Use of simulation models in water resources systems analysis

Transcription

1 ptial Allocation of Water Resources (Proceedings of the Exeter Syposiu, July 1982). 1AHS Publ. no. 15. INTRDUCTIN Use of siulation odels in water resources systes analysis D, N, KRBVA & V. I. PIZNER Water Probles Institute, USSR Acadey of Sciences, oscow, USSR ABSTRACT This paper discusses the state of the art in ethods of solving probles of water resources systes anageent. It is shown that the ethod of nuerical siulation is ost effective in the analysis of water resources systes behaviour. Peculiarities of its use caused by the particular nature of the water resources systes are discussed. The application of this ethod to the study and analysis of hydrological forecasts used for water resources systes anageent is shown. The increasing water deand for econoic developent, on the one hand, and the necessity of environental control including water control, on the other, akes the proble of water anageent one of the ost urgent tasks of today. To solve this proble it is essential to develop large-scale water resources systes. Water resources systes The ter "water resources systes" coprises water sources, eans of their control and transportation to water users. Though water resources systes have any coon features with all large-scale national econoic systes (e.g. transport, power production, etc.), they differ fro the to soe extent due to a nuber of peculiarities. ne of the, variability of a river runoff, causes the stochastic character of processes connected with the selection of paraeters of water resources systes and their operational rules. Water consuption is also stochastic. This is deterined by fluctuations of precipitation, processes of soil foration, solar activity in agriculture, biogenic flows in fishery, etc. oreover, other unknown or uncertain factors of a technical and econoic character ay also be of considerable iportance. Therefore, to solve the proble of water supply to the national econoy, one ust analyse the proble of coordination between stochastic water resources and the deand in the. The ain way of tackling the proble is the redistribution of water resources in tie by runoff regulation and in space by interbasin and interregional water transfer. River regulation by reservoirs Reservoirs are clearly the ain eleent of water resources systes ; 215

2 216 D.N.Korobova & V.I.Poizner characteristics of their design and operation for the basis for the theory of runoff regulation developed in the USSR ainly by Kritskii & enkel (1952). The theory of runoff regulation provides a eans of establishing relationships between three iportant paraeters of a water resources syste: usable storage of a reservoir (); its yield, or water supplied to users (a); and the reliability of water supply or probability of exceedance (p). To aintain control over the above paraeters in real tie operation, runoff regulation ust be carried out in accordance with soe rules, which incorporate conditions of water utilization and real hydrological inforation. These rules are based on the principle of "dispatching" of water resources systes regies. This principle eans that water supply (a) fro a reservoir is defined by content and tie as a characteristic of runoff distribution and water utilization. The principle of "dispatching" can be expressed in different ways. In the USSR, dispatcher rules are traditionally used. They allow one to define zones of reservoir storage which are associated with various purposes. Besides, in the USSR and in other countries, systes of priorities are widely used. These systes deterine the order and degree of water liitations according to the iportance of water users and the water abundance of the period. The desire to axiize the degree of runoff utilization necessitates attepts to use long-ter forecasts for operational ais fro a nuber of onths to a year ahead (Velikanov & Poizner, 198). Runoff forecasting and risk The probabilistic nature of long-ter forecasts iplies a risk of taking the wrong decision when the forecast is wrong. Recent studies show that the desire to axiize the utilization of runoff inevitably contradicts the necessity to aintain soe definite guarantees of water supply reliability. Real operational rules are aied at a coproise between the two ais. The relation between the is defined on the basis of trade-offs between the econoic effect fro the rise in the degree of water utilization and daages fro diinishing water supply reliability. Ecological aspects Considering coprehensive conditions of water resources systes designing and functioning, the constant growth of water utilization should be noted especially in agriculture, which has already caused an appreciable deficit of water in soe regions of the world. The consequent effects on the quality of fresh water ust be taken into account in public and industrial water supply. The proble of water pollution as a result of huan activities has not only a technological aspect, but also an ecological one as it threatens the stability of the fresh water ecosyste. The ecological aspect appears in the disturbance of seasonal water distribution and in the growth of unproductive water losses as a result of runoff regulation by reservoirs. This is especially iportant, when the interaction of rivers with inland seas and lakes can allow the effects of regulation in one river to influence the

3 Water resources systes analyses 217 biota of all connected systes. DEVELPENT F PERATING PLICIES All these factors ust be considered in the operational policies of water resources systes. At the planning stage, operating rules allow one to explore syste perforance and estiate its technical capacity and environental ipact. At the operational stage, the rules provide a way to aintain the fir yield of the syste or, when the projected conditions are changed, to correct the regie of the syste. The analysis of these tasks ust be based on the use of odern atheatical ethods and coputers. It should be noted that any resources probles have been solved with optiization techniques. The adequate atheatical developent of these techniques and the possibility of their nuerical realization on coputers allows us to use the widely in studies in hydropower engineering. ptiization techniques Soe essential difficulties in utilization of optiization techniques arise, however, due to the increasing coplexity of water resources systes. These difficulties are caused by the lack of reliable econoic inforation on the coponents of the syste and by the absence of cost characteristics of daages for soe coponents, which are necessary in optiization of the syste operation in deficit water periods. The above reasons ake it necessary to forulate the processes of water resources systes design and operation as ones of ulticriterion optiization, that cannot be solved directly. It should also be noted that, when optiization techniques are used to analyse these processes for large-scale systes with coplex internal and external connections, considerable siplifications of a foral picture of the syste are ade (i.e. linearization of characteristics, siplification of operation, an increase in estiated tie spans). The decisions, ade in keeping with this approach, are rather inaccurate and, therefore, they cannot be used in water resources practice. An analysis of experience of atheatical prograing ethods, used to optiise the paraeters and the regie of water resources systes, shows that they can be used successfully in solving large-scale regional tasks or soe particular tasks (usually operational ones) which can be forulated in ters of one criterion. The ethods are helpful also to establish the range of perissible decisions of ulticriterion optiization tasks. Therefore, we can state that it is ipossible to create optial rules of water resources systes anageent with the use of atheatical prograing alone. Those studying other large-scale systes have also encountered the sae difficulties. The only solution of this proble is active participation in all stages of data analysis and decision-aking.

4 218 D.N.Korobova S V.I.Poizner Nuerical siulation techniques For reasons given above there is increasing use of siulation odelling for study and analysis of water resources tasks. Siulation odelling opens up a wide range of possibilities for investigation of the large-scale water resources systes behaviour by cobining the eory and speed of coputers with the flexibility and judgeent of the huan intellect. The ability of decisionaking to find a coproise between different deands and to find satisfactory conditions in the vector space of syste conditions is of crucial iportance. The use of the ethodology of operational research, based on active an-achine dialogue can, even within the odel being used, give a new character qualitatively to syste developent. Analysing the obtained results, a decision aker learns ore about the peculiarities of the structure of the syste and the character of possible change of its ain paraeters. Therefore, siulation odelling allows a specialist to consider the whole range of possible operating effects and guarantees purposeful research, which leads to the required developent of the syste. Such a conclusion stresses the necessity for the ost serious attitude towards the representation of operational processes in siulation odels, which are used for studying large-scale water resources systes functioning. There are different approaches to the developent of a odel for siulation in different theoretical and applied branches of science. When analysing the above entioned processes, it is custoary to use the given theory and practice of water resources calculations, which can be viewed as a foralized reflection of the process of water resources functioning (Korobova & Poizner, 1978). USE F SIULATIN DELS: A CASE STUDY In the USSR, a set of siulation odels used for the analysis of water resources systes with one reservoir or a group of the under different operational conditions have been constructed. Such odels allow one to estiate the influence of different operational factors on these regies. It is iportant to estiate the efficiency of using long-ter hydrological forecasts as an integral part of a set of operating rules. This has been done by a series of experients using a siulation odel of a water resources syste with one reservoir and any water users, soe of which can utilize water surpluses. A technique has been developed to conduct siulation experients for estiation of the efficiency of different operational factors. This technique is based on the principle of creation of a zone of possible operation and localization of regies under study (Velikanov & Poizner, 1978). Soe regies are analysed in order to create the zone of possible operation of a siulation odel. They show extree operational strategies, i.e. regies of axiu possible aintenance of guaranteed supply (fir yield) and regies of axiu possible runoff utilization. In the first case, the guaranteed supply is aintained in all the volue of regulation, the rise up to a axiu value being possible only when the

5 Water resources systes analyses 219 reservoir is full and there are runoff surpluses. n the contrary, in the second case the axiu possible output for each water user is aintained in all the volue of regulation. When the level of the reservoir is lowered to a dead volue, the supply depletes to zero, and the water resources deficit is fixed. The reliability indices and the ean annual values of deficits and discharges are used as indices of the efficiency of the syste's functioning. A water deficit is defined as an average volue of water for a nuber of years which is insufficient to aintain the guaranteed water supply. The reliability indices in the studied regies will have extree values, i.e. (a) the reliability of fir yield is axiu for the guaranteed regie and iniu for the regie of axiu runoff utilization; (b) the volue of deficit for the guaranteed regie is iniu, for the regie of axiu runoff utilization it is axiu; (c) the volue of spills is axiu for the guaranteed regie and iniu for the regie of axiu runoff utilization. These two extree regies provide a way to create the so-called "standard" regie of runoff regulation prediction. In this case, runoff prediction is used for all the period of regulation. The standard regie is an optiu variant of operation. Spills and daages occurring in this regie at this level of water consuption cannot be eliinated by any operation action. All regies under investigation are located in the sphere of possible operation indices. After this, an additional analysis, which takes into account the specific peculiarities of the syste, can be ade. The proposed technique has been used for the efficiency analysis of operation of releases, for fishery purposes, fro the Tsylyanskoe Reservoir on the River Don. Factors affecting operating rules are the existing storage in a reservoir at the tie of decisionaking and a predicted value of the volue of water flow to a reservoir during the spring flood. A probabilitistic atheatical odel has been used to define the predicted runoff, based on the coposition of a three-paraeter gaa distribution for runoff volue and a noral distribution for the error of forecasts. Let the rando value x = A, an error of forecast, have a standardized (zero ean, standard deviation equal to unity) noral distribution with probability density function: P n (x) = =L exp(-x 2 /2) (1) and let the rando value y = W or, a forecasted supply (inflow) have a three paraeters gaa distribution with paraeters y Q, y, b and probability density (Stacy & ihra, 1965) : P 2 (y) = ly/b, (Y/b)-l -il/b r(y + b) 1 y_ r(y + b) r(y) r(y)b/y y Q exp y r W (2) then the density of their joint distribution can be expressed as ^x(x,y) = P 1 (x)p 2 (y){l + 6A(J)(x) [2p\P 2 (y)dy - l] + 5À 2 [6(j) 2 (x) - -] [6(/^P 2 (y)dy) 2 - Gj^P^yJdy + l] } ()

6 22 D.N.Korobova & V.I.Poizner where A is the coefficient of correlation between the probabilities of exceedance and <t>(x) is the probability integral. The conditional density of the error distribution of a forecast x with the predicted runoff y is l(j 2 (xjy) = P 1 (x){l + 6A<j>(x) [2F,(x) - l] } + 5A 2 [6(j) 2 (x) - W] x [6F^(y) - 6F 2 (y) + l] (4) where F2 (y) is the preset value of the function of the threeparaeter gaa distribution. The conditional expectation of distribution (4) is equal to x Q (y) = ^= [2F 2 (y) - l] (5) ' /IT and the conditional dispersion is ouy) = 1 - -^- * + 2i >'[2F 2 (y) - l] (6) This analysis shows that, when x <.5, the distribution (4) can be acceptably approxiated by a noral distribution, given the liited exactness of definitions of hydrological characteristics. Therefore, the conditional distribution of errors of forecasts can be considered noral with paraeters defined in (5) and (6). Siulation experients designed to evaluate the efficiency of using hydrological.forecasts in operational conditions have been conducted for a conditional average predicted runoff defined in () and with quantiles of 1%, 25%, 75% and 9% reliability of a conditional curve of errors of forecasts. Table 1 gives the results of these experients. As the table shows, the operating rules provide a eans of varying the regie of water resources systes widely. An analysis of the results allows us to conclude that the neglect of the stochastic essence of hydrological forecasts lead either to a definite rise in the projected water resources characteristics (regie 4 in the table, where forecasted inflows are equal to actual ones) or to irrational use of operational possibilities of a reservoir (regie 5 in which a release is deterined by the level of a reservoir only, and runoff is considered to be equal to its unconditional average). Further analysis of Table 1 (variants 6-1) and also an additional analysis allow us to give recoendations concerning the reliability of hydrological forecasts, which can be used to deterine fishery releases. CNCLUSIN With the growing coplexity of hydrological calculations, and the any conflicting criteria, of water resources systes it will be ore and ore difficult to select optiu control procedures. Under these conditions the foral use of atheatical prograing ethods (i.e. objective optiization) will lead to unsuitable results for water resources systes. The use of the ethod of nuerical siulation for this purpose can turn out to be ore effective than optiization

7 Water resources systes analysis 221 <D 'H 4H -H 4H q -v *? ft; o,^- en ^f ^ rs. en en en va oo c\] en N. en en oo oo co co co ta ^ Co Co C tu SH - tn En H rç -H.q S i-h fc. -H ^ KÇ E t v - t\ o-, on ^ ^H ^ co co on -^ C C C C to C co -H un ro q tu S in & -U fb -v tn En -H _ -H fc; il H" Qj r- -, fc> i-h En -U i-h H <B «-H S H 'H "H.Q * tn S d «C) S 4> SH 4H ftj «1 H g En 4J E W En H W -t -^ o\ En -U H -p " q H SH Q q fb H fl a, E <B H S l 4-1 fi g fc. Hi s 4J S. 1 U H to ui to co ^ \f o-,ono Q ^ i Q CtxtUn * tt t», o o o o < \)i t\ ^t l < H) en co en V VQ en on en C r- «y, I\ \f I\ LTl C i C C rx on rn C o co on in en co co oo to to K ni Un C tx C ui "* to ni oo to VQ rx Un C t C t C K H I co en co ^^Ji n ^ VQ C tri tt cnonon to to to N K C J un un N C Co > -U QH fei ^ cq *Z En H H U E «j H SH tn.q «B: t) q U <B noff u E E H X «s S; t u tb t q -u oo ÎH cor En -H -U 1 S - «u C ^, <*H ÊS *? Q II a, u <u is q as H un C II a* D in ondi 4J C8 D tn S U fc. IB *S un en» en II ft, CB II ftj -u rç ^ICCo^j, tfl tfl N l Q

8 222 D.N.Korobova S V.I.Poizner techniques either in the scientific study or in the design of water resources systes. REFERENCES Korobova, D.N. & Poizner, V.I. (1978) Nekotorye voprosy razrabotki ateaticheskikh odelei dlya vodokhozyaistvennykh issledovanii (Soe probles of developing atheatical odels for water resources studies). In: Probley Izucheniya i Kopleksnogo Ispolzovaniya Vodnykh Resursov, Nauka Press, oscow. Kritskii, S.N. & enkel,.f. (1952) Vodokhozyaistvenye Raschety (Water resources calculations). Gidroeteoizdat, Leningrad. Stacy, E. & ihra, G. (1965) Paraeter estiation for a generalized gaa distribution. Technoetrics 7, no.. Velikanov, A.L. & Poizner, V.I. (1978) etodika issledovaniya rezhiov vodokhozyaistvennoi sistey na iitatsionnoi odeli (Technique of studying regies of a water resources syste using a siulation odel). In: Inforatsionnyi Byulleten po Vodnou Khozyaistvu Stranchlenov SEV no. 1(21), Velikanov, A.L. & Poizner, V.I. (198) An analysis of the efficiency of using inflow forecasts in reservoir anageent. In: Hydrological Forecasting (Proc. xford Syp., April 198), IAHS Publ. no. 129.