Stochastic concomitance of water resources and needs

Abstract

One of the simplest ways of determining the dimensions of and controlling water resources is by comparison of some water shortage index with an upper limit value, called water deficiency tolerance, based on economic considerations. The situation is considered satisfactory if water shortage is smaller than the limit value. Otherwise the dimensions and operating rules of system elements (such as the volumes of storage reservoirs and water intakes) have to be changed. Earlier workers gave several indices of water shortage and showed their calculation when water demand is a constant value and water resources are characterized by a probability distribution function. Methods for the calculation of water shortage indices in this particular case have been given. Indices of water shortage when water demand is not constant but a stochastic or deterministic relation exists between water demand and resources are examined. Indices characterizing the concomitance of two arbitrary random variables are considered. Flow discharges and water consumption of the Tisza basin provide examples of their use. The calculation of water shortage indices depends on the relationship between resources and demands: 1. (a) If the relation between water resources and demand is stochastic, water shortage indices should be calculated either directly from the time functions of the two variables (by computer) or from their joint frequency function, by simple formulae; 2. (b) if there is a deterministic functional monotonic, non-increasing relationship of unknown form, the water balance may be based on the duration functions of the two variables; 3. (c) Finally, if the relationship between water resources and demand is known, the water shortage index can be calculated from a simple formula and the distribution function of water resources.