MARINE ECOLOGY PROGRESS SERIES Vol. 146: 189-205,1997 Published January 30 , Mar Ecol Prog Ser - Modelling the biogeochemical cycles of elements limiting primary production in the English Channel. 11. Sensitivity analyses Thierry Hoch, Alain Menesguen* Laboratoire de Chimie et Modelisation des Cycles Naturels, Direction de lVEnvironnernentet de 1'Amenagernent du Littoral, Institut Franqais de Recherche pour I'Exploitation de la Mer (IFREMER). Centre de Brest, BP 70,F-29280 Plouzane. France ABSTRACT: A general framework for an ecological model of the English Channel was described in the first of this pair of papers. In this study, it was used to investigate the sensitivity of the model to various factors: model structure, parameter values, boundary conditions and forcing variables. These sensi- tivity analyses show how important quota formulation for phytoplankton growth is, particularly for growth of d~noflagellates.They also stress the major influence of vanables and parameters related to nitrogen. The role played by rivers and particularly the rlver Selne was Investigated. Their influence on global Engl~shChannel phytoplanktonic production seems to be relativelv low, even though nutrlent inputs determine the intensity of blooms in the Bay of Seine. The geographical position of the rlver Seine's estuary makes ~t important in fluxes through the Stra~tsof Dover. Flnally, the multi-annual study highlights the general stability of the English Channel ecosystem. These global considerations are discussed and further lmprovements to the model are proposed. KEY WORDS: English Channel Sensitivity analyses . Ecological model INTRODUCTION variations on ecosystem behaviour at a central North Sea station. Jamart et al. (1979) carried out several numerical In the companion paper, Menesguen & Hoch (1997) experiments by varying the parameter values and equa- depicted a 2-element (N and Si) box-model. They tions of a previously published model. Moloney & Field described a physical sub-model combined with bio- (1991),following Platt et al. (19811, explored 4 areas of logical equations. This physical scheme integrates a model sensitivity: sensitivity to parameters, to inltial val- horizontal transport box-model and a vertical 2-layer ues, to functional form and to model structure. Fasham thermohaline model. Simulations clearly highlight the (1995) used a model to test 5 hypotheses in order to role of stratification in determining PI-imaryproduction explain differences encountered in phytoplankton dy- in the English Channel. namics between North Atlantic and North Pacific However, modelling is also a way to study system re- stations. His simulations were performed with the help of actions and sensitivity to fluctuations in parameters and 2 models: a simple one (phytoplankton-zooplankton- processes, terrestrial inputs and meteorological forcing. nutrient) and a model which also considered explicit pre- For instance, Fransz & Verhagen (1985) modelled the dation by carnivores, 2 compartments for dissolved in- ecosystem dynamics of the Dutch coast, which is directly organic nitrogen (nitrate and ammonium) and a detrital influenced by high nutrient river supply. Similarly, compartment. Chapelle et al. (1994)investigated eutrophication pheno- Thus sensitivity analyses are wide-ranging, and can mena in the Bay of Vilaine (South Brittany, France). be quite useful for modelling studies in that they repre- Radach & Moll (1993) studied the influence of seasonal sent a simple way of testing models. This paper will il- stratification and inter-annual meteorological forcing lustrate various aspects of sensitivity analysis and detail the results obtained for the English Channel. This sen- sitivity analysis will particularly emphasize the role of O lnter-Research 1997 Resale of full article not permitted Mar Ecol Prog Ser 146: 189-205, 1997 terrestrial inputs relative to the influence of meteoro- supply from rivers for the haline model. Evaporation logical forcing. In an epicontinental sea like the English and precipitation were not taken into account. Channel, the major question concerns the role of nutri- The thermal model reproduces western spring strat- ent supply from rivers in the ecosystem's dynamics. ification in the English Channel. Surface and bottom temperatures correspond closely to those measured by Pingree (1975), at Stn E,. Haline stratification is seen in THE MODEL AND METHODS OF the Seine plume. The thermohaline model provides ANALYSING SENSITIVITY exchange velocities between the 2 vertical layers in each box, which are then applied to any ecological The basic model variable, other than benthic. Biological sub-model. Conceptual scheme: The We will refer to the model described in Menesguen & global features of the biological sub-model were in- Hoch (1997).However, a slightly more complex model spired by the model described by Menesguen & Hoch will be used to investigate the influence of the intro- (1997). To investigate competition between diatoms duction of a cell-quota formulation for dinoflagellates. and dinoflagellates, 2 elements, nitrogen and silicon, Moreover, the biogeochemical cycle of the limiting ele- were considered in the previous model and phospho- ments is augmented by taking phosphorus into rus was included in this study. Phosphorus, like nitro- account. gen and silicon, appears to be one of the limiting Il'ydrodynamic submodel. Long-term circulation: elements of primary production in coastal waters. It Long-term 2-dimensional circulation is extrapolated has long been identified as the main limiting element from a numerical model elaborated by Salomon & Bre- in limnetic environments. In marine systems, its role is ton (1993). This lagrangian model takes into account open to debate, but cannot be ignored. Radach & Moll the coupled effects of tide and average wind on the (1993), for instance, used phosphorus as the only ele- residual circulation. Using this circulation, the English ment in their model which they applied to the North Channel was divided into 71 boxes, schematizing Sea. Including nitrogen, phosphorus and silicon in a the main physical and biological features of different single model allows the limiting elements in each area parts of the area. The following zones were defined of the English Channel to be identified. It also appears (see Fig. 1 of Menesguen & Hoch 1997): (1) coastal that phosphorus should be taken into account when zones, under the direct influence of nutrient inputs studying the influence of terrestrial inputs. from rivers, (2) eddy zones, characterized by high resi- The model considers these elements under the fol- dence times, (3) zones where trajectories can be con- lowing forms: total dissolved inorganic; phytoplank- sidered as being straight, associated with larger boxes. ton, divided into diatoms and dinoflagellates; detrital The Normand-Breton Gulf and the Bay of Seine are in water; organic in benthos. described with more accuracy, in order to better de- Dividing the phytoplankton into diatoms and dino- scribe the strong gyres and shallow areas in the former flagellates gives realistic representation of most situa- zone and the strong Seine plume horizontal gradient in tions encountered. A constant N:P:Si ratio was used for the latter. diatoms. Nutrient limitation by one of these elements Advection and diffusion processes between boxes was considered using a Michaelis-Menten formula- were considered. Diffusion depends on tidal current tion. According to Liebig's law, the final limitation velocity and water depth. Fluxes between boxes were results from the minimum of all limitations, including automatically calculated by ELISE ecological model- that of light: ling software (Menesguen 1991). Vertical structure: The importance of the seasonal pdral = Prnaxd~d! . LT . mln(fulal,f~~ld,~~): diatom growth rate (1) thermocline in the western English Channel and of the f~utdat = min(f~dr~~,fs,. [~dlat) nutnent limitation (2) halocline in the Bay of Seine has been amply proven [Nut1 with f~urdia! = (3) (Pingree et al. 1976, Holligan & Harbour 1977, Menes- k~ugdlat+[Nut] guen et al. 1995).To simulate a pycnocline occurrence, where fLdielis action of light limitation on diatoms (see we combined horizontal circulation with a vertical Menesguen & Hoch 1997), fT is action of temperature thermohaline model. This integral model, first devel- (see Menesguen & Hoch 1997), p,,, is the maximum oped by Niiler & Kraus (1977) and then adapted by growth rate, fNutdialis limitation function of diatom Agoumi et al. (1983), divides the water column into 2 growth by nutrients, [Nut]is concentration of nutrients layers. The thickness of these layers depends on turbu- in sea water (N, P, or Si), kNuldla,is half-saturation con- lence induced by either wind or tidal stirring and on stant for uptake of nutrients. the following 'source' and 'sink' terms: heat fluxes at Because of relatively slow dinoflagellate growth and the air-sea interface for the thermal model; freshwater the possibly long period between uptake and organic Hoch & Menesguen: English Channel model. 11. Sensitivity analyses 191 incorporation of nutrients, a cell-quota model was system is closed, and the renewal of inorganic nutri- tested for these algae. Tett et al. (1986) and Sharples ents during the winter. & Tett (1994) have already described phytoplankton Diatoms, dinoflagellates and total phytoplanktonic growth within a sharp pycnocline using such a model. production were calculated based on the equations This formulation was also applied to Dinophysis