Modélisation conceptuelle globale du régime du transport particulaire sur les fleuves tropicaux d'Afrique : application aux bassins du Niger supérieur et du Bani, Mali Lumped conceptual modelling of suspended sediment transport in African tropical rivers: the Upper Niger and Bani River basins

Résumé

Sur le fleuve Niger, les relations entre concentrations en Matières En Suspension (MES) et débits liquides montrent, à l'échelle d'une crue annuelle, des cycles d'hystérésis orthogrades. Le modèle présenté dans cet article reproduit les variations saisonnières de ces MES à partir du seul débit liquide. Il suppose que les MES proviennent de deux sources distinctes : le système " versants + réseau hydrographique secondaire ", siège d'une érosion saisonnière temporaire et le réseau hydrographique principal, siège d'une érosion permanente. Le modèle représente schématiquement la production de MES provenant de ces deux sources par le biais de deux réservoirs de MES. Le premier contient un stock en MES temporaire et limité. Ce stock, maximum au début de la crue annuelle (stock initial), est mobilisé et entraîné au cours de la saison pluvieuse en produisant un flux journalier, supposé être, à un instant donné, proportionnel au stock restant et à une fonction de puissance du débit. Le second, contient un stock de MES illimité et disponible en permanence. La mobilisation de ce stock produit un flux journalier, supposé être aussi une fonction de puissance du débit, et dont l'importance sera limité par la capacité du cours d'eau. Les cinq paramètres du modèle sont calibrés à l'aide des données acquises durant huit années hydrologiques (1991/92 à 1998/99) sur deux stations du Niger amont (Banankoro et Douna). Malgré les limites d'utilisation actuelles liées à la détermination du stock initial, le modèle présenté reconstitue de façon satisfaisante les variations annuelles des concentrations en MES et offre des perspectives intéressantes pour modéliser l'évolution temporelle des MES observées tant pour les fleuves tropicaux unimodaux que pour les petits bassins versants africains. En termes de flux annuels, le modèle n'apporte pas d'amélioration sensible par rapport à un ajustement statistique simple entre les volumes écoulés et les flux de MES. Cependant, il permet aussi de déterminer les variations de flux au cours de l'année, information qui ne peut être obtenue avec un modèle de régression statistique.

Mots-clés:

• Matières en suspension,
• érosion,
• hystérésis,
• modèle conceptuel,
• fleuve Niger,
• Mali

Abstract

Estimating temporal variability of suspended sediment concentrations in a watershed is important for a number of reasons (e.g., sediment yield estimation, provision of input data for reservoir sediment-deposition models and water quality models). Three different approaches have been adopted for modelling erosion and sediment transport: physical erosion models (Wicks and Bathurst, 1996); conceptual models (Negev, 1967; Pinheiro and Caussade, 1996); and empirical models (Walling, 1977; Asselman, 1977). Physical and conceptual models usually require rainfall intensity data. In African tropical river catchments, however, temporal and spatial variability of rainfall are not well known; in case of the Niger, water discharge is the only reliable hydrological parameter. This study proposes a model of temporal changes in suspended sediment concentrations using only water discharge data, thereby eliminating the need for rainfall parameters.

Daily discharge and weekly suspended sediment concentration data (from 1991/92 to 1998/99) gathered at two monitoring stations of the Upper Niger (Banankoro and Douna) (Figure 1) were used to study relationships between suspended sediment concentration and river discharge.

At each gauging station on the Niger, the relationship between water discharge and suspended sediment concentration during the annual flood is characterized by clockwise hysteresis (Figure 3). Moreover, several other African single-annual-flood rivers-unimodal rivers-also exhibit this type of relationship (Kattan et al., 1987; Olivry et al., 1988; Orange, 1992). This cyclicity suggests a three-stage description of sediment transport dynamics: (1) At the beginning of the rainfall season, sediments are imported by hill-slope surface runoff, re-entrainment of deposits in the channel network, and riverbed erosion. The first two sources consist of easily mobilizable material available throughout the catchment at the beginning of the hydrological year. (2) Sediment availability decreases with time as the soil becomes stabilised by vegetation during the rainy season. Erosion is consequently reduced, despite increased discharge. (3) During the period represented by the falling limb of the flood hydrograph, mobilizable material has been depleted or cannot be entrained; what suspended sediment there is originates upstream and from bank and bed erosion-permanently available sources. Non-seasonal sediment sources are grouped under the label of "continuous erosion."

We propose a lumped conceptual model of suspended-sediment concentration variations over the hydrological year. The model divides the erosion, transport and deposition processes into those acting on hill-slopes and those acting in the channel network, and assumes that both are explainable by water discharge Q(t) alone. The hill-slope/channel distinction is based on the fact that suspended sediment transport in a river depends not only on transport, bank and bed-erosion capacity, but also on the amount of available material in the drainage catchment.

Sediment transport (in tons per day) for the hydrological year is thus computed as the sum of two independent daily contributions of sediment discharge. The first, F_mob(t), originates from a limited reservoir which is full at the beginning of the flood and available only temporarily, during the rainy season. At a given time t, the sediment input F_mob(t) is proportional to the amount remaining in the limited reservoir and to a power function of water discharge (Eq. (1), Eq. (2)). The second reservoir, temporally and quantitatively unlimited, injects a daily sediment discharge F_ec(t) which is a power function of water discharge (Eq. (3)); F_ec(t) is limited only by river capacity. The final concentration is obtained from Equation (4).

The five model parameters were calibrated with concentration and discharge data from hydrological years 1991/92 to 1995/96. The unlimited reservoir parameters were estimated using Equation (6) with data taken during the decreasing stage. Initial sediment in the limited reservoir was estimated with Equation (7), using observed concentrations and concentrations derived from continuous erosion (Eq. (3)). Two parameters related to the decrease in initial sediment loads were obtained by optimization of the mean Nash criterion between observed and calculated concentrations (Figure 6). Some physical interpretations were ascribed to coefficients related to the limited reservoir.

Despite the limitations of assuming a single initial mobilizable reservoir, predictions of temporal sediment-concentration patterns during the annual flood were satisfactory (Figure 7, Table 2). The model also simulated some observed sediment concentration peaks associated with sudden water discharge variations during the rising limb of the annual flood. Best results were obtained by varying initial sediment reservoir estimates for different hydrological years (Table 3)-the model could therefore be improved by highlighting parameters that determine sediment loads at the beginning of the hydrological year.

The model does not give better estimates of annual sediment yield than simple regression of annual water volume (Table 4). However, it is able to reproduce the temporal variability of the sediment flux during the annual flood. The small size of the data set makes evaluation of the performance of this model difficult; for better assessment, it should applied to other data gathered on the same catchments or on other large tropical rivers. Model parameter values could also be explained by drainage basin characteristics.

Keywords:

• Suspended sediment transport,
• erosion,
• hysteresis,
• lumped conceptual model,
• Niger river,
• Mali