Étude et modélisation de la formation des dépressions piézométriques en Afrique sahelienne Formation of piezometric depressions in the Sahelian zone : study and modelling

Résumé

Parmi les différentes théories généralement considérées pour expliquer la formation et l'entretien des dépressions piézométriques régionales : surexploitation ; drainage profond ; tectonique subsidente ; réajustement du niveau marin ; reprise évapotranspiratoire, seule la dernière semble pouvoir s'appliquer à l'ensemble des cas décrits en zone sahélienne. Les études hydrogéologiques en cours dans cette région, et notamment les résultats des isotopes de l'environnement, mettent en effet en évidence le rôle prépondérent des transferts verticaux sur les écoulements latéraux.Le schéma conceptuel présenté est basé sur les hypothèses suivantes: considérant une nappe libre alimentée par ses bordures, en milieu à faible perméabilité ; (1) il existe, en tout point de la nappe, un déficit entre l'infiltration saisonnière et la reprise évapotranspiratoire ; (2) infiltration, évapotranspiration et déficit décroissent de façon exponentielle avec la profondeur de la nappe ; (3) la piézométrie actuelle est le résultat d'une évolution commencée depuis la fin d'une période humide correspondant au remplissage maximun de la nappe (dernier pluvial Holocène pour les grandes dépressions sahéliennes).Dans un premier temps, la validité de ce schéma est testée à l'aide d'un modèle analytique simple prenant en compte les caractéristiques climatiques (évolution temporelle du déficit hydrique), les propriétés hydrodynamiques (perméabilité, coefficient d'emmagasinement) et le « pouvoir évaporatoire » du sol (« facteur de forme » k). Ce dernier, expression principalement de la texture du terrain, apparaît logiquement comme le paramètre le plus sensible pour le modèle.Un modèle transitoire unidimensionnel est ensuite présenté afin de simuler la baisse piézométrique entre deux limites à potentiel constant. La surface piézométrique obtenue semble en accord avec les données observées sur le terrain.

Mots-clés:

• Hydrogéologie,
• dépressions piézométriques,
• Sahel,
• isotopes,
• modèles mathématiques,
• paléohydrologie,
• bilan hydrique

Abstract

The discovery of the large piezometric depressions in the Sahelian zone dates back to the 1950s, when the early hydrogeological studies took place in West Africa (DEGALLIER,1954 ; ARCHAMBAULT, 1960). Since then, numerous examples have been described throughout the region (aquifers of Trarza in Mauritania ; Ferlo in Senegal ; Gondo, Nara, Azaouad in Mali ; Kadzell in Niger ; Yaere in North Cameroon...), raising what was, certainly, the major enigma in Sahelian hydrogeology (fig. 1).

So far, none of the different theories put forward to explain this phenomenon has met with general agreement : (1) Overexploitation cannot be involved due to the insignificant pumping in comparison to the reserves. (2) Geological subsidence due to neotectonic causes would never be active enough in this stable part of the African shield. (3) Drainage to a deeper aquifer is impossible to - consider in this particularly flat area. (4) Changes in sea water level may explain the piezometric evolution of the coastal aquifers (DIENG, 1987) but cannot be considered for the whole Sahelian zone. (5) Evaporation and transpiration losses were often considered as insufficient to generate deep piezometric depressions. However, only this last hypothesis seems to fit the whole of the hydrogeologic and climatic Sahelian conditions and will therefore be considered as the governing factor in this paper.

Evidence of a vertical water deficit

The major role of evaporation and transpiration processes in the formation of the piezometric depressions is deduced from various data : (1) the geographical distribution of the « depressed aquifers », which is in accordance with the regional isohyets, suggesting that climatic factors are compulsory conditions ; (2) the piezometric measurements (figs.2, 3), which show a deficit between direct aquifer recharge by precipitation and evapotranspiration losses during the dry season ; (3) the environmental isotopic results, which demonstrate that vertical water movements prevail over lateral transfers (fig.4). Furthermore, evaporation effects and plant uptake may still be noticeable at relatively great depth : the presence of root activities of Acacia was, for instance, recently proven at a depth of 35m in North Senegal (DUPUIS et DREYFUS, 1989).

According to theoretical and experimental results from different approaches (isotopic interpretation of unsaturated soil profiles ; calculation of unsaturated soil suction profiles ; piezometric measurements and mathematical simulations) it can be assumed that steady-state exfiltration from an unconfined aquifer decreases exponentially with water table depth (ARANYOSSY, 1991).

Conceptual scheme

The conceptual model presented here (fig. 5) is based on the following assumptions : (1) there is, everywhere, a water deficit (D) between the seasonal infiltration and the evapotranspiration losses; (2) Infiltration, evapotranspiration and water deficit follow an exponential decrease with respect to the water table depth ; (3) the present piezometric profile is the result of an evolution that started at the end of a past period corresponding to a total replenishment of the aquifer (last pluvial Holocene period for the Sahelian region). Furthermore, it is considered that the climatic evolution towards arid conditions is accompanied by a parallel increase of the water Deficit (for simplification, D is assumed to be a linear function of time).

Considering a low permeability, unconfined aquifer system, the lateral water movement coming from the imposed constant head recharge zones on the boundaries (lake, river or sea) is not important enough to counterbalance evaporation losses. The water table therefore progressively drops, decreasing the evaporation losses, up to a quasi-steady state where, finally, lateral transfers just compensate the vertical water deficit (ARANYOSSY, 1988).

Mathematical simulation

In a first step, a simple analytical model is introduced to check the validity of this hypothesis. Parameters included depend on climatic conditions (evolution of the water deficit D) ; on hydrodynamic characteristics (permeability, storativity) and on the soil aptitude for evaporation (k factor). It follows that : (1) the water table decreases very rapidly during the first millenium and then slows down to a quasi stationary state ; (2) the maximum calculated water table depths correspond to those observed in the field ; (3) the most sensitive parameter is the « k factor » - the value of which depends mainly on the soil texture (fig. 6).

A transient numerical model is finally presented to depict, in one dimension, the evolution of an unconfined aquifer between two constant head boundaries. Simulation on an 8 000 year time scale generates a piezometric profile (fig.7) in conformity with the configuration observed in the field.

In conclusionThe formation of the Sahelian piezometric depressions results from the conjunction of several compulsory factors : (1) climatic conditions : evolution from a humid to an arid climate accompanied by a vertical water deficit ;(2) geological conditions : low permeability sedimentary formations ;(3) geographical conditions : constant recharge zones on the boundaries of the aquifer.

Keywords:

• Sahel,
• hydrogeology,
• piezometric depressions,
• environmental isotopes,
• mathematical models,
• paleohydrology,
• water deficit