Progress in Oceanography 58 (2003) 1–41 www.elsevier.com/locate/pocean

Simulated carbon and nitrogen flows of the planktonic food web during an upwelling relaxation period in St Helena Bay (southern Benguela ecosystem) Franck Touratier a,∗, John G. Field b, Coleen L. Moloney b a

Universite´ de Perpignan, EA 1947 BDSI, 52 avenue Paul Alduy, 66860 Perpignan, France b Zoology Department, University of Cape Town, 7701 Rondebosch, South Africa Received 30 April 2002; received in revised form 20 April 2003; accepted 14 May 2003

Abstract A vertically resolved ecosystem model is developed to simulate the dynamics of the pelagic food web in St Helena Bay during a representative period of relaxation after an upwelling event. The proposed model aims at coupling three biogeochemical cycles (carbon, nitrogen and silicon), using several recently developed concepts of the stoichiometric approach. A consequence of this approach is that important qualitative aspects are introduced, such as indicators of phytoplankton physiological state or variable food C:N ratios. For instance, the sedimentation and exudation rates for phytoplankton vary according to physiological state. An attempt is made to parameterize and simulate the diel cycles for vertical migration and feeding rhythms of large zooplankton, two important mesoscale processes that are thought to influence the overall dynamics of the huge phytoplankton blooms in the region. Observations of the Anchor Station Experiment 1987 (ASE’87) are used to assess the quality of the model. There is overall agreement between observations and the corresponding simulated results. The timing, the magnitude, and the vertical structure of the phytoplankton bloom are well reproduced. The balances for carbon and nitrogen flows and stocks compare well to the numerous estimates found from the literature for the southern Benguela region. On the basis of the model results, the origin of the new nutrients, the fate of the carbon fixed by phytoplankton, and the importance of the microheterotrophic pathways are discussed. It is concluded that sediments of the St Helena Bay and surrounding areas may play a crucial role in increasing the level of phytoplankton production. The results also suggest that exudation is the main process by which the carbon fixed by phytoplankton would have been lost, and that microheterotrophic pathways would have been intense during the experiment.  2003 Elsevier Ltd. All rights reserved.

Contents 1.

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Corresponding author. E-mail address: [email protected] (F. Touratier).

0079-6611/03/$ - see front matter  2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0079-6611(03)00087-9

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2. The Anchor station experiment 1987 (ASE’87) . . . . . . . . . . 2.1. Study site and literature . . . . . . . . . . . . . . . . . . . . . . 2.2. Data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. The hypothesis of horizontal homogeneity: justification for a

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3. Description of the model . . . . . . . . . . . . . 3.1. Parameterization of the biological processes 3.2. Forcing variables and vertical processes . . 3.3. Model implementation . . . . . . . . . . . . .

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4. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Comparison of model outputs to ASE’87 observations . . . . . . . . . . . . . . . 4.1.1. Distribution of nutrients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2. Distribution of phytoplankton and primary production . . . . . . . . . . . . . 4.1.3. Distribution of heterotrophs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4. Other variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Additional model outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Carbon and nitrogen flows for the pelagic food web in the southern Benguela 4.3.1. Phytoplankton biomass and processes (PC, F1, F16) . . . . . . . . . . . . . . 4.3.2. Zooplankton biomass and processes (ZC, F2, F9, F25) . . . . . . . . . . . . 4.3.3. Bacterial biomass and processes (BC, F6, F13) . . . . . . . . . . . . . . . . . 4.3.4. Sedimentation processes (F4, F12, F14, F21, F28, F30, R4, R12, R14) . . . 4.3.5. Supply of nutrients from sediments (F15, F31) . . . . . . . . . . . . . . . . .

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Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. Introduction The four largest coastal upwelling systems (the Humboldt, Benguela, Canary and California Current systems) account for more than 25% of the world catch of marine fish (FAO, 1990). Because of their large productivity, coastal upwelling systems are often seen as carbon sinks (Siegenthaler & Sarmiento, 1993), i.e. areas where excess atmospheric carbon is used by phytoplankton in the euphotic zone and then exported to the deep ocean by rapid sinking after exhaustion of available nutrients. The transfers and cycles of carbon and other nutrients in these ecosystems is therefore of interest. In the Benguela system off South Africa, the three main factors that govern upwelling events are climatic forcing via the south-east Atlantic high pressure anticyclone, which causes equatorward winds (Estrada & Marrase´ , 1987), the topography, and the influence of the Agulhas Current (Shannon, 1985). However, mesoscale variability plays an important role in system productivity. For example, it is well established that during the upwelling season, the system is continuously pulsed on a time scale of about 1 week on average (Chapman & Shannon, 1985), and according to Jury and Brundrit (1992), an optimum upwelling cycle of ca. 10 days would obtain maximum trophic efficiency. Not only the intensity and duration of the active phase of upwelling are critical variables for productivity, but also the duration of the relaxation period between two active phases. During relaxation of the system, chemical and biological processes become the major determinants of plankton dynamics (Pitcher, Brown, & Mitchell-Innes, 1992). The theoretical evolution of planktonic systems after upwelling events has been simulated using sizebased ecosystem models (Moloney & Field, 1991; Moloney, Field, & Lucas, 1991; Moloney, 1992), which were subsequently utilized by Painting, Moloney, Probyn and Tibbles (1992) and Painting, Moloney and Lucas (1993) to provide further insights into plankton dynamics in the southern Benguela region. In 1987,

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an extensive data set was obtained through an anchor station experiment (ASE’87) that was carried out on the plankton ecosystem in St Helena Bay in the southern Benguela (Fig. 1). This experiment covered a period of active upwelling and relaxation, and its results provide an excellent opportunity to develop ecological models and to test them during a representative period of relaxation. Models by Cochrane et al. (1991) and Plaga´ nyi, Hutchings, Field and Verheye (1999) used observations made during the ASE’87. Plaga´ nyi et al. (1999) simulated the dynamics of the zooplankton population using a simple model driven by surface chl a concentrations and temperatures. Cochrane et al. (1991) built up a 1D ecosystem model that synthesized the ASE’87 results in order to highlight critical processes and to reveal potential inconsistencies. The discrepancies between the observations and their simulated results were large. This paper has two objectives. The first is to try to improve the plankton model of the ASE’87, by building on the recommendations of Cochrane et al. (1991). For example, all state variables will be resolved vertically, daily solar radiation will be allowed to vary, and we do not try to simulate the active phases of upwelling. As proposed by Cochrane et al. (1991) in their conclusions, we also try to improve the parameterization of several processes, such as preferential nitrogen uptake by phytoplankton, sinking rates of diatoms (which are now variable), excretion and respiration of heterotrophs, and vertical migration of meso- and macrozooplankton. The second objective is to include new features in the plankton food web model, specifically by applying a stoichiometric approach. This approach will allow us to address uncertainties about the fate of carbon fixed by phytoplankton during the ASE’87 bloom, to assess the percentage of new nutrients that were supplied by the sediments before and during the relaxation period, and to quantify the importance of microheterotrophic pathways in nutrient flows. We aim to use the model to balance the carbon and nitrogen budgets in St Helena Bay, and to compare these balances to the numerous observations made in the southern Benguela region.

Fig. 1. Study area of the Anchor station experiment 1987. The black arrow indicates the direction of the surface Benguela current. The cyclonic gyre within the St Helena Bay is also indicated.

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2. The Anchor station experiment 1987 (ASE’87) 2.1. Study site and literature The ASE’87 involved the oceanographic vessel RS Benguela in St Helena Bay (Fig. 1) during the austral autumn (19 March to 16 April; Julian days 78 to 106). Cape Columbine is a major upwelling center along the west coast of southern Africa (Shannon, 1985) that exerts considerable influence on the properties of St Helena Bay, which is an important recruitment area for juveniles of several commercial fish species (e.g. sardine and anchovy). Offshore, the circulation is driven by the Benguela current that flows northward at the surface (Fig. 1). St Helena Bay is a shallow (depth ⬍100 m), semi-enclosed bay that is characterized by sluggish currents. Within the bay, a cyclonic gyre with mesoscale dimensions has often been described (Duncan & Nell, 1969; Shannon, 1985; Chapman & Bailey, 1991). Given the weak circulation and the mean duration of an upwelling cycle in the area (between 1 and 2 weeks; Chapman & Bailey, 1991), it was anticipated that a short-term study (28 days) at one vertical station (the Anchor station, Fig. 1) endowed with a high frequency sampling strategy both in time and space would be sufficient to fulfil the specific objectives of the experiment (see Chapman & Bailey, 1991). Most results of the experiment are detailed in the following literature: context and objectives of the study, Chapman and Bailey (1991); physical and chemical properties of the water column, Bailey and Chapman (1991) and Waldron and Probyn (1991); phytoplankton dynamics and related processes, Pitcher, Walker and Mitchell-Innes (1989), Mitchell-Innes and Walker (1991); Pitcher, Walker, Mitchell-Innes and Moloney (1991); Mitchell-Innes and Pitcher (1992), and Chapman, Mitchell-Innes and Walker (1994); distribution of zooplankton and related processes, Verheye (1989); Armstrong, Verheye and Kemp (1991); Verheye (1991) and Verheye and Field (1992); and ecosystem models using ASE’87 results, Cochrane et al. (1991) and Plaga´ nyi et al. (1999). 2.2. Data sets Due to instrument failure, no measurements of solar radiation were made during the experiment, and Cochrane et al. (1991) assumed that light at the surface remained constant in their model. As recognized by the authors, this assumption is a poor approximation, and we circumvent it by using hourly solar radiation data measured at Cape Town International Airport (ca. 150 km south of Cape Columbine) during the time period of the ASE’87. However, local peculiarities such as the occurrence of fog at St Helena Bay during the ASE’87 (Bailey & Chapman, 1991) may limit the applicability of the Cape Town data. Temperatures were measured using a CTD profiler, and samples for nitrates (NO3), ammonium (NH4), and silicates (Si(OH)4) were taken every 4 h at depths of 0, 5, 10, 20, 30, 37 and 43 m (the water column depth at the Anchor station was ca. 47 m) using a rosette sampler (Bailey & Chapman, 1991). Total chl a was sampled using the nutrient sampling grid, whereas size-fractionated (using a 10 µm filter) chl a and primary production were measured at additional stations sampled every morning at depths corresponding to 100, 50, 25, 10 and 1% of surface irradiance (Mitchell-Innes & Walker, 1991; Pitcher et al., 1991). The 14 C method was used to estimate primary production. This original data set is neither averaged over the day period nor depth integrated, so that Mitchell-Innes and Walker (1991) also provide daily averaged and depth integrated production data using a simple model (not presented here). A Bongo net fitted with a 200 µm mesh and a pump were used to sample the zooplankton daily (Verheye, 1991). Whatever the system, all samples were size-fractionated with a 500 µm and a 1600 µm mesh, so that wet weights of fresh biomass corresponding to three size classes (200–500, 500–1600 and ⬎1600 µm) were available. The estimates provided by both samplers compared well (Verheye, 1991). However, contrary to the Bongo net which only allowed estimates of depth-integrated biomass, the pump provided samples at five or six discrete

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depths. Because of the large size of the main diatom species Coscinodiscus gigas encountered during the ASE’87 (ca. 200–300 µm; Armstrong et al., 1991), Verheye (1991) estimated that the phytoplankton biomass accounted for up to 92% of the wet weight of the 200–500 µm size fraction used for zooplankton. Since there is still uncertainty over the real composition of these samples, they are not considered in the present study. Samples were taken every midday from five to seven depths to determine bacterial abundance following the method described by Painting (1989). This coherent data set has not yet been published. 2.3. The hypothesis of horizontal homogeneity: justification for a 1D (vertical) approach Southerly or south-easterly (Hart & Currie, 1960), persistent, and moderate to strong winds (⬎5 m s⫺1; Shannon, 1985) combined with a favorable topography promote upwelling in the Benguela system. When such winds blow on the Cape Columbine headland during summer and autumn (Lutjeharms & Meeuwis (1987) noted the highest frequency of upwelling during these periods), deep, cool, and nutrient-rich waters (the South Atlantic Central Water, SACW; see for example, Clowes, 1950) are advected to the surface, near the coast. After such events, a narrow tongue of this water was observed using field experiments or satellite imagery to extend northward and then north-eastward following the cyclonic trajectory of the gyre in St Helena Bay (e.g. Shannon, Hutchings, Bailey, & Shelton, 1984; Taunton-Clark, 1985; Armstrong, Mitchell-Innes, Verheye-Dua, Waldron, & Hutchings, 1987; Pitcher, 1988). Using drogues to follow the same body of water in the tongue, Painting, Lucas et al. (1993) noted that salinity profiles indicated that maturing upwelled water was located in the upper 20 to 30 m. The upwelling tongue may thus influence the surface layer properties of the cyclonic gyre, which is often described as a two-layer system (Bailey & Rogers, 1997). During the ASE’87, three upwelling events were recorded by Bailey and Chapman (1991) at the Anchor station, which was located approximately in the middle of the cyclonic gyre. The temperature profiles (Fig. 2b) show the periods of active upwelling called U1, U2 and U3 (see the horizontal bar in Fig. 2) which are separated by two periods of relaxation called R1 and R2. As expected, periods U1 to U3 are characterized by a cooling of the surface layer (upper 20 m), whereas this layer warms up rapidly during R1 and R2 due to the accumulation of solar energy. In the present paper, we focus our attention on the relaxation period R1; first because interesting chemical and biological events have been identified during R1, second because R1 is long enough to be modelled (21 days from day 80 to 101; 21 March to 11 April 1987), and third because the structure of the model can be greatly simplified to a 1D-vertical version if the hypothesis of horizontal homogeneity within the cyclonic gyre is assumed. This hypothesis will hold if the exchange of matter and/or energy between the gyre and the surrounding water bodies is negligible. Obviously, this is not the case during the periods U1, U2 and U3 when deep waters originating from the Cape Columbine upwelling center are imported into the surface layer of the cyclonic cell, but several observations show that it is generally true for periods of relaxation, as discussed below. Duncan and Nell (1969); Holden (1985) and Shannon (1985) already pointed out the stability of the water masses within the cyclonic gyre of St Helena Bay, with a residence time of ca. 1 month (Waldron, 1985). During the ASE’87, the water circulation was sluggish (Chapman & Bailey, 1991; Mitchell-Innes & Walker, 1991), a fact reinforced by the analysis of the chemical properties (Bailey & Chapman, 1991). (Brown & Hutchings, 1987a) considered that a low variability of salinity (⬍1%) mirrored a physical consistency of the water along their drogue tracks. The salinity during the ASE’87 varied by much less than 1% (the range is 34.70–34.82 ‰; Bailey & Chapman, 1991), which also indicates the physical consistency of the water column. After the upwelling events, when stratification develops within the cyclonic cell, biological activity becomes important and biological and chemical processes, rather than physical processes dominate the system (Bailey, 1985; Pitcher, 1988; Pitcher, Brown & Mitchell-Innes, 1992). From the preceding arguments, we assumed that the water body within the cyclonic gyre could be considered as an isolated cell during periods of upwelling relaxation. In contrast to Cochrane et al. (1991),

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Fig. 2. Forcing variables and bottom conditions for nutrients. (a) incident radiations; (b) temperature; (c) density (st); (d) vertical turbulent diffusion coefficient (Kv); and (e) bottom conditions for nitrate (NO3b) and silicate (SIb). The horizontal bar above panel (a) indicates the succession of the three active phases (periods U1, U2, and U3) and the two relaxation periods (R1 and R2) of the upwelling. Only period R1 is modeled.

who simulate the entire period of ASE’87 with their 1D ecological model, we do not include the periods of active upwelling where the hypothesis of horizontal homogeneity is violated.

3. Description of the model In the model, the real system is reduced to a much simpler case where only the vertical dimension is represented. The total water column is modelled by 47 layers of 1 m each. The spatial resolution adopted for the model is at least five times greater than that of the sampled variables. The number and the nature of units that should be chosen for ecological models is greatly debated. There are supporters of both oversimplified and very detailed descriptions of natural systems. The absence of an overall consensus on this crucial topic, however, mirrors our limited understanding of the real system. Numerous models use only one chemical element for model currency (e.g. Andersen & Nival, 1989; Fasham, Ducklow, & McKelvie, 1990; Carlotti & Radach, 1996). The relatively new theory of elemental stoichiometry is mainly concerned with the spatial and temporal variability of elemental ratios, as affected by chemical and biological interactions. Pioneering studies (e.g. Le Borgne, 1982; Sterner, 1990; Elser &

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Hassett, 1994) have demonstrated that biogeochemical cycles are neither independent, nor parallel, but deeply interconnected and complementary (Anderson, 1997). In other words, the study of one of these cycles allows us to understand only one piece of the puzzle, not the whole picture. These views stimulated the emergence of a new generation of ecosystem models, like those of Anderson (1997) and Touratier, Legendre and Ve´ zina (2000), where the variability of the most important elemental ratios is explicitly parameterised. For the present study, we propose to build a model of this type. Phosphorus (P) did not limit primary production during the ASE’87 (Bailey & Chapman, 1991; MitchellInnes & Walker, 1991). This seems to be a consistent feature of the St Helena Bay or even the southern Benguela ecosystem (e.g. Andrews & Hutchings, 1980; Barlow, 1982; Brown & Hutchings, 1987b). For nitrogen (N) and silicon (Si), the situation is unclear. An overall consensus indicates that NO3 often limits phytoplankton growth in the Benguela system (e.g. Andrews & Hutchings, 1980; Pitcher, 1988; Brown & Hutchings, 1987b), which is supported by the observations made by Bailey and Chapman (1991) during the ASE’87. However, NO3 is not the sole dissolved nutrient that contains nitrogen; regenerated nutrients like NH4 or urea are also assimilated by phytoplankton. In such conditions, the total amount of available dissolved nitrogen (NO3 + NH4 + urea + other forms) could perhaps be less limiting than other nutrients like silicate. Chapman and Shannon (1985) suggested that silicate could become limiting in St Helena Bay, especially because huge biomasses of diatoms often occur in this area. For the ASE’87, there is still some doubt about the nature of the nutrient that limited the phytoplankton bloom during R1: contrary to Bailey and Chapman (1991); Mitchell-Innes and Walker (1991) conclude that silicate was more limiting than NO3, based on the fact that the silicacline was deeper than the nitracline. Given the previous arguments, it is reasonable to build up a model where phytoplankton may be N or Si limited. To reconcile the different views, it seems necessary to admit that the type of element that limits the growth of phytoplankton may quickly vary with time and depth and that it depends largely on the nature of the phytoplankton (diatoms, dinoflagellates, etc.). Carbon (C) is chosen as the third unit of the model. Although phytoplankton growth is considered to be rarely limited by carbon, the choice of this element is motivated by three arguments: (1) C is closely related to the energy content of all organic entities; (2) C may limit the growth of heterotrophs (bacteria, zooplankton, etc.); (3) important processes are often measured in terms of carbon (e.g. the 14C method for primary production). C and N are, however, considered to be the main units of the present model because, contrary to Si, they are major elements of most system components. By describing the pelagic food web both in terms of C and N, an additional advantage of the stoichiometric approach is that the C:N ratios of components and flows represent a criterion of quality. In stoichiometric models, the criterion of quality plays a major role because elemental ratios constrain the overall structure of an ecosystem (Touratier, Field, & Moloney, 2001). The model has 19 state variables (Table 1). Several components are used to describe the pelagic food web: the nutrients (NO3; NH4; Si(OH)4), the autotrophic organisms (small phytoplankton, P1; large phytoplankton, P2), the heterotrophic organisms (bacteria, B; microzooplankton, Z1; mesozooplankton, Z2; macrozooplankton, Z3), the detritus (small detritus, D1; and intermediate-sized detritus, D2), and the dissolved organic matter (with low molecular weight, DOM1; and high molecular weight, DOM2). The size factor is widely used to specify the state variables (Table 1), as in several ecosystem models (e.g. Moloney & Field, 1991; Moloney, Field & Lucas, 1991). P2 is assumed to be exclusively composed of diatoms, the sole taxonomic group in this model to be potentially limited by silicate. Large detritus (⬎500 µm; i.e. carcasses and fecal pellets of Z2 and Z3) are not explicitly modelled because of their fast sinking velocities (often ⬎200 m d⫺1) relative to the water column depth (47 m). From this, a maximum residence time for large detritus within the water column of ca. 0.23 day can be computed. We therefore assume that large detritus particles are instantaneously exported to the sediment. For the variables used to describe DOM, only the labile fraction (i.e. the fraction rapidly available to bacterial growth) is modelled; DOM1 and

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Table 1 State variables of the model Symbol

Description

NO3 NH4 SI P1C P1N P2C P2N BC Z1C Z2C Z3C D1C D1N D2C D2N DOM1C DOM1N DOM2C DOM2N

Nitrate concentration Ammonium concentration Silicate concentration Small phytoplankton biomass (⬍10 µm) Small phytoplankton biomass (⬍10 µm) Large phytoplankton biomass (⬎10 µm) Large phytoplankton biomass (⬎10 µm) Bacterial biomass (0.2–2 µm) Microzooplankton biomass (2–500 µm) Mesozooplankton biomass (500 - 1600 µm) Macrozooplankton biomass (⬎1600 µm) Small detritus concentration (0.2–10 µm) Small detritus concentration (0.2–10 µm) Intermediate-sized detritus concentration (10–500 µm) Intermediate-sized detritus concentration (10–500 µm) Labile low molecular weight DOM concentration Labile low molecular weight DOM concentration Labile high molecular weight DOM concentration Labile high molecular weight DOM concentration

Units (mg m⫺3) N N Si C N C N C C C C C N C N C N C N

C, N, and Si, carbon, nitrogen, and silicon, respectively.

DOM2 correspond to the so-called ‘direct’ and ‘indirect’ bacterial growth substrates, as defined by Billen and Servais (1989) who specify that indirect substrates must be first hydrolysed into direct substrates to be readily assimilated by bacteria. The C:N ratios of phytoplankton, detritus and DOM are not constant, so that each size class is represented by two state variables called xC and xN (i.e. C and N biomass or concentrations), where C:N ratios are defined by the ratios xC:xN. The C:N ratios for bacteria (cnB) and zooplankton (cnZ1, cnZ2, cnZ3) are constant, so that only one state variable is used to model each group of organisms (BC, Z1C, Z2C, Z3C; the C unit is chosen arbitrarily). Using a constant C:N ratio for bacteria is consistent with the study of Goldman, Caron and Dennett (1987), who showed this ratio to be stable for a wide range of growth conditions. Although the variability of zooplankton elemental ratios seems to be more inter- than intraspecific (Urabe, 1993; Sterner & Hessen, 1994), several species of marine copepods living at high latitudes may build up large reserves of lipids, which increases the proportion of C relative to N in their bodies. The processes responsible for this variability are poorly known, so it would be premature to develop a model without the assumption of constant elemental composition. All C and N flows between the state variables are summarised in Table 2, where nine possible types of flow can be identified, i.e. decomposition (D), exudation (E), faeces production (F), bacterial assimilation and grazing (G), hydrolysis (H), mortality (M), excretion (N), respiration (R), and uptake (U). Any of the flows describe a local transformation from one variable to another. For all variables, three different kinds of vertical exchange may exist, i.e. diffusion (K), sinking (S), and migration (M) (main diagonal of Table 2). The variables DIC (dissolved inorganic carbon), BN, Z1N, Z2N and Z3N (i.e. the biomass of B, Z1, Z2 and Z3, in nitrogen) that appear in Table 2 are not state variables; they are added to better understand the origin or destination of each flow. Concerning the C cycle, P1 and P2 may respire and take up DIC (Table 2). P1 is a potential prey for Z1 and Z2, whereas the potential predators of P2 are Z2 and Z3. The dead cells of P1 and P2 supply the

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Table 2. The model connectivity matrix for a) the carbon cycle, and b) the nitrogen cycle. Boxes with border in bold only contain state variables. Other variables are in boxes without border. The flow is always from the row variable to the column variable. Vertical exchanges between the layers are on the main diagonal. D: decomposition; E: exudation; F: feces production; G: bacterial assimilation or grazing; H: hydolysis; K: diffusion; M: mortality; N: excretion; R: respiration; S: sinking; U: uptake; V: migration.

detritus D1 and D2, respectively. It is assumed that only P2 is able to exude significant amounts of DOM1. All heterotrophs respire DIC. B are prey for Z1; Z1 forms prey for Z2 and Z3; Z2 can be eaten by Z3, and Z3 has no potential predator in the model. Dead bacteria supply the D1 pool, whereas carcasses and faecal pellets of Z1 supply D2. D1 can also be ingested by Z1, and D2 may be used as food by Z2 and Z3. Both D1 and D2 are decomposed into DOM2. These organic compounds must be first hydrolysed into DOM1 owing to bacterial exo-enzymatic activities, to be directly assimilated by bacteria. The vertical distributions of all state variables, except those for Z2 and Z3, are influenced by vertical diffusion. We assume that the distribution of Z2 and Z3, because of their large size and their strong migratory capabilities, remains unaffected by vertical diffusion. Only P2 and D2 may sink in the water column, whereas only Z2 and Z3 may migrate up and down. The simulated C and N processes are similar, so that only the differences are highlighted. These differ-

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ences come from nitrate and ammonium, and their resulting links with the other nitrogenous compounds (see Table 2). Both NO3 and NH4 are taken up by P1 and P2. On the other hand, all heterotrophs excrete NH4, but only bacteria may compete with phytoplankton for this resource. 3.1. Parameterization of the biological processes Parameterizations of the above processes are listed in Table 3 (processes for nutrients and phytoplankton), Table 4 (processes for heterotrophs), and Table 5 (processes for detritus and DOM). The descriptions, symbols, values and units of parameters in the model are listed in Table 6. Symbols containing at least one upper case letter always indicate variables, whereas those with lower case letter(s) are parameters. Parts of the parameterization proposed here come from Touratier et al. (2000) who developed an ecosystem model to simulate the pelagic food web of an Arctic polynya. The nutrient uptake rates for nitrate, ammonium, and silicate (i.e. UNO3x, UNH4x, and USIP2, respectively; where subscript x stands for P1 or P2) are computed as the product of five terms (Eqs. 1 to 3 in Table 3 Processes for nutrients and autotrophs with x = P1 or P2 Nutrient uptake Nitrate uptake rate Ammonium uptake rate Silicate uptake rate Nitrate limitation Ammonium limitation Silicate limitation C:N ratio limitation Light limitation Growth (carbon) Net primary production rate Photoinhibition index C:N ratio limitation Growth (nitrogen) Growth rate Exudation (only P2) Exudation rate C:N ratio limitation

Mortality Mortality rate C:N ratio limitation Sinking (only P2) Sinking velocity C:N ratio limitation

UNO3x = umnx LNO3x LCN1x LT LI UNH4x = umnx LNH4x LCN1x LT LI USIP2 = umnP2 min[(LNO3P2 + LNH4P2) ,LSIP2]LCN1P2 LT LI LNO3x = (NO3 /(kno3x + NO3)) e(⫺yNH4) LNH4x = NH4 / (knh4x + NH4) LSIP2 = SI / (ksiP2 + SI) if cnix ⱕ CNx ⱕ cnmx then LCN1x = (CNx⫺cnix) / (cnmx⫺cnix) if cnmx ⬍ CNx then LCN1x = 1 if I ⬎ (I0 / 1000) then LI = 1 if Iⱕ(I0 / 1000) then LI = 0

(1) (2) (3) (4) (5) (6) (7)

UCx = [pmx(1⫺e(⫺axI / pmx)) e(⫺bxI / pmx)⫺rxpmx(ax / (ax + bx)) (bx / (ax + bx))(bx / ax)] chlcx LCN2x LT

(9)

bx = pmx / ibx if CNx ⱕ cnmx then LCN2x = 1 if cnmx ⬍ CNx ⱕ cnsx then LCN2x = (cnsx⫺CNx)/ (cnsx⫺cnmx)

(10) (11)

if x = P1 then UNP1 = umnP1(LNO3P1 + LNH4P1) LCN1P1 LT LI if x = P2 then UNP2 = umnP2 min[(LNO3P2 + LNH4P2) , LSIP2] LCN1P2 LT LI

(12)

EP2 = e0P2 + e1P2 LEP2 if CNP2 ⱕ cnmP2 then LEP2 = 0 if cnmP2 ⬍ CNP2 ⱕ cnsP2 then LEP2 = (CNP2⫺cnmP2) / (cnsP2⫺cnmP2)

(13) (14)

Mx = m0x + m1x LMx if cnix ⱕ CNx ⱕ cnmx then LMx = (cnmx⫺CNx) / (cnmx⫺cnix) if cnmx ⬍ CNx ⱕ cnsx then LMx = (CNx⫺cnmx) / (cnsx⫺cnmx)

(15) (16)

SP2 = s0P2 + s1P2 LSP2 if cniP2 ⱕ CNP2 ⱕ cnmP2 then LSP2 = (cnmP2⫺CNP2) / (cnmP2⫺cniP2) if cnmP2 ⬍ CNP2 ⱕ cnsP2 then LSP2 = (CNP2⫺cnmP2) / (cnsP2⫺cnmP2)

(17) (18)

(8)

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Table 4 Processes for heterotrophs with x = B, Z1, Z2 or Z3 (bacteria and predators), and y = P1, P2, B, Z1, Z2, D1, D2, or DOM1 (potential prey or growth substrate of x) Bacterial assimilation and grazing Assimilation or grazing if BIOx ⱕ bio0x then Gx = 0 rate of x if BIOx ⬎ bio0x then Gx = gmx LHx LBx LT Assimilation or grazing Gxy = (Gx exy yC) / BIOx rate of x on y Carbon concentration of BIOx = Σy = 1,8(exy yC) potential growth substrate or preys Limitation for daily LHx = h1x + (1⫺h1x) 2⫺h2x(1 + cos(2 p HOUR/ 24))h2x variation of grazing Limitation by growth LBx = (BIOx⫺bio0x) / (khx + BIOx⫺bio0x) substrate concentration C:N ratio for potential CNBIOx = Σy = 1,8(exy yC) / Σy = 1,8(exy yN) growth substrate or preys Feces production Feces production rate Fx = Gx(1⫺acx) Respiration and excretion Respiration rate for the RMx = gmx [(bio1x⫺bio0x)/ (khx + bio1x⫺bio0x)] LT acx maintenance No growth or negative growth (if Gx acxⱕRMx) Respiration rate Rx = RMx Excretion rate Nx = (Gx anx)/ CNBIOx + (RMx⫺Gx acx)/ CNx Positive growth (if RMx ⬍ Gx acx) Respiration rate Rx = Gx acx (1⫺K2Cx) Excretion rate Nx = Gx anx (1⫺K2Nx) /CNBIOx Nitrogen net growth if S1x ⬍ (CNBIOx acx / anx)ⱕS2x then efficiency K2Nx = (1⫺ax) (K2x / cnx) ((CNBIOx acx / anx)⫺cnx) + K2x if S2x ⬍ (CNBIOx acx / anx) then K2Nx = (1⫺ax) (K2x / cnx) ((CNBIOx acx / anx)⫺S2x) LNH4x + 1 Carbon net growth K2Cx = (K2Nx cnx anx)/ (CNBIOx acx) efficiency Net growth K2x = k2mx (Gx acx⫺RMx) /(kk2x + Gx acx⫺RMx) efficiencya Thresholds S S1x = (ax K2x cnx)/ (1 + (ax⫺1) K2x) S2x = (1⫺ax K2x)/ ((1⫺ax) K2x / cnx) Ammonium if x = B then LNH4x = NH4 / (knh4x + NH4) limitation if x ⫽ B then LNH4x = 0 Diel vertical migration (DVM) DVM velocity if Iⱖivx then Vx = vmx LBIOx LLx if I ⬍ ivx then Vx = ⫺vmx LBIOx LLx Food limitation if BIOxⱕbio0x then LBIOx = 1 if BIOx ⬎ bio0x then LBIOx = 1⫺[(BIOx⫺bio0x) /(kv1x + BIOx⫺bio0x)] Light limitation LLx = |I⫺ivx| / (kv2x + |I⫺ivx|) a

K2x is only defined for (CNBIOx acx / anx) = cnx because, in this case, K2Cx = K2Nx.

(1) (2) (3)

(4) (5) (6)

(7) (8)

(9) (10) (11) (12) (13)

(14) (15) (16) (17)

(18) (19)

(20)

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Table 5 Processes for detritus and dissolved organic matter with x = D1 or D2 Detritus decomposition Decomposition rate Dx = dmx LT Hydrolysis of DOM2 into DOM1 Hydrolysis rate H = hm (DOM2C / (kdom2 + DOM2C)) LT

(1) (2)

Table 3). These terms are the maximum growth rate (umnx) and four types of limitation induced by the nutrient concentrations, the phytoplankton C:N ratio, the temperature, and the water column light intensity. Nutrient limitations (LNO3x, LNH4x, and LSIP2; Eqs. 4 to 6 in Table 3) are computed with MichaelisMenten functions, but the sum of the limitations LNO3x and LNH4x follows the parameterization proposed by Wroblewski (1977), where y is a constant that parameterizes the strength of the inhibition exerted by NH4 on NO3 uptake. The sum LNO3x + NH4x must be ⱕ1, a condition that is not always respected by Wroblewski’s equation so that, during the simulations, this condition is checked and the equation is adapted when necessary, as proposed by Touratier (1996). When elements with different units (N and Si) are taken up by P2, the Liebig’s law of the minimum is applied (Eq. 3 in Table 3). The temperature (T; Fig. 2b) influences numerous chemical and biological processes. Consequently, most rates computed in the model are temperature-dependent. We assume that, whatever the process, the limitation by temperature (LT) obeys a classical law of Q10 (LT = Q10 exp([T⫺tref] / 10), where Q10 = 2 (Parsons, Takahashi, & Hargrave, 1984) and the reference temperature tref = 15 °C. The surface incident radiation (Fig. 2a) is multiplied by 0.5 to estimate the PAR (photosynthetically active radiation) available at the air–seawater interface (I0). The PAR available in each layer of the model is computed by using Beer’s law: I(z) ⫽ I0 e-aw Z -

冕

Z 0

(aP1CHLP1+aP2CHLP2)dZ

(1)

The light attenuation coefficient for water is aw=0.05 m⫺1, Eq. (1), which is close to the value of 0.03 m⫺1 proposed by Kirk (1983) for pure water. Constants aP1 and aP2 are the specific light attenuation coefficients due to the biomass of P1 and P2, respectively. The chosen values (respectively 0.1 and 0.009 m2 [mg Chl a]⫺1; Table 6) are close to those of Mitchell-Innes and Walker (1991) estimated for flagellates (0.136 m2 [mg Chl a]⫺1) and large diatoms Coscinodiscus gigas (0.009 m2 [mg Chl a]⫺1), i.e. the main constituents of P1 and P2, respectively, during ASE’87. It is interesting to note that the value obtained for flagellates is far from the range proposed by Bannister (1974) for phytoplankton (0.013–0.02 m2 [mg Chl a]⫺1). To compute the light I at any depth in the water column, Eq. (1), biomass of P1 and P2 in terms of Chl a (CHLP1 and CHLP2, respectively) must be known. This is done in Eq. (2) where P1C and P2C are multiplied by the corresponding Chl a:C ratio (chlcP1 or chlP2, Table 6). Values for parameters chlcP1 and chlP2 are provided by Cochrane et al. (1991). In the model, the total Chl a concentration (CHL) is computed, using Eq. (3). CHLP1 ⫽ P1C chlcP1, CHLP2 ⫽ P2C chlcP2

(2)

CHL ⫽ CHLP1 ⫹ CHLP2.

(3)

When light intensity is low at depth or zero at night, we assume that there is no uptake of nutrients (Eqs. 1–3, Table 3). This is done through limitation LI which is 0 when I is lower than 0.1% of I0 (Eq. 8 in Table 3). Parameterization of the net primary production rate (Eq. 9, Table 3) takes into account the effect of photoinhibition (Eq. 10, Table 3). Eqs. 9 and 10 in Table 3, without the limitations by temperature (LT)

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13

Table 6 Parameters of the model Description of the parameter

Symbols

Values

Parameters for nutrients and phytoplankton (subscript x stands for P1 or P2)

Units P1

P2

Specific light attenuation coefficient Chl a:C ratio Exudation product C:N ratio Minimum C:N ratio C:N ratio for healthy phytoplankton Maximum C:N ratio Minimum exudation rate Variable part of exudation rate Light for photoinhibition Ammonium half-saturation constant Nitrate half-saturation constant Silicate half-saturation constant Minimum mortality rate Variable part of mortality rate Maximum assimilation number for the PL curve Fraction for respiration Minimum sinking velocity Variable part of sinking velocity SI:N uptake ratio Maximum growth rate Initial slope for the PL curve

ax chlcx cne cnix cnmx cnsx e0x e1x ibx knh4x kno3x ksix m0x m1x pmx

0.1 0.024 nd 4 5.67 17 nd nd 10 000 7 14 nd 0.05 0.05 240

0.009 0.033 15 4 5.67 17 0.1 0.1 10 000 10 21 28 0.05 0.05 202.5

rx s0x s1x sinx umnx αx

0.1 nd nd nd 3.5 3

0.1 ⫺1.6 ⫺1.4 1.896 2.5 2

Nitrate uptake inhibition factor

ψ

0.1042

0.1042

Parameters for heterotrophs (subscript x stands for B, Z1, Z2 or Z3) B Fraction of assimilated carbon Fraction of assimilated nitrogen Growth substrate concentration threshold for grazing or assimilation Growth substrate concentration threshold for maintenance Heterotroph C:N ratio Capture efficiency of P1 by x Capture efficiency of P2 by x Capture efficiency of B by x Capture efficiency of Z1 by x Capture efficiency of Z2 by x Capture efficiency of D1 by x Capture efficiency of D2 by x Capture efficiency of DOM1 by x Maximum assimilation or ingestion rate

Z1

Z2

Z3

m2 (mg Chl a)⫺1 mg Chla (mg C)⫺1 mg C (mg N)⫺1 mg C (mg N)⫺1 mg C (mg N)⫺1 mg C (mg N)⫺1 d⫺1 d⫺1 µmol photons m⫺2 s⫺1 mg N m⫺3 mg N m⫺3 mg Si m⫺3 d⫺1 d⫺1 mg C (mg Chl a)⫺1 d⫺1 wd m d⫺1 m d⫺1 mg Si (mg N)⫺1 d⫺1 mg C (mg Chl a)⫺1 d⫺1 (µmol photons m⫺2 s⫺1)⫺1 m3 (mg N)⫺1

acx anx bio0x

1 1 0

0.7 0.8 10

0.7 0.8 50

0.7 0.8 80

wd wd mg C m⫺3

bio1x

2

20

60

90

mg C m⫺3

cnx exP1 exP2 exB exZ1 exZ2 exD1 exD2 exDOM1 gmx

4.5 0 0 0 0 0 0 0 1 5

4.5 0.8 0 0.6 0 0 0.2 0 0 2.55

5 0.2 0.8 0 1 0 0 0.3 0 1

5 0 0.6 0 1 1 0 0.2 0 0.5

mg C (mg N)⫺1 wd wd wd wd wd wd wd wd d⫺1 (continued on next page)

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Table 6 (continued) Description of the parameter

Symbols

Values

Parameters for heterotrophs (subscript x stands for B, Z1, Z2 or Z3) B Factor for daily variation of ingestion Factor for daily variation of ingestion Light for vertical migration Maximum net growth efficiency Half-saturation constant for assimilation or ingestion Half-saturation constant for the net growth efficiency Half-saturation constant for ammonium limitation Half-saturation constant for vertical migration Half-saturation constant for vertical migration Mortality rate Maximum downward vertical migration velocity Factor for the slope of K2N

Units

Z1

Z2

Z3

h1x h2x ivx k2mx khx

1 nd nd 0.4 10

1 nd nd 0.4 20

0 3 10 0.4 100

0 3 30 0.4 150

wd wd µmol photons m⫺2 s⫺1 wd mg C m⫺3

kk2x

0.1

0.1

0.1

0.1

d⫺1

knh4x

3.5

nd

nd

nd

mg N m⫺3

kv1x kv2x mx vmx

nd nd 0.05 0

nd nd 0.05 0

100 50 0.05 ⫺600

160 50 0.05 ⫺1000

mg C m⫺3 µmol photons m⫺2 s⫺1 d⫺1 m d⫺1

αx

0.2

0.5

1

1

wd

Parameters for dissolved organic matter and detritus (subscript x stands for D1 or D2)

Maximum hydrolysis rate Half-saturation constant for hydrolysis

Decomposition rate Sinking velocity

hm kdom2

d⫺1 mg C m⫺3

5 1500

dmx sx

D1

D2

0.1 nd

0.1 ⫺4

d⫺1 m d⫺1

wd, without dimension; nd, not defined.

and phytoplankton C:N ratio (LCN2x), are from Platt, Gallegos and Harrison (1980). The growth rate for P1 (UNP1, Eq. 12 in Table 3) is the sum of NO3 and NH4 uptake rates (UNO3P1 + UNH4P1), whereas the growth rate for P2 (UNP2, Eq. 12 in Table 3) is equal to USIP2 (Eq. 3, Table 3). Limitation by the phytoplankton C:N ratio, i.e. LCN1x and LCN2x (Eqs. 7 and 11 in Table 3, respectively), allows us to couple the N and C cycles between the nutrient uptake and phytoplankton growth processes. In order to achieve this, three characteristic values of the phytoplankton C:N ratio are used. The first is the C:N ratio for healthy phytoplankton (cnmx), which is considered to be equal to the Redfield ratio (Table 6). The two other values define the range of variation of the phytoplankton C:N ratio (CNx): the parameters cnix and cnsx are the minimum and maximum values of CNx, respectively, for which the condition cnix ⬍ cnmx ⬍ cnsx must be met. It is assumed that phytoplankton CNx tends to remain near cnmx, which is modelled by comparing CNx to values cnix, cnmx, and cnsx, and by modifying the net primary production or the nutrient uptake rates. Three different cases can occur: (1) When cnixⱕCNx ⬍ cnmx, all nutrient uptake rates are lowered (this is done through limitation LCN1x, Eq. 7, Table 3), whereas the net primary production rate remains unaffected by CNx (because LCN2x = 1 in this case; see Eq. 11, Table 3). (2) When CNx = cnmx, the phytoplankton is healthy so that both the net primary production and the nutrient uptake rates remain unaffected by CNx (LCN1x = 1 and LCN2x = 1, Eqs. 7 and 11 in Table

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15

3). (3) When cnmx ⬍ CNxⱕcnsx, the net primary production rate is reduced (this is done with LCN2x, Eq. 11, Table 3) and the nutrient uptake rates remain unaffected (LCN1x = 1 in this case, Eq. 7, Table 3). Another advantage of the stoichiometric approach is that it provides an indicator of the physiological state of phytoplankton. Since parameter cnmx represents the C:N ratio for healthy phytoplankton, a lower or higher value of CNx could be indicative of a deteriorated physiological state. Consequently, ratio CNx is chosen as the representative indicator of that state. In the present model, we assume that phytoplankton exudation (Eqs. 13 and 14, Table 3), mortality (Eqs. 15 and 16, Table 3), and sinking (Eqs. 17 and 18, Table 3) are processes influenced by the physiological state of phytoplankton. Lancelot (1983) observed that the exudation rate increases with N limitation (i.e. increasing phytoplankton C:N ratio). Because of the large contribution of P2 in total phytoplankton biomass during ASE’87 (Pitcher et al., 1991), and also a negligible contribution of small phytoplankton species in the overall exudation process (Lancelot, 1983), we assume that only P2 is affected by this process. The exudation rate EP2 (Eq. 13 in Table 3) is the sum of two rates, the first rate (e0P2, minimum or basic level for exudation rate) is constant, whereas the second one (e1P2 LEP2) is variable because of limitation LEP2 which takes into account the influence of the physiological state (Eq. 14, Table 7). Limitation LEP2 may vary between 0 and 1, so that the exudation rate EP2 may take any value between e0P2 and e0P2 + e1P2. When CNP2 ⱕ cnmP2, the exudation rate EP2 is constant and minimum. When cnmP2 ⬍ CNP2 ⱕ cnsP2, the exudation rate EP2 increases with CNP2. The C:N ratio for exuded products (cne) is kept constant, but this parameter only appears in the model differential equations (Table 7). The same principles are used to compute the mortality rate (Eq. 15, Table 3) and the sinking velocity (Eq. 17, Table 3) of phytoplankton. For low phytoplankton C:N ratios (cnix ⱕ CNx ⱕ cnmx), however, both mortality and sinking increase with decreasing C:Nx. It is assumed that only large phytoplankton P2 may sink in the water column. In the model, the adopted vertical structure imposes negative values for parameters involved in the computation of sinking (s0P2 and s1P2; see Table 6). Although ecological processes governing the dynamics of heterotrophic bacteria and zooplankton appear to be radically different, it is conceptually interesting to build up a common sub-model capable of simulating

Table 7 System of differential equations dNO3 /dt = ⫺UNO3P1 P1N⫺UNO3P2 P2N + KNO3 dNH4 /dt = ⫺UNH4P1 P1N⫺UNH4P2 P2N + NB BC + NZ1 Z1C + NZ2 Z2C + NZ3 Z3C + KNH4 dSI / dt = ⫺USIP2 P2N sinP2 + KSI dP1C / dt = (UCP1⫺MP1) P1C⫺GZ1P1 Z1C⫺GZ2P1 Z2C + KP1C dP1N / dt = (UNP1⫺MP1) P1N⫺(GZ1P1 Z1C + GZ2P1 Z2C) / CNP1 + KP1N dP2C / dt = (UCP2⫺MP2⫺EP2) P2C⫺GZ2P2 Z2C⫺GZ3P2 Z3C + KP2C + SEDP2C dP2N / dt = (UNP2⫺MP2⫺EP2 CNP2 / cne) P2N⫺(GZ2P2 Z2C + GZ3P2 Z3C) / CNP2 + KP2N + SEDP2N dBC / dt = (GBDOM1⫺RB⫺mB) BC⫺GZ1B Z1C + KBC dZ1C / dt = (GZ1P1 + GZ1B + GZ1D1⫺RZ1⫺mZ1⫺FZ1) Z1C⫺GZ2Z1 Z2C⫺GZ3Z1 Z3C + KZ1C dZ2C / dt = (GZ2P1 + GZ2P2 + GZ2Z1 + GZ2D2⫺RZ2⫺mZ2⫺FZ2) Z2C⫺GZ3Z2 Z3C + VMZ2C dZ3C / dt = (GZ3P2 + GZ3Z1 + GZ3Z2 + GZ3D2⫺RZ3⫺mZ3⫺FZ3) Z3C + VMZ3C dD1C / dt = MP1 P1C + mB BC⫺GZ1D1 Z1C⫺DD1 D1C + KD1C dD1N /dt = MP1 P1N + mB BC / cnB⫺GZ1D1 Z1C / CND1⫺DD1 D1N + KD1N dD2C / dt = MP2 P2C + (mZ1 + FZ1) Z1C⫺GZ2D2 Z2C⫺GZ3D2 Z3C⫺DD2 D2C + KD2C + SEDD2C dD2N /dt = MP2 P2N + (mZ1 / cnZ1 + FZ1 CNBIOZ1 (1 - acZ1)/ (1 - anZ1)) Z1C - (GZ2D2 Z2C + GZ3D2 Z3C) / CND2 - DD2 D2N + KD2N + SEDD2N dDOM1C / dt = EP2 P2C + H BC⫺GBDOM1 BC + KDOM1C dDOM1N / dt = EP2 P2N CNP2 / cne + H BC / CNDOM2⫺GBDOM1 BC / CNDOM1 + KDOM1N dDOM2C / dt = DD1 D1C + DD2 D2C⫺H BC + KDOM2C dDOM2N / dt = DD1 D1N + DD2 D2N⫺H BC / CNDOM2 + KDOM2N

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all heterotrophs involved in the model, but with their own specificity. This has two advantages: the model structure is greatly simplified and it allows us to unify some basic ecological concepts that normally would appear different between bacteria and zooplankton. Since the model structure is exactly the same for all heterotrophs, it is the parameter values that will specify the nature of the heterotrophs (bacteria or zooplankton) and their role in the ecosystem. For numerous reasons, not all growth substrates or prey can be ingested/assimilated by heterotrophs. Among the known reasons, the properties of organic food (e.g. molecular weight, size, shape, speed, taste) and those of heterotrophs (e.g. size, capture apparatus or mechanisms of assimilation) cannot be taken into account easily in ecological models. The capture efficiency of a food item y by heterotroph x (i.e. exy) aims at representing all known properties cited above and the unknowns. The capture efficiency varies between 0 and 1, i.e. when exy = 0, no food y is ingested/assimilated by heterotroph x and, when exy = 1, all food items y can be ingested/assimilated by heterotroph x. Eq. 3 in Table 4 is used to compute the C concentration of potential food for heterotroph x (BIOx), given the eight possible types of food present in the model (i.e. yC can be DOM1C, P1C, P2C, BC, Z1C, Z2C, D1C, or D2C). Grazing rate for zooplankton or assimilation rate for bacteria is symbolised by variable Gx, which is parameterised by Eq. 1 (Table 4). Rate Gx is zero when BIOx is lower than the food threshold bio0x (see Table 6 for parameter values), but it is the product of four terms when there is enough food in the medium (BIOx ⬎ bio0x), i.e. of the maximum assimilation or ingestion rate (gmx), and the three limitations LHx, LBx, and LT. It is well established that ingestion of numerous zooplankton species follows a daily cycle. In the Benguela system, this has been noted by Peterson, Painting and Hutchings (1990) for several species of copepods, and Timonin, Arashkevich, Drits and Semenova (1992) for the copepod Calanoides carinatus, which was the most important component of mesozooplankton in terms of biomass during ASE’87 (Verheye, 1991). Limitation LHx (Eq. 4, Table 4) varies between 0 and 1, and it aims at representing the effect of time of day (variable HOUR) on rate Gx. Parameter h1x specifies the magnitude of the daily variation (when h1x = 0, ingestion is maximum at midnight and zero at noon; and when h1x = 1, there is no daily variation of ingestion, thus LHx = 1), whereas parameter h2x controls the shape of the relationship. Limitation LBx (Eq. 5, Table 4) represents the influence of food concentration BIOx on grazing rate Gx. The grazing rate used to compute a flow connecting a specific prey y to its predator x is Gxy (Eq. 2, Table 4). The C:N ratio for growth substrates ingested or assimilated by the organism (i.e. CNBIOx) is provided by Eq. 6 (Table 4); it corresponds to the ratio of BIOx on its equivalent in nitrogen where yN is the prey nitrogen concentration (when yN is not a state variable, it is computed from yC/cny). The parameterization used to simulate the feces production rate follows the usual formulation, which is given in Eq. 7 (Table 4). Processes of respiration and excretion (Eqs. 8 to 17, Table 4) were examined in detail for bacteria and zooplankton by Touratier, Legendre & Ve´ zina (1999a,b), so that the parameterization is only summarized here. In the model, respiration and excretion depend on the quantity and quality of the ingested/assimilated food, and on temperature. The respiration rate for the maintenance (RMx) is first computed (Eq. 8, Table 4). The respiration and excretion rates are growth dependent, and two cases are envisaged: (1) when the growth is zero or negative (Gx acxⱕRMx), the rates for respiration (Rx) and excretion (Nx) are given by Eqs. 9 and 10 (Table 4), respectively; (2) when the growth is positive, the previous rates are computed with Eqs. 11 and 12 (Table 4), respectively. In the latter case, the respiration and the excretion rates are computed using the usual relationships (e.g. Billen, Joiris, Meyer-Reil, & Lindeboom, 1990; Weaver & Hicks, 1995), that depend on the carbon and nitrogen net growth efficiencies K2Cx and K2Nx, respectively. Parameterization of the efficiencies K2Nx and K2Cx (Eqs. 13 and 14, Table 4) largely depend on quality and quantity of food. Explaining the details of the parameterization used here for K2Nx and K2Cx, and the remaining variables K2x, S1x, S2x, and LNH4x (Eqs. 15 to 16, Table 4) goes beyond the objectives of the present study (all details are explained in Touratier et al., 1999a,b). During ASE’87, large zooplankton like the copepod Calanoides carinatus showed diel vertical migration

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(DVM) behavior (Verheye, 1991). As discussed by Moloney and Gibbons (1996), variables affecting DVM are numerous: environmental factors like the light, the concentration of food, and/or the presence of predators (Forward, 1988; Ohman, 1990; Verheye & Field, 1992; Gibbons, 1993), but also the genotype, the reproduction and the growth optimization strategies of zooplankton (Vidal, 1980; Verheye & Field, 1992) certainly explain a large part of DVM. Although the mechanisms that govern DVM are far from clearly understood, we attempt to include DVM in the present model because of their overall influence on the system. The DVM velocity for zooplankton (Vx) in our model is only driven by light (I) and food concentration (BIOx); see Eqs. 18 to 20 (Table 4) and Fig. 3. Limitation by food concentration (LBIOx; Eq. 19, Table 4) is equal to 1 when food concentration is lower than food threshold bio0x, and it tends toward zero for increasing food levels. Thus the absolute value of upward or downward DVM velocity (the maximum DVM velocity vmx is always negative; see Table 6) is an inverse function of food concentration (i.e. the migrating zooplankton will spend more time at depths where concentration of food is high). The light I is assumed to be the main driving force of DVM (Moloney & Gibbons, 1996). In our model, parameter ivx represents the intensity of light that zooplankton x should follow during the day by migrating up and down in the water column. Because food concentration may reduce DVM velocity, the zooplankton may be positioned at a depth where light I ⫽ ivx, so that the difference (I⫺ivx) can be used to build up the limitation by light LLx (Eq. 20, Table 4). The greater the difference (I⫺ivx), the more the absolute value of DVM velocity is increased through limitation LLx. The sign of the DVM velocity is determined from the comparison between I and ivx (Eq. 18, Table 4). As shown in Fig. 3, when the difference (I⫺ ivx) is positive or negative, the zooplankton migrates down or up in the water column, respectively. As mentioned above, the value of certain parameters involved in heterotrophic processes will determine the nature of the heterotroph. Let us briefly review the values of parameters acx, anx, exy, h1x, and vmx (Table 6). To specify that a heterotroph is a bacterium, both C and N assimilated fraction equal unity (acx = 1 and anx = 1), which means that ingestion and assimilation are not distinct processes and that fecal production is zero. Bacteria are able to take up DOM1 (eBDOM1 = 1), but no other substrate (all remaining exy = 0). Parameters h1x = 1 and vmx = 0 for bacteria, so that assimilation does not follow a diel cycle and there is no DVM, respectively. For zooplankton (Z1, Z2 and Z3), all fractions of assimilated C and N (acx and anx) are ⬍1, so that contrary to bacteria, ingestion is well distinct from assimilation and production of fecal materials exists. The zooplankton of the model are not able to utilize the resource DOM1

Fig. 3. The vertical migration velocity for zooplankton (Vx) as parameterized in the model, which depends on the food concentration (BIOx) and the light (I).

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(thus eBDOM1 = 0), but they can ingest numerous other particles (phytoplankton, detritus, etc.). Concerning the diel cycles for ingestion and vertical migration, Z1 behaves as bacteria (no diel cycles), but this does not hold for the large zooplankton (Z2 and Z3) for which parameters h1x = 0 and vmx ⫽ 0 (Table 6). Large zooplankton will thus ingest food relatively more at night when they occupy the surface layers than during the day when they are mainly found below the thermocline, i.e. a combined effect of the two diel cycles (ingestion and migration) that was noted by Peterson et al. (1990) for the southern Benguela system. The decomposition rates Dx for detritus D1 and D2 only depend on the temperature (Eq. 1, Table 5), whereas the hydrolysis rate H of high molecular weight DOM (DOM2) into low molecular weight DOM (DOM1) is a process which is influenced by temperature and DOM2 concentration. Hydrolysis is also under the control of bacterial biomass (see system of differential equations, Table 7). 3.2. Forcing variables and vertical processes The forcing variables of the present model are light (Fig. 2a), temperature (Fig. 2b), vertical turbulent diffusion (Fig. 2d), and two bottom conditions for the nutrients NO3 and SI (Fig. 2e). Vertical diffusion played an important role on the distribution and the dynamics of most chemical and biological components during period R1 (Bailey & Chapman, 1991; Pitcher et al., 1991; Waldron & Probyn, 1991). In the model, all state variables may diffuse vertically, except those for large zooplankton (Z2 and Z3), as stated by the presence/absence of the diffusion term Kx (x stands for a state variable) in the system of differential equations (Table 7). This term is computed as follows:

冉 冊

∂x ∂z 0.03 ; where Kv ⫽ . ∂z dst / dz

∂ Kv Kx ⫽

(4)

The vertical turbulent diffusion coefficient (Kv) is roughly approximated by using the property that vertical diffusion is inversely related to the stability of the water column (i.e. gradient dst/dz computed from Fig. 2c). The constant 0.03 is determined by model calibration and, in order to avoid extremely low or high diffusion, Kv values are constrained to remain in the range 0.0864 and 5000 m2 d⫺1. Estimated values for Kv during ASE’87 are shown in Fig. 2d. The exchange of nutrients (by diffusion, bioturbation, etc.) between sediments and the overlying water column played a role in maintaining high concentrations of NO3 and SI in the bottom mixed layer (BML) during the study (see Chapman & Bailey, 1991). Additional state variables and processes should be added into the present model to realistically simulate the nutrients exchange processes across the seawater–sediment interface. A much simpler solution is to impose the real concentrations of NO3 and SI measured at the bottom of the water column (called NO3b and SIb, respectively; see Fig. 2e) into the bottom layer of the model. Practically, at each new time step during a simulation, variables NO3 and SI in layer 47 of the model are prescribed. The concentration of NH4 in this layer is however computed by the model, and there are two main reasons for that. First, the concentrations of NH4 measured near the bottom were often lower than elsewhere in the water column, which is contrary to the fact that sediments would have supplied large quantities of ammonium. Second, we assume that if large quantities of NH4 have been effectively released from sediments, they have been rapidly transformed into NO3 by nitrification into the first meter above the sediments, as shown by Waldron and Probyn (1991) during period R1. The two last unidentified terms that appear in the system of differential equations (Table 7) are those for sedimentation (SEDx) and zooplankton vertical migration (VMx). Both terms have similar equations: SEDx ⫽ s

∂x ∂x ; VMx ⫽ Vx ∂z ∂z

(5)

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where symbol s stands for the variable sinking velocity of P2 (SP2) or the constant sinking velocity for D2 (i.e. sD2). 3.3. Model implementation The period R1 of ASE’87 begins approximately at day 80. The initial conditions for state variables are of three types: (1) initial values for nutrients are directly taken from field observations; (2) initial values for phytoplankon P1 and P2, bacteria and large zooplankton are derived from field data by using conversion factors; and (3) the other initial conditions cannot be derived from observations because either the variables were not measured (detritus) or, when measured, they were not representative (microzooplankton, DOM). The size-fractionated chl a data (⬍10 µm and ⬎10 µm) available for day 80 are converted into the initial conditions P1C and P2C, by using parameters chlcx of the model (Table 6). Assuming that all phytoplankton are healthy at the beginning of the bloom, the initial concentrations P1N and P2N are deduced from P1C and P2C, respectively, and parameters cnmx (Table 6). For the southern Benguela, Painting (1989) found that large cocci and small rods (averaged cell volumes are ca. 0.142 and 0.198 µm3 cell⫺1, respectively) dominate the bacterial communities during phytoplankton blooms. Consequently, an averaged cell volume of 0.17 µm3 cell⫺1 and a conversion factor of 0.121 pg C (µm3)⫺1 (Watson, Novitsky, Quinby, & Valois, 1977) are used to convert bacterial abundance data into biomass in terms of carbon (BC). We convert the wet weights (WW) for large zooplankton into carbon biomass (Z2C and Z3C) with a C:WW weight ratio of 0.05 (Mullin, 1969). This value seems well adapted for zooplankton in the Benguela system since ratios of 0.04 (Parsons, Takahashi & Hargrave, 1984) and 0.065 (Cushing, 1971) have been utilized by Verheye, Hutchings, Huggett and Painting (1992) and Shannon and Pillar (1986) for the region, respectively. As initial conditions for detritus (D1C and D2C) we assume a value of 10 mg C m⫺3. A C:N ratio of 10 mg C (mg N)⫺1 is chosen to compute D1N and D2N. Few data are available for the microzooplankton biomass in the southern Benguela. Lucas, Probyn and Painting (1987) incubated newly upwelled water from the southern Benguela region in a laboratory microcosm, and the range of biomass obtained for flagellates was ca. 0–100 mg C m⫺3. Painting et al. (1992) compiled the information available on several groups of plankton from which the range of biomass for ciliates + tintinnids is ca. 0– 218 mg C m⫺3. Other groups compose the microzooplankton, like the young stages of most copepod species. Because of the difficulty of assigning realistic initial conditions for Z1C from the previous ranges, we chose Z1C = 60 mg C m⫺3 from model calibration. Some profiles for DON (dissolved organic nitrogen) concentration are available for ASE’87, but they are not used for comparison with model output because of their unrealistic range of concentrations (0–100 g N m⫺3). However, the vertical distribution pattern of DON for day 80 remains coherent, and we used it for the initial condition profiles of DOM1N and DOM2N. We assume that DOM1N is ca. 10% of DOM2N. A C:N ratio of 6 mg C (mg N)⫺1 is then used for conversion into DOM1C and DOM2C. Few model parameter values were measured during ASE’87. The values for the maximum assimilation numbers of the PL (photosynthesis-light) curve, i.e. parameters pmx (see Table 6), were both used by Cochrane et al. (1991) in their model. In fact, the value pmP1 = 240 mg C (mg Chl a)⫺1 d⫺1 is the maximum value of the range provided by Mitchell-Innes and Walker (1991), whereas the value for diatoms, pmP2 = 202.5 mg C (mg Chl a)⫺1 d⫺1, is that given by Brown and Field (1986) for upwelling zones in the southern Benguela. During ASE’87, the sinking velocity for phytoplankton was estimated to ca. 0–0.91 m d⫺1 using the SETCOL method (Pitcher et al., 1989), and to 1.6 m d⫺1 (Pitcher et al., 1991) after analysis of the C. gigas bloom vertical distribution. Cochrane et al. (1991) used a slightly higher value (1.8 m d⫺1). In the present model, sinking velocity of P2 may vary between 1.6 m d⫺1 and 3 m d⫺1 (Table 6), where the maximum of that range corresponds to the one provided by Andersen and Nival (1989) for diatoms. The SI:N uptake ratio for diatoms (parameter sinP2, Table 6) is equal to 1.896 mg Si (mg N)⫺1, i.e. the lowest value of the range (1.896–3.522) measured by Bailey and Chapman (1991). The value chosen for

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sinP2 is thus close to the corresponding Si:N Redfield ratio of 1.875 mg Si (mg N)⫺1. It also corresponds to typical ranges provided by Brown & Hutchings, 1987b) for the southern Benguela region. Other parameter values in the model do not originate from ASE’87, they come either from experimental studies made in the region (e.g. Lucas et al., 1987; Peterson et al., 1990; Verheye et al., 1992), from other regions in the world (e.g. Steeman Nielsen & Hansen, 1959; Andersen & Fenchel, 1985; Hansen, Bjørnsen, & Hansen, 1997), from ecosystem models (e.g. Fasham, Ducklow & McKelvie, 1990; Cochrane et al., 1991; Touratier et al., 2000), from stoichiometric models (e.g. Touratier et al., 1999a,b), or they have been determined after model calibration (several capture efficiencies exy, or the decomposition rates dmx).

4. Results and discussion 4.1. Comparison of model outputs to ASE’87 observations 4.1.1. Distribution of nutrients The main characteristics for NO3 and SI (Fig. 4a,e) are fairly well simulated by the model (compare with Fig. 4b,f, respectively). In the surface layer, these nutrients are rapidly assimilated by phytoplankton, whereas in the lower part of the water column their concentrations remain high and relatively constant during period R1 (23–27 mmol N m⫺3 and 35–50 mmol Si m⫺3, respectively; Bailey & Chapman, 1991). The NO3 and SI bottom conditions used to force the model (Fig. 2e), in close association with the vertical turbulent mixing (Fig. 2d), allow the model to reproduce the three main events of NO3 supply (i.e. periods 80 to 83, 87 to 90, and 92 to 94) and the two main events of SI supply (i.e. periods 83 to 85 and 93 to 100) from the sediment. Since the model is able to correctly reproduce these events, it is reasonable to assume that horizontal influences (advection, diffusion) in the BML during period R1 were negligible. Obviously, the sediments played an important role in maintaining high and relatively constant levels of NO3 and SI in BML throughout the period R1. This is in agreement with the overall consensus that regeneration of nutrients within the sediments of St Helena Bay is an important process (e.g. Bailey, 1987; Bailey & Chapman, 1991; Bailey & Rogers, 1997). Comparable levels of NO3 and SI in the BML of the bay were measured in October 1985 (Pitcher, 1988) and December 1987 (Walker & Pitcher, 1991). Outside the bay (south of Cape Columbine), Brown & Hutchings, 1987b measured comparable levels for NO3 in the BML (range, 10.4–26.8 mmol N m⫺3), but much lower concentrations for SI (range, 5.8–25.1 mmol Si m⫺3). This suggests that regeneration of SI may be a process particularly intensive within the bay, perhaps in response to the frequent blooms of diatoms that occur in the area. As noted by Bailey and Chapman (1991), the distribution of NH4 is patchy in time and depth (Fig. 4c). However, two main characteristics emerge from this picture, i.e. the maximum of NH4 concentration is about 8 mmol N m⫺3 and the vertical position of the maxima in the water column are often below the mixing depth, but above the 1% light depth (both depths are shown in Fig. 5a). NH4 subsurface maxima were often recorded in St Helena Bay (Chapman & Shannon, 1985; Bailey & Chapman, 1991) and off Cape Columbine (Shillington, Hutchings, Probyn, Waldron, & Peterson, 1992); it is thus interesting to envisage the possible sources of NH4 production. Waldron and Probyn (1991) consider that large grazers (e.g. copepods) and decomposer communities (e.g. bacteria) are the main producers, whereas Bailey and Chapman (1991) assume that fishes, because of the high biomass found in St Helena Bay during ASE’87, are a more likely source. According to Probyn (1987), the accumulation of NH4 near the thermocline could result from a lower phytoplankton demand for NH4 through light limitation and/or the assimilation of other nitrogenous nutrients (e.g. NO3). The evidence accumulated over the past 15 years, however, strongly supports the idea that small zooplankon (nano- and microzooplankton) are often the main producers of NH4 (e.g. Goldman, Caron, Andersen, & Dennett, 1985; Newell & Turley, 1987; Probyn, 1987; Painting

Fig. 4.

Comparison between observations made during ASE’87 and results of the model.

F. Touratier et al. / Progress in Oceanography 58 (2003) 1–41 21

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Fig. 5. Comparison between the ASE’87 observed and the simulated depths for (a) the 1% light level; (b) the nitracline; (c) the silicacline; (d) the maximum of ammonium concentration; (e) the maximum of Chl a concentration; (f) the maximum of bacterial biomass.

et al., 1992). Despite their small size, bacteria are not the main producers because they also assimilate NH4, and thus they may outcompete phytoplankton for this resource, when their growth becomes N limited (e.g. Lancelot & Billen, 1985). Large zooplankton (copepods, euphausiids, etc.) and fishes, because of their size and relatively low biomass in ecosystems, are thought to have a negligible impact on the overall NH4 production. Some aspects of the behavior of these organisms (migration, aggregation, etc.) may, however, counteract this view since NH4 excretion by a population may be massive, but localized in space and time. The NH4 maximum reached with the model is only 4 mmol N m⫺3 (Fig. 4d), which is half the observed maximum. It must be noted however that observed NH4 concentrations ⬎5 mmol N m⫺3 are exceptional events (Fig. 4c). Two main characteristics of NH4 distribution are approached with the model: the level of NH4 concentration in the water column increases during period R1, and the simulated NH4 maxima occur around the mixing depth (i.e. just above the observed maxima) and in the BML at the end of period R1.

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4.1.2. Distribution of phytoplankton and primary production As proposed by Pitcher, Brown and Mitchell-Innes (1992), the dynamics of phytoplankton in the Benguela system seem to be characterized by sequential changes (the variability in the composition of species results from a change in water mass; e.g. the active phase of an upwelling) and succession (the variability in the composition of species results from the variability in the physical, chemical, and biological properties within a specific water mass). The period R1 of ASE’87 illustrates a case of succession of two main phytoplankton groups (diatoms and microflagellates). It is interesting to note that diatoms first dominate the total biomass when turbulence and nutrient concentrations are high, and temperature is ⬍15 °C. The microflagellates (cell size ⬍10 µm) appear in the surface layer at the end of period R1 when vertical stability of water and temperature (⬎15 °C) are elevated, and concentrations of nutrients are low (Pitcher et al., 1991; Mitchell-Innes & Pitcher, 1992). These trends in the succession were often observed within (Walker & Pitcher, 1991; Pitcher, Richardson, & Korruˆ bel, 1996) and outside the bay (Armstrong, MitchellInnes, Verheye-Dua, Waldron & Hutchings, 1987; Brown & Hutchings, 1987b). During ASE’87, the large diatom C. gigas dominated the total phytoplankton biomass (ca. 83% in terms of carbon; Mitchell-Innes & Walker, 1991). In the present paper, the observed and the simulated results for phytoplankton biomass are presented in terms of total Chl a (Fig. 4g,h). In the model, 95.4% of the total biomass is dominated by P2, which is not significantly higher than the 83% found by Mitchell-Innes and Walker (1991), given the fact that our value is computed from period R1 only. Both the observed and the simulated total Chl a concentrations reach a maximum of ca. 68 mg Chl a m⫺3 (Fig. 4g,h). This value is higher than the maxima observed previously in the same area, in the Benguela system, or even in other upwelling systems (15– 30 mg Chl a m⫺3; see Mitchell-Innes & Walker, 1991), but lower than the red tide bloom maximum (139 mg Chl a m⫺3) measured by Walker and Pitcher (1991) within St Helena Bay, during December 1987. The thickness of the chlorophyll maximum layer (defined for concentrations ⬎10 mg Chl a m⫺3; see the thick isolines in Fig. 4g,h) was 12 m deep between days 85 and 93 (Fig. 4g; Mitchell-Innes & Walker, 1991). The simulated thickness (Fig. 4h) reproduces this trend. The bloom of diatoms sinks slowly in the water column (Mitchell-Innes & Walker, 1991; Pitcher et al., 1991). From day 84 to 90, the maximum of Chl a remains in the layer 11–13 m (Fig. 4g), and then sinks to about 20 m for the next 3 days. From day 95, the bloom goes below the 1% light level (compare with Fig. 5a) and then sinks rapidly to the sediments. Most of these events are well simulated with the model (Fig. 4h). Mitchell-Innes and Walker (1991), and Pitcher et al. (1991) noted that sinking velocity of the bloom did not remain constant during period R1. When located near the nitracline and the silicacline (Fig. 5b,c), the phytoplankton sank less rapidly than elsewhere in the water column. The deceleration of sinking velocity, which is closely related to the physiological state and age of phytoplankton, seems to play an important role in the formation of subsurface Chl a maxima (e.g. Bienfang, Szyper, & Laws, 1983). The model parameterization of the phytoplankton sinking process, which takes into account the influence by the physiological state, seems to be particularly well adapted for the present study. The observed and simulated cycles of the bloom development and decline are completed in ca. 16 days (from day 81 to 97; Fig. 4g,h). The period of development alone lasts for ca. 11.5 days (from day 81 to 92.5), which is approximately twice as long as the development duration (ca. 6 days) of another bloom measured by Pitcher, Richardson and Korruˆ bel (1996) in St Helena Bay, during February/March 1991. The magnitude of the latter bloom was much lower however (0–20 mg Chl a m⫺3). The total duration of a bloom (development and decline) in St Helena Bay is significantly longer than outside the bay (Pitcher et al., 1992): between Cape Peninsula and Cape Columbine, Brown & Hutchings (1987a) noted that the blooms were completed in 6–8 days, and Lucas et al. (1987), using recently upwelled water in a microcosm, mentioned a duration of ca. 10 days. Several hypotheses have been proposed to explain the patchy distribution of the bloom (Fig. 4g), a characteristic that could not be reproduced with the model (Fig. 4h). Considering that horizontal influences

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were negligible during period R1, such high frequency variability may be due to vertical physical processes, sampling artefacts or/and biological activity. Bailey and Chapman (1991) reported the occurrence of both tidal and inertial variations whose effects are clearly visible on the vertical distribution of several variables (e.g. temperature, Fig. 2b; st, Fig. 2c; NO3, Fig. 4a; SI, Fig. 4e). These oscillations generated by the physics of the system (the amplitude is ca. 10 m; Bailey & Chapman, 1991) may have played a role, not only in the patchy distribution of phytoplankton biomass (Waldron & Probyn, 1991), but also in the supply of nutrients from the BML to the upper mixed layer or UML (Cullen, Stewart, Renger, Eppley, & Winnant, 1983). Despite a high frequency of sampling for chl a (every 6 h, and approximately every 7 m in depth), Mitchell-Innes and Walker (1991) argue rightly that high concentrations may have been missed due to the confinement of the bloom within a narrow layer. They show also that patchy distribution of phytoplankton follows a diel cycle where the difference in concentration between day and night is within the range 1– 144%. Mitchell-Innes and Walker (1991) propose that the patchy distribution of phytoplankton could partly result from the biology, i.e. a coupling between the daily growth cycle of phytoplankton and a daily predation cycle exerted by zooplankton and fishes. The results of our model (Fig. 4h) suggest that the daily variation of phytoplankton biomass cannot entirely result from biological activity alone. Profiles for primary production were determined once a day with the 14C method by Mitchell-Innes and Walker (1991); see Fig. 4i. The gross primary production simulated with the model is shown in Fig. 4j. Two main differences appear between observed and simulated primary production. First, the model simulates the daily variation of primary production (the production is zero at night), whereas the observed data are not representative of the diel cycle. Second, the simulated range (0–5475 mg C m⫺3 day⫺1; Fig. 4j) is more than twice the observed range (0–2054 mg C m⫺3 day⫺1; Fig. 4i). Two reasons could explain the difference: (1) the measurements of primary production were done every morning, so that the daily maximum of production was not recorded; (2) given the duration of the incubation period (4 h) used by Mitchell-Innes and Walker (1991) to measure the primary production with the 14C method, the observed data should be more representative of the net than the gross primary production (Brown, Painting, & Cochrane, 1991). The vertical and temporal trends for the observed and the simulated primary production are similar however (compare Fig. 4i and j): the production remains closely associated with the biomass peaks, and the production of large diatoms dominates (87% of the total primary production according to Mitchell-Innes and Walker, 1991; whereas 89.4% is computed with our model). By applying a simple model to the observed data, Mitchell-Innes and Walker (1991) provide daily averaged and depth integrated primary production that compare well with the model outputs (Fig. 4k). The observed values are in the range 0.99–7.85 g C m⫺2 day⫺1, whereas the simulated gross and net primary productions are in the ranges 0.85–10.87 and 0.65–6.67 g C m⫺2 day⫺1, respectively. 4.1.3. Distribution of heterotrophs The range for bacterial biomass found in the Benguela system (0–233 mg C m⫺3; Brown, Painting & Cochrane, 1991; Painting et al., 1992) does not differ significantly from that of other oceanic regions in the world (0–200 mg C m⫺3; Azam et al., 1983). During ASE’87, the bacteria reached a maximum biomass of 180 mg C m⫺3 in the BML (Fig. 4l), but most peaks of biomass were associated to those of sinking phytoplankton (compare with Fig. 4g). By following the evolution of recently upwelled water in a microcosm, Lucas et al. (1987) showed that bacteria developed just after the phytoplankton bloom to reach a concentration of ca. 125 mg C m⫺3. In the culture, a second peak with higher bacterial biomass (ca. 240 mg C m⫺3) occurred 15–20 days later. According to Painting (1989), the latter peak resulted from a weak response of flagellates to the increase of bacterial biomass, perhaps because of the larger size of bacterial cells or a higher proportion of bacteria attached to the detritus. The dynamics of bacteria during period R1 (Fig. 4l) shows a similar pattern: the bacteria develop rapidly in the water column in response to the phytoplankton bloom, and later reach greater biomass in the BML. Most events are well reproduced with the model (Fig. 4m), but the maximum of bacterial biomass observed in the BML is not simulated. A

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likely reason is that the structure of the present model does not allow the accumulation of detritus at the water/sediment interface. The zooplankton size fraction 500–1600 µm (mesozooplankton; Z2) was largely dominated by large calanoid copepods (mainly from copepodites CIII to adults of Calanoides carinatus) during the ASE’87, both in terms of abundance and biomass (Verheye, 1991). The predominance of C. carinatus is well known in the Benguela system (e.g. Verheye & Hutchings, 1988; Hutchings, Pillar, & Verheye, 1991; Timonin et al., 1992; Verheye et al., 1992). The contributions of C. carinatus and mesozooplankton to the total zooplankton biomass increase from offshore to inshore and they are generally largest during the upwelling season. Although the observed distribution of mesozooplankton is patchy during the ASE’87 (Fig. 4n), the water column integrated biomass (Fig. 4r) remained constant, but uncorrelated to phytoplankton biomass throughout the time series (Verheye, 1991). In fact, the seasonal variability of mesozooplankton biomass in St Helena Bay seems to be controlled by the presence of predators (e.g. the mesozooplankton biomass was low during the peak recruitment of the anchovy Engraulis japonicus in 1978; see Verheye et al., 1992) rather than by the biomass of food (mainly phytoplankton). This does not hold outside the bay, where a strong coupling between phytoplankton and mesozooplankton biomass has been reported by Verheye et al. (1992), probably because the phytoplankton biomass becomes limiting in these areas. Since mesozooplankton were sampled once a day during ASE’87 (around midday; Fig. 4n), it is not possible to show the DVM performed by these organisms. Using DVM models, Moloney and Gibbons (1996) analyzed the influence of sampling frequency on the representativeness of measured gut contents for migrant zooplankton. Only sampling frequencies ⬎12 profiles per day are predicted to provide consistent results. Despite the sampling strategy adopted during the ASE’87, Verheye (1991) showed that stages from copepodite CIII to adults of C. carinatus remained at intermediate depths (between 15 and 40 m) during the day, a characteristic that is well reproduced with the model. The comparison between simulated and observed mesozooplankton biomass (Fig. 4n and o) is difficult, mainly because the model provides profiles with a higher frequency (four profiles per day) that is chosen in order to visualize the mesozooplankton DVM. For example, the model provides a range of 0–1400 mg C m⫺3 for mesozooplankton biomass, whereas the range for observed data is only 0–346 mg C m⫺3. From this, however, it is not possible to conclude that model outputs are overestimated because inadequate sampling strategies may strongly underestimate the range of zooplankton biomass, both in time and space, by missing the dense populations that rapidly migrate up and down in the water column. The bongo net samples, that directly provide integrated biomass, show however that the simulated range for water column averaged mesozooplankton biomass (i.e. 21.5– 57 mg C m⫺3) falls within the observed range (7–108 mg C m⫺3) (Fig. 4r). Fig. 4o shows that the simulated mesozooplankton spend more time at depths where concentrations of food are high, i.e. during the C. gigas bloom (compare Fig. 4h and o), whereas the amplitude of DVM seems greater when food becomes limiting (beginning and end of period R1). These trends are however in contradiction with the observations made by Verheye and Field (1992) that the amplitude of migration increases with the level of available food. In the model, the large diatom C. gigas (i.e. P2) is an important prey of mesozooplankton (Z2) because of the capture efficiency eZ2P2 = 0.8 (Table 6). Mitchell-Innes and Walker (1991) expected the grazing of the diatoms C. gigas by the copepod C. carinatus to be low because of the large size of the prey. Armstrong et al. (1991) found, however, a positive correlation between egg production of C. carinatus and C. gigas biomass during the ASE’87, showing that large diatoms have to be broken before being ingested by the copepods, and that the quantity and quality of this food were both suitable for their reproduction. The chaetognaths dominated the size fraction ⬎1600 µm (macrozooplankton; Z3) during the ASE’87 (Verheye, 1991), but some large-sized CVs and adults of C. carinatus were also present in the samples. Verheye and Hutchings (1988) noted that macrozooplankton represented ca. 55% of the total zooplankton (⬎200 µm) biomass during May 1983, in the southern Benguela, showing that large-sized and often carnivorous zooplankton are major components of the system. The presence of chaetognaths (especially Sagitta

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friderici in the southern Benguela; Gibbons, Stuart, & Verheye, 1992) has often been noted in different areas of the Benguela system (Verheye & Hutchings, 1988; Timonin et al., 1992; Gibbons, Stuart & Verheye, 1992), but euphausiids (mainly the species Euphausia lucens in the southern Benguela; see Barange, Pillar, & Hutchings, 1992) are regularly recognized as the most abundant organisms of macrozooplankton (Hutchings, Pillar & Verheye, 1991). Euphausiids were not frequently found in the ASE’87 macrozooplankton samples (Verheye, 1991), but these organisms are particularly able to avoid sampling nets (Timonin et al., 1992). Since chaetognaths are strict carnivores that prey upon copepods (Gibbons, Stuart & Verheye, 1992; Verheye et al., 1992), Z1 and Z2 are the main preys of Z3 in the model (the capture efficiencies eZ3Z1 and eZ3Z2 = 1; see Table 6). Because of the presence of copepods in the macrozooplankton samples, Z3 in the model is also able to ingest P2 (eZ3P2 = 0.6; see Table 6). Several of the previous comments we made on the observed and simulated biomass of Z2 are also valid for Z3: Fig. 4p and q allow qualitative comparison of the distribution of the observed and simulated Z3 biomass. The average macrozooplankton biomass estimated from the Bongo net samples is in the range 2–570 mg C m⫺3, whereas the simulated range is only 14–40 mg C m⫺3 (Fig. 4s). The maximum reached during day 89 is certainly not due to a local outburst of macrozooplankton populations, but horizontal migration of foreign populations to the Anchor station site probably occurred. Before this event, the simulated results often correspond to the observations. As noted for Z2, the Z3 biomass appears to be uncorrelated to phytoplankton biomass and the upwelling cycle (Verheye, 1991).

4.1.4. Other variables The depth of the 1% light level remained initially between 12 and 18 m (days 80–83; Fig. 5a), and then deepened to 24–34 m during the C. gigas bloom (days 84–95). During the bloom of small phytoplankton in the upper mixed layer (days 95–100), the depth of the euphotic zone is between 28 and 32 m (MitchellInnes & Walker, 1991). Brown & Hutchings, 1987a), and Painting et al. (1993) reported similar depths for the euphotic zone during blooms in the southern Benguela, whereas Pitcher (1988) also noted that the depth of the 1% light level decreased with increasing biomass of phytoplankton. The model is not able to reproduce the observed trends before the C. gigas bloom (days 80–85; Fig. 5a), perhaps indicating that components other than phytoplankton (e.g. detritus) may have influenced the light attenuation profile in the water column. Thereafter, observed and simulated depths for the euphotic zone are in close agreement. As observed by Brown & Hutchings, 1987a) in drogue studies between Cape Peninsula and Cape Columbine, the 1% light level is usually found below the mixing depth (Fig. 5a). The simulated depths for the nitracline and the silicacline (Fig. 5b,c, respectively) are not very different, which is in contradiction with the observation that the nitracline was often located above the silicacline (Mitchell-Innes & Walker, 1991). The difference that appears between observations and simulations may be due to our assumption that the phytoplankton SI:N uptake ratio is a constant (parameter sinP2; see Table 6). The simulated and observed depths corresponding to the NH4 maximum concentration are similar during the first part of the bloom (days 82–93; Fig. 5d), but they diverge during the remaining period (days 93– 100): the model suggests that NH4 maxima are located close to the mixing depth (compare Fig. 5a,d), whereas the observations show that these maxima remain between the mixing and the 1% light level depths. The depth of the maximum Chl a concentration (Fig. 5e) is well simulated, except at the end of period R1 when small phytoplankton becomes the main primary producer. The factors that explain the decline of the C. gigas bloom (i.e. the position of the chlorophyll maximum layer relative to the light level and the positions of the nitracline and silicacline) are detailed by Mitchell-Innes and Walker (1991), and Pitcher et al. (1991). An interesting feature concerning the end of the diatom bloom during the period between days 95–100 is suggested by the model: simulations show that the occurrence of the small-sized phytoplankton bloom in the surface layer during that period, despite their low biomass, may have accelerated the collapse process because of their high specific attenuation coefficient (aP1 = 0.1 m2 (mg Chl a)⫺1; see Table

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1). In other words, the small-sized phytoplankton would have prevented the deepening of the 1% light level, and thus precipitate the end of the diatom bloom that sank below the 1% light level after day 95. The depths corresponding to the observed and simulated bacterial biomass maxima are presented in Fig. 5e. The overall trends are in agreement, and these maxima occupy a position in the water column that is similar to that of Chl a (compare Fig. 5d and e), indicating that there is no delay between the phytoplankton and the bacterial peaks. 4.2. Additional model outputs The model outputs for the microzooplankton biomass (Z1C), the detritus (the sum D1C + D2C), the labile DOC (the sum DOM1C + DOM2C), the phytoplankton C:N ratio, and the f-ratio, are presented in Fig. 6. These important variables of the model have in common that corresponding observations were either missing or not fully representative. The abundance of ciliates, one of the constituents of microzooplankton, was estimated during ASE’87 (Mitchell-Innes, unpublished data), and according to Armstrong et al. (1991), the ciliates reached their highest biomass (12% of POC) during the bloom of small phytoplankton in the surface layers, as simulated by the model (Fig. 6a). The main preys of microzooplankton in the model are the bacteria and the small

Fig. 6. Additional model results. (a) microzooplankton biomass (Z1C); (b) detritus (D1C + D2C); (c) labile DOC (DOM1C + DOM2C); (d) phytoplankton C:N ratio; and (e) the f-ratio (the hatched area in this panel indicates that the f-ratio cannot be estimated).

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phytoplankton. From the scarce information available on the biomass ranges observed for ciliates (0.1–218 mg C m⫺3; Pitcher et al., 1996) and flagellates (0–100 mg C m⫺3; Lucas et al., 1987), the simulated range for microzooplankton (0–132 mg C m⫺3) is plausible for the southern Benguela. The detritus and the labile DOC distributions (Fig. 6b and c, respectively) closely follow the evolution of the main phytoplankton bloom. Most detritus originated from dead cells of diatoms, whereas labile DOC is essentially produced by large phytoplankton when growth conditions are unsatisfied, i.e. when the phytoplankton C:N ratio is high (Fig. 6d). Extremely low phytoplankton C:N ratios (⬍4 mg C (mg N)⫺1) appear in the BML. These unrealistic values, often associated with low phytoplankton biomass, may occur when the uptake of NO3 and NH4 is zero (i.e. when light is ⬍0.1% I0), whereas cells still respire. The variability of the phytoplankton C:N ratio is however widely recognized; Banse (1974) found an increase of the phytoplankton C:N ratio by a factor of 3 between the beginning and the end of a spring bloom. More recently, according to Lancelot, Billen and Barth (1991) and Baumann, Lancelot, Brandini, Sakshaug and John (1994), it was found that the C:N ratio of Phaeocystis sp. was more than five times the Redfield ratio at low concentrations of ambient N sources. Many other contributions like those of, for example, Tezuka (1989) and Sterner and Hessen (1994) show and discuss the variability of elemental composition in autotrophs. Fig. 6d shows that at depths corresponding to the main phytoplankton bloom, the C:N ratio is close to the Redfield ratio (i.e. cnmx; Table 6), whereas the ratio can be as high as 17 mg C (mg N)⫺1 when N limits the growth in the surface layer. For the upwelling areas, Barlow (1982) noted that the carbohydrates over proteins ratio (often comparable to the C:N ratio) increased as blooms aged, and that it could be used as an indicator of the physiological state of phytoplankton. An indirect method to assess the importance of the microbial food web relative to that of a classic linear food chain (diatoms→copepods→fishes) is to estimate the f-ratio that measures the proportion of new nutrients (NO3) assimilated by phytoplankton, relative to that of all potential sources of nitrogen (NO3, NH4, urea, etc.). It is expected that oceanic regions with a low f-ratio would be characterized by a welldeveloped microbial food web, as it is often noted for the southern Benguela system (e.g. Painting et al., 1993). During the first part of the bloom (days 81 to 86), Waldron and Probyn (1991) measured water column f-ratios in the range 0.29–0.35, and they noted that the ratio decreased with time. The simulated f-ratio is computed as follows: f-ratio ⫽

UNO3P1

UNO3P1 ⫹ UNO3P2 ⫹ UNO3P2 ⫹ UNH4P1 ⫹ UNH4P2

(6)

This ratio is highly variable both in time and space (Fig. 6e). It cannot be computed however when nutrient uptake is zero, i.e. when light intensity is low or zero in the water column. When the f-ratio exists, it is high where diatoms growth conditions are optimal (Fig. 6e). The simulated f-ratio decreases rapidly toward zero with time, especially in the surface layer. 4.3. Carbon and nitrogen flows for the pelagic food web in the southern Benguela In the previous sections, the ASE’87 experimental data sets were used to assess the realism of several simulated variables, and there is overall agreement between observations and simulated results. Many other interesting observations are available, not only from St Helena Bay during autumn, but also from several other areas in the Benguela system for different periods of the year, that provide ranges for measured variables and processes. In the following discussion, we review and compare the observed ranges to the model outputs. To allow the comparison, but also to emphasise the main features of the simulated ecosystem, flows and variables of the model are depth integrated, time averaged (over the period R1), and often aggregated as indicated in Fig. 7. The description and the units of the symbols in Fig. 7 are given in Table 8. The

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Fig. 7. Conceptual diagrams showing all flows and stocks involved in the computation of the balance for (a) the carbon cycle; (b) the nitrogen cycle; (c) the silicon cycle; and (d) the C:N ratios. All symbols are explained in Table 8. All stocks and flows are depth integrated (the entire water column) and time averaged (period R1).

flows and variables for the C cycle (Fig. 7a), the N cycle (Fig. 7b), the Si cycle (Fig. 7c), and the C:N ratios (Fig. 7d) provide a synthetic view on the functioning of the simulated ecosystem. Results of the model are shown in Fig. 8. 4.3.1. Phytoplankton biomass and processes (PC, F1, F16) The integrated biomass for total phytoplankton is estimated to 9.25 gC m⫺2 with the model (PC; Fig. 8). From CZCS data, a mean phytoplankton biomass of 11 gC m⫺2 for ‘productive areas’ of the southern Benguela was estimated by Shannon and Field (1985), a value that compares well to the 11.2 gC m⫺2 given by Andrews and Hutchings (1980) for an upwelling area, off the Cape Peninsula. For the southern Benguela west coast, however, Brown, Painting and Cochrane (1991) found a value which is approximately

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Table 8 Symbol, description and units of the time averaged (simulated period) and depth integrated (water column) variables Symbol

Description

B BC BN D DC DN DOM DOMC DOMN F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15 F16 F17 F18 F19 F20 F21 F22 F23 F24 F25 F26 F27 F28 F29 F30 F31 F32 NH4 NO3 P PC PN R1 R2 R3 R4

C:N ratio for bacteria Bacterial biomass in carbon Bacterial biomass in nitrogen C:N ratio for total detritus Total detritus concentration in carbon Total detritus concentration in nitrogen C:N ratio for total dissolved organic matter Total dissolved organic carbon Total dissolved organic nitrogen Net primary production Grazing in carbon Phytoplankton mortality in carbon Phytoplankton sedimentation in carbon Phytoplankton exudation in carbon Bacterial respiration Ingestion of bacteria by zooplankton in carbon Bacterial mortality in carbon Zooplankton respiration Net loss of detritic carbon by zooplankton in the water column Detritus decomposition in carbon Detritus sedimentation in carbon Dissolved organic carbon uptake by bacteria Net loss of detritic carbon by zooplankton in the sediment Supply of nitrate from the sediment Nitrate uptake by phytoplankton Ammonium uptake by phytoplankton Bacterial excretion Grazing in nitrogen Phytoplankton mortality in nitrogen Phytoplankton sedimentation in nitrogen Phytoplankton exudation in nitrogen Ingestion of bacteria by zooplankton in nitrogen Bacterial mortality in nitrogen Zooplankton excretion Net loss of detritic nitrogen by zooplankton in the water column Detritus decomposition in nitrogen Detritus sedimentation in nitrogen Dissolved organic nitrogen uptake by bacteria Net loss of detritic nitrogen by zooplankton in the sediment Supply of silicate from the sediment Silicate uptake by phytoplankton Ammonium concentration Nitrate concentration C:N ratio for total phytoplankton Total phytoplankton biomass in carbon Total phytoplankton biomass in nitrogen C:N uptake ratio for phytoplankton (F1:[F16+F17]) C:N ratio for grazing (F2:F19) C:N ratio for phytoplankton mortality (F3:F20) C:N ratio for phytoplankton sedimentation (F4:F21)

Units g C (g N)⫺1 g C m⫺2 g N m⫺2 g C (g N)⫺1 g C m⫺2 g N m⫺2 g C (g N)⫺1 g C m⫺2 g N m⫺2 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g C m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g N m⫺2 d⫺1 g Si m⫺2 d⫺1 g Si m⫺2 d⫺1 g N m⫺2 g N m⫺2 g C (g N)⫺1 g C m⫺2 g N m⫺2 g C (g N)⫺1 g C (g N)⫺1 g C (g N)⫺1 g C (g N)⫺1 (continued on next page)

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Table 8 (continued) Symbol

Description

Units

R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 SI Z ZC ZN

C:N ratio for phytoplankton exudation (F5:F22) Respiration:excretion ratio for bacteria (F6:F18) C:N ratio for ingestion of bacteria by zooplankton (F7:F23) C:N ratio for bacterial mortality (F8:F24) Respiration:excretion ratio for zooplankton (F9:F25) C:N ratio for detritus net loss by zooplankton in the water column (F10:F26) C:N ratio for detritus decomposition (F11:F27) C:N ratio for detritus sedimentation (F12:F28) C:N uptake ratio of dissolved organic matter by bacteria (F13:F29) C:N ratio for detritus net loss by zooplankton in the sediment (F14:F30) Silicate concentration C:N ratio for total zooplankton Total zooplankton biomass in carbon Total zooplankton biomass in nitrogen

g g g g g g g g g g g g g g

C (g N)⫺1 C (g N)⫺1 C (g N)⫺1 C (g N)⫺1 C (g N)⫺1 C (g N)⫺1 C (g N)⫺1 C (g N)⫺1 C (g N)⫺1 C (g N)⫺1 Si m⫺2 C (g N)⫺1 C m⫺2 N m⫺2

half as large (6.4 gC m⫺2). The difference between the estimates partly depends on the conversion factors that are used to deduce the phytoplankton C biomass from satellite imagery or Chl a measurements. The simulated net primary production is 2.75 gC m⫺2 d⫺1 (flow F1, Figs. 7 and 8). The value of 3.27 gC m⫺2 d⫺1 reported by Mitchell-Innes and Walker (1991) for primary production during ASE’87 is higher than F1 but lower than the simulated gross primary production (5.02 gC m⫺2 d⫺1). This means that, in the simulation, ca. 45% of the carbon assimilated by phytoplankton was lost through respiration. Numerous studies provide primary production estimates for the Benguela system. From a transect inshore/offshore near Cape Columbine, Armstrong et al. (1987) found a range from 1.94 to 4.48 gC m⫺2 d⫺1; the range 2.9–3.4 gC m⫺2 d⫺1 was established by Walker and Pitcher (1991) for a bloom in St Helena Bay during December 1987; recently, in an area located north of St Helena Bay (Elands Bay), Pitcher et al. (1996) found a production of 3.92 gC m⫺2 d⫺1 during summer 1991. Surprisingly, annual estimates for primary production are not significantly lower: 3 gC m⫺2 d⫺1 for the inshore region of the southern Benguela (Brown & Hutchings, 1985) or 2.8 gC m⫺2 d⫺1 for productive areas of the southern Benguela (Shannon & Field, 1985), showing that upwelling areas remain productive throughout the year. A productivity of 0.3 d⫺1 can be deduced from Fig. 8 (from the ratio F1:PC), which corresponds to the productivity of 0.31 d⫺1 estimated by Brown et al. (1991) for the southern Benguela. The simulated uptake of nitrate by phytoplankton is 0.25 gN m⫺2 d⫺1 (flow F16, Figs. 7 and 8), i.e. an overestimated value when compared to the range 0.12–0.2 gN m⫺2 d⫺1 measured by Waldron and Probyn (1991) during days 81 to 86 of ASE’87. As shown by Probyn (1992), however, there is much variability in the magnitude of this process in the Benguela system. Despite the above difference, the observed and the simulated biomass and processes for phytoplankton are often in good agreement. 4.3.2. Zooplankton biomass and processes (ZC, F2, F9, F25) The integrated biomass for total zooplankton computed in the model is 4.45 gC m⫺2 (ZC, Figs. 7 and 8). Zooplankton Z1, Z2, and Z3 represent 31.6% (1.4 gC m⫺2), 42.84% (1.9 gC m⫺2), and 25.54% (1.13 gC m⫺2) of the total zooplankton, respectively. During March/February 1991, north of St Helena Bay, Pitcher et al. (1996) measured an averaged biomass of 26.2 mgC m⫺3 for ciliates, a figure that compares well to the 29.9 mgC m⫺3 obtained for Z1 in the present model. The integrated Z2 and Z3 biomasses measured during ASE’87 were 2.52 and 0.9 gC m⫺2, respectively (Verheye, 1991; Verheye et al., 1992). Higher biomass of zooplankton is generally found in the northern (0.63–2.04 gC m⫺2) than in the southern

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Fig. 8. Results obtained with the model for the balance of flows and stocks, for (a) the carbon cycle; (b) the nitrogen cycle; (c) the silicon cycle; and (d) the C:N ratios. The description of flows and stocks, and their units are shown in Fig. 7 and Table 8.

Benguela (1.02–1.59 gC m⫺2; Shannon & Pillar, 1986). For the central Benguela that encompasses St Helena Bay, Verheye and Hutchings (1988) compiled data on the zooplankton biomass (⬎200 µm), and the resulting range was 2.44–5.25 g DW m⫺2, i.e. 0.97–2.1 gC m⫺2 when a C:DW ratio of 0.4 is chosen for the conversion. Due to ASE’87, the maximum value of that range has considerably increased: the sum of only meso- and macrozooplankton (i.e. zooplankton ⬎500 µm) biomass is already 3.04 gC m⫺2 (i.e. 2.52 + 0.9, see above), showing that zooplankton biomass may reach considerable levels in St Helena Bay following upwelling events. The simulated zooplankton biomass (ZC) represents ca. 48% of the total phytoplankton biomass (PC), i.e. an intermediate value between those found by Carter (1983) during winter (5%) and summer (64%). For the ASE’87, a mean total production of 79.9 and 225.6 mgC m⫺2 d⫺1 (equivalent to 2 and 7% of the primary production, respectively) was estimated by Verheye (1991) for juveniles and adults of C.

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carinatus and herbivorous copepods, respectively. Direct comparison with model output is difficult since variables Z1 and Z2 do not solely represent copepods. A secondary production of 107 mgC m⫺2 d⫺1 for Z1 and Z2 is estimated with the model, i.e. 3.9% of the primary production. Verheye (1991) also estimated that herbivores in the size range 200–1600 µm grazed ca. 752 mgC m⫺2 d⫺1, i.e. 22% of the primary production. Model estimates are in good agreement with this picture: grazing of 665.11 mgC m⫺2 d⫺1 is computed for Z1 and Z2, which represents 24.18% of the primary production. The grazing exerted by Z3 was negligible in the model (only 0.67% of primary production). For the Benguela system, other estimates concerning the percentage of primary production that is grazed by zooplankton range usually between 10 and 53% (Shannon & Field, 1985; Walker & Peterson, 1991), but lower percentages were also found by Peterson et al. (1990) or Brown & Hutchings, 1987a). When related to the phytoplankton biomass, the simulated zooplankton grazed 7.35% of that biomass every day (Fig. 8), a value close to the 8% estimated by Verheye (1991) for ASE’87. After compiling several observations made by Brown and Hutchings (1987a); Peterson et al. (1990); Matthews (1991); Walker and Peterson (1991); Timonin et al. (1992), and Painting et al. (1993), it seems that the latter percentage often varies between ca. 1 and 25% with a trend to increase when upwelled water is maturing. Gibbons, Stuart and Verheye (1992) also estimated that the grazing impact of chaetognaths on copepods was in the range 0.6–5.3% in the Benguela system. The model provides a realistic grazing impact of Z3 on Z2 (mainly represented by chaetognaths and copepods during ASE’87, respectively), which is ca. 1.1%. Using the Electron Transport System (ETS) methodology, Chapman et al. (1994) were able to estimate the zooplankton (meso- and macrozooplankton) respiration during ASE’87 (from day 79 to 90). The observed range for respiration is 0.075–1.27 gC m⫺2 d⫺1, with a mean of 0.34 gC m⫺2 d⫺1. The total respiration for zooplankton (Z1, Z2, and Z3), computed in the model, is ca. 0.98 gC m⫺2 d⫺1 (flow F9, Figs. 7 and 8). Considering Z2 and Z3 only, the respiration represents 23.46% of the total respiration, i.e. 0.23 gC m⫺2 d⫺1, a value that compares well with the above observed mean. Chapman et al. (1994) also provide indirect estimates of the nitrogen excreted by zooplankton larger than 200 µm. The range for excretion is 0.025–0.44 gN m⫺2 d⫺1, and the mean is 0.12 gN m⫺2 d⫺1. Total NH4 excretion by zooplankton is larger in the model (i.e. 0.18 gN m⫺2 d⫺1; flow F25, Figs. 7 and 8), but unlike within the model, the excretion by small zooplankton (⬍200 µm) was not quantified during ASE’87. Among the simulated zooplankton, Z1 was the largest producer of NH4 with 77.22% of the flow F25, whereas Z2 and Z3 accounted for 19.18 and 3.58% of F25, respectively. 4.3.3. Bacterial biomass and processes (BC, F6, F13) The integrated bacterial biomass reaches 1.05 gC m⫺2 (BC; Figs. 7 and 8), and the mean bacterial biomass for the water column is 22.52 mgC m⫺3. Whatever the depth, or the season, Brown et al. (1991) observed that the mean biomass for bacteria in the Benguela system is in the range 15–93 mgC m⫺3. Within the euphotic zone and according to the same authors, the overall mean is 39 mgC m⫺3. The biomass of bacteria (BC) represents ca. 11.4% of the phytoplankton biomass (PC; Fig. 8), which seems realistic given the estimates provided by Brown et al. (1991) for the northern and the southern Benguela, i.e. 8.4 and 18.6%, respectively. Painting et al. (1993), however, showed that larger percentages can be found in the southern Benguela (from 17 to 50%). From Fig. 8, an averaged bacterial production of 0.49 gC m⫺2 d⫺1 can be computed from the difference between the bacterial DOM uptake (F13; 1.51 gC m⫺2 d⫺1) and the respiration (F6; 1.02 gC m⫺2 d⫺1). Higher production (0.51 to 1.3 gC m⫺2 d⫺1) was generally measured by Armstrong, Mitchell-Innes, Verheye-Dua, Waldron and Hutchings (1987) along an inshore/offshore transect near Cape Columbine, but the water column there is much deeper (up to ca. 400 m) than in St Helena Bay. The production value, averaged over the water column, is thus more appropriate for comparison. From the model, the corresponding production is 10.4 mgC m⫺3 d⫺1, a value that falls between two estimates of the mean, i.e. 5.52 and 17.76 mgC m⫺3 d⫺1, provided by Painting, Lucas and Muir (1989) when using two different methods (the

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thymidine incorporation and the population growth methods) during a microcosm study. Also during the previous study, the mean bacterial productivity was estimated to be 0.46 d⫺1, i.e. a value close to that (0.47 d⫺1) computed in the model ([F13-F6]:BC; Figs. 7 and 8). In the model, the bacterial production is equivalent to 17.8% of the primary production. In a microcosm study, using recently upwelled water, Lucas et al. (1987) found 20%, but a range as large as 3–104% emerges after compiling the estimates provided by Painting (1989) and Brown et al. (1991). Chapman et al. (1994) also provide estimates of the bacterial respiration for the ASE’87. The range is 0.5–1.95 gC m⫺2 d⫺1, with a mean of 1.1 gC m⫺2 d⫺1. A similar value of 1.02 gC m⫺2 d⫺1 is obtained with the model (flow F6, Figs. 7 and 8). 4.3.4. Sedimentation processes (F4, F12, F14, F21, F28, F30, R4, R12, R14) Considering the C cycle, the large phytoplankton (flow F4; Figs. 7 and 8), the large detritus (flow F12), and the fecal material and bodies of large zooplankton (flow F14) may reach the sediments in the model. The total mean export of C to the sediments (F4 + F12 + F14) is 0.9 gC m⫺2 d⫺1, which represents ca. 32.7% of the simulated primary production. The export of POC from day 78 to 101 during ASE’87, was estimated by Pitcher et al. (1991) by using sediment traps positioned at depths of 29 and 39 m. Ranges for POC sinking are 0.19–0.71 (at 29 m) and 0.37–6.1 gC m⫺2 d⫺1 (at 39 m), corresponding to 4.6–40.1% and 9.4–185.4% of the measured primary production, respectively. Despite the fact that measurements made at 39 m were certainly influenced by a possible re-suspension of materials from sediments to the water column (Pitcher et al., 1991), most previous observations support the model values. For phytoplankton alone (flow F4; Fig. 8), 0.23 gC m⫺2 d⫺1 is on average exported to the sediments. Observed ranges for phytoplankton export are 0.01–0.23 (at 29 m) and 0.04–0.21 gC m⫺2 d⫺1 (at 39 m; Pitcher et al., 1991), i.e. significantly lower than model outputs showing that sinking of living phytoplankton is probably overestimated by the model. However, when previous observations are expressed in terms of percentage of the primary production (i.e. 0.3–13.8 and 1–6.4% of primary production at 29 and 39 m, respectively; Pitcher et al., 1991), the overestimation is not obvious since a corresponding value of 8.4% is computed in the model. On the other hand, Pitcher et al. (1989), using SETCOL measurements, showed that sedimentation of phytoplankton did not exceed 6.1% of primary production. These measurements were made at the end of period R1 and after (from day 96 to 105), when the bulk of the C. gigas bloom had already reached the sediments. Verheye et al. (1992) estimate that the flow of mesozooplankton fecal material reaching the sediments was 0.16 gC m⫺2 d⫺1 during ASE’87. In the model, this flow corresponds to 37% of F14 (Figs. 7 and 8), i.e. 0.1 gC m⫺2 d⫺1. Important events of sedimentation occur sporadically in St Helena Bay, probably in response to the upwelling cycles, as measured by Bailey (1987) during December 1984 (4.8 gPOC-C m⫺2 d⫺1) and March 1986 (3.67 gPOC-C m⫺2 d⫺1). This shows that values obtained during the ASE’87 are not beyond the expected range. The corresponding N flows were also estimated by Bailey (1987): 1.2 (December 1984) and 0.54 gPON-N m⫺2 d⫺1 (March 1986), from which we can deduce POC:PON ratios of 3.97 and 6.79 (w:w ratios), respectively. With the model, an average of 0.2 gN m⫺2 d⫺1 (i.e. the sum F21 + F28 + F30; see Figs. 7 and 8) reaches the sediments, and a corresponding C:N ratio of 4.45 can be computed. 4.3.5. Supply of nutrients from sediments (F15, F31) The supply of inorganic N from sediments to the water column computed in the model averages 0.16 gN m⫺2 d⫺1 (flow F15; Figs. 7 and 8), which is slightly higher than the estimate of 0.11 gN m⫺2 d⫺1 provided by Bailey and Chapman (1991) for the ASE’87. The value provided by the model is however lower than previous measurements made in St Helena Bay. According to Bailey (1987), 0.34 and 0.35 gN m⫺2 d⫺1 were supplied during December 1984 and March 1986, respectively, whereas Probyn (1987) reported a value ⬍0.24 gN m⫺2 d⫺1. Concerning the supply of SI from the sediments to the water column, an average of 0.18 gSi m⫺2 d⫺1

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is computed in the model (flow F31; Figs. 7 and 8), and no equivalent measurement originates from ASE’87. The sole data available come from Bailey (1987) for several stations located within and outside the St Helena Bay, with a huge range from ⬍0.28 to 2.24 gSi m⫺2 d⫺1. This shows that the model may perhaps underestimate the supply of SI.

5. Conclusions When compared with the ASE’87 data (see Section 4.1), most simulated variables remain similar in their magnitude, and also in their temporal and spatial distributions. Specific problems arise for the maximum simulated NH4 concentration, for the simulated depth of the silicacline, and for the patchy distribution of phytoplankton that cannot be reproduced in the model. There is also a discrepancy at the beginning of period R1 for the depth corresponding to the 1% light level. Concerning the balance for C, N and Si cycles (see Section 4.3), overall agreement can be noted between simulated flows and stocks, and corresponding observations originating from the southern Benguela region. Among the differences that appear between observations and simulated outputs, the NO3 uptake and the sinking of phytoplankton are probably slightly overestimated, whereas the sedimentation of zooplankton detritus is probably underestimated. It must be kept in mind however that, due to the large number of observations available for the region and the large variability of most variables, the size of ranges used for comparison is large enough to allow validation of most simulated variables. A complete balance for flows and stocks originating from ASE’87 would be essential to correctly assess the quality of model outputs. The overall quality of the simulated results is encouraging, but crucial estimates for several stocks (detritus, DOM) and flows (phytoplankton mortality, exudation, and Si uptake; zooplankton faeces production and mortality; bacterial grazing, mortality, and net nitrogen uptake; detritus decomposition) are often lacking for the southern Benguela region. Some additional efforts should be done in the future to fill these gaps in our knowledge. Considering that the model provides a realistic picture of what happened within the planktonic food web during the relaxation period, several results can be used to debate important questions on the functioning of the system. For instance, it is known that waters upwelled near Cape Columbine are enriched by large quantities of nutrients which are supplied by local coastal sediments (Bailey & Chapman, 1991). This is shown by comparing ranges for NO3 and SI concentrations of the true South Atlantic Central Water (SACW; 10–18 mmol N m⫺3 and 6–15 mmol Si m⫺3, respectively; Jones, 1971) to those of the water column at the beginning of period R1 during ASE’87 (ca. 10–27 mmol N m⫺3 and ca. 10–37 mmol Si m⫺3, respectively; see Fig. 4a and e). The sediments of St Helena Bay may be responsible for a large part of the pelagic productivity by maintaining high concentrations of nutrients in the BML. Many physical processes could then be involved in an effective transfer of nutrients from the BML to the UML (intense mixing of the water column during the active phase of the upwelling, tidal influences, or slow diffusion processes through the thermocline during the periods of relaxation). Model results agree with the overall picture that local sediments played a major role during ASE’87: the supply of NO3 from sediments (flow F15; see Table 8, and Figs. 7 and 8) represents on average 64% of the NO3 uptake by phytoplankton (F16). Concerning SI, a lower percentage (26.5%) can be computed from flows F31 and F32. This shows that processes involved in the dynamics of sediments are fundamental components and that a model describing these processes more accurately (e.g. Luff, Wallmann, Grandel & Schlu¨ ter, 2000) could be coupled to a pelagic model such as the present one. As debated by Verheye (1991), the fate of the C fixed by phytoplankton during ASE’87 is only partially known: according to Pitcher et al. (1991), a maximum of 14% of the primary production is exported to the sediments, whereas 22% of the primary production may have been grazed by herbivores (Verheye,

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1991), and the fate of the remaining part of the primary production (i.e. 64%) could not be identified (Verheye, 1991). The present model can be used to provide a more complete picture of the fate of the primary production during ASE’87 (see Table 8, and Figs. 7 and 8): from the net primary production (F1), 24.7% were grazed by zooplankton (F2), 28.7% were due to the mortality (F3), 8.4% were exported to the sediment (F4), and 41% were exuded in the form of DOM. These estimates show that most of fixed carbon was probably lost through the processes of exudation and mortality. This view contradicts the hypothesis proposed by Verheye (1991) that a large part of the unexplained carbon loss (i.e. 64%, see above) would have been consumed by other heterotrophs such as the microzooplankton (⬍200 µm), but it corresponds to the picture proposed by Hutchings and Field (1997) that recycling of organic material is considerable during periods of relaxation. A low f-ratio often implies the presence of an active microbial food web in the environment. Probyn (1992) reviewed the available f-ratios measured in the southern Benguela: all values were within the range ⬍0.1 to 1, i.e. the largest possible range for this ratio. Such a range is also found with the model (Fig. 6e), but the mean value given by Probyn (1992) is only 0.39, whereas the mean f-ratio computed in the model reaches 0.63 (i.e. F16 / [F17 + F16]; Table 8 and Figs. 7 and 8). Our simulated value is also much higher than the f-ratios measured by Waldron and Probyn (1991) during the phytoplankton growing phase of ASE’87 (0.29 to 0.35 between days 81 to 86). There are many possible explanations for the discrepancy; two of them are a bad parameterization of the inhibition exerted by NH4 on NO3 uptake in the model, or an underestimation of the f-ratios measured by Waldron and Probyn (1991). Perhaps the model provides incorrect estimates, but Probyn (1992) measured a f-ratio of 0.64 during the maximum growth phase of a phytoplankton bloom in another area of the southern Benguela in February 1991. According to the author, this higher f-ratio is a consequence of a bloom which was dominated by large phytoplankton cells, as was the case during ASE’87. The latter measurement agrees closely with our model estimate of 0.64, but it is far from the range measured by Waldron and Probyn (1991), showing that it is difficult to settle once and for all on this topic. Macroscale observations show that the southern Benguela ecosystem is dominated by small phytoplankton cells, which means in turn that microheterotrophic pathways are preponderant and that f-ratios are rather low (0.2–0.3; Probyn, 1992). From mesoscale observations however, it appears that when a bloom of large phytoplankton develops, the classical and almost linear food chain (i.e. NO3– diatoms–mesozooplankton–fish) becomes relatively more important and the f-ratio increases.

Acknowledgements This work was supported by a grant from the Benguela Ecology Programme (BEP), funded by the South African Foundation for Research Development and the Department of Environmental Affairs and Tourism, and a grant from the University of Cape Town. We are very grateful to the scientists of the Marine and Coastal Management of Cape Town, especially those involved in the Anchor Station Experiment 1987. This work would not have been possible without their valuable help in getting the data sets and for the numerous and stimulating discussions on the topic. Special thanks also for M. Majodina and D. Esterhuyse from the South African Weather Bureau for providing the irradiance data.

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