The CSTT model Page updated: 10 February 2008

ENVIRONMENTAL BIOLOGY Research in the School of Life Sciences, Napier University Go back to Environmental Biology front page

The model originated with the UK's Comprehensive Studies Task Team in a report first published in 1994 (CSTT, 1994, 1997). The Team was set up to consider the 'comprehensive studies' needed for Article 6 of the Urban Waste Water Treatment Directive (UWWTD), including a requirement to identify waters that were at risk of eutrophication. The CSTT proposed a simple model for identifying such waters. The model calculates the maximum phytoplankton chlorophyll concentration that could occur in Summer for a given nutrient loading, where 'nutrient' means compounds of nitrogen and phosphate in chemical forms available to phytoplankters. This concentration can be compared to a pre-determined threshold to determine trophic state or to decide whether an 'Ecological Quality Objective' (EcoQO) has been achieved.

The CSTT model was intended as a screening model to identify water bodies that might be eutrophic, or might become eutrophic if nutrients were added in an UWW discharge. The diagnosis could either be accepted, or could lead to monitoring programme or the use of more complex models. The main ideas in the model came from two sources. Tett (1986) described a box model of the effects of sea-loch exchange on phytoplankton biomass in fjordic sea-lochs. Gowen et al. (1992) introduced the idea of the yield of phytoplankton chlorophyll from assimilated nutrient as a way of predicting the response of coastal waters to added nutrient. The CSTT model was further documented and tested during the OAERRE project (Tett, 2003). The 'equilbrium concentration enhancement' (ECE) component, mentioned below, was independently used by Gillibrand & Turrell (1997).

The CSTT model applies to the 'water-body, or zone B, scale' defined by the Comprehensive Studies Task Team and further discussed below. The model treats any identifable water-body of this size as a mixed box of known volume, exchanging water with theadjacent sea at a known relative rate.

Nutrient input to the box by rivers, fish farms, the discharge of waste water, etc, adds to the nutrient orginally present in the seawater. Exchange with the sea removes the added nutrients, but if inputs continue and exchange remains constant, the rates of addition and removal come into balance to create an enhanced 'equilbrium' concentration that depends on (1) the background concentration in the sea, and (2) the added nutrient load relative to the box's volume and exchange rate. The model allows this equilbrium concentration to be calculated.

In some cases the predicted equilbrium concentration, or the 'ECE' (the 'Equilibrium Concentration Enhancement' over the background concentration), can be checked by water sampling. However, during the phytoplankton growth season, most nutrients in most water bodies are removed by phytoplankton. Furthermore, the CSTT took the view that nutrient enhancement alone is not an indicator of eutrophication. Instead, problems only begin to arise when or some or all of the nutrient is used to make phytoplankton biomass, which can be recognized by an increase in the chlorophyll concentration. Thus, the model predicts the worst case outcome of nutrient enrichment, by calculating the amount of chlorophyll that could be formed by converting all available nutrient into chlorophyll at a fixed yield.

If this worst case, maximum, chlorophyll were to exceed a pre-defined EQS, the water body would be diagnosed as eutrophic. However, there are some environmental factors that must be taken into account before confirming a diagnosis. It could be that, even under enriched conditions, lack of light prevents algal populations from increasing. Alternatively, accumulation of phytoplanktonic biomass might be hindered by dilution of phytoplankter populations as a result of water exchange with the sea, or by removal of algal cells by zooplankters or benthic filter-feeders. The CSTT model deals with this by making the diagnosis of eutrophic state depend also on a comparison of light-limited growth rate with rates of physical exchange and biological loss.

Units for nutrient and chlorophyll concentration are given in base form. In many cases it will be better to calculate nutrient concentrations in microMolar and chlorophyll in microgram per litre; appropriate factors should be introduced into the equations.

The definition of eutrophication given in the UWWTD is:

"the enrichment of water by nutrients especially compounds of nitrogen and phosphorus, causing an accelerated growth of algae and higher forms of plant life to produce an undesirable disturbance to the balance of organisms and the quality of the water concerned."

Neither nutrients nor accelerated growth of algae (etc) are themselves bad; they become so only when they cause an 'undesirable disturbance to the balance of organisms' and water quality. In the absence of a means of recognizing undesirable disturbance, the CSTT took a precautionary approach and agreed that a water body would be diagnosed as at risk of eutrophication if the model's value for maximum chlorophyll exceeded 10 milligrams per cubic metre during Summer - or, indeed, if more than 10 mg chl m^-3 was regularly observed in Summer.

The underlying rationale for the use of (phytoplankton) chlorophyll was that chlorophyll is (i) easy to monitor and (ii) indicates the potential for the primary production of organic material. Thus, it is a good indicator of trophic status. The threshold was set for Summer, rather than the whole growth season, (i) to avoid Spring blooms, which may naturally reach high concentrations of chlorophyll, and (ii) because it is the Summer period, when nutrient levels are naturally at their lowest, that is most sensitive to enrichment.

It is the comparison of maximum chlorophyll concentration with a threshold that is an essential feature of the CSTT procedure, and not the value of the threshold, which may depend on local circumstances and knowledge about them. The value of 10 mg m^-3 was set by CSTT (1994) because (i) it is a level at which phytoplankton visibly discolour typical UK coastal waters, and (ii) it was above the upper (95 percentile) limit of the chlorophyll envelope of loch Creran (Tett & Wallis, 1978), where moderately high chlorophyll concentrations were sometimes observed during Summer, despite lack of nutrient enrichment. The value may be revised upwards, but made applicable to the entire year, for some UK waters. Painting et al.( 2005) considers thresholds set at 50 percent above a regional-specific 'natural background' maximum during the phytoplankton growth season. The threshold could be set lower for other waters - such as those near Mediterranean coasts, where natural maxima of chlorophyll are much less than 10 mg m^-3.

The CSTT model relates to EcoQO 2; although CSTT (1994) proposed a threshold, as exemplified in EcoQO 3, the model prediction can be compared with any specified chlorophyll EcoQO.

Scales, and defining the water body

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The CSTT report also introduced the idea that discharges had different impacts on different scales. It distinguished three scales or zones around a point-source discharge:

• zone A: the local scale, within which sinking particles mostly reach the seabed and in which the residence time of discharged water (or neutrally buoyant tracer) is a few hours, too short for nutrients to be converted into phytoplankton;
• zone B: the water body scale, in which water residence time is a few days, adequate for the the conversion of nutrients into phytoplankton if other conditions permit this;
• zone C: the regional scale, in which the residence time of water is months.

The CSTT model is appropriate for zone B calculations, with zone C providing the background or boundary conditions.

Zone B may be an obvious water body, such as a semi-enclosed bay, an estuary or a fjordic basin in a Scottish sea-loch, with obvious boundaries and place of exchange with the sea. It may also be a part of a more open coastal sea, in which case its extent can be defined by residence time considereations. In a tidal region the extent will be similar to that of the tidal ellipse.

In all cases, the initial requirement is to define the spatial limits of the water body and hence its volume V (which should be a mid-tide if the water is tidal), the diffuse and point source inputs of nutrients that are to be included, and the boundary conditions (the values of S₀ and X₀.

This annotated aerial photograph illustrates this for the Gulf of Fos, in southern France. The box for the CSTT model is here defined as the inner part of the gulf, with exchange taking place across the entrance line with the Mediterranean Sea. The boundary conditions are those in the Mediterranean water crossing the line.

In mixed waters, the CSTT box extends to the seabed, but in stratified waters the box may be limited by the pycnocline: the test is the residence time criterion.

Exchange rate, E, is the proportion of the water-body's content exchanged each day with the adjacent sea. A more precise definition is that it is the instantaneous probability, expressed as a daily rate and averaged over all box contents (and over a semi-diurnal tidal cycle), that a packet of water will be displaced by a packet of the same volume coming from the external sea. This definition does not include the effect of displacement by locally input freshwater. The diagram shows both types of displacement. In it, Y stands for a generalized variable - which could be instanced as nutrients or chlorophyll - and:

is the probability E.δt of displacement during a period δt of a typical packet (of concentration Y) by a packet of seawater of concentration Y0; is the probability (F/V).δt of displacement of a typical packet by water discharged from local rivers with concentration Yf; gives the total displacement probability (E + (F/V)).δt of a typical packet.

Treating the probabilities as rates at which fractions of the box volume are gained or lost, and assuming that no biological or chemical processes occur, leads to the following equation for change in the total amount of substance in the box:

d(Y.V)/dt = E.V.Y₀ - E.V.Y - F.Y + F.Y_f + y_i

where y_i is the (sum of) the local input rates of the relevant substance. Now, d(Y.V)/dt = V.(dY/dt) + Y.(dV/dt), but if volume is conserved (e.g. by averaging over a tidal cycle), dV/dt =0, and so:

dY/dt = -E.(Y - Y₀) + (y_i/V) + (F/V).(Y_f - Y)

In the original CSTT model, it was assumed that the daily river discharge F is small compared with the daily volume exchange E.V betwen the water body and the sea, and hence that its displacement effect can be ignored, giving the simplification, for the nutrient case,

dS/dt = -E.(S - S₀) + (Σs_i/V)

Σs_i indicates that river nutrients have been aded to other inputs. This rate-of-change equation has the steady state solution:

S ==> S_eq = S₀ + ((Σs_i/(E.V))

as used in the equation for equilbrium nutrient concentration.

Exchange, as thus defined, may be result from any of the following processes:

• estuarine circulation (net of the freshwater discharge volume);
• wind-driven horizontal circulation;
• wind-driven vertical upwelling;
• intermediate layer exchange (driven by external density changes);
• net tidal exchange (i.e., the tidally exchanged prism of water, corrected for the proportion of outflow water returned on the next flood tide);
• residual circulation;
• horizontal eddy diffusion insofar as not included in the other processes.

Exchange can be estimated in several ways, including by dye dispersion studies, measurements of currents across the mouth of a semi-enclosed water body, the use of numerical hydrodynamic models, and the calculation of salt (or freshwater) budgets. In the last case, the generalized exchange equation is rewritten with the substitution of salt content C for Y:

dC/dt = -E.(C - C₀) -F.C

with the well-known steady state solution for salinities which allows exchange (as defined here) to be estimated from:

E = (F/V).(C_eq/(C₀ - C_eq))

where C_eq is the steady-state mean salinity of the box defined for CSTT purposes, and C₀ is the outside salinity.

The definition of exchange rate that is given above (i.e., ignoring freshwater displacament), was chosen for simplicity. In most cases the results obtained by using a differently-defined E would be indistinguishable (given imprecisions in the other data) from those calculated using the simply-defined E. In cases of substantial freshwater inflow, however, the following equations may be used for the CSTT model:

The idea of chlorophyll yield is, in essence, simple. It is that phytoplankters assimilate dissolved nutrient and use it to make biomass including chlorophyll. The ratio of chlorophyll synthesized to nutrient removed from the sea thus indicates the efficiency of nutrient use, and can be used to predict the amount of chlorophyll that will result from future additions of nutrient.

There is a long history to the idea, commencing with Justus von Liebig's insight in 1840 that the harvest of an agricultural crop was set by the soil nutrient in shortest supply relative to need (Liebig, 1841). A century later, Jaques Monod (1942) quantified the growth of bacteria in laboratory culture in terms of yield of biomass from substrate used. Arthur Redfield (1934, 1963) developed the idea that both the composition of marine organisms, and the relative abundances of dissolved nutrient elements, tend to what is now called the Redfield ratio, of 106 atoms of carbon to 16 atoms of nitrogen to 1 atom of phosphorus. Redfield's work led many oceanographers to assume a constant yield of (for example) carbon biomass from assimilated nutrient-nitrogen. However, precise laboratory studies of algal culture showed that the yield of carbon from N or P (or other nutrients, including vitamin B12) could vary (Droop, 1968; 1983). The idea of the yield of phytoplankton biomass from nutrient on an ecosystem or water body (i.e. zone B) scale was developed in freshwaters, with work in (amongst other places) Canadian experimental lakes. It was found that when lakes were enriched to varying extents with phosphate, graphs of lake annual mean chlorophyll against annual mean total phosphorus could be well fitted by a linear regression, the slope giving the typical yield of chlorophyll from phosphorus (Schindler, 1977). Hecky & Kilham (1988), however, concluded that relationships between chlorophyll and nutrients were less clear in estuaries and coastal waters than they were in lakes.

The use of the yield of chlorophyll from dissolved nutrient for estimating the risk of marine eutrophication was proposed by Gowen et al. (1992), based on work aimed at setting an upper limit to the stock of nutrient producing salmon or trout that could be held in a given water body. They estimated values for this yield, q mainly by regression of chlorophyll on DAIN in samples from sections of Scottish sea-lochs. This method assumes that when sea-water, comparatively rich in nutrient, enters a loch, chlorophyll increases as water moves towards the head of the loch. 95% of significant regressions obtained by Gowen et al. had slopes between 0.25 and 4.4 mg chl (mmolDAIN)^-1, with a median of 1.05 mg chl (mmol DAIN)^-1.

The yields of chlorophyll from nitrogen in Scottish coastal waters were further investigated, under more controlled conditions, during microcosm experiments initially funded by SEPA and subsequently carried out as part of OAERRE, and reported by Edwards (2001), Edwards et al. (2003) and Edwards et al. (2005).

Apparatus used in microcosm experiments. Seawater, containing phytoplankton and pelagic bacteria and protozoa, but filtered to exclude mesozooplankton, was placed in the central reaction vessel. Seawater, filtered of all organisms, and nutrient enriched, was placed in the reservoir on the left and steadily pumped into the reactor, giving a dilution rate of about 0.2 per day.

Cumulative data from a typical experiment (Edwards et al., 2003), calculated by correcting observed changes in the reactor vesssel for losses and gains due to dilution. Steady-state q was calculated from the ratio of the day 8 values of cumulative chlorophyll formation and cumulative DAIN depletion. Note that the initial response to nutrient enrichment was a rapid increase in chlorophyll, followed by a decrease in chlorophyll befoire equilbrium was attained. These changes were explained in part by adjustments in algal physiology and in part by increases in protozoan grazers that followed the increase in micro-algae. Thus the initial yield (at day 2) is greater than the day 8 yield. The latter is most appropriate for the steady-state assumptions of the CSTT model.

The following values are suggested for yield. Normally, the 'steady-state' values should be used with the CSTT model. However, applications to non-steady state cases may use the higher values.

The values for chlorophyll yields from DAIN are based on Edward's (2001) work with Scottish coastal microplankton, in which diatoms were dominant. The ranges span the 25%ile to the 75%ile of 19 successful experiments in which chlorophyll was measured by the spectrophotometric method of Lorenzen (1967) and either nitrate or ammonium, or neither, were enriched. Phosphate and silicate were added in excess, to ensure that nitrogen remained the limiting nutrient. Controls were run without any enrichment. There were trends amongst the data suggesting that q was greater for nitrate than ammonium, and that q was lower during Spring, but they were not statistically significant. Results from diatom-dominated phytoplankton from the Ria Formosa, in Portugal, fell into the same range (Edwards et al., 2005). An estimate of 0.8 mg chl (mmol DAIN)^-1, made by plotting spring maximum chlorophyll against winter nitrate from the Swedish Himmerfjord (Tett et al., 2003) falls within the range of the steady state values, as does the median of 1.05 mg chl (mmol DAIN)^-1 of Gowen et al. (1992).

However, values obtained from experiments with phytoplankton dominated by dinoflagellates and small cyanobacteria, from Portuguese coastal upwelling, were higher, with a steady-state yield of 3.1 mg chl (mmol DAIN)^-1 (Edwards et al., 2005), and more work on this kind of phytoplankton is needed. The phosphorus yield was taken from freshwater studies in the Canadian experimental lakes (Schindler, 1977), and its application to marine phytoplankton is less certain.

Using von Liebig's 'Law of the Minimum', the limiting nutrient element can be identified from:

The CSTT equation for light-controlled growth, μ_I=α.(I-I_c), is intentionally simple. The compensation illumination, I_c, is the level of light at which photosynthsis and respiration are exactly in balance, when averaged over 24 hours. Photosynthetic efficiency, α, linearly converts illumination exceeding this into growth. However, although intended for use in predicting chlorophyll concentration, a property of phytoplankton, the CSTT model is in fact a microplankton model and predicts microplankton growth rate. In order to understand why this is better and to follow the derivation of values for α and I_c, it is helpful to see something of the theory behind such models.

The microplankton includes all pelagic micro-organisms: bacteria, micro-algae, protozoans and other primitive unicellular eukaryotes. Some of these organisms are photo-autotrophs (i.e. belong to the phytoplankton); others are heterotrophs. Myxotrophs have a pseudopodium in both camps. Microplankters are distinguished from mesozooplankters both by size and by life cycle. Typically, microplankters reproduce by binary fission, in contrast to mesozooplankton (or macroalgal) sexual reproduction with a necessary delay bewteen embryo and adult. Consequentially, the abundance of protozoans can change about as quickly as that of the phytoplankters that they graze, and it is permissible to assume a rough equilbrium amongst microplankton components on a zone B timescale. The microplankton 'compartment' (Tett, 1987) is a way of parameterizing the overall effects of the 'microbial loop' of Williams (1981). Within the compartment, carbon fixed by photosynthesis is metabolized by microheterotrophs (protozoans and bacteria) as well as autotrophs (phytoplankters). N or P assimilated by phytoplankters is shared with the microheterotrophs, and some it is mineralized by them, to be re-assimilated by the autotrophs.

The microplankton can be looked on as a suspension of chloroplasts (together with photosynthetic bacteria) and mitochondria (together with free-living bacteria. In essence, the photosynthesis of the chloroplasts ( the autotrophic part of the compartment) has to support the metabolism of the whole (i.e. of all the mitochondria).

In order to implement this theory, the CSTT growth equation is first expanded so that it can be rewritten using three basic microplankton parameters, α', r_o and I_c.

These parameters can be derived (Tett & Wilson, 2000; Lee et al., 2003) from autotroph and heterotroph parameters and the heterotroph fraction, η, the ratio of microheterotroph carbon biomass to total microplankton biomass. In addition, micro-algal photosynthetic efficiency is calculated from biophysical theory.

Subscripts _a refer to autotroph parameters and subscripts _h refer to heterotroph parameters. Here are values for the respiration parameters:

The other parameters, and their 'standard' values are:

* value might vary with water-type or phytoplankter-type

From these values, the following values of the CSTT model parameters can be calculated. They are shown for several values of the heterotroph fraction. η = 0.50 should be used as default under Summer conditions.

Finally, the CSTT model assumes a linear response to light. This is of course not the case; photosynthesis-irradiance relationships are curves that show saturation at higher illuminations. However, the linear approximation is satisfactory when dealing with low illuminations at which light can limit growth. See Tett (1990).

In the context of photosynthesis, 'light' means 'photosynthetically active radiation' (PAR), commonly measured as a flux per unit area of photons with wavelengths between 400 and 750 nm. A suitable unit is a μEinstein m^-2 s where an Einstein is a mole (Avogadro's number, 6.022 x 10²³) of photons. However, data are more widely available for the heating effect of radiation, including the infrared and ultraviolter components of the sun's output as received at the Earth's surface. In such cases, irradiance is commonly given as an energy flux per unit area, and so in J m^-2 s (≡ W m^-2) or MJ m^-2 d^-1. The following equation for the mean light (i.e, PAR), required for the calculation of light-limited growth in the CSTT model, can be entered with either unit; it calculates a photon flux density, as required by the equation discussed in the previous section for light-controlled growth.

I = m₂.I₀.(1 - exp(-k_D.h))/(k_D.h)

where:

• h is the mean depth of the box identified for the CSTT model - i.e. the depth to the seabed, or pycnocline, as appropriate;
• I₀ is the 24-hour mean irradiance at the sea surface, at a time of year appropriate to the EQS; in the UK the value should be that for a typical summer's day with good weather (i.e. conditions having the greatest potential for good growth of phytoplankton);
• k_D is the 'diffuse attenuation coefficient for downwelling PAR': see below;
• m₂ contains several factors; the first two need be used only if surface irradiance is given in energy units (e.g. W m^-2) and includes all radiation (i.e. infrared and UV as well as PAR):

  PAR as proportion of total irradiance	0.46	(ratio)
  conversion of PAR energy to photons	4.15	μE/J
  mean proportion of PAR photons penetrating the sea surface	0.94	(ratio)
  correction for hyperexponential decay, adjustment of photon angle, and linearization of photosynthesis	0.37	(ratio)

Further background, and the derivation of the equation, is given by Tett (1990).

The diffuse attenuation coefficient is a measure of the rate at which submarine light decreases with increasing depth in the sea. According to the Beer-Lambert law, this decay is exponential, and therefore a value of k_D can be estimated from theslope of a regression of ln(I_z/I₀) against depth, z. Such a regression is best made to the exclusion of near-surface measurements, since light typically decays hypereponentially near the surface.

Linear and logarithmic plots are illustrated below. The examples were plotted using data from in loch Creran, taken by R.Raine in August 1983. The internationally accepted symbol E for irradiance is used to label the right-hand graph. I is used elsewhere in this account of the CSTT model so that E can used for exchange. The attenuation coefficient estimated for this example (and excluding near-surface measurements) was 0.17 m^-1.

If underwater light measdurements are not available, an approximate value of the attenution coefficient can be calculated from the Secchi depth, z_Secchi:

k_D = f/z_Secchi

where the factor f is reported as having values between 1.4 in turbid water (Holmes, 1970) and 1.7 (Tyler, 1968) in clear water. However, it can vary more widely, and should if possible be determined locally.

Finally, measured values of the attenuation coefficient sums the effects of light absorption and scattering by water, dissolved substances, and suspended particles including those of phytoplankton. The CSTT model needs the value at the chlorophyll EQS. One way to estimate this is to measure the attenuation under conditions in which very little phytoplankton is present, giving k_D,w. To this can be added a contribution for chlorophyll, using parameter values from the photosynthesis model:

k_D = k_D,w + m₁.a^*_PH.X_EQS

This section summarizes what muust be done to employ the CSTT model.

• Data needs

  Here is a summary of data needs:

  1. Box volume V, mean depth, h, and exchange rate E;
  2. Boundary conditions for nutrients S₀ and chlorophyll, S₀;
  3. Nutrient inputs Σs_i to the box;
  4. Typical (24-hr mean) surface irradiance I₀, and diffuse attenutaion coefficient at zero chlorophyll k_D,w.

  The linked pdf document, prepared for work in the ECASA project, may provide a convenient template on which to assemble the data.

• Calculation Scheme

  An Excel workbook is available for applying the CSTT model, given the data mentioned in the preceeding subsection. The first page of the workbook applies equations (1) and (2) of the CSTT model for a single nutrient; the calculation should be repeated for the other potentially limiting nutrient. The second page makes the calculation of light-limited growth. Page 3 calculates mean light. The fourth page derives the CSTT model photosynthetic parameters from those for microplanktonic autotrophs and heterotrophs.

• Outcomes

  The main outcome from the model is a diagnosis of trophic state. According to the CSTT, a water body would be eutrophic if model-calculated Summer chlorophyll concentrations exceeded the CSTT's threshold of 10 mg m^-3 for present nutrient loadings, and would be at risk of eutrophication if proposed future loadings were to increase maximum chlorophyll above this threshold. A diagnosis of eutrophic state made in this way is, however, not binding. The consequential options are:

  • to accept the diagnosis (and implement appropriate measures, including nutrient stripping of waste water before discharge), or
  • to implement a monitoring programme or studies with a more complex model to confirm the diagnosis.

• Reliability

  The CSTT model is appropriate for zone B scale water bodies that can treated as (at least, approximately) homogenous, so that a single value of E (etc) can be applied throughout. It was tested at a number of European sites during the OAERRE project (Tett et al., 2003) and found to be reliable at all but two sites. 'Reliable' in this context means correctly predicting, or over-predicting, maximum chlorophyll concentration; the model fails when it under-predicts X_max. The two sites of failure included one at which the boundary data was inadequately known (and later remedied, giving a reliable prediction), and one at which the steady state assumption was incorrect, the water body receiving occassional pulses of nutrient-rich water through its entrance as a result of a wind-driven river plume.

A dynamic version of the CSTT model also exists. Originally called 'Riley+' by Tett & Wilson (2000), the dynamic CSTT, or dCSTT, model has been further developed in the context of sea-loch mariculture (Laurent et al., 2006; Portilla & Tett, 2006). dCSTT can be seen either as a more general model from which the CSTT model is obtained by simplifying for steady-state conditions, or as an extension of the CSTT model to deal with seasonally varying conditions. In the equations that follow, such seasonal variation in boundary and forcing conditions is shown by (t).

Another issue is the value of q that should be used. This depends on both the aim of modelling and the frequency of change in forcing variables. If the aim is to simulate typical seasonal cycles in a water body in which the boundary conditions and local nutrient inputs change relkatively slowly, and on a seasonal basis, the steady-state value of q should be used. In contrast, if boundary conditions or nutrient inputs can change unpredictably and at high frequency (compared with the exchange rate of water in the CSTT box), or if the aim of simulation is to generate an upper limit to seaosnally-changing chlorophyll (for example, to reproduce the upper limit of the envelope of chlorophyll in a Scottish sea-loch described by Tett & Wallis, 1978), then the maximum value of q should be used.

The equations are given only for a limiting nutrient. In cases where several nutrient elements might be potentially limiting, the term for nutrient controlled growth in equation (2) can be expanded:

μ_m.min(f(S₁), f(S₂))

Finally, the remarks made above about the definition of exchange also apply to these equationse, which need modification in the case of an estuary receiving a significant freshwater input.

Cite this web page (or the associated spreadsheet) as: Tett, P. (2006). The CSTT model. Environmental Biology: Research in the School of Life Sciences, Napier University. ( + URL and date of visiting). There are no restrictions on the use of the model or associated spreadsheet, but any consequences of an application are the responsibility of the users of the model and not of Napier University.

Funding for work carried out in Napier University on the CSTT has come from several sources, including SNIFFER, SARF, the European Commission through the OAERRE and ECASA projects, and Napier University itself. The CSTT was chaired, and the development of the model stimulated by Dr Willie Halcrow, of the Forth River Purification Board.