predictive power of empirical models is restricted
within the observed range of data. Therefore process oriented models have to be developed in
parallel with empirical models in order to evaluate possible future management strategies. Prior
experience shows that many mechanistic, reductionist modelling projects, particularly of entire
ecosystems, have usually failed if they are based on a `bottom-up' approach. Thus, a detailed
understanding of various processes, used as sub-models and assembled into an `ecosystem' model,
do not describe total system properties (see for instance Platt et al., 1981). An holistic approach is
necessary where the goals of the models and the critical scales are defined, prior to model
formulation and simulation. The model is in itself a hypothesis, and the numerical simulation is a tool
to test this hypothesis, not a goal in itself. It is likely that development of more detailed models,
through a number of iterative steps where model evaluations interact with field measurements, will
only be possible for coastal regions with highly developed databases and resident scientists with the
necessary modelling skills. The development of typological relationships among coastal regions will
play an important role in exporting such detailed models to other areas.
3.3 The LOICZ Classification of Modelling Approaches
The LOICZ Science and Implementation Plans (Holligan and de Boois, 1993; Pernetta and Milliman,
1995) have identified four general kinds of numerical modelling approaches that are of use to LOICZ
research. They are budget models, process models, system models and prognostic models. It must
be emphasised that these general categories of numerical models do not represent clearly defined
divisions and that classifying a particular model can be difficult. Especially confusing at times is
where to draw the line between budget and systems models. In reality, there is a wide spectrum of
modelling techniques available ranging from simple budget models at one end, to the more
complicated ecosystem process models at the other. In most, if not all cases, model construction
begins with some basic information on the system in question such as spatial extent, topography,
water volumes, dominant habitat types, number of trophic levels, etc. The easiest way to start
modelling is to prepare a simple mass balance budget for the variable(s) of interest. One can then
move along the spectrum from budget models to the more complicated systems modelling if required
and if the necessary resources are available. If one cannot create a simple budget for an area, it is
unlikely that one can develop a reasonable ecosystem model no matter how many resources are at
hand.
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3.4 Budget Models
Budget models are generally defined as mass balance calculations of specific variables (for example,
water, sediment, carbon, nitrogen, phosphorus, etc.) for a defined geographic area and time period
(for example, monthly, annual, or decadal). The geographic scope can range from a particular
coastal habitat (for example, a mangrove system) to a semi-enclosed sea such as the Mediterranean
or to the global ocean. The model should include all major sources and sinks, both external and
internal, as well as the dominant internal transformation processes for the variable(s) in question. For
example, a carbon budget for a coastal bay should include delivery by freshwater, exchange at the
seaward boundary, production-respiration, sedimentation, etc. Focus is placed on resolving fluxes at
the boundaries. The development of a budget usually requires a substantial amount of quantitative
data for the geographic area in question. Although in some instances the lessons and experience of
modelling can be transferred from one region to another with similar characteristics, most budgets
usually consider only one variable for particular sites and this limits the ability to generalise model
results between areas. Recently there has been a move to develop budgets that link several
variables using known relationships, for example building linked CNP budgets using stoichiometric
relationships such as Redfield ratios. The use of known stoichiometric relationships allows linked
budgets to be applied in new areas, with limited data availability in order to infer underlying fluxes.
3.5 Process Models
Process models describe specific physical, chemical and biological processes which are important in
understanding biogeochemical fluxes in the coastal zone and how they are influenced by major
environmental forcing functions such as tide, wind, temperature and light. They are generally
constructed on the basis of process studies done in the laboratory, mesocosms and the field. In most
instances, they are developed in isolation from the total natural system and therefore tend to be
reductionist in nature. Each contains a limited number of variables and parameters.
While developed using empirical data gathered at specific geographic locations, process models tend
to be generic in nature and can often be applied with confidence to other geographic locations. For
example, formulations developed to describe phytoplankton photosynthesis as a function of light,
temperature and nutrient supply for the North Sea should also be applicable to other geographic
areas with a similar environmental setting and forcing. In general, the best studied and described
coastal processes are those operating in temperate regions. Process models of important
environmental processes in tropical and polar regions are not as well developed and demand
increased attention.
Also important to the long term success of LOICZ is the availability of process models dealing with
the major exchanges of materials between the coastal zone and its boundaries. Probably the most
important are inputs from the land which include river runoff, groundwater seepage and coastal
erosion. Also important are the exchanges with the atmosphere and the seaward boundary that are
controlled primarily by physical processes. Individual process models are important building blocks
for building systems models as described below.
3.6 System Models
These models embrace aspects of physics and chemistry in addition to biological aspects and should
not be confused with the purely biological models discussed in Section 3.4. They are models that
attempt to describe the behaviour of whole ecosystems.
One type of system model is of a budgetary nature and summaries fluxes through the various
pathways of the ecosystem. Others are coupled process models that describe internal dynamics.
System models integrate information on what are considered to be the most important variables and
processes for the total environmental system of particular interest. They have well defined spatial
boundaries and temporal scales. Spatial scale can range from a particular coastal habitat, such as an
individual coral reef, to an estuary, coastal bay or the entire continental shelf depending upon the
objectives of the modelling project. Temporal scales usually range from tidal cycles to several
decades. The behaviour of a system model depends very much upon the spatial and temporal scales
selected. Systems models are commonly built using process models and often the first step is to
construct a simple mass balance budget. Particular attention is given to describing the interaction
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among state variables. System models can be either descriptive (for example, flow or network
analysis ) or dynamic (for example, simulation models).
The most advanced systems models are those describing coastal circulation. The major physical
forcing functions are limited in number and relatively well understood. Three dimensional circulation
models with high spatial resolution have been developed for a large number of estuaries, bays and
entire continental shelf regions (for example, Haidvogel and Beckmann, submitted). These coastal
circulation models provide an essential foundation for the development of sediment transport, water
quality, geochemical and ecosystem models.
The most complicated and least reliable systems models tend to be ecosystem models which of
necessity contain a large number of physical, chemical and biological processes, variables and
parameters many of which are poorly understood. Their development also requires a substantial
investment of resources. However, very often submodels from existing models can be used in
developing new models for similar geographic areas such as has been done with the ERSEM
modelling activities in the North Sea described in Baretta et al. (1995).
The accuracy of mechanistic ecosystem simulation models (that is built from the bottom up from
process models) has been questioned because they do not include the qualitative changes of state
that commonly occur in the real world, the inherently greater variability in the parameters fed into
biological models compared with engineering models, the hierarchical nature of ecosystems and the
capacity for self-organisation that ecosystems possess (Platt et al., 1981). Other more holistic
approaches are needed for understanding important fluxes in marine ecosystems and some of these
are reviewed by Ulanowicz and Platt (1985). One approach which has received considerable
attention in recent years is network analysis (Wulff et al., 1989).
Another different approach to systems modelling is top-down modelling (Silvert, 1981) which is the
process of describing a set of models which generate output consistent with the empirical data and
then analysing the structure of these models to arrive at smaller sets of acceptable models. This
method facilitates the development of models having new and unexpected structural features, makes
it possible to build new models which correctly describe emergent properties and assists in the
diagnosis of errors in the interpretation of experimental data.
When correctly constructed, system models can be used to produce mass balance budgets. The
comparison of such a budget with a budget from the raw data can be a very powerful way of
validating process or system models. Nevertheless there is a real danger in using the output from
system models as real data. Great care must be taken to ensure that the system models are
operated within the data range of the process models that make them up and that the process
models reasonably describe the observed conditions and processes in the system being studied. This
again emphasises the importance of empirical data in the construction of all types of models.
3.7 Prognostic Models
Prognostic models are those that have the ability to predict how selected environmental variables
may change if conditions are changed (for example rising sea level, increased temperature, reduced
freshwater runoff, etc.). All three of the general model types described above have some degree of
predictive ability. Although systems models offer great potential in generating an understanding on
which to base predictions, it is most likely that within the relatively short time frame of LOICZ, the
best predictive power will be found in empirical correlational models constructed for specific
management objectives.
3.8 Historical Perspective
As has been stated, the main thrust of LOICZ is towards determining the biogeochemical fluxes of
carbon, nitrogen and phosphorus through coastal ecosystems, and their interactions with parameters
of global change. In the past, the majority of models developed for coastal ecosystems have been
directed towards understanding the biological processes within those systems as an aid to
management. These have usually been in the form of models of energy-flow or carbon-flow through
the biological community. Occasionally, attempts have been made to determine fluxes across the
boundaries of these systems, but the results have often been disappointing. For the needs of LOICZ,
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it is initially more important to get good estimates of the inputs and outputs of a coastal system than
to capture the details of processes within the system. Hence the recommendation to begin with
developing biogeochemical budgets which incorporate major, physical oceanographic exchange and
mixing processes. Here, we review the differences between the biological energy/carbon flow models
and the biogeochemical models required by LOICZ.
3.8.1 Energy flow/carbon flow models of biological communities.
In any given system the primary producers absorb solar energy and fix it into carbon compounds.
Energy fixation during photosynthesis is often measured from the uptake of radioactive carbon
isotopes. It is a matter of choice whether the investigator uses this information as the basis of an
energy flow model or a carbon flow model, for the data may be expressed either way. Let us for
convenience refer to them as carbon models.
By identifying the trophic pathways and the biomass and metabolic rates of the main consumers, we
can budget the pathways in which carbon fixed is eventually converted back to carbon dioxide and
energy is dissipated as heat. The detailed process has been codified in software known as
ECOPATH (Christiansen and Pauly, 1993) by which attention is drawn to any gaps in the data that
need to be filled with estimates from the literature, and by means of which different biological
systems can be compared. A simpler alternative is to apply highly aggregated models such as the
size-spectrum models of Platt and Denman (1978) and Silvert and Platt (1980).
Often, the data for such models are collected from a discrete geographic area, but in most cases the
fluxes across the boundaries of that area are not of primary concern. While these models reveal the
total amount of carbon dioxide fixed during photosynthesis and balance this against the amount
released via respiration, there is seldom an accounting for the amount of carbon that is released to
the atmosphere, the amount fixed in calcification or buried in the sediments, and the amount
imported or exported in dissolved or particulate form across the boundaries with adjacent water
masses. Yet data on these fluxes are the primary requirements of LOICZ.
There are examples of strenuous attempts to measure boundary fluxes in conjunction with biological
carbon models. For example, Ong (1993) discusses the carbon fluxes within a mangrove system. As
is discussed in Section 4, attempts to determine the time-varying fluxes in a water column at different
seasons and at various states of the tide along a hydrodynamically complex boundary are extremely
difficult, and estimates made in this way often fail to match the internal estimates of biological fluxes.
For this reason, we recommend an entirely different approach which circumvents many of the
difficulties encountered in the past.
3.8.2 Biogeochemical flux models.
The process of developing biogeochemical flux models begins with determining the spatial and
temporal scales of the coastal system of interest, after which the physical, chemical and biological
properties can be described and a water budget developed. It is essential to understand the basic
physical mechanisms at work, including amongst other, estuarine circulation, upwelling, and tidal
mixing, in order to have a qualitative grasp of the pattern of water movement and to delineate the
boundaries of the system being studied. A useful guide to this stage is found in Mann and Lazier
(1991). The terms in a water budget of a coastal system include river inflows, groundwater seepage,
exchange at the seaward boundary, precipitation and evaporation, although in many circumstances
river inflow overwhelms all of the other freshwater fluxes. On first approximation, one assumes that
imports of water are balanced by loss across the boundary with adjacent water masses.
To get a better estimate of the exchanges with adjacent waters, that is water exchange by both flow
and mixing of water masses, as well as the freshwater flow, it is often possible to construct a salt
budget. If there are distinct salinity differences across the interface, salinity measurements will permit
refining of the water budget.
One then moves on to construction of budgets for nonconservative materials, in particular carbon,
nitrogen and phosphorus. As will be shown in Section 5, it is not necessary to investigate all of these
materials. Phosphorus has the simplest biogeochemical pathways, and it is often sufficient to make a
detailed study of the phosphorus budget and calculate other elements on the basis of stoichiometric
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relationships. The mathematics involved is relatively straightforward, and the method has been
shown to give good results in a number of habitats (see case studies in Section 5). Although adoption
of this method will involve a radical change in methodology for groups already involved in biological
ecosystem modelling, we maintain that this is the only way that flux data for use in global
models can be obtained in a reasonably short time.
At the same time it is also necessary to continue improving scientific knowledge of the internal
dynamics of carbon, nitrogen and phosphorus in coastal systems, and how they influence overall
biogeochemical fluxes, through the development of process-oriented system models as is being done
for some regions of the world's coastal seas such as the North Sea (Baretta et al., 1995).
3.9 Modelling Requirements of LOICZ
The first step in achieving regional and global estimates of flux requires the development of a global
coastal typology. A preliminary version on a regional scale has been prepared (LOICZ, 1995d) and
was discussed at the Second LOICZ Open Science Meeting (LOICZ, 1995a). The intention is that
such a system will subdivide the world's coastal zone into clusters of discrete, scientifically valid units
based on both natural and socio-economic features and processes (see Table 1 for examples).
Such a system is necessary if the global syntheses which form a long-term goal of LOICZ are to
adequately encompass the spatial and temporal heterogeneity of the world's coastal zone.
Development of an appropriate typology will help determine the appropriate weighting to be applied
to recognisable classes of coastline in preparing global syntheses, scenarios and models on the basis
of spatially and temporally limited data.
The biogeochemical modelling requirements of LOICZ can be broken down into two general
categories. The first is to develop an improved understanding of important biochemical fluxes in the
coastal zone. The second is to develop prognostic models that can describe existing biogeochemical
processes and predict how they will be altered due to environmental change.
The modelling procedures presented in this document will describe the integrated biogeochemical
and ecological functioning of coastal marine ecosystems. The specific purpose of presenting such
procedures is to guide the development of a global data base which characterises the role of the
coastal zone as a source or sink for the biogeochemically reactive elements: carbon, nitrogen, and
phosphorus.
For LOICZ it is essential to identify and quantify the major net fluxes in representative parts of the
world's coastal seas. This information will indicate whether the coastal seas are a net importer or
exporter of carbon, nitrogen and phosphorus and indicate what the dominant processes are likely to
be. There are several advantages to developing simple models of fluxes, often thought of simply as
nutrient budgets. They are both simple and comprehensive so they give an overall picture of the
system very quickly. In addition, their computation requires only the summation of the boundary
fluxes of the system. A consequence of their simplicity is that limitations on the availability of data
rapidly become evident. As a result, budget models provide both robust estimates of the flux across
the coastal zone boundaries and long-term, integrated biogeochemical performance of the entire
system. Furthermore, by treating the budget as a first step in the modelling procedure rather than as
an end in itself, one can proceed to identify the major processes which determine the fluxes and
make the important transition from a purely descriptive budget to a predictive process-based model.
Ecological simulation models, some with relatively sophisticated description of the physics of water
flow and substantial details of biogeochemical processes, have been widely applied in ecosystem
analysis and are of great use in the evaluation of the instantaneous function of systems. Simulation
models are usually limited by: the limits of our theoretical and experimental knowledge of the
performance of all components in the system; by mathematical chaos which exists within any
ecosystem; and, by computational limitations (such as rounding errors). Despite the limitations, when
applied correctly such models can provide useful insights into the internal processes of the system.
The description of these processes can be used to attempt predictions of system behaviour with
changes in the control functions, such as are envisaged with environmental change.
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TABLE 1.
FACTORS RELATING TO THE DEFINITION OF THE COASTAL ZONE AREAS
FOR THE DEVELOPMENT OF COASTAL BUDGET MODELS.
Physical Description
Topography/bathymetry
Shelf edge, bay mouth, estuary, coastal lagoons
Current system
Tidal excursion, boundary of residual circulation
Gradient of material Frontal structure
concentration
Energy regime
Tidal or river dominated, waves, currents, closed,
etc.
Drainage basin
Soil type, runoff, input of dissolved & particulate
material
Biological Description
Habitat type
Coral reef, seagrass, mangrove, salt marshes
Biological production
Length of growing season, production
Chemical Description
Nutrients
CNP concentration and flux
Socio-Economic Description
Demographics
Population density, growth
Land use
Land cover, crop type, human activity, etc.
3.9.1 Understanding biogeochemical fluxes for global models
The most important biochemical fluxes from the LOICZ perspective are those across the major
boundaries of the coastal zone (that is, land-ocean inputs, air-sea interaction, and exchanges with the
open ocean) as well as those associated with benthic/pelagic coupling and exchanges. These must
first be determined at the local/regional scale but in time the results must be integrated into regional
and global models of the coastal zone. It is argued that biogeochemical fluxes are best estimated in
the first instance by the construction of budgets. This simple class of mathematical model provides
the most robust estimates of integrated ecosystem performance. Budget models are little more than
an ordered, objective description of what is known about the system in question. In many instances,
collection of data which can be used in a budget may have occurred incidentally in other studies.
Conservation of mass is, of course, a fundamental principle of nature. Therefore a comprehensive
budget of the inputs of materials into the system of interest, outputs from that system and amount in
the system is an objective description that goes beyond, simple tabulation of such data. While such
budgets provide neither direct experimental nor direct theoretical information about how the system
works, the budgets can describe the system at space and time scales which may not be amenable to
experimentation or detailed simulation modelling. One result is that the descriptive output from
budgets can be used in a statistical sense to evaluate and compare how systems work and how the
parts of the Earth system are linked together.
In Section 5, detailed procedures for developing a class of mass balance budgets that we define as
"stoichiometrically linked water-salt-nutrient budgets" are presented. The elements of specific interest
here are carbon, nitrogen, and phosphorus, all of which are essential to life. As will be seen, these
budgets can be used in comparative studies to generalise coastal biogeochemical processes in two
ways:
time-series analysis of budgets within systems; and,
comparison of "static" (or average) budgets between systems.
Both of these types of studies will be used to achieve the goals of LOICZ.
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3.9.2 Use of prognostic models for predicting consequences of global change
While budget models provide robust overviews of the flow of nutrients and material across
boundaries, they are very limited in their ability to identify the actual processes that are taking place
within the coastal zone. They are also very limited in their ability to extrapolate beyond the conditions
for which they are created and thus allow prediction of the system functioning under new conditions.
The coastal zone is subjected to various kinds of environmental change, due to both natural
variability and human activity. These include changing sea level, habitat alteration and release of
contaminants. For LOICZ to achieve its objectives of understanding the processes, predicting
response and investigating alternative management and response scenarios to climate change, it is
necessary to develop prognostic models which can be used as management tools. The best method
to achieve these goals is to develop numerical simulation models which focus on the internal
dynamics of coastal systems and describe how critical biogeochemical processes are influenced by
environmental variables. This class of models can be used to explore numerically the potential
impacts of different environmental scenarios. In LOICZ they should be developed in conjunction with
budget models and will be constrained by the boundary conditions and overall fluxes identified by the
budget models. These will have to be developed at different spatial and temporal scales depending
upon the particular issue(s) of concern.
3.10 Importance of Scaling in Modelling
In concluding this section on general considerations in developing coastal biogeochemical models for
LOICZ, we wish to emphasise again the importance of scaling. At the very outset of a coastal
modelling project, it is absolutely essential to clearly defined the spatial boundaries of the system, as
well as the temporal scale of the model. Decisions will depend upon the properties of the system and
on the overall objectives of the model. They should be made in full consultation with the entire
project team, both natural and social scientists. Whenever possible, model boundaries should reflect
the natural boundaries of the particular coastal system being studied (for example Table 1).
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4. THE MERBOK MANGROVE EXPERIENCE
While modelling techniques as outlined in the previous section are very powerful tools to investigate
the functioning of a system, the successful use of these techniques in many cases requires a number
of iterative steps that involve careful thought, data collection and analysis and the selection of
alternative approaches. In an effort to illustrate such steps in the evolution of a real modelling
exercise, this section presents a case study of a long-term programme to determine the fluxes of
water, carbon, nitrogen and phosphorus from a tropical, mangrove ecosystem.
Mangrove forests constitute a dominant ecosystem of the low energy tropical coastlines of the world.
In these areas the forests not only occupy, but in many ways determine, the nature of the interface
between land and sea and the fluxes across this interface. They play many roles in the coastal zone
including protection from coastal erosion, the provision of direct products, such as wood, and indirect
products, such as nursery areas for coastal fisheries, and tourism. The impact of environmental
change on these ecosystems is clearly identified as an important LOICZ research question in the
Implementation Plan and details of an overall economic assessment of the importance of their
diverse roles is treated in more detail in LOICZ. Mangrove forests are currently subjected to
considerable human-induced change including: clear-cutting for timber; changes of use to mariculture
and rice production, and use for human habitation. These changes in regions such as Southeast Asia
and Central America are affecting, to an unknown degree, the flux of nutrients and organic carbon to
coastal and near-shore waters.
There are numerous physical, chemical and biological processes that occur between the head and
the mouth of an estuary. As water flows from rivers into estuaries, mixing with seawater causes
numerous chemical transformations to occur. Changes in both chemical (such as redox) states and
physical processes (such as electrical charges) result in some of the chemical settling out (for
example, through flocculation). Some of these chemical species are also taken up or transformed by
living organisms. The important processes occurring between the inputs from the riverine end and
outputs at the marine end of the estuary must be identified and quantified. Biogeochemical modelling
can play an important role in quantifying these processes sufficiently to produce a balanced budget.
The primary site for this study is the Sungai Merbok mangrove estuary in Malaysia 5°40'N, 100°25'E).
The physical characteristic of the site have been described by Ong et al. (1991). The estuary is 30
km long and its depth varies from 3 - 15 m. Mangroves, dominated by Rhizophora apiculata and
Bruguiera parviflora that grow to about 30 m, cover an area of about 50 km2. The estuary is
characterised by a 1.7 m semidiurnal tide, with peak currents of 1.3 m s-1, and mean freshwater
discharge of 20 m3 s-1. The estuary displays a pronounced neap-spring stratification-destratification
cycle, and the effective longitudinal dispersion is approximately 107 m3 /d.
The main aim of the programme which started in the mid 1970's is to determine the fluxes of carbon
and nutrient from the mangrove estuary. Initially this was linked to the question of the extent to which
mangroves can be put to alternative uses without affecting the mangrove ecosystem and adjacent
capture fisheries. Some 10 to 15 years later the question remains: are mangroves a source or a sink
of atmospheric carbon? (Ong, 1993).
4.1 Single Cross-section Hydrodynamic Budgeting
The initial information required to model a system such as the Merbok Mangroves is an
understanding of the underlying physical transport system. Initially the Kjerfve method (Kjerfve et al.,
1981) using measurements of current speed and direction across the width of the estuary was used.
It involved using these data to obtain the covariance with the concentration of the scalar, at the
mouth of the mangrove estuary. Despite data from 45 tidal cycles (4 to 9 stations, 3-5 depths at lunar
hourly intervals), including a set with 31 continuous tidal cycles that covered a full spring/neap tidal
cycle, estimates of water flux remained about an order of magnitude higher than those based on
calculations from rainfall, evapotranspiration and catchment area. The difficulty with this application
was that a salt balance could not obtained (Dyer et al., 1992). The reason for this failure is not clear
but it may have resulted from inaccuracies in the current measurements made with simple current
vanes.
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Although this method appears to be successfully applied in the salt marsh estuary of North Inlet,
South Carolina, there appear to be problems when applied to mangrove estuaries, not only in the
Merbok Mangrove estuary but also in the Ranong Mangroves in Thailand (Wattayakorn et al., 1990).
Fortunately in the Thai study it was possible to apply the modelling method of Wolanski and Ridd
(1986) with better success. Unfortunately this method is applicable only during the dry season when
there is no freshwater flow and thus cannot be applied to mangroves situated in areas where there is
no dry season such as the Merbok.
In the Merbok case, trying to resolve a small residual from a huge tidal variation would require much
more accurate current measurements as well as possibly more complete temporal and spatial
sampling. Ten years down the hydrodynamics road from these first attempts to measure water flux
through the system, there is still no solution, although much has been learned about the estuary
(Uncles et al. 1990; Ong et al., 1991; Uncles et al., 1992; Ong et al., 1993). A recent assessment of
the data (Simpson et al., in press) suggests that it may be possible to arrive at a solution with more
accurate measurements.
4.2 3-D Numerical Hydrodynamic Flow Modelling
The more numerical fluid modelling approach has also been explored for the Sungai Merbok Estuary
(see Haidvogel and Beckmann (submitted) for a review of available methods). Three-dimensional
hydrodynamic models are designed to mimic the flow of water in an estuary based on mathematical
description of bathymetry, tides, currents, and other physical parameters. An attempt was made by
Phang (1994) to apply a small data set for the Sungai Merbok mangrove estuary to the TRIM 3D
numerical model (Cassuli and Cheng, 1992; Cassuli and Cattani, 1993). Although this application of
the TRIM model indicated that the results are often too complicated for use in understanding the
biology of an ecosystem, they also suggested that this approach may be worth following up if better
bathymetric and hydrographic data were available. Application of the TRIM model may be more
appropriate if Acoustic Doppler Current Profilers (ADCP) can be used to more accurately measure
current speeds in future research efforts.
4.3 Modelling The Mangrove-Atmosphere Interface
As with the measurement and modelling of the water movement in a system, a significant effort is
often required to quantify a single important biogeochemical process. A second example of this from
the Merbok study is the atmospheric inputs to the system. Budgets cannot be complete if the
atmospheric interface is not considered, so another aspect of this study, though more related to
GCTE and IGAC than to LOICZ, is on fluxes from mangrove tree canopies. A number of
photosynthesis and related environmental and ecophysiological parameters in the mangrove canopy
have been measured (Ong et al., in press). This study has reached a stage where there is a need to
carry out detailed modelling, such as the MAESTRO model of Jarvis et al. (1990), that will allow a
certain amount of prediction of this one particular aspect of the ecosystem.
A project is also being initiated on measuring carbon dioxide fluxes from mangrove canopies using
the eddy covariance method. This is essentially based on the same principle as the Kjerfve method
that is used for measuring fluxes in the water but converted from hydrodynamics to aerodynamics.
This again is a pure single point budgeting procedure with no predictive capacity; nevertheless it is
hoped that it will be useful in quantifying fluxes in the mangrove forest.
4.4 A Mass Balance Carbon And Nutrient Budget In A Mangrove Ecosystem
In the absence of raw data for the system being studied, it is often possible to use substitute
information from other sites or known relationships between easily measured variables and those that
cannot be measured to estimate required information. For mangrove forests the standing biomass of
trees and or parts of trees like leaves, branches, trunk and roots can be estimated using allometric
relationships between easily measured parameters such as circumference of the tree trunk. Standard
equations are now available for a number of mangrove species from a few different sites so it is not
absolutely necessary to go through the rather tedious process of deriving your own equations.
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Net primary production of a mangrove forest consists of a number of components: fine litter
production, fine root turnover, herbivory, dead trees and tree growth. In mature or steady state
systems the biomass that goes into dead trees is about equal to tree growth so that the standing crop
or biomass remains constant. The other components detach from the trees and are either, buried, as
in the case of the fine roots, leaf litter and some dead trees, eaten by detritivores such as sesarmid
crabs that feed on leaf litter, or are removed from the system by tides. These components are thus
released and part or all may be exported from the system. Using established relationships it is
possible to estimate the standing crop and fluxes of nutrients in a mangrove swamp. When using a
combination of measured and estimated values a budget can often be compiled to obtain at least an
order of magnitude estimate of plant biomass (= carbon) and nutrient flux. Gong and Ong (1990)
have attempted this for the Matang Mangrove Forest. They showed that annual export of N and P
from the Matang Mangrove system was approximately 0.3 tonne ha-1 in both cases.
4.5 Mangrove Modelling with STELLA
In a mangrove ecosystem the mangrove trees are both the major primary producers and the major
constituent of the standing crop or biomass. These plants take up nutrients like nitrogen and
phosphorus from the estuarine waters, and return them to the water via decomposition of litterfall,
dead trees and fine root turnover. If the litter, parts of dead trees and fine root get buried, then the
estuary becomes a sink for carbon and mineral nutrients. This has to be taken into account in the
input-output budget (often termed "storage"). In many places the plants are harvested, and so this
amount has to be accounted for in the estimates of output.
A considerable amount of data, along with a few assumptions, are required to carry out budgeting
that can accurately account for all of the sources, sinks and exports from such a system.
Nevertheless the "storage" and harvest terms can be calculated (Gong and Ong, 1990).
Unfortunately, as stated above in the last section, this empirical approach does not have a predictive
capacity beyond the range of the empirical observations. As an alternative, this process may be
modelled by using system modelling techniques and software. For this example the modelling tool
STELLA is used (see Section 6 and Annex 1 for details).
One particularly useful aspect of STELLA as a tool for modelling is that one can use it to
conceptualise how a particular system works. It is possible to build conceptual models that are either
very simple or very complex. If the relevant data are available it is possible to turn the conceptual
model into a quantitative model that can be used in a "predictive" mode. Two examples using
STELLA are given here.
The first is a simple example of what happens to the mangrove biomass under different management
strategies. In this case the modelling software is used to investigate how the amount of harvest
changes with changes in the thinning and rotation periods. In Malaysia, many of the mangrove
forests are managed for the production of timber. The management system used varies from state to
state. In the Merbok Mangroves the forest is harvested in patches of a few hectares over a 30-year
rotation. If there are 3,000 hectares of productive forest then the coupes, that is the size of area cut
at a single harvest, can only be around 100 hectares, that is 100 hectares of forest are harvested
each year. The Matang Mangroves located in another State are reputedly the world's best managed
mangroves. A 30-year rotation is also used but here, instead of harvesting in coupes or patches, the
trees are thinned at 15 years and at 20 years. About half the trees are removed at each thinning.
Since the forests are managed and the forestry departments keep records of the coupes, it is
possible to estimate the age of trees in particular stands to within a year or two. Allometric equations
of the girth of the tree against the total biomass of the tree are used to estimate the above- and
below-ground biomass of the different aged stands. Ltterfall data for the different age stands are also
available. From these it is possible to make very reliable estimates of the above-ground net
productivity of these forests. One unknown in the biomass and productivity estimates is rate of
turnover in the fine roots of the trees which could be almost as high as total litterfall.
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~
MORTALITY
NATURAL
Graph 1
TREEMASS
YIELD
~
GROWTH
HARVEST
HARVESTS
PROPORTION
CROPNOW
YOUTHF
AGE
Figure 2. Detailed model for Merbok mangrove developed using STELLA software.
HARVESTS(t) = HARVESTS(t - dt) + (CROPNOW) * dt
INIT HARVESTS = 0
CROPNOW = PULSE(1,15,5)-(1.)
TREEMASS(t) = TREEMASS(t - dt) + (GROWTH - MORTALITY - HARVEST) * dt
INIT TREEMASS = 0
GROWTH = GRAPH(AGE)
(0, 0) (5, 2.8) (10, 18) (15, 12.5) (20, 12) (25, 12) (30, 12) (35, 12) (40, 12) (45, 12) (50, 12)
MORTALITY = TREEMASS*NATURAL
HARVEST = CROPNOW*TREEMASS*PROPORTION
YIELD(t) = YIELD(t - dt) + (HARVEST) * dt
INIT YIELD = 0
HARVEST = CROPNOW*TREEMASS*PROPORTION
AGE = TIME-YOUTHF*HARVESTS*PROPORTION*PROPORTION
PROPORTION = 0.5
YOUTHF = 20
NATURAL = GRAPH(TREEMASS)
(0.00, 7.77e-18), (25.0, 0.0105), (50.0, 0.0235), (75.0, 0.039), (100, 0.0545), (125, 0.0705),
(150, 0.07), (175, 0.0705), (200, 0.0705), (225, 0.0695), (250, 0.0695)
Text Box 2. Equations generated by STELLA software to implement the mangrove model.
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Using this data it is the possible to build a model of the change in forest biomass with time as a result
of different harvesting strategies (Figure 2). Using STELLA the state variables (squares), flows
(arrows), processes (circles) and sinks are identified and their quantities are estimated. STELLA
converts graphic representations such as shown in Figure 2 to mathematical equations such as
shown in Text Box 2. It is then possible, without too much expenditure of time and effort, to run the
model and predict standing biomass and the amount of wood that could be harvested from the
forests over a period of time (Radford, 1990). From the model, predictions can be made of what will
happen if the thinning regime or the harvest cycle is modified. Since data on the nutrient content of
the trees are available, it is also be possible to run a model based on nitrogen and phosphorus and
thus get a good idea of the transformation of inorganic to organic nutrients.
Figure 3. Complex system model of the Merbok Mangrove system generated using STELLA
software.
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The second example deals with a more complex three-compartment model looking at the flow of
water, salt (conservative) and dissolved organic matter (non-conservative) through the estuary.
Although there are not enough data to run this model, STELLA provides a useful way of identifying
the main compartments of the ecosystem that might require quantification. Figure 3 shows how
complex the model can become and also shows that by going through such an exercise, it is possible
to identify exactly what types of data are required, thus the model helps in the conceptualisation as
well as the design of the experiment. By developing such a conceptual model it is possible to avoid
the unnecessary collection of considerable quantities of irrelevant data. In many cases the use of
simple modelling software such as STELLA may be usefully applied at the very start of a new project.
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5. RESPONSE TO FIRST LOICZ MODELLING REQUIREMENT - QUANTIFY FLUX
5.1 Describing Physical/Biological Systems and Defining Natural Boundaries
In order to build a budget model, it is necessary to define the spatial domain to be modelled. The
definition of the land boundary is usually relatively easy; it is likely to be defined by the shore line or
the limit of tidal excursion. Except for systems which are dominated by intertidal habitats (for
example, mangroves or salt marshes), this exact position is not likely to be critical. The open, or
"oceanic," boundary of in-shore waters may not be so readily chosen. To a great extent, breaking the
world's coastal zone into typological units implies the recognition of classes of systems which might
be useful in building an inventory of systems to be modelled within the context of LOICZ (LOICZ,
1995d). Regions will, however, be modelled at different spatial resolutions depending on a number of
local and regional considerations. Many factors may need to be considered in defining the open
boundary of the model domain: topography, habitat type, current system, and the distribution of
material concentrations (Table 1).
In the case of topography, shelf edge, bay or estuary mouth, and sills between topographic basins
are obvious candidates for definition of a "natural" open boundary. Particularly in the case of benthic
dominated systems, habitat type (coral reef, seagrass bed, etc.) may provide useful boundaries. If
there is no characteristic topography or habitat type in the model domain, it may be necessary to
consider the current system or gradients of material concentration. For example the tidal excursion,
the boundary between horizontal residual circulation water masses, and the frontal structure of
material concentration are additional candidates for natural boundaries.
5.2 Defining the Questions to be Addressed
For the preparation of wider regional and global syntheses and estimates, the LOICZ Project requires
data on carbon fluxes, but these guidelines show that it is more efficient to approach estimates of
carbon flux through nutrient fluxes. Hence, the budget models discussed here will deal with fluxes of
carbon, nitrogen, and phosphorus (CNP).
Within the context of LOICZ biogeochemical modelling, the primary questions to be addressed
concern the role of the coastal zone as a source or sink for carbon, nitrogen, and phosphorus.
Clearly, individual regions may function as sources or sinks for different materials, and equally
clearly, the role of the coastal ocean, or parts thereof, may vary temporally between being material
sources and material sinks. For example, many aquatic ecosystems take up dissolved inorganic
carbon during the day (are sinks) and release inorganic carbon during the night (are sources). There
are also clear seasonal cycles in biogeochemical fluxes within many systems. Scientific and
management interest in the role of a system as a source or sink operates across a range of time and
space scales. For example, systems receiving heavy nitrogen loading from sewage input may have
primary production which is not nitrogen limited. With distance away from the nitrogen sources,
primary production in many marine ecosystems may become nitrogen limited. Daily or seasonal
changes in the biogeochemical performance of a system may provide information on the temporally
varying cycles (for example, light and temperature) controlling such performance. It is necessary to
identify the time and space scales and the processes by which such variations occur.
For the purpose of supplying data for global biogeochemical models, it is proposed that the flux
estimates generally be aggregated into time steps of months to years. In some cases long-term
steady state estimates may be all that are feasible or required. The smallest spatial scale which
seems likely to be justified within the context of LOICZ in most instances is probably about 1 km, with
space scales of 10's to 100's of km providing adequate resolution in many instances. It is often easier
to develop robust budgets of systems at the larger spatial scales than the smaller spatial scales,
because of decreased temporal variability of grid-averaged data. At the same time, the coarser
spatial scales may sacrifice the ability to resolve the data by habitat or to extract detailed process-
related information from the budgets. Final selection will depend on a balance of these
considerations.
A total-system mass-balance budget is a simple class of mathematical models that tends to provide
robust estimates of integrated ecosystem performance on the time and space scales of interest here.
This class of model is little more than an ordered, objective description of what is known about the
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system in question. In many instances, collection of data which can be used in a budget may have
occurred incidentally to other studies. Conservation of mass is, of course, a fundamental principle of
nature. Therefore a comprehensive budget of the inputs of materials into the system of interest,
outputs from that system, and amount in the system is an objective description that goes beyond
simple tabulation of such data. While such budgets provide neither direct experimental nor direct
theoretical information about how the system works, the budgets can describe the system at space
and time scales which may not be amenable to experimentation or detailed simulation modelling.
One result is that the descriptive output from budgets can be used in a statistical sense to evaluate
and compare how systems work and how the parts of the Earth system are linked together.
5.3 General Methodological Background
In this chapter, a class of mass balance budgets are presented which are called here
"stoichiometrically linked water-salt-nutrient budgets." The nutrients of specific interest here are
carbon (C), nitrogen (N), and phosphorus (P), all of which are essential to life.
Stoichiometrically linked water-salt-nutrient budgets actually comprise a series of budgets which are
solved in a prescribed order as described in Text Box 3. There is progressively more information
about ecosystem performance to be derived by proceeding in the prescribed order. A note of caution
seems warranted at this point. There are, in the ecological and geochemical literature, many so-
called "budgets." Some of these are only partial budgets, and there may be more misinformation than
information in a budget which is either partial or otherwise sloppily constructed. Consequently, any
person constructing a budget should proceed in a careful fashion, with attention to completeness, and
any person studying other persons' budgets is wise to consider just how carefully that budget has
been constructed. At the same time, it should be appreciated that the construction of usable budgets
requires judgements of what is (or is not) quantitatively important. A further point is that an overall
"recipe" for the preparation of stoichiometrically linked budgets can be developed here, but the
flavour of the eventual product will reflect the seasonings added by the individual cook working with
the ingredients which are available.
1. Water budget: Establish a budget of freshwater inflows (such as runoff, precipitation,
groundwater, sewage) and evaporative outflow. There must be compensating outflow (or inflow)
to balance the water volume in the system.
2. Salt budget: Salt must be conserved in the system. Therefore salt flux not accounted for by the
salinities used to describe the freshwater flows in Step #1, above, must be balanced by mixing. If
there is no salinity difference between the system of interest and adjacent systems, or if the
pattern of water exchange is too complex to be amenable to be described by the combined water
and salt budgets, some more complex form of circulation analysis will be required. Steps #1 and
#2 describe the exchange of water between the system of interest and adjacent systems by the
processes of advection and mixing.
3. Budgets of nonconservative materials: All dissolved materials will exchange between the
system of interest and adjacent systems according to the criteria established in Steps #1 and #2,
above. Deviations of material concentrations from predictions based on these two previous steps
are quantitatively attributed to net nonconservative reactions of materials in the system.
4. Stoichiometric relationships among nonconservative budgets: It can often be assumed that
the nonconservative flux of dissolved inorganic phosphorus is an approximation of net
metabolism at the scale of the ecosystem, because there is no gas phase for phosphorus flux.
Nitrogen and carbon both have other major flux pathways (notably denitrification, nitrogen
fixation, gas exchange across the air-sea interface, and [in some systems] CaCO3 reactions).
The deviation of the fluxes of these materials from expectation based on C:N:P composition
ratios of reactive particles in the system can be assigned to other processes in a quantitatively
reproducible fashion.
Text Box 3. Summary of sequential steps in budgetary modelling analysis.
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In general terms, the sequence of budgets for use in stoichiometrically linked CNP budgets follows
four steps: water budgets, salt budgets, nonconservative materials and stoichiometric linkages
among nonconservative budgets.
Water Budgets: The concept of the hydrological cycle is well established, and is often presented
(both globally and locally) in terms of water budgets. The conceptual model may be represented by a
simple box diagram (Figure 4). An accounting of freshwater inflows to a coastal marine system (such
as runoff, precipitation, groundwater) and of evaporation from the system is often rather easy to
accomplish. The fundamental concept behind the budgets, of course, is the conservation of water
mass. If it is assumed that either water volume remains constant or that the change of water volume
through time is known, then net water outflow from the system can be estimated by difference. This
flow is known as "residual flow;" there are likely to be other flows, but the difference between inflows
and evaporative outflow must be balanced by this residual flow. As examples of judgement about
individual systems, it is often (but not always) legitimate to assume that the system volume remains
constant. Groundwater, sewage discharge, and other freshwater sources may often, but not always,
be ignored. Often, but not always, runoff overwhelms the direct meteorological fluxes of precipitation
and evaporation. Simple calculations can usually be made to estimate whether terms such as these
are likely to be significant above the errors in the other terms.
Precipitation (VP)
Evaporation (VE)
Runoff (VQ),
Groundwater (VG),
Other (VO)
COASTAL
WATER BODY
Residual flow (VR);
VR from Eq. 3
volume = V1
Figure 4. Generalised box diagram illustrating the water budget for a coastal water body. The arrows
show the net water flow associated with each process. Quantities which are generally
measured are shown in light typeface, while the quantity which is calculated to balance the
budget (that is, VR) is shown in bold typeface. In systems with net freshwater inflow, VR will
be negative (that is, out of system). System volume (V1) is in units of volume, while all flow
volumes are in units of volume per time.
Salt Budgets: Coastal marine systems have flows across the system boundaries in addition to the
residual flow. For example, these systems have water inflow and outflow associated with tides, winds,
density, and large-scale circulation patterns. If the salinity of the system of interest as well as that of
adjacent systems exchanging water with that system is known, then it may be possible to construct a
salt budget (Figure 5) which includes these exchange flows in addition to residual flow. These
exchanges are often modelled as mixing, rather than as advection. The salinity balance accounts for
these additional exchange flows. In this case, note that any material in the water which is not
changing by internal reactions within the system (in general, the salt of any abundant, highly soluble
material) can be used in place of salinity. "Salinity", as defined by oceanographers, is in effect the
sum of those salts and is readily measured. Because salt is not being either produced or consumed in
the system, salinity is said to be "conservative" with respect to water within the system. Specific
materials with similarly non-reactive properties (chloride is a common example) are said to be
"conservative" with respect to salinity.
- 25 -

---

Precipitation
Evaporation
(SP 0)
(SE 0)
Runoff (SQ),
Residual salt flux
Groundwater (SG),
(VR SR); SR = (S1+S2)/2.
Other (SO).
COASTAL
Salinities usually 0.
WATER BODY
Ocean salinity (S2)
System salinity
(S1)
Mixing salt flux
(Vx[S1 - S2]);
Vx from Eq. 8.
Figure 5. Generalised box diagram illustrating the salt budget for a coastal water body. The arrows
show the net salt flux associated with each process. In general, residual flow (that is, VRSR)
is negative indicating flow from the system. Under such conditions, mixing (VX) is likely to
transport salt into the system. Quantities which are generally measured are shown in light
typeface, while quantities which are calculated within the budget are shown in bold
typeface.
The concept of "conservative" should be treated with some caution. On some time scales all of the
salts in the ocean react. Therefore no salt dissolved in water is truly conservative with respect to
water. Systems which include significant evaporite deposits may exhibit very nonconservative
behaviour of salinity. In low salinity systems, ion ratios may vary significantly; the entire concept of
"salinity" becomes qualitative. In such systems it may be safer to use a property which is more
explicitly defined (for example, Cl). Having pointed to these cautionary notes with respect to salinity,
it is useful to realise that salinities of streams or groundwater flowing into estuarine systems or the
slight salt content of precipitation can be ignored in most cases. Again, simple calculations to
evaluate this assumption are a useful precaution.
In the absence of salinity gradients or adequate data to establish salt budgets or, in the presence of
spatial distribution patterns which are too complex for simple water and salt budgeting, it may be
feasible to develop 2 dimensional or 3 dimensional numerical models of water circulation (Haidvogel
and Beckmann, submitted). The output from such numerical circulation models may subsequently be
substituted for water and salt budgets in order to estimate water exchange.
Budgets of nonconservative materials
The next step in the budgeting exercise is to consider materials which may not behave
conservatively with respect to salinity (Figure 6). These budgets may be termed budgets of
nonconservative materials. While this might be done with any reactive material (for example, Si,
which is actively involved in both biotic and abiotic reactions), the particular interest here is in the
balance among the essential plant nutrient elements C, N, and P. Water exchange, defined by the
water and salt budgets, describes the exchange fluxes of these elements along with salt. Clearly,
total C, N, and P are conserved, but these elements may be transformed from measured, such as
dissolved, to unmeasured, such as particulate or gaseous, phases. All dissolved phases of these
materials are known to be involved in biochemical and abiotic reactions, so they are not likely to be
conservative with respect to salinity. In the case of salinity, the budget is exactly balanced by water
exchange. In the case of dissolved C, N, and P, the budgeted exchange fluxes are likely to leave
some residual flux which is not balanced by these calculations. This residual for each element is a
measure of the net internal fluxes (that is, sources minus sinks) of these materials. In fact,
"conservative behaviour" of these materials with respect to salt would be taken to reflect one (or
perhaps both) of two conditions: either the exchange rates of these materials in the water are fast
relative to the internal fluxes, or the "conservative behaviour" represents the sum of uptake and
release fluxes which cancel one another out. If turnover dominates over net flux in the cycle of a
particular material, then the proportionality between salinity and this material is likely to be
accompanied by a great deal of scatter in the data, reflecting rapid turnover but little net change (see
examples in Imberger et al., 1983).
- 26 -

---

Precipitation
Evaporation
(YP may or
(YE 0)
may not 0)
Runoff (YQ),
Residual Y flux
Groundwater (YG),
(VR YR); YR = (Y1+Y2)/2.
Other (YO).
Y values usually 0.
COASTAL
WATER BODY
Ocean Y (Y2)
System Y (Y1)
Mixing Y flux
(Vx[Y1 - Y2]);
Vx from Eq. 8.
Net internal source or sink
(Y), from Eq. 20.
Figure 6. Generalised box diagram illustrating the budget for a nonconservative material, Y, in a
coastal water body. The arrows show the net flux of Y associated with each process. Mixing
(VX) may be to or from the system. Quantities which are generally measured are shown in
light typeface, while quantities which are calculated within the budget are shown in bold
typeface. Y denotes the nonconservative flux of Y, and can be positive or negative with
respect to the system.
Two other cautions are in order here. Firstly, it was pointed out above that water input from processes
like groundwater and sewage could often be ignored, and that the contributions of these terms to the
salt balance could likewise usually be ignored. It is clearly not the case that the nutrient content of
this water can be ignored; that should never be done for systems receiving significant sewage input
and should be done only with some caution for groundwater and precipitation. If there is runoff, the
nutrient input from that runoff must be included in the budget.
Secondly, the budgets present here generally involve only dissolved materials. While there are
methods to construct very useful budgets for particle fluxes, for example, sediment input by streams
and deposition within the system, in general, salinity-based budgets must be treated with great
caution in constructing budgets for particulate materials in shallow water systems. The reason is
relatively simple. Dissolved materials have no gravitational component of flux within the water while
particles do. Therefore particle distribution in the water column is likely to be extremely "patchy," with
respect to both time and space, in areas subject to heavy loading with stream sediments, as well as
in systems where wave mixing or active bioturbation is stirring the bottom sediments up into the
water column. These processes can generate great heterogeneity in estimates of particle
concentrations. While budgetary calculations for particles can be made according to the procedures
to be outlined here, sampling artefacts may make the results quantitatively unreliable. As a result, the
use of salt and water balance calculations are not generally useful to estimate particle budgets. It is
worth recalling, however, that conservation of mass is a fundamental law of nature. Therefore, for
materials without a gas phase, any deviation of dissolved forms of that material from conservative
behaviour must represent net uptake or release with respect to particles. This point is used in the
interpretation of output from the budgets.
Stoichiometric linkages among nonconservative budgets
The next step involves developing the stoichiometric linkages among nonconservative budgets. The
basic assumptions here are that net biogeochemical processes in coastal marine systems are
dominated by a few specific chemical reactions; that the biogeochemical cycles of C, N, and P are
intimately linked; and that the approximate stoichiometric relationships among these elements for the
dominating reactions can be written. Much of the flux of C, N, and P in coastal waters is attributed to
production and consumption of organic matter, and the composition of organic matter tends to be
relatively constant within the ocean. If plankton metabolism dominates, then the well-established
- 27 -

---

"Redfield Ratio" (Redfield, 1934) is likely to be a reasonable approximation of the C:N:P ratio of
locally produced (or consumed) organic matter. If the system metabolism is dominated by seagrass
or benthic algal metabolism, then some other composition may be more appropriate (Atkinson and
Smith, 1983). For systems in which sedimentary materials apparently dominate the local reaction, or
in which particle inputs and outputs can be assumed to be small, then the sediment composition may
be an appropriate compositional ratio to consider. In any case, some estimate can be made of the
local organic matter composition. This point will be developed in the case studies, below.
For the sake of linking the C, N, and P budgets, phosphorus may be considered to have the simplest
chemical pathways. All phosphorus in the system can be considered to be in either the dissolved
phase or the particulate phase, and phosphorus reactions involve transfers between these phases;
there is no gas phase. In contrast, both nitrogen and carbon have prominent gas phases, and carbon
and nitrogen fluxes involving the gas phases are known to be important in coastal systems. The
working assumption is therefore made that the internal reaction flux of phosphorus is proportional to
production and consumption of particulate material (generally dominated by organic matter). That is,
phosphorus moves back and forth between dissolved and particulate material. N:P and C:P flux
ratios are calculated from the budgetary analyses, and deviations of these flux ratios from
proportionality with respect to the particle composition are attributed to gas-phase reactions for
nitrogen and carbon (Figure 7).
Air-sea exchange of materials such
as N and C, with an active gas
phase. Yg calculated from Eqs. 31
or 33.
Precipitation
Evaporation
(YP may or
(YE 0)
may not 0)
Runoff (YQ),
Residual Y flux
Groundwater (YG),
(VR YR); YR = (Y1+Y2)/2.
Other (YO). Y values
usually 0.
COASTAL
WATER BODY
Ocean Y (Y2)
System Y (Y1)
Mixing Y flux
(Vx[Y1 - Y2]);
Vx from Eq. 8.
Net internal source or sink
(Y), from Eq. 20; scaled to
biogeochemical estimates of
process rates with Eqs. 29-33.
Figure 7. Generalised box diagram illustrating the budget for a nonconservative material, Y, which
has an active gas phase in a coastal water body. In this case, appropriate stoichiometric
linkages are used to scale the nonconservative fluxes (Y's) to system-scale estimates of
internal biogeochemical processes. The arrows show the net flux of Y associated with each
process. Quantities which are generally measured are shown in light typeface, while
quantities which are calculated are shown in bold typeface.
- 28 -

---

In the case of nitrogen, the gas-phase reactions require biochemical activity to transfer nitrogen
between fixed inorganic (NO3, NH4, and small amounts of NO2) and organic (dissolved organic
nitrogen (DON) and particulate nitrogen (PN)) pools and gaseous nitrogen (dominated by N2). These
reactions may be taken to represent the net difference between nitrogen fixation (represented in
simplified form here as N2 organic nitrogen) and denitrification (in simplified form, NO3 N2 +
N2O). N2 and N2O) are not generally measured in seawater. In any case, the amount of N2 in
seawater is so large in comparison to all other forms of nitrogen that transfers to or from the fixed
nitrogen pools are insufficient to affect N2 measurably (generally << 1% change in N2, even though
the changes in the other pools may be large). For all practical purposes, it may be considered that
the N2 content of seawater is strictly controlled by gas solubility and equilibration of N2 partial
pressure between seawater and the overlying atmosphere. It will be seen in the case studies that the
reactions involving nitrogen transfer to or from the gas phase generally must account for a large
fraction of the net nonconservative fluxes of nitrogen in coastal systems. Therefore this
stoichiometric procedure is a relatively robust way to estimate the difference between nitrogen
fixation and denitrification. See, for example, Webb (1981) and Carpenter and Capone (1983) for
discussions of nitrogen biogeochemistry and chemical ecology in the marine environment.
In the case of carbon, the transfers between the gas phase (CO2 and its hydrated form H2CO3) and
the dissolved phase are rapid responses to thermodynamic equilibration. Moreover, in the case of
carbon, the gaseous phase is not large and is typically either measured or calculated
thermodynamically. Further, the gaseous CO2 content of seawater is typically measurably out of
equilibrium with the atmosphere, so that gas exchange processes are constantly tending to cause
CO2 flux across the air-water interface. Deviations of carbon flux with respect to predictions based on
phosphorus are therefore measures of the exchange flux of CO2 across the air-sea interface. As was
pointed out with nitrogen, the carbon fluxes which are not proportional to phosphorus are often large
and are therefore useful measures of this gas flux. These and other complications in the carbon
fluxes are considered in the case studies. Skirrow (1975) and Smith (1985) provide syntheses of the
chemistry and chemical ecology, respectively, of CO2 in aqueous systems.
5.4 Mathematical Structure of the Budgeting Procedure
With this background on the budgeting sequence, a very generalised mathematical description of the
budgeting procedure can be laid out. The general procedure cannot deal with all of the details
encountered in real-world situations, so the user of these guidelines is urged to gain a sufficient
understanding of these rules to be able to use common sense in developing budgets. Following this
section on the general mathematical structure of budgeting and the next section on information
requirements, specific case studies are presented in which the mathematical formulation and other
aspects of model development are explored in more detail. Officer (1980) provides a detailed and
comprehensive review and analysis of calculating both water and salt budgets and nonconservative
fluxes according to box models. The analysis presented here is a greatly shortened version of
Officer's literature review and algebraic analysis. Officer also discusses the relationship between
such box models and mixing diagrams widely used by geochemists to characterise materials which
are not conserved relative to salinity. In this latter context, the short paper by Officer (1979) is a
particularly clear explanation of the algebra behind mixing diagrams. Officer and Lynch (1981) and
Loder and Reichard (1981) discuss, via numerical analysis, apparent nonconservative behaviour
which can be generated as analytical artefacts if mixing diagrams are used to describe the
distribution of materials in systems which are not at steady state. Kaul and Froelich (1984) give a
specific example of this point. Formal extension of the nonconservative flux calculations to
stoichiometric linkages and explicit numerical treatment of data not at steady state have been
explored by Smith and his colleagues (Smith et al, 1991; Smith and Atkinson, 1994).
- 29 -

---

5.4.1 Water budget
Water is conserved. Therefore, the water volume entering a system must equal water volume
storage within the system minus the water volume flowing out of the system (Figure 4). Inflows
include stream runoff (VQ), direct precipitation (VP), and groundwater (VG). There might be other
inflows (VO) such as sewage. There is also hydrographically driven advective inflow (Vin). Removals
include evaporation (VE) and advective outflow of water from the system (Vout). Water storage may
be represented by the change in system of interest with time (dV1/dt):
dV1 =V +V +V +V +V -V -V
(1)
dt
Q
P
G
O
in
E
out
In concept, Equation (1) is simple enough. For the purposes of actual budgeting, the equation may be
difficult to implement. In practice, in any situation, there may be multiple source terms for VQ, VG,
and VO. In a large system, precipitation and evaporation may vary over the area of the system.
These complications of multiple terms are relatively easily dealt with, if the data base is adequate to
sum up the parts. Vin and Vout are the only terms in Equation (1) which are not readily measured. By
rearrangement of Equation (1):
dV
V -V
=
1 -V -V -V -V + V
(2)
in
out
dt
Q
P
G
O
E
It is useful to consider the difference between Vin and Vout as the residual flow driven by the water
budget; This is identified as VR. Further, in many cases dV1/dt may be considered constant,
simplifying the equation. Vout and Vin cannot be solved individually from this equation, but they can be
used to evaluate VR.
All of these terms have the units of volume per time (in most examples presented here represented
by m3 d-1). VQ, perhaps VG, and perhaps VO are likely to be measured directly in units of volume per
time. Precipitation (P) and evaporation (E) are typically measured in units of length per time (mm d-
1); volumetric estimates (that is, VP, VE) are derived by multiplying P and E (in length per time units)
by system area (that is, the map area of the water surface being budgeted). In general, VQ is likely to
be the largest term on the right hand side of Equation (2) and is unlikely to be estimated to closer
than 5-10% accuracy. Therefore any term much smaller than 5% of VQ, or, if VQ is not the largest
term, of the largest term in the equation, can be ignored as being within the noise of the data. In most
applications, VO and probably VG are sufficiently small to be ignored in the water budget; in many
applications, VQ may be the only term large enough to figure in the estimation of VR. All freshwater
inputs minus evaporation are combined into a single term (VQ*). Equation (2) can be simplified
accordingly:
dV
V = V -V
=
1 -V
(3)
R
in
out
dt
Q*
While most coastal aquatic systems have inflows and outflows forced by winds and tides, the
difference between inflows and outflows will tend towards 0 when averaged over periods
progressively longer than a single tide cycle. VR remains as the "residual flow" required to balance
the water budget. Note that VR is positive only in systems with evaporation in excess of precipitation
and river inflow; that is, residual flow is into the system. The more usual case where freshwater input
dominates, yields a negative value for VR. The ratio of the absolute value of the system volume to
the residual flow, that is, V1/VR with units of days, is sometimes referred to as the freshwater
residence time, or the hydraulic residence time, of the system. The total water exchange time is
usually much shorter than the freshwater residence time, as demonstrated below.
- 30 -

---

5.4.2 Salt budget
Tidal or wind-induced inflows and outflows are not important to the water budget because they tend
to balance out over time. However, these flows do exchange salt and other materials between the
system of interest and the "outside world," so they are important to the budgets of these materials. In
effect, these exchange fluxes can be considered to be mixing terms (Figure 5). The horizontal
exchange flux is represented by Vin and Vout. Dimensionally these fluxes, like the terms in the water
budget, have the units of volume per time. The primary equation representing the salt budget states
that the salt flux is equal to each of the volume fluxes multiplied by the salinity (S) of each water
type. In the case of the residually advecting water, the salinity is taken at the system boundary.
Water in the system of interest is designated by subscript 1; water outside the system is designated
by subscript 2. These conventions lead to the following equation:
d V
( S )

1 1
= V S +V S -V S
(4)
dt
Q* Q*
in 2
out 1
Equation (4) can be simplified somewhat. For most applications, all salinities except S1, and S2 are
likely to be small and can be considered to be 0. If there is doubt about the validity of this simplifying
assumption, the investigator should evaluate the sensitivity of Equation (4) to that assumption with
sample numerical values. Dropping the terms with small salt addition is useful for discussion without
sacrificing anything in the algebra:
d V
( S )
1 1
= V S -V S
(5)
dt
in 2
out 1
In Equation (5), the mixing exchange terms (Vin, Vout) remain as the unknowns. By combining
Equations (3) and (5) and expanding the term d(V1S1), Vin and Vout can now be evaluated individually:
1

dS1
V =
V S -V
(6)
in
(S - S
Q
1
1
)
*
2
1


dt
and
1

dS1 dV
V
=
V S -V
1
V
(7)
out
(S - S
Q
1
1
)
*
*
2
1


dt -
+
dt
Q
It can be seen that Equations (6) and (7) simplify considerably if either dS1/dt or dV1/dt, or both, can
be treated as constant. In particular, if dV1/dt = 0, Vin = Vout - VQ*. That is, Vin and VR move water back
and forth with respect to the system, with the difference between these terms being -VQ*, the residual
flow (Equation 3). It is therefore convenient to redefine Vin as the water exchange flow, VX. Moreover,
because the residual flow (VR) can be either out of the system, that is, a system in which freshwater
inflow exceeds evaporation, or into the system, that is, net evaporation, the appropriate salinity to
use for residual flow is the salinity at the boundary between boxes 1 and 2. This salinity at the
boundary is defined as SR, the average of S1 and S2. By rearrangement of Equation (6) and use of
the notation VR and SR for residual flow and the salinity of that flow:
1
dS1

V =
V
+ V S
(8)
X
(S - S
1
)
1
2


dt
R
R
In many cases, system volume (V1) is treated as constant; V1 can be taken outside the derivative on
the left side of the equation. If S1 is also constant, then the salt content of the system is said to be at
steady state. The entire derivative (d(V1S1)/dt) becomes 0, and the equation simplifies. This steady-
state solution is the most common solution encountered in the literature for marine system; in lakes
or other very confined water bodies, volume and/or salinity may vary with time. The full derivative
term in the algebraic analysis will be retained, although most of the case studies presented will
consider only the steady-state solution.
- 31 -

---

Total water exchange time is given by the ratio V1/(VR + Vx). Note that this value will in general be
smaller than freshwater residence time, often much shorter. A point to note in this derivation of
circulation from a combined water and salt budget is that there must be a salinity difference between
S1 and S2. In practice, the absolute value of this term should deviate from 0 by at least several tenths
(p.s.u.) in order to achieve a robust estimate of Vx. In time trend data, Vx values which are large
(positive or negative) with respect to their neighbour values are likely indicators that the term (S1-S2)
is not reliably different from 0. Note that the exchange terms are readily derived if there is only one
external salinity (S2) mixing with the system salinity (S1).
This 0-dimensional structure developed is readily expanded into a 1-dimensional series. Moreover,
because many aquatic systems are stratified, it is often useful to lay out a two-layer analysis. The
basic analytical structure which will be developed corresponds to surface outflow of less saline water
and deep inflow of more saline water, with vertical mixing in each sub-basin. This model corresponds
closely with both the classical analysis by Knudsen (1900) for the water and salt balance of the Baltic
and the general concept of two-layer estuarine circulation (Pritchard, 1969), as presented in the form
of box models by Officer (1980). In the following expansion, only the case where both volume and
salinity of each box remain constant with time, that is, dV/dt = dS/dt = 0, is considered. This
assumption simplifies the algebra but is by no means required. For more detail, the reader is referred
to Wulff et al. (1994).
Each of n sub-basins (with n = 1 being the closest to shore) is divided into a surface box (s) and a
deep box (d). At steady state, vertical entrainment (Vent(n)) of water from the deep to the surface box
of basin n equals the difference between water flowing horizontally to and from the deep box (i.e.,
Vind(n) - Voutd(n)). For the surface box, horizontal outflow - inflow (Vouts(n) - Vins(n)) equals freshwater
inflow (VQ*(n)) plus vertical entrainment. Further, the salt exiting the surface box (Vouts(n)Ss(n)) equals
the salt input to the deep box (Vind(n)Ss(n+1)) . Vertical mixing exchange (Vz(n)) between each surface
and deep box also occurs and balances the salt budget.
V
= V
-

V
ent (n)
in d (n)
out
(9)
d ( n)
V
+ V
=
-
( )
*( )
[V
V
ent n
Q n
out s(n)
in
(10)
s(n) ]
V
=

S
V
(11)
( )
( )

S
out
s n
s n
in d (n)
s(n+ )
1
dS
V
s(n) = V S
-
-
V
(12)
1

S
+V S
+V
-
( )
in s(n)
s( n )
out
s(n)
s(n)
ent
d (n)
z(n) [S
S
s n
d ( n)
s(n) ]
dt
dS
V
d (n) = V S
-
+
V
(13)
1

S
-V S
- V
-
( )
in d (n)
d (n )
in d (n)
d (n)
ent
d (n)
z(n) [S
S
d n
d (n)
s(n) ]
dt
In this system of equations, surface inflow to the nth basin equals surface outflow from basin n-1;
deep inflow to the nth basin equals outflow from basin n+1. For the first basin (n=1), surface inflow
and deep outflow = 0. As with the 0-dimensional case, salinity differences between horizontally
adjacent water masses are required to be non-0 values.
5.4.3 Estimates of water exchange via numerical modelling
It is, of course, possible to develop nutrient budgets in the absence of salt budgets. Examples of this
include the classical "flow respirometry" measurements across coral reef flats (Odum and Odum,
1955) and budgets of materials flowing in and out the mouths of tidal channels (Kjerfve et al., 1981;
Wattayakorn et al., 1990). In such instances it will be necessary to turn to an alternative estimate of
water exchange, possibly including complex 2 or 3 dimensional numerical circulation models in order
to describe the exchange terms. It is beyond the scope of this report to discuss this array of
methodology in detail (see, for example, Haidvogel and Beckmann, submitted), but a brief review is
helpful.
- 32 -

---

From the physical viewpoint, the magnitude of horizontal mixing Vx is determined by the dominant
current system around the open boundary of the model area. If the tidal current is dominant, the
effect of tidal mixing is the largest for the determination of the magnitude of Vx. If the density-driven
current or the wind-driven current is dominant, the effect of water exchange due to the vertical
gravitational circulation or that of water exchange due to the horizontal residual circulation is the
largest for the determination of the magnitude of Vx respectively. In the case where the open
boundary is the shelf edge, the effect of the boundary current is frequently dominant in addition to the
three currents system mentioned above. The water exchange between the shelf and the open sea
due to frontal eddies, which is generated by the instability of the boundary current, mainly determines
the magnitude of Vx.
The results of direct current measurement around the open boundary of the model area are
separated into tidal current, density-driven currents, and wind-driven currents by statistical analysis
and harmonic analysis. The magnitude of Vx can then be estimated with the current data, as follows.
For the contribution from tidal currents (Vx(t)):
2 a U L l
V
=

(14)
x(t )

Here a ( 0 < a < 1.0 ) denotes the mixing rate of water mass during one tidal cycle. The magnitude of
`a' depends upon the horizontal geometry and bottom topography around the system. It ranges
between 0.2-0.4 in narrow straits and 0.1 on wide shelves (Yanagi, 1989). U is the vertically
averaged tidal current amplitude, L is the tidal excursion, and l the horizontal length of the open
boundary of the model area.
For density-driven currents (Vx(d)):
U h l
V
u
=

(15)
x(d )
2
Here, Uu denotes the current speed of the density-driven current in the upper layer; and h is the water
depth.
For wind-driven currents (Vx(w)):
U h l
V
w
=

(16)
X ( w)
2
Here Uw denotes the maximum speed of barotropic wind-driven current normal to the open boundary.
For frontal eddies (Vx(f)):
V
= b r D C
(17)
x( f )
Here b ( 0 < b < 1 ) is the entrainment ratio of shelf water in the frontal eddy, r is the wave length of
frontal eddy, D is the thickness of frontal eddy and C is the phase speed of frontal eddy. The
magnitude of b ranges from 0.01 to 0.05 (Lee et al., 1981).
The terms may then be linearly superimposed to derive an overall estimate of VX:
V = V
+V
+V
+V

(18)
X
x( t )
x(d )
x( w)
x( f )
- 33 -

---

In the real world of the coastal sea, the residual flow field is not steady. Tidal currents and tide-
induced residual currents are nearly steady throughout the year with the spring-neap tidal cycle
modulation. The density-driven current, however, varies seasonally in temperate and high latitudes,
and strong episodic density-driven currents are sometimes generated by high freshwater inflows from
flooding. The most variable component of residual flow is the wind-driven current due to the wind
above the sea surface. It is difficult to estimate an appropriate "typical" Vx when the residual flow field
is highly variable and complex around the open boundary. In such case, some averaging procedure
on the residual flow field is carried out in order to estimate a correct Vx for material transport under
particular circumstances.
5.4.4 Summary of conservative material balance
It follows from the above analysis that the balance, or budget, of salt in the system of interest is
defined by the following general equation describing the mass of material S in the system (dVS/dt),
where Vin and Vout represent all of the hydrographic inputs and outputs (including in this case
exchange flow in and out) of each water type and Sin and Sout represent the salinity of those water
inputs and outputs:
d VS
( )

= V S - V S
(19)
dt
in in
out
out
Expanding this equation:
dS
dV
V
+ S
= V S - V S
(20)
dt
dt
in in
out
out
Steady state assumptions of either dS/dt or dV/dt may simplify Equation (20). It is worth
remembering at this point that various of the water sources entering the system are likely to have a
salinity near 0 (p.s.u.).
5.4.5 Budgets of nonconservative materials
Equation (20) represents a salt balance for the system, whether determined by means of a water and
salt budget or direct estimates of water advection and mixing. Materials which are not conservative
with respect to water and salt can be assumed to be represented by the same hydrographic inputs
and outputs as govern the water and salt. Thus, the advection and the mixing exchange derived for
water and salt are equally well applied to these other materials (Figure 6). For any material Y,
Equation (20) is modified to include the sum of the nonconservative processes acting in the system
to add and remove Y (that is, Y). It is assumed that the concentration of Y in evaporating water is 0,
but it is not assumed that inputs of Y in the other water sources are 0.
dY
dV
V
+ Y
= V Y - V Y + Y

(21)
dt
dt
in in
out out
Again, steady state assumptions may allow one or both of the derivatives on the left side of the
equation to be dropped. In some cases individual fluxes may be directly available, rather than being
the product of concentration and flow. For example, sewage input of Y may be directly known,
without data on sewage volume. The summed nonconservative fluxes (Y) are the information
desired and are derived by rearrangement:

dY
dV
Y = V
+ Y
- V Y + V Y
(22)
dt
dt
in in
out out
The units of Y are mass per time; generally presented in this report as moles (mol) or kilomoles per
day. Note two aspects of this equation. In the first place, this derivation gives no information about
the processes leading to Y, either the number of processes or the general form of those processes.
Physical, abiotic chemical, or biotic chemical processes may contribute to Y, and they are
- 34 -

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indistinguishable from this derivation. Such information is derived through other considerations, as
discussed in the next section and exemplified in the case studies. Some terms, again sewage is an
example, may be directly entered as known values in Equation (22), or may be part of the term Y.
In the second place, while this budgeting procedure based on a salt balance is in principle applicable
to any material in many situations, it often cannot be applied with much quantitative success to
particulate materials. The concentrations of these materials tend to be so patchy both spatially and
temporally in response to sedimentation and resuspension that they are not adequately sampled in
the context of a budgetary procedure derived for application to tidally averaged data.
In general is useful to express Y per unit area, by dividing the value estimated according to
Equation (22) by the system area, often expressed as mol or mmol m-2 d-1.
5.4.6 Stoichiometrically linking the nonconservative CNP budgets
One procedure for gaining insight into the processes leading to the nonconservative fluxes is to
examine the "stoichiometric linkages" between the fluxes. The underlying assumptions behind this
approach are firstly that a small number of processes can be enumerated which are likely to
dominate these nonconservative fluxes, and secondly, that the underlying chemical stoichiometry of
each of these processes can be approximated. Each of the nonconservative flux pathways likely to
be important for these elements are considered in this subsection, proceeding from carbon fluxes, as
the currency of primary interest, to the stoichiometric relationships among carbon, phosphorus, and
nitrogen. In the remainder of this subsection, it is assumed that nonconservative fluxes of dissolved
C, N, and P have been derived as discussed above. The nonconservative fluxes are here noted with
the symbol "."
Carbon fluxes
CO2 in seawater moves among several dissolved inorganic ions according to rapid chemical
equilibration reactions: H
-
2-
2CO3 HCO3 + H+ CO3 + 2H+. The sum of these ionic forms is often
written as "DIC" (dissolved inorganic carbon). Adequate measurement of the dissolved inorganic C
system in water requires the measurement of two components related to the CO2 system.
Measurement of two components, plus temperature and salinity, allows a complete description of DIC
partitioning. Realistic measurement possibilities include pH, total alkalinity (TA), DIC, and pCO2. In
practice, pH and TA are the most commonly measured variables; in principle, the most useful ones
to use for budget calculations are DIC and TA. It is beyond the scope of this report to discuss the
measurements further. Skirrow (1975) provides a detailed discussion of the theory and practice of
measuring the CO2 system in water.
Carbon fluxes in aquatic ecosystems include organic biogeochemical fluxes, inorganic
biogeochemical fluxes, and abiotic fluxes controlled by physical-chemical considerations. The
prevailing organic fluxes are primary production of organic matter and oxidation of organic matter via
various pathways. It is convenient to represent primary production and aerobic respiration by an
equation of the form:
CO + H O CH O + O
(23)
2
2
2
2
The reaction proceeding from left to right represents a geochemical simplification of primary
production, while the reaction proceeding from right to left represents respiration. Any budgetary
analysis, including traditional flow respirometry or incubation techniques, measures the net of these
processes over the budget period. It is thus concluded that the net reaction primary production minus
respiration (p-r) with respect to carbon is equal to the net decrease in CO2 according to Equation (23).
Because CO2 equilibrates rapidly among its dissolved ionic forms, change in DIC is the variable of
immediate interest here. Decreasing DIC may indicate net production of organic carbon, while
increasing DIC may indicate net consumption of organic carbon. Let us denote the change of DIC
due to organic metabolism as DICo.
DIC flux is involved in two other reactions which are likely to be important at the scale of the system.
If the CO2 partial pressure of the water (pCO2(w)) differs from that of the air (pCO2(a)), then there will
be gas flux across the air-sea interface from high to low pCO2. This change in DIC is denoted as
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DICg. DIC changes in the water also occur during the precipitation (DIC decrease) or dissolution
(DIC increase) of CaCO3 (DICc). These three basic pathways account for most DIC flux in most
aquatic ecosystems. Thus the total nonconservative change in DIC (DICt) can be described as
follows:
DIC = DIC + DIC + DIC
(24)
t
o
g
c
Note that there usually are some minor pathways of DICo associated with respiration such as
sulphate reduction (DICs) and denitrification (DICd). These, and other, usually even more minor
respiratory pathways, are part of DICo.
Total alkalinity flux (TA) is a useful component to estimate in CNP budgeting. The definition of TA
can be simplified, leaving out the contribution of borate alkalinity, as TA [HCO -
-2
3 ] + 2[CO3 ] + [OH-]
- [H+]. Although the contributions of OH- and H+ to TA itself are minor it will be seen that their
contributions to TA are significant.
Total alkalinity changes in response to calcification. The calcification reaction, or its reverse, CaCO3
dissolution, may be written several ways, all of which have the same effect on TA. For example:
Ca2+ HCO-
CaCO
H+
+

+

(25)
3
3
This version of the reaction has been deliberately chosen to demonstrate that TA decreases in
response to HCO -
3 consumption on the left side of the equation and H+ production on the right. An
alternative, apparently more straightforward way to write the reaction (Ca+2 + CO -2
3 CaCO3) does
not explicitly introduce H+ but has the same TA (TAc = 2DICc).
There is a minor change associated with nutrient fluxes, as discussed below, but this can be explicitly
corrected out of the measured TA and is ignored here (see Brewer and Goldman, 1976; Gaines and
Pilson, 1972; Smith et al., 1991). More importantly, there is also an alkalinity change due to net
sulphate reduction; that is, sulphate reduction - sulphate oxidation (Berner et al., 1970; Gaines and
Pilson, 1972; Smith et al., 1991):
2CH O + 2 +
2
H + SO - 2CO + H S
(26)
2
4
2
2
According to Equation (26), or alternative versions of the reaction, DICs = TA. It is important to
think of this reaction as a net reaction. H2S is thermodynamically unstable in the presence of free O2
and will rapidly oxidise back to SO 2-
4 . However in the presence of metal ions, especially Fe, the H2S
will rapidly become bound into metal sulphides.
For each mole of DICs released, there is 0.5 mole of sulphate reduced. Available studies have used
alkalinity flux as either a measure of calcification or sulphate reduction. This is, in general, probably
valid. Systems with high carbonate accumulation tend not to have much available terrigenous Fe,
hence they tend to have most of the sulphate, which has been reduced to sulphide, oxidised back to
sulphate, hence, TAs ~ 0. Systems with high terrigenous load tend to have low accumulation of
carbonate materials, hence, TAc ~ 0. This topic, including a consideration of systems in which both
TAs and TAc are significant, merits further investigation. For the present analysis, however, it is
assumed that TA can either be assigned to sulphate reduction or to calcification. With this caveat,
TA is interpreted according to the more important of these two processes in any particular system:
DICc = TAc/2; or DICs = TAs.
It follows from the above description that, in any particular system, TA is uniquely describing carbon
flux associated either with calcification or with some portion of (p-r). However, a budget of DIC and
TA cannot uniquely define DICo and DICg. Both of these fluxes are desired terms to extract from
budgetary analysis.
Another component of nonconservative dissolved carbon flux can also be measured: the flux of
dissolved organic carbon (DOC). While few such studies are available, it seems generally likely that
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the absolute value of DOC is small compared to the absolute value of DIC at the scale of total
ecosystems. Note that the production or consumption of DOC represents conversion between DOC
and either DIC or particulate organic carbon (POC).
General basis for stoichiometric modelling
A generalised equation for primary production and respiration is reported above in Equation (23).
Because organic matter contains carbon, nitrogen, and phosphorus in an almost constant ratio within
any one ecosystem, and tends to have a rather similar ratio, the Redfield C:N:P molar ratio of
106:16:1, throughout much of the ocean, the reactions of primary production and respiration can be
represented by somewhat more complex equations. It should be recognised that the equations are
not intended to describe the actual chemical reaction which goes on, but they do appear to
approximate the stoichiometric relationship among carbon, nitrogen, and phosphorus, and oxygen.
For primary production, where NO -
3 is the nitrogen source and where the starting organic matter has
a Redfield composition, the charge-balanced net reaction can be represented by an equation of the
form:
106CO + 16H + + 16NO- + H PO + 122H O

2
3
3
4
2

(27)
(CH O
NH
H PO +
O
2
) (
)
138
106
3 16
3
4
2
Various modifications have been offered to make the details of this stoichiometry more
"biochemically reasonable" (Anderson, 1995). In general, these changes involve the oxygen and
hydrogen content of the organic matter, not the carbon, nitrogen, and phosphorus content. Because
the interest here is in the carbon, nitrogen, and phosphorus relationships of the organic matter, the
older formulation is retained without loss of generality in the analysis.
This reaction, or one like it to represent slightly different estimates of oceanic organic matter C:N:P
ratios, is typically written for the open ocean. In the coastal ocean or other situations where NH +
4 is
the nitrogen source, the reaction may be written as:
106CO + 16NH + + 16OH - + 90H O
2
4
2

(28)
(CH O
NH
H PO +
O
2
) (
)
106
106
3 16
3
4
2
There are two points to laying out these two alternate equations explicitly. In the first place, although
the two equations do involve different stoichiometries with respect to the relationship between free
oxygen and CNP, the CNP stoichiometry being covered in the present discussion is unaffected. In
the second place, coastal systems may have NH +
4 as an externally supplied nutrient. This is in
contrast to the upper water column of the open ocean, where NH +
4 is almost inevitably associated
with recycling (Dugdale and Goering, 1967). If the sum of NO -
+
3 + NH4 is simply treated as "DIN," no
assumption need be made about NH +
4 as a new versus a recycled source of nitrogen.
The primary release of inorganic nitrogen during decomposition is as NH +
4 , that is, the reverse of
equation (28). Nitrogen flux, as discussed below, is associated with denitrification and uses NO -
3 .
Therefore, the process of nitrification is important:
NH + 2O HNO + H O
(29)
3
2
3
2
The important point to note with this reaction is that carbon and phosphorus are not directly involved
in the net reaction. Again this makes the point that the relationship between NO -
+
3 and NH4 may be
considered an "internal cycle" which need not be dealt with directly. The above reactions have been
in terms of the uncharged forms of DIN. Note, however, that net uptake of one mole of NO -
3
consumes a mole of H+ , while net uptake of a mole of NH +
4 consumes a mole of OH- (Equations 27,
28). These second-order corrections on TA can be readily made.
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A reaction which is of great importance to nitrogen cycling in benthic systems is denitrification
(Seitzinger, 1988). This respiration pathway is minor with respect to total carbon oxidation, but can be
of great significance with respect to nitrogen loss. Stoichiometrically this reaction can be represented
by an equation of the form (see also, Smith and Hollibaugh, 1989; Richards, 1965):
(CH O
+ 94 4
.

2
) (NH ) H PO
HNO
106
3 16
3
4
3

(30)
CO
106
+ 177 2
. H O + H PO + 55 2
. N
2
2
3
4
2
The important point to note in this reaction is that fixed inorganic nitrogen is consumed, but that the
DIC:DIP flux ratio is preserved. A further nitrogen related process in many systems is nitrogen
fixation. Although the biochemical process of nitrogen fixation is by no means the reverse of
Equation (30), it is stoichiometrically useful to think of it in such a manner. That is, nitrogen fixation is
the process by which N2 gas is directly incorporated into organic matter. Again, the stoichiometry is
preserved.
One final point needs to be made in this general treatment. Conversions back and forth between
particulate and dissolved organic matter are clearly of potential importance in chemical ecology. The
assumption is made for the sake of CNP stoichiometric budgeting that these conversions do not
involve phase changes between organic and inorganic carbon.
The above discussion has been presented in terms of the familiar Redfield Ratio, because it is
heuristically useful to work with "real numbers." In explicit situations where the reacting organic
matter has a composition different from the Redfield Ratio, the stoichiometry can be modified
accordingly. Atkinson and Smith (1983) report an example of such stoichiometry for benthic plants,
which differ markedly from Redfield C:N:P composition, and Smith et al. (1991) give derivations in
terms of algebraic expressions. While it is sometimes instructive to look at the full equations as laid
out above, stoichiometric analysis at the ecosystem level can simply deal directly with the individual,
local C:P and N:P ratios. These are discussed below.
Phosphorus-carbon stoichiometry
While the details of phosphorus chemistry are complex (Froelich, 1988), budgetary interpretations
may be regarded as somewhat simpler than that of carbon. Analytically there is only a need to
consider dissolved inorganic phosphorus, here denoted DIP, and dissolved organic phosphorus,
DOP, conversions to and from particulate phosphorus. In general the nonconservative flux of DOP is
small compared to the flux of DIP. Measurement and budgeting of DOP data are advocated when
available, but DIP is of primary interest to the budgetary analyses.
The nature of particulate phosphorus becomes problematical, because there may be both organic
matter and inorganic matter as part of the particulate phosphorus. To a great extent this
problematical area can be avoided in budgets by the analysis of total particulate phosphorus (PP) in
any particular compartment. In general, it appears that most conversion between dissolved and
particulate phosphorus in open seawater involves organic material. Thus, the ratio of C:P in the
particulate material (C:P)part, multiplied by the nonconservative flux of DIP, becomes an estimate of
organic matter (p-r):
DIC = DIP (C: P

(31)
o
)part
That is, DIP scaled by (C:P)part ratio becomes a measure of net ecosystem metabolism. A system
with DIP > 0 is interpreted to be producing DIC via net respiration (p-r < 0), while a system with
DIP < 0 is interpreted to be consuming DIC via net organic production (p-r > 0). This assumption is
most likely not to work in systems with an anaerobic water column, or with sediments anaerobic to
the sediment-water interface. Under either of these conditions, redox-mediated phosphorus
desorption from inorganic particles is likely to occur.
Conceptually, a carbon budget is what is likely to be of most immediate ecological or biogeochemical
use. However, if Equation (31) is accepted, then DIP, rather than DIC, may be the best record of
net system metabolism. It is suggested that DIP be the first priority for ecosystem nutrient
budgeting.
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If both DIP and DIC data are available, Equations (24) and (31) can be further developed. If the
system is a calcifying system, then:


TA
DIC = DIP :
+
+

(32)
t
(C P)
DIC
part
g
2
Equation (30) can be rearranged and solved for DICg:


TA
DIC = DIC - DIP :
-

(33)
g
t
(C P)part
2
If the system is interpreted not to be a calcifying system, then the TA term drops out of Equations
(32) and (33).
At this point, a useful check on Equation (30), and also on Equation (31), can be offered. It is
possible to calculate pCO2(w) from the TA and DIC data, or other variable pairs in the CO2 system. A
generally accepted equation to describe gas flux across the air-water interface is:
DIC = K (pCO - pCO

(34)
g
2(a )
2( w) )
where K is the exchange rate coefficient (in m d-1) and is the CO2 gas solubility in seawater as a
function of temperature and salinity. K varies primarily as a function of wind speed and tends to
range between about 0.5 and 5 m d-1. Hartman and Hammond (1985) provide a particularly useful
discussion of K. If everything else is known, it is possible to substitute DICg derived according to
Equation (33) into Equation (34) and see if a reasonable value for K is derived. K derived in this
fashion should, in general, be higher than would be predicted from the mean wind speed over the
study period, because of the non-linear response of gas exchange to wind speed. An example of
such calculations is found in Smith et al. (1991).
Nitrogen-phosphorus stoichiometry
Budgets of nitrogen fluxes include three forms of dissolved inorganic nitrogen (NO -
-
+
2 , NO3 , and NH4 )
and dissolved organic nitrogen (DON). Typically, NO -
-
3 and NO2 are measured together and reported
as "NO -
3 " which is usually the dominant form. For many purposes it is sufficient to group the inorganic
forms into DIN. A characteristic of the nitrogen system which makes it very different from either the
carbon or phosphorus system is the dominance of gaseous N2 over other forms of dissolved nitrogen
in seawater. Moreover, this N2 gas is neither measured (because there is so much of it, at analytically
nearly constant concentrations) nor in equilibrium with the other forms of nitrogen. Conversion from
N
-
2 gas to organic nitrogen is termed "nitrogen fixation," while conversion from NO3 to N2 is termed
"denitrification." Both of these processes require biotic mediation (primarily by various forms of
bacteria) and usually require locally anaerobic conditions to proceed in aqueous ecosystems. This
discussion of the biochemistry of the nitrogen system is necessarily greatly oversimplified, but more
detail is beyond the scope of these guidelines. The interested reader is referred to Webb (1981) for
more detail. The important point for the sake of budgetary analysis is that significant amounts of
nitrogen are transferred between so-called "fixed nitrogen" (DIN, DON, PN), which is measured, and
gaseous nitrogen (N2), which is not. The net effect of this transfer is here termed (nfix-denit) and is
often quantitatively significant to the nitrogen budget.
Assuming that the N:P ratio of particulate material in the system (N:P)part is know, the dissolved
nitrogen flux associated with production and decomposition of particulate material is the dissolved
phosphorus flux (P = DIP + DOP) multiplied by (N:P)part. It follows, that (nfix - denit) is the
difference between the measured dissolved nitrogen flux (N = NO3 + NH4 + DON) and that
expected from production and decomposition of organic matter:
(nfix - denit)= N - P (N:P)
(35)
part
DON, NH +
-
4 , and DOP tend to be small relative to NO3 . Hence, solution of Equation (33) without
these terms is generally likely to introduce a rather small error in the estimation of (nfix-denit).
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Summary of stoichiometric analyses of nonconservative CNP fluxes
In general it is useful to derive nonconservative phosphorus fluxes first. If DIP and (C:P)part are both
known, then it is feasible to use Equation (31) as an estimate of net system carbon metabolism (p-r,
or DICo). If phosphorus data are available, it is likely that nitrogen data are available as well. With
data on (N:P)part, estimates can be made of (nfix-denit) from Equation (35). Adequate data for DIC
and TA are less likely to be available. However, if they are available, then Equation (33) can be
solved to derive an estimate of DICg. If the system is a noncalcifying system, then TA is an
estimate of DIC release during sulphate reduction; if the system is a calcifying system, then TA/2 is
an estimate of DIC uptake by CaCO3 precipitation.
5.5 Preparation for the Case-Study Calculations
Examination of the case studies presented in the next sub-section, along with the cautionary lesson
from the Merbok mangrove system (Section 4), provides insight into the application of this sort of
budgetary modelling. The technique is widely, but by no means universally, applicable. First and
foremost there must be some method to estimate the residence time of the water within the system
of interest. In many instances a straightforward way of establishing water residence time is by means
of combined water and salt budgets. Establishing such budgets, however, may not always be
practical. In that case, the alternative approach is by means of a numerical model of water exchange.
Detailed procedures for the establishment of such a numerical circulation model is beyond the scope
of this report, although some background information has been provided. For the remainder of this
discussion, it is assumed that some method to estimate water residence time in the system of interest
is available.
Given an estimate of water residence time, there must be a net biogeochemical signal relative to
material flux due to physical transport. Ability to extract a budgetary signal for any particular reactive
material Y is determined by the absolute value of the ratio of net biogeochemical change of Y, in the
earlier notation, the reaction rate, Y, multiplied by time, to the sum of the physical influxes, or
effluxes, of Y, for example, VinYin; that is, by the ratio Ytime/VinYin. If this "reaction ratio" is >
1, a change is readily measured by such budgets. However, the net change may have occurred
rapidly initially, with little subsequent change. Resolution of the rate of change and location of change
within the system has been lost. As the ratio falls below about 0.1, Y will become progressively less
readily determined. The critical reaction ratio for determining Y cannot be more rigorously defined,
because it will depend upon the precision with which Y can be measured and on various time scales
of variation of both Y and VinYin.
The ecosystem budgetary approach may be viewed as a large-scale incubation. Therefore an
experimental analogue to this situation is an incubation in which the starting water mass defines
VinYin and the difference in water composition over the incubation time defines Y, the reaction rate.
A short incubation time defines the reaction rate under more or less constant conditions, but the
incubation time must be sufficiently long to measure this quantity precisely. The experimental
solution to the problem of a small reaction ratio is to increase the incubation time--with potential
"chamber effects." If this ratio is too low in a natural system to be readily determined, again Y must
be increased relative to VinYin. One obvious solution to the problem in many instances is to increase
the size of the system being budgeted. If the volume flow rate through the enlarged system remains
constant, VinYin will remain constant. With more reaction time, Ytime is likely to increase, thus
increasing the ratio. Note that this quantity will not necessarily increase as the time increases; Y,
that is, the net reaction rate, may decrease over that greater time. The choice facing the ecologist or
biogeochemist determining any such budget is between raising the ratio, hence improving the quality
of its resolution, and losing both spatial and temporal resolution of Y.
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With the above background in mind, what is actually necessary to apply the budgetary techniques
laid out here? Basic requirements can be summarised under five categories: system definition,
freshwater inputs, salinity of the water, nutrient concentrations and other nonconservative
components in water and other relevant information. These requirements are summarised in Text
Box 4.
1. System definition: The boundaries of the system should be clearly defined and based on
physiographic properties or water composition. The area of the system, divided into subtidal and
intertidal areas, in the case of systems with extensive emergent vegetation, and the water volume
or average depth are required. The area of the watershed may be required if data on freshwater
flow, described below, are not well known.

2. Freshwater: Estimates of total stream flow and, if volumetrically important, groundwater flow
and other freshwater discharges into the system are required to establish the water budget. Lacking
direct flow data, information on precipitation and evapotranspiration in the watershed may suffice
as a first approximation.

3. Salinity: Salinity of the system itself and of adjacent systems is required. Inflow water from
land can probably be assumed to have a salinity of 0 p.s.u. For a first approximation the data
should be summarised into arithmetic means (either long term or, if available, into shorter time
increments) for the system(s) of interest and the adjacent water bodies.

4. Nutrients and other nonconservative components: In order of decreasing importance, data
are required for the following variables: dissolved inorganic phosphorus, nitrate, ammonium,
dissolved organic nitrogen, dissolved organic phosphorus, total alkalinity, pH (or other secondary
measurement in the aqueous CO2 system), and dissolved organic carbon. These data should be
handled the same as salinity, with the exception that the nutrient concentrations in land water
sources should not be ignored.

It should be emphasised that item numbers 1-3, above are required to establish a water
and salt budget for estimating water exchange. Item 4 is required to estimate aspects of net
system metabolism, with the relative importance of the variables being the order listed.

5. Other: Data on C:N:P ratios of suspended materials, major primary producers, sediments, and
inflowing materials are extremely useful. It is useful to have a general description of major biotic
components and the proportion of the system covered by those components. Other ancillary
information on component metabolism and other aspects of the system, such as sedimentation
rate, will assist in interpretation of the budgets.
Text Box 4. Summary of requirements for budget modelling analysis.
System definition
It is essential to have a clear image of the system to be budgeted. What are its spatial boundaries,
both in terms of its landward boundaries and the "open" or oceanic boundary? With respect to the
oceanic boundary, and if there is more than one region of exchange between the system and
adjacent ocean, what are the relative cross sectional areas at the boundaries? These are likely clues
as to relative water exchange volumes. The area of the system and the average water depth should
be known. If the system is divided into obvious sub-basins, distinct water depths, or spatially discrete
habitat types, it may be useful, although by no means required, to have some knowledge of area and
dept within subsystems of the overall system. That information may or may not be helpful for
budgeting. High precision on this information is not required. Adequate information can usually be
extracted from hydrographic charts.
All of the information to follow can be profitably approached in either of two fashions. If available
data are very restrictive, then reliable mean values over some period of time, the longer the better,
can be used to establish static or steady state budgets. If the available system has a large amount of
data, then it becomes useful to use the data to establish some sort of averaged trend. Minimal
smoothing is recommended. For example, in one result presented below in some detail, data are
reported averaged into two-month blocks.
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Freshwater Input
Given this general information on the system, the next point is to establish a water budget.
Precipitation is monitored in many areas of the world. Much of this information ends up in various
national or regional governmental agency files. Some may be maintained by local agencies or even
private groups. Those data, for a period as long prior to the study time as available, are invaluable. In
many instances, those same files may include either pan evaporation data or wind speed and relative
humidity data from which evaporation can be calculated by long established techniques (see for
example Sverdrup et al., 1942). Lacking that information, even regional seasonal evaporation maps
can be used. Other freshwater sources of possible importance are likely to be gauged streams, if the
watershed area is as large as, or larger than, the system area. Such data tend to be maintained by
national government agencies. If only part of the watershed area draining into the system of interest
is gauged, one may use gauged to ungauged watershed area ratios, perhaps including estimates of
relative precipitation in the two areas, to extrapolate the gauged data to a system average. Lacking
runoff data, consultation with local terrestrial ecologists and hydrologists may lead to estimates of
vegetation evapotraspiration rates which can be used to approximate runoff from precipitation. Data
on groundwater flow may also be available. In terrestrial systems with high precipitation and highly
permeable soil, this freshwater source may be important. More often it appears to be a second order
correction to the water budget. There may be other freshwater sources such as sewage. Again these
are not likely to be quantitatively significant to the water budget. Examination of equations presented
in the previous sections makes it obvious that the main role of freshwater input and evaporative
water losses is likely to derive information about the system water budget.
The data to follow are less likely to be available in general government documents. They may be in
technical papers, either formal publications or "grey literature" such as environmental impact reports.
While assembling any such data for budgetary analysis, some effort should be made to evaluate the
quality of the data (precision, accuracy, etc.). Of course these are also the kinds of data which should
be collected during any serious budgetary study.
Salinity of water masses
Salinity data should next be examined to see if a salt budget, and thus an estimate of water
exchange rate, can be established. In general it is safe to assume that all of the freshwater sources
described above, as well as the evaporative loss term, have a salinity of 0 p.s.u. Of course if salinity
data are available for any of these sources, they can be used in the calculations. Salinity in the
system of interest and in the adjacent, oceanic system(s) are required, and there must be a salinity
difference between the system and the ocean. If there is a vertical salinity gradient, those data are
useful. It is recommended that the data in such stratified systems be divided into two "boxes"
representing surface and deep waters with an estimate of the thickness of each box. Salinity
differences of less than about 0.3 p.s.u., vertically and between horizontally adjacent boxes, are likely
to be insufficient for establishing quantitatively useful salt budgets; greater differences will, of course,
lead to more robust budgetary calculations.
Nutrient concentrations and other nonconservative components
Having arrived at the data for the water and salt budgets, the next requirement is for information on
nutrients. As an absolute minimum, data on DIP and NO -
+
3 are required. NH4 , DOP and DON data
are also highly recommended. Data on the aqueous CO2 system may also be of great use (with pH
and total alkalinity being the most likely data to be available). DOC data are useful, although rarely
available. Other materials, such as Si, can also be readily budgeted if the data are available. It
should be stressed that for all of these variables, the best available accuracy and especially precision
are needed, because one is often looking for relatively small differences in water composition
between adjacent water masses. Clean techniques of collecting, preserving and analysing the
nutrients should be employed and high-precision measurements of the DIC-related variables are
required if the data are to be useful. None of this is difficult, even under rather rudimentary field and
laboratory conditions, but it does require attention to detail.
It should not be assumed that most freshwater sources delivering water to the system lack nutrients,
even though this assumption is generally reasonable for salt. In many cases the levels are likely to be
very high, especially in stream water, groundwater and any sewage sources. In some cases, sewage
data may be available as mass emission rates, either based on direct data of per capita discharge
estimates, rather than as concentrations in a waste stream of known volume.
- 42 -

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Other relevant information
It is highly desirable to have data on the suspended load C:N:P composition ratio. Although data on
the concentrations of these suspended materials are not required for budgeting purposes, these data
clearly are useful. For both suspended load and sediment composition, a serious research
programme should measure these quantities but reasonable guesses can probably be made for
preliminary budgetary calculations.
Finally, other ancillary information is likely to be useful for amplifying from the system-level budgets
to the performance of components in the system: for example, primary production of phytoplankton
or benthic plants; respiration rates of components in the system, sedimentation rate, etc. If the
overall budgetary characteristics of the system are known and specific budgetary components are
known, then other components may be considered by difference. Estimates of the number of humans
in the watershed, the distributions of those humans, and major aspects of terrestrial vegetation, land
use, and other activities in the watershed will be useful in interpreting the budgets.
5.6 Case Studies
Eight case studies have been chosen to illustrate the use of the general budgetary approach outlined
above. Each is chosen to illustrate specific aspects of the use of budgets.
Bahia San Quintín, Mexico, introduces the use of this approach as an exploratory exercise, in a
coastal lagoon for which there are only very limited data.

Klong Lad Khao Khao, Thailand, is a mangrove estuary for which an extensive general data set
on salinity, nitrogen, and phosphorus is available. This system is used to present, in a step-by-
step manner, an example of the budgetary calculations.

Tomales Bay, California, United States is used to present non-steady state water, salt, and
dissolved inorganic phosphorus budgets; then to discuss the stoichiometric approach in detail; and
finally to demonstrate how one can compare total system metabolism with major metabolic
components.

Gulf of Bothnia, at the head of the Baltic Sea, illustrates a system in which the assumption of a
constant water volume is not appropriate and in which temporal variation of water composition
should also be considered.

The Baltic-Kattegat System, illustrates steady-state analysis for a large estuarine sea which is
divided into a horizontal series of basins with two-layer vertical stratification.

Spencer Gulf, Australia, examines water, salt, and CNP budgets in a system dominated by
calcification.

Tokyo Bay, Japan, illustrates a water exchange budget for Tokyo Bay, established on the basis
of a direct three-dimensional numerical model, rather than a salt budget to establish exchange.

East China Sea illustrates the numerical analysis of two-dimensional pattern of water flow in a
stratified system.
As a cautionary note, the Merbok mangrove system of Malaysia, discussed in Section 4, serves as
an example where various techniques, including budgets based on measurement of tidally induced
current flow, have been tried and have generally not worked well to describe nonconservative fluxes
of carbon, nitrogen, and phosphorus.
It should be further noted that in these guidelines there is an attempt to be internally consistent in the
application of the stoichiometric budgeting. One result is that some of the calculated rates differ
slightly from previously published estimates. This brings up the point that it is important for the sake
of detailed comparison that either consistent rules be applied, or that changes in the rules be clearly
spelled out.
- 43 -

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5.6.1 Bahia San Quintín: Exploratory steady-state NP budgets in a coastal lagoon
Bahia San Quintín (area = 42 x 106 m2, volume = 90 x 106 m3) (Figure 8) is a coastal lagoon in
Mexico for which only a limited amount of salinity, nutrient, and weather data are available. This
hypersaline system is presented as the first case study to show what insights can be gained by using
limited data to generate biogeochemical budgets. In Figure 8, it is obvious that the Bay consists of
two distinct sub-basins. Although more detailed studies will eventually develop calculations for the
sub-basins individually, the present data set is not considered adequate for that exercise. Published
weather maps demonstrate that this system is net evaporative most of the time. Precipitation data
are available from a weather station slightly south of the Bay, and there is no significant surface
runoff except during some major storm events. Groundwater in the watershed has been intensively
studied, because it is the only freshwater source supporting extensive agriculture in the watershed.
Although the groundwater is so heavily exploited that flow is reduced to near 0, estimates of
groundwater input have been included for illustrative purposes.
Figure 8. Location of Bahia San Quintin, Mexico.
- 44 -

---

Figure 9 illustrates the steady state water and salt budgets. Typically it is most useful to consider
these budgets together. Precipitation is seasonal but averages about 170 mm yr-1. Summed over the
bay area, this is approximately 20,000 m3 d-1 (VP). Groundwater inflow (VG) totals only about 1,000
m3 d-1. Evaporation is by far the major term in the freshwater budget, averaging about 1,100 mm yr-1.
Over the bay area, this is equivalent to evaporative removal (VE) of approximately 130,000 m3 d-1.
Thus there is a net freshwater loss of 109,000 m3 d-1. According to Equation (2), there is seawater
inflow into the bay to balance this loss; VR is + 109,000 m3 d-1. The hydraulic residence time of the
system is given by the system volume divided by this residual flow: about 800 days.
V P = 20
V E = 130
V Q = 0
V G = 1
V O = 0
Bahia
V
San Quintín
R = + 109
W a ter Budget (fluxes in 103 m 3 d-1)
V R SR = +3,679
S G 0 psu;
Bahia
V GSG 0.
San Quintín
S 2 = 33.0 psu
S 1 = 34.5 psu
V X(S2 - S1) = -3679;
V X = 2,453.
S a lt Budget (fluxes in 103 kg d -1)
Figure 9. Steady-state water and salt budgets for Bahia San Quintín. Quantities estimated from
data independent of the budgetary calculations are shown in light typeface; quantities
calculated within the budget are shown in bold typeface.
The seawater inflow delivers salt to the system advectively, and the elevated salinity of the bay
results in outward mixing of salt. The salinity of the inflowing seawater is taken to be the average of
the bay and ocean salinity (that is, 33.75 p.s.u.), so the advective salt delivery is about 3.7 x 106 kg
d-1. VX to remove this excess salt must be about 2.5 x 106 m3 d-1. Thus the total exchange time for
the system is the system volume divided by the sum of VR + VX: about 35 days.
- 45 -

---

Preliminary versions of the dissolved inorganic phosphorus and dissolved inorganic nitrogen budgets
are presented in Table 2 and Figure 10. There are no data for dissolved organic nutrients, and the
nitrogen budget does not include NH +
4 (which is reported to be low and variable for this system).
However, estimates derived from other systems (below) are used to conclude that the DIP and NO -
3
fluxes probably dominate. Nonconservative processes in the bay produce about 3,700 mol d-1 of DIP
(DIP) and 14,000 mol d-1 of DIN (DIN).
Table 2. Nonconservative dissolved inorganic P and N fluxes in Bahia San Quintin.
PROCESS
RATE (mmol m-2 d-1)
area
42 km2
DIP
+0.09
DIN
+0.33
(nfix - denit) (1)
-1.4 to -2.6
(p-r)(2)
-10 to -50
1) (N:P)part assumed to be between 16 (plankton) and 30 (seagrass).
2) (C:P)part assumed to be between 106 (plankton) and 550 (seagrass).
D I P P 0 µ M ;
V P D I P P 0.
V R D I P R = + 2 5 1
D I P
B a h i a
G 5 µ M ;
V
S a n Q u i n t í n
G D I P G 5.
D I P 2 = 1 . 5 µ M
D I P 1 = 3 . 1 µ M
V X( D I P 2 - D I P 1) = -3,925
D I P = + 3 , 6 6 9
D i s s o l v e d I n o r g a n i c P B u d g e t ( f l u x e s i n m o l d -1)
( n f i x - d e n i t ) = - 4 4 , 7 2 3 t o
D I NP 0 µ M ;
- 9 6 , 0 8 9
V P D I NP 0.
V R D I NR = + 3 , 6 7 9
B a
B h
a i
h a
i
D I NG 5 0 µ M ;
S a
S n
a
n Q
u
Q i
u n
i t
n ít n
D I N
í
V
2 = 1 . 1 µ M
G D I N G 50.
D I N 1 = 7 . 0 µ M
V X ( D I N 2 - D I N 1) = -14,473
D I N obs = + 1 3 , 9 8 2 ;
D I N exp = + 5 8 , 7 0 4 t o + 1 1 0 , 0 7 0
D i s s o l v e d I n o r g a n i c N B u d g e t (flu x e s in m o l d -1)
Figure 10. Steady-state DIP and DIN budgets for Bahia San Quintín. Quantities estimated from data
independent of the budgetary calculations are shown in light typeface; quantities
calculated within the budget are shown in bold typeface.
- 46 -

---

Independent estimates suggest that organic metabolism in this system is dominated by plankton and
seagrass. Moreover, because terrigenous inputs to this system are small, inward drift of either
plankton or benthic detritus is likely to dominate the net metabolism. The ranges of values for
DINexp from particle decomposition and (nfix - denit) are based on a range for N:Ppart between
plankton (N:Ppart 16:1) and seagrass (N:Ppart 30:1), as plausible sources of particulate material to
be accounting for decomposition. As a result DIN is expected to range from 59,000 to 110,000 mol
d-1. Because the observed DIN is only about 14,000, the remainder of the expected DIN is
assumed to be lost via (nfix-denit) of about 45,000 to 98,000 mol d-1. Over the bay area, the average
rates are between -1.1 to -2.3 mmol m-2 d-1. This is well within the range of denitrification rates
reported by Seitzinger (1988) for coastal marine systems.
Plankton and seagrass have C:P ratios of about 106:1 and 550:1, respectively. The value for DIP is
equivalent to DIP release of about 0.08 mmol m-2 d-1. If plankton dominate input of organic matter
from outside the system, then (p-r) is about 9 mmol C m-2 d-1; if seagrass dominates, (p-r) is about 44
mmol Cm-2 d-1. Limited data on primary production in this system suggest that p is near 160 mmol
carbon m-2 d-1. r can be estimated to be between about 170 and 200 mmol m-2 d-1. If the
stoichiometric assumptions are valid, this system is net heterotrophic (r > p) by about 5 to 20%.
Thus, from very limited data on the freshwater budget and the salinity and nutrient composition of
this system, it has been possible to construct a preliminary estimate of how fast the system
processes dissolved nutrients.
5.6.2 Klong Lad Khao Khao: Exploratory steady-state NP budgets in a mangrove estuary
The following case study was developed during the SARCS/WOTRO/LOICZ Workshop on
Biogeochemical Modelling held in Penang, Malaysia (4-8 December 1995) to try out an earlier draft
of these guidelines (LOICZ, 1995c). Data from 11 field sites in Southeast Asia were examined
according to the draft guidelines, and it was felt that having one of the participants in the workshop
(Dr. Gullaya Wattayakorn, Chulalongkorn University, Bangkok) work through the procedures in detail
would further clarify the use of these budgetary methods. Therefore this section is presented with
only limited modification of Dr. Wattayakorn's working notes, modified to correspond to the general
outline presented in Text Box 4.
System definition: Figure 11 is a map of the area. The mangrove + waterway area occupies
approximately 6 x 106 m2; the waterway itself occupies about 10% of this area (6 x 105 m2). Mean
water depth in the waterway is about 6 m, while the average depth in the mangroves themselves is
about 1 m. Thus, the average depth of the entire mangrove/estuary system is approximately 1.5 m.
The watershed is estimated to be about 10 times the mangrove/waterway area, that is about
60 x 106 m2.
Freshwater: Stream flow is not well monitored, but precipitation is estimated to be about 2,600 mm
yr-1, or about 7 mm d-1. Evapotranspiration from similar areas in Queensland, Australia, is estimated
to be about 5 mm d-1. Data on groundwater flow or sewage discharge directly into the mangroves is
not available.
Salinity: Salinity of precipitation and stream inflow is assumed to be 0; average estuarine salinity is
about 29 p.s.u.; coastal seawater averages about 33 p.s.u.
Nutrients and other nonconservative components: Data are available for DIP, DOP, NO3, NH4,
and DON in this system (Table 3).
Other: Mangrove litter is estimated to have a C:N:P molar ratio of about 1,300:11:1. It is assumed
that this is also the approximate ratio of C:N:P in sediments delivered from the watershed. Plankton
seem unlikely to be a major component because of high water turbidity in the open waterway.
Mangrove primary production is typically about 8-10 tons ha-1 yr-1 of leaf litter and an equivalent
amount of woody material (a total of 18 is used here). If this material is 40% carbon, it is equivalent
to approximately 160 mmol C m-2 d-1.
From these data it is possible to go through the sequence of budgetary analysis presented in Text
Box 4.
- 47 -

---

Table 3. Average nutrient concentrations (µmol) for components of the Klong Lad Khao Khao
system.
Nutrient
Seawater (Y2)
System (Y1)
Freshwater (YQ)
DIP
0.3
1.5
0.4
DOP
0.3
0.6
0.7
NO3
0.2
0.4
2.6
NH4
0.9
1.5
1.7
DON
97.0
170.0
220.0
Figure 11. Location of Klong Lad Khao Khao, Thailand.
- 48 -

---

Water budget: Figure 12 illustrates the water budget for Klong Lad Khao Khao. Freshwater flow (VQ)
is estimated as P - E (2 mm d-1) multiplied by the watershed area: 120,000 m3 d-1. Direct precipitation
(VP) and evaporation (VE) are estimated as 42,000 and 30,000 m3 d-1, respectively, based on the
mangrove + waterway area. Other components of inflow (VG, VO) are assumed small. It is also
assumed that, averaged over a tidal cycle, system volume remains constant. From Equation (2):
dV
V =
1 - V -V - V - V + V =
R
dt
Q
P
G
O
E
-
,
-
,
- - +
,
= -
,
m3d -1
0 120 000 42 000 0 0 30 000
132 000
That is, VR is negative, indicating residual outflow.
Salt budget: Figure 12 also summarises the salt budget. Residual outflow water has a salinity which
is the average of estuary and ocean salinity, that is, 31 p.s.u., so salt export is VRSR4.1 x 106 kg d-1.
Exchange of estuary water with ocean water must replace this salt export. The simplified version of
Equation (8) (with V1dS1/dt = 0) becomes:
1
1
V =
V S =
-132 000
,
31 102
.
106 3 -1
R
R
(
)
x
m d
X
(S - S )
(29 - 33)
1
2
VP = 42
VE = 30
Klong Lad Khao
VQ = 120;
V
V
R = - 132
Khao
G, VO ~ small.
Water Budget (fluxes in 103 m3 d-1)
VRSR = - 4,092
SQ 0 psu;
VGSG 0.
S2 = 33.0 psu
S1 = 29 psu
VX(S2 - S1) = + 4,092;
VX = 1,023.
Salt Budget (fluxes in 103 kg d-1)
Figure 12. Steady-state water and salt budgets for Klong Lad Khao Khao. Quantities estimated from
data independent of the budgetary calculations are shown in light typeface; quantities
calculated within the budget are shown in bold typeface.
- 49 -

---

Budgets of nonconservative materials: Figure 13 summarises the dissolved P and N budgets for
this system. NO -
+
3 and NH4 are lumped into DIN. First consider DIP. Stream inflow delivers 48 mol
DIP d-1 (VQDIPQ); residual outflow removes about 119 mol d-1 (VRDIPR, where DIPR is the average
of the ocean and estuary DIP); mixing removes an additional 1,228 mol d-1 (VX[DIP2 - DIP1]). In order
to support this net export, there must be a positive value for DIP. Solving Equation (20) at constant
volume and DIP concentration:

dY
dV
DIP = V
+ Y
- V Y + V Y
dt
dt
in in
out out
= + -
+
+
=
mol d -
0 0 48 119 1
1
1
,228
,299
The other components are calculated similarly: DOP = + 282 mol d-1; DIN = +500 mol d-1, DON =
+65,901 mol d-1.
DOPP 0 µM;
DIPP 0 µM;
VPDOPP 0.
VPDIPP 0.
VRDIPR = - 119
DIPQ = 0.4µM
DIP1
DIP2 = 0.3 µM
1.5 µM
VQDIPQ = 48
VX(DIP2 - DIP1) = -1,228
VRDOPR = - 59
DOP1
VQDOPQ = 84
DOP
0.6 µM
2 = 0.3 µM
.
DOPQ = 0.7 µM
VX(DOP2 - DOP1)= -307
DIP = + 1,299
DOP = + 282
Dissolved Phosphorous Budget (fluxes in mol d-1)
(nfix - denit) = + 49,010
DINP 0 µM;
DONP 0 µM;
VPDINP 0.
VPDONP 0.
VRDINR = - 198
DIN
DIN
Q = 4.3 µM
1
DIN2 = 1.1 µM
1.9 µM
VQDINQ = 516
VX(DIN2 - DIN1) = - 818
VQDONQ = 26,400
VRDONR = - 17,622
DON1
170 µM
DON2 = 97 µM
DONQ = 220 µM
VX(DON2 - DON1) = -74,679
DONobs = + 65,901
DINobs = + 500
(DIN + DON)exp = + 17,391
Dissolved Nitrogen Budget (fluxes in mol d-1)
Figure 13. Steady-state dissolved phosphorus and nitrogen budgets for Klong Lad Khao Khao.
Quantities estimated from data independent of the budgetary calculations are shown in
light typeface; quantities calculated within the budget are shown in bold typeface.
- 50 -

---

Stoichiometric relationships among nonconservative budgets: At the outset, several problems
might occur here. There is the potential of either groundwater contamination with nutrients or direct
discharge of sewage effluent into the system. Secondly, and perhaps more importantly, sediments
are very organic rich and largely anaerobic. As a result, dissolved nutrients, especially phosphorus,
may be released either from the organic matter itself or from inorganically sorbed materials on the
mineral surfaces.
Initially, decomposition of mangrove litter is considered to be the most obvious source of CNP
release. Upon reflection, that is not the case. That material was produced in the system, so there was
initial uptake of nutrients into the litter. While there could be lags between uptake and release, and
those lags might show up in a time series analysis, the assumption behind the steady state analysis is
that average conditions in a system are being described with unchanging composition. Nevertheless
the incoming terrigenous material is assumed to have a composition near that of the mangrove litter,
a C:N:P ratio of 1,300:11:1.
First consider the N expected from the decomposition of organic matter into DIP + DOP. The
expected value from particle decomposition (nfix - denit) based on a N:Ppart ratio of terrigenous
material of 11:1, is about N = 11(DIP + DOP) = 11(1,299+282) = 17,391 mol d-1. The observed
N flux, overwhelmingly dominated by DON, is 66,401 mol d-1. From Equation (33) it can be
calculated that:
(nifx - denit) = N - P (N: P)
= (
+ ,901) - ( ,299 +
)
=
,
mol d -


500 65
1
282 11 49 010
1

part
The solution to this equation is positive, so it represents apparent net nitrogen fixation. If this rate
were occurring throughout the entire mangrove + waterway area, it would yield a net nitrogen fixation
rate of about 8 mmol m-2 d-1. This rate seems too high in comparison with limited data for mangrove
nitrogen fixation rates and more extensive data for other rapidly fixing environments (typically 2-5
mmol m-2 d-1, from summary data in Capone, 1983). Note that even if DIP is abiotic, rather than
metabolic, it would have relatively minor effect on this calculation. One possible explanation for this
high DON, which should be closely examined in this system, is substantial DON input in
groundwater or sewage.
Next consider DIP as an estimate of (p - r) in the estuary, assuming that the decomposing material
is dominated by terrigenous material with a C:P ratio similar to mangrove detritus (that is, 1,100:1).
Applying Equation (31):
DIC = DIP C P
= 1 299 1100 1 4x106 mol d -
( : )
,
,
.
1
o
part
Dividing by mangrove + waterway area, a rate of about 230 mmol m-2 d-1 can be calculated. Because
this rate is almost 50% higher than the net primary production of the mangroves, it is probably not a
correct representation of (p - r) in this system. This would require a very large import of organic
matter from outside the system. Plausible alternative explanations include desorption of phosphorus
from sedimentary particles, a large input of P in groundwater or sewage, or the possibility that
terrigenous material entering the system has a substantially lower C:P ratio than assumed here.
The budgetary calculations for this system appear algebraically robust. Shifts in the compositions of
the various boxes or in the freshwater flow would need to be large in order to alter the budgetary
calculations significantly. However, the calculated nonconservative fluxes yield stoichiometric
implications about both (p - r) and (nfix - denit) which appear somewhat too high. There are at least
two plausible alternative explanations for this discrepancy. Either there are additional inputs of
nutrients, at a minimum DIP and DON, which are not being included in the budgets, or the organic-
rich sediments exhibit substantial releases of these materials which are not directly accounted for by
these metabolic pathways. In either case, the budgets point to directions which should be
investigated further in order to understand the processes accounting for CNP fluxes in this system.

- 51 -

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5.6.3 Tomales Bay: Time-varying CNP fluxes in a well mixed estuary
Tomales Bay, California (Figure 14), has been the site of intensive studies of total ecosystem
metabolism (Hollibaugh et al., 1988; Smith et al., 1991; etc.). This budget for a temperate climate
estuary illustrates time-varying, non steady-state, calculations. Only the inner two thirds of the bay
area is included in this budget, because the outer third has water composition similar to that of the
coastal ocean.
Non-steady state water, salt, DIP, DOP, NO -
+
3 , NH4 , DON, TA, DIC, and DOC budgets were
established for the inner portion of this bay at two-month intervals between 1987 and 1994. Some of
these data are illustrated for the period up to mid 1991. Specifically, the two-month time steps of
calculated water exchange flux (VX) and DIP, are presented in order to illustrate the calculations in a
system for which time series data are available. Secondly, the average nonconservative fluxes for
each of the above materials is used over the period from 1987 to 1991 in order to illustrate the
stoichiometric calculations of the metabolically related processes discussed in Sections 5.4.6. Finally,
ancillary data on component metabolism is used to further elaborate the total system metabolism and
to show how the budgets can be used in conjunction with such additional data.
Figure 14. Location of Tomales Bay, California, United States.
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The inner bay (area = 16 x 106 m2; volume = 48 x 106 m3) is treated as a single well-mixed system
receiving inputs from stream runoff and precipitation, losing water to evaporation, exchanging water
with the outer bay, and having internal reactions which vary over time. Tables 4-6 summarise the
data used here to describe the freshwater fluxes and water composition over time. Precipitation and
evaporation rate (P, E, in mm d-1; Table 4) are converted to volume fluxes (VP, VE; Table 5) by
multiplying the area of the Bay. Note that time-varying data for ocean, bay, and stream water
composition are available. Because precipitation was not sampled on a regular basis, a constant
value of 0.20 is used for DIP flux due to precipitation. It is obvious from inspection of the data that
this assumption does not seriously affect the budgets. This is not always true; for example, in some
systems precipitation is a significant source of nitrogen delivery. From separate studies it has been
determined that groundwater is quantitatively insignificant to these budgets, and that there are no
other significant water or nutrient sources such as sewage discharge.
Table 4. Stream flow (VQ) , precipitation (P), and evaporation (E) data for Tomales Bay, July 1987-
July 1991, at two-month increments.
Year
VQ (103 m3 d-1)
P (mm d-1)
E (mm d-1)
87.500
14
0.01
3.11
87.667
5
0.00
3.10
87.833
6
0.55
1.81
88.000
223
5.92
0.57
88.167
461
3.89
0.41
88.333
44
1.42
2.57
88.500
17
0.85
3.52
88.667
10
0.01
3.76
88.833
10
0.25
2.16
89.000
95
5.87
0.61
89.167
87
2.19
0.44
89.333
563
6.66
1.26
89.500
24
0.14
3.00
89.667
11
0.00
3.77
89.833
24
2.19
1.59
90.000
52
1.33
0.60
90.167
232
4.97
0.53
90.333
75
1.30
1.53
90.500
62
3.15
2.95
90.667
13
0.00
3.23
90.833
11
0.10
1.20
91.000
41
1.40
0.42
91.167
83
3.07
0.36
91.333
518
9.74
0.90
91.500
25
0.17
2.71
Table 5 and Figure 15 present the water volume exchange rates (VX) over time as calculated from
the salt and water budgets according to Equation (8). With real world data, some adjustments may be
needed in order to generate realistic results. It was found that, for months with (S1-S2) < 0.3 p.s.u.,
calculated exchange rates were highly variable and often < 0 which is a physical impossibility.
Salinity in this system alternates between slightly above oceanic during the summer to below oceanic
during the winter. Hence, there were two times in the year when the difference between the bay and
the ocean is close to 0 which yields unstable estimates of Vx. For these times, when (S1-S2) was
below this cut-off, the value for Vx was set to the value from the preceding time step. Two time steps
adjacent to those adjusted by this procedure gave negative values for Vx. These adjacent values
were set equal to the preceding time step. It should be noted that this particular problem is less likely
to arise in systems which are consistently above or consistently below the ocean in their salinities.
- 53 -

---

Table 5. Water circulation, residual flow and water exchange rates as calculated from the water
and salt budgets for Tomales Bay, July 1987-July 1991. The subscript "Q" indicates
streams; "P" is precipitation; "E" is evaporation, "1" is the Bay, "2" is the ocean. As
discussed in the text, two versions of the daily exchange volume are provided: the
uncorrected exchange volume (VX(unc)), and values corrected (VX(cor)) to the previous
two-month interval for those periods when the difference between bay and ocean salinity
was less than 0.3 p.s.u.
Year
#days
VQ
VP
VE
S2
S1
SQ
SP
VX(unc)
VX(cor)
p.s.u.
p.s.u.
p.s.u.
p.s.u.
m3 d-1
m3 d-1
87.472
14
0
50
33.83
34.03
0.00
0.00
87.650
65
5
0
50
33.62
34.68
0.00
0.00
997
997
87.850
73
6
9
29
33.27
33.74
0.00
0.00
2,313
2,313
88.005
56
223
95
9
32.19
28.35
0.00
0.00
1,233
1,233
88.190
68
461
62
7
33.11
31.63
0.00
0.00
12,850
2,850
88.368
65
44
23
41
33.67
32.81
0.00
0.00
2,018
2,018
88.536
62
17
14
56
33.99
34.74
0.00
0.00
-847
2,018
88.724
68
10
0
60
33.68
34.67
0.00
0.00
1,776
1,776
88.839
42
10
4
35
33.46
34.25
0.00
0.00
1,508
1,508
89.016
65
95
94
10
32.71
30.70
0.00
0.00
1,519
1,519
89.175
58
87
35
7
32.13
29.77
0.00
0.00
1,182
1,182
89.348
63
563
107
20
32.87
31.51
0.00
0.00
16,360
6,360
89.521
63
24
2
48
33.95
33.96
0.00
0.00
-111,966
16,360*
89.685
60
11
0
60
33.71
34.62
0.00
0.00
1,259
1,259
89.852
61
24
35
25
33.46
33.17
0.00
0.00
-29
1,259*
90.016
60
52
21
10
33.31
32.08
0.00
0.00
966
966
90.173
57
232
80
8
32.33
29.96
0.00
0.00
3,242
3,242
90.355
66
75
21
24
33.68
32.89
0.00
0.00
5,731
5,731
90.567
77
62
50
47
33.63
33.65
0.00
0.00
-133,018
5,731*
90.671
38
13
0
52
33.59
34.19
0.00
0.00
1,066
1,066
90.839
61
11
2
19
33.40
34.13
0.00
0.00
342
342
90.996
57
41
22
7
33.33
32.89
0.00
0.00
1,841
1,841
91.159
60
83
49
6
30.91
27.47
0.00
0.00
191
1,841
91.333
63
518
156
14
32.80
30.69
0.00
0.00
11,092
11,092
91.528
71
25
3
43
33.86
34.10
0.00
0.00
-7,482
11,092*
* |Ssys-Socn| < 0.3; Vx set to previous month.
Unreasonable value of Vx; value set to previous month.
Figure 15. Time series of daily water exchange volume (VX) between the inner and outer portions of
Tomales Bay. The difference between the uncorrected and corrected values for VX is
discussed in the text.
- 54 -

---

Table 6 and Figure 16 give one example of calculated nonconservative fluxes for DIP. Similar
budgets are available for other forms of dissolved phosphorus, nitrogen and carbon. To aid the
comparison of biogeochemical rates among systems, it is convenient here to scale the
nonconservative rates obtained by the system area. The system is a nonconservative source of DIP
(DIP) averaging +0.16 mmol m-2 d-1. The seasonal variation in DIP ranges from 0.0 mmol m-2 d-1 in
December-January to greater than +0.4 mmol m-2 d-1 in June-July. Based on the assumption that DIP
release largely represents decomposition of organic matter, these data indicate that the system p-r
indicates net respiration, and that this occurs during most of the year.
Table 6. Nonconservative flux calculations for DIP in Tomales Bay, July 1987-July 1991. Notation as
in previous table; YP = 0.20.
Year
#days
VQ
VP
VE
VX(cor)
Y2
Y1
YQ
DIP
kmol
mmol m-2 d-1
87.472
14
0
50
1.29
2.01
0.47
87.650
65
5
0
50
997
1.15
3.10
0.55
2,651
0.17
87.850
73
6
9
29
2,313
0.95
2.81
0.80
4,079
0.25
88.005
56
223
95
9
1,233
1.33
1.92
0.80
269
0.02
88.190
68
461
62
7
12,850
1.27
1.37
0.46
1,353
0.08
88.368
65
44
23
41
2,018
1.54
2.05
0.61
1,547
0.10
88.536
62
17
14
56
2,018
1.18
2.76
0.29
3,653
0.23
88.724
68
10
0
60
1,776
1.23
3.56
0.32
4,580
0.29
88.839
42
10
4
35
1,508
1.59
3.34
0.92
2,325
0.15
89.016
65
95
94
10
1,519
1.62
1.84
0.83
-561
-0.04
89.175
58
87
35
7
1,182
1.67
1.74
0.92
109
0.01
89.348
63
563
107
20
16,360
1.44
1.55
0.63
2,250
0.14
89.521
63
24
2
48
16,360
1.54
1.95
0.67
6,957
0.43
89.685
60
11
0
60
1,259
1.13
3.44
0.58
3,983
0.25
89.852
61
24
35
25
1,259
1.48
3.19
0.48
2,018
0.13
90.016
60
52
21
10
966
1.33
1.80
0.42
-586
-0.04
90.173
57
232
80
8
3,242
1.20
1.47
0.82
797
0.05
90.355
66
75
21
24
5,731
1.55
1.80
0.85
1,725
0.11
90.567
77
62
50
47
5,731
1.46
2.61
1.13
7,148
0.45
90.671
38
13
0
52
1,066
1.50
3.31
0.69
2,711
0.17
90.839
61
11
2
19
342
1.32
3.37
0.92
724
0.05
90.996
57
41
22
7
1,841
1.16
1.84
0.83
9
0.00
91.159
60
83
49
6
1,841
1.37
1.65
1.04
502
0.03
91.333
63
518
156
14
11,092
1.04
1.34
0.62
3,525
0.22
91.528
71
25
3
43
11,092
1.04
1.78
0.71
8,466
0.53
Figure 16. Time series of net nonconservative flux of DIP (DIP) in Tomales Bay.
- 55 -

---

From the average DIP of +0.16 mmol m-2 d-1, the C:P ratio of organic matter, and Equation (31),
DICo can be calculated to be approximately +17 mmol m-2 d-1. It follows that p-r -17 mmol m-2d-1.
From independent data (Cole, 1989; Hollibaugh, unpublished), plankton primary production in this
system is known to average about 70 mmol m-2 d-1 over the study period. Other primary producers
(benthic algae, seagrass) are estimated to contribute an additional 30 mmol C m-2 d-1. Respiration
exceeded primary production by an estimated 17 mmol m-2 d-1, so r 117 mmol m-2 d-1. The p:r ratio
of this system is thus estimated to be about 0.85. Note that obtaining p-r in this fashion is
independent of direct estimates of either p or r, and that the p:r ratio is relatively insensitive to the
value used for p.
Table 7 summarises the mean fluxes of dissolved forms of C, N, and P, and Table 8 gives the
calculated stoichiometric characteristics of the system. One goal of this exercise is to apply
stoichiometric reasoning in order to estimate the actual biogeochemical processes accounting for the
calculated biogeochemical fluxes. Particulate material in this system has a C:N:P molar ratio
approximating the Redfield Ratio (106:16:1).
Table 7. Average nonconservative fluxes for dissolved carbon, nitrogen, and phosphorus in
Tomales Bay, July 1987 - July 1991.
VARIABLE
FLUX (mean ± standard error)
DIP (mmol m-2 d-1)
0.16 ± 0.03
DOP (mmol m-2 d-1)
0.02 ± 0.01
NO -
3 (mmol m-2 d-1)
-1.46 ± 0.54
NH +
4 (mmol m-2 d-1)
-0.07 ± 0.07
DON (mmol m-2 d-1)
0.63 ± 0.19
TA (meq m-2 d-1)
13.43 ± 3.51
DIC (mmol m-2 d-1)
7.10 ± 2.59
DOC (mmol m-2 d-1)
2.38 ± 0.88
This system accumulates little CaCO3 in the sediments, so TA is assigned to sulphate reduction
(see Equation 26). TA is 13 meq m-2 d-1, so the estimated net rate of sulphate reduction, that is,
gross sulphate reduction - sulphide oxidation, is TA/2, or about 7 mmol m-2 d-1. This figure is
somewhat higher than the burial rates of chromium reducible sulphur measured by Chambers et al.
(1994) as 3 mmol m-2 d-1 at two subtidal sites in the bay, but lower than the rate of 30 mmol m-2 d-1
reported by those authors using 35S incorporation rate experiments. The carbon decomposition
associated with the budgeted rate of sulphate reduction is about 13 mmol m-2 d-1, implying that about
12% of the respiration in this system is associated with sulphate reduction. Because this is not a
calcifying environment, Equation (31) can be used here without the TA term to estimate the rate of
CO2 gas flux across the air-water interface: DICg = DICt - DIP x (C:P)part = 7 - 17 -10 mmol m-2
d-1. This represents gas evasion from the water.
The changes in dissolved phosphorus and nitrogen, Table 8, the N:P ratio of local particulate organic
matter (16:1), and Equation (35) are used to calculate (nfix - denit): (nfix-denit) = N - P x (N:P)part
(-1.5 -0.1 + 0.6) - (0.16+ 0.02) x 16 -3.9 mmol m-2 d-1. That is, the system seems to be denitrifying
about 4 mmol m-2 d-1 more nitrogen than it is fixing. How much would this number be altered by the
absence of DON and DOP data? In that case, estimated (nfix - denit) becomes 5.1 mmol m-2 d-1.
Note also that the calculation is not particularly sensitive to NH4 flux. In many cases, this term largely
represents turnover, rather than net flux. Joye et al. (in press) have measured in situ subtidal
denitrification rates between 1 and 9 mmol m-2 d-1 in this system. While nitrogen fixation does occur
on some parts of the mud flats of this system with rates generally well less than 1 mmol m-2 d-1, it
appears to be spatially a restricted process (Joye and Paerl, 1993).
- 56 -

---

Table 8. Average stoichiometric fluxes in Tomales Bay, July 1987-July 1991, calculated from data in
Table 7.
VARIABLE
FLUX (mean ± std. Error) (mM m-2 d-1)
(p-r) (BASED ON PARTICLE C:P OF 106)
-16.6 ± 3.3
(nfix-denit) (BASED ON PARTICLE N:P OF 16)
-3.9 ± 0.8
DICs
+13.4 ± 1.8
CO2 gas flux
-9.5 ± 3.1
plankton p (INDEPENDENTLY MEASURED)
70
other p (AS DISCUSSED IN TEXT)
30
r (p - [p-r])
81 ± 11
5.6.5 Gulf of Bothnia: NP Budgets in a System with Time Varying Volume
In a study of the nutrient budget of the Gulf of Bothnia (Figure 17) (area = 108 x 109 m2; volume =
5,900 x 109 m3), encompassing the two northern basins of the Baltic Sea, an intensive field
programme was initiated during 1991 and yielded data with a monthly time resolution (Wulff et al.,
1994). This study is presented as a case in which it was possible to evaluate fluxes with a high
temporal resolution, in which it was possible to follow both organic and inorganic nutrient fractions,
and in which the temporal variation of water volume was important.
Figure 17. Location of the Baltic-Kattegat system.
- 57 -

---

In this study, it was found that it is not sufficient to use the variations in total amounts to estimate the
fate of the nutrient load to the Gulf of Bothnia. The different fluxes between the sub-basins, that is
the Bothnian Bay, the Bothnian Sea and between the Bothnian Sea and the Baltic proper, had to be
estimated. The basic reasons for this were large differences in nutrient load, hydrography and
biogeochemistry. The Gulf of Bothnia could then be represented by a simple two box model with only
narrow connections between the sub-basins and to the Baltic proper. The water level variations were
obtained from monthly means measured at several stations in each sub-basin. The net turbulent
diffusive exchange between the sub-basins is included in the advective transports. The advective net
volume exchanges are then estimated from volume and mass balances by using salt as a
conservative tracer.
Volume changes, V, in each sub-basin over monthly time increments have been derived from
changes in average sea level (Figure 18). Those data, along with monthly average salinity, are used
in Equations (6) and (7) in order to estimate water exchange between the two basins and between the
Bothnian Sea and the Baltic Proper.
Figure 18. Monthly variations in freshwater inputs, water level, and water exchange in Bothnian Bay
(solid) and Bothnian Sea (dashed).
The model parameters are, as mentioned above, assumed to be homogeneous within the basin.
These volume-weighted averages are obtained using the calculated total amounts. The monthly
mean salinity is obtained by interpolation of the averages based on relatively few observations. This
interpolation will smooth events on the scale of a month or shorter. A simple scale analysis with
regard to the time-dependent terms of water volume and salinity demonstrates that an average
freshwater supply of 135 x 106 m3 d-1, which is about half the mean supply to the Bothnian Bay, will
yield h 0.1 m, if all the water were retained in the Bay over a month's time.
The significance of this calculation is that monthly water level changes on the order 0.1 m will have
the same impact as half the mean freshwater input in the volume balance. A similar analysis in the
salt balance yields
S
Qf S
V
1
~
1 1
1 t
- 58 -

---

or
Qf S T
S ~
1 1
V1
Typical data for Bothnian Bay give S ~ 0.01 p.s.u., which is a monthly change well within the
observed range. An analogous analysis of the Bothnian Sea gives similar figures to that of the
Bothnian Bay. The importance of this scaling analysis is that one cannot calculate monthly averaged
fluxes in the Gulf of Bothnia without considering the time-dependent variations of the water level.
With the volume flows, loads and total amounts given, it is straightforward to estimate the sources
and sinks in the system using Equations of the form of (21) and (22). The variables in the annual
budgets are "organic" nitrogen and phosphorus, calculated as the difference between total nitrogen or
phosphorus and the inorganic fractions (DIN or DIP).
From the monthly time-stepped nonconservative fluxes presented here, Figure 19, it is evident that
the nitrogen and phosphorus cycles are neither constant over the year nor exactly balanced over an
annual cycle in the Gulf of Bothnia. For the year illustrated, 1991, there is an accumulation of
phosphorus, as organic phosphorus, and a loss of nitrogen, as inorganic nitrogen, in the water
column reservoirs. There is also a redistribution between the dissolved inorganic and the organic
(dissolved + particulate) fractions.
Figure 19. Monthly variations in the nonconservative fluxes of materials in Bothnian Bay (solid) and
the Bothnian Sea (dashed).
- 59 -

---

Figure 20 shows fluxes to and from the Baltic including residual flow and mixing. DIN to organic
nitrogen conversion is calculated from DIP to organic phosphorus conversion using an assumed
N:Ppart of 12:1, and nitrogen burial is calculated from phosphorus burial with an assumed burial
particle N:Ppart ratio of 7:1. The quantity (nfix - denit) (in both cases net denitrification) is then
calculated to balance the nitrogen fluxes between DIN and ON and between ON and burial.
Baltic input = 119
VQ*DIPQ* = +123
DIP = -342
Baltic input =113
584
OP = + 697
VQ*OPOPQ* = +119
Burial = 119
Phosphorus Budget (106 mol yr-1)
-5,127
-12,168
(nfix - denit)
Baltic output=
2,036
VQ*DINQ* = +8,464
DIN =
-5,707
Baltic input =
2,871
7,008
ON =
VQ*OPONQ* = +4,150
+ 697
Burial = 833
Nitrogen Budget (106 mol yr-1)
Figure 20. Annual budgets of phosphorus and nitrogen in the Gulf of Bothnia 1991.
Quantities calculated within the budget are shown in bold typeface.
- 60 -

---

The phosphorus budget (Figure 20) shows a substantial import from the Baltic Proper, almost twice
the load coming from the drainage basin to the Gulf. For the 1991 data, most of the phosphorus
entering the Gulf remained in the water column. Phosphorus, not remaining in the water column or
not exported hydrographically, is assumed to be exported to the sediments. The drainage basins are
the major net source of nitrogen delivery; inorganic export to the Baltic Proper approximately
balanced organic import (Figure 20). Nitrogen in the water column actually decreased over the
budgeted year, with some nitrogen apparently accumulating in the sediments.
As demonstrated with Equations (27-31) and (35), the budgets for inorganic nitrogen and phosphorus
involve transfer to and from organic matter due to assimilatory and respiratory processes.
Qualitatively, the seasonal variation in NO -
+
3 , NH4 , and DIP seems to be a common example of
community production and regeneration. In the winter there is release of DIP, release of NO -
3 , and
uptake of NH +
4 . This appears to represent net respiration of organic matter, with nitrification of
released NH +
4 , Equation (28) proceeding in reverse, accompanied by nitrification according to
Equation (27). Both DIP and NO -
+
3 are taken up in the spring, Equation (27), while NH4 release during
the late spring and summer reflects nitrogen recycling.
Although the annual budget estimates may give only a little information about the mechanisms
behind these bulk fluxes, they can be used to assess the overall magnitude and significance of the
different processes. By calculating N:P ratios of the different pools and fluxes (Figure 20), typically
very high ratios are found for the inorganic pool in the Bothnian Bay and for the organic pools in both
basins. Only the inorganic pool in the Bothnian Sea is close to the Redfield Ratio of 16:1. However, it
is noteworthy that the N:P ratios for the net transfer of inorganic nutrients to organic are very close to
the Redfield Ratio of assimilative nutrient uptake, in spite of the highly different ratios of the pools.
This might imply that these calculated fluxes are actually related to the net primary production of
these systems. Furthermore, net organic carbon production, calculated from these rates, are 4-6 mol
C m-2. Annual phytoplankton production measurements for these regions are comparable to these
estimates considering that these estimates should be closer to `new' production than to either gross
or net primary production in the sense of Eppley and Peterson (1979).
Denitrification rates from these system level data can be compared with "direct" assays. Stockenburg
and Johnstone (1994) measured denitrification directly in the Gulf of Bothnia during 1991. They
obtained rates of 45-60 mmol m-2 yr-1 in the Bothnian Bay (1/3 of the Gulf area) and 100-350 mmol
m-2 yr-1 in the Bothnian Sea. An area-weighted average of these figures is about 170 mmol m-2 yr-1.
The budgetary estimates yield an estimated (nfix-denit) equivalent to about 160 mmol m-2 yr-1.
Other denitrification estimates in the Baltic and adjacent marine sea areas (Koop et al., 1990) have
ranged between 140 and 660 mmol m-2 yr-1. However, none of these studies has been in the Gulf of
Bothnia.
The above fluxes for the Gulf of Bothnia provide some sense of seasonal variation in fluxes, the
short-term importance of water column storage, and explicit treatment of exchange between the
inorganic and organic phosphorus and nitrogen reservoirs. In the next case study, analysis of sub-
basins within the entire Baltic-Kattegat system, treated as a steady-state system based on data over
approximately 20 years is carried out.
5.6.6 Baltic-Kattegat: Steady-state NP budgets in the sub-basins of an estuarine sea
The Baltic Sea (Figure 17) is one of the most intensively studied marine areas in the world, and this
wealth of existing information can be utilised to develop budget calculations and empirical models.
These budgets give estimates of the relative importance of advective import/export, of inputs from
the atmosphere and drainage basins and of internal sources and sinks for the concentration of
nutrients and other substances in the basins. They also give estimates of the critical scales, such as
the residence times of salt, water and other substances.
The Baltic Sea is an ideal system to use for this budget approach, due primarily to the long residence
times of both water and of non-conservative substances, the possibility to use salt as a conservative
tracer, and the long and extensive time series of data available. Using long time series of data on
inputs and concentrations of salt and other substances in the basins, it should be possible to find
empirical relationships between inputs and conditions in the sea.
- 61 -

---

Estimates of inputs of fresh water and nutrients combined with calculations of total amounts of salt
and nutrients in different subregions of the Baltic have been used to develop nutrient budgets and
models of the entire Baltic Sea (Wulff and Rahm, 1988; Wulff and Stigebrandt, 1989) and for sub
regions like the Gulf of Riga (Yurkovskis et al., 1993) and the Gulf of Bothnia (Wulff et al., 1994).
This approach has even been used in budgets and models of toxic substances, for example, the fate
of pulp mill effluents (Wulff et al., 1993; Wulff and Rahm, 1993).
The Baltic Sea, including several of its sub-basins, has been used to develop a detailed budget of
dissolved nitrogen and phosphorus fluxes (Wulff and Stigebrandt, 1989). More recently, Smith and
Richardson (in preparation) have developed a stoichiometrically based budget for the Kattegat. The
combination of these two studies provides several interesting opportunities. The paper by Wulff and
Kattegat
Belt
Baltic
Bothnian
Bothnian
Sea
Proper
Sea
Bay
assume 0
assume 0
266
105
104
791.7
1,177.0
668.2
352.3
144.7
385.3
123.5
49.9
102.6
40.7
44.4
10.5
236.8
550.3
483.7
702.0
316.7
193.2
143.3
40.7
WATER BUDGET (109 m3 yr-1)
0 psu
0 psu
0 psu
0
0
0
23,658
10,608
4,811
1,691
261
20.1 psu
13.4 psu
7.2 psu
4.8 psu
1.8 psu
12,911
3,073
589
657
163
141
2,723
2,531
774
98
23,658
10,608
4,811
1,691
261
33.5 psu
24.9 psu
11.8 psu
6.4 psu
4.0 psu
33.7 psu
SALT BUDGET (109 Kg yr-1)
Figure 21. Steady-state water and salt budgets for the Baltic-Kattegat system to illustrate horizontal
and vertical linkages between compartments. Quantities calculated within the budgets are
shown in bold typeface. The slanted arrows in the upper boxes represent loading from land;
the horizontal arrows illustrate advective flows between boxes; the single-headed vertical
arrows indicate entrainment; and the double-headed vertical arrows illustrate vertical mixing.
- 62 -

---

Stiegebrandt (1989) provides an example of analysing three systems in series, Bothnian Bay,
Bothnian Sea and Baltic proper, while the addition of the Kattegat actually adds two basins to the
series, because the Belt Sea lies between the Baltic proper and the Kattegat (Figure 17).
Fluxes for any nonconservative material (Y) are calculated exactly as for the 1-layer case, by the
addition of other known inputs, such as sewage, precipitation, groundwater, and Yu(n) and Yd(n) to
Equation (21). One problem encountered by Smith and Richardson (in preparation) is that they did
not have reliable data on DON and DOP for the Kattegat. However, both the Tomales analysis and
data in Wulff and Stiegebrandt (1989) suggest that, while these terms may be important to the overall
system hydrographic fluxes, they tend to be minor contributors to the nonconservative fluxes. In
order to compare the two data sets, inorganic nitrogen and phosphorus data are used exclusively in
the analysis presented here.
Figures 22 and 23 summarise the inorganic phosphorus and nitrogen balances for this system. In
Figure 22 all of the upper boxes show DIP to be negative (net uptake). It is assumed that this
material falls out as particles, rather than either accumulating in the upper boxes or being removed
as particle fluxes. Some of that material regenerates in the lower boxes (DIP is positive). It is
assumed that particulate fallout which does not regenerate is buried, rather than either accumulating
in the lower boxes or being removed as particle fluxes. Vertical mixing (heavy, solid arrows between
surface and deep boxes) are positive for net flux into surface box.
Kattegat
Belt
Baltic
Bothnian
Bothnian
Sea
Proper
Sea
Bay
42
60
1,908
126
106
317
353
234
0.35 µM
53
14
0.40 µM
0.15 µM
0.30 µM
0.10 µM

DIP =-134

DIP = -1,835

DIP = -190

DIP =-300

DIP = -105
294
157
108
103
13
300
134
1,835
190
105
fallout
fallout
fallout
fallout
fallout
491
238
135
72
12
0.75 µM
0.70 µM
0.50 µM
0.30 µM
0.20 µM

DIP = +41

DIP = +54

DIP = +45

DIP = +43

DIP = +1
0.70 µM
259
80
1,790
147
104
burial
burial
burial
burial
burial
DISSOLVED INORGANIC P BUDGET (106 mol yr-1)
Figure 22. Steady-state dissolved inorganic phosphorus budget for the Baltic-Kattegat system.
Quantities calculated within the budgets are shown in bold typeface. The slanted and
horizontal arrows are the same as in Figure 21; the solid vertical arrows combine entrainment
and mixing fluxes; the dashed vertical arrows indicate particle fallout from the surface boxes
and burial flux from the bottom boxes, both inferred from the dissolved P fluxes.
- 63 -

---

In Figure 23, nitrogen fallout from the surface boxes is fixed by the N:Ppart ratio of 12:1. To account
for the net loss, the remaining nonconservative DIN flux in the surface boxes is balanced with (nfix-
denit). Nitrogen burial is fixed by the N:Ppart ratio of buried materials, 7:1, and the remainder of the
nitrogen flux, gains or losses, in the deep boxes is balanced by (nfix-denit). Vertical mixing is
represented by heavy solid arrows between surface and deep boxes, and are positive for net flux into
surface box. Other assumptions and notations are as on Figure 22.
Kattegat
Belt
Baltic
Bothnian
Bothnian
Sea
Proper
Sea
Bay
-1,208
-5,318
-47,513
-3,075
-2,358
nfix-denit
nfix-denit
nfix-denit
nfix-denit
nfix-denit
3,402
6,000
68,886
6,079
4,293
1,069
1,942
802
1.35 µM
969
2.75 µM
608
1.65 µM
1.20 µM
4.20 µM

DIN = -4,808

DIN = -6.926

DIN = -69,533

DIN = -5,355

DIN = -3,618
2,279
1,193
480
363
67
3,600
1,608
22,020
2,280
1,260
fallout
fallout
fallout
fallout
fallout
3,580
1,837
811
272
67
5.80 µM
4.20 µM
1.90 µM
1.65 µM
1.40 µM

DIN = +536

DIN = +167

DIN = -59

DIN = -568

DIN = -134
5.10 µM
1,813
560
12,530
1,029
728
burial
burial
burial
burial
burial
-9,549
-1,251
-881
-1,819
-666
nfix-denit
nfix-denit
nfix-denit
nfix-denit
nfix-denit
DISSOLVED INORGANIC N BUDGET (106 mol yr-1)
Figure 23. Steady-state dissolved inorganic nitrogen budget for the Baltic-Kattegat system.
Quantities calculated within the budgets are shown in bold typeface. The slanted and
horizontal arrows are the same as in Figure 21; the solid vertical arrows combine
entrainment and mixing fluxes; the dashed vertical arrows indicate particle fallout from the
surface boxes and burial flux from the bottom boxes, both inferred from the dissolved P
fluxes. The dotted arrows represent (nfix-denit) inferred from the discrepancy between
dissolved and particulate N fluxes.
In this case study, all fluxes, including the nonconservative fluxes, are most conveniently left as
basinwide total fluxes, rather than being scaled per unit area, in order to describe the mass
exchanges between sub-basins. However, Table 9 presents each sub-basin's nonconservative fluxes
and the stoichiometrically derived rates scaled per unit area for ease of comparison.
Note that each basin shows an uptake of DIP in the surface box and a release in the deep box. This
presumably represents net organic production in the surface and regeneration in the deep box. The
pattern is somewhat more complicated for DIN. All surface boxes show net uptake, but the deep
boxes are more variable. The stoichiometric balance is calculated by assuming that the phosphorus
uptake in the upper box is matched by an nitrogen uptake which is 12 times as large, that is, (N:P)part
= 12:1. This ratio is based on summary data by Smith and Richardson (in preparation) for the
Kattegat and may not be entirely appropriate for the other basins; it is used here for illustrative
purposes only. Nevertheless it is seen that the various sub-basins of the Baltic have rates of (nfix-
denit) ranging from about -100 to -300 mmol m-2 yr-1, that is, they exhibit net denitrification.
- 64 -

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Table 9. Nonconservative nitrogen and phosphorus fluxes and stoichiometric calculations for sub-
basins of the Baltic-Kattegat system (fluxes in mmol m-2 yr-1).
Kattegat
Belt Sea
Baltic
Bothnian
Bothnian
Proper
Sea
Bay
Area (103 km2)
21
20
267
72
36
DIP
(1)
surface
-14
-7
-7
-3
-3
Surface Deep P fallout(2)
14
7
7
3
3
DIP
(1)
deep
2
3
0
1
0
P burial(3)
12
4
7
2
3
DIN
(1)
surface
-229
-346
-260
-74
-101
Surface Deep N fallout(4)
171
80
82
32
35
(nfix-denit)
(5)
surface
-58
-266
-178
-42
-66
DIN
(1)
deep
26
8
0
-8
-4
N burial(6)
86
28
47
14
20
(nfix-denit)
(4)
deep
-59
-44
-35
-26
-19
(1) Net nonconservative flux in hydrographic budget.
(2) Assume all particles produced settle from that sub-basin's surface box to the deep box.
(3) Assume surface deep fallout which does not regenerate is buried in that sub-basin.
(4) Assume N:P ratio of surface deep particle flux = 12:1; calculate from phosphorus particle flux.
(5) Balance the nonconservative nitrogen flux.
(6) Assume N:P ratio of burial flux = 7:1; calculate from phosphorus burial flux
It is assumed that all particle formation settles from the upper box where formed, into the lower box
for that basin. The deep DIP regeneration is derived from the settling particles, and the phosphorus
not regenerated is assumed to accumulate in that basin. Again, using Kattegat data from Smith and
Richardson (in preparation), the N:P ratio of sediment, 7:1, is used to calculate the burial flux of
nitrogen. The nitrogen imbalance in this box is then attributed to denitrification.
Quantitatively, the nitrogen and phosphorus fluxes are not balanced without an additional nitrogen
sink. The nitrogen fluxes are scaled via a particle uptake N:P ratio of 12:1 for p-r in the water and
with a sediment N:P accumulation ratio of 7:1 (see section 5.4.6). Imbalances of the nitrogen budget
are attributed to (nfix-denit). Some nitrogen and phosphorus are, of course, lost by being bound into
refractory organic matter in the sediments. There is experimental evidence (Carman and Wulff,
1989) that DIP concentrations in the interstitial water are high enough to cause significant losses by
adsorption to particles. This can be accounted for in the stoichiometric calculations by using the
sediment N:P ratios. The stoichiometric calculations scaling nitrogen fluxes to phosphorus fluxes
suggest that (nfix-denit) has consumed nitrogen both from the inorganic load in the water column
and, primarily, nitrogen reaching the bottom as organic matter. The calculations suggest that about
70% of the nitrogen losses through denitrification occur in the sediments.
The points which emerge from this analysis are that the budgets of the individual sub-basins may be
tied together, that the fluxes between the individual sub-basins must be retained in total mass units,
but that the comparisons among the nonconservative fluxes are most constructively examined once
scaled to rates per unit area. It is further noteworthy that the nitrogen fluxes can only be balanced
relative to phosphorus fluxes if there is substantial nitrogen removal from the system via
denitrification. The derived rates of denitrification are within the range of rates which have been
independently estimated for portions of the Baltic-Kattegat system, suggesting that this procedure
provides a robust assessment of denitrification for other coastal systems in general.
- 65 -

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5.6.7 Spencer Gulf: Steady-state CNP fluxes in a calcifying hypersaline system
Nutrient budgets are available for Spencer Gulf, Australia (Figure 24) (Smith and Veeh, 1989). This
hypersaline system dominated by calcareous sediments is used both to illustrate a simple 2-box
linked model and also to illustrate calculation of CaCO3 reactions from alkalinity fluxes. Modification
of these budgets to the same stoichiometric framework discussed here provides further insight into
the budgeting procedure. Spencer Gulf is a slightly hypersaline system, with salinity increasing from
values near 36 p.s.u. in the ocean to salinities in excess of 45 p.s.u. at the head of the Gulf. There is
insignificant surface inflow of freshwater, little precipitation, and apparently little groundwater inflow.
The southern, or outer, portion of the system is a deep-water region, in which plankton are assumed
to dominate primary production. The northern area is much shallower, with abundant seagrass.
Figure 24. Location of Spencer Gulf, Australia.
Waters of the adjacent Southern Ocean are very low in nutrients, yet DIP decreases with distance
from the ocean into the Gulf (Figure 25). The conspicuous break in the salinity-DIP plot near a
salinity of 38 p.s.u. is used as basis to divide the Gulf into two hydrographic regions, denoted here as
the Lower Gulf [area = 15.6 x 109 m2; volume = 420 x 109 m3 ], and the Upper Gulf [area = 6.1 x 109
m2; volume = 30 x 109 m3]. The evaporative water flux (VE) is defined by evaporation (2.6 mm d-1)
and the area of the Gulf. The system is not vertically stratified, so the Lower and Upper Gulf boxes
are linked by the 0-dimensional exchange and nutrient flux equations, Equations (1)- (22). Available
data are sufficient for development of steady-state calculations, but insufficient to develop time-
course calculations.
Figure 25. Distribution of DIP as a function of salinity in Spencer Gulf. The distinct slope break near a
38 p.s.u. is used to separate the Gulf into two regions.
- 66 -

---

Figure 26 summarises the water and salt budgets for the two regions. Precipitation and evaporation
are grouped together into a single term of net evaporation (VP - VE). This flux pathway removes 16 x
106 m3 d-1 of water from the Upper Gulf and 40 x 106 m3 d-1 from the Lower Gulf. As a result of this
removal, residual seawater inflow occurs to offset the evaporative loss. Residual flow (VR) into the
entire Gulf is thus 56 x 106 m3 d-1, with 16 x 106 m3 d-1 of that residual flow moving northwards from
the Lower to the Upper Gulf. Residual salt flux into the Upper Gulf from the Lower Gulf is 608 x 106
kg d-1, and into the Lower Gulf from the ocean is 2,005 x 106 kg d-1. From these fluxes VX can be
calculated between the Upper and Lower Gulf as 290 x 106 m3 d-1, and between the lower Gulf and
ocean as 1,823 x 106 m3 d-1.
ocean
VP - VE = -40
VP - VE = -16
VQ, etc. 0
VR = 56
VR = 16
Lower Spencer
Upper Spencer
Gulf
Gulf
Water Budget (fluxes in 106 m3 d-1)
ocean
VRSR = 2,005
VRSR = 608
Lower Spencer
Upper Spencer
Gulf
Gulf
S3 = 35.8 p.s.u.
S2 = 36.9 p.s.u.
S1 = 39.0 p.s.u.
VX(S3 - S2) = -2005
VX(S2 - S1) = -608
VX = 1,823
VX = 290
Salt Budget (fluxes in 106 kg d-1)
Figure 26. Steady-state water and salt budgets for Spencer Gulf. The heavy mixing arrows show the
direction of net flux. Quantities calculated within the budget are shown in bold typeface.
Figures 27-29 summarise the dissolved C, N, and P budgets. The system is a net calcifying system,
with little terrigenous material accumulating in the sediments. Hence, the change in total alkalinity
(TA) can be used as a measure of CaCO3 precipitation (Equation 25), rather than of sulphate
reduction in this system. The residual fluxes and exchange fluxes are calculated using the
concentrations of these materials and the values for VR and VX. Nonconservative fluxes, that is, Y's
for each of these terms, are calculated according to Equation 22, with all the freshwater inputs having
values of 0. Although the various portions of each budget are included in the notation on the box
diagrams, note that there is no gradient of DOP, NO3, or NH4 between the ocean and Gulf. The
residual fluxes of these materials are small, driven by evaporative inflow of seawater, and the
exchange fluxes are effectively equal to 0. DOC shows a slight increase from the ocean to the Gulf,
but the calculated fluxes are small compared to TA and DIC. DIP, TA, DIC, and DON all show
significant net nonconservative fluxes.
- 67 -

---

ocean
VRDIPR = 11
VRDIPR = 1
Lower Spencer
Upper Spencer
Gulf
Gulf
DIP3 = 0.19 µM
DIP2 = 0.12 µM
DIP1 = 0.06 µM
VX(DIP3 - DIP2) = 28
VR(DIP2 -DIP1) =17
DIP = -121
DIP = -18
Dissolved Inorganic P Budget (fluxes in 103 mol d-1)
ocean
VRDOPR = 18
VRDOPR = 5
Lower Spencer
Upper Spencer
Gulf
Gulf
DOP3 = 0.33 µM
DOP2 = 0.33 µM
DOP1 = 0.33 µM
VX(DOP3 - DOP2) = 0
VR(DOP2 -
DOP1) = 0
DOP = -13
DOP = -5
Dissolved Organic P Budget (fluxes in 103 mol d-1)
Figure 27. Steady-state dissolved phosphorus budgets for Spencer Gulf. Quantities calculated within
the budgets are shown in bold typeface. Note that there is uptake of DIP in both boxes.
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---

ocean
VR[NO3]R = 11
VR[NO3]R = 3
Lower Spencer
Upper Spencer
Gulf
Gulf
[NO3]3 = 0.19 µM
[NO3]2 = 0.19 µM
[NO3]1 = 0.19 µM
VX([NO3]3 - [NO3]2) = 128
VR([NO3]2 -
[NO3]1) = 0
NO3 = -8
NO3 = -3
ocean
VR[NH4]R = 13
VR[NH4]R = 4
Lower Spencer
Upper Spencer
Gulf
Gulf
[NH4]3 = 0.24 µmol
[NH4]2 = 0.24 µM
[NH4]1 = 0.24 µM
VX([NH4] 3 - [NH4]2) = 0
VR([NH4]2 -
[NH4]1) = 0
NH4 = -9
NH4 = -3
ocean
VRDONR = 267
VRDONR = 100
Lower Spencer
Upper Spencer
Gulf
Gulf
DON3 = 4.77 µM
DON2 = 5.52 µM
DON1 = 6.96 µM
VX(DON3 - DON2) = 1,367
VR(DON2 -
DON1) = 418
DON = + 782
DON = +318
Dissolved Organic Nitrogen Budget (fluxes in 103 mol d-1)
Figure 28. Steady-state dissolved nitrogen budgets for Spencer Gulf. Quantities calculated within the
budgets are shown in bold typeface. Note that there is very slight uptake of NO3 and NH4
and a large release of DON. There must be positive DON (hence [nfix-denit] is positive)
to balance the nitrogen budget.
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ocean
VRTAR = 136
VRTAR = 40
Lower Spencer
Upper Spencer
Gulf
Gulf
TA3 = 2.428 meq/l
TA2 = 2.480 meq/l
TA1 = 2.530 meq/l
VX(TA3 - TA2) = -95
VR(TA2 - TA1)
= -15
TA = -16
TA = -25
ocean
VRDICR = 117
VRDICR = 35
Lower Spencer
Upper Spencer
Gulf
Gulf
DIC3 = 2.088mM
DIC2 = 2.142 mM
DIC1 = 2.183 mM
VX(DIC3 - DIC2) = -98
VR(DIC2 -DIC1)
= -12
DIC = +4
DIC = -23
ocean
VRDOCR = 2
VRDOCR = 1
Lower Spencer
Upper Spencer
Gulf
Gulf
DOC3 = 0.039 mM
DOC2 = 0.042 mM
DOC1 = 0.048 mM
VX(DOC3 - DOC2) = -3
VR(DOC2 -
DOC1) = -1
DOC = + 3
DOC = 0
Dissolved Organic Carbon Budget (fluxes in 106 mol d-1)
Figure 29. Steady-state fluxes of total alkalinity, dissolved inorganic carbon, and dissolved organic
carbon in Spencer Gulf. Quantities calculated within the budget are shown in bold
typeface.
Table 10 summarises the stoichiometric calculations based on the net fluxes of dissolved carbon,
nitrogen, and phosphorus in this system. Based on TA, scaled per unit area, the system apparently
calcifies more rapidly in the Upper Gulf than the Lower Gulf. Based on the distribution of plant
communities in the Gulf, it is assumed that the dominant primary producer shifts from plankton in
the Lower Gulf to seagrass in the Upper Gulf. This shift and the composition shift of particulate
material produced by these two plant groups are used to calculate (p-r) from the DIP data. The two
basins are calculated to be slight net producers of organic carbon. The stoichiometric calculations
- 70 -

---

also suggest that the system (nfix - denit) is positive; the system appears to be fixing more nitrogen
than is lost to denitrification. The net rates of (nfix- denit) appear reasonable in comparison with data
for shallow systems of this kind (Capone, 1983).
Table 10. Nonconservative carbon, nitrogen and phosphorus fluxes and stoichiometric calculations
for sub-basins of Spencer Gulf (fluxes in mmol m-2 d-1, except TA, which is in
meq m-2 d-1 ).
Lower Gulf
Upper Gulf
Area (km2)
15,600
6,100
DIP
-0.008
-0.003
DOP
-0.001
-0.001
NO3
-0.001
-0.000
NH4
-0.001
-0.000
DON
-0.050
-0.052
TA
-1.03
-5.10
DIC
+0.25
-3.77
DOC
+0.19
+0.00
(p-r)
+1.0(1)
+1.7(2)
DICc
-0.5(3)
-2.1(3)
DICo
-1.0(4)
-1.7(4)
DICg
+1.8(5)
0.0(5)
(nfix-deniti)
+0.23(6)
+0.13
(1) Lower Gulf is plankton dominated; (p-r) = -125 x DIP (from local plankton C:P ratio).
(2) Upper Gulf is seagrass dominated; (p-r) = -660 x DIP (from local seagrass C:P ratio).
(3) DICc = TA/2.
(4) DICo = -p-r.
(5) DICg = DIC - DICc -DICo.
(6) (nfix-denit) based on average N:P ratio of approximately 20:1.
5.6.8 Tokyo Bay: Numerical analysis of water circulation from current data
Tokyo Bay (area = 1000 km2; volume = 17 x 109 km3) provides an example of a system for which the
circulation is estimated via numerical analysis of circulation, rather than water and salt budgets. At
this writing sufficient data is not available to develop nutrient budgets of this system. The water
exchange is estimated with a three-dimensional numerical model. The observed freshwater
discharge from rivers and the estimated heat transfer through the sea surface from meteorological
data in both the summer and winter are inputs to the model. Evaporation and precipitation at the sea
surface are neglected because they are nearly balanced in Tokyo Bay. Groundwater inflow is also
ignored because it is very small compared with freshwater discharge from rivers. Water from sewage
is mainly loaded into rivers and it is included in the river discharge. The observed water temperature
and salinity distributions are also given along the open boundary of the model basin. The interpolated
sea surface wind field based on the observed wind on land is given to the model basin. The tidal
stress, which generates the tide-induced residual current, is included in the momentum equation of
this model on the basis of the results of tidal current calculations. The calculated quasi-steady
residual flow field in the upper layers of Tokyo Bay are shown in Figure 30 (Yanagi and Shimizu,
1993). The residual flow consists of the density-driven current, the wind-driven current and the tide-
induced residual current. Such results are verified by the limited observed data of current
measurements in the field. It is possible to estimate Vx at the mouth of Tokyo Bay by using the results
of the calculated tidal current and residual flow fields (Figure 31). Additional examples of the
methodology and results can be found in Yanagi (1996).
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---

Figure 30. Calculated residual flow in the upper layers of Tokyo Bay in the summer and winter.
Figure 31. Estimated exchange flow (VX) at the mouth of Tokyo Bay on the basis of calculated tidal
currents and residual flow.
- 72 -

---

Figure 32. Calculated residual flow in the upper and lower layers of the East China Sea and the
Yellow Sea in the summer and winter.
- 73 -

---

5.6.9 East China Sea: Numerical analysis of water circulation in a shelf sea estimated from the
temperature and salinity field
In the East China Sea (area = 1.2 X 106 km2; volume = 4.5 x 104 km3), the seasonal variation of the
three dimensional residual flow field is calculated by means of the robust diagnostic numerical model
with the use of historically observed water temperature, salinity, and wind data (Figure 32). The
estimated residual flow fields at the upper and lower layers in summer and winter are shown (Yanagi
and Takahashi, 1993). Those in spring and autumn are similar to that in winter. It is nearly impossible
to carry out the direct current measurements in order to obtain the whole current field in a coastal sea
such as the East China Sea, because trawl fishing activity is very intense. However, the
accumulation of water temperature and salinity data is relatively easy. The robust diagnostic
numerical calculation technique is a very promising method for estimating the current field
quantitatively in a coastal sea using observed water temperature and salinity data. This estimated
current field then can be used to develop a water budget, such as here, for the East China Sea. Such
results are a fundamental requirement for the subsequent development of regional budget models for
salt, phosphorus, nitrogen, and carbon. For example, it is possible to estimate Vx across the shelf
edge of the East China Sea.
This method is basically the same as that used for the ERSEM (European Regional Seas Ecosystem
Model) developed for the North Sea (Lenhart et al. 1995). These authors calculated the seasonal and
year-to-year variation of three dimensional current field in the North Sea from 1970 to 1992 with use
of a general circulation model. Their circulation model was driven by implementing the observed
meteorological data of sea surface wind, air pressure and sea surface temperature. They estimated
the water budget in the North Sea on the basis of the calculated current field.
5.7 Summary of Case Studies
The various case studies have provided examples of the use of stoichiometrically linked water-salt-
nutrient budgets in coastal marine systems, including some of the complications which can arise.
Eight case studies are presented, each providing slightly different insight into budgeting material
fluxes in such environments. The insights which emerge from these examples can be generally
characterised as follows.
Preliminary data can be used to gain insight into how systems process carbon, nitrogen, and
phosphorus as was done for Bahia San Quintín and Klong Lad Khao Khao Bay. The Klong Lad Khao
Khao study developed as a workshop exercise while these guidelines were in draft stage and is
worked through in explicit detail. In that system, the stoichiometric calculations yield results which
may not be entirely reasonable. While more detailed assessment would be necessary to verify this
apparent discrepancy and isolate the basis for it, the very existence of such potentially problematical
results is itself insight into other processes which may be occurring in the system.
Two systems allowed examination of non-steady state salinity: Tomales Bay and the Gulf of Bothnia.
The Gulf of Bothnia allowed further examination of changing system water volume. Because of
rather detailed data available for both of these systems, they are further useful for the more detailed
examination of stoichiometric linkages between carbon, nitrogen and phosphorus. These data are
compared with available data for component metabolism in these two systems. In the case of
Tomales Bay, time-stepped data for freshwater inputs and for the salinity and DIP concentration of
the various water types are given so that the calculations may be duplicated in detail. Furthers point
for that system are: 1) nonconservative total alkalinity flux in that system is used to estimate system-
level rates of sulphate reduction; and 2) CO2 gas flux is calculated to close the DIC budget.
Three cases of geographic linkages between systems were presented, Bothnian Gulf, Baltic-Kattegat,
and Spencer Gulf. One of these, the Baltic-Kattegat, includes both horizontal linkages between
adjacent basins and vertical linkages between surface and deep waters. Spencer Gulf was used to
introduce the concept of nonconservative total alkalinity flux as a measure of calcification in actively
calcifying systems.
Finally, two examples, Tokyo Bay and the East China Sea, were given in which numerical simulation
models, rather than water and salt budgets, provide information on water circulation.
- 74 -

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6. RESPONSE TO SECOND LOICZ MODELLING REQUIREMENT - PREDICTION
Budget calculations, however useful, describe essentially a static situation. By comparing budgets of
similar systems under different environmental conditions or by following the same system over time
under changing conditions, it is possible to derive empirical relationships useful for prediction. Thus
budgets and empirical relationships can be merged into dynamic simulation models. This has been a
very successful approach used in limnology (Vollenweider, 1969) and there are no reasons why such
an approach could not be used for coastal systems as well. A good recent example is the analysis of
North Atlantic shelf data made by Nixon et al. (in press) showing that the net fractional transports of
nitrogen and phosphorus are inversely correlated with the mean residence time of water in the
system. Examples of dynamic time-dependent empirical models are the nutrient budget of the Baltic
Sea developed by Stigebrandt and Wulff (1989) and the modelling of Ver et al. (1994).
In the short term, budget calculations and empirical models are likely to have a greater value as
predictive tools of different management strategies than the development of detailed mechanistic
models. Mechanistic models serve initially as a `workbench' where model evaluations can be
compared with field measurements to improve our overall scientific understanding.
Empirical models are generally limited in their predictive capabilities to the range of observed data
for which they were generated. As a result process oriented system models also need to be
developed in order to evaluate the effects of perturbations outside the range for which there exists
empirical data.
Most dynamic simulation models are `mechanistic'. That is, they attempt to integrate existing
knowledge derived from studies of different processes, into simulations for entire ecosystems.
Experience to date shows that many mechanistic modelling projects, particularly those that attempt
to replicate the functioning of entire ecosystems, have failed because they are often based on a
`bottom-up' approach. This has demonstrated that even a detailed understanding of various
processes, expressed as sub-models and assembled into an `ecosystem' model, is often insufficient
to describe total system properties (see for instance Platt et al., 1981).
A holistic approach is required where the goals of the models and the critical scales are defined prior
to model formulation and simulation. The model is in itself a hypothesis, and the numerical
simulation is a tool to test this hypothesis, not a goal in itself.
From the LOICZ perspective, the question is how will the nutrient budget of a coastal system be
affected by environmental change, primarily changes in climate and nutrient load. Thus, the LOICZ
objective necessarily restricts the required model resolution from an infinite number of possible
ecosystem components to a few important state variables. Even with this recognition, as noted in
Section 3, there is a tendency to disaggregate unnecessarily, that is to add additional variables or
data, simply because the information is available, or because researchers feel that the model cannot
be developed without incorporating all available expertise.
What then are the minimum key processes that have to be included in a dynamic process oriented
model of a coastal ecosystem? This chapter attempts to present these along with a few simple
guidelines, illustrated by examples.
As has been described earlier in the section on budget modelling (Section 5.3), the basic differences
between a conservative material, such as salt, and a non-conservative substance, such as nutrients,
are the internal sources and sinks. Nitrogen, as inorganic nutrients, can be added through N2-fixation
and lost through denitrification. Phosphorus can be adsorbed to particles. In some systems, a large
proportion of the nutrients is stored in living organic matter or in detritus in the sediments. A dynamic
simulation model must therefore be able to describe the physical and biogeochemical processes that
control the fluxes between inorganic and organic pools and the environment (inputs, internal sources
and sinks).
As a simple first example, consider a simple well-mixed estuary where primary production is
dominated by phytoplankton. In such a system, nutrients and suspended organic matter are exported
(or imported) through water exchange. Additional inputs occur through river inputs, points sources
and atmospheric deposition. Primary production and sedimentation of organic matter are then the
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key processes that deplete the water column of nutrients. From an offshore perspective, these are
the key biological processes that have to be described. Nutrients are reaching the productive surface
layer, assimilated and recycled and eventually lost through sedimentation. Models describing these
processes in the open ocean are a key objective for Joint Global Ocean Flux Study (JGOFS) Core
Project of the IGBP, where the biological model is incorporated into ocean circulation models
(Fasham et al., 1990; Sarmiento et al., 1993). The models usually have a fixed stoichiometry,
assuming a constant C:N ratio. Phosphorus is rarely included in ocean `blue water' models where
nutrient ratios generally follow the Redfield Ratios. The primary reason for this is that
remineralisation is to a great extent occurring in the water column and little organic matter will
eventually reach the sediments which are situated at great depths (> 1000 m). The basic flow
structure that has to be resolved in an oceanic biological model is illustrated in Figure 33.
water exchange
reminera-
inorganic
lisation
nutrients
suspended
organic
primary
matter
production
advection
from deep
sedimentation
water
Figure 33. The basic flow structure that is resolved in most oceanic model of nutrient fluxes.
In the coastal zone however, a large fraction of the organic matter falls to the bottom where it is
partly accumulated and buried and partly decomposed. Some of the nutrients are returned to the
water column; some are lost through the internal sinks. One important difference between oceanic
and coastal models is the role of sediment processes for the recycling of nutrients. Another important
difference is that the sediment biogeochemical processes are likely to change nutrient concentration
due to the fact that substantial proportions of the nutrient are buried as organic matter or lost through
sinks, like denitrification for nitrogen and adsorption for phosphorus. These sinks will also change the
N:P ratio since more nitrogen is usually retained compared to phosphorus in most marine sediments.
nutrient inputs from land
water exchange
reminera-
inorganic
lisation
nutrients
suspended
organic
primary
matter
production
sediment
release to
sedimentation
water
sediment
inorganic
sediment
nutrients
organic
matter
sinks
sediment
burial
Figure 34. A simplified conceptual flow diagram of nutrient cycles in a coastal ecosystem.
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The conceptual model of a coastal system must therefore include sediment processes as illustrated
in Figure 34. The basic configuration is in principle the same, independently of which nutrient (CNP)
we are describing, although the processes controlling the fluxes, particularly the internal
sinks/sources are different.
This simple compartment flow diagram consists of only four state variables, the four boxes in Figure
34, and would be considered to be overly simplified by most ecologists. The immediate reaction for
most ecologists is to disaggregate this further by adding additional boxes. However, for the present
purposes, this may not be necessary as even this highly simplified system contains a complex flow
structure. It may also be possible to validate such a simple model using data that is readily available.
Simple standard measurements of inorganic and `total' nitrogen and phosphorus in the water column
may have already been made or may be possible with limited effort. Measurements of the
concentrations of suspended and dissolved nutrient fractions are rarely available. Similarly
measurements of both organic and inorganic CNP fractions in the sediment may be difficult to
achieve. To carry out further disaggregation, it would be necessary to identify appropriate
measurements of nutrient inputs from different sources on land, collected with the same methods as
used for the water. The concentrations in the sea outside the bay would also have to be known. A
common experience is that the compilation of data to support even a highly aggregated system such
as this is difficult.
As a result, it is very important to ensure that a higher level of detail can be supported by available
data before disaggregating. For instance, it is `natural' for the plankton ecologist to describe
phytoplankton-zooplankton interactions, the microbiologist to include all the interesting features of the
microbial loop, and so on for other fields of coastal zone research. However, at each step, the
decisive questions are: do we have sufficient quantitative data to address these issues, and is the
inclusion of these issues relevant to the objective of the model?
After defining the compartments and basic flow structure of the system, the next step in the
development of a dynamic simulation model is to define the processes that need to be included. As
with the compartments, there is an infinite number that could be included. Again, the objective of the
model and the specific characteristics of the system will determine what is to be included or
excluded. In the simple example presented here, the effects of seasonal variation in temperature and
insolation would be important and should be included only if the bay was situated on a temperate
latitude. These effects would be irrelevant if the bay is located near the equator. Since, in this
dynamic model, the aim is primarily to describe how the system changes with respect to time, the
temporal resolution of the model must also be decided. For instance, if the purpose is to study the
effect of climate change, it may be necessary to have data describing the bay for hundreds of years.
If the purpose is to study the effect of changes in nutrient inputs due to the building of a sewage
plant, it may only require measurements for a time period of a decade or less. If episodic events, like
flooding and hurricanes, are important, the temporal resolution of the data may have to be as high as
daily or hourly. In addition to the requirements set by the different questions to be asked, the
behaviour of the system, such as the residence time of water and that of different nutrient
compartments, as described in section 5.4, will also define the data requirements at the different
temporal scales.
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Figure 35 demonstrates some of the phenomena usually encountered in coastal and marine systems
along with their spatial and temporal scales. The lower diagram shows the need to identify the model
definition and the scale of interest. Phenomena that occur on other scales have to be parameterised
or treated as external forcing functions. For instance, if a model is developed to follow the seasonal
succession of the entire pelagic community it may not be necessary to resolve phenomena on shorter
time scales such as the individual movement of an organism. The phenomena that occur on lower
scales can be described in aggregated functional relationships, that is "parameterised", relative to the
scale of interest. For the same model it may not be necessary to describe all of the processes that
control the system such as water temperature. These higher scale phenomena may be given as an
"external function".
SCALES
1 mm 1 cm 1 dm 1 m 10 m 100 m1 km 10 km 100 km1000 km
1 sec Molecular
processes
Surface waves
1 min
Turbulent
patch
Individual
Langmuir
1 hour
size
movement
cells
Inertial/internal*Internal Surface
wave
tides
tides
1 day
Plankton
Synoptic
migration
storms
1 week
Phytoplankton
Coastally trapped
patch
waves
1 month
Fronts &
Zooplankton
Seasonal
Eddies
patch
biomass cycles
1 year
Gyre
circulations
10 years
1 sec 1 min 1 hour 1 day 1 week
1 month 1 year 10 years
To study
To parameterize
External forcing
Figure 35. A schematic illustration of spatial and temporal scales of coastal and marine systems. A
model aimed at describing a coastal ecosystem must resolve only a part on this entire
spectra. Processes that occur on a lower scale will be parameterised while those on larger
scales will be treated as external forcing functions.
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The use of highly aggregated compartments in a simple model means that it is difficult to directly use
field data and laboratory experiments to scale the functional relationships that the model aims to
describe. However, these difficulties remain even if the model is disaggregated into `functional'
groups for which there are experimental data. As an example of this difficulty, one mistake that is
often made in modelling the trophodynamics of coastal populations is to use data from zooplankton
feeding rate experiments in models of phyto-zooplankton interactions. Such simulations show that
the modelled zooplankton population will die because the phytoplankton concentration is too low to
maintain the herbivores! The simple explanation for this result is that the model assumes that
average concentrations of zooplankton feed on average concentrations of phytoplankton. This is not
true in the `real world' where various adaptive strategies and processes occur on spatial and temporal
scales that are not included in the model. Figure 35 attempts to illustrate that it is imperative to
consider these scaling arguments in the model development. A recent extensive treatment of the
problem of scaling issues in modelling, as well as in general ecological research, can be found in
Giller et al. (1994).
Traditionally, numerical modelling of complex systems required a considerable skill in mathematics,
systems or control theory and computer programming. Although some tools now exist to aid
development, this is still true and there are many technical and mathematics challenges in achieving
the successful implementation of large numerical models. A good recent example of such a complex
systems model which includes the variables and processes of interest to LOICZ and what is needed
in terms of technical and logistic support is the ecosystem model of the North Sea (ERSEM). A
detailed description of this model development and its results are described by Blackford and
Radford (1995) and Ruardij et al. (1995).
6.1 The Development of a Dynamic Simulation Model - A Simple Demonstration
As stated previously, the process of model development is often as useful as the final model itself. It
has also been stated that even a very simple model may contain features not easily understood
without carrying out a simulation exercise. As a simple but concrete demonstration of this, a software
modelling application, STELLA (see Annex 1 for reference information), is used here to implement
and simulate the nutrient dynamics of the simple hypothetical bay illustrated in Figure 34. In this
case, the focus for the simulation exercise is on the effects of water exchange on the net export of
nutrients from the bay to the outside sea. The question to be asked is: Will an increased water
exchange affect how much nutrient that is imported, exported or retained in the bay?
The initially step in building the model with STELLA is to place state variables (squares), flows (broad
arrows) and processes (circles) in a flow diagram using the STELLA symbols (Figure 36).
To accurately describe the flows of nitrogen in this example, the minimum number of state variables
are: DIN (dissolved inorganic nitrogen), PON (particulate organic nitrogen in the water column),
sediment organic nitrogen and sediment DIN.
The processes that are controlling the fluxes between the state variables in the model are:
assimilation, sedimentation, sediment burial, sediment mineralisation, denitrification, DIN release and
input and water exchange of DIN and PON with the sea outside the bay.
For the `Model Bay', assume that measurements are available showing that the maximum growth
rate of PON is 50% per day under ideal conditions, with no factors limiting growth. The only limiting
factors to be considered here are nutrients, DIN, and the light shading effect of biomass represented
as PON. The difference equation showing the change in biomass of algae with respect of time (dt) is
scaled as:
d[PON ] = growth - losses
(36)
dt
In the simple model, growth is equalised with (net) assimilation and sedimentation. A maximum
assimilation rate of 3% per day is defined so that it is convenient to develop functional relationships
for nutrient, called here Nmax,, and biomass shading, called here Pmax, so that they attain values
between 0 and 1. Thus, Equation (34) equation becomes:
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d[PON] = assimilation - sedimentation
(37)
dt
Thus
assimilation = P N
.
0 5 PON
(38)
max
max
if the nutrient concentration is high and biomass is low enough to ensure that the algae grow at their
maximum rate, Pmax and Nmax are equal to 1. If there are no nutrients and the biomass is very high,
Pmax and Nmax are equal to 0. Thus, with this simplistic formulation the limitations due to multiple
factors can be described. For instance, there will be no algae growth if there is a high nutrient
concentration but Pmax is 0. It remains to scale these functions for values between 0 and 1. For
nutrients the classical Michaelis-Menten, also called Monod, relationship can be used. Assume that
experimental data is available that show that the algae grow at half of their maximum rate at a DIN
concentration of 0.5 µmol. The Michaelis-Menten equation for Nmax is then
DIN
N
=
(39)
max
.
0 3 + DIN
THE 'MODEL BAY'
THE SEA
OUTSIDE BAY
water exchange
DIN
PON
assimilation
exchange of DIN
Sea DIN conc
DIN input
exchange of PON
Nmax
Pmax
DIN release
Sea PON conc
Sedimentation
Sediment DIN
sediment orgN
Graph 1
Sed mineralisation
Sediment burial
Denitrification
Figure 36. The graphical flow diagram of nutrient dynamic in the `Model Bay' using STELLA software.
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When the concentration of particles in the water column increases, less light will penetrate and the
assimilation will become light limited. Assume that the assimilation will decrease to 50% when the
concentration of PON reaches 2 µmol. Again, the Michaelis-Menten equation can be used, in this
case inverted to formulate Pmax:
PON
P max = 1 -
(40)
2 + PON
Assimilation in this model is then a function of nutrient concentration and of PON. Measurements are
available that show that 10% of the PON particles sediments out each day. Since the factors that
affect the growth and loss is known, a differential equation can be written that describes PON change
with respect to time:
d[PON ] = P N .05 PON - PON .010
(41)
dt
max
max
It is further assumed that 5% of the organic matter in the sediment is degraded per day. Of the
nutrients that are released into the sediment, 50% is released into the water column and 10% is
denitrified each day. Thus, the differential equations for all of the state variables can be written. With
STELLA software, these equations are automatically generated when the flow diagram is drawn and
the processes are defined. The equations generated by STELLA for the structure depicted in Figure
36 are listed in Text Box 5.
DIN(t) = DIN(t - dt) + (DIN_release + DIN_input - assimilation - exchange_of_DIN) * dt
INIT DIN = 10
DIN_release = Sediment_DIN*0.50
DIN_input = 0
assimilation = PON*Nmax*Pmax*0.5
exchange_of_DIN = water_exchange*(DIN-Sea_DIN_conc)
PON(t) = PON(t - dt) + (assimilation - Sedimentation - exchange_of_PON) * dt
INIT PON = .1
assimilation = PON*Nmax*Pmax*0.5
Sedimentation = PON*0.10
exchange_of_PON = water_exchange*(PON-Sea_PON_conc)
Sediment_DIN(t) = Sediment_DIN(t - dt) + (Sed_mineralisation - DIN_release - Denitrification) * dt
INIT Sediment_DIN = .001
Sed_mineralisation = sediment_orgN*.05
DIN_release = Sediment_DIN*0.50
Denitrification = Sediment_DIN*.0
sediment_orgN(t) = sediment_orgN(t - dt) + (Sedimentation - Sed_mineralisation -
Sediment_burial) * dt
INIT sediment_orgN = 1
Sedimentation = PON*0.10
Sed_mineralisation = sediment_orgN*.05
Sediment_burial = 0*sediment_orgN
Nmax = DIN/(0.5+DIN)
Pmax = 1-(PON/(2+PON))
Sea_DIN_conc = 0
Sea_PON_conc = 0
water_exchange = 0.0
Text Box 5. The STELLA presentation of differential equations and processes of the Model Bay.
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STELLA lists the differential equations in a format: X(dt) = X(t-dt) + inputs - losses, where dt is the
timestep. The statements starting with INIT gives initial concentrations of the state variables. State
variables are all scaled in mmol m-3 and rates are d-1. For the sediment, assume that the average
depth of the bay is 5 m. Thus, the sediment concentrations could be scaled to unit m-2, simply by
multiplying them with the area:volume ratio (5 in this case).
It is important to gradually develop the model. In this case, the first simulation is run without any
inputs of nutrients to the system, nor any losses. This is done by changing the constants for sediment
burial; denitrification, DIN input, and water exchange are all set to zero. Thus DIN can be used by
PON, sedimentated out to sediment organic N (SEDN), or be mineralised and immediately returned
to the water column. With the scaling used here, the simulation, running for one year, generates
results shown in Figure 37.
1: PON
2: DIN
3: sediment orgN
4: Sediment DIN
15.00
C
o
n
c
e
n
t
7.50
r
3
3
3
3
a
t
I
1
1
1
o
n
2
1
4
2
4
2
4
2
4
0.00
0.00
91
182
273
365
Days
Figure 37. The change in concentration of nitrogen (µM) of the four state variables in the model when
there are no inputs, water exchange nor internal losses through sediment burial or
denitrification.
This simulation illustrates how inorganic nutrients (DIN) will rapidly decrease from the initial
concentration (10 µM) to about 1 within 40 days. The rate of decrease is naturally a reflection of the
scaling that has been applied to the assimilation function, transferring nutrient from DIN to PON.
After the initial increase of PON and sediment organic N, a mirror of the DIN decrease, the increase
of organic matter will continue. The system will reach a steady state with no change in concentration
after about 60 days. The final concentrations are a sum of all the initial amounts found in all
compartments. Thus, this first simulation can be used to check the consistency of the model and that
the numerical solution scheme does not create numerical instabilities and `leak' nutrients. There are
several numerical methods (and variable time steps) that can be used in STELLA in order to ensure
numerical stability.
In the second simulation, a check that the formulation of water exchange is consistent is carried out:
exchange_of_DIN=water_exchange*(DIN-Sea_DIN_conc)
Here the water exchange is changed from 0 to 1.2 % per day, in steps of 0.2 %. This is a kind of
sensitivity analysis that shows that even very small variations are critical. These runs also confirm
that the formulation of water exchange has the desired effect (Figure 38).
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1-23: DIN
15.00
C
o
n
c
e
n
t
7.50
r
a
t
I
o
n
0.00 0.00
91
182
273
365
Days
Figure 38. Variations with time in concentration of dissolved inorganic nitrogen, DIN, with different
levels of water exchange, from 0 to 1.2 % per day. The straight line shows the
concentration when there is no water exchange. The curves with decreasing concentration
result from simulations where the external concentration is zero, the increasing
concentrations result from simulations where the external concentration is set to 15 µM. In
this sensitivity analysis the concentrations are not affected by processes other than water
exchange (DINinput, Assimilation, DIN release are all set to zero).
By successively changing various parameters, continued checks can be made on the ability of the
model to produce results that compare favourably with available data and understanding. This
sensitivity analysis is presented only as an example of the methodology as the number of
perturbations on even this simple model are too numerous to present in these guidelines.
In the "final" simulation, the original model formulation and rates are used (Text Box 5) with the
exception that there is a daily DIN input of 0.1 µM. The model is then run until a steady state with a
varying water exchange state is reached, here expressed in water residence time. From each of
these simulations, the net export of nitrogen (DIN+PON) as percentage of nitrogen inputs per day is
calculated when the system has reached steady state (Figure 39).
100
80
60
40
20
% export of input
0
0
50
100
150
200
Residence time, days
Figure 39. The percentage of inputs that are exported from the bay when the water residence time is
changed.
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With very short residence times, on the order of a few weeks, most of the nitrogen that enters the bay
will be immediately exported. With longer residence times less nitrogen is exported. In the model this
is apparently caused by an increasing importance of the internal losses, primarily through
denitrification. A decreased water exchange means that inorganic nutrients will cycle through the four
compartments of the system several times. For each time a nitrogen unit passes through the
sediment DIN pool, there is a likelihood (10%) that it will be lost through denitrification. More
recycling means that more is lost through this process. This simple model thus demonstrates the
importance of considering the interactions between physics and biogeochemistry.
Model simulations can often be useful in the initial phase of a research programme before actual
measurements are made. Although not all data are yet available, there is usually enough information
to scale the system in terms of its physical dimensions and the concentrations of the state variables
to be initially considered, as demonstrated in the example above. Literature information can often be
used to formulate and scale initial processes. The scientists involved in the project can then use the
model to test the importance of various processes and interactions. For instance, will the outputs
change if the rate of denitrification is not constant but changes in relation to sedimentation of organic
mater? Is it important to consider the "microbial loop" and nutrient recycling in the water column? Will
the importance of internal losses versus exports change with increasing nutrient loads?
The modelling of dynamic systems on the computer has, with software like STELLA, become a real
possibility for ecologists. A significant preparation in mathematics and programming was needed
earlier to develop even a simple model like the example used here. This prevented many coastal and
marine scientists from utilising modelling as a tool to formally describe and test hypotheses on the
structure and functioning of the world around us.
In summary, modelling is an essential tool in the analysis and hypothesis testing of coastal and
marine ecosystems. It is however, essential to remember that numerical simulation is only a tool,
however powerful, and not a goal in itself. Some basic advice on how to best use this tool is
summarised Text Box 6.
Define objectives and goals for the simulation model. What are the problems to be study? If
the system is complex, define subsystems and partial goals. Should the model be descriptive
or predictive?

Define spatial and temporal resolution for the model. What should be inside the model, what
should be external?

Define the state variables; as few as possible. Determine what units are going to be used.

Describe the important flows in the system and those processes that control them. Define
units and temporal resolution.

Ensure that the model is consistent in term of units, conservation of mass, etc.

Discuss how the model should reflect the real world situation before the simulation is carried
out. Select a time period, check the integration method. Run the model.

Carry out sensitivity analyses using different parameters and different values.

Compare the model results with field and experimental data.

Document each step.
Text Box 6. Basic advice for carrying out general system modelling.
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7. MEETING THE GLOBAL BIOGEOCHEMICAL MODELLING OBJECTIVES OF LOICZ
It is anticipated that biogeochemical models of different parts of the world's coastal zone will be
developed under LOICZ as part of national and regional programmes by following the guidelines
outlined in this document. These guidelines recommend that at a minimum the new applications
models should initially focus on mass balance budget models of carbon, nitrogen and phosphorus.
However, as described earlier in this report, there is also the need in some situations to develop
system models which can be used to increase understanding of the internal dynamics of the key
environmental processes that control biogeochemical fluxes.
Since most model development under LOICZ is expected to be supported primarily at the national or
regional level, the spatial extent will probably be relatively small in order to address important local
management issues. The majority will presumably describe specific nearshore habitats (such as
mangrove systems, seagrass beds, coral reefs, etc.) or particular estuaries and coastal embayments.
Hopefully a number of studies will also describe relatively large areas of the continental shelf such as
the North Sea and East China Sea.
In order to meet the long term, global objectives of LOICZ, it is essential to scale-up or compile the
results of these local and regional models into global coastal zone models. This important activity,
which marks the culmination of the LOICZ modelling strategy, Text Box 1, will be undertaken as a
framework activity and a proposed programme of activities is outlined in the Implementation Plan
(Pernetta and Milliman, 1995).
It is intended that budgets developed at the local and regional levels will be integrated into global
estimates of fluxes and that local and regional system simulation models will be coupled to global
atmosphere/ocean models. Both of these activities will require the coupling of models with relatively
small scale, short term processes into models of large scale, longer term processes. The task of
developing improved methods for assimilating fine scale models into large scale models and the task
of developing global models of biogeochemical processes will be developed in conjunction with these
guidelines and the results that they produce. The first step is the establishment of a limited number of
common questions that can be addressed by comparable model outputs.
If there are good estimates of carbon, nitrogen and phosphorus fluxes to and from each type of
coastal system identified in the LOICZ typology exercise, and estimates of the proportion of each
type in each climatic zone are available, it would be a fairly straightforward matter to derive better
estimates of global fluxes by weighted summation. It should be noted that integration of the fluxes
from small units, such as the individual salt marshes or seagrass beds within an estuary can be
achieved by constructing the budget model for the estuary as a whole rather than for its component
parts. At the same time such an approach loses information on specific habitats of local interest.
Scaling up system simulation models will be a much more difficult endeavour because of numerous
problems. Even within a single model, there are problems with the coupling of processes on very
different time scales. For example, a model that has time steps short enough to represent the growth
of bacterial populations on a scale of hours cannot readily accommodate parameters of fish
populations that vary on a time scale of years. In general, longer time scales integrate variations on
shorter time scales. Day-to-day fluctuations in the biomass of phytoplankton can be integrated into
the rates of growth and reproduction of zooplankton that feed on the phytoplankton, but the details of
the phytoplankton changes will not be represented. Similarly, week-by-week fluctuations in
zooplankton populations can be integrated into the parameters of planktivorous fish populations.
The question of scale is also important in coupling physical oceanographic and biological processes.
Large scale turbulence is progressively degraded into smaller and smaller scales of turbulence, but it
is not possible to predict the properties of the large scale process by observing the smaller scales.
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The many problems associated with the scaling up of models were discussed at length in a recent
symposium of the British Ecological Society held jointly with the American Society for Limnology and
Oceanography (Giller et al., 1994). Although the problems were raised and discussed, no clear
solutions emerged. Apparently, the standard application of predictive models that can adequately
address scale, pattern, and hierarchies will not be available for some time. The latest ideas on this
subject are explored in Pahl-Wostl (1993a, b). Hofmann (1991) Also has considered the
generalisation of coastal models to the global scale.
From the point of view of developing the global scale estimates required by LOICZ, it is necessary to
select appropriate geographic units for analysis as illustrated by the following three examples from
the scientific literature.
Nixon et al. (in press) have used a budgetary approach to examine the fate of nitrogen and
phosphorus at the land-sea margin of the entire the North Atlantic. They estimate that estuarine
processes retain and remove 30-65% of the total nitrogen and 10-55% of the total phosphorus that
would otherwise pass into the coastal ocean. The major process removing nitrogen is denitrification
and the amount lost appears to be proportional to the residence time of water. This study is a good
example of the kind of methodology that might be used to scaling-up from local to regional
summaries. It is hoped that this analysis for the North Atlantic can be refined with compilation and
inclusion of additional regional information and that the application of this kind of approach to other
oceans of the world for inter-comparison can be used in arriving at global models.
Ver et al. (1994) have developed a global biogeochemical model which has been used to evaluate
coupled CNP cycles in the coastal zone and how they can be affected by terrestrial processes. Model
results show that the coastal zone is extremely sensitive to changes in the dissolved and particulate
organic matter loadings from the land delivered by rivers. In a global warming scenario with
enhanced terrestrial denitrification, the coastal zone is predicted to become more autotrophic relative
to its current heterotrophic state. In a cooling scenario, with decreased terrestrial denitrification, the
coastal zone becomes more heterotrophic. Model output clearly indicates that the trophic status of
the coastal zone is governed principally by the flux of organic matter from the land and that the
coastal zone must be viewed as a separate entity in considerations of global change.
Smith and Hollibaugh (1993) have examined the role of the coastal ocean in the global oceanic
carbon budget. Analysis of data from various sources on long-term rates of river loading of organic
carbon, organic burial, chemical reactivity of land-derived organic matter and rates of community
metabolism led them to conclude that the ocean as a whole is a net source of CO2 release to the
atmosphere. Their analysis suggests that about 30% of this net oceanic oxidation takes place in the
coastal zone despite its relatively small area. Oxidation in the coastal zone takes on particular
importance in the context of LOICZ and the IGBP because input rates are likely to be altered by
human activities on land.
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8. ACKNOWLEDGEMENTS
The authors wish to thank the large number of people who contributed ideas, support and
encouragement to the development of this document. In particular, the authors wish to thank Dr. P.
Ruardij, Dr. S. Ibarra-Obando, and Dr. K. Webb, as well as the participants of the
SARCS/WOTRO/LOICZ Workshop on Biogeochemical Modelling, for their comments and
suggestions during the development of these guidelines. The major portion of writting was conducted
during the Canadian workshop in September 1995 which was ably assisted by Ms. Kora Pfinder, Ms.
Lousie Foley and Ms. Heather Gordon. Throughout the development of these guidelines, the Core
Project Office of LOICZ provided leadership, administrative support and financial resources.
Additionally, Dr. John C. Pernetta, Core Project Director, has kindly provided editorial assistance.
The authors would like to acknowledge their use of unpublished manuscripts by Haidvogel and
Beckmann (submitted) and Nixon et al. (in press). The case studies on Tomales Bay have used data
collected by the National Science Foundation-Land Margins Ecosystem Research Program.
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9. REFERENCES
Anderson, L.A. 1995. On the hydrogen and oxygen content of marine phytoplankton. Deep Sea
Research. 43: 1675-1680.
Atkinson, M.J. and S.V. Smith. 1983. C:N:P ratios of benthic marine plants. Limnology and
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ANNEX 1 REVIEW OF SELECTED MODELLING SOFTWARE PACKAGES
The following list of modelling software packages was prepared at the request of the LOICZ
community. It is by no means exhaustive. The purpose is to merely provide an introduction to some
of the software packages that are currently available. The focus is on general modelling packages
that can be used to build system process models, not the models themselves. They are listed in
alphabetical order.
BSIM
BSIM is a software package designed to help develop ecosystem models. It is based on the idea that
it is relatively easy to translate scientific concepts into a computer simulation model if you don't have
to worry about the technical details that programming entails. The BSIM package is intended to
handle all of the hard parts of programming and let the users focus on translating their ideas into
quantitative expressions that a computer can deal with. BSIM is available for virtually any computer
which has a FORTRAN-77 compiler. It currently runs on microcomputers (both MS-DOS and
Macintosh) as well as UNIX systems and mainframes. BSIM is copyrighted by the Government of
Canada but is available free of charge. Further information and the software can be obtained from:
Dr. William Silvert
Department of Fisheries and Oceans
Bedford Institute of Oceanography
P.O. Box 1006
Dartmouth, N.S.
B2Y 4A2
CANADA
E-Mail: silvert@biome.bio.ns.ca
ECOS Version 2
ECOS is a software package designed to run water quality simulations of estuaries on a PC which
was developed at the Plymouth Marine Laboratory in consultation with the UK National Rivers
Authority. Special features include rapid simulations, versatile process specification, particle-water
partitioning, particulate transport, sediment transport, contaminant degradation, atmospheric
exchange, multiple interacting contaminants, contaminant transformations, tidal or tidally-averaged
simulations, enhanced graphics, enhanced function handling, on screen data comparisons and
spread-sheet compatible output. Current price is 560 pounds Sterling (excluding VAT) but discounts
are available for academic and multiple purchases. Site licenses and network versions are available.
For further information or a free demonstration disk, contact:
Plymsolve
Plymouth Marine Laboratory
Prospect Place
Plymouth PL1 3DH
UNITED KINGDOM
Phone: (01752)222772
Fax: (01752)670637
MATLAB
The name MATLAB stands for matrix laboratory. MATLAB is a technical computing environment for
high-performance numeric computation and visualisation. It integrates numerical analysis, matrix
computation, signal processing and graphics into an easy-to-use environment where problems and
solutions are expressed just as they are written mathematically without traditional programming. It is
an interactive system whose basic data element is a matrix that does not require dimensioning.
MATLAB has evolved over a period of years with input from many users. Typical uses include
general purpose numeric computation, algorithm prototyping and special purpose problem solving
with matrix formulations that arise in disciplines such as automatic control theory, statistics and
digital signal processing (time-series analysis). It also features a family of application-specific
solutions called toolboxes which are available for signal processing, control systems design, dynamic
systems simulation, systems identification and others.
For further information, contact:
E-Mail: info@mathworks.com
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ModelMaker
ModelMaker is a modelling software package developed for PC's running Windows. In-depth
mathematical and programming skills are not necessary to assemble and analyse models. Models
are constructed conceptually using a diagram which shows how the various elements are interrelated.
The model diagram gives an overall view of the model and provides constant feedback about it. The
model equations are instantly accessible so there is no need to search through computer code of find
key relationships. For further information, contact:
Cherwell Scientific Publishing, Inc.
744 San Antonio Road
Suite 27A
Palo Alto, CA 94303
United States
E-Mail: modelmaker.usa@cherwell.com
http://www.cherwell.com/cherwell
Network Analysis Software
This software is designed to analyse the structure of marine foodwebs. Unlike the above software
packages, it can not be used to developed simulation models. Full details are provided by Wulff et al.
(1989). To obtain a diskette containing the software for these techniques (for IBM or compatible
computers on a MS-DOS 360 KB diskette, for a Macintosh computer on a 3.5" diskette) send a
money order or bank draft for US $10.00 payable to SCOR requesting the network analysis software
to:
Executive Secretary, SCOR
Department of Earth and Planetary Sciences
John's Hopkins University
Baltimore, Maryland 21218
United States
E-mail: scor@jhu.edu
SENECA Version 1.2
SENECA is an ecological modelling package developed by the Dutch Delta Institute for
Hydrobiological Research. Like BSIM, it is user friendly and is designed to perform most of the
routine tasks automatically. Models built using SENECA can be easily manipulated, even by people
without programming experience. Values of parameters and forcing functions can be adjusted in
menus and source files of process formulations can be easily edited. Little learning time is required to
work with SENECA. SENECA has been developed in FORTRAN 77 and runs on PC's with MS-DOS.
It is available at the cost of Dfl 150 to users who are willing to share the modelling experience. The
licence fee includes Version 1.2 and one update. For information and orders, contact:
Delta Institute for Hydrobiological Research
Department of Modelling and Statistics
Vierstraat 28
4401 EA Yerseke
The Netherlands
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SESAME
SESAME stands for Software Environment for the Simulation and Analysis of Marine Ecosystems. It
is an ecological modelling package developed and used by the European Regional Seas Ecological
Modelling (ERSEM) Project. The software implementing the OpenSESAME Modelling Environment
has been developed to run on most UNIX systems, either SYSTEM V or BSD compliant, and is
written in (standard) C. The software enables the development of large and complex models in a
modular way by a number of different researchers.
The user communicates with OpenSESAME through a graphical user interface based on Sun
OpenWindows Version 3.x or through an ASCII interface if there are no graphics capabilities
available. The graphical user interface allows the user to perform many actions by using the point-
and-click method. Full details are provided in a recent publication Ruardij et al. (1995). For more
information, contact:
Dr. P. Ruardij
Netherlands Institute for Sea Research
P.O. Box 59
1790 AB Den Burg , Texel
The Netherlands
Phone: (31) 0222 3 69300
E-Mail: rua@nioz.nl
STELLA
STELLA is a multi-level hierarchical environment for constructing and interacting with a model. It was
originally developed for Macintosh computers but is now available for the Windows graphical
environment as well. It is highly graphically oriented. The user usually starts by drawing a diagram of
the system, using a simple symbol language describing state variables, processes and flows. One
then continues to define the numerical values for rate constants, initial conditions, etc. The functional
relationships that drive the model can be described either by mathematical equations or graphically
by drawing curves. The differential equations that actually constitute the model in mathematical
terms are generated by the software without the user having to write a single line of code. The user
can also interact with the mathematics of the model, select integration methods, time steps etc. if
desired. Although models can be built up hierarchically with submodels in different levels, STELLA is
not meant for highly complex systems, particularly highly resolved 2D or 3D systems.
STELLA is an excellent teaching tool for systems thinking and for the development of models. The
graphical environment helps the user to concentrate on model formulation. It is easy to learn and less
intimidating to students that have limited experience in mathematics and programming. But it is also
very useful for the professional scientist in developing models and should be an excellent tool for
many of the models that have to be developed in the LOICZ context.
The Macintosh (System 7) version allows a flexible data exchange between the model (inputs or
outputs) and other programs or files on the computer. A new version, STELLA 4, has just been
released with the same features for both Macintosh and Windows computers. There is also a `Stella
Research 4.0' version available that makes it possible to use arrays for models of greater structural
complexity than in earlier versions.
STELLA 4 is available for a price of approximately 500 US $ from:
High Performance Systems Inc.
43 Lyme Road, Suit 300
Hannover , NH 03755
United States
Phone: 603-643-9636
Fax 603-643-9502
E-Mail: support@hps-inc.com
WWW Site: http://www.hps-inc.com
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