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  Received: 30 Apr 2019 – Discussion started: 09 Jul 2019 – Revised: 16 Jul 2020 – Accepted: 01 Aug 2020 – Published: 25 Sep 2020
  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 20+ optically active constituents. The BGC model itself cycles carbon, nitrogen, phosphorous and oxygen through multiple phytoplankton, zooplankton, detritus and dissolved organic and inorganic forms in multiple water column and sediment layers. The water column is dynamically coupled to the sediment to resolve deposition, resuspension and benthic–pelagic biogeochemical fluxes. With a focus on shallow waters, the model also includes detailed representations of benthic plants such as seagrass, macroalgae and coral polyps. A second focus has been on, where possible, the use of geometric derivations of physical limits to constrain ecological rates. This geometric approach generally requires population-based rates to be derived from initially considering the size and shape of individuals. For example, zooplankton grazing considers encounter rates of one predator on a prey field based on summing relative motion of the predator with the prey individuals and the search area; chlorophyll synthesis includes a geometrically derived self-shading term; and the bottom coverage of benthic plants is calculated from their biomass using an exponential form derived from geometric arguments. This geometric approach has led to a more algebraically complicated set of equations when compared to empirical biogeochemical model formulations based on populations. But while being algebraically complicated, the model has fewer unconstrained parameters and is therefore simpler to move between applications than it would otherwise be. The version of EMS described here is implemented in the eReefs project that delivers a near-real-time coupled hydrodynamic, sediment and biogeochemical simulation of the Great Barrier Reef, northeast Australia, and its formulation provides an example of the application of geometric reasoning in the formulation of aquatic ecological processes.
  The first model of marine biogeochemistry was developed more than 70 years ago to explain phytoplankton blooms (Riley, 1947). Today, the modelling of estuarine, coastal and global biogeochemical systems has been used for a wide variety of applications including coastal eutrophication (Madden and Kemp, 1996; Baird et al., 2003), shelf carbon and nutrient dynamics (Yool and Fasham, 2001; Dietze et al., 2009), plankton ecosystem diversity (Follows et al., 2007), ocean acidification (Orr et al., 2005), impact of local developments such as fish farms and sewerage treatment plants (Wild-Allen et al., 2010), fishery production (Stock et al., 2008) and operational forecasting (Fennel et al., 2019), to name a few. As a result of these varied applications, a diverse range of biogeochemical models has emerged, with some models developed over decades and being capable of investigating a suite of biogeochemical phenomena (Butenschön et al., 2016). With model capabilities typically dependent on the history of applications for which a particular model has been developed, and perhaps even the backgrounds and interests of the developers themselves, significant differences exist between models. Thus, it is vital that biogeochemical models are accurately described in full (e.g. Butenschön et al., 2016; Aumont et al., 2015 and Dutkiewicz et al., 2015), so that model differences can be understood and, where useful, innovations shared between modelling teams.