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Estuarine Eutrophication Models

Final Report Project E6 National River Health Program
Water Services Association of Australia Melbourne Australia
John Parslow, John Hunter, Adam Davidson.
CSIRO Marine Research. Hobart, Tasmania

Foreword

This report describes the outcomes of a research project conducted under the Urban Research and Development sub-program of the National River Health Program (NRHP).

The NRHP is an on-going national program established in 1993, managed by the Land and Water Resources Research and Development Corporation (LWRRDC) and Environment Australia. Its mission is to improve the management of Australia's rivers and floodplains for their long-term health and ecological sustainability, through the following goals:

Urban streams and estuaries (i.e. those affected by runoff and discharges from urban areas) are an important subset of Australia's waterways. Most are degraded biologically, physically and chemically and therefore require appropriate methods to be developed for health assessment and management. The Urban R&D Sub-program, managed by the Water Services Association of Australia, comprises 8 research projects which were developed to meet research priorities for urban streams and estuaries within the goals of the NRHP and to complement existing NRHP projects on non-urban rivers. Thus, research focuses on development of standardised methods for assessing the ecological health of urban streams and estuaries which can be linked with data on water and sediment quality. The urban R&D projects commenced in 1996.

The definition of health in urban waterways used is "the ability to support and maintain a balanced, integrative, adaptive community of organisms having a species composition, diversity and functional organisation as comparable as practicable to that of natural habitats of the region".

The eight projects of the Urban Sub-Program are:

Decision support system for management of urban streams	Dr John Anderson Southern Cross University, Lismore
RIVPACS (River InVertebrate Prediction and Classification System) for urban streams	Dr Peter Breen CRC for Freshwater Ecology, Monash University, Melbourne
DIPACS (Diatom Prediction and Classification System) for urban streams	Dr Jacob John Curtin University, Perth
Sediment chemistry- macroinvertebrate fauna relationships in urban streams	Dr Nick O'Connor Water EcoScience, Melbourne
Classification of estuaries	Dr Peter Saenger Southern Cross University,Lismore
Literature review of ecological health assessment in estuaries	Mr David Deeley Murdoch University, Perth
Estuarine health assessment using benthic macrofauna	Dr Gary Poore Museum of Victoria, Melbourne
Estuarine eutrophication models	Dr John Parslow CSIRO Marine Laboratories, Hobart

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Published Electronically on au.riversinfo.org by the Environmental Information Association (Incorporated) with the permission of LWRRDC and Environment Australia. Environment Australia assisted by providing copies of the manuscript for electronic publication. The Natural Heritage Trust provided project funds which were used to assist in publishing this material. In the case of variation between this document and the hard copy original the original takes precedence. (Bryan Hall).

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Publication data:
Estuarine Eutrophication Models Final Report Project E6 National River Health Program Water Services Association of Australia Melbourne Australia John Parslow, John Hunter, Adam Davidson. CSIRO Marine Research. Hobart, Tasmania
Report No 12, LWRRDC Occasional Paper 19/99.

Executive Summary

Increased human development in the coastal zone leads to increased nutrient loads to estuaries and coastal waters both through changes in catchments and river runoff, and point source discharges to estuaries. Eutrophication (ie the response of ecosystems to these increased nutrient inputs) is recognised as a major environmental problem, both nationally and internationally.

This study has been undertaken "to develop and demonstrate a widely applicable model of eutrophication processes in urban estuaries which can predict the potential for phytoplankton blooms and bloom type on the basis of environmental data". Existing estuarine eutrophication models range from simple load-response relationships to complex "realistic" process-based simulation models. After reviewing these models in Sections 1 to 3, we focus on the development of relatively simple process-based models, which incorporate the core variables and processes controlling the cycling of nutrients and bloom development in estuaries. Models of this kind offer advantages over load-response models in dealing with the wide range of physical environmental conditions in estuaries, and offer advantages over more complex models in reduced data requirements, lower implementation costs, and amenability to analysis and understanding.

The core state variable description used here describes nitrogen cycling and algal biomass in terms of 4 pools: phytoplankton N, dissolved inorganic N (DIN), labile organic N and refractory organic N. The core processes include phytoplankton uptake and growth (dependent on light and nutrient levels), phytoplankton mortality, production and breakdown of labile and refractory organic N, and sediment respiration and denitrification. This core biogeochemical process model is implemented in two physical contexts: a steady-state one-box model, and a dynamical spatially-resolved model.

We present an analysis of the behaviour of the one-box steady-state model in response to changes in external loads, and compare this with simple load-response models developed for lakes. By analogy with the load-response models, the model defines two kinds of relationships involving total nitrogen (TN):

The relationship between TN load and TN pool in estuaries is controlled by a combination of physical exchange with the ocean, and the magnitude of internal sinks. In the absence of an internal sink, the steady-state TN pool is equal to load multiplied by flushing time. In the models discussed here, the principal internal sink for nitrogen is denitrification. In estuaries with long flushing times (order 100 days), denitrification may account for more than 80% of the nitrogen load, and maintain the estuary in a mesotrophic condition under loads which, in the absence of denitrification, would create eutrophic blooms. In estuaries with short flushing times, of order 10 days, export dominates over denitrification, and there is no critical transition in water quality with increasing load.

In estuaries with long flushing times, increases in loads lead to increases in the production and remineralization of organic matter in both water column and sediment. Sufficient increases in load and sediment respiration rates can shut down sediment denitrification (Murray and Parslow, 1997), leading to a "catastrophic" transition from mesotrophic to eutrophic status. Results from Port Phillip Bay suggest a critical nitrogen load (denitrification capacity) of about 30 mg N m^-2 d^-1. Coastal lagoons with restricted or intermittently open entrances are likely to be especially vulnerable to denitrification failure.

Phytoplankton utilisation of DIN is controlled by light attenuation and depth. In estuaries with low background attenuation, increasing loads of DIN will lead to increased phytoplankton biomass, until phytoplankton biomass is limited due to self-shading at high levels (order 20 to 50 mg Chl a m^-3). Further increases in load result in accumulation of DIN. In deep estuaries which have high light attenuation due either to suspended solids or gelbstoff, light limitation can limit maximum phytoplankton biomass to quite low levels (order 2 to 5 mg Chl a m^-3), and excess DIN will accumulate even at low loads.

Most estuaries contain high levels of refractory organic N derived both from the catchment and from exchange with coastal marine waters. At low to moderate loads of available N (oligotrophic to mesotrophic conditions), this refractory N dominates the TN pool and mass balance in estuaries.

For many estuaries with long-estuary salinity gradients, the one-box model with its single flushing time is simply not valid, and a spatially-resolved model is required. In this study, we use a spatially resolved model (the Simple Estuarine Eutrophication Model, or SEEM) based upon an n-layer hybrid inverse model. This approach can be regarded as an extension of more traditional methods which use the salinity distribution to infer flushing rates.

A key limitation of the inverse model is the assumption of steady-state flow and exchanges. This is reasonable provided river flow changes on time scales which are not too short compared with flushing times. Many Australian estuaries are subject to long periods of low flow, with intermittent flood events. The steady-state assumption works quite well during the low-flow periods, but is likely to fail during brief flood events. In those urban estuaries where point source loads are the major cause of eutrophication, water quality problems are most apparent during low-flow periods. Where diffuse loads dominate, or the interaction between diffuse and point source loads is thought to be critical, more sophisticated dynamical models may be required.

The spatially resolved biogeochemical model has been applied at steady state to three test cases: the Derwent, Brunswick and Hardy estuaries. These represent contrasting physical environments in terms of morphology, runoff and stratification. The Derwent is a deep, strongly-stratified estuary, with high river runoff and high light limitation due to humics. The Brunswick is a shallow, tidally-dominated, turbid estuary, while Hardy Inlet represents a broad shallow lagoon connected to the sea by a deep channel. Both the Brunswick and Hardy receive very low river runoff for long periods.

Model and data analysis suggest that phytoplankton biomass in the Derwent is primarily light-limited, especially in winter, when DIN levels are high due both to point source loads and elevated nitrate concentrations on the adjacent continental shelf. In the Brunswick, point sources loads are dominant during periods of low river flow, while the Hardy receives diffuse catchment loads. Both the Brunswick and Hardy appear to operate as P-limited systems, and the N-limited model was successfully adapted as a P-limited model for these systems. While light attenuation coefficients are much higher in the Brunswick than in the Derwent, the Brunswick is much shallower and supports higher phytoplankton biomass.

The use of the inverse transport model allows us to budget total N and P, and to identify internal sinks of N or P which are not represented by the model. However, this is made more difficult by the presence in all three estuaries of high levels of organic N and P, presumably refractory, which tend to dominate the mass balance, especially in the case of N. The problem is that internal sinks may be an appreciable part of the "available" N budget, but a small part of the total N budget.

Model experiments with the Derwent and Brunswick test cases highlight the importance of the location of point source discharges within the estuary. Effective flushing rates can vary by more than an order of magnitude along estuary. In the case of the Derwent, shifting an outfall by 10 km in the mid-estuary has a major impact on resulting water quality. In strongly stratified salt-wedge estuaries, the two-layer circulation, combined with sinking of detritus, can act to trap nutrients in the estuary, and discharging effluent into bottom waters can greatly increase residence time and water quality impacts.

The SEEM model has been calibrated using test case data collected on more or less "routine" environmental surveys. These surveys comprised from 5 to 20 stations, sufficient to resolve the long-estuary salinity gradient. Samples were taken in top and bottom layers in stratified estuaries. The minimum standard water quality measurements required by the model are Chl a, DIN, DIP, organic N (TKN), organic P and secchi depth. The model requires river flow and diffuse and point source loads (as DIN, organic N, DIP, organic P) at the time of surveys. The model calibration and analysis underscores the need to develop operational methods to distinguish labile and refractory organic N and P in field surveys.

The SEEM model has been developed in JAVA, with a graphical user interface providing run management and graphical displays of output results. It has been designed so that implementation and application to new estuaries can be undertaken quickly. It is our intention to apply it to a broad range of test cases as data become available.

A high priority for further development is the implementation of a robust statistically rigorous parameter estimation framework around the model. Bayesian techniques, such as the Monte Carlo Markov Chain method, would allow the user to establish prior probability distributions for the parameters, and characterise their joint posterior probability distribution. These methods can be used not only to quantify the uncertainty in management predictions, but also to quantitatively assess the information content provided by alternative field measurement programs.

Acknowledgements

This study was supported by the Water Services Association of Australia, under the National River Health Program. The authors gratefully acknowledge Christine Coughanowr, Bradley Eyre and David Deeley who provided test data sets. The authors would also like to acknowledge the valuable contributions of Graham Harris, Sandy Murray, Peter Thompson, Sue Blackburn and Stephen Walker through collaboration and discussion.

1. Introduction

The term eutrophication is used generally to refer to the response of ecosystems to increases in nutrient loads. In many natural systems, primary production and community biomass and composition are thought to be limited or controlled by rates of nutrient supply. Systems which are severely nutrient limited are described as oligotrophic. As nutrient supply increases, systems are successively described as mesotrophic, eutrophic and hypertrophic. A quantitative definition of these classes in terms of areal rates of primary production has been proposed by Nixon (1995). Gray (1992) provides a description of the effects or symptoms of marine eutrophication as evident in macroalgae, phytoplankton, benthic communities and fish. Gray argues that small increases in nutrient supply can result in an increase in production without serious modification of community composition (the enrichment phase), but further increases in nutrient loads result in more serious impacts on water and sediment quality and community composition and function, leading ultimately to anoxia and loss of most taxa.

It should be emphasized that natural marine systems cover the span from oligotrophic (eg the subtropical gyres and coastal seas) to mesotrophic (temperate coastal waters) to eutrophic (upwelling systems). Natural processes can also produce increases in nutrient loads on a range of time scales. However, eutrophication is widely used to refer to the effects of anthropogenic increases in nutrient loads. In this sense, eutrophication is widely recognised as one of the most important environmental issues for coastal marine systems, both internationally (eg GESAMP, 1990, Richardson and Jorgensen, 1996) and nationally.

It is hardly surprising that eutrophication is an important environmental issue. Both in Australia and internationally, human population growth and development is concentrated in the coastal zone, and has led directly to large increases in nutrient loads into estuaries, coastal embayments and coastal seas. These loads occur at population centres through direct point source inputs (eg from wastewater treatment plants and industrial outfalls). They also occur as increased diffuse catchment loads resulting from widespread modification of catchments, and intensive agricultural development and use of fertilizers.

Environmental managers dealing with eutrophication are faced with difficult choices. Reducing wastewater nutrient loads from large cities can require infrastructure investment amounting to many hundreds of millions of dollars. Reductions in loads from catchments may require extensive changes to land use practices, and/or investment in infrastructure (eg development of artificial wetlands) in streams, with uncertain outcomes. These financial and opportunity costs are ultimately borne by the general community, or particular sectors of the community.

Management decisions should be based on appropriate information. Managers require an assessment of the current state of the ecosystem, and how this has changed over time. Where there is evidence of unacceptable environmental impact, managers need an attribution of cause and effect. Is degradation caused by nutrient loads, and if so, is it due to specific point source or diffuse loads? Perhaps most importantly, managers need predictions about the likely response of the ecosystem to alternative management actions, including increasing or decreasing nutrient loads from specific sources. Predictions of this kind can be incorporated into informal or formal decision analysis procedures, addressing tradeoffs between environmental and other values or costs (Holling, 1978).

The predictions needed by managers are all based on models, in the broad sense of the term. These may be simple heuristic models, based on accumulated experience, or complex process-based simulation models. In fact, scientific understanding and modelling of eutrophication are arguably well-developed, compared with other marine ecological issues. Eutrophication is an important and obvious environmental problem, and has attracted much applied research. More generally, marine biogeochemistry has been a major focus of scientific research, and this attention has increased recently due to concern about global biogeochemical cycles, and the carbon cycle in particular (Evans and Fasham, 1993; Gordon et al, 1996). Some of the key processes in eutrophication (eg nutrient and light limitation of phytoplankton growth) are among the best studied and understood of ecological processes (eg Falkowski and Woodhead, 1992) However, while eutrophication may be comparatively well-studied, there are still questions, gaps and surprises in eutrophication modelling and prediction.

Models of eutrophication can be divided roughly into two classes: simple load-response models, due to Vollenweider (1975) and subsequent authors, and process models, which address the underlying physical, chemical and biological processes.

The load-response models were originally developed and applied to phosphorus limitation in temperate northern hemisphere lakes (Vollenweider, 1975; Schindler, 1978). While these are often referred to as empirical models, they are, as we discuss in Chapter 2, based on an elegant and careful abstraction of a few key processes. It is generally agreed that understanding and prediction of eutrophication is better for lakes than for estuaries, partly because limnologists have the advantage of many more replicate studies. Even so, attempts to extend the load-response models to a wider variety of lakes have encountered significant problems (eg Smith and Shapiro, 1981). There have also been attempts to extend this approach to estuaries (Monbet, 1992). In general, estuaries are more complex than lakes, both physically and biogeochemically, and it is not at all clear that the approximations implicit in the load response models are appropriate.

Over the last decade or so, the rapid increase in computing power, combined with increased process understanding, has seen an explosion in the development of process-based models of nutrient cycling and eutrophication in estuaries and coastal waters. International research programs such as JGOFS and LOICZ have also contributed strongly to model development (Evans and Fasham, 1993; Gordon et al, 1996). These process-based models generally have core processes and variables in common, but vary in detail. Some are based on high-resolution, realistic physical models, while others are based on simple 1-box or vertical column models. Some incorporate many trophic levels and large numbers of functional groups at each trophic level, while others deal only with nutrient and phytoplankton.

In Australia, the 1990s have seen a series of large studies of environmental impacts of nutrient loads in coastal waters in Perth, Sydney, Melbourne, Brisbane. Each of these studies has included a significant program of model development, and these models have contributed significantly to both scientific understanding and management decision-making. It is fair to say that scientific understanding is at a point where a substantial investment in eutrophication model development by competent scientists can be expected to yield useful results for managers.

That said, there are still compelling reasons to look carefully at the relationship between simple semi-empirical models and complex process models. Complex models still tend to be developed independently in individual studies, and modified to fit local interests and results. These models are often used to make predictions about the effects of changing loads outside the range of observed loads, and their reliability under these conditions is not well understood. More generally, it is not clear what level of model complexity yields the most accurate or reliable predictions for managers. It is generally thought that models with intermediate levels of complexity perform best, but there have been few studies which have attempted an objective assessment (eg Costanza and Sklar, 1985). Certainly, the number of parameters and computational load in complex realistic models have to date precluded formal approaches to parameter estimation and model identification, and model calibration has generally remained a heuristic process.

In the Port Phillip Bay Environmental Study, Murray and Parslow (1997) showed that simple process models derived by careful approximation can capture the key dynamical feedbacks in a complex simulation model, and contribute significantly both to parameter estimation and system understanding. Such simplified models offer the potential for application of new sophisticated statistical approaches to parameter estimation (eg Harmon and Challenor, 1997).

Finally, while the major metropolitan centres may be able to afford significant investments in large environmental studies and associated model development, smaller regional centres must deal with significant eutrophication problems with smaller resources. There is an important role for simpler models which can be implemented quickly, with minimal data requirements, to provide useful management support. The cost of the field surveys and process studies needed to calibrate complex models may represent more of a constraint than model implementation itself, especially as improvements in support tools and user interfaces reduce the time and resources needed to implement more sophisticated models.

This study has focused on the development and analysis of simple robust models which can be used in situations where a large investment in surveys, process studies and model development is not practical. The formal objectives of the study have been "to develop and demonstrate a widely applicable model of eutrophication processes in urban estuaries which can predict the potential for phytoplankton blooms and bloom type on the basis of environmental data".

As Gray (1992) points out, the impacts of eutrophication extend well beyond phytoplankton to affect benthic communities and higher trophic levels. We can roughly separate impacts into changes in water and sediment quality (nutrient concentrations, phytoplankton biomass, turbidity, dissolved oxygen) and ecological impacts (benthic plants and fauna, plankton composition, fish communities). The former are well-addressed by biogeochemical models, while the latter are still primarily addressed qualitatively, using comparative studies.

This study deals with the biogeochemical aspects of eutrophication, and the prediction of phytoplankton biomass in particular. We address the issue of bloom composition qualitatively in Chapter 7, but the report does not attempt to address the problem of setting water quality criteria to protect particular ecosystems or communities.

The report is structured as follows. Chapter 2 briefly reviews the classical load-response models and their application to estuarine systems. Chapter 3 reviews process-based eutrophication models, and proposes a core biogeochemical description which forms the foundation of the simple models used here. Chapter 4 presents results obtained using the simplified biogeochemical model in a 1-box, steady-state framework, which allows direct comparison with the load-response models. Chapter 5 addresses physical transport in estuaries, and presents a simple robust inverse modelling approach to quantifying horizontal and vertical physical exchanges in estuaries. This is used as a basis for a spatially-resolved biogeochemical model, and Chapter 6 presents a set of case study applications of the spatially-resolved model. Chapter 7 discusses the prediction of algal bloom composition, and its implications for eutrophication modelling. Chapter 8 provides a general discussion and conclusions. Detailed documentation of the spatially-resolved model is presented in a separate publication (Parslow et al, 1999).

2. Load-Response Models

Load-response models were originally developed by Vollenweider (1975), Schindler (1978) and others to describe temperate northern hemisphere lakes. They are designed to predict mean chlorophyll levels from phosphorus load. They include empirical constants, and have the advantage of having been calibrated against a large number of lakes encompassing a wide range of nutrient loads and chlorophyll concentrations. However, these are not simply black box empirical models.

These models treat lakes as well-mixed boxes, with a flushing time t defined by the ratio of the lake volume V (m³) to the volume flux through the lake, R (m³ d^-1). The flushing rate r = R/V (d^-1) is just the inverse of t . If we consider a conservative tracer with concentration M, the load L_M into the lake must be balanced by the export from the lake, R.M:

L_M = R.M.

2.1

If L_M = L_M/V is the load per unit volume, then it follows that:

L_M = r.M.

2.2

The total phosphorus concentration in the lake, TP, might be expected to be approximately conservative. Phosphorus may be subject to a wide range of transformations within the water column (eg assimilation by phytoplankton into organic matter, consumption and remineralization by zooplankton and bacteria, adsorption onto inorganic suspended sediment), but these will not change TP. However, there is an internal sink S of TP within lakes due to burial of adsorbed P or organic P in the sediments. Mass balance then gives:

L_P = R.TP + S

2.3

In order to predict TP, we need to know how S is related to load or TP. Based on analysis of a large number of lakes, Vollenweider (1975) found that the sink S per unit area is proportional to TP, with a constant of proportionality which is independent of load, or lake geometry and flushing rate. This constant w has units of velocity, and is typically about 10 m y^-1. If A is lake area, we can then write:

L_P = R.TP + w .TP.A

2.4

TP = L_P/(R + w .A)

2.5

Even setting aside the empirically derived dependence of the internal sink on depth, this formula incorporates the mass-balance effects of load, lake volume and flushing time on total phosphorus concentration.

While TP is a logical choice for mass-balance, it is not necessarily a useful indicator of water quality. The model has been extended using a direct empirical relationship between chlorophyll a and TP. Early results showed that linear regressions of log chlorophyll on log TP explained about 90% of the variance in log chlorophyll (Dillon and Rigler, 1974; Schindler, 1978). (As both chlorophyll and TP in these plots spanned over 2 orders of magnitude, this does not necessarily mean that these regressions give precise chlorophyll estimates.) More recent analyses of data spanning a wider range of TP and chlorophyll have argued for a sigmoid relationship between log TP and log chlorophyll (Chow-Fraser et al, 1994).

Attempts to generalise on these early successes in temperate lakes by applying the models more broadly have met with mixed success. Both the prediction of TP from loads, and the prediction of chlorophyll from TP, have proven less straightforward in sub-tropical and tropical systems (Kaiser et al, 1994). The early results were obtained using annual average (or summer average) results from lakes with a very pronounced seasonal cycle in load, flushing and production. Australian lakes have highly intermittent loads, and much higher suspended sediment loads than Canadian lakes. It has also been suggested that nutrients other than phosphorus may be limiting at times (Harris, 1996), and statistical approaches to deal with this have been suggested (Kaiser et al, 1994).

There are a number of complications involved in applying the Vollenweider approach to estuaries (Harris, 1996). Estuaries are subject to flushing both through freshwater runoff and exchange with the ocean, and flushing rates cannot be simply calculated by dividing river flow by volume. (However, as discussed in Chapter 5, salt balance does allow effective flushing rates to be estimated simply.) Many estuaries have strong horizontal and vertical gradients, and treating these estuaries as simple well-mixed boxes may be quite inappropriate.

While limnologists have generally assumed that phosphorus is limiting in lakes, nitrogen is thought to be limiting in most marine systems. However, the situation in estuaries has been subject to considerable debate, and it is generally agreed that nitrogen, phosphorus and silicate can all be limiting at times in estuaries (Richardson and Jorgensen, 1996). (As noted above, this may also be true in freshwater systems see Harris, 1996.)

While the general mass balance principles underlying the Vollenweider models still apply in estuaries, it is not at all clear that the internal sink can be modelled in the same way. The principal sink for P in lakes may be adsorption to inorganic sediments, but marine sediments are known to be less effective at binding phosphate (Jorgensen, 1996). Where nitrogen is limiting, the principal internal sink may be denitrification rather than burial (Seitzinger, 1987, 1988, Harris et al 1996; Jorgensen, 1996). In undertaking mass balance for estuaries, it must be remembered that there is two-way exchange at the marine boundary, and coastal seawater contains a quite large concentration of total N, typically 50 to 100 mg N m^-3. Part of this represents a refractory background pool of oceanic DON. This marine contribution not only affects the mass balance of TN, but is likely to complicate any empirical relationship between TN and chlorophyll in the estuary. This is especially the case when the estuary is subject to large catchment loads of organic N which, depending on the state of the catchment, may be labile or refractory (Harris, 1996).

Monbet (1992) has assembled data on 40 estuaries, and found a convincing relationship between mean annual DIN and chlorophyll. However, this relationship is only apparent when the estuaries are divided into microtidal and macrotidal (< 2 m and > 2 m tidal amplitude respectively). His log-log plot suggests that chlorophyll a increases roughly in proportion to DIN, although the residual scatter is large, and spans a factor of ca 2 about the mean. The proportionality constant is approximately 1 mg Chl a (mM N)^-1 for macrotidal estuaries, and 10 mg Chl a (mM N)^-1 for microtidal estuaries. If we assume a C:Chla ratio of 40, and a Redfield C:N ratio, there should be ca 2 mg Chl a (mM phytoplankton N)^-1. This implies that (on an annual average basis) the phytoplankton N pool is about half the DIN pool in macrotidal estuaries, and 5 times the DIN pool in microtidal estuaries.

According to Monbet�s analysis, DIN is on average strongly utilized under conditions of weak tidal mixing, and only weakly utilized under conditions of strong tidal mixing. This is most likely due to the effects of increased vertical mixing on light availability to phytoplankton, either through increasing the mixed layer depth, or through an increase in suspended sediment and turbidity. This effect highlights the importance of turbidity and light attenuation in controlling utilization of nutrient (Harris, 1996), and raises the potential importance of sediment resuspension in controlling sediment nutrient fluxes and burial in estuaries.

Monbet�s analysis refers only to the relationship between DIN and chlorophyll, but DIN itself is likely to be a highly dynamic variable, not necessarily easily predicted from loads. In general, we would expect the proportion of TN present as DIN and phytoplankton N to increase, and the proportion present as refractory PON or DON to decrease, as systems become more eutrophic. In oligotrophic systems, the N load is dominated by inputs of refractory DON or PON from undisturbed catchments, and refractory DON from coastal waters. Loads from disturbed or agricultural catchments will contain increased amounts of DIN and labile organic N. Point source loads are generally dominated by DIN or labile organic N. In highly eutrophic systems, most of the TN load may consist of DIN, and a substantial fraction of this may remain unutilized due to light limitation.

In the course of this study, we have assembled 39 sets of observations of chlorophyll and nutrients in Australian estuaries and coastal embayments. DIN as a proportion of TN increases with increasing TN up to a maximum of 70% (Fig. 2.1), although the scatter also increases substantially at high TN. Phytoplankton N is less than 30% of total N, and as a percentage also appears to increase with TN, although again the scatter increases substantially at high TN (Fig 2.1). (Phytoplankton N is calculated assuming 2 mg Chl a (mM N)^-1) . Because the size and composition of N loads are not known for many of these estuaries, it is not possible to tell whether the large scatter in these ratios is driven by variability in composition of loads, or variation in nutrient cycling and phytoplankton dynamics between estuaries.

Fig. 2.1. DIN and Phytoplankton N as a fraction of Total N, plotted vs Total N, for observations drawn from a wide range of Australian estuaries.
(original size image)

3. Biogeochemical Process Models

Biogeochemical models describe nutrient cycling and system responses in terms of pools and fluxes of nutrient. The state of the system at any given time is described by a set of state variables specifying the amount or concentration of nutrient contained in a series of functional components in a set of spatial cells. The time rate of change of these state variables is specified in terms of the physical transport in and out of spatial cells, and the local sources and sinks associated with biological and chemical reactions. We focus on local reactions here, and deal with physical transport in Chapter 5.

In this chapter, and in the rest of this report, we deal primarily with N-based models of estuarine eutrophication, consistent with the view that marine systems are generally N-limited. We do address other limiting nutrients below, and in Chapter 6.

The basic step in model definition is the selection of state variables or functional components. There is a widely accepted core set of components for marine biogeochemical models, namely DIN, Phytoplankton, Zooplankton and Detritus. These form the basis of so-called NPZ or NPZD models (Fennel, 1995; Murray and Parslow, 1997; Parslow, 1997). As we discuss below, either zooplankton or detritus may be omitted depending on the application. More complex biogeochemical models (eg Murray and Parslow, 1997, Radford, 1993, Evans and Garcon, 1997) represent elaborations of this core description. We discuss the reasons for these elaborations, and the implications of omitting them, at the end of this chapter.

To avoid confusion with the use of P for phosphorous, etc, we use DIN, PHY, ZOO and DET to represent DIN, phytoplankton, zooplankton and detritus pools here. In the following subsection, we describe standard formulations of the key biogeochemical / ecological processes which control exchanges among these pools.

3.1 Phytoplankton Growth And Nutrient Uptake.

Phytoplankton growth is obviously a critical step in the nitrogen cycle, affecting both the fate of DIN loads, and the phytoplankton biomass response. It is also arguably the best understood process in eutrophication, supported by a long history of laboratory and field studies of phytoplankton physiology and ecology (eg Harris, 1986, Falkowski and Woodhead, 1992). The phytoplankton specific growth rate m (d^-1) is conventionally modelled as a maximum growth rate m max, reduced by dimensionless multiplicative factors for light and nutrient limitation:

m = m max.h_N.h_I.

3.1

Both h_N and h_I are typically formulated as saturating relationships eg the Monod relationship

h_N = DIN / (K_N + DIN)

3.2

where K_N is the half-saturation constant for N-limited growth, and

h_I = 1. � exp(-I/I_K)

3.3

where I_K is the light saturation intensity (Platt and Jassby, 1976). More complex physiological models of nutrient uptake and growth (eg Droop, 1983; Tett et al, 1986) and alternative models of light limitation (Steele 1962, Platt and Jassby, 1976 ) are also used.

The light intensity experienced by phytoplankton depends not only on the surface light intensity, I₀, but on the depth-distribution of phytoplankton, and light attenuation with depth. Light intensity at depth z is given by:

I = I₀.exp(-K.z)

3.4

where K is the diffuse attenuation coefficient (m^-1). (Where K varies with depth, K.z should be replaced by the depth integral of K from the surface to depth z.) In a well-mixed water column of depth H, the average light intensity <I> experienced by phytoplankton is given by:

<I> = I₀.(1 � exp(-K.H))/(K.H)

3.5

The attenuation coefficient K is a result of absorption and scattering by the water and optically active constituents such as inorganic sediment, detritus, coloured dissolved organic matter (CDOM) and phytoplankton chlorophyll. Their combined contributions can be approximated by a sum:

K = K₀ + k*_CHL.CHL + k*_DET.DET + k*_DON.DON + �

3.6

where K₀ is the background attenuation, and the k*_X represent specific attenuation coefficients for constituents X. It is important to account for the effect of phytoplankton and other model components on light attenuation, and therefore on phytoplankton growth, because this represents a critical feedback (self-shading) at high phytoplankton biomass, under eutrophic conditions (see Chapter 4).

3.2 Phytoplankton Loss Rates.

Phytoplankton biomass is lost as a result of grazing or other "natural" mortality, or through sinking and horizontal exchange. Phytoplankton biomass is determined by a balance between local growth and loss rates, so the prescription of loss rates is critical. There is much more uncertainty associated with the formulation of loss rates than growth rates.

In oligotrophic and mesotrophic conditions, loss rates are dominated by grazing. The NPZ models and their derivatives explicitly include zooplankton or other filter-feeders as dynamical state variables. These models then prescribe the phytoplankton consumption per unit zooplankton G as a function of phytoplankton biomass PHY (the so-called functional response). Commonly used formulations include a simple saturating response eg

G = Gmax.PHY / (K_P + PHY)

3.7

where Gmax is the maximum consumption rate, and K_P the half-saturation constant, and a response with reduced or zero clearance rates at low phytoplankton biomass eg

G = Gmax.(PHY � PHY₀) / (K_P + PHY � PHY₀)

3.8

where PHY₀ is a threshold below which grazing is zero. These are Holling Type II and TYPE III functional responses respectively (Holling, 1966).

An alternative approach is to omit the zooplankton state variable, and represent grazing losses along with other phytoplankton losses implicitly, as a specific phytoplankton mortality rate m_P. This mortality rate is often treated as a constant, but may vary with phytoplankton biomass PHY (see below).

3.3 Zooplankton Growth and Losses.

Where zooplankton are included explicitly, the phytoplankton consumption G is converted into a zooplankton growth rate by multiplying by a conversion efficiency E_Z (the gross growth efficiency). The growth efficiency allows for losses associated with messy feeding, assimilation, and respiration and excretion. Some models represent respiration separately as an explicit loss process.

As well as physiological losses, zooplankton biomass is also lost to predation and "natural mortality". Very few models choose to represent carnivores explicitly, and predation is represented implicitly as a specific mortality rate. This truncation of the trophic chain is known as "trophic closure", and represents a significant unresolved issue for biogeochemical models (Totterdell et al, 1993).

Many NPZ models represent predation by a constant specific zooplankton mortality rate. Others use a specific mortality rate proportional to zooplankton biomass (total losses are then proportional to biomass squared and this is often referred to as quadratic mortality). Steele (1976), Steele and Henderson (1992) and Murray and Parslow (1997) have shown that the specification of zooplankton mortality rate has a profound effect on the stability and qualitative behaviour of NPZ models, and have argued that the quadratic formulation gives more realistic behaviour.

For a given functional response, G(PHY), and quadratic zooplankton mortality rate m_Q.ZOO, the rate of change of zooplankton is given by:

d ZOO / dt = E_Z.G(PHY).ZOO � m_Q.ZOO²

3.9

and the steady-state specific mortality rate exerted by zooplankton grazing on phytoplankton is then given by

m_P(PHY) = (E_Z/m_Q).G(PHY)²/PHY

3.11

For example, if G(PHY) = Gmax.PHY/(K_P + PHY), then

m_P(PHY) = (E_Z/m_Q).Gmax².PHY/(K_P + PHY)²

3.12

The increase in zooplankton biomass with increasing phytoplankton biomass is referred to as the numerical response. The expression given for m_P(PHY) incorporates both the zooplankton functional and numerical response. We can use this expression to provide a more realistic formulation for m_P in models where zooplankton are not represented explicitly. When used in a dynamical model, it is only an approximation, as it does not allow for the lags involved in the zooplankton numerical response to changes in phytoplankton abundance. These approximations are an unavoidable consequence of truncating the trophic chain at phytoplankton. Interestingly, in this formulation, m(PHY) increases linearly with PHY at low phytoplankton biomass (cf quadratic mortality for zooplankton), but declines at large PHY, as zooplankton numerical and functional responses saturate. This has important consequences for the qualitative behaviour of NPD models (see Chapter 4).

3.4 Detritus and Nutrient Recycling.

In NPZD or NPD models, phytoplankton and/or zooplankton losses are assumed to result both in direct production of DIN through zooplankton excretion, and in production of non-living organic N (detritus). The partitioning of phytoplankton losses between DIN and detritus may be fixed, or allowed to vary as a function of phytoplankton and zooplankton biomass. In general, the larger the fraction allocated directly to DIN, the higher the efficiency of nitrogen recycling in the water column.

In the water column, the detrital organic N is broken down over a range of time scales, both through bacterial attack and through ingestion by zooplankton, to release DIN. In simple NPZD or NPD models, this remineralization is represented by a constant specific breakdown rate, r_DET. In more complex models, bacteria may be represented explicitly (eg Fasham et al, 1990). In NPD models, it can be argued that the "detritus" pool represents all non-photosynthetic organic matter, including living zooplankton and higher trophic levels. However, it is still treated as a single pool with a fixed breakdown rate.

3.5 Sediment Biogeochemistry.

The models described to this point have been used to address both open ocean biogeochemical cycles and coastal eutrophication. The key distinguishing feature of shallow coastal systems is the close coupling between water column and sediment, and the importance of sediment biogeochemistry. The coupling between water column and sediment occurs via settling and resuspension of particulate matter, especially detritus, and by diffusion and bio-irrigation of dissolved constituents, including DIN.

In the context of simple NP(Z)D models, the sediments are primarily a site for sedimentation and breakdown of detritus. Again, detrital breakdown occurs through a combination of bacterial attack and consumption by suspension and deposit feeders. Supply of oxygen is a major constraint on biogeochemical processes in the sediment, and there are a complex set of bacterially-mediated reactions controlled by oxygen concentration. Nitrification (conversion of ammonium to nitrate in oxic sediments) and denitrification (conversion of nitrate to N₂ gas) are of particular importance for the nitrogen cycle, because nitrogen gas is inert, and denitrification represents a loss of TN from the combined water column-sediment system.

Quite complex models of sediment biogeochemistry have been developed (Blackburn and Blackburn, 1993; Boudreaux, 1997). These require fine depth and time resolution, because of the fine-scale gradients and rapid oxygen kinetics in the sediment, and are not suitable for incorporation in general eutrophication models. A key qualitative prediction from these models is that the denitrification efficiency (ie proportion of DIN produced through remineralization which is lost to denitrification) decreases as sediment respiration rates become large, and ultimately drops to zero as surface sediments become anoxic. This trend was confirmed in sediment flux studies in Port Phillip Bay (Harris et al, 1996), and Murray and Parslow (1997) used a simple empirical formula based on Port Phillip Bay data to relate denitrification efficiency E_DEN to sediment respiration rate R_SED:

E_DEN = E_DEN^max . (1 � R_SED/R₀)

3.13

where E_DEN^max is the maximum observed denitrification efficiency, and R₀ is the respiration rate at which E_DEN falls to zero.

3.6. Simple vs Complex Process Models.

Simple NP(Z)D models capture, at least in a crude sense, the major processes controlling the fate of nitrogen loads into coastal waters. Specifically, they represent nutrient uptake and growth by phytoplankton, the loss terms controlling phytoplankton biomass, the conversion and temporary accumulation of organic N as detritus, and the direct and indirect regeneration of DIN. With a simple sediment component added, they can also represent water column-sediment coupling, and the important internal sink of denitrification.

Simple models of this type have been used to represent nitrogen cycling and eutrophication in a number of applications (eg Fennel, 1995). However, other studies have adopted more complicated models (Radford, 1993; Murray and Parslow,1997). Here we review briefly the rationale for adopting more complex models, and the limitations involved in using simple models.

3.6.1. Multiple Nutrients.

The simple NPZD models represent the nitrogen cycle, and the living and non-living organic components are normally represented as equivalent N concentrations (mg N m^-3). One can convert these to carbon equivalents (or chlorophyll equivalents for phytoplankton) if one is prepared to assume a fixed stoichiometry. We noted earlier that phosphorus and silicate may at times be limiting or co-limiting in estuaries. The simple NPZD model can serve as a P-limited model, with minor adjustments to parameters to reflect the different stoichiometry. Denitrification of course has no equivalent in a P-based model, which should instead represent the adsorption of phosphate to inorganic material, and its dependence on oxic state and ionic strength.

In some estuaries, phosphorus is limiting in upstream low salinity waters and nitrogen in downstream marine waters. One can allow for both P and N limitation by explicitly representing the P and N content of all components separately, or by assuming fixed stoichiometry for the organic components, and duplicating only the dissolved inorganic pools. Silicate is normally a co-limiting nutrient, as it limits growth of siliceous phytoplankton (principally diatoms), but not others. Its principal effect may be to control phytoplankton composition, although there is evidence that it can also affect phytoplankton bloom magnitude (Murray and Parslow, 1997).

Some nitrogen-based models explicitly distinguish ammonium and nitrate. Phytoplankton take up ammonium in preference to nitrate, and may respond more quickly to ammonium enrichment. In oceanic systems, nitrification is thought to occur primarily below the euphotic zone, and so ammonium uptake is equated to regenerated production. It is important to distinguish ammonium and nitrate in explicit process models of sediment biogeochemistry, and they can serve as a useful diagnostic even where simple empirical sediment models are used (Murray and Parslow, 1997). Finally, in some estuarine systems where nitrate is present at very high concentrations in the water column, the flux of nitrate which diffuses into the sediment and is denitrified there is significant (Nielsen et al, 1994).

3.6.2. Trophic Complexity.

Some models represent more than one functional component at each trophic level. Plankton ecologists commonly separate both phytoplankton and zooplankton into size groups (eg pico-, nano- and micro- phytoplankton, and nano-, micro- and meso- zooplankton). These are useful both descriptively and as functional components. Small phytoplankton (pico and nano) are typically grazed by small zooplankton (nano and micro), which have rapid maximum growth rates, approaching or exceeding those of phytoplankton. It has been suggested that this rapid numerical response allows small zooplankton to control the biomass of small phytoplankton, and field observations show that small phytoplankton are typically present at relatively low background concentrations which respond only weakly to transient nutrient injections (Beardall et al, 1997).

Large phytoplankton, especially diatoms and dinoflagellates, are typically grazed by crustaceans with slow numerical responses, and appear able to escape grazing control and form blooms in the presence of excess nutrients. It could be argued models of eutrophication should concentrate on representing the dynamics of bloom phytoplankton. However, explicitly including both small and large phytoplankton may allow models to represent the transition from oligotrophic or mesotrophic to eutrophic conditions.

Different nutrient requirements provide another reason for distinguishing phytoplankton functional groups. Diatoms require silicate, and diatom bloom magnitude may be constrained by silicate limitation. In fresh and brackish waters, N-fixing cyanobacteria are favoured by excess phosphate and low DIN. It is still puzzling (and fortunate) that N-fixing cyanobacterial blooms appear to be rare in temperate and subtropical coastal waters (but see Chapter 7).

Some models have included higher trophic levels, extending to carnivorous zooplankton and fish (eg Radford, 1993). These models have generally been more concerned with the ecology of higher trophic levels than with their top-down effects on eutrophication. At least in marine systems, integration of biogeochemical models of lower trophic levels with ecological or population models of higher trophic levels is still poorly developed.

3.6.3. Organic Matter.

The NPZD models represent only one pool of non-living organic matter, which is assigned a characteristic remineralization time scale. In practice, the non-living organic matter pool consists of both dissolved and particulate matter, and includes both labile and refractory compounds. The sources and fates of these components may also differ widely. Particulate detritus is subject to sedimentation, is more likely to be recycled or buried in the sediment, and is therefore strongly linked to internal sinks. Dissolved organic nitrogen is more likely to be exported from the estuary, especially if it is refractory.

Catchment runoff can act as a significant source of both dissolved and particulate organic N. This material is more likely to be refractory if the catchment is relatively undisturbed. As noted above, seawater at the estuary mouth will generally contain quite high concentrations of DON, most of which may be refractory.

Refractory DON and PON are likely to dominate the water column TN pool in most estuaries, and therefore to dominate the export of nitrogen from the estuary. It follows that, if models are to reproduce TN observations and N budgets, they need to explicitly represent refractory material. On the other hand, the labile detrital pools control the sedimentation of organic matter from phytoplankton production, and consequently sediment respiration and denitrification sinks. Thus, there are strong arguments to divide the detrital pool into at least two functional components, even in simplified eutrophication models.

Our understanding of the processes controlling production and consumption of refractory PON and DON (on time scales of months to years) is poor, and this is an area deserving further research. In fact, monitoring programs usually measure total organic N (or TKN), but do not discriminate DON from PON (this is relatively straightforward) or refractory and labile ON (this is not). This makes it very difficult to allocate loads or boundary concentrations of organic N to model functional components.

3.6.4. Benthic Communities.

The NPZD models represent only planktonic primary producers. Phytoplankton blooms are often the primary concern in eutrophication, and are the principal focus of this study in particular. However, benthic plants such as seagrass, macroalgae and microphytobenthos can be major or dominant primary producers in shallow coastal systems. It is possible to represent these explicitly in eutrophication models (Murray and Parslow, 1997). The formulation for nutrient uptake and growth by benthic plants is basically similar to that for phytoplankton, except that benthic plants respond to bottom light levels (and are therefore much more sensitive to changes in light attenuation), and seagrass and microphytobenthos have access to nutrients in sediment pore waters.

Benthic filter feeders can make an important and even dominant contribution to phytoplankton grazing in shallow coastal systems (eg Clapham, 1996). They can also serve to increase the effective sedimentation rate of organic matter. It is again relatively straightforward to represent these explicitly in models, using similar grazing, growth and mortality formulations to those used for zooplankton.

3.6.5. Complexity and Data Requirements.

A truly comprehensive and versatile model of coastal biogeochemistry and eutrophication might be expected to incorporate all the processes described above. Examples of models with this kind of scope include the Port Phillip Bay Integrated Model (Murray and Parslow, 1997) and the North Sea ERSEM model (Radford, 1993). The N cycle represented in the Port Phillip Bay model is shown schematically in Fig. 3.1. The ERSEM model is still more complex. Model complexity of this order offers realism and versatility, but at the expense of increased requirements for field surveys and process studies for model calibration. The Port Phillip Bay model contains 18 state variables and 70 parameters. Model calibration and analysis required extensive effort and was only possible because an unusually comprehensive program of observations and process experiments was conducted as part of the Port Phillip Bay Environmental Study (Murray and Parslow, 1997).

The NPD model formulation involves significant simplifications and approximations. These will result in acceptable errors in some circumstances, while the model may not be applicable at all in others. However, where eutrophication problems involving major algal blooms in urban estuaries result from large point source or diffuse loads of available nitrogen, the NPD models incorporate the core processes needed to address them. Because of their simple structure and small number of variables and parameters, these models can be implemented and calibrated relatively quickly using the results of routine monitoring (see Chapter 6).

Fig. 3.1. Nitrogen cycling in the Port Phillip Bay Integrated Model.

4. Analysis of a Steady-State 1-Box Model.

In Chapter 3, we argued that a simple NPD biogeochemical model should be able to capture many of the key processes controlling nitrogen cycling and phytoplankton biomass in estuaries. This chapter analyses the steady-state behaviour of a model of this kind. The chapter includes some moderately detailed equations and algebra, which we have enclosed in boxes. Readers who don't wish to follow the analysis in detail may wish to skip over the boxes. Those who are interested only in the principal conclusions may jump to the concluding section of this Chapter.

4.1 Model Definition.

The model is implemented within the simplest possible physical context, representing the estuary as a single well-mixed compartment, with a prescribed flushing rate r (d^-1). Sediment pools, and sediment water column exchanges, are represented implicitly by assuming that a fixed proportion s of the total pool of each particulate component is suspended in the water column, with the remainder in the sediment. This is a reasonable approximation, at least in shallow waters where exchange between water column and sediment is likely to be dominated by physical processes of sinking and resuspension. The suspended fraction s is subject to horizontal transport (ie flushing), while the sedimented fraction (1-s) is subject to benthic remineralization and denitrification.

The model includes 4 state variables: phytoplankton biomass (PHY), DIN, labile organic detritus (DET) and refractory organic detritus (REF). Depending on the assigned suspended fraction, DET and REF can be treated as particulate or dissolved. All variables are defined in nitrogen equivalent concentrations as mg N m^-3 and all fluxes as mg N m^-3 d^-1.

The dynamical equations defining the model are:

dDIN/dt = L_DIN - m.PHY + (1-f_DET).m.PHY + (1-E_DEN).R_SED + R_W - r.(DIN - DIN_O)

4.1

dPHY/dt = m.PHY � m.PHY - r.(PHY-PHY_O)

4.2

dDET/dt = L_DET + f_DET.m.PHY - r_DET.DET - r .(s_DET.DET - DET_O)

4.3

dREF/dt = L_REF + f_REF.r_DET.DET - r_REF.REF - r.(s_REF.REF - REF_O)

4.4

In each equation, L_X represents the load, and X_O the ocean concentration, of constituent X. In Eq 4.1 and 4.2, m is the phytoplankton growth rate, m the phytoplankton loss rate, f_DET the proportion of phytoplankton loss assigned to DET, R_SED is the sediment respiration rate, E_DEN the denitrification efficiency, and R_W is the water column respiration rate. In Eq 3 and 4, r_DET and r_REF are the breakdown rates of labile and refractory detritus, and f_REF is the proportion of labile detritus converted to refractory detritus.

As discussed in Chapter 3, the phytoplankton growth rate is given by:

m = mmax.h_N.h_I

4.5

The light limitation term h_I is based on a depth integrated version of Steele's (1962) equation:

h_I = (exp(1. � 2.exp(-K.H)) � exp(-1)) / (K.H)

4.6

where H is estuary depth. The light attenuation coefficient K is given by:

K = K_O + k*_PHY.PHY + k*_DET.DET + k*_REF.REF

4.7

Following the discussion in Chapter 3, the phytoplankton mortality rate is given by

m(PHY) = m₀ + 4.m₁.PHY/(K_P + PHY)²

4.8

and has a maximum value m₀+m₁ at PHY = K_P. The sediment respiration rate is given by:

R_SED = r_DET.(1-s_DET).DET . (1-f_REF) + r_REF.(1-s_REF).REF

4.9

and the water column respiration rate is given by

R_W = r_DET.s_DET.DET . (1-f_REF) + r_REF.s_REF.REF

4.10

The denitrification efficiency E_DEN is given by

E_DEN = E_DEN^max . (1 � R_SED / R₀)

4.11

4.2 Steady-state Analysis.

4.2.1 Total N Balance.

If Eq 4.1 to 4.4 are summed, the internal transformations of N cancel out, yielding

d TN / dt = L_TN - r .(TN_W � TN_O) � E_DEN.R_SED

4.12

where TN is total nitrogen in the system (TN = DIN+PHY+DET+REF), and TN_W is total nitrogen in the water column (TN_W = DIN + PHY + s _DET.DET + s _REF.REF). At steady-state,

L_TN = r .(TN_W � TN_O) + E_DEN.R_SED

4.13

that is, Load = Net Export + Internal Sink. We can also rewrite Eq 4.13 as

TN_W = TN_O + (L_TN � E_DEN.R_SED) / r

4.14

Equation 4.14 is the equivalent of Vollenweider's equation for N-limited estuaries. As for lakes, the flushing rate r plays a dominant role in determining the concentration of TN in the water column. In the absence of any internal sink, the entire N load is exported to the ocean, and TN is increased above the ocean background by TN* = L_TN/r , the concentration needed to flush the load out of the estuary. TN is reduced below TN* according to the proportion of the total N load lost to the internal sink rather than exported from the estuary.

4.2.2 Composition of TN.

The steady-state equations are just:

0 = L_DIN - m .PHY + (1-f_DET).m.PHY + (1-E_DEN).R_SED + R_W - r .(DIN - DIN_O)

4.15

0 = m .PHY � m.PHY - r .(PHY-PHY_O)

4.16

0 = L_DET + f_DET.m.PHY - r_DET.DET - r .(s _DET.DET - DET_O)

4.17

0 = L_REF + f_REF.r_DET.DET - r_REF.REF - r .(s _REF.REF - REF_O)

4.18

It is possible to solve Eq 4.16 to 4.18 explicitly for DIN, DET and REF in terms of PHY. These solutions determine the relative composition of the TN_W pool as a function of TN_W.

First, Eq 4.17 can be rearranged to give

DET = (L_DET + f_DET.m.PHY + r .DET_O )/(r_DET + r .s _DET).

4.19

The sum r_DET + r .s _DET is the combined physical and biological turnover rate of labile detritus in the system, while L_DET and f_DET.m.PHY represent the external and internal loads of labile detritus. The concentration of DET resulting from internal production is

DET_I = f_DET.m.PHY / (r_DET + r .s _DET)

4.20

Thus, DET_I/PHY increases as mortality rate m increases, and decreases as remineralisation (r_DET) and flushing rate (r ) increase. DET/PHY increases as s _DET decreases (that is, more detritus accumulates in bottom sediments if the suspended fraction is low), but the concentration of detritus suspended in the water column, s _DET.DET, increases as s _DET increases.

Next, Eq 4.18 can be rearranged to give

REF = (L_REF + r .REF_O + f_REF.r_DET.DET) / (r_REF + r .s _REF)

4.21

Again, r_REF + r .s _REF is the combined turnover rate of refractory detritus. The refractory detritus produced internally, REF_I, is present in fixed ratio to the labile detritus DET:

REF_I = (f_REF.r_DET / (r_REF + r .s _REF)) . DET.

4.22

The concentration of refractory detritus in the water column is given by s _REF.REF, and increases with s _REF.

If we assume PHY_O is small compared with PHY (likely to be true for eutrophic estuaries), then

m » m + r

4.24

Recall that m = m max.h_N.h_I, where h_N = DIN/(K_N+DIN), and h_I depends on light limitation and light attenuation, and therefore on PHY, DET and REF through Eq 4.6 and 4.7. The mortality rate m is also a function of PHY (Eq 7). Substituting in Eq 4.24 gives:

h_N » (m(PHY) + r ) / (m max.h_I) = h_N*(PHY),

4.25

where h_N*(PHY) depends explicitly on PHY through m(PHY), and implicitly on PHY, DET and REF via h_I and K.

We can then solve Eq 4.25 explicitly for DIN:

DIN = K_N . h_N* / (1 � h_N*)

4.26

h_N* is just the ratio of the phytoplankton loss rate to the light-limited nutrient-saturated phytoplankton growth rate, m _I = m max.h_I. At steady-state, the DIN concentration must be such as to reduce phytoplankton growth rates by a factor h_N*. At low values of PHY, the model constituents make an insignificant contribution to light attenuation, so K » K₀, h_I is constant, and h_N* is proportional to m(PHY) (Fig. 4.1). However, as PHY increases, phytoplankton and detritus make an increasing contribution to light attenuation, K increases, h_I decreases, and h_N* increases steeply. Eventually, at very high values of PHY, h_N* exceeds 1. But h_N = DIN/(K_N+DIN) cannot exceed 1. The phytoplankton concentration PHYmax where h_N* = 1 represents a maximum upper limit to phytoplankton biomass due to self-shading.

Fig. 4.1. Change in N-limitation factor h_N* with phytoplankton biomass PHY

Symbol	Description	Units	Value
mmax	Maximum phytoplankton growth rate	d^-1	1.5
K_N	Half-saturation constant for phytoplankton growth on DIN	mg N m^-3	10
m₀	Background constant phytoplankton loss rate	d^-1	0.1
m₁	Maximum grazing loss rate	d^-1	0.4
K_P	Phytoplankton biomass corresponding to maximum grazing loss rate	mg N m^-3	20
f_DET	Fraction of grazing losses to labile detritus		0.5
f_REF	Fraction of labile detritus to refractory detritus		0.2
r_DET	Breakdown rate of labile detritus	d^-1	0.1
r_REF	Breakdown rate of refractory detritus	d^-1	0.01
E_DEN^max	Maximum denitrification efficiency		0-0.7
R₀*	Sediment respiration rate at which E_DEN = 0.	mg N m^-2 d^-1	250
K₀	Background light attenuation	m^-1	0.1-0.9
k*_PHY	Specific light attenuation for phytoplankton	m² (mg N)^-1	0.0035
k*_DET	Specific light attenuation for labile detritus.	m² (mg N)^-1	0.0035
k*_REF	Specific light attenuation for refractory organic N	m² (mg N)^-1	0.0009
s_DET	Suspended fraction of labile detritus		0.3
s_REF	Suspended fraction of refractory organic N		0.3
H	Depth	m	10
r	Flushing rate	d^-1	0.1-0.01
Table 4.1. Parameter set used for steady-state examples. See text for details where a range of values is given.

q_i,i+1^j = R w^j / 2 [I] + (q_i,i+1^j - R w^j/2) [II]	5.37
q_i+1,i^j = - R w^j / 2 [I] + (q_i+1,i^j + R w^j / 2) [II]	5.38

Table 6.1. Location, distance downstream from New Norfolk, and magnitude of DIN and DET loads for Derwent Estuary point sources.
Location	Distance downstream	DIN Load (mg N s^-1)	DET Load (mg N s^-1)
New Norfolk	0	939	94
ANM Paper Mill	3	21	1600
Bridgewater	20	685	69
Cameron Bay	28	1671	167
Macquarie Point	32	2609	261
Prince of Wales Bay	32	3202	320
East Risdon	32	48	5
Pasminco EZ	34	412	0
Selfs Point	36	913	91
Rosny	39	2844	284
Sandy Bay	42	1128	113
Taroona	47	310	31
Blackmans Bay	55	1088	109

Table 6.2. "Standard" parameter set used in Derwent simulations (see text).
Symbol	Description	Units	Value
mmax	Maximum phytoplankton growth rate	d^-1	1.5
K_N	Half-saturation constant for phytoplankton growth on DIN	mg N m^-3	10
I_K	Light saturation intensity	W m^-2	10
m₀	Background constant phytoplankton loss rate	d^-1	0.1
m₁	Maximum grazing loss rate	d^-1	0.6
K_P	Phytoplankton biomass corresponding to maximum grazing loss rate	mg N m^-3	20
f_DET	Fraction of grazing losses to labile detritus		0.5
f_REF	Fraction of labile detritus to refractory detritus		0.1
r_DET	Breakdown rate of labile detritus	d^-1	0.1
r_REF	Breakdown rate of refractory detritus	d^-1	0.01
E_DEN^max	Maximum denitrification efficiency		0.6
R₀	Sediment respiration rate at which E_DEN = 0.	mg N m^-2 d^-1	250
K₀	Background light attenuation	m^-1	0.7
k*_PHY	Specific light attenuation for phytoplankton	m² (mg N)^-1	0.0035
k*_DET	Specific light attenuation for labile detritus.	m² (mg N)^-1	0.0035
k*_REF	Specific light attenuation for refractory organic N	m² (mg N)^-1	0.0009
w_PHY	Sinking rate of phytoplankton	m d^-1	0
w_DET	Sinking rate of labile detritus	m d^-1	1
w_REF	Sinking rate of refractory organic N	m d^-1	0

Table 6.4. Range of TN and TP loads (as adjusted in the model) for the low flow periods of April, September and December.
Source	TN Load (mg N s^-1)	TP Load (mg P s^-1)
River	22 - 66	3 - 14
Mullumbimby WTP	117	4 - 18
Ocean Shores WTP	29 - 36	4 � 19
Brunswick WTP	58 �72	19 - 22

Table 7.1. Requirements of functional groups across 9 environmental factors.
Factor	Small cells	Dino- flagellate	Freshwater cyano-bacteria	Brackish cyano-bacteria	Diatoms	Euglenoids
Organics	some spp	Humics	none	?	none	high
Salinity	variable	variable	<10	<25-30	variable	low
Si	none	none	none	none	high	none
N	low	high	low	low	low	?
P	low	high	high	high	low	high
Stratification	variable	high	high	variable	low	?
Light	mod-high	high	high	high	low	low
Flushing	high	low	low	low	high	low
Temperature	high	variable	high	cool	variable	warm

Symbol	Units	Description
t	d	Flushing time.
R	m³ d^-1	River or freshwater flow.
r	d^-1	Flushing rate
V	m³	Lake / estuary volume
M	mg m^-3	Concentration of generic tracer "M"
L_M	mg M d^-1	Total load of tracer M
L_M	mg M m^-3 d^-1	Load of tracer M per unit volume (= L_M/V).
TP	mg P m^-3	Total Phosphorous
S	mg P d^-1	Total internal sink of TP.
w	m d^-1	Effective "sedimentation rate" of TP.
DIN	mg N m^-3	Dissolved inorganic nitrogen
PHY	mg N m^-3	Phytoplankton concentration (nitrogen)
DET	mg N m^-3	Labile detrital nitrogen.
ZOO	mg N m^-3	Zooplankton biomass as nitrogen.
m	d^-1	Phytoplankton growth rate
m max	d^-1	Maximum phytoplankton growth rate.
h_N		Growth limitation factor due to nutrient.
hI		Growth limitation factor due to light.
K_N	mg N m^-3	Half-saturation constant for growth.
I_K	W m^-2	Saturation light intensity
I₀	W m^-2	Surface light intensity
K	m^-1	Diffuse light attenuation
H	m	Depth
<I>	W m^-2	Average water-column light intensity.
K₀	m^-1	Background light attenuation.
k*_X	m² (mg X)^-1	Specific light attenuation for constituent X.
G	d^-1	Phytoplankton N consumed per unit zooplankton N per day.
Gmax	d^-1	Maximum phytoplankton N consumed per unit zooplankton N per day.
K_P	mg N m^-3	Half-saturation constant for zooplankton grazing on phytoplankton.
PHY₀	mg N m^-3	Threshold phytoplankton biomass for grazing.
E_Z		Zooplankton gross growth efficiency.
m_Q	d^-1 (mg N m^-3)^-1	Zooplankton quadratic mortality cooefficient.
r_DET	d^-1	Remineralization rate of labile detritus.
E_DEN		Denitrification efficiency.
E_DEN^max		Maximum denitrification efficiency.
R_SED	mg N m^-3 d^-1	Sediment respiration rate / depth.
R₀	mg N m^-3 d^-1	Value of R_SED at which E_DEN =0.
R₀*	mg N m^-2 d^-1	Sediment respiration rate (ie per unit area) at which E_DEN =0.
s _X		Fraction of constituent X suspended in water column.
REF	mg N m^-3	Refractory detrital N
f_DET		Fraction of phytoplankton losses assigned to labile detritus.
m	d^-1	Phytoplankton loss rate
r_REF	d^-1	Remineralization rate of refractory detritus.
f_REF		Fraction of labile detritus converted to refractory detritus.
X_O	mg N m^-3	Ocean concentration of constituent X.
m₀	d^-1	Base phytoplankton loss rate.
m₁	d^-1	Maximum phytoplankton loss rate due to grazing.
TN	mg N m^-3	Total nitrogen concentration
TN_W	mg N m^-3	Concentration of total nitrogen suspended in water column.
TN*	mg N m^-3	Value of TN_W for export to balance loads
DET_I	mg N m^-3	Concentration of labile detritus produced internally.
REF_I	mg N m^-3	Concentration of refractory detritus produced internally.
h_N*		Nutrient-limited growth reduction factor required for phytoplankton growth to balance losses.
L*(PHY)	mg N m^-3 d^-1	DIN load required to balance losses at phytoplankton concentration PHY.
U_s	m s^-1	Surface current
U_f	m s^-1	Sectionally-averaged current.
d S		Top-to-bottom salinity difference.
S_O		Sectionally-averaged salinity.
n		Diffusive fraction.
q_i,i+1	m³ s^-1	Horizontal volume flux from cell i to i+1.
C_i	mg C m^-3	Concentration of tracer C in cell i.
S_i		Salinity in cell i.
Q_i	mg C m^-3 s^-1	Source of tracer C in cell i.
C_i^u, C_i^l	mg C m^-3	Concentration of tracer C in column i, and upper or lower cell respectively.
q_i⁺, q_i^-	m³ s^-1	Volume flux in column i from lower to upper, and upper to lower cell respectively.
q_i,i+1^u, _qi,i+1^l	m³ s^-1	Volume flux from column i to i+1 in upper and lower layers respectively.
C_i^j	mg C m^-3	Concentration of tracer C in column i, layer j.
q_i^j,j+1	m³ s^-1	Volume flux in column i from layer j to j+1
q_i,i+1^j	m³ s^-1	Volume flux in layer j from column i to i+1.
Q_i^j	mg C m^-3 s^-1	Source of tracer C in column i, layer j.
SVD		Singular value decomposition.
w^j		Weight assigned to layer j in computing diffusive fraction.
T	m³ s^-1	Flow component due to river flow.
A	m³ s^-1	Remaining advective flow component.
D	m³ s^-1	Diffusive component of fluxes.
d	m³ s^-1	Flux correction for upstream differencing
Q^k_l	m³ s^-1	Vector of fluxes associated with river flow l.
z_k	m	Height of top of layer k.
H_k	m	Thickness of layer k.
<I>_k	W m^-2	Mean light intensity in layer k.
Su	d^-1	Resuspension rate in layer k
w_X	m d^-1	Sinking rate of constituent X.
A_k	m²	Area of top of layer k

Estuarine Eutrophication Models

Contents

Foreword

Publication Details

Executive Summary

Acknowledgements

1. Introduction

2. Load-Response Models

3. Biogeochemical Process Models

3.1 Phytoplankton Growth And Nutrient Uptake.

3.2 Phytoplankton Loss Rates.

3.3 Zooplankton Growth and Losses.

3.4 Detritus and Nutrient Recycling.

3.5 Sediment Biogeochemistry.

3.6. Simple vs Complex Process Models.

3.6.1. Multiple Nutrients.

3.6.2. Trophic Complexity.

3.6.3. Organic Matter.

3.6.4. Benthic Communities.

3.6.5. Complexity and Data Requirements.

4. Analysis of a Steady-State 1-Box Model.

4.1 Model Definition.

4.2 Steady-state Analysis.

4.2.1 Total N Balance.

4.2.2 Composition of TN.

4.2.3. Response to Nitrogen Load.

4.2.4 Phytoplankton Mortality and Multiple Stable States.

4.2.5. Denitrification as an Internal Sink.

4.2.6. Organic Nitrogen Loads.

4.3. Conclusions.

5. Simple Inverse Models for Driving Estuarine Transport and Eutrophication Models

5.1. Introduction

5.2. Hansen-Rattray Estuary Classification

5.3. Summary of Possible Models

5.3.1. Nomenclature.

5.3.2. A Pseudo-Potential Method

5.3.3 One-Dimensional Single-Layer Model.

5.3.4. One-Dimensional Two-Layer (Pritchard) Model.

5.3.5. One-Dimensional Two-Layer Hybrid Model

5.3.6. One-Dimensional

5.4. Implementation of One-Dimensional n-Layer Hybrid Model

5.4.1. Weighting of Fluxes and Equations

5.4.2. The Diffusive Fraction

5.4.3. Upstream Differencing

5.4.4. Evaluation of Time-Dependent Flow Fields

6. Application of a Simple Spatially-Resolved Eutrophication Model

6.1. The spatially-resolved model.

6.2. Derwent River Estuary.

6.2.1. General Description.

6.2.2. Data Sets.

6.2.3. Estuary Geometry and Physical Exchanges.

6.2.4. Nutrient Loads and Boundary Conditions.

6.2.5. Model � Data Comparisons.

6.2.6. Model Behaviour And Experiments.

6.2.7. Implications For Point Source Locations.

6.3. Brunswick River Estuary.

6.3.1. General Description.

6.3.2. Data Sets.

6.3.3 Estuary Geometry and Physical Exchanges.

6.3.4. Nutrient Loads and Boundary Conditions.

6.3.5. Model-Data Comparisons.

6.3.6. Model behaviour and experiments.

6.3.7. Implications for Point Source Location.

6.4. Hardy Inlet.

6.4.1. General Description.

6.4.2. Data Sets.

6.4.3. Estuary Geometry and Physical Exchanges.

6.4.4. Nutrient Loads and Boundary Conditions.

6.4.5. Model-Data Comparisons.

6.4.6. Model Behaviour.

6.5. Conclusions from Test Cases.

7. Algal Bloom Composition

7.1. Introduction.

7.2. Predicting Bloom Composition.

7.3. Feedback of algal composition on biomass models.

7.3.1 Loss rates.

7.3.2 Growth Rates.

7.3.3 N-fixation.

7.3.4 Implementation.

8. Conclusions