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Mathematical Models in Hydrology

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Mathematical Models in Hydrology General description of the Vistula River Project and basic planning data Maciej Jedrysik, Aleksander taski and Jan Zielinski Abstract. The Vistula is the largest river in Poland and the development of its water resources has a fundamental significance for the overall development of the country. The most recent studies concerning comprehensive development of the Vistula River water resources were under- taken within the framework of the UNDP/UNVistula River Project. They are a continuation of the previous studies which have been in progress for several years. The purpose of the Vistula River Project is to determine the optimal basin-wide solutions by applying mathematical modelling techniques. The present paper describes the Vistula basin and the Vistula River Project. Special emphasis is laid on the methodical preparation of the basic planning data and their scope (input data for the mathematical models). Résumé. L'aménagement intégré des ressources hydrauliques du bassin de la Vistule, le plus grand fleuve de Pologne, est un problème essentiel pour le développement du Pays. L'étude récemment entreprise dans le cadre du Projet Vistule, patron6 par le PNUD (Nations Unies) fait suite aux études polonaises commencées depuis plusieurs années. Le but de cette étude est de définir la solution optimale de l'aménagement intégré du bassin au moyen d'un modele mathématique d'utilisation des eaux. La présente communication contient une description du bassin de la Vistule et du Projet Vistule, ainsi que la méthode de préparation des données pour le modèle mathématique. INTRODUCTION AND GENERAL DESCRIPTION OF THE VISTULA BASIN The water economy problems of the Vistula basin and its development have for a long time been of particular interest to Polish hydraulic engineers. The solutions to the problems of developing the Vistula basin and obtaining the optimal utilization of its water resources to meet the demands of the national economy,constitute the basic conditions for a master plan for the development of all Polish water resources. For this reason the people concerned with the general development of the country are also very interested in the results of such studies. The catchment area of the Vistula River covers 174,000km2or 56 per cent of the Polish territory. The catchment area includes the main industrial centres of Upper Silesia, Lódf,Warsaw and Kraków,and huge rural areas, which produce more than 60 per cent of the country's agricultural output. At the same time the Vistula Valley can be thought of as a principal axis of the national economy as it attracts the major new industrial investments. These very general facts help show the exceptional significance which the situation within the Vistula basin and the other factors, that govern the proper development programme, has for the whole national economy.Among these factors are, the water resources, their magnitude, degree of present utilization and prospects of future exploitation.Table 1 shows the water resources of the Vistula basin in selected cross sections of the Vistula River and its main tributaries. The table is concerned with surface water only; the estimation of the water resources, however, cannot be limited to it, as the potential utilizable groundwater resources of the Vistula basin approximate 19,000m3 x IO6 yearly. Such a volume constitutes a considerable share of the total water resources,as the mean annual General description of the Vistula River Project 1057 TABLE 1 Q-discharge (m3/s) Catchment cross area Mean Qmax River section (km2) Min annual Max Qmin Upper Vistula Dwory 5,300 11.6 56 1950 168 Middle Vistula Pufawy 57,100 97.1 422 7390 76 Lower Vistula Tczew 193,900 238.0 976 9170 39 Dunajec (tributary of Upper Vistula) N. Sgcz 4,360 7.7 61 3510 455 San (tributary of Upper Vistula) Radomys'l 16,700 16.1 129 3770 234 Narew (tributary of Lower Vistula) Zegrze 69,050 54.0 281 2940 54 outflow is 31,000 m3 x lo6.Despite the fact that this volume seems remarkable the present level of draw-offoccasionally encounters periodical limitations or involves negative phenomena,closely linked with the hydrological conditions of the basin. A characteristic of the hydrology of the Vistula River and the majority of its tributaries is the great seasonal variation in discharge. The flow pattern is one of long periods of low discharges during the summer,autumn and winter seasons, interspersed with occurrences of violent flood waves. The course of the Vistula River may be divided into three sections,namely: the Upper,Middle and Lower courses, depending upon the morphology,hydrology and degree of development of the adjacent areas. THE UPPER VISTULA The Upper Vistula, which runs along the southern mountainous (Carpathians) part of the country,drains about 25 per cent of the whole basin and receives the highest precipitation, namely mean annual totals ranging from 600 to 1000mm.Several mountain tributaries characterized by very unstable flow and of considerable flood potential join the Vistula along this section. The floods are mainly from summer storms. The water resources of this part of the basin greatly exceed the average resources of the basin and consequently at the lowest point of the Upper Vistula (below the confluence with San River) the mean annual outflow reaches 40 per cent of the total outflow of the Vistula River. This part of the basin has a decisive influence on the regime of the Middle Vistula and is clearly observable in the flow pattern of the Lower Vistula. The Upper Vistula runs across the intensively industrialized centre of Upper Silesia and then through the Kraków Industrial Centre. A considerable amount of effluent is carried into the Vistula from the Upper Silesia industrial centre by a tributary,the Przemza River and so the water pollution level is high. The water is practically unacceptable for domestic use and only partially'suitable for industrial consumers. To cover the water requirements of these centres, a programme of con- struction of storage reservoirs was initiated and has been going on for several years. The programme also includes a system of water transfer installations. The reservoirs are generally located on the tributaries of the Vistula River, where a reserve of clean water is still available. Despite these measures a serious water deficit is experienced within this area which necessitates further studies and urgent decisions. Because of the rich natural deposits (coal) and the high degree of industrialization in the vicinity of the river, development of navigation has been discussed for a long 1058 Maciej Jqdrysik, Aleksander taski and Jan Zielitkki time. This stretch of the river was controlled before the First World War. The develop- ment of a navigable waterway was started in the fifties (three barrages provided with navigation locks were built) but the idea was later abandoned and still awaits a final decision. As already mentioned the Upper Vistula basin suffers from frequent floods that cause serious economic losses. The flood storage capacity of the existing reservoirs is insufficient and therefore the compilation of the flood-controlprogramme for this portion of the basin, taking into account both the Vistula River and its tributaries, is an urgent and very important task. THE MIDDLE VISTULA The Middle Vistula is the most neglected stretch of the river. Here the channel has a character of a typical lowland river. Often the unstable channel consists of several branches, enclosing islands, and the main river current changes its position after almost every flood. Navigation is practically non-existent here because the width and shallowness make its development almost impossible. The shallow channel and difficult flow conditions are factors that make the threat of ice jams and resulting floods very real. The river carries an adequate supply of water and runs through the centre of the country. Labour is readily available from the adjacent agricultural areas. All these circumstances make the region suitable for the development of large industrial establishments;this factor has been reflected in the investment policy of the Govern- ment in recent years. Thus there is an urgent need to develop the river, the undisputable priorities being bed stabilization and the establishment of navigation. In recent years controlling work has been started along several stretches of this part of the river. Water shortages occur in the basin on both sides of the river as a result of industrial and agricultural activities. Solutions to the problem involve either erection of local water storage reservoirs on the tributaries or the transfer of water from the Vistula River. The selection of the best solution to this problem requires complex studies and investigations. THE LOWER VISTULA The water resources of the Lower Vistula are enriched considerably by tributaries, the Narew and the Bug. For centuries it has constituted an important axis of economic development of the country. The relatively deep valley, convenient for the building of dams,and the considerable hydropower development potential of the Lower Vistula, has attracted the interest of Polish hydraulic engineers for a long time. The studies being carried out indicate that the building of a series of barrages from Warsaw to the mouth of the river is an economic undertaking. Apart from the power generated, the scheme would create an excellent waterway, provide several bridges over the river, create several artificial lakes, as well as introducing convenient conditions for water intakes and cooling systems of the thermal power stations. There is only one barrage built at present. It is located at Wfodawek. Among the tributaries of the Lower Vistula the Narew and the Bug deserve the greatest attention. The main problems linked with these rivers are the large quantity of water needed for the intense agricultural development in the region and the flood control of this area.
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