A stage resolving model of Copepods coupled with a 3-dimensional biogeochemical model of the Baltic Sea

Transcription

1 Not to be cited without prior reference to the author Theme Session on Marine Ecosystem Function Physical-Biological Interactions in Marginal and Shelf Seas CM 2003/P:20 A stage resolving model of Copepods coupled with a 3-dimensional biogeochemical model of the Baltic Sea THOMAS NEUMANN, CHRISTINE KREMP and WOLFGANG FENNEL Baltic Sea Research Institute Warnemünde Germany Abstract Understanding of fish recruitment success requires insight into the function of the bottom up control of the food web. A key factor for the survival of fish larvae is the availability of prey at the right time, place and quality. The bottomup approach involves physical, chemical and biological processes, which can be computed with coupled physical biological models and describe the critical prey for fish larvae, i.e. naupliar stages. This paper contributes to an ecosystem approach for the assessment of recruitment success and is based on an advanced ecosystem model of the Baltic Sea, (ERGOM, [30]), but with an increased resolution of the zooplankton stage variable ([11, 12]). The model copepods are represented by five stages: eggs, an aggregated variable of nauplii, two aggregated groups of copepodites and adults. The transfer among the stages, i.e. hatching, molting and reproduction are controlled by food availability and temperature. The dynamical signature of the model-copepod reflects properties of Pseudocalanus, but the model can be applied to other species in a straightforward way. The model food web is truncated at the level of zooplankton. A sound description of the top down control (mortality) on zooplankton is a necessary prerequisite for quantitative simulations. The paper explores the effects of different parameterization of zooplankton mortality. Different choices of the mortality parameters can result in considerable differences in abundances and biomass as well as in the timing of the development. 1

2 Simulations with a 3 dimensional circulation model give insight in the timescale of the physical biological interaction. Different spatial patterns of the different zooplankton stages can be attributed to the timescales of mesoscale physical features and biological processes. 1 Introduction In the last years some progress in theoretical understanding and quantifying the responses of marine ecosystems to changes in physical forcing or nutrient input was achieved by coupled ocean circulation models and chemical-biological model components. The models can be applied to quantify fluxes of matter cycling through state variables, to understand and quantify carbon fluxes in the ocean. Coupled models are powerful tools to study eutrophication scenarios in coastal oceans or marginal seas in response to environmental loads and physical processes, e.g. [29]. However, there is still a large gap between models of the lower and upper trophic levels, i.e. models of nutrients to zooplankton and fish. Marine ecosystem and biogeochemical models consider the lower part of the food web, which is truncated at the level of zooplankton, either including grazing implicitly in phytoplankton mortality, (e.g. [15, 33, 22]), or by a bulk zooplankton state variable, which provides grazing pressure on the phytoplankton (e.g. [34, 1, 2, 10, 4, 13, 30]). In fish stock assessment models the lower part of the food web, including nutrient dynamics and physical features is widly be ignored. The models depend on landing data and statistics, which may carry a lot of implicit information of the bottom up processes, e.g. [17], [32]. Attempts to link fish aspects and ecosystem models were made in studies of the recruitment success of fish, in particular, of the survival of larvae. This requires an appropriately detailed resolution of the model zooplankton. Stage resolving descriptions of copepods allow explicit estimations of evolution and distribution of prey fields for fish larvae. This kind of modeling involves growth, development, and reproduction of copepods, controlled by food web interactions and by physical transports through advection and mixing by small scale turbulence. Stage resolving population models were used by [35], [18] and [26]. Individualbased modeling of population dynamics has been considered for example by [3] and [28]. Such an individual-based population model was linked to circulation by using archives of modeled advection in [27]. These population models used experimental data of stage duration as prescribed parameters, which depend on temperature (Belehradek formulas). An integration of mean individual properties and population dynamics was proposed by [8], and [7], where the equations for the numbers of individuals have been linked to the evolution of the mean individual mass of the cohort which obeys a growth equations with allometric scaling. Models incorporating phytoplankton production and population dynamics as de- 2

3 scribed by a von Foerster equation for the population density in conjunction with growth of the mean individual mass have been embedded in flow fields in Lagrangian fashion by [19] and as a spatially distributed array of boxes in an Eulerian approach by [5]. A review of a variety of existing zooplankton models was given in [6]. In the present paper we aim to integrate a stage resolving zooplankton model ([11]) into a 3D Baltic Sea ecosystem model ([30]). The model system consists of a circulation model and a chemical biological model which describes the dynamics of nutrients, phytoplankton, stage resolved zooplankton, and detritus. The explicit description of the food web allows in principle to simulate the survival conditions of fish larvae, i.e. timing and location of nauplii abundance, in a bottom up approach. A first attempt to model such a system was presented in [12]. A second fish related aspect concerns the mortality of the copepods in the model. Refined approximations of the mortality terms can be achieved by taking properties of the predator-prey interaction into account. It is known, e.g. [14], that the grazing efficiency of fish larvae is related to the visual range. In this study we explore the effects of different mortality approaches, which reflect the visibility of prey items. The paper is structured as follows: Section 2 outlines the model system with a detailed description of the stage resolving copepod model. In section 3 we describe three dimensional simulations with the model system of the Baltic Sea over the model year 1999 and discuss effects of several choices of the zooplankton mortality. Discussions and conclusions are presented in section 4. 2 The Model System This study is based on an advanced three dimensional ecosystem model of the Baltic Sea, see [30] and [29] for details. The physics of the system is governed by a full three dimensional circulation model, the Modular Ocean Model. In the present paper we use in particular version MOM 3 ([31, 16]). The biological part of the model consists originally of nine state variables. The phytoplankton functional groups are diatoms, flagellates, and cyanobacteria, the nutrients are ammonium, nitrate, and phosphate. Moreover, detritus and oxygen (hydrogen sulfate as negative oxygen) are included. The model zooplankton, which was originally represented by a single bulk biomass state variable, is in the present study described by a stage resolving model ([11]). 2.1 Stage Resolving Model of Copepod Dynamics We start with a brief outline of the model of copepods with enhanced process resolution by incorporation a stage resolving biomass and population model. For a more detailed description we refer to [11] and [12]. We consider five stages of the model-copepod: eggs, nauplii, copepodites 1 and 2, and adults, i.e., the nauplii stages are merged into one state variable model-nauplii and the copepodites stages are aggregated into the 3

4 state variables model-copepodites 1 and 2. The corresponding biomass-variables per unit of volume are Z e, Z n, Z c1, Z c2, and Z a. The corresponding numbers of individuals per unit of volume are N e, N n, N c1, N c2 and N a Dynamical Equations The dynamical equations for Z i and N i are and d dt Z e = τ ae Z a µ e Z e τ en Z e, (1) d dt Z n = τ en Z e + (g n l n µ n )Z n τ nc1 Z n, (2) d dt Z c 1 = τ nc1 Z n + (g c1 l c1 µ c1 )Z c1 τ c1 c 2 Z c1, (3) d dt Z c 2 = τ c1 c 2 Z c1 + (g c2 l c2 µ c2 )Z c2 τ c2 az c2, (4) d dt Z a = τ c2 az c2 + (g a l a µ a )Z a τ ae Z a, (5) d dt N e = τ ae µ e N e τ en, (6) d dt N n = τ en µ n N n τ nc1, (7) d dt N c 1 = τ nc1 µ c1 N c1 τ c1 c 2, (8) d dt N c 2 = τ c1 c 2 µ c2 N c2 τ c2 a, (9) d dt N a = τ c2 a µ a N a. (10) In order to prescribe the transfer among the stages we introduce filter functions, which decreases the growth and activates the transfer if a substantial part of the population in a certain stage has approached the molting mass. This can be accomplished by comparing the mean individual mass of a certain stage, m i = Z i /N i, with the maximum mass, X i, represented by the molting mass of the considered stage. We choose a Fermi-function, which provides a representation of the step-function with a smooth transition 1 f(m i, X i ) = 1 + exp( κ X i (m i X i )), (11) where κ is a parameter which controls the smoothness of the filter edge. The effective growth rate, g i l i will be multiplied by this function, see Figure 1. 4

5 grazing rates/d n c 1 c 2 a P/mmolC/m 3 Fermi functions <m> c2 X c mass/µgc Figure 1: Top: Grazing rates versus food for T = 10 o C. For the lower stages the ratio of ingested food to body mass increase while for low food the higher stages are more efficient in catching food. Bottom: Fermi-functions f(z i /N i, X i ) (solid) as low pass and f(< m > i, Z i /N i ) (dash-dot) as high pass filter to control the development for the example i = c 2. 5

6 egg mass m e = 0.1 µgc stage molting maturation mean nauplii X n = 0.3µgC - < m > n = 0.22µgC copepodites 1 X c1 = 0.8µgC - < m > c1 = 0.6µgC copepodites 2 X c2 = 2µgC - < m > c2 = 1.6µgC adults - X a = 3µgC < m > a = 2.6µgC Table 1: Mass parameters of the model copepods. At the same time a transfer rate to the next stage must be activated. Noting the property of the Fermi-functions, f(x, y) = 1 f(y, x), the transfer rates can be defined as τ i,i+1 = 1 i,i+1 f(< m > i, m i ). (12), where i,i+1 is the time interval needed for the molting process and f(< m > i, m i ) ensures that the transfer to the next stage starts not before the mean individual mass, m i, exceeds a certain value < m > i. We choose the < m > i s somewhat smaller than the molting mass of the corresponding stages. Moreover, i,i+1 is defined as i,i+1 = 1 X i ln( ). g i l i < m > i The death rates, µ i, and the transfer rates, τ i,i+1 s are the same as in the set (1) to (5). The use of the filter function (11) implies that both biomass variables and number of individuals are needed to compute the mean mass of the individuals for each stage. The interfaces for the integration of the biological equations (1) to (10) into the circulation model are advection-diffusion equations, one for each state variable. The inclusion of the biomass state variables implies the explicit conservation of mass in the model. Population models are not constraint in such an easy way because there is no law for the conservation of the number of individuals Process Descriptions and Parameter Choices In order to specify our model-copepod we choose parameter values that correspond to Pseudocalanus, which is an important copepod in the Baltic and which is described in detail in the review article of [9]. The mass parameters listed in Table 1 were derived from data of the Baltic Sea ([20]). 6

7 Stage β i (0) d 1 Ii mmolc 2 m 6 eggs - - nauplii copepodites copepodites adults Table 2: Stage dependent grazing rates, β i for T = 0 o C, where β i = b i, and Ivlev constants Ingestion Grazing rates describe the amount of ingested food per day in relation to the biomass and are formulated in terms of a modified Ivlev expressions g i (P ) = β i (1 exp( I 2 i P 2 sum)) f(m i, X i ). (13) Here P sum = P d + P f + P c is the food concentration, which consists of diatoms P d, flagellates P f, and cyanobacteria P c. The I i s are stage-dependent Ivlev-constants, and f is Fermi function (11) which was discussed earlier. The maximum grazing rate, β i, depends on the temperature through an Eppley factor β i = b i exp(at ), (14) with a = 0.063( o C) 1. The numerical values are listed in Table 2 and a sketch is given in 1. The ingested food is partly used for growth and partly for the metabolism of the animals. We assume that 35% of the ingestion is lost as egestion, 10% as excretion, 10% by respiration, and 15% is needed for the molting processes (e.g. [9]). These losses are expressed by the rates l i = 0.7 g i (P, T ) + l 0, for (i = n, c 1, c 2 ), and l a = 0.8 g a (P, T ) + l 0 for the adults, (i = a). Moreover, we included a certain basic respiration rate, l 0 = 0.03 d 1, which is independent of the ingested food. The rate l 0 is set to zero if the adults enter the dormant stage for overwintering Transfer among Stages Transfer rates are needed to prescribe molting, egg laying, and hatching. The molting rates of biomass and abundance, τ i,i+1, are defined by (12), respectively. The rate of reproductions, τ ae, describes the egg production of the female adults after reaching the maturation mass. We assume that half of the adults are female and 30% of the ingested food is transferred into egg biomass. τ ae = ( 1 2 ) 0.3 g a, (15) 7

8 with g a = β a (1 exp(i 2 ap 2 sum))f(< m > a, m). Then the number of new eggs per day is given by N e = τ ae Z a /m e. (16) This approach implies that the egg-rate depends on food availability and temperature through the grazing rates, but ignores the discontinuous release of clutches of eggs with time intervals of a couple of days (see e.g. [21]). The transfer from eggs to nauplii (hatching) is set by the embryonic duration, about 10 days time, for low temperatures ([9]). The effect of temperature is accounted for by an Eppley factor, τ en = h θ(t T 0 ) exp(a(t T 0 ), (17) with h = d 1. The involved step-function implies that the model eggs hatch to model-nauplii only for temperatures exceeding the threshold, T 0 = 2.5 o C Mortality and Overwintering The model food chain is truncated at the level of zooplankton where the mortality involves both death rates and predation by planktivorous fish. The choice of the mortality rate is difficult, because the basic factors are poorly known. In the literature, stage dependent mortalities with some seasonal variation are often used (e.g. [18]). The typical orders of magnitude vary from µ d 1. In this paper we look at the development of the model zooplankton over one model year with two different choices of mortality rates. In particular, we use constant rates for each stage and compare the results with two examples of variable light dependent mortality. A light dependent mortality of copepods reflects the role of the visibility of prey, which can increase or decrease the predation by planktivorous fish including larval stages. It was pointed out, e.g. [14], that the grazing efficiency of cod and herring larvae, which are main predators in the Baltic Sea, are strongly connected with the visual range. The predation pressure on copepods could virtually be neglected for light levels below a certain threshold value. The solar radiation arriving at the sea surface is computed in the model system, in particular in the atmospheric boundary layer module, and can be passed to the ecosystem model to estimate the light level in the water column. The actual light intensity decreases with depth due to the attenuation of the water and the shading effects of the model plankton. We assume that the mortality for each stage, i, consists of a variable contribution, µ (i) v, which depends on the depth, z, through the light level and a constant background value, µ (i) 0, µ i = µ (i) 0 + µ (i) v (z), (18) 8

9 constant case 1 case 1 case 2 case 2 Stage µ c (i) d 1 µ (i) 0 d 1 C i d 1 µ (i) 0 d 1 C i d 1 eggs nauplii copepodites copepodites adults Table 3: Mortality of copepod stages, i, where i refers to (e, n, c 1, c 2, a), µ (i) c refers to constant mortalities. For variable mortalities the parameters C i and µ (i) 0 are needed in (18) and (19). where µ (i) v = C i I(z) I h + I(z). (19) Here I(z) is the light level at the depth z and I h is a half saturation constant which sets the light level where visual predation becomes less important, for example I h = 1W m 2, ([14]). Moreover, C i is the maximum mortality of the copepod stage i due to predation by visual predators. The numerical values of the mortality parameters are listed in Table 3. For depleted food the basic respiration, l 0, reduces the biomass while the number of individuals is not affected. This implies that the individuals lose weight and may starve. We take the starvation effect into account by adjusting the mortality, which acts on the abundance, in such a way that the mean individual mass of adults cannot fall below a hunger threshold. As threshold we choose the mid interval mass, < m > c2, (table 1), of copepodites 2. In our model only the adult stages, which actually aggregate copepodites VI and adults, do overwinter. In order to mimic the overwintering we assume that the mortality of the adults vanishes below a biomass threshold of Z a 0.3mmolCm 3. To illustrated the performance of the model we simulate the development of a cohort of eggs in a rearing tank with constant food supply, temperature and mortality rates by integrating the model equations (1) - (5) and (6) - (10). The results are shown in Fig. 2. In the first phase the egg-signal propagates through the stages while the total number of individuals decreases due to mortality. After a generation time of 30 days the adults have matured and the female start to lay new eggs, after 55 days the abundance of adults has increased significantly in response to the reproduction. The time spans where the molting processes occur covers several days. The general behavior and the duration times of the stages compare well with experimental finding in tank experiments reported in [24]. 9

10 ind. m t/day e n c1 ind. m c2 a t/day Figure 2: Simulation of the evolution of an egg-pulse under constant food level, (4.5mmolN m 3 ), and temperature, (T = 8C),in a rearing tank. Top: abundance of eggs, nauplii, and copepodites-1. Bottom: abundance of copepodites-2 and eggs. After a generation time of 30 days adults have developed and start to lay new eggs, after 55 days the abundance of adults has increased significantly in response to the reproduction. 10

11 Figure 3: The model topography where the label AS means Arkona Sea, BS Bornholm and SGS Southern Gotland Sea, respectively. 3 Three Dimensional Simulations The zooplankton model component outlined in the previous section was integrated into the fully three dimensional model system of the Baltic Sea, ([30, 29])), and several model experiments for the year 1999 were performed. The different runs assume different parametrization of zooplankton mortality, starting with constant, but stage dependent mortalities as a reference case. In the following we concentrate the discussion mainly on the dynamics of the model zooplankton. For a description of the biogeochemical aspects of the model simulation we refer to [29]. The model bathymetry of the Baltic Sea with indications of three geographic regions for later reference is shown in Fig. 3. The model is driven with meteorological data compiled in the frame of the BALTEX project, which were made available to us. Moreover, for the treatment of the open boundary condition at the western border of the Skagerrak sea level data from the gauge at Kunksvik were employed. The initial distribution of temperature and salinity fields were taken from the climatological data set provided by [23]. The run starts three months earlier in order to allow currents and stratification to evolve from the initial fields in response to the forcing. Data to prescribe river runoff, nutrient loads and atmospheric nutrient deposition were constructed on the basis of climatological data. Unfortunately, data for the riverine nutrient inputs were not available. To fill this gap we used river load data for the 1980 ies, which were drawn from the Baltic Environmental Database of the university of Stockholm, ( and adjusted the data with the help of in- 11

12 Country Reduction Reduction of Nitrogen [%] of Phosphorus [%] Denmark Estonia Finland Germany Latvia Lithuania Russia Poland Sweden Poland and Germany Table 4: Estimated reduction for the 90ies compared with climatological nutrient loading data from 70ies and 80ies. formation on load reductions, listed in table 4, which are available for the different parts of the Baltic ([25]). For the initialization of the biogeochemical state variables we employed an initialization run which was used in [29]. For the initialization of the copepods we assume an evenly distributed background population of overwintering copepods with the biomass and abundance of Z a 0.3mmolCm 3 and 2400ind/m 3, respectively. This seed population remains in a dormant stage until the phytoplankton spring bloom commences. In response to the food signal the overwintering model copepods starts to grow and lay eggs after reaching the maturing mass. The parametrization of the model copepods was derived from Pseudocalanus data compiled for the Baltic ([20]). However, in our model the stages of the modelcopepod are aggregated variables which comprise the corresponding stages of several copepod genera, although their characteristic mass values are somewhat different ([20]). Moreover, such an aggregation is a somewhat crude approximation for genera with a different overwintering strategy as, e.g. Acartia, where the life cycle is characterized by overwintering of dormant eggs resting at the bottom in the shallower areas. It is assumed that the dormant eggs of Acartia commence hatching at the same time as Pseudocalanus starts to lay eggs. Thus our model copepod develops both in colder and warmer areas, where the state variables refers to Acartia in the near shore regions and to Pseudocalanus in the off shore areas and below the seasonal thermocline. Consequently, the aggregated state variables consist of different genera at different locations. The approach of lumping the stages to aggregated variables is supported by the findings of [24], which suggest a near-isochronal development of Acartia, Temora and Pseudocalanus. In spite of these simplification the present approach is a step beyond the bulk zooplankton models, where all zooplankton is lumped together into one variable. 12

13 Figure 4: Relative Chlorophyll and abundances of model copepods averaged over the upper 15m in the central part of the Bornholm Sea. 3.1 Reference Run First we discuss the results of the reference run with constant mortalities for the different stages as listed in Table 3. To discuss the succession and development of the copepod stages we start with spatial averages of the state variables for selected regions of he Baltic Sea. The mean abundance of the stages of the model copepods and the sum of the model phytoplankton (chlorophyll) in the Bornholm Sea is shown in Figure 4. The quantities are expressed in relative units, i. e. normalized by the maximum of the corresponding variable. The corresponding body mass of the model adults, expressed as biomass over abundance, is shown in Figure 5. In order to indicate the importance of the starvation adjustment the development of the mean individual mass of adults is also shown for mortality without hunger threshold. The phytoplankton vernal bloom starts in April, Figure 4, and the overwintering model adults respond with increasing body mass, (Figure 5). They reach their maturation mass after about a week and start to lay eggs. While just after the onset of the spring bloom the increase in body mass is rather strong, we find thereafter a mass level near the maturation mass over the whole vegetation period. In the autumn the individual mass decreases towards the overwintering level. The eggs propagate through the stages of nauplii, copepodites 1 and 2, succeeding within one week, and arrive at adult stage with a generation time of about 30 days. The same generation time was observed in rearing tank experiment, [24], and was also found in our tank simulation shown in Figure 2. A similar behavior was found in the Arkona Sea and the Gotland Sea, except that the timing is somewhat different due to an earlier spring bloom in the Arkona Sea and a later bloom in the Gotland Sea where the spring bloom starts not before May. In order to visualize the development of spatial distributions of the model copepods, we discuss a series of snapshots of selected state variables, averaged over two days and over the upper 10m. Four snapshots of the total model chlorophyll, which 13

14 Figure 5: Mean individual mass of adults averaged over the upper 15m in the central part of the Bornholm Sea, with and without starvation effect. refers to the sum of the three functional phytoplankton groups, are shown in Figure 6. The modelled spring bloom commences in the south-western Baltic by the end of March and propagates toward the Baltic Proper during April and May, see Figure 6. The strongest signals are found in the coastal areas, in particular near the river outlets. In August the concentration are relatively small. Strong signals occur locally in some of the river plumes. The seed population of adult copepods starts to lay eggs in response to the spring bloom signal of the phytoplankton, (not shown). These response patterns emerge, with a small delay due to the hatching process, also in the model nauplii distribution, which are shown in Figure 7. The model nauplii abundance, which is an important food source for fish larvae, increases from spring to summer, from about 3, 000 to about 32, 000 ind m 3 in the Arkona and Bornholm Sea while in the central part of Gotland Sea the abundance is smaller. Higher values are found in the summer with maximum values close to 80, 000 ind m 3 in the coastal regions. After the time interval needed to reach the molting mass, the nauplii appear in the copepodites stages, see Figures 8, ( copepodites 2 are not shown). The concentration of the model copepodites is smaller than that of nauplii, but the general distribution is similar. The abundance of the adults, which increases two month after the spring bloom, shows a similar spatial structure as the other stages, but the abundance is higher as for copepodites, because the individuals accumulate in the adult stage, Fig. 9. In the summer the abundance of all stages approach their maximum level. The spatial patterns of the model copepods for a certain moment in August is shown in Fig. 10. The spatial distributions of the different stages are similar in some areas, e.g. in the eastern Gotland Sea and the Bay of Gdansk. Different distribution patterns for different stage are found, for example, in the Arkona and Bornholm Sea. This indicates that in some cases the mesoscale circulation is weak and allows the development of the individuals through the stages in a certain flow pattern, while in other areas the current patterns vary rapidly and the different stages are transported in different ways during their development. This illustrates that the distribution patterns of the different stages 14

15 are formed by the mesoscale currents during the temporal development of the stages. Owing to the very sparse date sets of zooplankton it is hard to verify the model results with the help of observations. However, data were collected during ship campaigns in May and August 1999 in the Bornholm Sea (Möllmann, personal communication) in the frame of the STORE Project. The observed abundance are of the same order of magnitude as simulated and show similar structures when the corresponding stages of the different genera (Pseudocalanus, Arcartia, and Temora) are lumped together. 3.2 Variable Mortality The truncation of the model food web at the level of zooplankton involves implicitly zooplankton mortality through predation by planktivorous fish. In the reference run constant stage-dependent mortalities were used. This approach can qualitatively justified by the high mobility of fish, which follow the prey and maintain a certain predation level. Since both planktivorous fish and their larvae are primarily visual predators, the effect of the visibility of the prey on the degree of predation and hence the mortality is important ([14]). In order to take such effects into account we repeat the simulation for a variable mortality controlled by the light climate in the water column. To this end we use the mortality rates given by (18) and (19). We consider two cases, which are characterized by the parameter sets listed in Table 3. The constant background values refer to the sum effect of natural mortality as well as grazing by tactile and filtering predators. The variable, light dependent part of the mortality rates depends on the annual cycle of solar radiation and the light attenuation in the water. The two cases of light dependent mortalities are shown in Figures 11 and 12 for nauplii and adults at an example location in the central Baltic (57.25N, 20E), using the solar radiation computed in the circulation model. The time series of the yearly cycle of the mortality rates for case 1 and 2 show that in the one to ten meter depth intervals the light dependent values exceed the constant rates in the period from spring to autumn. Below ten meters the variable mortality rates are always smaller than the constant rates. The maximum rates for the case 2 are smaller in the upper ten meters than for case 1, but larger below ten meters. The largest effective mortalities occur in the reference case and the smallest ones in case Total Changes of Stages in selected Basins of the Baltic We start the description of the results with the phytoplankton development and discuss then the development of the model zooplankton using basin averages of the state variables. The spring bloom starts first in the Arkona Sea and commence with delay in the Bornholm basin and then in the Baltic proper. We confine the discussion of the mean quantities to only two regions, the Arkona Sea and the Bornholm Sea. The results for 15

16 Figure 6: Snapshots of the development of the spatial distribution patterns of the model Chlorophyll averaged over a ten meters thick surface layer for a) , b) , c) , d)

17 Figure 7: Snapshots of the development of the spatial distribution patterns of the model nauplii averaged over a ten meters thick surface layer for a) , b) , c) , d)

18 Figure 8: Snapshots of the development of the spatial distribution patterns of the model copepodites 1 averaged over a ten meters thick surface layer for a) , b) , c) , d)

19 Figure 9: Snapshots of the development of the spatial distribution patterns of the model adults averaged over a ten meters thick surface layer for a) , b) , c) , d)

20 Figure 10: Snapshots of the distribution patterns of a) eggs, b) nauplii, c) copepodites 1 and d) adults for the 10th August. 20

21 Figure 11: Light dependent mortality rates (case 1) for the levels of 0, 5, 10, 20 and 40m depth for nauplii (left) and adults (right). The mortality in 40m depth is practically independent of light. The reference case mortality, drawn as a dashed line, is smaller than the light dependent mortality for the upper ten meters but larger below the upper layer. Figure 12: Light dependent mortality rates (case 2) for the levels of 0, 5, 10, 20 and 40m depth for nauplii (left) and adults (right). The mortality in 40m depth is practically independent of light. The reference case mortality, (dashed line), is smaller than the light dependent mortality for the upper ten meters but larger below the upper layer. Compared to case 1, Fig. 11, the mortality levels below 10m depth are elevated. 21

22 Figure 13: The development of the averaged phytoplankton concentration in the Arkona Sea for different mortalities. the development of the mean values in the Baltic Proper are very similar to those of the Bornholm Sea, expect that in the Baltic Proper the development is delayed by a couple of days and the peak values of the mean abundance show larger differences among the considered experimental simulations Arkona Sea The spring bloom in the Arkona Sea commences in March and is not affected by the differences in the mortalities. However, in the declining phase after the spring bloom peak the number of copepods has increased to a level that the different mortalities affect the phytoplankton concentration in different ways. Higher effective mortalities imply a smaller zooplankton biomass and a reduced grazing pressure and, hence higher phytoplankton concentrations, see Fig. 13. A slight autumn peak occurs in September. With the onset of the spring bloom the adults start grazing and lay eggs. The egg abundance shows a strong increase in May, see Fig. 14. For the smallest effective mortality, case 1, the peak of the egg abundance is reached in the second half of June while for constant mortality the peak is reached about three weeks later, Fig. 14. The peaks of the biomass of adults, Fig. 15, are delayed for higher mortalities (constant mortality case) while the peak levels are inverse to the effective mortalities. The response of egg abundance to the slight increase in chlorophyll in September is strongest for the constant mortality case. This follows from the higher level of phytoplankton which can develop in the case of stronger effective top down control of the zooplankton. Then the adults can respond with a stronger reproduction as in the cases 1 and 2, where the abundance is higher and keep the phytoplankton on a lower level. The abundance of nauplii follows that of eggs with a delay of about ten days, which corresponds to the time scale of hatching, see Fig. 14. Note that the abundance of nauplii is inversely proportional to the effective mortality during the whole annual cycle. The copepodites stage show a similar development (not shown). The abundance 22

23 Figure 14: The development of the averaged egg (left) and nauplii (right) abundance in the Arkona Sea for different mortalities. of the adults assume the highest level in July, Fig. 15. The top-down effect imposed by the different mortalities is established by the different peak values and delayed occurrence of the peak for higher mortalities. We note that the development of the mean abundance and biomass shows no distinct different generations in the course of the year. Although all simulation were performed with the starvation adjustment it is elucidating to discus briefly how the results would be changed without a hunger threshold. Since eventually the individual model copepods accumulate in the adult stage we use the model adults to demonstrate the role of the starvation effect. The abundance of adults without the starvation term is shown in Fig. 16. The biomass is virtually not affected. Obviously, without starvation mortality the abundance decrease much slower than the biomass, implying a substantial decrease of the mean individual weight of adults as depicted in Fig. 17, where the case 1 is shown and Fig. 5 showing the reference case. The effect is strongest for the smallest effective mortality, case 1. The case 2 (not shown) lies in the middle. As discussed in subsection 2.1.5, the dynamical reason is the role of the basic respiration which acts to reduce the biomass but not the number of individuals. Since the strongest starvation effects occur in the autumn it follows that for simulations over several years the starvation adjustment of the mortalities is of particular importance Bornholm Sea In the Bornholm Sea the spring bloom starts a little later than in the Arkona Sea and develops during April and May where the peak value is reached, Fig. 18. The peak values are smaller than in the Arkona Sea, partly because there is less phytoplankton in the mixed layer, compare Fig. 6, and partly because the averages are taken over 60m and include a deeper water column. However, a relatively strong secondary peak occurs in August. 23

24 Figure 15: The development of the averaged adult biomass (left) and abundance (right) in the Arkona Sea for different mortalities. Figure 16: The development of the averaged adult abundance in the Arkona Sea for different mortalities but without the starvation effect. Figure 17: The development of the adults mean individual weight in the Arkona Sea with and without starvation included into the mortality description for the case 1. 24

25 Figure 18: The development of the averaged phytoplankton concentration in chlorophyll (left) and the averaged egg abundance (right) in the Bornholm Sea for different mortalities. Figure 19: The development of the averaged abundance of nauplii (left) and adults (right) in the Bornholm Sea for different mortalities. The general development shown for abundance of eggs, nauplii, and adults is similar as in the Arkona basin, see Figures 18, and 19. However, the strongest egg-peak occurs for the constant mortality case in August, where the adults individual weight is higher than for the other cases and, hence, the egg production is driven by higher abundance and stronger food signals. Contrary to the findings for the Arkona Sea, the time series allow clearly to distinguish three generations during the course of the year. The effect of the different mortalities on the averaged abundance is as expected from the discussion in the previous subsection. Stronger top down control reduces the peak levels and delay the development. The differences of the state variables resulting from the different mortalities vary among the stages and show a seasonal cycle as seen in the basin averages. The dif- 25

26 Figure 20: Difference of the constant mortality case (reference case) minus the variable mortality case 1 for abundance of a) nauplii and b) adults at 10 August in the upper 10m. The solid line in b) marks the zero value. ferences show also spatial structure. We show as an example the difference values of nauplii and adults for the reference case minus case 1 mortalities for the 10 August 1999 in Figure 20. This examples show that there are general regional differences, with positive values of adults and negative values of nauplii, in particular in the relative shallow southwestern Baltic. There are also indications of mesoscale structure in the plots of the differences. This results show that changes of the top down control, represented by different zooplankton mortalities, affect not only biomass and abundance but also the basin scale and mesoscale distribution of the model copepods. 4 Discussion and conclusions Based on an advanced ecosystem model of the Baltic sea ([30, 29]) with an integrated stage resolving copepod model ([11]) the effect of different approaches of the zooplankton mortality on the yearly cycle of zooplankton was studied for the model year The model food web is truncated at the level of the zooplankton by zooplankton mortality, which includes predation by planktivorous fish. We considered three examples of stage dependent mortality rates, constant values as reference simulation and two cases of light dependent mortality rates. The rationale is that fish has a high mobility and follows the prey, but the foraging for prey depends on the visibility, i.e., the light conditions. However, mortality is 26

27 difficult to constrain and there is no data base to provide the mathematical formulation. Therefore the choices of parameters is supported only by qualitative arguments. The study is intended as a theoretical investigations which becomes possible with the help of our ecosystem model. It is hoped that this contribution can help to stimulate the discussion of field experimentally oriented scientists and modelers towards a better quantification of the processes. The development of the mean abundance and biomass in the simulation showed clearly separated three generations of copepods in the Bornholm Sea, while in the Arkona Sea different generations cannot be distinguished. The absence of separated peaks in the Arkona Sea can be attributed to the different timing of the development in shallow and deep parts which smoothes the resulting basin wide averages during the year. The differences of the state variables, caused by different approximations of mortality, vary among the stages during the year and show also spatial structures. Thus changes of the top down control, represented by different zooplankton mortalities, affect the mean levels of abundance and biomass concentrations as well as basin scale and mesoscale distribution patterns of the model copepods. The model system has the potential to assess variations in the recruitment conditions, by computing development of larvae food (distribution of nauplii) in time and space in response to climate changes or altered river loads. The bottom-up approach provides the possibility to study how changes in the physical control or in nutrient inputs cascades through the food web and may affect the recruitment processes. The stage resolving model combines elements of biomass and population models and allows a consistent formulation of the equations for the state variables, abundance and biomass. Although the present model is quite complex, it is still a simplified description of the natural system. For example, the stage resolving model formulation involves still aggregated state variables by lumping together several genera into the corresponding stages. The signatures of the model-copepod, in particular the table of characteristic mass-parameters correspond to Pseudocalanus, which are thoroughly described in [9]. It was assumed that the model-copepod comprises other Baltic copepod genera although their parameters differ somewhat from those of Pseudocalanus. Other taxa such as Cladocera and Rotifera were not explicitly taken into account in the present model approach. Active vertical motion both in response to environmental signals and ontogentic migration is planned in future model upgrades. The influence of salinity and oxygen on the physiological rates has not been considered. For the study the model year 1999 was chosen because there exist some high resolution zooplankton data sets from the Bornholm Sea which were made available to us. The comparison with the data showed that the model generates the right order of magnitude for abundance and biomass and reproduces qualitatively the observed mesoscale patterns. This study also highlights that more observational data with relatively high temporal and spatial resolution are needed to initialize model runs, to compare model output with measurements and improve process formulations. 27

28 Acknowledgement Supercomputing power was provided by the HLRN (Norddeutscher Verbund für Hochund Höchstleistungsrechnen) and NIC (John von Neumann Institute for Computing). We thank the modeling group of Baltic Sea Research Institute for supporting the circulation model. The provision of the BALTEX data set for the meteorological forcing is grateful acknowledged. We thank Christian Möllmann for making available not yet published data from the STORE Project, which we could use to compare the model results with observations. The work was financially supported by the BMBF in the frame of the German GLOBEC project (No. FKZ 03F0320A-E). References [1] D. L. Aksnes and U. Lie. A coupled physical-biological pelagic model of a shallow sill fjord. Estuarine, Coastal and Shelf Science, 31: , [2] D. L. Aksnes, K. B. Ulvestad, B. M. Balino, J. Berntsen, J. K. Egge, and E. Svendsen. Ecological modeling in coastal waters: towards predictive physicalchemical-biological simulation models. Ophellia, 41:5 36, [3] H. P. Batchelder and C. B. Miller. Life history and population dynamics of metridia pacifica: results from simulation modelling. Ecological Modelling, 48: , [4] N. Broekhuizen, M. R. Heath, S. L. Hay, and W. S. C. Gurney. Modelling the dynamics of the North Sea s mesozooplankton. Netherlands Journal of Sea Research, 33: , [5] A. D. Bryant, M. Heath, W. S. G. Gurney, D. J. Beare, and W. Robertson. The seasonal dynamics of calanus finmachicus: development of a three-dimensional structured population model and application to the northern North Sea. Netherlands Journal of Sea Research, 38: , [6] F. Carlotti, J. Giske, and F. Werner. Modeling zooplankton dynamics. In R. Harris, P. Wiebe, J. Lenz, H. R. Skjoldal, and M.Huntley, editors, ICES Zooplankton Methodology Manual, pages Academic Press San Diego, [7] F. Carlotti and P. Nival. Model of copepod growth and development: moulting and mortality in relation to physiological processes during individual moult cycle. Marine Ecology Progress Series, 83: , [8] F. Carlotti and A. Sciandra. Population dynamics model of euterpina acutifrons ( copepoda: Harpacticoida) coupling individual growth and larval development. Marine Ecology Progress Series, 56: ,

29 [9] C. J. Corkett and I. A. McLaren. The biology of pseudocalanus. In F. S. Russell and M. Yonge, editors, Advances in Marine Biology, pages Academic Press, London New York San Francisco Boston Sydney TokyoSan Diego, [10] M. J. R. Fasham, H. W. Ducklow, and S. M. McKelvie. A nitrogen-based model of plankton dynamics in the oceanic mixed layer. Journal of Marine Research, 48: , [11] W. Fennel. Modeling of copepods with links to circulation models. Journal of Plankton Research, 23: , [12] W. Fennel and T. Neumann. Variability of copepods as seen in a coupled physical biological model of the baltic sea. ICES Marine Science Symposia, 219, [13] W. Fennel and Th. Neumann. The mesoscale variability of nutrients and plankton as seen in a coupled model. German Journal of Hydrography, 48:49 71, [14] O. Fiksen, A.C.W. Utne, D.L. Aksnes, K. Eiane ane J.V. Helvik, and S.Sundby. Modelling the influence of light, turbulence and ontogenetic on ingestion rates in larval cod and herring. Fisheries Oceanography, 7(3/4): , [15] H. G. Fransz and J. H. G. Verhagen. Modelling research on the production cycle of phytoplankton in the southern bight of the North Sea in relation to river-borne nutrient loads. Netherlands Journal of Sea Research, 19: , [16] S.M. Griffies, R.C. Pacanowski, M. Schmidt, and V. Balaji. Tracer conservation with an explicit free surface method fo z-coordinate ocean models. Monthly Weather Review, 129: , [17] J. A. Gulland. The Management of Marine Fisheries. Scientechnica, Bristol, [18] S. Gupta, D. J. Lonsdale, and D. P. Wang. The recruitment pattern of an estuarine copepod: A biological-physical model. Journal of Marine Research, 52: , [19] M. Heath, W. Robertson, J. Mardaljevic, and W. S. G. Gurney. Modelling population dynamics of calanus in the Fair Isle off northern Scotland. Jour. Sea Research, 38: , [20] L. Hernroth. Recommendations on methods for marine biological studies in the Baltic Sea: Mesozooplankton assessment. Baltic Marine Biologists WG 14, Publication No. 10, [21] H. J. Hirche, U. Meyer, and B. Niehoff. Egg production of calanus finmarchius: effect of temperature, food and seasons. Marine Biology, 127: ,

30 [22] Ch. Humborg, K. Fennel, M. Pastuszak, and W. Fennel. A box model approach for a long-term assessment of estuarine eutrophication, Szczecin Lagoon, southern Baltic. Journal of Marine Systems, 25: , [23] F. Janssen, C. Schrum, and J. Backhaus. A climatological dataset of temperature and salinity for the North Sea and the Baltic Sea. German Journal of Hydrography, 9:245, [24] W. C. M. Klein-Breteler, N. Schogt, and J. van der Meer. The duration of copepod life stages estimated from stage frequancy data. Journal of Plankton Research, 16: , [25] Ain Lääne, Heikki Pitkänen, Berit Arheimer, Horst Behrendt, Waldemar Jarosinski, Sarmite Lucane, Karin Pachel, Antti Rike, Alexander Shekhovtsov, Lars M. Swendsen, and Simonas Valatka. Evaluation of the implementation of the 1988 ministerial declaration regarding nutrient load reductions in the Baltic Sea catchment area. Technical report, Finish Environment Institute, [26] D. R. Lynch, W. C. Gentleman, D. J. McGillycuddy, and C. S. Davis. Biologicalphysical simulations of calanus finmarchius population dynamics in the Gulf of Maine. Marine Ecology Progress Series, 169: , [27] C. B. Miller, D. R. Lynch, F. C. Carlotti, W. Gentleman, and C. V. W. Lewis. Coupling of an individual-based population model of calanus finmarchicus to a circulation model of the Georges Bank region. Fisheries Oceanography, 7: , [28] C. B. Miller and K. S. Tande. Stage duration estimation for calanus populations, a modelling study. Marine Ecology Progress Series, 102:15 34, [29] T. Neumann, W. Fennel, and Ch. Kremp. Experimental simulations with an ecosystem model of the Baltic Sea: A nutrient load reduction experiment. Global Biogeochemical Cycles, 16: , [30] Thomas Neumann. Towards a 3d-ecosystem model of the Baltic Sea. Journal of Marine Systems, 25(3-4): , [31] R. C. Pacanowski and S. M. Griffies. Mom 3.0 manual. Technical report, Geophysical Fluid Dynamics Laboratory, [32] B. J. Rothschild. Dynamics of Marine Fish Populations. Harvard University Press, Cambridge, U.S.A., [33] A. Stigebrandt and F. Wulff. A model for the dynamics of nutrients and oxygen in the Baltic proper. Journal of Marine Research, 45: ,