Rapp. P.-v. Réun. Cons. int. Explor. Mer, 180: 228-233. 1982. Simulation model of in coastal 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), -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 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 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 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. All the velocities in proposed by Dugdale and Maclsaac (1971): the model are proportional to Uo and can be scaled with this parameter. Therefore, a change in Uo or its Uptake (N,P) = P * Vmax * F equivalent, the wind stress, linearly affects the entire velocity field. Likewise, the vertical transport of water where F is the minimum of the two values taken by the is proportional to DE and greatly affects the values of expressions the vertical velocity W that increases with DE. Al­ though it does not affect the overall transport of water N/(KN + N) and I/(KI + I), across the open-sea boundary, DR affects the horizon­ tal acceleration of the water as it moves offshore and, ^max being the maximum possible nutrient uptake rate, therefore, the distribution of W, concentrating and taken as 0-08/h, which produces two cell doublings per increasing the intensity of upwelling for small values of day. KN and KI are the half-saturation constant for Dr and spreading and decreasing this intensity with nutrient and light respectively. KN is taken as 0-5 ugat large values. Uo also affects, in a non-linear way, the Ml, the value commonly found in the literature, and KI residence time of the water in the area of the model, is taken as 10 % of the incident light intensity that especially in the surface Ekman layer, with the corre­ fluctuates with the time of the day, following a sinusoi­ sponding changes in the plankton “wash-out” effect. dal function during the daylight hours and a null func­ tion during the night hours. I, the light intensity reach­ ing one element of the model, is also a function of the water properties above this element. The decay of light Diffusion intensity in the sea is given by Lambert-Beer's law This is a complex concept that, in simulation models, includes all those aspects of the circulation and turbu­ dlldZ = - K* I lent diffusion that take place at a scale smaller than the size of the model building blocks. Two-way flow of where K is the extinction coefficient. In the model, this properties depends on the rates at which water is coefficient, far from being constant in the marine envi­ exchanged between adjacent blocks and on the spatial ronment, has been considered a linear function of the

230 cm/sec

m/sec x 10'

2.0

•0.5 2.5

}jg-at N /

Figure 179. “Standard solution” of the model in a plane perpendicular to the coastline similar to that of Figure 178. Upper left: distribution of the horizontal component of the velocity U. Upper right: distribution of the vertical component of the velocity W. Lower left: distribution of the dissolved nutrient N. Lower right: distribution of the phytoplankton nutrient P.

phytoplankton density (self-shading effect) in each of puted by integration of the Lambert’s equation from the layers above the corresponding element the surface to the depth of the corresponding element. The distribution of nutrients (Fig. 179) is greatly K = KA + KB * P. affected by the uptake process. Nutrient uptake basi­ cally controls the nutrient concentrations in the surface KA is the extinction coefficient of pure sea water, layer in which the water flows in the offshore direction taken as 0-042/m, corresponding to a Secchi-disc read­ (Ekman layer) while, in the zone in which water flows ing of about 40 m; KB is the contribution of the phyto­ in the opposite direction, the distribution of nutrients is plankton to the self-shading effect, taken as 0-047 strongly affected by the concentration of nutrients in m2/mg Chi, corresponding to a Secchi-disc reading of the inflowing water, corresponding to the boundary about 19 m for an average chlorophyll concentration of condition. At the offshore end, only diffusion controls 1 mg Chl/m3 in the water column. This term allows also the upward transport of nutrients and an oligotrophic for attenuation due to unknown dissolved and sus­ zone is always present, especially when the wash-out pended materials. The light intensity / is then com­ effect is not important owing to a large residence time.

231 Therefore, large values of Uo, caused by high wind proportional to the available food P. In the surface forces, extend the eutrophic zone in the offshore direc­ layers of the open ocean about one half of the smaller tion, eventually beyond the 40 km of the model geo­ zooplankters caught with a 300 micron net do not metry. De also has a strong influence on the extension migrate vertically, and this proportion may be even of the eutrophic zone, especially through the depth at higher in waters over the shelf (Fernandez, 1976). which the vertical gradient of the nutrients is largest. density strongly affects the phyto­ D r affects the residence time of the water in the model plankton distribution but has a minor influence on the area and therefore the extension of the nutrient-rich dissolved nutrients. An extreme case is when zooplank­ water, although opposite from the way that Uo does. ton is not allowed to graze. Then, phytoplankton The distribution of phytoplankton is affected by the density is higher everywhere, especially in the deeper nutrient uptake process to a lesser extent, although it layers and in the offshore zone. This should be ex­ has an important influence on the nutrient distribution pected since no other mechanism is provided in the through the self-shading effect. Increasing influence of model for the removal of matter from the system. On the phytoplankton density on the extinction coefficient the other hand, the standard solution does not properly KB produces a considerable decrease in the extension reproduce the observed decrease in the phytoplankton of the oligotrophic zone, owing to a reduction of the concentration towards the open sea. An increase in the uptake capacity to a thinner layer, especially near the herbivore density in the offshore zone, keeping the coast where the phytoplankton density is high, allowing coastal zone unchanged, produces the desired tilt of the the nutrients to be washed out to a greater extent. corresponding isopleths.

Grazing Boundary conditions Following Walsh’s approach of approximating the gen­ The boundary conditions of the model have been eral predator-prey non-linear relationship by means of established in such a way that no exchange of matter a hyperbolic expression that includes a threshold term can take place at the air-sea and sea-bottom interfaces (Walsh, 1975), grazing has been formulated in the while diffusion and advection act at the open-sea end. model They have been established taking into account two factors: a) the circulation pattern given by the solution Grazing (P,Z) = Z * Gmax ^°p of the hydrodynamical submodel, and b) the observed vertical distribution of nitrate-N and chlorophyll a (Fig. where Gmax is the maximum possible ingestion rate for 178). According to the direction of flow, distinction zooplankton. It has been taken as 0-16/h, equivalent to between the two layers is made: In the surface layer, about 4 times the weight of the zooplankton ingested with offshore-going flow, the last column of elements is per day. This rate, although apparently large, has to assigned identical values of N and P as the previous compensate for various experimental errors, namely one. In the interior zone, with the onshore-going the fact that in areas of large blooms, the herbivorous water, N increases linearly with depth from the deepest organisms may ingest a larger amount of particulate element in the surface layer to a maximum at the bot­ matter than they can assimilate, high activity also evi­ tom, while P decreases exponentially with depth from denced by the large amounts of faecal pellets present in the value at the deepest element in the surface layer the underlying sediments, as well as the vertical in­ and a rate of decrease corresponding to a decrease of e homogeneities in zooplankton concentration due to times for an increase in depth of 10 times DZ. algal blooms. KP, the phytoplankton density at which ingestion rate is half the maximum, is taken as 1-5 ugat Ml, and Po, the threshold value below which grazing is Conclusions no longer possible, is established at 0-5 jxgat Ml. In the model, the horizontal distribution of zoo­ On the basis of the hydrodynamics of the model, Uo plankton has been established according to observa­ and De determine the maximum upwelling intensity tions made in the area off Cape Bojador (Rubies, 1976) and, if nutrient distribution is taken into account, the parameterized by a linear relationship and corrected overall potential primary production capacity in the for the existence of other herbivorous organisms not plane of the model. Therefore, these two parameters caught by the 300 micron net: should be studied with great attention in the real world. Intensity of upwelling shows a maximum near the Z = 0-16 + 0-08 * X/40, shore and decreases in the offshore direction. The spa­ tial distribution of this intensity is determined by the Z being the average zooplankton density in ugat Ml at horizontal acceleration of the water in the nearshore a water column distant X km from shore. Within the zone. Therefore, detailed studies of the cross-circula­ water column, vertical distribution has been considered tion at every location are badly needed.

232 Horizontal distribution of vertical turbulent diffusion Cruzado, A. 1976. Afloramiento costero en el Atlântico may also have some significance, especially in relation Nororiental. Doctoral dissertation. Univ. of Barcelona. to the density structure. The fact that water properties Cruzado, A. 1979. Coastal upwelling off Western Sahara. Invest. Pesquera, 43(1): 149-160. show some degree of stratification in the offshore zone Dugdale, R. C., and Maclsaac, J. J. 1971. A computational while they are extremely homogeneous nearshore with model of the nitrogen flow in the Peruvian upwelling re­ a strong front over depths between 50 and 100 m, sug­ gion. Invest. Pesquera, 35(1): 309-330. gests larger values of the diffusion coefficient in the Fernandez, F. 1976. Influencia de la luz, temperatura y materia orgånica particulada en la actividad metabôlica y en nearshore as compared with the offshore zone. la alimentaciön de los copépodos planctönicos. Doctoral The strong influence of the open-sea boundary con­ dissertation. Univ. of Barcelona. dition on the model solution is crucial, especially for Font, J., and Cruzado, A. 1977. Simple two-dimensional the distribution of dissolved nutrients. Therefore, steady-state model of coastal upwelling circulation. CUE A Newsletter, 6(4): 33-38. proper establishment of the boundary conditions is a Hidaka, K. 1954. A contribution to the theory of upwelling basic requirement if realistic solutions are to be ob­ and coastal current. Transac. Amer, geophys. Union, 35' tained. 431-444. The fact that small zooplankters cannot account for Johnson, D. R., and Mooers, C. N. K. 1973. Current profiles in the upwelling region off Northwest Africa. CUEA News­ all the grazing activity taking place in the model indi­ letter, 2(5): 5-22. cates the possibility that a larger number of herbivores Neumann, G., and Pierson, W. J. 1966. Principles of physical graze especially in the offshore zone. In fact, some fish oceanography. Prentice-Hall, Englewood Cliffs, New species that can feed on phytoplankton have been Jersey, USA. O ’Brien, J. J. 1973. A simple model of a coastal upwelling reported in large schools in the region (sardine, an­ event. CUEA Newsletter, 2(2): 3-5. chovy). O ’Brien, J. J., and Wroblewski, J. S. 1972. An ecological Although three-dimensional effects cannot be simu­ model of the lower marine trophic levels on the continental lated with the present formulation, they may be very shelf off West Florida. Florida State University, Tech. Rep. Rubies, P. 1976. Distribution de la biomasa zooplanctönica important as a cause of increased primary production entre C. Bojador y C. Blanco. Resultados preliminares. and should be considered in future development of the Res. Exp. Cient. B/O Cornide, 5: 209-216. model. Salat, J., and Font, J. 1977. Internal waves in the NW Africa upwelling. Elsevier oceanogr. Ser., 19: 269-273. SCOR Working Group no. 36. 1974. Coastal upwelling pro­ cesses. CUEA Newsletter, 4(3): 12-20. Shaffer, G. 1974. On the Northwest Africa coastal upwelling References system. Doctoral dissertation. Christian-Albrechts-Univer- sität, Kiel. Barton, E. D., Pillsbury, R. D., Smith, R. L. 1975. A com­ Sverdrup, H. U., Johnson, M. W., and Fleming, R. H. 1942. pendium of physical observations from JOINT-I. Vertical The Oceans. Their physics, chemistry and general biology. sections of temperature, salinity and sigma-/. Oregon State Prentice-Hall, Englewood Cliffs, New Jersey, USA. University. Spec. Rep., 75(17): 1-60. Walsh, J. J. 1975. A spatial simulation model of the Peru Brooks, N. H. 1959. Diffusion of sewage effluent in an ocean upwelling ecosystem. Deep-Sea Res., 22: 201-236. current. In Waste disposal in the marine environment. Ed. Walsh, J. J., and Dugdale, R. C. 1971. A simulation model of by E. A. Pearson. Pergamon Press, New York. the nitrogen flow in the Peruvian upwelling system. Invest. Cruzado, A. 1974. Resultados del anâlisis continuo en Africa Pesquera, 35(1): 309-330. del NO entre 23° y 28°N. Res. Exp. Cient. B/O Cornide, Wroblewski, J. S. 1976. A model of the spatial structure and 3:117-128. productivity of phytoplankton populations during variable Cruzado, A. 1975. Is wind stress the main driving force in upwelling off the coast of Oregon. Florida State University. coastal upwelling? Third Int. Symp. Upwell. Ecos., Kiel, Tech. Rep. 25-28 August.

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