Rapp. P.-v. Réun. Cons. int. Explor. Mer, 180: 228-233. 1982. Simulation model of primary production in coastal upwelling off Western Sahara Antonio Cruzado1 Institute) de Investigaciones Pesqueras, Paseo Nacional s/n, Barcelona-3, Espana Introduction Since the trophic chain concept was introduced by downwards like temperature in this part of the ocean, Lindeman, a number of papers have been published on shows a surface minimum in the upwelling nucleus, the trophic structure of marine ecosystems (see increasing with distance to the shore. Nutrient concen­ O’Brien and Wroblewski, 1972, for a review). Upwell­ trations, especially those of nitrate, show absolute ing ecosystems are known to be highly productive sys­ maxima at the centre of the upwelling nucleus where tems based on short trophic pathways basically control­ the lowest temperature is found, and decrease in the led by the distribution of the primary producers and the offshore direction. Chlorophyll concentrations, rela­ pelagic herbivores feeding on them. Since phytoplank- tively low at the upwelling centre, increase in the off­ tonic algae are bound to follow the displacement of the shore direction and are largest where the nutrients water parcels in which they live, upwelling ecosystems show the maximum horizontal gradient. The density models require, more than others, a proper treatment front that follows the 70 m isobath (Cruzado, 1974; of the physical frame of reference. In the more recent 1979) is responsible for the large rise in temperature work carried out by Walsh and Dugdale (1971), Walsh and salinity and the decrease to very low values of both (1975), Wroblewski (1976), and Cruzado (1976), com­ nutrients and chlorophyll on the offshore side of the plex upwelling ecosystems models have incorporated front. important hydrodynamic components that allow a bet­ The region is almost permanently under the influ­ ter understanding of the biological processes. ence of the trade wind system. Although the wind This paper is concerned with a two-dimensional blows at times with abnormally high intensity in the simulation model of the coastal upwelling ecosystem coastal zone between 21°N and 27°N, more commonly, located off Western Sahara across the Canary Current. periods of about one week, with quasi-steady state vel­ The model takes into account the flow of matter ocities of about 10 m/s, allow the organization all along through the most important biological components: the coast of the upwelling nuclei that seem to be undis­ dissolved-N (N), phytoplankton-N (P), and zooplank- turbed by the high-frequency fluctuations (Barton et ton-N (Z), according to the sensitivity analysis made by al., 1975). Johnson and Mooers (1973) have shown the Wroblewski (1976). It is based on the general law of velocity field near Cape Bojador to have a maximum distribution of the intensive properties in the sea (Sver­ intensity of about 90 cm/s over the shelf and of 60 cm/s drup et al., 1942) and covers the hydrodynamic as well on the slope, always at the surface, uniformly decreas­ as the biological processes. The geometry has been ing downwards with minimum values of about 10 cm/s established following the morphology of the Cape over the bottom. This is in accordance with the Bojador area, that is, without shelf and with a constant generalization made by Shaffer (1974), who postulates bottom slope dipping from the shore to 400 m at a for the eastern boundary current systems a surface jet distance of 40 km offshore. Generality and precision of about 1 knot, 20 km wide and 50 m thick, associated have been balanced with spatial resolution within the with horizontal density fronts. limits imposed by the capacity of the computer used, an Even under extremely calm conditions, Salat and IBM 1130. Font (1977) have observed off Cape Bojador an equatorwards motion of the 5 m deep water with a The real world velocity of 30 cm/s in the direction of the local depth contours, concurrent with a lowering of the nearshore Observations off Cape Bojador (Fig. 178) show all the surface temperature of about 5°C below that of the isopleths rising towards shore. Salinity, decreasing offshore water. This gives support to the hypothesis that interaction between the longshore current and the bottom topography may, at least, be as important a 1 Present address: UNEP Geneva Office, Mediterranean Action Plan, Palais des Nations, 1211 Geneva 10, Switzer­ mechanism as Ekman transport in inducing coastal land. upwelling in the region (Cruzado, 1975). Circulation 228 36.7 100 100 .36.5 • 36.3 150 150 36.1 200 200- 250 250 300 300 350 350 4 0 0 i 0 i 1. 100 60- CL 150 200 2 . i 250 — 05 ’ 300 3 5 0 - 400 Figure 178. Distribution of properties in a plane perpendicular to the coastline off Cape Bojador. T = temperature (°C). S = salinity (%o). N 03 = nitrate (ugat N/l). CL = Chlorophyll a (mg/m3). 14C = carbon uptake (mg C/m3/h). off Cape Bojador, unlike that over the wide shelf = 100 min) according to Walsh (1975). The model was farther south, may be simply defined as a one-cell integrated following Euler’s method. Advection and Ekman system. Diffusion are terms that depend on the values that the state variables (N and P) take at the corresponding element, the ones taken at adjacent elements and the The model velocity and diffusion fields. These terms are therefore formulated as finite differences. Uptake and Grazing The simulation model consists of a matrix of 40x40 are biological terms that depend only on the values elements, of which only those above the diagonal rep­ taken by the state variables at the corresponding resenting the sea bottom are defined. Each element is element. formed by two generalized non-linear differential equations: 3 N Advection — 1- Advection (N) = Diffusion (N) — dl Uptake (N,P) The velocity field is computed by means of a hydro- dynamical submodel that has been described in detail d P —— I- Advection (P) = Diffusion (P) + elsewhere (Cruzado, 1976; Font and Cruzado, 1977). dt Uptake (N, P) - Grazing (P, Z) This submodel considers the field entirely driven by wind stress as if it blew along a straight coastline. Due The fulfillment of the two stability criteria, U dr/dr < 1 to the two-dimensionality, the longshore circulation and W dtldz < 1, and the von Neuman condition for should not affect the model solutions and therefore the the parabolic part of the equations, Kv dtidz2 < 0-5, flow of water in the plane of the model (X,Z ) is of the allows the solution to reach a quasi-steady state for greatest importance for the biological processes. The integration times sufficiently large (1000 iterations, dt horizontal velocity U is made up of two components. 229 One, directly generated by wind stress, contains all the changes of these properties. Mechanical energy enter­ baroclinicity of the motion and has a major effect in the ing the sea through air-sea interactions is degraded offshore transport within the surface Ekman layer. The downwards via turbulent motion. Therefore, the turbu­ other, mainly owing to surface slope, provides a baro- lent diffusion coefficients would be expected to tropic compensation flow and keeps the sea level decrease with increasing depth. Palmén (see Neumann steady, due to the longshore homogeneity and the con­ and Pierson, 1966) suggested this decrease to be expo­ tinuity condition. nential. In this model, horizontal and vertical diffusion The parameters of this submodel and the values have been given different treatment. The horizontal assigned to them for the “standard solution” are as diffusion coefficient, independent of X and Z, has been follows: computed by means of Brooks’s (1959) formula Kh = Uo, the maximum value of the horizontal velocity, 0-01 D XAß — 4-5 104cm2/s. The vertical diffusion coeffi­ only possible at an infinite distance from shore, has cient has been assigned a maximum value at the sur­ been assigned a value of 17-86 cm/s corresponding to a face, computed by means of the Neumann and Pierson wind velocity of 36 km/h (wind stress of 3-5 dynes/cm2) (1966) equation that takes into account the wind veloc­ at the latitude of Cape Bojador. ity V, Kv = 0-1825 10-4 V5/2 = 100 cm2/s. The minimum De, the Ekman depth, has been estimated by the value, asymptotically approached as depth goes to depth at which current reversal takes place at station infinity, has been computed by means of Hidaka’s Foxglove (Barton et al., 1974), corresponding to an (1954) relationship Kv - KhW2IU2 — 10 cnr/s. The Ekman depth of 100 m. depth dependence of the vertical diffusion coefficient is Dr , the Rossby radius of deformation, is a funda­ then given by the equation mental horizontal length scale arising in the theory of time-dependent, rotating, stratified fluids (O’Brien, Kv (Z) = Kv («>) + Kv (0) exp (-Z /D Z ). 1973). The value of 10 km given to it means that the predominant upwelling takes place within this distance U ptake from the coastline. The velocity field obtained (Fig. 179) corresponds to The process of nutrient uptake is controlled by two a single-cell cross-circulation mode (SCOR, 1974). The factors occurring in every parcel of water: nutrient maximum upward vertical velocity is found at the bot­ availability and existence of a sufficient light intensity. tom, at depths around 0-75 DE. It can easily be demon­ The double effect of nutrient and light limitation is strated that the total transport of water in the offshore- expressed in the model by means of hyperbolic equa­ going Ekman layer between the surface and 0-75 DE is tions analogous to the Michaelis-Menten expression proportional to both Uo and DE.