Vízügyi Közlemények, 1992 (74. évfolyam)
2. füzet - Domokos Miklós: A statikus összesítő vízgazdálkodási mérleg számítása időben ingadozó vízigény esetén
A statikus összesítő vízgazdálkodási mérleg számítása időben ingadozó vízigény esetén 185 Calculating the static summarizing water management balance in the case of fluctuating water demand by Dr Miklós DOMOKOS C.E., mathematician The most simple tool of supporting decisions in water resources management is the summarizing water management balance assuming a so called static or "frozen-in" water management development level. The theory of this method has been developed by the author ( Domokos 1989) for the special case - frequently encountered in the present Hungarian practice - when the balance arm called "water demand" has no stochastic component, or this component is negligible. Thus in this case the water demand time series can be approximated by a periodic step function. As the continuation of or supplement to Ihe former study, the author searches answer to ihe question of how the static water balance can be determined by assuming a non-constant water demand that fluctuates around a "frozen-in" expected value. For this purpose the author reviews formulae (3), (4), and (5) providing the generation of the resultant effective function I(t) for the outflow (budgeting) cross section, resulting from the water demand time functions lift) of water users located in a scattered manner over a certain drainage basin. Application of these relationships is illustrated in conjunction with a case study for the 1 lungarian part of the Tisza River Hasin (Figs. 1. and 2.) Functions and indices characterizing the joint occurrence of two arbitrary probability variables are considered in a general way as follows: - The joint frequency function И (x, y) and its tabulated form (Fig. 3). - The Reimann index R (X, Y) (Eq. 13), having an expressive power significantly higher than that of the correlation coefficient г (X, Y). - The deterministic functional relationship Y = / (X). the special case of which is when one of the two variables is constant. The use of the above indices and functions is demonstrated for the example of the Tisza River Basin, shown in Fig. /., in conjunction with the concomitance of flow discharges of Tisza River stations and the resultant water consumption rates of major water intakes (Table /., Fig. 4). The method of making use of informations on the relationship between water resource and water demand in the water balance depends on the character of that relationship: - If the relationship is of stochastic nature then the results of the water balance can be obtained from the time series of the two water balance arms (by respective computer algorithms), or from the joint frequency function (by hand calculation), (Fig. 5). - If there is a functional relationship of unknown form but of known tendency (monoionlous, non-increasing) between the two arms of the water balance, the water balance based on ihe duration curves of the two variables can be used in a favourable way (Fig. 6). - If there is an acceptable deterministic relationship of known form between water resource and water demand, then this together with the distribution function of water resources can be used for calculating the result of the water balance by some of Ihe respective expressions (for example, by Fqs (29) and (.30)). I he conditions of applying the above methods are reviewed in Table II. supplemenled by a numerical example - involving all methods - as shown in Fig. 7.
