Empirical strategy for water resources system management: Example of a semi arid irrigated perimeter
An empirical inter-annual management rule is defined to operate a reservoir for irrigation use in a semi-arid zone. Management rules for hydro-agricultural systems in semi-arid zones consist of establishing a trade-off between the total quantity of water to be distributed for summer irrigation and the indispensable volumes to be held in store for the raising of future seedlings during the following autumn. In less arid countries, water is sufficiently cheap so that it is economically profitable to deliver great quantities to sustain maximum agricultural output. Indeed, water is sufficiently abundant so that it is generally useless to conserve reserves for the next year. Such an inter-annual compromise is not the norm for water resources managers in humid climates. For instance, the two consecutive dry summers in Europe in 1989 and 1990 would not have had the same impact on the agricultural economy in the semi-arid zones. There rules of management would have been adapted to obtain of an inter-annual balance. Numerous mathematical methods have been used in the domain of water resource systems management, sustained by the constant increase of computer performances. Reservoir management issues have consequently been widely studied and solved both from the viewpoint of the art of modeling and the methods of optimization. Nevertheless it is necessary to ensure that the mathematically correct optimal solution is also implementable when one leaves the computer screen to get back to the field: the success of this passage depends largely on the ability of the objective function to quantify the economic stakes encoded in the choice of a management rule. Except for hydropower generation, the various uses of a dam are most unlikely to be integrated into an aggregative utility function under the form of separable additive criteria. A way to bypass the inherent difficulties in the design of a realistic objective quantification is to restrict the search of the operation rule to the class of strategies compatible with the commonly met attitude of semi-arid water resources system managers. The structure of the rule is designed from the observation of the effective management presently in operation. Its logic fits to the following reasoning: - when the reservoir level is low, as soon as it starts to vary, the irrigation perimeter manager will behave very prudently. i.e. by reducing the proportion of the allocated irrigation water to the amount in store; - for average working conditions, the system manager will deliver a constant fraction of the available reservoir storage for irrigation; - when the quantity stored in the dam is high, the manager tends to satisfy completely the irrigation demand. The parameters of this piecewise linear rule are adjusted so as to minimize the probability of discrepancy between demands and resources on series obtained after a brief hydrological study. The Ghezala perimeter in Tunisia, which is situated in the watershed of lake Ichkeul, has been taken as a case study. With a thousand hectares of irrigated crops to be satisfied from an upstream 12 hm3 reservoir, and 625 mm rain per year on the watershed with a strong seasonal dependence, the Ghezala perimeter is quite representative of Tunisian irrigation practices. The method developed in this paper allows to balance the risk of failure all over the year and to adapt the strategy of irrigation according to critical vegetative phases of the crops. A statistical analysis of possible deficits according to the improved rule reveals that the method improves the performance of irrigation and decreases its sensitivity to the critical vegetative phases that are of critical importance in agriculture in semi-arid zones. The management model is unsophisticated but its objective is to provide elements of appreciation to the manager of the irrigated perimeter. Each component of the model can be improved and more finely described. Advantages and drawbacks of this empirical approach with regards to more conventional dynamic programming techniques are finally discussed and underlined for water resource systems with specific attention to their management in semi-arid zones.