Vízügyi Közlemények, 1989 (71. évfolyam)

4. füzet - Domokos Miklós: Az összesítő vízgazdálkodási mérleg mennyiségi oldalának elmélete

Az összesítő vízgazdálkodási mérleg mennyiségi oldalának elmélete 509 Theory of the quantitative side of integrated water management balance by Dr. M. DOMOKOS, С. E., Dipl. Appt. Math. The two basic tools of decision-making in water resources development are : simulative systems modeling and water management balancing (Fig. I). The use of the latter tool is justified up till necessary information - in quantity and reliability - is at hand for modeling. Since the 2nd Master Plan for Water Management (OVE, 1965) has been edited, a great number of water management balances were prepared in Hungary, from year to year, by unchanged methodology. In this paper, the overall knowledge about the theory of the quantitative side of water management balances is compiled with a viewpoint and the drawing ups of today. In Chapter 1 the basic notions are defined : water management balance; "freezing" of the level of development (Fig. 2) ; (areal) units in water management (Fig. 3) ; the reference period of the balance which is a unification of identical calendar periods (e.g. months) in consecutive years according to Eq. (1). In Chapter 2 - a short detour - relationships among the various waterbalance-notions are explained. The so-called hydrological balance Eq. (3) is a special form of the most general waterhousehold balance Eq. (2) as seen in Fig. 4 (where resultant antropogeneous influences are neglected. Table Г). In the water management balance natural components are taken into account, according to Eq. (6), through runoff (the resultant effect) whereas antropogeneous components are investigated in detail. In Chapter 3 a special case of the water management balance the integrated water management balance is discussed - according to Eq. (7) - in which the processes are reduced to a single point (e.g. the outlet of a catchment), while the elements of the balance are agglomerated in two groups: usable water resources as in Eq. (9) and Eq. (10) and in Fig. 5, and water demand according to Eq. (12). In Chapter 4, aspects of definition, grouping and of calculation of the resultant effects of selected water balance elements (minimum acceptable flow, diverted and rebooked water resources, changes due to storage and mining, wastewater disposal, etc.) are discussed. In Chapter 5. simplification for easier handling of the time-functions in the balance arms had been investigated. The trend components of the natural discharge time-series Q(t) are removed (if any) by physical and mathematical means. Periodic components of annual cycles are also eliminated by a proper selection of the reference period. The remaining ergodic, stationary process then can be equivalently substituted by its F

Q(x) empirical or filling distribution function appearing in the form of Eq. (21). Trend in Ç

k(t) time-functions of antropogeneous balance elements is zero (due to "freezing" of the level of development), while the stochastic component is neglected (rough approximation!). The remaining deterministic part is then substituted by a step-function (Fig. 6). By a proper selection of the reference period it is possible to substitute both the resultant demand time-function and the resultant time-function of antropogeneous components of the usable water resources by constants. The distribution function F

K(x) of usable water resources - as in Eq. (24) - can then be calculated by a shift to the right of the distribution curve of natural flows F

Q(x) by this second constant (see Fig. 7). According to the principle of Eq. (25), the qualification of a water management balance is active - as elucidated in Chapter 6 by analog argumentation taken from the theory of strength if the actual or expected value y of water shortage is less than its economically sound upper limit y*. i.e. the so-called water deficiency tolerance. The water shortage index y is, according to Eq. (27), the expected value of the water shortage indicator function u(t) or u(x) in Figs. 9 and 10, which should be in close contact with the economic losses induced (Fig. 8). Index y, can be calculated by Eq. (34) to represent the relative duration of water shortage periods; y

2 is obtained by Eq. (35) to represent average relative water deficit, and y

3 is generated by Eq. (36) to represent average squared water deficit. From these, only y

x has been used in Hungary although it is the least expressive index (Fig. 11). Its use allowed to apply, however, an elastic qualification (Fig. 12) according to Eqs. (42) and (43) covering also the so-called equilibrium range of the water management balance.