Résumés
Résumé
La modélisation du comportement hydrologique des bassins versants est incontournable dès lors que l'on s'intéresse à des problématiques relatives à l’évaluation et la gestion optimale des ressources en eau. Ceci s’illustre par un aspect quantitatif, dans les pays comme l’Algérie où l’alimentation en eau est un facteur limitant. L’objectif principal de cet article est d’expliciter les relations entre les conditions hydrologiques et la disponibilité en eau de surface. A cet effet, un modèle pluie-débit à l’échelle annuelle qui prend en compte les paramètres physiques et climatiques a été mis au point. L’application porte sur l’Algérie du Nord dont la superficie est de 325 000 km2.
La mise au point de ce modèle nécessite au préalable une base de données qui a été acquise lors des travaux antérieurs incluant la carte des pluies médianes, la carte des perméabilités et le modèle numérique de terrain. Afin de compléter cette base de données, la cartographie des pluies des différentes années pour lesquelles on dispose des débits a été réalisée en utilisant une méthodologie intitulée "cartographie de la pluie centrée réduite". Ainsi, les données de 467 postes pluviométriques ont été traitées et ont permis de tracer les cartes des isohyètes annuelles.
L’étude de la relation pluie-débit à l’échelle annuelle est basée sur les données de débits de 50 stations hydrométriques réparties à travers la zone d’étude. La démarche utilisée s’est inspirée de la fonction de production du S.C.S (Soil Conservation Service). Les résultats du modèle après calage ont permis d’obtenir un coefficient d’explication de 0,75, ce qui signifie que 75 % de la variance est expliquée par la pluie moyenne, la surface et un coefficient (a) qui correspond à la pente moyenne des bassins versants.
Mots-clés:
- Algérie du Nord,
- bassins versants,
- cartographie automatique,
- débits,
- krigeage,
- système d’information géographique,
- fonction de production du SCS
Abstract
Modelling the hydrological behaviour of drainage basins is very important for solving problems related to the evaluation and optimal management of water resources. This is illustrated quantitatively in countries such as Algeria where water supply is a limiting factor. The principal aim of this paper was to explain the relationship between hydrological conditions and the availability of surface water. A model of rainfall-discharge was developed on a yearly scale, taking into account physical and climatic parameters. The application was carried out in northern Algeria where the total land surface is about 325 000 km2.
The development of this model required a database, which was acquired during previous studies where maps of median rainfall and permeability as well as the digital elevation model were developed. In order to complete this database, the cartography of rainfall for the years for which we have discharge data was carried out using a methodology entitled "mapping standardized rainfall". To estimate and map annual rainfall, the kriging method was used. Two problems were encountered:
- The presence of a drift highly altered the variogram and made it very difficult to infer a sub- structure function;
- The variogram is significant only if the hypothesis of ergodicity is valid, which was not easy to assume for any given year.
In order to resolve these difficulties, a homogeneous random and secondary stationary order function (same mean at all points and same covariance function) must be calculated. A previous study by ANRH (1993) allowed us to know the statistical parameters of the distribution at each point. These parameters were mapped, taking into consideration the topographical relief and distance to the sea. For every year and at each rainfall measure point, the standardized rainfall could be deduced. The correlogram gave information about the spatial variability of the phenomenon and its range, and subsequently the standardized rainfall was then interpolated. Annual rainfall was calculated by combining the grids of the means, the variances and the centered reduced rainfall (TOUAZI and LABORDE, 2000). Thus, the data of 467 rainfall gauges were used in order to create maps of the yearly isohyets.
The rainfall-discharge relationship on an annual scale was based on 50 hydrometric stations distributed throughout the study area. The methodology used was derived from the production function of the S.C.S (Soil Conservation Service). This production function was part of modelling, which transformed total rainfall to net rainfall. This method was very representative of the natural hydrological processes. Indeed, it takes into account rainfall and the maximum infiltration capacity (S), which depends on the nature of the soil (lithology), vegetation and soil moisture content. In the current study, the basin surface and a regional parameter (a) were introduced in order to calibrate the model. This production function was implemented by supplying different values for the parameter (S). The values (n+1) were obtained by increasing the previous value (n) by 10 %. We evaluated the different values of (S) in the same way to obtain the last value (i). We calculated for these different values of the parameter (S) the square of the difference between the measured and estimated discharges for each year by measuring the discharge at different stations. For each station, we calculated the sum of these values for all the years and we retained the value of (S) that gave the minimal value. The results demonstrated that the values of (S) obtained were not significant because they tend to the infinite. For this reason, (S) was considered as a constant. In order to improve the model, we repeated the same operation, but instead of (S), we used the parameter (a) and performed the same calculation. After calibration of the model the results gave a coefficient of determination of 0.75, which means that 75 % of the variance was explained by the mean rainfall, the surface and the parameter (a).
To explain the parameter (a), we calculated the correlation between its value at each station with the corresponding geology. This latter variable was characterized by the average storage capacity, which corresponds to the weighted average of the surfaces of the basin assigned to each permeability category (TOUAZI, 2001). The results demonstrated a coefficient of determination of 0.1. The correlation with the topographical relief was not necessary because it was taken into account in the cartography of the rainfall. We then proceeded to the cartography of the parameter (a). The results demonstrated an east-west gradient that was constant and a north-south gradient that decreased from north to south. With the digital elevation model, we used a geographical information system to deduce the slopes. For each basin, the average slope was calculated by taking the average of the values of the slopes of all the pixels that constituted the individual basin. The correlation between slopes and corresponding values of the parameter (a) gave a coefficient of correlation of 0.6.
The results obtained by this model after calibration gave a coefficient of determination of 0.75, which means that 75% of the variance was explained by the mean rainfall, the surface and a coefficient (a), which corresponds to the average slope of the drainage basins.
Keywords:
- Northern Algeria,
- soil conservation service production function,
- discharge,
- drainage basin,
- automatic mapping,
- kriging,
- geographical information system