Development of a coupled physical–biological ecosystem model ECOSMO

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Journal of Marine Systems xx (2006) xxx – xxx www.elsevier.com/locate/jmarsys

Development of a coupled physical–biological ecosystem model ECOSMO Part I: Model description and validation for the North Sea Corinna Schrum a,b,⁎, Irina Alekseeva c , Mike St. John c a

c

Danish Institute of Fisheries Research, Copenhagen, Denmark b Geophysical Institute, University of Bergen, Norway Institute of Hydrobiology and Fisheries Research, Center for Marine and Climate Research, University of Hamburg, Germany Received 11 October 2004; accepted 30 January 2006

Abstract A 3-D coupled biophysical model ECOSMO (ECOSystem MOdel) has been developed. The biological module of ECOSMO is based on lower trophic level interactions between two phyto- and two zooplankton components. The dynamics of the different phytoplankton components are governed by the availability of the macronutrients nitrogen, phosphate and silicate as well as light. Zooplankton production is simulated based on the consumption of the different phytoplankton groups and detritus. The biological module is coupled to a nonlinear 3-D baroclinic model. The physical and biological modules are driven by surface forcing at temporal scale of 6 h using atmospheric re-analysis data. The model was integrated for 1984 and 1986. The simulated fields for 1984 were used to investigate the annual spatial distribution of phytoplankton and zooplankton biomass and their production in the North Sea. A detailed validation showed that the model, based on consideration of limiting processes, is able to reproduce the observed spatial and seasonal variability of the North Sea ecosystem e.g. the spring bloom, summer sub-surface production and the fall bloom. Distinct differences in regional characteristics of diatoms and flagellates could be modeled and their different roles in the seasonal cycle were resolved by ECOSMO. Moreover, the model was able to describe seasonal and regional characteristics of zooplankton biomass. In contrast to earlier models ECOSMO was able to identify frontal environments as zones of high productivity, and the simulations characterized the dynamics of different zooplankton feeding environments with special emphasis on the role of frontal production. For the second trophic level the regional increase of production in the frontal zone was found to be several times higher than for the first trophic level. © 2006 Elsevier B.V. All rights reserved. Keywords: North Sea; Primary production; Secondary production; 3-D ecosystem modeling; Fronts; Bottom-up control

1. Introduction Scientific interest in shelf sea ecosystem dynamics is motivated by the substantial contribution of shelf ⁎ Corresponding author. Allégaten 70, N-5007 Bergen, Norway. Tel.: +47 55 58 26 20; fax: +47 55 58 98 83. E-mail address: [email protected] (C. Schrum).

regions to the overall production of fish. Moreover, the ecosystem dynamics of shelf regions have been identified as critical for the understanding of the global carbon cycle (e.g. Tsunogai et al., 1999; Yool and Fasham, 2001). One of the major challenges facing the marine community is therefore developing an understanding of the effects of global climate change on the dynamics of marine ecosystems and the subsequent

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effects of changes in ecosystem dynamics on the earth system. In shelf seas, the dynamics of the key biogeochemical and ecosystem players are influenced by mesoscale features such as frontal processes (e.g. St. John et al., 1993; Richardson et al., 2000). Recently published observations provided evidence that increased frontal productivity even has to be considered as an important signal for air–sea CO2 gas exchange (Thomas et al., 2004). However, at present, quantitative estimates of the importance of mesoscale features are lacking and developing a predictive capacity for continental shelf systems focused on mesoscale frontal regimes is becoming increasingly important as these areas serve as feeding and nursery habitats for many exploited fish stocks (e.g. Vezzulli et al., 2005). Within the EU-project LIFECO (http://www.lifeco.dk) this topic has been addressed for the North Sea ecosystem by examining the role of frontal processes with respect to their potential importance as feeding environments for different key species. One of the main tools to address this key issue is coupled hydrodynamic-ecosystem modeling. The North Sea is one of the best studied shelf regimes, with a number of 3-D modeling efforts performed in the past to describe the ecosystem dynamics. The state-of-the art in ecosystem modeling in the North Sea has recently been reviewed in detail by Moll and Radach (2003). In this article, seven threedimensional models, i.e. NORWECOM (Skogen et al., 1995), GHER (Delhez, 1998), ECOHAM (Moll, 1998), ERSEM (Baretta et al., 1995), ELISE (Menesguen, 1991), COHERENS (Luyten et al., 1999) and POL3dERSEM (Allen et al., 2001) were compared in terms of their complexity by spatial resolution and the resolution of trophic structure. Moll and Radach (2003) showed annual primary production estimates from four of the seven ecosystem models described. None of the models examined displayed a production maximum at frontal locations, (potentially due to their inability to spatially resolve frontal activity) which has been reported by experimental findings (e.g. Creutzberg, 1986; Baars et al., 1991). In resume from this review (Moll and Radach, 2003), none of the existing models was found to be appropriate for the goals addressed within LIFECO. Some of these ecosystem models involve only one or two nutrient cycles and hence might not be flexible enough for simulating primary production under different nutrient limiting conditions occurring in the North Sea, such as the coastal waters mostly limited by phosphorus and the open sea regimes with nitrate, ammonium and silicate

becoming the general limiting factors. For example, ECOHAM uses the phosphate cycle only, and is not sufficient to describe limiting processes in the northern North Sea. GHER and COHERENS simulate only the nitrogen cycle and are therefore not suitable for depicting the coastal regimes or the dynamics of the spring diatom bloom limited by silicate. Furthermore, most models are not aimed to address zooplankton feeding environments, using bulk formulations for zooplankton (GHER), prescribing zooplankton biomass (ECOHAM, COHERENS), or not including zooplankton at all (ELISE, NORWECOM). Contrastingly the most detailed ecosystem model ERSEM and its coupled hydrodynamic-ecosystem version POL3dERSEM employs circa 100 state variables to describe the marine ecosystem. Although sensitivity tests have been performed and the model has been used widely, the complexity of the model makes it difficult to investigate its behavior and sensitivity when using a high spatial resolution. ERSEM parameter fitting and most of the sensitivity tests performed were based on box configurations rather than using a 3-D coupled hydrodynamic modeling approach (e.g. Lenhart et al., 1997). Due to its complexity the potential of ERSEM for predictive system understanding using an adequate spatial resolution is limited. The goal within LIFECO was to develop a new model of sufficient complexity to resolve the 3 important macronutrient cycles and the most important functional groups of phytoplankton and zooplankton. Contrastingly to ERSEM, this model should be simple enough to provide a practical tool to be used in combination with a high resolution frontal resolving 3D hydrodynamic model and capture the seasonal dynamics of nutrients, phytoplankton and zooplankton. In addition, this model should be suitable for application to examine the effects of mesoscale physical processes, such as frontal processes, thereby providing a tool for investigating the effects of these processes on ecosystem functioning and for scenario testing the potential influence of climate variability. In this first exercise we concentrate on the development and validation of the coupled hydrodynamicecosystem model over the seasonal cycle. To keep the present paper focused we concentrate here only on the North Sea. 2. Model description The coupled physical–biological model ECOSMO (ECOSystem MOdel) was developed for the shelf seas North Sea and Baltic Sea to include the interaction of

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water masses, nutrients and biomass. The interconnection was included as it is potentially important for interannual variability of larval fish feeding environments in the North Sea. The model has been developed as an extension of an existing hydrodynamic/sea ice model (Schrum and Backhaus, 1999). The hydrodynamic module has remained largely unchanged compared to the previously existing version. In the following, the description is separated into a description of the physical and ecosystem components as well as a description of configuration and additional technical information for the model. 2.1. Physical module The hydrodynamic component of the present model is based on the nonlinear primitive equation model HAMSOM (HAMburg Shelf Ocean Model). HAMSOM has been developed at the Institute of Oceanography at the University of Hamburg and continuously improved during the last 20 years by contributions of

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different authors. It has successfully been applied to several shelf sea regions to investigate hydro- and thermodynamics. A detailed list of references and a full description of the most comprehensive and developed model version, including a coupled sea ice model, which was set up for the North Sea and the Baltic Sea was given in Schrum and Backhaus (1999). The turbulent vertical exchange processes are calculated within HAMSOM by using an algebraic first-order k–ε model, as first described by Pohlmann (1996), and modified by Schrum (1997a). The prognostic variables of HAMSOM include temperature, salinity, relative sea surface elevation, 3-D-transports, vertical exchange coefficients and turbulent air–sea exchange. Furthermore, ice state is estimated including ice compactness, level ice thickness and ridging ice thickness as well as ice transport velocities. The application of HAMSOM to the North Sea and Baltic Sea (Schrum, 1997b; Schrum and Backhaus, 1999) provides the basis of our coupled ecosystem model. In Fig. 1, the model region and topography are

Fig. 1. The bottom topography of the model domain [m].

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shown. For this application the model has a horizontal resolution of 10km and a vertical grid spacing which is able to resolve stratification. Specifically, for the upper 40m, a vertical resolution of 5 m was used and between 40 and 88m the vertical grid spacing is 8 m to ensure resolution of the Baltic halocline. The lower layers are more coarsely resolved. The performance of the North Sea/Baltic Sea version of the model relative to climatic variability was investigated by Schrum et al. (2000), Janssen et al. (2001) and Janssen (2002). In these studies the models ability to realistically simulate the hydrodynamics of the North Sea and the Baltic Sea was demonstrated, thereby justifying it as the basis for the development of the coupled ecosystem model. 2.2. The ecosystem module Detailed explanations of model equations as well as a list of model variables and a list of parameters and coefficients (Tables 1 and 2) are presented in Appendix B. Hence, in this section we include only brief information about the processes employed in the model and a discussion on the general model concept and the comprehensive model capabilities. ECOSMO includes interactions between 12 state variables. The basis of the model are 3 nutrient cycles, the nitrogen cycle, the phosphorus cycle and the silica cycle, covering the main macro nutrients limiting phytoplankton production in shelf seas. The specific nutrients included in the ecosystem block are nitrate (NO3), ammonium (NH4), phosphate (PO4) and silicate (SiO2). Based on availability of these nutrients and light availability, ECOSMO simulates the dynamics of two

functional groups of phytoplankton diatoms (Pd) and flagellates (Pf), with the dynamics of each group simulated based on their respective physiological characteristics. The fate of two zooplankton functional groups are estimated, these being microzooplankton (Zs) and macrozooplankton (Zl) with the dynamics based on their specific feeding behavior. Other state variables are nitrite (NO2), detritus (D), biogenic opal (Opal) and oxygen (O2). The flow of nutrients and biomass in the model is calculated based on the concept of Redfield stoichiometry (Redfield, 1934; Harris, 1986) using carbon units as a coin of transfer (Fig. 2). In this exercise we avoid to address the effects of temperature dependence on plankton growth-, respiration- and remineralization-rates, focusing on the effects of nutrient and food limitation in different environmental conditions in the North Sea. Hence, our model concept differs from various previous concepts by consideration of temperature dependencies for nitrogen oxidation–reduction reactions only. Since temperature has generally a strong effect on biological processes, a brief discussion about temperature dependencies is needed to justify and discuss our approach. Temperature effects on specific growth rates have been widely investigated. Usually for many species the rates increase with increasing temperatures. However, resulting response of a plankton community assemble or its total nutrient uptake is not evident. For instance, Caron et al. (1986) showed that temperature had an effect on rates of all physiological processes for heterotrophic microflagellates (Paraphysomonas imperforata) but did not affect the overall magnitude of carbon or nutrient cycling when summed over its population growth cycle. Typically temperature

Fig. 2. The interaction between compartments in the ecological module of ECOSMO. In this figure, the blue line represents the pathways of the nutrients nitrogen and phosphorous; the green line represents the pathways of oxygen; the black line is the flow of organic carbon; the brown line represents the pathways of silica. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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dependent growth of phytoplankton and zooplankton is modeled to follow an exponential temperature dependence (i.e. Arrhenius/Q10) with a Q10 value close to 2 for phytoplankton and 3 for zooplankton, respectively (see e.g. Denman and Peña, 2002) and a species- or community-dependent maximum growth rate. Alternatively linear temperature response in growth rate is found (e.g. for diatoms estimated by Montagnes and Franklin, 2001). Improved description of phytoplankton growth is possible by considering the interacting effects of different nutrient, light and temperature conditions in a Chemical Reaction model (CR; Baird and Emsley, 1999). Employment of this model showed exponential and linear temperature dependent growth as well as temperature independent growth for a plankton community under different light and nutrient conditions (Baird et al., 2001). Phytoplankton and zooplankton state variables in ECOSMO have to be understood and modeled as functional groups rather than single species, and hence growth rates describe the effect of an integrated community response. Since maximum growth rates as well as optimal temperatures are species and thus plankton community dependent, realistic modeling of temperature dependencies requires in addition a good knowledge on species composition, independently of the specific growth temperature dependency considered. However, species composition in open marine environments are by itself influenced by environmental factors like water temperature and water exchange and far away from being constant in time (e.g. Vezzulli et al., 2005). Taking into account these uncertainties, it is likely that consideration of a specific temperature dependence without consideration of species composition changes will introduce an artificial bias hampering scenario investigations. Estimations of temperature dependency for remineralization processes show similar uncertainties. Q10 values found in literature cover a wide range from at least 1 to 10. Denman and Peña (2002) e.g. used a Q10 of 3, near the midrange of recent estimation (White et al., 1991; Kirchman et al., 1993; Kirchman and Rich, 1997; Li, 1998). The uncertainty of temperature dependency as described by this range is quite high compared to the temperature dependence as described by the midrange value. Therefore we decided as a first approach to neglect temperature dependencies as well for remineralization processes. With respect to scenario testing of climatic variability, our concept might result in underestimation of ecosystem variability and impact on quantitative estimates. However, the interannual temperature changes in the

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North Sea/Baltic Sea system are typically below 2 °C (Janssen et al., 1999), hence resulting response in growth rate changes are only weak and well in the range of uncertainties. Furthermore, with respect to quantitative predictions, impact studies on realistic interannual temperature changes are in any case strongly limited, since the predictions are significantly influenced by the specific model choice (Denman and Peña, 2002). Since regional bottom temperature differences in the North Sea are much stronger than the interannual variability (Janssen et al., 1999), we have to admit that an underestimation of regional variability in intra-annual re-cycling of nutrients is likely to be expected from neglecting temperature dependence in remineralization processes. This is especially the case for the near coastal environment which is characterized by higher bottom temperatures (e.g. Janssen et al., 1999). Another important simplification which needs to be discussed is the neglect of diatom sinking, in contrast to sinking behaviour of diatoms as reported from field observations. Reported sinking velocities from field observations cover a wide range. Fast sinking (10– 100 m/day, Smetacek, 1985) to even buoyant diatoms were reported (Peperzak, 2002), with generally low sinking rates below 2 m/day in shelf seas, which was partly explained by near bottom turbulence (e.g. Peperzak, 2002). The deterministic implementation of diatom sinking as a function of stress and increasing viability as experimentally found (e.g. Eppley et al., 1967) is still not realized for current medium complexity ecosystem models, which typically consider diatom sinking only with a constant rate. Neglecting or underestimation of diatom sinking in stable stratified environments would result in underestimation of sedimentation during or after diatom blooms, overestimation of sinking results in faster nutrient deposition and hence underestimation of diatom and nutrient availability in the mixed layer. However, for the North Sea the consideration of diatom sinking is of minor relevance since the sea is still well mixed during the phase of major diatom blooming in March/April. Convective mixing and tidal induced turbulence significantly erode bottom accumulation of diatoms, detritus and opal, independently of considered sinking rates. This is partly the case also for the Baltic Sea, since as a result of thermal convection the water column above the halocline layer is well mixed until May (Janssen et al., 1999). Previous results of coupled convection-primary production modelling showed that convection results in keeping plankton particles in the mixed layer, even if additional sinking is considered (Wehde, 2001). Therefore we do not expect severe limitations of model

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capabilities from neglecting diatom sinking in the present configuration. However, for the Baltic Sea, longer-term integrations might significantly be biased by neglecting diatom sinking. For all biological and chemical state variables except oxygen, with air–sea exchange considered, non-flux boundary conditions are prescribed for both the sea surface and the bottom. Although no bottom sub-model is used, bottom processes are not completely neglected. Detritus will accumulate in the nepheloid bottom layer and is exposed to slow near bottom transports (McCave, 1986). In case of increasing turbulence due to wind stress or tidal mixing, detritus material is mixed back into the water column. Such an approximation of bottom processes is justified for the highly turbulent North Sea which has no significant nutrient sink due to sedimentation. In the North Sea only about 1% of the annual primary production is assumed to be buried ultimately in the sediments (DeHaas et al., 2002). For the aims addressed with the current model development, such an approximation is justified as well for the less turbulent environment of the Baltic Sea, since due to the stable haline stratification in the Baltic Sea, only near bottom concentrations of nutrients are effected by neglected sediment fluxes. Although, we have again to mention that long-term investigations of carbon and nutrient fluxes from the Baltic Sea could be biased by such an assumption, we suggest this being no severe limitation since estimations of these fluxes from 3-D z-level models like those currently used in Baltic Sea ecosystem modeling (e.g. Neumann, 2000) are anyway biased and influenced by conceptual problems of the z-level approach (e.g. Janssen, 2002). 2.3. Model setup The model has been integrated for the year 1984, employing realistic atmospheric boundary data as external forcing. The atmospheric variables employed to force the model are air temperature, relative humidity, wind speed and direction. Furthermore, the model employs mean sea level pressure, cloudiness and radiation data. The surface boundary conditions are taken from the atmospheric NCEP/NCAR re-analysis data (Kalnay et al., 1996) which are available with a temporal resolution of 6 h and a horizontal resolution of ∼ 2°. To overcome known problems with the NCEP data, in relation to radiation and 2 m-temperature, a climatic correction has been applied. The climatic correction was taken from the ECMWF re-analysis data (Gibson et al., 1996) and applied on each of the model wet grid points (Schrum and Siegismund, 2002).

At the open boundaries to the North Atlantic Ocean the model is dynamically forced using daily sea surface variations from a coarser diagnostic model (Smith et al., 1996) and furthermore, 20 min variations of tidally induced sea surface elevation, derived from the major tidal constituents M2, S2 and O1. The boundary conditions for temperature and salinity were taken from monthly climatic fields available for the model grid (Janssen et al., 1999). The monthly boundary values for inorganic nutrients were taken from World Ocean Atlas 2001 (WOA01, Conkright et al., 2002). The WOA01 data provides objectively analyzed fields of inorganic nutrients (phosphate, nitrate, and silicate) and dissolved oxygen on a 1° grid, defined at 33 standard depth levels. Monthly means are given for the upper 500 m and seasonal means for the deeper part, thus a combination of climatic monthly and seasonal means was used. Open boundary conditions for phyto- and zooplankton, detritus and biogenic opal are based on local production using the climatic nutrient boundary conditions. Furthermore, fresh water runoff and nutrient river loads are employed to force the model. Here, fresh water runoff for the North Sea was taken from Damm (1997) while for the Baltic Sea runoff was obtained by the data compiled by Bergström and Carlssen (1994). Only inorganic nutrient river loads are included for the main rivers for the North Sea and for the coastal runoff into the Baltic Sea. The data are obtained from sources compiled by Skogen and Søiland (2001) and Leppänen (2002). The model was employed without a spin-up phase for the ecosystem using initial climatic January conditions for the nutrients and winter seasonal plankton values (WOA01). Initial conditions for temperature and salinity were taken from previously validated long-term model runs (Schrum et al., 2003). The conducted detailed validation of these model runs showed that spin-up problems for the present shelf sea configuration are only small when starting from climatic distributions. The model adopts the spatial distribution of interpolated climatic fields to actual topography in a couple of weeks. The main problem resulting from this strategy is the mismatch of average climatic and actual conditions (Janssen et al., 2001; Janssen, 2002), a problem which is for the North Sea due to the short residence time less severe than for the Baltic which residence time is in the order of decades (Stigebrandt and Gustafsson, 2003). However, due to the previously mentioned numerical problems which all current z-level models for the Baltic Sea are facing, long-term spin-up integrations are not capable to create a better approximation of initial conditions than provided by climatic averages.

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2.4. Technical details The model as presented has a large number of variables requiring a high degree of computational efficiency. The model coding was therefore vectorized for an application on a distributed-memory multi-vector processor NEC SX-6 (HLRE of the German Climate Computing Center (DKRZ)). To solve the model on the North Sea grid matrix (177 ⁎ 207 ⁎ 20 grid points) with 10 km resolution for the simulated period of 1 year, 3 h of CPU time is required on the HLRE of DKRZ. However, the model coding is universal and can be used on different platforms (including different operational systems and FORTRAN compiler versions). CPU time required for running the present configuration on a PC with 2.8 GHz is about 12h per simulation year. The degree of computational efficiency was achieved via two approaches. First, the vector structure of the model coding avoids loss of CPU time by operating only on ‘wet’ grid points of the model grid. This is especially important as in the present configuration of the model domain (Fig. 1) only about 10% of model grid nodes are ‘wet’ points requiring calculation. Secondly, the semiimplicit methods in HAMSOM, first described by Backhaus (1983) contributed to the efficiency of the model allowing a rather large time stepping of 20 min for the 10km model grid. 3. Results and discussion 3.1. Primary production, phytoplankton biomass and nutrient dynamics Validation of coupled ecosystem models is critical for assessing their ability to capture the dynamics of the ecosystem they are designed to study. A first step in this validation process is a comparison of simulation outputs with existing climatic data as well as other simulation estimates. Before observational data are employed for model validation, the properties of the respective data sets have to be discussed. Typically, climatic data from field sampling (e.g. from ICES database) used for model validations are based on fixed depth observations (e.g. Ebenhöh et al., 1997; Radach and Pätsch, 1997; Moll, 2000). This approach is appropriate for a well-mixed water column where typically no strong gradients in parameters such as nutrients and phytoplankton biomass occur. After the onset of stratification, phytoplankton and nutrient concentrations become heterogeneously distributed vertically with, for example the formation of a chlorophyll maximum in proximity to the pycnocline

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and a nutricline which can be well below the pycnocline (e.g. Richardson et al., 2000). Obviously any sampling program not sensitive to these heterogeneous vertical distributions might result in significant uncertainties in estimations of integrated phytoplankton biomass. Further systematic uncertainties in gridded database on observations are caused by the fact that available observations are not equally or even normally distributed in space nor in time. This can be assumed to be especially important for describing topographic structures like e.g. coastal/offshore gradients, since in coastal region most of the observations are from standard stations at the coast or near islands e.g. Helgoland Roads. This problem was discussed in detail for hydrographic data from the North Sea by Janssen et al. (1999) and Janssen (2002) and was found to be important even within a certain grid box. Further limitations for model validation arising due to unknown conversion factors from chlorophyll (given in climatic data) to carbon (as calculated by the model). The common strategy of using a constant conversion ratio in case chlorophyll is not considered as model variable, although appropriate for annual averages, introduces a bias when applied to resolve the seasonal cycle. Chl/C ratios especially deviate for nutrient and light limiting conditions and are function of physiology. They might show significant regional variability already on small spatial scales and clear seasonal variability (Cloern et al., 1995; Behrenfeld et al., 2005). For the evaluation of annual and seasonal characteristics as it is planned here, only two North Sea wide climatic data sets for nutrients and biomass exist. The ECOMOD-ICES database (Radach et al., 1995) is available as gridded data with monthly resolution only on the coarse ICES grid, which is much too coarse to provide a sufficient resolution to validate the spatial characteristics of the model. For the finer 1° grid as presented by Radach et al. (1995) and statistically investigated by Radach and Pätsch (1997), no attempt was made to close the gaps. Thus, no gridded data set is available from the ECOMOD database to describe the seasonal dynamics of basin wide chlorophyll and nutrient characteristics in the North Sea. To the authors knowledge the only available alternative is the World Ocean Atlas (WOA01; Conkright et al., 2002). This data set is sufficiently resolved for the nutrients but provides seasonal surface values for chlorophyll only. Although some problems of climatic data sets have been identified, they nevertheless provide the best database guess on average seasonal nutrient and chlorophyll dynamics and hence will be used for validation purposes. Before going into detail, the first step in validating a model is always the verification of regional

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average characteristics, here performed using the annual mean upper 30 m depth averaged phytoplankton biomass, from the WOA01 database and from model results. Furthermore regional patterns are evaluated from annual primary production and compared to earlier published model estimations. Our comparison of annual average biomass results in a reasonable agreement between observations and model results (Fig. 3). Model results and observations cover the same quantitative range of spatial variability. However, the model predicts lower values in the shallower eastern North Sea. In this context it needs to be mentioned that the model predicted structures are closely related to topographic and hydrodynamic structures, such as the biomass maximum in the tidal frontal zone at the Dogger Bank and along the coast, a structure which is not clearly separated in the observational based climatic data. Since the occurrence of this feature has been reported in a number of field studies (e.g. Richardson et al., 2000), the mismatch can be interpreted as the result of a lack in horizontal resolution for the observational database. Another feature predicted by the model is a biomass minimum in the central southern bight, caused here by the greater water depths and weaker vertical mixing of nutrients to the euphotic zone. Although less pronounced, this minimum is indicated as well in the climatic data. The model reproduces furthermore well the biomass minimum off the Scottish coast and again increasing biomass values towards the North Atlantic.

The spatial structure of predicted net primary production (Fig. 4) illustrates the regional variability in ecosystem dynamics. In our simulation for 1984, the North Sea depth-integrated annual net primary production was predicted to vary between 60 and 150g C m− 2 year− 1. Primary production in the southern North Sea along the tidal mixing front towards the mixed side of the front and in the southern Bight, as well as off Jutland is the highest modeled in the North Sea. In this region, frontal mixing processes, onshore near bottom transport and offshore surface transport as well as vertical frontal mixing at the edge of the front (see e.g. for the frontal vertical circulation Schrum, 1997a) make nutrients from lower layers available during the nutrient limited summer season. Furthermore, increased recycling via zooplankton production and respiration contributes to the maximum primary production at the mixed side of the front. A comparison of our results with those of existing threedimensional models and field observations as reviewed in Moll and Radach (2003) show our model being at the lower edge of modeled production. These authors cited magnitudes of observed and predicted primary production below or from 50 to 100g C m− 2 year− 1 in the central part of the North Sea, above 200g C m− 2 year− 1 in the coastal areas with values of below 100g C m− 2 year− 1 in the English Channel off the south British coast. Annual production estimates of nearly the same order of magnitude and similar structures as predicted by ECOSMO have recently been published by Skogen et al. (2004) in a simulation using NORWECOM.

Fig. 3. Annual mean phytoplankton biomass (1984) vertically averaged in upper 30m, ECOSMO results (left) and WOA 2001 database (right, Conkright et al., 2002) [mg C m− 3].

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Fig. 4. Modeled annual primary production (left) and secondary production (right) in the North Sea (1984) [g C m− 2 year− 1].

Annual values of primary production from field observations were presented by Dippner (1998, after Van Beusekom and Diel-Christiansen, 1994) reporting ranges from 120 to 500 g C m− 2 year− 1 for the near coastal area. Comparing to these estimates the model is with near coastal production of about 125–130g C m− 2 year− 1 clearly at the lower edge of reported production rates. From the British North Sea Project in 1988–1989 carbon fixation in excess of 200g C m− 2 year− 1 in the nutrient-rich, high chlorophyll, waters of the southern North Sea were reported (Joint and Pomeroy, 1992; Howarth et al., 1993; Tett et al., 1993). These estimates of annual phytoplankton production are as well slightly higher than those obtained by ECOSMO as presented in Fig. 4, which partly might be a result of the discrepancy between net and gross primary production. The performance of the model to describe the seasonal dynamics of nutrients and phytoplankton was evaluated with respect to WOA01 database and the ECOMOD data. The model validation of seasonal dynamics of phytoplankton biomass and nutrients is presented in the following for three positions which are chosen to demonstrate the dynamics of different hydrodynamic regimes on the ecosystem characteristics. The first and second are examples of stable stratified conditions occurring in summer in the northern and northeastern North Sea and the third is an example for the frontal zone south of Dogger Bank. The model data presented are 1° box averaged values (hindcast for year 1984) centered at 53.5N 2.5E, 56.5N, 5.5E and 55.5N 2.5E, corresponding to the WOA01 1° grid boxes and

the ECOMOD/ICES ND130 grid boxes 56, 49 and 74, respectively (Fig. 5). The data presented are depth averages of the uppermost 30m. Monthly mean nutrient data (Fig. 5) show similar seasonal cycles for model results and observations, both in magnitudes and timing for the stratified North Sea, well in the range of uncertainties as estimated from climatic averages of the 2 data sets and the ranges provided from ECOMOD data. The 2 different climatic data sets show substantially deviations in monthly means, potentially pronounced in wintertime. In the stratified North Sea the model results for Nitrate and Phosphate are generally closer to the WOA01 data. ECOSMO is able to provide a realistic prediction of the seasonal cycle for all 3 nutrients, including silicate, which supports the models' performance to be used for scenario testing of climatic variability. However, significant deviations between model results and climatic estimates are found for silicate and nitrate in late summer and autumn, when the model overestimates the nutrient concentrations. Although these differences might be partly caused by oversimplification or wrong parameterizations in ECOSMO, it has to be noticed that the range of variability as estimated from the ECOMOD database for spring and autumn might be an indication of mesoscale or interannual variability not resolved by the climatic data sets. Since WOA01 database provides only seasonal chlorophyll averages in the surface layer, validations of modeled phytoplankton biomass are performed only using climatic data provided by ECOMOD/ICES

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Fig. 5. Validation of seasonal cycle for chlorophyll and nutrients for characteristic hydrographic regions with stable stratified (upper: φ = 55.5 N, λ = 2.5 W; middle: φ = 56.5 N, λ = 5.5 W) and frontal (lower: φ = 53.5 N, λ = 2.5 W) conditions. Nutrient and biomass values are averaged in upper 30m layer. Presented are daily means from model results for 1984 (full line), monthly climatic means from the WOA01 database (dashed) and monthly climatic means (horizontal lines) with the range between 17% and 83% quantiles (bar) from the ECOMOD/ICES database.

database. The conversion factor of Chl/C = 1:40 was used to calculate equivalent chlorophyll values from model units. Within the 3 characteristic ICES boxes, calculated daily phytoplankton biomass time series (ECOSMO hindcast 1984) are compared to monthly mean climatic chlorophyll data and the observed range of variability within the box (range estimated from 17% to 83% quantiles) (ECOMOD, Radach et al., 1995). Characteristic deviations are found for all sites in winter values, with model results significantly underestimating the biomass, likely to be influenced by insufficient consideration of Chl/C ratio variability. Model simula-

tions are well in the observational range for the weakly stratified regions south of the 50 m depth line (box 74), although the start of the bloom is simulated later by the model. For the more stable stratified regions north of the Dogger Bank (box 49, box 56) the modeled start of the bloom fits better with climatic chlorophyll values. 3.2. Zooplankton biomass and production As pointed out by Radach et al. (1998) there is little evidence elucidating the annual or interannual biomass of zooplankton in the North Sea. Typically data are

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given without ranges of variability or lacks the original data. Information available from the Continuous Plankton Recorder (e.g. Beaugrand et al., 2004), which provides a sufficient spatial and temporal resolution for the surface mixed layer is in the form of an index of abundance, with unknown and potentially variable conversion factors. Models are typically Eulerian in nature, with prediction of biomass based on the potential production by phytoplankton. Actual zooplankton biomass has the potential to be significantly different due to e.g. variations in transfer efficiency between phytoplankton and zooplankton as well as the aggregation of zooplankton due to behavioral or physical accumulation and due to nonlinear grazing pressure on zooplankton by larval fish. Comparison of our model with other model results of zooplankton production and biomass is also difficult. Many previous modeling exercises address zooplankton only as closing variable rather than resolving the zooplankton dynamics (T. Neumann, personal communication, Institute of Baltic Sea Research, Warnemünde, Germany). Therefore detailed discussion of spatially variable zooplankton dynamics in the North Sea is rare. To the authors knowledge there has been no investigation of the evolution of the seasonal cycle of zooplankton published from 3-D models in this region. However, in the ERSEM box model a validation was performed (Broekhuizen et al., 1995). Broekhuizen showed scaled CPR biomass data taking into account an undersampling rate of approximately 25% for the omnivores biomass and about 60% of the carnivores biomass, which was estimated based on previous comparisons of independent observations with CPR data (Krause and Radach, 1980; Williams and Lindley, 1980; Lindley and Williams, 1980; Fransz and Diel, 1984). Additionally Broekhuizen et al. used zooplankton biomass estimates from 2 other data sets, i.e. data compiled by Adams (1987) and data obtained from the NERC North Sea database. We compiled mesozooplankton (sum of omnivorous and carnivorous) estimates from these publications and comparable model predictions (total biomass) in Table 1 for two ICES boxes (for the exact positions of the ICES grid see e.g. Broekhuizen et al., 1995). The comparison to literature values confirmed that ECOSMO calculated zooplankton biomass levels are very close to the reported biomass levels. In the deeper ICES box 4 (center located at φ = 57.5° N, λ = 3° W), the model predictions are close to the average from the 3 different observational data sets and equal to estimates given by Adams (1987). Seasonal dynamics are close to observations as depicted from the 3 different databases, with the exception of

11

winter values, when we did not take into account overwintering populations. Temperature independent mortality rates used in ECSOMO cause decrease of zooplankton biomass to unrealistic low winter values. For ICES box 5 (center located at φ = 54.75°N, λ = 4°W), which is located in the near coastal biomass maximum, the model results are slightly higher than the climatic estimates, but well in the range deviations between different climatic data. Timing of the maximum biomass varies for the different data sets from May to July, in model results for 1984 it occurs in May. The only study providing synoptic spatial estimates of zooplankton biomass covering the whole North Sea comes from the German BMBF ZISCH project (1986/ 1987; Krause and Knickmeyer, 1992; Krause et al., 1995). Since sampling during the ZISCH experiment took about 6 weeks (Fig. 6), there is an inherent seasonality in the data which needs to be taken into account when comparing the data to model results. In Table 2, a comparison between weekly averages from ZISCH data and model results is shown. To account for the interannual variability in zooplankton biomass and to allow for a better validation of models zooplankton parameterization, not biased by interannual shifts of the seasonal cycle, an additional model run was performed with the same initial settings and boundary settings for the year 1986. The model results for 1986 were added in Table 2. The comparison to ZISCH data confirmed that ECOSMO calculated zooplankton biomass is similar Table 1 Averaged zooplankton biomass (mg C m− 3) estimated for the ICES boxes 4 (center located at φ = 57.5°N, λ = 3°W) and 5 (center located at φ = 54.75°N, λ = 4°W), from CPR data, after Adams (1987), from BODC data; as presented by Broekhuizen et al. (1995) and calculated from model results

ICES box 4 Seasonal max Max. biomass Season

ICES box 5 Seasonal max Max. biomass Season

ICES box 4 + 5 Winter concentration

CPR data

Adams (1987)

BODC data

Model results

June 35 April– Nov

May 30 April–Nov

July 20 April– Nov

May 30 April–Nov

June 45 April– Oct.

– – –

June 32 April– Oct.

May 50 April–Nov

2.5–5

2.5–5

2.5–5

0.1

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Fig. 6. Experimental grid of the ZISCH field campaign in May/June 1986. Different colours indicate different sample weeks (Krause et al., 2003).

to the reported biomass levels and its spatial variability is predicted in accordance to observed variability. Deviations were found for the northern North Sea, where the model predicts significantly lower biomass than what was observed. Modeled and observed zooplankton biomasses are almost equal for the Central and the shallow North Sea. A cross-check of simulated zooplankton biomass values for 1984 indicates clear

interannual variability in biomass with an in general better match between observed and calculated zooplankton biomass for the hindcast simulation of 1986. Further comparison of local structures such as high integrated biomass in the postglacial Elbe river estuary and lower integrated biomasses at the North Frisian Coast e.g. as reported by Krause et al. (2003) from the German BMBF experiment PRISMA, were successfully simulated by ECOSMO (Fig. 7). Despite of the limited potential for validation of zooplankton biomass and secondary production a discussion of the dynamics is warranted. In our simulations, the spatial distribution of primary production turned out to be the key for the zooplankton biomass dynamics. High primary production in the southern North Sea and the English Channel results in high secondary production (Fig. 4), which in our analysis includes all zooplankton production resulting from feeding on phytoplankton, detritus and on microzooplankton. High secondary productivity can be found in the inflow region along the Norwegian trench, where from observations, high Calanus abundance is reported (e.g. LIFECO 3rd Progress Report, 2004; Vezzulli et al., 2005). Interestingly, the increase in secondary production at the tidal mixing front is much stronger than the corresponding increase in primary production, locally it might be even higher than the integrated primary production. This potentially has two reasons. Firstly, a more efficient trophic carbon transfer in the flagellates dominated frontal environment and

Table 2 Validation of modeled zooplankton biomass with those obtained during the ZISCH field experiment in 1986 Time period

Observed zooplankton biomass

Simulated zooplankton biomass 1986

Simulated zooplankton biomass 1984

1 week, 3–10 May 2 week, 11–17 May 3 week, 18–24 May 4 week, 25–31 May 5 week, 1–7 June 6 week, 8–12 June

0.58

0.15

0.1

0.76

0.30

0.42

0.84

0.89

1.63

0.86

0.85

1.39

1.51

1.16

1.02

1.09

0.90

1.36

Vertically integrated values (g C m− 2) were averaged for the whole observational period and weekly averaged in respect to the time– spatial coverage of the observations (Fig. 6) for both the collected data and model results. The columns show the period of averaging, values are calculated from observations and from model results for years 1986 and 1984, respectively.

Fig. 7. Modeled annual mean vertically integrated zooplankton biomass (1984) [g C m− 2].

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secondly the potential role of advection of phytoplankton and detritus for local secondary production. Due to our simplified approach of modeling zooplankton dynamics, incorporating predation on zooplankton by predators as a constant mortality rate and hence linearly dependent on zooplankton biomass, the similarity of spatial structures of zooplankton biomass and secondary production predicted by ECOSMO is subject to question. However, the calculated zooplankton biomass provides a useful indicator for the potential of a region as feeding ground for higher trophic levels. ECOSMO calculates the highest levels of zooplankton biomass and secondary production for the shallow well mixed regions along the tidal mixing front and in the trench inflow (Figs. 4 and 7), indicating that these regions are potentially valuable feeding zones for some North Sea fish species. In contrast, the Central North Sea shows lowest total zooplankton biomass. 3.3. Seasonal dynamics: diatoms vs. flagellates For 1984, the simulated temporal development of total phytoplankton and zooplankton biomass over the entire North Sea are presented (Fig. 8). In 1984, a spring phytoplankton bloom commences at the end of February and reaches its maximum with values up to 200 mg C m− 3 in the beginning of April. This first phytoplankton maximum consists mainly of diatoms, with low flagellate biomass. Diatoms remain being the dominant phytoplankton group until silicate limitation is reached and diatoms biomass starts to decrease (Dippner, 1998). The following second peak of phytoplankton biomass occurring in May is then based mainly on flagellates. During summer average phytoplankton biomass ranges from 80 to 120 mg C m− 3 dominated by flagellates biomass. In the fall, flagellate biomass shows a rapid decrease in September and October with a small fall bloom of diatoms. Significant phytoplankton

13

biomass was predicted to occur until end of November. For mesozooplankton biomass two peaks occur in April and June with maximum of about 40 and 60mg C m− 3, respectively. Herbivores zooplankton biomass is relatively low during the entire season, indicating only a minor relevance of the chosen zooplankton group separation, at least for the current parameterization. The model predicts that vertical thermal stratification does not start to develop before May (Schrum et al., 2003), in accordance to climatologic estimates (Janssen et al., 1999). Hence, the early spring diatom bloom is reaching its peak in March/April in unstratified conditions (e.g. Hickel et al., 1992; Radach and Pätsch, 1997). Reported blooming before establishment of a summer thermocline (Townsend et al., 1992; Huisman et al., 1999) and hence in contrast to the Sverdrup-critical depth model (1953) was previously explained by frequent return of phytoplankton cells to the euphotic zone as a result of thermal convection (Wehde, 2001). Although primary production occurs in stratified as well as unstratified conditions, productions show a generally slower increase in deeper and mixed regions. Regardless, deep water regions appear to result in slower increase in biomass caused by the dependence of total production on biomass concentration in the euphotic zone. Haline stratification is an important factor favoring the bloom prior to the onset seasonal thermal stratification. This is especially import for early blooms in the Skagerrak, despite of the deeper water there as evidenced in Fig. 9. The biomass distribution later in the year shows different regional characteristics as illustrated by the snapshots of phytoplankton biomass for April and beginning of July (Fig. 9). During summer, local maximums of biomass are found in frontal regions which favor production due to more intense vertical mixing of nutrients into the euphotic zone. As the temporal snapshots suggest, phytoplankton dynamics in the North Sea have in general different spatial structures

Fig. 8. The seasonal dynamics of phytoplankton and zooplankton biomass averaged in the North Sea [mg C m− 3].

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Fig. 9. Modeled vertically integrated total phytoplankton biomass [g C m− 2], 1st of April (left) and 1st of July (right).

for diatoms and flagellates. This is illustrated by the annual average diatom and flagellates biomass (Fig. 10) and integrated production separated for the 2 functional groups (Fig. 11). These differences reflect the respective hydrodynamic conditions controlling the light-nutrient balance and thereby influencing the dynamics of diatoms and flagellates. Spatial structure of diatom production is controlled by water depth in the shallow regions like Dogger Bank, where silicate limitation occurs prior to thermocline establishment. Exceptions

are found only in regions with additional silicate supply by upward silicate flux like in the postglacial old Elbe valley or by Atlantic inflow. In the stratified summer period, the phytoplankton community is dominated by flagellates as was previously found in field observations (e.g. Hickel et al., 1992; Richardson et al., 2000). Here primary production is limited to regions where vertical mixing or vertical advection results in the flux of nutrients into the euphotic zone. These areas, which coincide with zones of frontal activity, are predicted to

Fig. 10. Vertically integrated annual means of diatoms (left) and flagellates biomasses [g C m− 2].

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Fig. 11. Vertically integrated annual primary production [g C m− 2 year− 1] of diatoms (left) and flagellates (right).

contain high flagellate biomass (Fig. 10) and increased flagellate based primary production (Fig. 11). From model results flagellates production dominates the shallow part of the North Sea and the frontal zone along the tidal mixing front. Further significant production maxima are found at the flanks of the Dogger Bank and along the Scottish coast. ECOSMO

has clearly indicated the role of fronts as key areas for the North Sea marine ecosystem in particular their influence on the production and biomass of flagellates as seen in field programs (e.g. Richardson et al., 2000). Simulated flagellate biomass in the frontal region is about 2 times of the biomass in the Central North Sea with production rates more than 4 times higher. This

Fig. 12. Annual time series of modeled σt-profiles (left) [kg m− 3] and primary production [mg C m− 3 day− 1] for two positions north (upper, 2°20′ E,56°5′N) and south (lower, 2°20′E,54°5′N) of Dogger Bank.

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provides evidence for increased reproductive cycling as previously indicated from field programs (Richardson et al., 2000). As a consequence, increased frontal flagellate production contributes to an increase in zooplankton production due to the higher availability of detritus and phytoplankton biomass here. The temporal development of primary production is shown in Fig. 12 for a position in stratified waters, north of Dogger Bank and a position in mixed waters from south of Dogger Bank. The two time series clearly illustrate the dynamics of the different regimes. The northern stratified area is characterized by production maxima in the surface layer in end of March and in May. From end of May, production in the surface layer is limited by nutrient availability and occurs only at the thermocline as subsurface production. The region south of Dogger Bank, located in mixed or only very weakly stratified waters in contrast shows a continuous surface production throughout the summer period, favoured by continuous tidal induced mixing of nutrients to the surface layer, which is responsible for the high productivity in this region, making the frontal regions unique as ideal feeding grounds for higher trophic level species. 4. Conclusions With ECOSMO an ecosystem model was developed to describe bottom-up control of the marine ecosystem. ECOSMO describes the seasonality of biological processes fully based on light and nutrient limitation rather than using a parameterization connected to the seasonal temperature cycle. The basic findings can be summarized as follows. Based on the consideration of limiting processes only, ECOSMO was able to 1) characterize the seasonal dynamics of the planktonic components of North Sea ecosystem, and resolve the spatial differences in the different dynamic regimes, 2) identify the spatial and temporal dynamics of important feeding environments of larvae fish in the North Sea and 3) assess the importance of frontal systems for the planktonic dynamics. Due to its sufficient resolution of trophic dynamics, in time and in space, ECOSMO allowed a clear separation between diatom and flagellate dominated regimes and the identification of importance of frontal processes both from tidal mixing and freshwater and shelf break fronts for both these functional groups. Using ECOSMO diatoms were modeled to be the important phytoplank-

ton group in the spring bloom, an occurrence which reflects field observations in most marine systems (e.g. Hickel et al., 1992). Flagellates were predicted to be the important phytoplankton component later in the season during the stratified period as suggested earlier by Richardson et al. (2000). During this period flagellates appear to be the main contributors of carbon transfer to higher trophic levels. Although, the intensity of the re-cycling is sensitive to parameterizations in the model, especially to the food preference and transfer efficiencies (e.g. Gentleman et al., 2003), the specific choice of growth rates and the remineralization rates, we believe that the qualitative results, pointing to the significance of flagellates production for secondary production and their role for frontal production is a robust one, which can be explained by the interplay of hydrodynamic processes and the seasonality and nutrient dynamics of flagellates and diatoms. The second trophic component is critical for the dynamics of marine fish populations and in a system of global change, and is key for understanding the structure and functioning of marine ecosystems. ECOSMO contributes to the development of predictive capacities for coastal marine ecosystems, in particular by resolving the spatial and temporal dynamics of zooplankton production. The results from validation of zooplankton biomass against observed field data from the ZISCH experiment showed that a close correspondence between model results and observations was found for 1986 (the year of ZISCH field campaign), but model results for 1984 show a time lag compared to ZISCH data. This gives rise to the expectation that the model may be used to understand the interannual variability in timing of secondary production caused by climatic and hydrodynamic variability and to assess climatic impacts on zooplankton dynamics and interannual variability of larvae feeding conditions. As a key result from ECOSMO, the increasing frontal productivity was found to be more pronounced for the second trophic level. The increase of secondary production was found to be several times higher than the increase in primary production. Whether increasing relative productivity with increasing trophic level is a general phenomenon in frontal environments, is one of the key questions to be addressed in future studies. Acknowledgments The present study is a contribution to EU FP6, TP 8.8 Specific Targeted Research Projects 502482 (BECAUSE).

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Model development was supported by the EU in the frame of the LIFECO-project (Q5CA-2000-30183). ZISCH zooplankton data were kindly provided for model validation purposes by Dr. Michael Krause, University of Hamburg. For critical discussions and comments on the present model approach we like to thank especially the members of the interdisciplinary ecosystem modelling group in the Centre for Marine and Climate research of University Hamburg. Furthermore we are thankful to two anonymous reviewers for critical and helpful comments, and to Dr. Henning Wende for his comments.

Parsons et al. (1984), the following definitions of primary production (ΦPd,ΦPf) are used: UPf ¼ UPf ðPAR; NH4 ; NO3 ; PO4 Þ ¼ minðaðIÞÞ; bN ; bP Þ

ð4Þ

UPd ¼ UPd ðPAR; NH4 ; NO3 ; PO4 ; SiO2 Þ ¼ minðaðIÞÞ; bN ; bP ; bSi Þ

ð5Þ

aðIÞ ¼ tanhðad Iðx; y; z; tÞÞ; Iðx; y; z; tÞ Z 0 ðPf þ Pd Þ∂zÞ ¼ Is ðx; yÞexpð−kw z−kphyto

ð6Þ

z

bN ¼ bNH4 þ bNO3 ; bNH4 ¼

Appendix A. Ecosystem model equations The ecosystem model is based on the following form for the prognostic equations of the state variables;

17

¼

NH4 rNH4 þNH4

; bNO3

NO3 expð−W⁎NH4 Þ: rNO3 þ NO3

PO4 rPO4 þ PO4   SiO2 −RrSiO2 bSi ¼ max 0; : rSiO2 þ SiO2

bP ¼ Ct þ ðvdjÞC þ ðwd ÞCz ¼ ðAv Cz Þz þ RC ;

ð1Þ

with C representing any of the 12 state variables (Table 1). Here, the hydrodynamic transports, i.e. the vertical turbulent sub-scale diffusion coefficient (Av) as well as the advective grid scale transport (v = (u,v,w)) are estimated online by using the model equations and schemes implemented in the hydrodynamic model HAMSOM (see for details Schrum and Backhaus, 1999). The additional sinking rate (wd) is a non-zero constant for detritus and opal. Concurrently chemical and biological interactions are employed in the term RC which is different for each variable based on the specific processes involved defining the dynamics of the component simulated. The biological interaction terms for the 2 phytoplankton groups diatoms (Pd) and flagellates (Pf) are functions of growth, grazing by micro- and mesozooplankton and mortality: RPd ¼ rd UPd Pd −G1 ðPd ÞZs −G2 ðPd ÞZl −mPd Pd

ð2Þ

RPf ¼ rf UPf Pf −G1 ðPf ÞZs −G2 ðPf ÞZl −mPf Pf :

ð3Þ

In ECOSMO primary production of phytoplankton (ΦPf,ΦPd) depends on the maximum phytoplankton growth rate—σ limited by light or nutrients as previously described by e.g. Parsons et al. (1984). Parameterization of primary production is based on the well-known Liebig's law (Liebig, 1947). Following

ð7Þ ð8Þ ð9Þ

Micro and macro-zooplankton production is a function of available phytoplankton and detritus biomass with macro-zooplankton also consuming microzooplankton, and is limited by the food availability. Respiration or mortality causing a decrease of biomass due to direct mineralization or converting into detritus. The equations are written as follows RZs ¼ g1 ½G1 ðPd Þ þ G1 ðPf ÞZs þ g2 G1 ðDÞZs −G2 ðZs ÞZl −ls Zs −mZs Zs

ð10Þ

RZl ¼ g1 ½G2 ðPd Þ þ G2 ðPf Þ þ G2 ðZs ÞZl þ g2 G2 ðDÞZl −ll Zl −mZl Zl :

ð11Þ

Zooplankton grazing rates Gi are defined by the Michaelis–Menten equation also called the Monod equation (Michaelis and Menten, 1913; Monod, 1942). The formulations of selective zooplankton feeding on multiply food resources were reviewed and examined by Gentleman et al. (2003). The formulation selected for the present study is one of the most commonly used for zooplankton feeding on multiple resources (e.g. Mayzaud et al., 1998). Zooplankton feeding on Pf, Pd, Zs and D depend on the food preference coefficients (aij), defined using the following relation:   aij Cj Gi Cj ¼ ri ; ð12Þ ri þ Fi where i = 1, 2 corresponds to the zooplankton class and j = 1, 2,…, 5 is the order of model state variables serving

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as zooplankton prey, i.e. diatoms, flagellates, detritus, microzooplankton and mesozooplankton. Fi = ∑aijCj is the total available food for the i zooplankton class. Food preference coefficients (aij) are given in Table 3 of Appendix B. The budget of organic biomass is closed by the reaction equation of detritus. Detritus increases due to phytoplankton and zooplankton mortality and decreases due to feeding by zooplankton. Remineralization rate of detritus is assumed to be spatially and temporally constant. The reaction equation for detritus is given as: RD ¼ tð1−g1 Þ½G1 ðPd Þ þ G1 ðPf Þ−g2 G1 ðDÞbZs þ ½ð1−g1 Þ½G2 ðPd Þ þ G2 ðPf Þ þ G2 ðZs Þ−g2 G2 ðDÞZl þ mPd Pd þ mPf Pf þ mZs Zs þ mZl Zl −eD ðT ÞD:

ð13Þ

The sources for biogenic opal are mortality of diatoms and grazing of micro- and mesozooplankton on diatoms. Biogenic opal is assumed to be remineralized at a spatially and temporally constant rate. Uptake rates are estimated from Redfield stoichiometry. Oxidation and reduction rates for nitrification/ denitrification are calculated dependent on oxygen and temperature. N2 production by denitrification is considered as a nitrogen sink. The resulting nutrient budgets are described by the following equations: 1 RNH4 ¼ REDFC=N  b  −ðrd UPd Pd þ rf UPf Pf Þ NH4 þ eD D ð14Þ bN  þls Zs þ ll Zl −Xa ðO2 ; T ÞNH4 RNO2 ¼ Xa ðO2 ; T ÞNH4 −Xn ðO2 ; T ÞNO2 þ Xr ðO2 ; T ÞNO3 −Xd ðO2 ; T ÞNO2 ð15Þ   bNO3 1 −ðrd UPd Pd þ rf UPf Pf Þ RNO3 ¼ REDFC=N bN þ Xn ðO2 ; T ÞNO2 −Xr ðO2 ; T ÞNO3 ð16Þ RPO4

1 ¼ REDFC=P

1 ½−Ud rd Pd þ eSi Opal REDFC=Si

ROpal ¼

1 REDFC=Si

RO2 ¼

1 ½ðrd UPd Pd þ rf Pf UPf Pf Þ REDFC=O2 6:625bNH4 þ 8:125βNO3 −6:625ð eD D þ ls Zs þ ll Zl Þ  bN 2 − ðXa ðO2 ; T ÞNH4 þ Xn ðO2 ; T ÞNO2 Þ þ Xr ðO2 ; T ÞNO3 3 þ Xd ðO2 ; T ÞNO2 : ð20Þ

Appendix B Table 1: List of variables 1 2 3 4 5 6 7 8 9 10 11 12

Pf Pd Zs Zl D NH4 NO2 NO3 PO4 SiO2 SiO2·2H2O O2

mg C m− 3 mg C m− 3 mg C m− 3 mg C m− 3 mg C m− 3 mmol N m− 3 mmol N m− 3 mmol N m− 3 mmol P m− 3 mmol Si m− 3 mmol Si m− 3 ml l− 3

Flagellates Diatoms Small zooplankton Large zooplankton Detritus Ammonium Nitrite Nitrate Phosphate Silicate Biogenic opal Oxygen

Table 2: List of parameters used for the model

 ½−ðrd UPd Pd þ rf Uf Pf ÞeD ðT ÞD þ ls Zs ll Zl  RSiO2 ¼

Oxygen is coupled to the nitrogen cycle following Neumann (2000). Processes included in the model relevant for the oxygen dynamics are production via photosynthesis, nitrification, denitrification, consumption by zooplankton respiration and remineralization of detritus. Hydrogen sulphide produced from denitrification is incorporated as a negative oxygen concentration. Oxygen transfer across the sea surface is taken into account and parameterized by forcing the surface toward the saturated oxygen concentration at a rate dependent on the piston velocity (Liss and Melivat, 1986). The solubility values of dissolved oxygen are computed according to the B & K equations (Benson and Krause, 1984).

ð17Þ ð18Þ

 ½G1 ðPd ÞZs þ G2 ðPd ÞZl þ md Pd −eSi Opal ð19Þ

Abbr.

Definition

Value Units

σPf

1.10

day− 1

σPd α kw kphyto

Pf maximum growth rate (flagellates) Pd maximum growth rate (diatoms) Photosynthesis efficiency parameter Water extinction coefficient Phytoplankton extinction coefficient

1.30 0.01 0.05 0.2

ψ

NH4 inhibition parameter

3.00

rNO3

NO3 half saturation constant

0.50

day− 1 (W/m2)− 1 m− 1 m2 (mmol C)− 1 m3 (mmol N)− 1 mmol N m− 3

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NO4 half saturation constant

0.20

rPO4

PO4 half saturation constant

0.05

rSiO2

SiO2 half saturation constant

0.50

RrSiO2

SiO2 constant

1.00

mPf mPd σZs σZl σZlonZs rZ

Pf mortality Pd mortality Zs maximum grazing rate Zl maximum grazing rate on Pd, Pf, D Zl maximum grazing rate on Zs Zs, Zl half saturation constant

0.08 0.05 1.0 0.8 0.5 3.3

mZs mZl μZs μZl γ1

Zs mortality rate Zl mortality rate Zs excretion rate Zl excretion rate Assimilation efficiency, grazing on Pd, Pf, D Assimilation efficiency, grazing on D NH4 maximum oxidation rate NO2 maximum oxidation rate NO3 maximum reduction rate NO2 maximum reduction rate D remineralization rate SiO2 remineralization rate D and Opal sinking velocity Oxygen piston velocity Redfield ration (C/N)

0.2 0.1 0.08 0.06 0.75

γ2 ΩaMax ΩnMax ΩrMax ΩdMax εD εSi wd O2vel REDFC/N

REDFC/P Redfield ration (C/P) REDFC/Si Redfield ration (C/Si) REDFC/O2 Transfer unit (mg C: mmol C)

mmol N m− 3 mmol P m− 3 mmol Si m− 3 mmol Si m− 3 day− 1 day− 1 day− 1 day− 1 day− 1 mmol C m− 3 day− 1 day− 1 day− 1 day− 1

0.30 0.05 0.10 0.01 0.01 0.15 0.015 5.00 5.00 6.625

day− 1 day− 1 day− 1 day− 1 day− 1 day− 1 m day− 1 m day− 1 mol C/mol N 106 mol C/mol P 6.625 mol C/mol Si 12.01 mg C/mmol C

Table 3: Food preference coefficients ai,j Pf Zs Zl D Zooplankton group Pd (i)/food source (j) a11 = 0.7 a12 = 0.25 0 0 a15 = 0.1 Zs Zl a21 = 0.1 a22 = 0.85 a23 = 0.15 0 a25 = 0.1

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