Since the mid-1990s, Australia's Commonwealth Science Industry and Research Organisation (CSIRO) has been developing a biogeochemical (BGC) model for coupling with a hydrodynamic and sediment model for application in estuaries, coastal waters and shelf seas. The suite of coupled models is referred to as the CSIRO Environmental Modelling Suite (EMS) and has been applied at tens of locations around the Australian continent. At a mature point in the BGC model's development, this paper presents a full mathematical description, as well as links to the freely available code and user guide. The mathematical description is structured into processes so that the details of new parameterisations can be easily identified, along with their derivation. In EMS, the underwater light field is simulated by a spectrally resolved optical model that calculates vertical light attenuation from the scattering and absorption of

The first model of marine biogeochemistry was developed more than 70 years ago to explain phytoplankton blooms

Estuarine, coastal and shelf modelling projects undertaken over the past

Model domains of the CSIRO EMS hydrodynamic and biogeochemical applications from 1996 onwards. Additionally, EMS was used for the nationwide Simple Estuarine Response Model (SERM) that was applied generically around Australia's 1000

Australian shelf waters range from tropical to temperate, micro- to macro-tidal, with shallow waters containing coral-, seagrass- or algae-dominated benthic communities. With generally narrow continental shelves, and being surrounded by two poleward-flowing boundary currents

As the national science body, CSIRO needed to develop a numerical modelling system that could be deployed across the broad range of Australian coastal environments and capable of resolving multiple anthropogenic impacts. With a long coastline (60 000

In the aquatic sciences, there has been a long history of experimental and process studies that use geometric arguments to quantify ecological processes, but these derivations have rarely been applied in biogeochemical models, with notable exceptions (microalgal light absorption and plankton sinking rates generally, surface-area-to-volume considerations,

Examples of geometric descriptions of ecological processes.

Perhaps the most important consequence of using geometric constraints in the BGC model is the representation of benthic flora as two-dimensional surfaces, while plankton are represented as three-dimensional suspended objects

In addition to geometric constraints derived by others, a number of novel geometric descriptions have been introduced into the EMS BGC model, including

geometric derivation of the relationship between biomass,

impact of self-shading on chlorophyll synthesis quantified by the incremental increase in absorption with the increase in pigment content (Sect.

mass-specific absorption coefficients of photosynthetic pigments better utilised to determine phytoplankton absorption cross-sections

the space limitation of zooxanthellae within coral polyps using zooxanthellae projected areas in a two-layer gastrodermal cell anatomy (Sect.

preferential ammonium uptake, which is often calculated using different half-saturation coefficients of nitrate and ammonium uptake

To be clear, these geometric definitions have their own set of assumptions (e.g. a single cell size for a population) and simplifications (e.g. spherical shape). Nonetheless, the effort to apply geometric descriptions of physical limits across the BGC model appears to have been beneficial, as measured by the minimal amount of re-parameterisation that has been required to apply the model to contrasting environments. Of the above-mentioned new formulations, the most useful and easily applied is the bottom cover calculation (Fig.

The geometrically constrained relationship between bottom cover and seagrass biomass,

In addition to using geometric descriptions, there are a few other features unique to the EMS BGC model including

calculation of scalar irradiance from downwelling irradiance, vertical attenuation and a photon balance within a layer (Sect.

an oxygen balance achieved through use of biological and chemical oxygen demand tracers (Sect.

the stoichiometric link of excess photons to reactive oxygen production in zooxanthellae.

This document provides a summary of the biogeochemical processes included in the model (Sect.

The optical and biogeochemical models are linked by the dependence of scattering and absorption on the state of optically active biogeochemical quantities. The optical model undertakes calculations at distinct wavelengths of light (say 395, 405, 415, … 705 nm) representative of individual wavebands (say 400–410, 410–420 nm, etc.) of the vertically resolved downwelling and scalar irradiance that are used by the biogeochemical model to drive photosynthesis. The optical model includes the effect of Earth–Sun distance, Sun angle, atmospheric transmission, surface albedo and refraction on the downwelling surface irradiance. In the water column, the model attenuates light based on the spectrally resolved total absorption and scattering of microalgae, detritus, dissolved organic matter, inorganic particles and the water itself (Fig.

Schematic of the CSIRO Environmental Modelling Suite illustrating the biogeochemical processes in the water column, epipelagic and sediment zones, as well as the carbon chemistry and gas exchange used in vB3p0 for the Great Barrier Reef application. Orange labels represent components that scatter or absorb light.

The biogeochemical model is organised into three zones: pelagic, epibenthic and sediment. Depending on the grid formulation, the pelagic zone may have one or many layers of similar or varying thickness. The epibenthic zone overlaps with the lowest pelagic layer and the top sediment layer and shares the same dissolved and suspended particulate material fields. The sediment is modelled in multiple layers with a thin layer of easily resuspendable material overlying thicker layers of more consolidated sediment. Each sediment layer contains both particles and porewater

Dissolved and particulate biogeochemical tracers are advected and diffused throughout the model domain in an identical fashion to temperature and salinity. Additionally, biogeochemical particulate substances sink and are resuspended in the same way as sediment particles. Biogeochemical processes are organised into pelagic processes of phytoplankton and zooplankton growth and mortality, detritus remineralisation and fluxes of dissolved oxygen, nitrogen and phosphorus; epibenthic processes of growth and mortality of macroalgae, seagrass and corals, and sediment-based processes of plankton mortality, microphytobenthos growth, detrital remineralisation and fluxes of dissolved substances (Fig.

The biogeochemical model considers four groups of microalgae (small and large phytoplankton representing the functionality of photosynthetic cyanobacteria and diatoms, respectively, microphytobenthos and

Photosynthetic growth is determined by concentrations of dissolved nutrients (nitrogen and phosphate) and photosynthetically active radiation. Autotrophs take up dissolved ammonium, nitrate, phosphate and inorganic carbon. Microalgae incorporate carbon (C), nitrogen (N) and phosphorus (P) at the Redfield ratio (

Micro- and mesozooplankton graze on small and large phytoplankton, respectively, at rates determined by particle encounter rates and maximum ingestion rates. Additionally, large zooplankton consume small zooplankton. Of the grazed material that is not incorporated into zooplankton biomass, a fraction is released as dissolved and particulate carbon, nitrogen and phosphate, with the remainder forming detritus. Additional detritus accumulates by mortality. Detritus and dissolved organic substances are remineralised into inorganic carbon, nitrogen and phosphate with labile detritus transformed most rapidly (days), refractory detritus slower (months) and dissolved organic material transformed over the longest timescales (years). The production (by photosynthesis) and consumption (by respiration and remineralisation) of dissolved oxygen is also included in the model and, depending on prevailing concentrations, facilitates or inhibits the oxidation of ammonium to nitrate and its subsequent denitrification to dinitrogen gas which is then lost from the system.

Additional water column chemistry calculations are undertaken to solve for the equilibrium carbon chemistry ion concentrations necessary to undertake ocean acidification (OA) studies and to consider sea–air fluxes of oxygen and carbon dioxide. The adsorption and desorption of phosphorus onto inorganic particles as a function of the oxic state of the water are also considered.

In the sediment porewaters, similar remineralisation processes occur as in the water column (Fig.

Schematics of sediment nitrogen (top) and phosphorus (bottom) pools and fluxes. Processes represented include phytoplankton mortality, detrital decomposition, denitrification (nitrogen only), phosphorus adsorption (phosphorus only) and microphytobenthic growth. Grey boxes are particles.

The biogeochemical model presented in this paper is process based. That is, the rate of change of each ecological state variable is determined by a mathematical representation of each process that moves mass between one variable and another, conserving total mass. For dissolved inorganic phosphorus, the equation in the bottom water column layer (excluding advection, diffusion and particle sinking) could be written as

In Sects.

The model contains state variables that quantify the mass of carbon, nitrogen, phosphorus and oxygen, as well as state variables that contain stoichiometrically constant combinations of carbon, nitrogen, phosphorus (

The local rate of change of concentration,

The microalgae are particulates that contain internal concentrations of dissolved nutrients (C, N, P) and pigments that are specified on a per cell basis. To conserve mass, the local rate of change of the concentration of microalgae,

The optical model calculates the spectrally resolved light field in each vertical column and uses it to drive the photosynthesis of phytoplankton and benthic plants in the biogeochemical model. Following the terminology of aquatic optics

Pigment-specific absorption coefficients for the dominant pigments found in small phytoplankton determined using laboratory standards in solvent in a 1 cm vial. Green and red lines are photosynthetic pigments constructed from 563 measured wavelengths. Circles represent the wavelengths at which the optical properties are calculated in the simulations. The black line represents the weighted sum of the photosynthetic pigments (Eq. 3), with the weighting calculated from the ratio of each pigment concentration to chlorophyll

Similarly, for large phytoplankton and microphytobenthos

Pigment-specific absorption coefficients for the dominant pigments found in large phytoplankton and microphytobenthos determined using laboratory standards in solvent in a 1 cm vial. The aqua line represents the weighted sum of the photosynthetic pigments (Eq. 4), with the weighting calculated from the ratio of each pigment concentration to chlorophyll

Pigment-specific absorption coefficients for the dominant pigments found in

The absorption cross-section at wavelength

The use of an absorption cross-section of an individual cell has two significant advantages. Firstly, the same model parameters used here to calculate absorption in the water column are used to determine photosynthesis by individual cells, including the effect of packaging of pigments within cells. Secondly, the dynamic chlorophyll concentration determined later can be explicitly included in the calculation of phytoplankton absorption. Thus, the absorption of a population of

Both schemes have drawbacks. Scheme 2, using the concentration of dissolved organic carbon, is closer to reality but is likely to be sensitive to poorly known parameters such as remineralisation rates and initial detritial concentrations. Scheme 1, a function of salinity, will be more stable but perhaps less accurate, especially in estuaries where hypersaline waters may have large estuarine loads of coloured dissolved organic matter.

The remote-sensing reflectance of the 21 mineral mixtures suspended in water as measured by

For the terrestrially sourced particles, we used observations from Gladstone Harbour in the central Great Barrier Reef (GBR) (Fig.

Inherent optical properties (total absorption and total scattering) at sample sites in Gladstone Harbour on 13–19 September 2013

The absorption due to calcite-based NAP is given by

Constants and parameter values used in the optical model.

State and derived variables in the water column optical model.

Traits of suspended microalgae.

Spectrally resolved energy distribution of sunlight, clear-water absorption and clear-water scattering

The optical model is forced with the downwelling short-wave radiation just above the sea surface, based on remotely sensed cloud fraction observations and calculations of top-of-the-atmosphere clear-sky irradiance and solar angle. The calculation of downwelling radiation and surface albedo (a function of solar elevation and cloud cover) is detailed in Sect. 9.1.1 of the hydrodynamic scientific description (

The downwelling irradiance just above the water interface is split into wavebands using the weighting for clear-sky irradiance (Fig.

The vertical attenuation coefficient at wavelength

The downwelling irradiance at wavelength

Assuming a constant attenuation rate within the layer, the average downwelling irradiance at wavelength

We can now calculate the scalar irradiance,

The spectrally resolved light field at the base of the water column is attenuated, from top to bottom, by macroalgae and seagrass (

The light absorbed by corals is assumed to be entirely due to zooxanthellae and is given by

The optical model in the sediment only concerns the benthic microalgae growing in the porewaters of the top sediment layer. The calculation of light absorption by benthic microalgae assumes they are the only attenuating component in a layer that lies on top layer of sediment, with a perfectly absorbing layer below and no scattering by any other components in the layer. Thus, no light penetrates through to the second sediment layer where benthic microalgae also reside. Thus, the downwelling irradiance at wavelength

Given no scattering in the cell, and that the vertical attenuation coefficient is independent of azimuth angle, the scalar irradiance that the benthic microalgae is exposed to in the surface biofilm is given by

The model contains four functional groups of suspended microalgae: small and large phytoplankton, microphytobenthos and

The growth of microalgae has been modelled in many ways, from simple exponential growth and logistic growth curves, to single- and multiple-nutrient-based curves, through to equations that contain a state variable for the physiological state of the cell (variously described as stores, quotas, reserves, etc.) and to consider the complex processing of photons in the microalgae photosystem. It is now common for complex biogeochemical models to contain state variables for the physiological state of each of the potentially limiting nutrients

In the microalgae model (most fully described in

State and derived variables for the microalgae growth model. DIN is given by the sum of nitrate and ammonium concentrations, [

The model considers the diffusion-limited supply of dissolved inorganic nutrients (N and P) and the absorption of light, delivering N, P and fixed C to the internal reserves of the cell (Fig.

Schematic of the process of microalgae growth from internal reserves. Blue circle: structural material; red pie: nitrogen reserves; purple pie: phosphorus reserves; yellow pie: carbon reserves; green pie: pigment content. Here, a circular pie has a value of 1, representing the normalised reserve (a value between 0 and 1). The box shows that generating structural material for an additional cell requires the equivalent of 100 % internal reserves of carbon, nitrogen and phosphorus of one cell. This figure shows the discrete growth of two cells to three, requiring both the generation of new structural material from reserves and the reserves being diluted as a result of the number of cells in which they are divided increasing from two to three. Thus, the internal reserves for nitrogen after the population increases from two to three is given by two from the initial two cells, minus one for building structural material of the new cell, shared across the three offspring, to give one-third. The same logic applies to carbon and phosphorus reserves, with phosphorus reserves being reduced to one-sixth and carbon reserves being exhausted. In contrast, pigment is not required for structural material so the only reduction is through dilution; the three-fourths content of two cells is shared among three cells to equal one-half in the three cells. This schematic shows one limitation of a population-style model whereby reserves are “shared” across the population (as opposed to individual-based modelling;

The molar ratio of a cell, the addition of structural material and reserves, is given by

The diffusion-limited nutrient uptake to a single phytoplankton cell,

Numerous studies have considered diffusion-limited transport to the cell surface at low nutrient concentrations saturating to a physiologically limited nutrient uptake at higher concentrations

Light absorption by microalgae cells has already been considered above (Eq. 6). The same absorption cross-section,

The rate of synthesis of pigment is based on the incremental benefit of adding pigment to the rate of photosynthesis. This calculation includes both the reduced benefit when carbon reserves are replete,

Microalgae growth model equations. The term

For each phytoplankton type, the model considers multiple pigments with distinct absorption spectra. The model needs to represent all photo-absorbing pigments as the

When photons are captured, there is an increase in reserves of carbon,

A linear mortality term, resulting in the loss of structural material and carbon reserves, is considered later.

As mentioned above, the nutrient uptake and light absorption rates are calculated on a per cell basis. This has allowed geometric considerations to be explicitly used and contrasts with most biogeochemical models that formulate planktonic rates based on population interactions. However, the state variables for microalgae (and zooplankton) are for the population. Therefore, rates per cell need to be multiplied by the number of cells to obtain population rates. In the case of microalgae, the number of cells

The conservation of mass of cells containing structural material and reserves during transport, growth and mortality is established in

The state variables, equations and parameter values for microalgae growth are listed in Tables

Constants and parameter values used in the microalgae model.

The growth of

Parameter values used in the

Nitrogen fixation occurs when the DIN concentration falls below a critical concentration,

The energetic cost of nitrogen fixation is represented as a fixed proportion of carbon fixation,

The rate of change of

The major pools of dissolved inorganic carbon species in the ocean are

The Ocean Carbon-Cycle Model Intercomparison Project (OCMIP) has developed numerical methods to quantify air–sea carbon fluxes and carbon dioxide system equilibria

We altered the OCMIP scheme by increasing the search space for the iterative scheme from

Nitrification is the oxidation of ammonium to form nitrite followed by the rapid oxidation of nitrite to nitrate. This is represented in a one-step process, with the rate of nitrification given by

State and derived variables for the water column inorganic chemistry model.

Equations for the water column inorganic chemistry.

Constants and parameter values used in the water column inorganic chemistry.

The rate of phosphorus desorption from particulates is given by

At steady state, the PIP concentration is given by

Phosphorus adsorption–desorption equilibria,

In the simple food web of the model, herbivory involves small zooplankton consuming small phytoplankton, and large zooplankton consuming large phytoplankton, microphytobenthos and

State and derived variables for the zooplankton grazing. Zooplankton cell mass,

Constants and parameter values used for zooplankton grazing. Dissipation rate of turbulent kinetic energy (TKE) is considered constant.

Equations for zooplankton grazing. The terms represent a predator

The rate of zooplankton grazing is determined by the encounter rate of the predator and all its prey up until the point at which it saturates the growth of the zooplankton (Eq. 75), and then it is constant. This is a Holling type I grazing response

Unlike the microalgae, zooplankton does not contain reserves of nutrients and fixed carbon, and therefore has a fixed stoichiometry of the Redfield ratio. As the zooplankton are grazing on the phytoplankton that contain internal reserves of nutrients, an additional flux of dissolved inorganic nutrients (

It is important to note that the microalgae model presented above represents internal reserves of nutrients, carbon and chlorophyll as a per cell quantity. Using this representation, there are no losses of internal quantities with either grazing or mortality. However, the implication of their presence is represented in the

An alternative and equivalent formulation would be to consider total concentration of microalgal reserves in the water column, then the change in water column concentration of reserves due to mortality (either grazing or natural mortality) must be considered. This alternate representation will not be undertaken here as the above considered equations are fully consistent, but it is worth noting that the numerical solution of the model within the code represents total water column concentrations of internal reserves and therefore must include the appropriate loss terms due to mortality.

Large zooplankton consume small zooplankton. This process uses similar encounter rate and consumption rate limitations calculated for zooplankton herbivory (Table

Equations for zooplankton carnivory, representing large zooplankton

In the model, there is no change in water column oxygen concentration if organic material is exchanged between pools with the same elemental ratio. Thus, when zooplankton consume phytoplankton, no oxygen is consumed due to the consumption of phytoplankton structural material (

The rate of change of plankton biomass,

A combination of linear and quadratic mortality rates are used in the model. When the mortality term is the sole loss term, such as zooplankton in the water column or benthic microalgae in the sediments, a quadratic term is employed to represent increasing predation/viral disease losses in dense populations. For suspended microalgae, we have used only a linear term (i.e.

As described in Sect.

Constants and parameter values used for plankton mortality.

Equations for linear phytoplankton mortality.

Equations for the zooplankton mortality.

Air–sea gas exchange is calculated using wind speed (we choose a cubic relationship;

In practice, the hydrodynamic model can contain thin surface layers as the surface elevation moves between

The saturation state of oxygen

The change in surface dissolved inorganic carbon concentration, DIC, resulting from the sea–air flux (positive from sea to air) of carbon dioxide is given by

Note the carbon dioxide flux is determined not by the gradient in DIC but the gradient in [

In the model, benthic communities are quantified as a biomass per unit area or areal biomass. At low biomass, the community is composed of a few specimens spread over a small fraction of the bottom, with no interaction between the nutrient and energy acquisition of individuals. Thus, at low biomass, the areal fluxes are a linear function of the biomass.

As biomass increases, the individuals begin to cover a significant fraction of the bottom. For nutrient and light fluxes that are constant per unit area, such as downwelling irradiance and sediment releases, the flux per unit biomass decreases with increasing biomass. Some processes, such as photosynthesis in a thick seagrass meadow or nutrient uptake by a coral reef, become independent of biomass

To restate, at low biomass, the area on the bottom covered by the benthic community is a linear function of biomass. As the total leaf area approaches and exceeds the projected area, the projected area for the calculation of water-community exchange approaches 1 and becomes independent of biomass. This is represented using

The parameter

The macroalgae model considers the diffusion-limited supply of dissolved inorganic nutrients (N and P) and the absorption of light, delivering N, P and fixed C, respectively. Unlike the microalgae model, no internal reserves are considered, implying that the macroalgae has a fixed stoichiometry that can be specified as

Nutrient uptake by macroalgae is a function of nutrient concentration, water motion

The calculation of light capture by macroalgae involves estimating the fraction of light that is incident upon the leaves and the fraction that is absorbed. The rate of photon capture is given by

For more details on the calculation of

The growth rate combines nutrient, light and maximum organic matter synthesis rates following

The maximum growth rate is inside the minimum operator. This allows the growth of macroalgae to be independent of temperature at low light but still have an exponential dependence at maximum growth rates

Mortality is defined as a simple linear function of biomass:

The full macroalgae variables, equations and parameters are listed in Tables

State and derived variables for the macroalgae model. For simplicity, in the equations, all dissolved constituents are given in grams, although elsewhere they are shown in milligrams.

Equations for the macroalgae model. Other constants and parameters are defined in Table

Constants and parameter values used to model macroalgae.

Seagrasses are quantified per m

State and derived variables for the seagrass model. For simplicity, in the equations, all dissolved constituents are given in grams, although elsewhere they are shown in milligrams. The bottom water column thickness is spatially variable depending on bathymetry.

Equations for the seagrass model. Other constants and parameters are defined in Table

Constants and parameter values used to model seagrass.

The coral polyp parameterisation consists of a microalgae growth model to represent zooxanthellae growth based on

The state variables for the coral polyp model (Table

Model state variables for the coral polyp model. Note that water column variables are three-dimensional, benthic variables are two-dimensional, and unnormalised reserves are per cell.

The zooxanthellae light absorption capability is resolved by considering the time-varying concentrations of pigments chlorophyll

The coral host is able to assimilate particulate organic nitrogen either through translocation from the zooxanthellae cells or through the capture of water column organic detritus and/or plankton. The zooxanthellae varies its intracellular pigment content depending on potential light limitation of growth, and the incremental benefit of adding pigment, allowing for the package effect

Here, we present the state variables (Table

Derived variables for the coral polyp model.

Equations for the interactions of coral host, symbiont and environment excluding bleaching loss terms that appear in Table

Equations for the coral polyp model. The term

Equations for symbiont reaction centre dynamics. Bleaching loss terms appear in Table

Equations describing the expulsion of zooxanthellae and the resulting release of inorganic and organic molecules into the bottom water column layer.

Constants and parameter values used to model coral polyps.

Constants and parameter values used in the coral bleaching model. “RCII” indicates the reaction centre of photosystem II.

The rate of coral calcification is a function of the water column aragonite saturation,

Equations for coral polyp calcification and dissolution. The concentration of carbonate ions,

In addition to the dissolution of carbonate sands on a growing coral reef, which is captured in the net dissolution quantified above, the marine carbonates on the continental shelf dissolve

We assume carbonate dissolution from the sediment bed is proportional to the fraction of the total surface sediment that is composed of either sand or mud carbonates. Other components, whose fraction do not release DIC and alkalinity, include carbonate gravel and non-carbonate mineralogies. Thus, the change in DIC and

The EMS model contains a multi-layered sediment compartment with time- and space-varying vertical layers and the same horizontal grid as the water column and epibenthic models. All state variables that exist in the water column layers have an equivalent in the sediment layers. The dissolved tracers are given as a concentration in the porewater, while the particulate tracers are given as a concentration per unit volume (see Sect.

The sediment model contains inorganic particles of different sizes (dust, mud, sand and gravel) and different mineralogies (carbonate and non-carbonate) (Table

Characteristics of the particulate classes. Y – yes, N – no, I – initial condition, C – catchment, OM – remineralisation from organic matter, B – brown, W – white

The critical shear stress for resuspension and the sinking rates are generally larger for large particles, while mineralogy only affects the optical properties. The size-class dust only has a non-carbonate form. FineSed also only has a non-carbonate form and has the same physical and optical properties as non-carbonate mud, except that it is initialised with a zero value. Dust and FineSed are particles that enter the domain from rivers during the simulation.

The organic matter classes are discussed in the Sect.

Nitrification in the sediment is similar to the water column but with a sigmoid rather than hyperbolic relationship at low oxygen for numerical reasons (Eq. 204). Denitrification occurs only in the sediment.

Sediment phosphorus absorption–desorption is similar to water column (Eq. 206). There is an additional pool of immobilised particulate inorganic phosphorus (PIPI) which accumulates in the model over time as PIP becomes immobilised and represents permanent sequestration (Eq. 207).

The non-living components of the C, N and P cycles include the particulate labile and refractory pools, and a dissolved pool (Fig.

State and derived variables for the sediment inorganic chemistry model.

Constants and parameter values used in the sediment inorganic chemistry.

Equations for the sediment inorganic chemistry.

State and derived variables for the detritus remineralisation model in both the sediment and water column.

Equations for detritus remineralisation in the water column and sediment.

Constants and parameter values used in the water column detritus remineralisation model. Red is the Redfield ratio (

The processes of remineralisation, phytoplankton mortality and zooplankton grazing return carbon dioxide to the water column. In oxic conditions, these processes consume oxygen in a ratio of DIC :

When oxygen and

Most of the ecological processes contain a temperature dependence and, for those uptaking dissolved inorganic nitrogen, preferential ammonium uptake. To simplify the description of the above processes, these common parameterisations are described separately in this section. An additional processes common to all variables, and across multiples zones, is the diffusive sediment–water exchange.

The model contains two forms of dissolved inorganic nitrogen (DIN) used by photosynthetic organisms, dissolved ammonium (

As the nitrogen uptake formulation varies for the different autotrophs, the formulation of the preference of ammonium also varies. The diffusion coefficient of ammonium and nitrate are only 3 % different, so for simplicity we have used the nitrate diffusion coefficient for both.

Thus, for microalgae (Eq. 40) and

For macroalgae (Eq. 108) and seagrass leaves (Eq. 122), which also have diffusion limits to uptake but are not represented with internal reserves of nitrogen, the terms are

Zooxanthellae is a combination of the two cases above, because in the model they contain reserves like microalgae, but the uptake rate is across a 2-D surface like macroalgae.

In the case of nutrient uptake by seagrass roots (Eq. 124), which has a saturating nitrogen uptake functional form, the terms are

One feature worth noting is that the above formulation for preferential ammonium uptake requires no additional parameters, which is different to other classically applied formulations

For all autotrophs, the uptake of a nitrate ion results in the retention of the one nitrogen atom in their reserves or structural material, and the release of the three oxygen atoms into the water column or porewaters.

For simplicity, in the equations for autotroph-driven changes in dissolved oxygen above, we have assumed that DIN uptake is ammonium. Thus, after partitioning on nitrogen uptake, the term in Eq. (235) needs to be added to change in oxygen in microalgae (Eq. 40),

Physiological rate parameters (maximum growth rates, mortality rates, remineralisation rates) have a temperature dependence that is determined from

Note that while physiological rates may be temperature dependent, the ecological processes they are included in may not. For example, for extremely light-limited growth, all autotrophs capture light at a rate independent of temperature. With the reserves of nutrients replete, the steady-state realised growth rate,

Similar arguments show that extremely nutrient limited autotrophs will have the same temperature dependence to that of the diffusion coefficient. Thus, the autotroph growth model has a temperature dependence that adjusts appropriately to the physiological condition of the autotroph and is a combination of constant, exponential and polynomial expressions.

Physiological rates in the model that are not temperature dependent are mass transfer rate constant for particulate grazing by corals,

Due to the thin surface sediment layer, and the potentially large epibenthic drawdown of porewater dissolved tracers, the exchange of dissolved tracers between the bottom water column layer and the top sediment layer is integrated in the same numerical operation as the ecological tracers (other transport processes occurring between ecological time steps). The flux,

While, in reality,

The numerical solution of the time-dependent advection–diffusion–reaction equations for each of the ecological tracers is implemented through sequential solving of the partial differential equations (PDEs) for advection and diffusion, and the ordinary differential equations (ODEs) for reactions. This technique, called operator splitting, is common in geophysical science

Under the sequential operator splitting technique used, first the advection–diffusion processes are solved for the period of the time step (15 min–1 h; Table

Integration details. Optical wavelengths are 290, 310, 330, 350, 370, 390, 410, 430, 440, 450, 470, 490, 510, 530, 550, 570, 590, 610, 630, 650, 670, 690, 710 and 800 nm.

The PDE solvers are described in the physical model description available at

The code allows fourth- to fifth-order and seventh- to eighth-order adaptive ODE solvers following

The solution of the ecological equations are independent for each vertical column and depend only on the layers above through which the light has propagated. For an

The inherent and apparent optical properties are calculated between the hydrodynamic and ecological integrations. The light field used for each ecological time step is that calculated at the start time of the ecological integration. The spectral resolution of 25 wavebands has been chosen to resolve the absorption peaks associated with Chl

In this model description, we have chosen to explicitly include atomic mass as integer values, so that the unit conversions are more readable in the equations than if they had all been rendered as mathematical symbols. Nonetheless, these values are more precisely given in the numerical code (Table

Atomic mass of the C, N, P and

It is worth remembering that the atomic masses are approximations assuming the ratio of isotopes found in the periodic table

A check of mass conservation of total C, TC, total N, TN, total P, TP, and oxygen, [

The total mass and conservation equations are same for the water column and porewaters, with the caveats that (1) air–sea fluxes only affect surface layers of the water, (2) denitrification only occurs in the sediment, and (3) the porosity,

The total carbon in a unit volume of space and its conservation are given by

The total nitrogen in a unit volume of space and its conservation are given by

The total phosphorus in a unit volume of space and its conservation are given by

The concept of oxygen conservation in the model is more subtle than that of C, N and P due to the mass of oxygen in the water molecules not being considered. When photosynthesis occurs, C is transferred from the dissolved phase to reserves within the cell. With both dissolved and particulate pools considered, mass conservation of C is straightforward. In contrast to C, during photosynthesis, oxygen is drawn from the water molecules (i.e.

In order to obtain a mass conservation for oxygen, the concept of biological oxygen demand (BOD) is used. Often BOD represents the biological demand for oxygen in say a 5 d incubation, BOD

Anaerobic respiration reduces BOD

In addition to dissolved oxygen, BOD and COD, nitrate (

Mass conservation in the epibenthos requires consideration of fluxes between the water column, porewaters and the epibenthic organisms (macroalgae, seagrass and coral hosts and symbionts).
The total carbon in the epibenthos, and its conservation, is given by

Similarly, for nitrogen, phosphorus and oxygen in the epibenthos,

In addition to the above standard numerical techniques, a number of innovations are used to ensure model solutions are reached. Should an integration step fail in a grid cell, no increment of the state variables occurs, and the model continues with a warning flag registered (as

The EMS BGC model has been deployed in a range of environments around Australia. With each deployment, a skill assessment has been undertaken (for a history of these applications, see Sect.

A more recent assessment of the BGC model (vB2p0) in the GBR compared simulations against a range of in situ observations that included 24 water quality moorings, two nutrient sampling programmes (with a total of 18 stations) and time series of taxon-specific plankton abundance. In addition to providing a range of skill metrics, the assessment included analysis of seasonal plankton dynamics

In this section, we assess version B3p0 in the 4 km GBR configuration. First, we consider the behaviour of the microalgae physiology as a means to understanding the dynamics of the microalgal growth model. Secondly, the techniques and observations used in

The microalgae growth model (Sect.

To illustrate these dynamics, we look at a vertical profile of a deep site in the Coral Sea with a 1 and 2.5

Vertical profiles of physiochemical variables

In addition to being a measure of the quantity of nutrient reserves, normalised reserves (

The elemental ratios of the microalgae can be calculated from the reserves (in wt wt

The 1 and 2.5

In summary, the application of simple physical limits to uptake, a restraint of constant stoichiometric conversion to structural material, and cells synthesising chlorophyll to maximise photon absorption when light limited, generates the typical physiological properties of microalgae seen in vertical profiles in the ocean.

A detailed comparison of a GBR simulation against observations of Chl

The most accurate measurements of water column chlorophyll concentrations in the GBR are obtained using high-performance liquid chromatography (HPLC) and chlorophyll extractions from water column samples. Chlorophyll extractions have been taken at 36 locations along the GBR (S5, Sect. 10; for site locations, see S5, Sect. E1). As an example, a time series at Pelorus Island in the central GBR (Fig.

Observed surface chlorophyll concentration from chlorophyll extraction (red dots) at the Pelorus Island Marine Monitoring Program site (

Moored fluorometers are generally less accurate than chlorophyll extractions but provide a greater temporal resolution of chlorophyll dynamics. Here, we show observations from a mooring at Palm Passage (Fig.

Skill metrics for the comparison of chlorophyll extracts at the long-term monitoring sites against observations for model versions 2p0 and 3p0. For more information, see Fig.

The model represents dissolved nitrate, ammonium and phosphorus nutrients. In the surface waters of the inshore GBR, nutrients are generally at very low concentrations, with modest increases seen each wet season. At High Island in the central GBR (Fig.

Observed chlorophyll fluorescence (red dots) at 60 m depth at the Palm Passage site with a comparison to configurations vB3p0 (blue) and vB2p0 (pink).

Dissolved inorganic phosphorus

The model contains two state variables to represent the state of carbon chemistry, dissolved inorganic carbon and alkalinity, from which, at equilibrium and known temperature and salinity, other variables such as pH may be calculated. The biogeochemical model provides highly skilful predictions of pH and aragonite saturation (Fig.

Aragonite saturation state calculated from temperature, DIC and alkalinity at 20 m depth at the Integrated Marine Observing System (IMOS) Yongala mooring, central GBR: observations (red dots), simulations B2p0 (pink) and B3p0 (blue).

The outputs of all hindcasts in the eReefs project can be downloaded from

A web-based interface, RECOM, has been developed to automate the process of downscaling the EMS model using an existing hindcast as boundary conditions (

The EMS BGC model development has been a function of the historical applications of the model across a rage of ecosystems, so it is worth giving a brief history of the model development.

The EMS biogeochemical model was first developed as a nitrogen-based model for determining the assimilative capacity for sewerage discharged into Port Philip Bay, the embayment of the city of Melbourne

The next major study involved simulating a range of estuarine morphologies (salt wedge, tidal, lagoon, residence times) and forcings (river flow seasonality, nutrient inputs, etc.) that were representative of Australia's

Following studies in the phosphorus-limited Gippsland Lakes and macro-tidal Ord River system led to the refinement of the phosphorus absorption–desorption processes. Further studies of the biogeochemical–sediment interactions in the subtropical Fitzroy River

The next major change in the BGC model involved implementing variable

From 2010 onwards, EMS has been applied to consider the impacts of catchment loads on the Great Barrier Reef. The focus on water clarity led to the development of a spectrally resolved optical model and the introduction of simulated true colour

As introduced earlier, there are a number of complex marine biogeochemical models. The most similar model in scope and approach to EMS is the ERSEM (European Regional Seas Ecosystem Model) model

The last two decades have seen addition modelling approaches emerge: trait-based models that consider changing processes rates as populations vary

EMS has been developed to address specific scientific questions in Australia's coastal environment. As a result, the set of processes the EMS considers varies from those typically applied by other groups developing marine BGC models. Processes which have not been considered but often are considered in marine BGC models, include iron and silicate limitation (which are not common on the Australian continental shelf or estuaries), photo-inhibition of microalgae, explicit bacterial biomass. Each of these will be considered as the need arises.

A deliberate decision in the development of the EMS BGC model was made to avoid higher-trophic-level processes, such fish dynamics and reproduction of long-lived species. This decision was made because (1) including these longer timescale, often highly non-linear, processes reduces the ability of development to concentrate on BGC processes; and (2) it was recognised that CSIRO has developed a widely used ecosystem model (Atlantis,

A recent capacity introduced to EMS is the development of a relocatable capability (RECOM; Sect.

Future enhancements in the EMS BGC model for tropical systems are likely to continue to pursue those components at risk from human impacts, such as dissolution of marine carbonates affecting sediment substrate and herbicide interactions with photosystems. We also expect to continue to refine the optical model and in particular the relationship between particle size distribution and mass-specific scattering and absorption properties. In temperate systems, current and near-future deployments of EMS in Australia will be focused on coastal system characterisation for aquaculture, carbon sequestration and management decision support for the blue economy. Ongoing research includes improved methods for model validation against observations and translation of model outputs into knowledge that informs stakeholder decisions.

The BGC model in the CSIRO EMS has developed unique parameterisation when compared to other marine biogeochemical models applied elsewhere due in part to a unique set of scientific challenges of the Australian coastline. It has proved to be useful in many applications, most notably the Great Barrier Reef where extensive observational datasets has allowed new process model development and detailed model skill assessment (

The model web page is

The web page links to an extensive user guide for the entire EMS package, which contains any information that is generic across the hydrodynamic, sediment, transport and ecological models, such as input/output formats. A smaller biogeochemical user guide documents details relevant only to the biogeochemical and optical models (such as how to specify wavelengths for the optical model), and a biogeochemical developer's guide describes how to add additional processes to the code.

A permanent link to the EMS C code used in this paper is

The code available is also available on GitHub at

The list of processes that this paper describes is given in a configuration file in the Supplement (S1). The library contains other processes that have been retained for backward comparability or for other applications (i.e. mussel farms). The methods by which differential equations described in this scientific description are incorporated into the model code are described in the Supplement (S2).

The supplement related to this article is available online at:

All authors contributed to the CSIRO EMS BGC model through either proposing model formulations, writing significant components of the code or applying the model. The primary model developers were MEB, KWA, JP, MM, BR and FR. MEB wrote the manuscript with co-authors contributing analyses, figures and revisions. JS and MEB prepared the article Supplements.

The authors declare that they have no conflict of interest.

Many scientists and projects have contributed resources and knowhow to the development of this model over

Mike Herzfeld, Philip Gillibrand, John Andrewartha, Farhan Rizwi, Jenny Skerratt, Mathieu Mongin, Mark Baird, Karen Wild-Allen, John Parlsow, Emlyn Jones, Nugzar Margvelashvili, Pavel Sakov (BOM, who introduced the process structure), Jason Waring, Stephen Walker, Uwe Rosebrock, Brett Wallace, Ian Webster, Barbara Robson (AIMS), Scott Hadley (University of Tasmania), Malin Gustafsson (University of Technology Sydney, UTS) and Matthew Adams (Queensland University of Technology).

We also thank Britta Schaffelke and her colleagues in the Marine Monitoring Program for their commitment to obtaining the observations that enabled the model evaluation. We also acknowledge the use of data from the AIMS Long Term Monitoring Program, Australia's Integrated Marine Observing System and the Future Reef 2.0 Program funded by GBRF, Rio Tinto and CSIRO. We greatly appreciate Cedric Robillot for his leadership of the eReefs project.

Collaborating scientists include Andy Steven, Thomas Schroeder, Bronte Tilbrook, Craig Neill, John Akl, Erik van Ooijen, Nagur Cherukuru, Peter Ralph (UTS), Russ Babcock, Kadija Oubelkheir, Bojana Manojlovic (UTS), Stephen Woodcock (UTS), Stuart Phinn (UQ), Chris Roelfsema (UQ), Miles Furnas (AIMS), David McKinnon (AIMS), David Blondeau-Patissier (Charles Darwin University), Michelle Devlin (James Cook University), Eduardo da Silva (JCU), Julie Duchalais, Jerome Brebion, Leonie Geoffroy, Yair Suari, Cloe Viavant, Lesley Clementson (pigment absorption coefficients), Dariusz Stramski (inorganic absorption and scattering coefficients), Erin Kenna, Line Bay (AIMS), Neal Cantin (AIMS), Luke Morris (AIMS), Daniel Harrison (SCU) and Karlie MacDonald.

Funding bodies include CSIRO Wealth from Oceans Flagship, Gas Industry Social & Environmental Research Alliance (GISERA), CSIRO Coastal Carbon Cluster, Derwent Estuary Program, INFORM2, eReefs, Great Barrier Reef Foundation, Australian Climate Change Science Program, University of Technology Sydney, Department of Energy and Environment, Integrated Marine Observing System (IMOS), National Environment Science Program (NESP TWQ Hub) and the Royal Australian Navy.

Finally, we greatly appreciate Marcello Vichi's in-depth and insightful review that has much improved the manuscript.

This paper was edited by Julia Hargreaves and reviewed by Marcello Vichi and one anonymous referee.