Chapter 9

Biogeochemical modelling

CHAPTER
COORDINATORS

Elodie Gutknecht

CHAPTER
AUTHORS

Laurent Bertino, Pierre Brasseur, Stefano Ciavatta, Gianpiero Cossarini, Katja Fennel, David Ford, Marilaure Grégoire, Diane Lavoie, and Patrick Lehodey

9.1 General introduction to Biogeochemical models

Marine biogeochemistry is the study of essential chemical elements in the ocean (such as carbon, nitrogen, oxygen, and phosphorus), and of their interactions with marine organisms. Biogeochemical cycles are driven by physical transport, chemical reactions, absorption, and transformation by plankton and other organisms, which form the basis of the oceanic food web.

In the last decades, the interest for this cross-disciplinary science has greatly increased due to the occurrence of significant changes in the marine environment closely linked to the alteration of the biogeochemical cycles in the ocean. These alterations include phenomena such as acidification, coral bleaching, eutrophication, deoxygenation, harmful algal blooms, regime shifts in plankton, invasive species, and other processes deteriorating water quality and impacting the whole marine ecosystem.

Monitoring and forecasting the biogeochemical and ecosystem components of the ocean, also referred to as “Green Ocean”, are essential for a better understanding of the current status and changes in ocean health and ecosystem functioning. Such operational systems provide indicators useful to scientists, industry (e.g. fisheries and aquaculture), policy makers and environmental agencies for the prediction of events, the management of living marine resources, and can support the decision-making process to respond to environmental changes.

This chapter gives an overview of the Green Ocean component of OOFS. The first section addresses the objectives, applications and beneficiaries of the Green Ocean and introduces the fundamental theoretical knowledge of marine biogeochemical modelling. The second section details and discusses each component of a biogeochemical OOFS to guide new forecasters in biogeochemistry. Modelling of higher trophic levels is introduced. Finally, several operational systems are mentioned as examples.

9.1.1 Objective, applications and beneficiaries

Human activities, primarily the combustion of fossil fuels, cement production, and the industrial production of nitrogen-based fertilisers, are leading to ocean warming, acidification, deoxygenation, and coastal eutrophication, thus putting ever-increasing and compounding pressures on marine ecosystems (Figure 9.1).

Figure 9.1. Threats on marine ecosystems. Changes and alterations in the marine environment observed in recent decades include acidification, coral bleaching, eutrophication, deoxygenation, harmful algal blooms, changes in planktonic regimes, invasive species, etc.

At the same time, the ocean is serving as a major sink of carbon dioxide (CO2), the most important anthropogenic greenhouse gas. This contributes to mitigating global warming, but the magnitude of this sink is likely to diminish. Our ability to quantify these phenomena and project their future course hinges on a mechanistic understanding of the biogeochemical cycles of carbon, oxygen, and nutrients in the ocean and how they are changing.

The Marine BGC, the study of elemental cycles and their interactions with the environment and living organisms, is a multidisciplinary science at the crossroads between ocean physics, chemistry, and biology, and intersects with atmospheric and terrestrial sciences as well as social science and environmental policy. As an example, Figure 9.2 illustrates the complex carbon cycle in the ocean and the interactions between biological, chemical, and physical processes.

Figure 9.2. Cycling of carbon in the marine food chain. Phytoplankton assimilate CO2 via photosynthesis in the euphotic zone and are consumed by zooplankton. Zooplankton are the initial prey for many small and large aquatic organisms. Carbon is thus transferred further up the food web to higher-level predators. Different mechanisms contribute to the export and storage of carbon into the deep ocean. The carbon cycle in the ocean is complex and influenced by biological, chemical, and physical processes - credit: Oak Ridge National Laboratory at https://www.ornl.gov/

Ocean BGC models describe the base of the marine food chain from bacteria to mesozooplankton and couple the cycles of carbon (C), nitrogen (N), oxygen (O2), phosphorus (P) and silicon (Si). They mostly focus on plankton, classifying the plankton diversity in accordance with their functional characteristics, the so-called Plankton Functional Types (PFTs). Species at higher trophic levels, such as fish and marine mammals play a lesser role in elemental cycling, they are thus generally not explicitly represented in BGC models, but they are very important for ecosystem models that focus on the ecology/biology of marine organisms. BGC and ecosystem models are sometimes referred to indistinctly because they can overlap in their representation of the lower trophic levels. Specific modelling approaches, like Lagrangian modelling, habitat modelling, or food web models, are used to connect BGC with the high trophic levels (e.g. fish).

The implementation of accurate OOFSs requires sustained, systematic, and NRT observation from (sub)mesoscale to large scale to initialise, parameterize, and validate ocean models. NRT information in operational oceanography means a description of the present situation with a delay of a few minutes to a few days.

The forecast of ocean physics has considerably improved in the last decades, reaching a high level of predictability (Chapter 5). The evolving equations governing the physical dynamics are based on physical laws, the model parameterizations are quite well-established, and the abundance of observations for temperature, salinity, and sea level height offers a way to improve model predictions through data assimilation. Forecasting of the Green Ocean has been developed more recently and it has not yet reached the same level of maturity, in most cases being incorporated into already existing physical OOFS. The formulation of ecosystem models is still empirical and the scarcity of in-situ biological and BGC data critically limits the capabilities to constrain their parameterization and to improve their performances through a robust data-model comparison exercise and data assimilation. The scarcity of data is even more critical in NRT, limiting data assimilation to surface chlorophyll-a (Chla) derived from satellite reflectance (Fennel et al., 2019).

The advent of in-situ robotic platforms combined with high resolution satellite products for the Green Ocean have the potential to palliate this deficiency. For instance, the advent of hyper-spectral satellites is promising in terms of delivery of surface information on PFTs, detection of harmful algal blooms, and benthic habitat mapping, while the boost in robotic platforms will offer huge opportunities to map the (deep) seafloor with an unprecedented level of details. The combination of marine robotics, image analysis, machine learning, new sensor development, and the coordination of robotic platforms and satellite sensors will constitute a significant breakthrough in our knowledge of marine ecosystems. All this information would need to be integrated in models for forecasting and producing high quality reanalysis of the Green Ocean to support the production of added value products and innovative services. Coordination of Ocean OSSEs can help to design the new observing biological and biogeochemical systems with maximal impact to users, yet their development is still insufficient and should be encouraged (Le Traon et al., 2019).

Ultimately, BGC OOFS systems serve major environmental and societal issues, including the Ocean's role in the global carbon cycle and the impacts of natural changes and anthropogenic stressors in the physical-chemical marine environment on ecosystems and human activities. Applications range from multi-decadal retrospective simulations (namely, “reanalyses”), operational analysis of the current conditions (“nowcasts”), short-term and seasonal predictions (“forecasts”), scenario simulations, and climate change projections. These integrated systems are essential not only for a better understanding of the current status of key biogeochemical and ecosystem processes in the ocean and how they are changing, but also to provide stakeholders, policy makers and environmental agencies with indicators of ocean health in order to take appropriate mitigation, adaptation, conservation, and protection measures for living marine organisms and their habitats but also for human health.

“A predicted ocean whereby society has the capacity to understand current and future ocean conditions, forecast change and impact on human wellbeing and livelihoods” is an expected outcome of the United Nations Decade of Ocean Science for Sustainable Development, 2021-2030 (Ryabinin et al., 2019), supported also by the Sustainable Development Goals 14 (Life below water), 8 (Decent work and economic growth), and 9 (Industry, innovation and infrastructure).

9.1.2 Fundamental theoretical background

9.1.2.1 Biogeochemical modelling

Plankton (including phytoplankton and zooplankton) are organisms which are carried by tides and currents, or do not swim well enough to move against them. They form the base of the marine ecosystem and are a central component of the BGC models that simulate the cycling of elements through seawater and plankton.

Most models take an “NPZD” approach, simulating:

Nutrients: substances which organisms require for growth.
Phytoplankton: microscopic algae which obtain energy from sunlight through photosynthesis.
Zooplankton: planktonic animals which obtain energy by eating other organisms.
Detritus: dead and excreted organic matter.

Each of these is represented by one or more state variables, depending on the complexity of the model. Rather than considering individual organisms, state variables represent concentrations of elements such as nitrogen or carbon. They are often called tracers because they are transported and diffused by ocean dynamics.

As with physical models, BGC models are discretized on a grid covering the region of interest and require suitable initial and boundary conditions for each state variable. At each grid point, the evolution of a state variable C is given by the equation:

where ∇ ∙ (CU) and DC are the advection and diffusion terms equivalent to those used for temperature and salinity in physical models (please refer to Chapter 5). ∇ is the generalised derivative vector operator, t is the time, U the vector velocity, and D^c is the parameterization of small-scale physics for the tracer. The SMS(C) stands for source-minus-sink terms for the tracer C and represents the BGC processes simulated by the model. Each 1D water column is normally treated independently, with lateral interactions limited to advection and diffusion. Most BGC models are formulated to conserve mass.

Figure 9.3. Schematic of a basic NPZD model considering four state variables, one for each compartment.

Unlike the Navier-Stokes equations for physical models (Chapter 5), there is no known set of laws defining biological behaviour. Instead, empirical relationships are used to describe observed processes such as growth and mortality.

The basic source-minus-sink terms usually modelled in a NPZD model (Figure 9.3) are:

Phytoplankton growth or Primary production: the creation of organic matter through photosynthesis. It is a function of phytoplankton concentration, nutrient availability, and light availability. It can also be regulated by temperature.
Grazing: zooplankton eating phytoplankton and detritus.
Mortality: death through natural causes, e.g. viruses, predation by higher trophic levels (fish and marine mammals), etc.
Messy feeding: zooplankton graze inefficiently, and a proportion of organic matter enters the nutrient or detritus pool rather than being ingested by zooplankton.
Remineralisation: bacteria break down the organic matter in detritus, which is converted back to nutrients.
Sinking: detritus sinks through the water column due to gravity.

In this case, the differential equations for phytoplankton (P), zooplankton (Z), detritus (D), and nutrients (N) are as follows:

where phytoplankton evolution depends on primary production, grazing and mortality;

where zooplankton evolution depends on grazing and mortality;

where detritus evolution depends on mortality, grazing, messy feeding, remineralisation and sinking;

where nutrients evolution depends on primary production, messy feeding, and remineralisation.

µ_P is the growth rate of phytoplankton due to photosynthesis; m_P and m_zare the mortality rates of phytoplankton and zooplankton; G_P and G_D are the grazing rates of zooplankton on phytoplankton and detritus; α_Dand α_Nrepresent the efficiency of the grazing; (1-α_D) and (1-α_N) the non-assimilated fractions of grazing by zooplankton that return to detritus and nutrients; rem_D is the remineralisation rate of detritus and w_D is the sinking speed of detritus.

The exact equations used differ between models, the ones given above are common examples. Other processes are often considered as well, notably respiration, excretion, and egestion, which cause loss of organic matter. Of course, additional processes may be included in more complex models.

The processes can be modelled using different mathematical forms, often with parameter values which are uncertain and can be tuned. While sinking and mortality rates are usually single parameters (linear functions), phytoplankton growth rate requires multiple parameters. µ_P is usually a function of nutrients, light and temperature:

µ_P^ma^xis the maximum growth rate, f(T) is the temperature effect, f(I) and f(N) are the limitation terms due to light and nutrients. Different formulations exist for each of these terms, but usually NPZD-type models characterise nutrient limitation of phytoplankton growth rate using Michaelis-Menten kinetics:

K is known as the half-saturation constant for nutrient uptake, and N is the nutrient concentration. If nutrient is plentifully available, then N/(K+N) ≈1 and phytoplankton growth is not limited by the nutrient.

The state variables of NPZD models represent concentrations of a given chemical element, often nitrogen, with other elements such as carbon derived using constant stoichiometry between carbon, nitrogen and phosphorus, i.e. the Redfield ratio of 106:16:1 (Redfield, 1934).

More complex models include additional variables for each compartment. Phytoplankton can be split into PFTs, grouping together species which perform a similar function within the ecosystem (Le Quéré et al., 2005). PFTs are often based on organism size. It is also common to separate out diatoms, which form silicate shells and play an important role in the sinking of carbon. In models, PFTs are distinguished by differing parameters for traits such as maximum phytoplankton growth rates, grazing, and nutrient affinity. Zooplankton can also be split into functional types, again often based on size, with different feeding preferences. Note that the current paradigm neglects the fact that many plankton are mixotrophs: they both photosynthesize and eat other organisms (Flynn et al., 2013; Glibert et al., 2019).

Variable stoichiometry (elemental ratios) can also be introduced. Each PFT is then described by separate state variables for each element, such as nitrogen, carbon, and phosphorus.

Chla is often included into BGC models as it is the main photosynthetic pigment found in phytoplankton, and measurement of its concentration in water is used as an indicator of the phytoplankton biomass. Chla can be represented as a constant ratio to the carbon biomass, or a variable ratio depending on nutrient, light levels, and temperature (Geider et al., 1997).

Most models incorporate dissolved inorganic nitrogen as a nutrient, which includes nitrate and ammonium. Phosphate and iron may be modelled too, and silicate if diatoms are a PFT. Nutrient inputs from rivers and the atmosphere can also be specified. Detritus may be split into different sizes, with different sinking rates, and into different elements. Some models explicitly simulate bacteria and viruses, rather than just parameterising their effects.

Besides NPZD variables, models can also include other related processes, such as the oxygen and carbon cycles. The carbon cycle is usually represented by the state variables DIC and total alkalinity, the latter being the capacity of seawater to neutralise an acid. From these and other variables, quantities such as pH and air-sea CO2 flux can be calculated (Zeebe and Wolf-Gladrow, 2001).

BGC models are closely related to higher trophic level models or ecosystem models. The latter require the underlying biogeochemistry, and BGC models require at least some parameterisation of the ecosystem, i.e. the explicit representation of part of the living component of the ocean (e.g. phytoplankton, zooplankton) with zooplankton mortality as a closure term, parameterising the predation of zooplankton by higher trophic levels such as fish and top predators (see Section 9.2.8).

Adding complexity to BGC models means that less important processes are neglected or amalgamated, but also increases the uncertainties associated with approximated formulations. There is no consensus on optimal structure and complexity, which will vary depending on the purpose (Fulton et al., 2003). Adding extra variables also increases computational cost, split between the computation of transport (advection and diffusion) for each state variable and the computation of the non-linear functions relating the state variables of the BGC model. In an operational context, the balance between model complexity and computational costs is critical and must be carefully evaluated. BGC models should be as simple as possible and as complex as necessary to answer specific questions.

9.1.2.2 Model calibration

As already mentioned, biogeochemical models are based on empirical relationships to describe the dynamics of biological processes. Observational data are then essential for tuning, adjusting or revising the formulations, i.e. making the model results match the observed distributions and fluxes of inorganic and organic quantities. Model calibration can be performed "by hand", i.e. by adjusting certain parameters of the biogeochemical models until the models show a "good" fit to the observed tracer fields, or by using objective optimisation methods (Kriest et al., 2020). The resulting set of biogeochemical parameters is often closely linked to the ocean circulation, mixing, and ventilation derived from the physical model used, with its specificities and defaults.

9.1.2.3 Physical-Biogeochemical coupling

Ocean physics advects and diffuses BGC model variables, thus redistributing inorganic and organic amounts. In addition, some BGC processes depend on physical conditions such as temperature or salinity, particularly crucial for the carbon cycle. Thus, there is a very strong link between the physical conditions and the BGC, which makes the BGC models closely dependent on the physical models.

Vertical motions are particularly critical to bring nutrients from nutrient-rich deep waters into the uppermost layer that receives the sunlight needed for photosynthesis and marine life. Two critical layers together regulate phytoplankton production:

The mixed layer is the upper layer of the ocean that interacts with the atmosphere. It is assumed to be mixed and homogeneous through convective/turbulent processes, generated by winds, surface heat fluxes, or processes modifying salinity. The deeper it is, the deeper phytoplankton are mixed, which will take them away from the light required for photosynthesis. Deep mixing also replenishes near-surface nutrient stocks.
The euphotic zone is the layer from the surface down to the depth at which irradiance is 1% of the surface irradiance. The deeper the euphotic depth, the deeper the layer in which photosynthesis and phytoplankton production can occur. It extends from a few metres in turbid estuaries to approximately two hundred metres in the open ocean.

Figure 9.4. Schematic representation of the interplay between mixed layer depth (yellow line) and upper-ocean euphotic zone (light blue area) on the initiation of phytoplankton bloom (modified from Dall'Olmo et al., 2016).

The mixed layer may develop within the euphotic layer (in stratified situations), or over a greater thickness of up to several hundred metres (in well-mixed situations). The interplay between these two critical layers controls the plankton exposure to sunlight and the coincident exposure to nutrients, thus regulating phytoplankton production (Figure 9.4). Exact mechanisms are still debated. Please refer to Ford et al. (2018) for more details.

In turn, phytoplankton abundance may feed back to physics, by absorbing radiation in the surface layers and therefore affecting heat penetration into the water column (Lengaigne et al., 2007).

9.1.2.4 From open ocean to coastal ecosystems

Different considerations are generally needed for open ocean and coastal ecosystems. In the open ocean, the seasonal cycle is quite well defined and recurring (Figure 9.5). Seasonal increases in temperature and solar radiation drive the phytoplankton spring bloom. The peak persists for a few weeks to months until nutrient limitation and grazing cause the bloom to collapse. A secondary biomass peak can develop in late summer or autumn.

Figure 9.5. Seasonal cycle of phytoplankton relative to variations in sunlight, nutrients, and zooplankton (Copyright: 2004 Pearson Prentice Hall, Inc).

In contrast, coastal ecosystems can be very complex, subject to a succession of blooms having different origins, thus requiring additional model complexity. Correct specification of river inputs also becomes more critical. Furthermore, the equations in Section 9.1.2.1 are for the pelagic (water column) ecosystem. In shallow waters, such as shelf seas, it becomes important to include the benthic (seafloor) ecosystem into the BGC models. This requires the addition of extra variables, though they do not need to be advected or diffused. Finally, coastal waters are often turbid, and the effect of sediments and coloured dissolved organic matter on light and therefore primary production should be included. Dedicated optical models are sometimes used for this purpose (Gregg and Rousseaux, 2016).

9.1.2.5 Potential predictability of ocean biogeochemistry

The potential predictability of ocean biogeochemistry varies considerably depending on the scales and quantities of interest. A lot of variability is driven by physics, with changes in mixing and stratification affecting light and nutrients and therefore primary production. When these physics changes can be predicted, e.g. changes in stratification with a warming climate and interannual variability related to phenomena such as the El Niño Southern Oscillation, associated large-scale changes to ocean biogeochemistry can also be predicted. Similarly, changes to the ocean carbon cycle and acidification with increasing atmospheric CO2 concentrations can be predicted. When considering local regions and/or shorter time scales, both physics and biogeochemistry become harder to be accurately predicted.

Furthermore, various biogeochemical quantities change at very different rates. Phytoplankton react quickly to changes in light and nutrient availability and can double in concentration over a day (Laws, 2013). Zooplankton will exhibit a slightly more lagged response to these changes. Meanwhile, nutrient concentrations will typically change more slowly, and the carbon cycle even more slowly, although surface concentrations (of nutrients and carbon) can change rapidly, for example during a storm. These different rates of change have implications for the scales of predictability.

For accurate predictions, it is important to initialise models using data assimilation (see Section 9.2.5). At seasonal-to-decadal time scales, predictability is dominated by physics, and this must be accurately initialised and simulated. Physics remains important at shorter time scales, but is essential to initialise nutrient concentrations correctly, as this will help to determine the primary productivity. For short-range predictions, phytoplankton concentrations should be initialised, though the memory of the phytoplankton variables may be as short as a few days, given that they react to changes in nutrients and mixing. Accurate model formulations and parameterisations are also required, otherwise the model will react incorrectly to the data assimilation.

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