Description: Estuary-type circulation is a residual circulation in coastal systems with horizontal density gradients. It drives the accumulation of suspended particulate matter in coastal embayments where density gradients are sustained by some freshwater inflow from rivers. Ebenhöh et al. (Ecol Model 174(3):241–252, 2004) found that shallow water depth can explain nutrient gradients becoming established towards the coast even in the absence of river inflow. The present study follows their concept and investigates the characteristic transport of organic matter towards the coast based on idealised scenarios whereby an estuary-type circulation is maintained by surface freshwater fluxes and pronounced shoaling towards the coast. A coupled hydrodynamical and biogeochemical model is used to simulate the dynamics of nutrient gradients and to derive budgets of organic matter flux for a coastal transect. Horizontal nutrient gradients are considered only in terms of tidal asymmetries of suspended matter transport. The results show that the accumulation of organic matter near the coast is not only highly sensitive to variations in the sinking velocity of suspended matter but is also noticeably enhanced by an increase in precipitation. This scenario is comparable with North Sea conditions. By contrast, horizontal nutrient gradients would be reversed in the case of evaporation-dominated inverse estuaries (cf. reverse gradients of nutrient and organic matter concentrations). Credible coastal nutrient budget calculations are required for resolving trends in eutrophication. For tidal systems, the present results suggest that these calculations require an explicit consideration of freshwater flux and asymmetries in tidal mixing. In the present case, the nutrient budget for the vertically mixed zone also indicates carbon pumping from the shelf sea towards the coast from as far offshore as 25 km.

Description: In this paper, we review the state of the art and major challenges in current efforts to incorporate biogeochemical functional groups into models that can be applied on basin-wide and global scales, with an emphasis on models that might ultimately be used to predict how biogeochemical cycles in the ocean will respond to global warming. We define the term “biogeochemical functional group” to refer to groups of organisms that mediate specific chemical reactions in the ocean. Thus, according to this definition, “functional groups” have no phylogenetic meaning—these are composed of many different species with common biogeochemical functions. Substantial progress has been made in the last decade toward quantifying the rates of these various functions and understanding the factors that control them. For some of these groups, we have developed fairly sophisticated models that incorporate this understanding, e.g. for diazotrophs (e.g. Trichodesmium), silica producers (diatoms) and calcifiers (e.g. coccolithophorids and specifically Emiliania huxleyi). However, current representations of nitrogen fixation and calcification are incomplete, i.e., based primarily upon models of Trichodesmium and E. huxleyi, respectively, and many important functional groups have not yet been considered in open-ocean biogeochemical models. Progress has been made over the last decade in efforts to simulate dimethylsulfide (DMS) production and cycling (i.e., by dinoflagellates and prymnesiophytes) and denitrification, but these efforts are still in their infancy, and many significant problems remain. One obvious gap is that virtually all functional group modeling efforts have focused on autotrophic microbes, while higher trophic levels have been completely ignored. It appears that in some cases (e.g., calcification), incorporating higher trophic levels may be essential not only for representing a particular biogeochemical reaction, but also for modeling export. Another serious problem is our tendency to model the organisms for which we have the most validation data (e.g., E. huxleyi and Trichodesmium) even when they may represent only a fraction of the biogeochemical functional group we are trying to represent. When we step back and look at the paleo-oceanographic record, it suggests that oxygen concentrations have played a central role in the evolution and emergence of many of the key functional groups that influence biogeochemical cycles in the present-day ocean. However, more subtle effects are likely to be important over the next century like changes in silicate supply or turbulence that can influence the relative success of diatoms versus dinoflagellates, coccolithophorids and diazotrophs. In general, inferences drawn from the paleo-oceanographic record and theoretical work suggest that global warming will tend to favor the latter because it will give rise to increased stratification. However, decreases in pH and Fe supply could adversely impact coccolithophorids and diazotrophs in the future. It may be necessary to include explicit dynamic representations of nitrogen fixation, denitrification, silicification and calcification in our models if our goal is predicting the oceanic carbon cycle in the future, because these processes appear to play a very significant role in the carbon cycle of the present-day ocean and they are sensitive to climate change. Observations and models suggest that it may also be necessary to include the DMS cycle to predict future climate, though the effects are still highly uncertain. We have learned a tremendous amount about the distributions and biogeochemical impact of bacteria in the ocean in recent years, yet this improved understanding has not yet been incorporated into many of our models. All of these considerations lead us toward the development of increasingly complex models. However, recent quantitative model intercomparison studies suggest that continuing to add complexity and more functional groups to our ecosystem models may lead to decreases in predictive ability if the models are not properly constrained with available data. We also caution that capturing the present-day variability tells us little about how well a particular model can predict the future. If our goal is to develop models that can be used to predict how the oceans will respond to global warming, then we need to make more rigorous assessments of predictive skill using the available data.

Description: Highlights • We objectively identify and remove unconstrained parameters from a marine ecosystem model. • Optimal model complexity is identified using three model selection metrics. • As many as 14 of the model’s 30 parameters can be removed, with no significant reduction in model-data misfit. • Optimal model structures and parameters are different at two different North Atlantic locations. • The specialised structures and parameters at each site may be unsuitable for new environments The degree of structural complexity that should be incorporated in marine biogeochemical models is unclear. We know that the marine ecosystem is complex, and that its observed behaviour is attributable to the interaction of a large number of separate processes, but observations are scarce and often insufficient to constrain more than a small number of model parameters. This issue is addressed using a novel algorithm that systematically removes model processes that are not constrained by observations. The algorithm is applied to a one-dimensional, eight component ecosystem-biogeochemistry model at two North Atlantic time-series sites. Between 11 and 14 of the 30 model parameters can be removed at each site with no significant reduction in the model’s ability to fit upper ocean (0–200 m) biogeochemical tracer and productivity data. The statistically optimal model structures and parameters provide estimates of the most likely state variables and fluxes at each site. Differences in these estimates between the two sites indicate that the optimal models are specialised to both the physical environment and the assimilated observations. At each site the heavily reduced models may thus be suitable for diagnostic purposes but may not be sufficiently complex for more general applications, such as in global ocean general circulation models, or for predicting the response of marine systems to environmental change.

Description: Application of biogeochemical models to the study of marine ecosystems is pervasive, yet objective quantification of these models' performance is rare. Here, 12 lower trophic level models of varying complexity are objectively assessed in two distinct regions (equatorial Pacific and Arabian Sea). Each model was run within an identical one-dimensional physical framework. A consistent variational adjoint implementation assimilating chlorophyll-a, nitrate, export, and primary productivity was applied and the same metrics were used to assess model skill. Experiments were performed in which data were assimilated from each site individually and from both sites simultaneously. A cross-validation experiment was also conducted whereby data were assimilated from one site and the resulting optimal parameters were used to generate a simulation for the second site. When a single pelagic regime is considered, the simplest models fit the data as well as those with multiple phytoplankton functional groups. However, those with multiple phytoplankton functional groups produced lower misfits when the models are required to simulate both regimes using identical parameter values. The cross-validation experiments revealed that as long as only a few key biogeochemical parameters were optimized, the models with greater phytoplankton complexity were generally more portable. Furthermore, models with multiple zooplankton compartments did not necessarily outperform models with single zooplankton compartments, even when zooplankton biomass data are assimilated. Finally, even when different models produced similar least squares model-data misfits, they often did so via very different element flow pathways, highlighting the need for more comprehensive data sets that uniquely constrain these pathways.

Description: Many critical processes of ecosystem function, including trophic relationships between predators and prey and maximum rates of photosynthesis and growth, are size-dependent. Size spectral data are therefore precious to modellers because they can constrain model predictions of size-dependent processes. Here we illustrate a multi-step statistical approach to create size spectra based on a reanalysis of plankton size data from the IronEx II experiment, where iron was added to a marked patch of water and changes in productivity and community structure were followed. First, bootstrapping was applied to resample original size measurements and cell counts. Kernel density estimation was then used to provide nonparametric descriptions of density versus size. Finally, parametric distributions were used to obtain parameter estimates that can more easily be applied in models. A major advantage of this approach is that it provides confidence envelopes for the density distributions. Our analyses suggest three basic distributional patterns of cell concentration versus logarithm of equivalent spherical diameter for individual taxa. Composite size-densities of heterotrophs and photoautotrophs reveal important aspects of the coupling between protist grazing and the phytoplankton community.

Description: Effects of CO2 concentration on elemental composition of the coccolithophore Emiliania huxleyi were studied in phosphorus-limited, continuous cultures that were acclimated to experimental conditions for 30 d prior to the first sampling. We determined phytoplankton and bacterial cell numbers, nutrients, particulate components like organic carbon (POC), inorganic carbon (PIC), nitrogen (PN), organic phosphorus (POP), transparent exopolymer particles (TEP), as well as dissolved organic carbon (DOC) and nitrogen (DON), in addition to carbonate system parameters at CO2 levels of 180, 380 and 750 µatm. No significant difference between treatments was observed for any of the measured variables during repeated sampling over a 14 d period. We considered several factors that might lead to these results, i.e. light, nutrients, carbon overconsumption and transient versus steady-state growth. We suggest that the absence of a clear CO2 effect during this study does not necessarily imply the absence of an effect in nature. Instead, the sensitivity of the cell towards environmental stressors such as CO2 may vary depending on whether growth conditions are transient or sufficiently stable to allow for optimal allocation of energy and resources. We tested this idea on previously published data sets where PIC and POC divided by the corresponding cell abundance of E. huxleyi at various pCO2 levels and growth rates were available.

Description: Highlights: • Elemental C:N:P variations of organic matter are simulated at monitoring site BY15. • No N2 fixation needed to explain observed PO4PO4 and pCO2pCO2 levels after spring bloom. • Model features relevance of DOP production and remineralization for N2 fixation. • Model estimates of annual N2 fixation are View the MathML source297±24mmolNm-2a-1. • Model estimates of annual total production are View the MathML source14.16±0.71molCm-2a-1. Abstract: For most marine ecosystems the growth of diazotrophic cyanobacteria and the associated amount of nitrogen fixation are regulated by the availability of phosphorus. The intensity of summer blooms of nitrogen (N2) fixing algae in the Baltic Sea is assumed to be determinable from a surplus of dissolved inorganic phosphorus (DIP) that remains after the spring bloom has ended. But this surplus DIP concentration is observed to continuously decrease at times when no appreciable nitrogen fixation is measured. This peculiarity is currently discussed and has afforded different model interpretations for the Baltic Sea. In our study we propose a dynamical model solution that explains these observations with variations of the elemental carbon-to-nitrogen-to-phosphorus (C:N:P) ratio during distinct periods of organic matter production and remineralization. The biogeochemical model resolves seasonal C, N and P fluxes with depth at the Baltic Sea monitoring site BY15, based on three assumptions: (1) DIP is utilized by algae though not needed for immediate growth, (2) the uptake of dissolved inorganic nitrogen (DIN) is hampered when the algae׳s phosphorus (P) quota is low, and (3) carbon assimilation continues at times of nutrient depletion. Model results describe observed temporal variations of DIN, DIP and chlorophyll-a concentrations along with partial pressure of carbon dioxide (pCO2)(pCO2). In contrast to other model studies, our solution does not require N2 fixation to occur shortly after the spring bloom to explain DIP drawdown and pCO2pCO2 levels. Model estimates of annual N2 fixation are View the MathML source297±24mmolNm-2a-1. Estimates of total production are View the MathML source14200±700mmolCm-2a-1, View the MathML source1400±70mmolNm-2a-1, and View the MathML source114±5mmolPm-2a-1 for the upper 50 m. The models C, N and P fluxes disclose preferential remineralization of P and of organic N that was introduced via N2 fixation. Our results are in support of the idea that P uptake by phytoplankton during the spring bloom contributes to the consecutive availability of labile dissolved organic phosphorus (LDOP). The LDOP is retained within upper layers and its remineralization affects algal growth in summer, during periods of noticeable N2 fixation.

Description: During phytoplankton growth a fraction of dissolved inorganic carbon (DIC) assimilated by phytoplankton is exuded in the form of dissolved organic carbon (DOC), which can be transformed into extracellular particulate organic carbon (POC). A major fraction of extracellular POC is associated with carbon of transparent exopolymer particles (TEP; carbon content = TEPC) that form from dissolved polysaccharides (PCHO). The exudation of PCHO is linked to an excessive uptake of DIC that is not directly quantifiable from utilisation of dissolved inorganic nitrogen (DIN), called carbon overconsumption. Given these conditions, the concept of assuming a constant stoichiometric carbon-to-nitrogen (C:N) ratio for estimating new production of POC from DIN uptake becomes inappropriate. Here, a model of carbon overconsumption is analysed, combining phytoplankton growth with TEPC formation. The model describes two modes of carbon overconsumption. The first mode is associated with DOC exudation during phytoplankton biomass accumulation. The second mode is decoupled from algal growth, but leads to a continuous rise in POC while particulate organic nitrogen (PON) remains constant. While including PCHO coagulation, the model goes beyond a purely physiological explanation of building up carbon rich particulate organic matter (POM). The model is validated against observations from a mesocosm study. Maximum likelihood estimates of model parameters, such as nitrogen- and carbon loss rates of phytoplankton, are determined. The optimisation yields results with higher rates for carbon exudation than for the loss of organic nitrogen. It also suggests that the PCHO fraction of exuded DOC was 63±20% during the mesocosm experiment. Optimal estimates are obtained for coagulation kernels for PCHO transformation into TEPC. Model state estimates are consistent with observations, where 30% of the POC increase was attributed to TEPC formation. The proposed model is of low complexity and is applicable for large-scale biogeochemical simulations.

Description: Highlights: • Sensitivities of annual carbon (C), nitrogen (N) and phosphorus (P) flux estimates to parameter variations are determined. • Model parameters that specify annual inventories are compared with those that determine timing and magnitude of bloom events. • Seven model parameters are of primary importance, affecting C, N and P budgets simultaneously. • Nine parameters have negligible effects on annual budget estimates and on seasonal trajectories. • Parameter categorization provides important prior information for parameter optimization in the central Baltic Sea. Abstract: This study describes a sensitivity analysis that allows the parameters of a one-dimensional ecosystem model to be ranked according to their specificity in determining biochemical key fluxes. Key fluxes of interest are annual (a) total production (TP), (b) remineralization above the halocline (RM), and (c) export at 50 m (EX) at the Baltic Sea monitoring site BY15 located in the Gotland Deep basin. The model resolves mass flux of carbon (C), nitrogen (N), and phosphorous (P), while considering nitrogen fixation explicitly. Our first null hypothesis is that the variation of the value of every single model parameter affects each annual C, N, and P budget simultaneously. Our second null hypothesis states that the variation of every parameter value induces changes at least in either of the annual C, N or P budgets. Our analyses falsify both null hypotheses and reveal that 8 out of 36 parameters must be regarded redundant, as their variation neither alter annual key fluxes nor produce considerable time-shifts in model trajectories at the respective site. Seven parameters were found to induce substantial changes in annual C, N, and P flux estimates simultaneously. The assimilation efficiency of zooplankton turned out to be of vital importance. This parameter discriminates between the assimilation and destruction of algal prey during grazing. The fraction of unassimilated dead algal cells is critical for the amount of organic matter exported out of the euphotic zone. The maximum cellular N:C quota of diazotrophs and the degradation/hydrolysis rate of detrital carbon are two parameters that will likely remain unconstrained by time series data, but both affect the annual C budget considerably. Overall, our detailed specification of model sensitivities to parameter variations will facilitate the formulation of a well-posed inverse problem for the estimation of C, N and P fluxes from stock observations at the Gotland Deep.

Description: To describe the underlying processes involved in oceanic plankton dynamics is crucial for the determination of energy and mass flux through an ecosystem and for the estimation of biogeochemical element cycling. Many planktonic ecosystem models were developed to resolve major processes so that flux estimates can be derived from numerical simulations. These results depend on the type and number of parameterizations incorporated as model equations. Furthermore, the values assigned to respective parameters specify a model's solution. Representative model results are those that can explain data; therefore, data assimilation methods are utilized to yield optimal estimates of parameter values while fitting model results to match data. Central difficulties are (1) planktonic ecosystem models are imperfect and (2) data are often too sparse to constrain all model parameters. In this review we explore how problems in parameter identification are approached in marine planktonic ecosystem modelling. We provide background information about model uncertainties and estimation methods, and how these are considered for assessing misfits between observations and model results. We explain differences in evaluating uncertainties in parameter estimation, thereby also discussing issues of parameter identifiability. Aspects of model complexity are addressed and we describe how results from cross-validation studies provide much insight in this respect. Moreover, approaches are discussed that consider time- and space-dependent parameter values. We further discuss the use of dynamical/statistical emulator approaches, and we elucidate issues of parameter identification in global biogeochemical models. Our review discloses many facets of parameter identification, as we found many commonalities between the objectives of different approaches, but scientific insight differed between studies. To learn more from results of planktonic ecosystem models we recommend finding a good balance in the level of sophistication between mechanistic modelling and statistical data assimilation treatment for parameter estimation