T h e use of analog and
digital computers in hydrology
Proceedings of the Tucson Symposium
L'utilisation des calculatrices analogiques et des ordinateurs
f^TI i\\T(\"TOI 0 0 * 1 (* Actes du colloque de Tucson
Volume 1
A contribution to the International Hydrological Decade U n e contribution à la Décennie hydrologique internationale
IASH/AIHS-Unesco
Braamstraat 61 (rue des Ronces), Gentbrugge (Belgium) and Unesco, Place de Fontenoy, 75 Paris-7e
Printed by Imprimerie Ceuterick, Louvain (Belgium) Publié en 1969 conjointement par
l'Association internationale d'hydrologie scientifique (secrétaire : L . J. T I S O N ) Braamstraat 61 (rue des Ronces), Gentbrugge (Belgique)
et par l'Unesco, place de Fontenoy, 75 Paris-7e
Imprimerie Ceuterick, Louvain (Belgique)
© Unesco/IASH 1969 Printed in Belgium S C . 6 8 / X X . 3 / A F
The International Hydrological Decade ( I H D ) 1965-1975 was launched by the thir- teenth session of the General Conference of Unesco to promote international co-operation in research and studies and the training of specialists and technicians in scientific hydrol- ogy. Its purpose is to enable all countries to m a k e a fuller assessment of their water resources and a more rational use of them as m a n ' s demands for water constantly increase in face of developments in population, industry and agriculture. In 1968 National Committees for the Decade had been formed in 100 of Unesco 's 125 M e m b e r States to carry out national activities and to contribute to regional and international activities within the programme of the Decade. The implementation of the p r o g r a m m e is supervised by a Co-ordinating Council, composed of twenty-one M e m b e r States selected by the General Conference of Unesco, which studies proposals for developments of the pro- g r a m m e , recommends projects of interest to all or a large number of countries, assists in the development of national and regional projects and co-ordinates international co- operation.
Promotion of collaboration in developing hydrological research techniques, diffusing hydrological data and planning hydrological installations is a major feature of the pro- g r a m m e of the I H D which encompasses all aspects of hydrological studies and research.
Hydrological investigations are encouraged at the national, regional and international level to strengthen and to improve the use of natural resources from a local and a global perspective. The p r o g r a m m e provides a means for countries well advanced in hydrolog- ical research to exchange scientific views and for developing countries to benefit from this exchange of information in elaborating research projects and in implementing recent developments in the planning of hydrological installations.
A s part of Unesco's contribution to the achievement of the objectives of the I H D the General Conference authorized the Director-General to collect, exchange and disseminate information concerning research o n scientific hydrology and to facilitate contacts between research workers in this field. T o this end Unesco has initiated two collections of publica- tions "Studies and Reports in Hydrology" and "Technical Papers in Hydrology".
T h e collection "Studies and Reports in Hydrology" is aimed at recording data collected and the main results of hydrological studies undertaken within the framework of the Decade as well as providing information on research techniques. Also included in the collection will be proceedings of symposia. Thus, the collection will comprise the compila- tion of data, discussion of hydrological research techniques and findings, and guidance material for future scientific investigations. It is hoped that the volumes will furnish material of both practical and theoretical interest to hydrologists and governments parti- cipating in the I H D and respond to the needs of technicians and scientists concerned with problems of water in all countries.
Unesco and the I A S H have together undertaken the implementation of several important projects of the I H D of interest to both organizations, and in this spirit a number of joint U n e s c o - I A S H publications are envisaged.
Préface
L a Décennie hydrologique internationale ( D H I ) 1965-1975 a été ouverte par la Conférence générale de l'Unesco à sa treizième session pour favoriser la coopération internationale en matière de recherches et d'études et la formation de spécialistes et de techniciens de l'hydrologie scientifique. S o n but est de permettre à tous les pays d'évaluer plus complè- tement leurs ressources en eau et de les exploiter plus rationnellement, les besoins en eau augmentant constamment par suite de l'expansion démographique, industrielle et agricole. E n 1968, des comités nationaux pour la Décennie ont été constitués dans 100 des 125 États m e m b r e s de l'Unesco en vue de mener à bien les activités nationales et de participer aux activités régionales et internationales dans le cadre du p r o g r a m m e de la Décennie. C e p r o g r a m m e est exécuté sous la direction d'un Conseil de coordination composé de vingt et un États membres désignés par la Conférence générale de l'Unesco, qui étudie les propositions d'extension d u programme, r e c o m m a n d e l'adoption de projets intéressant tous les pays ou un grand n o m b r e d'entre eux, aide à la mise sur pied de projets nationaux et régionaux et coordonne la coopération à l'échelon international.
L e p r o g r a m m e de la D H I , qui porte sur tous les aspects des études et des recherches hydrologiques, vise essentiellement à développer la collaboration dans les domaines delà mise au point de techniques de recherches hydrologiques, de la diffusion des données hydrologiques et de l'organisation des installations hydrologiques. Il encourage les en- quêtes nationales, régionales et internationales visant à accroître et à améliorer l'utilisation des ressources naturelles, dans une perspective locale et générale. Il offre la possibilité aux pays avancés en matière de recherches hydrologiques d'échanger des idées, et aux pays en voie de développement de profiter de ces échanges d'informations pour l'élabo- ration de leurs projets de recherche et pour la planification de leurs installations hydrolo- giques selon les derniers progrès réalisés.
Pour permettre à l'Unesco de contribuer au succès de la D H I , la Conférence générale a autorisé le Directeur général à rassembler, échanger et diffuser des renseignements sur les recherches d'hydrologie scientifique et à faciliter les contacts entre chercheurs de ce domaine. A cette fin, l'Unesco publie deux nouvelles collections : «Études et rapports d'hydrologie» et «Documents techniques d'hydrologie».
L a collection «Études et rapports d'hydrologie» a pour but de présenter les données recueillies et les principaux résultats des études hydrologiques effectuées dans le cadre de la Décennie, et de fournir des renseignements sur les techniques de recherche. O n y trou- vera aussi les Actes de colloques. Cette collection comprendra donc des données, l'exposé de techniques de recherches hydrologiques et des résultats de ces recherches, et une documentation pour des travaux scientifiques futurs. O n espère que ces volumes fourni- ront aux hydrologues et aux gouvernements qui participent à la D H I des matériaux d'un intérêt tant pratique que théorique et qu'ils répondront aux besoins des techniciens et des h o m m e s de science qui s'occupent, dans tous les pays, des problèmes de l'eau.
L ' U n e s c o et l ' A I H S ont entrepris de réaliser conjointement plusieurs projets impor- tants de la D H I qui les intéressent l'une et l'autre; dans cette perspective, elles ont prévu un certain n o m b r e de publications U n e s c o - A I H S .
Table des matières
T O M E I — V O L U M E ]
Foreword / Avant-propos xi/xn I. A N A L O G U E COMPUTING TECHNIQUES
E . V A R R Ó K (Hungary). — Electrolytic tank type models for predicting the position of the
groundwater table and the loss of river discharges 3 J. NÈMEC (Czechoslovakia). — Simultaneous use of an analogue single-purpose electronic
computer and a physical model of a watershed 10 T . W . A N D E R S O N (United States). — Electrical-analog analysis of the hydrologie system
in Tucson basin, Arizona 15 J.P. R I L E Y , D . G . C H A D W I C K and E . K . ISRAELSEN (United States). — Watershed simulation
by electronic analog computer 25 V . V . D . N A R A Y A N A and J.P. R I L E Y (United States). — Application of an electronic analog
computer to the evaluation of the effects of urbanization on the runoff characteristics of
small watersheds 38 E . K . ISRAELSEN and J.P. R I L E Y (United States).—Application of an electronic analog
computer to a study of water resources management 49 I.I. K R A S H I N and D . I . P E R E S U N J K O (USSR). — Application of analogue computers for pre-
dicting the ground water regime of artesian basins under conditions of their development 59 A . G . L E V I N ( U S S R ) . — Specialized analog computers for hydrological calculations and
forecasts 67 K . K h . H O V S E P I A N , R . S. AVETISIAN and A . G . N A Z A R I A N ( U S S R ) . — The solution of direct
and inverse problems of outlet waves spreading o n analogue computers 73 G . G . O K R O A S H V I L I and G . G . S V A N I D Z E ( U S S R ) . — The M A R analog computer for
modelling hydrological series by the Monte Carlo method 81 D . L . S O K O L O V S K Y and I. A . S H I K L O M A N O V ( U S S R ) . — Estimation of floods with the aid
of analogue computers 87 P. K U M A R A S W A M Y (India). — N e w approach suggested for design of electrical analog
computers for groundwater flow studies 95
B. K O R D A S (Pologne). — Étude par analogie de l'influence d'une crue sur l'évolution
d'une nappe phréatique placée à proximité d'une rivière 112
II. D I G I T A L C O M P U T I N G T E C H N I Q U E S
G . A . S C H U L T Z (Germany). — Digital computer solutions for flood hydrograph prediction
from rainfall data 125 M . K O Z Á K (Hungary). — Determination of the runoff hydrograph on a deterministic basis
using a digital computer 138 J. D E R I (Hongrie). — Determination of the quantity of water to be stored by digital
computers 152 M . S U G A W A R A (Japan). — O n a method of flood forecasting using a digital computer
connected with a weather radar 161 M . S U G A W A R A (Japan). — A comparative analysis of digital and analog computers as to
their effectiveness in solving runoff analysis 170 V . P I E T R A R U (Roumanie). — Sur la solution des problèmes d'infiltration à l'aide des ordi-
nateurs électroniques 175 R . AMAFTIESEI and F. I O N E S C U (Romania). — S o m e remarks on the use of digital computers
and hydraulic methods for flood routing and flood forecasting problems 189 D . L . C H E R Y (United States). — The assistance of digital computers in hydrologie research
and its consequences 198 T . D . STEELE (United States). — Digital-computer applications in chemical-quality studies
of surface water in a small watershed 20.1 E . M . W E B E R , H . J . PETERS and M . L . F R A N K E L (United States). — California's digital
computer approach to groundwater basin management studies 215 D . K L E I N E C K E (United States). — Preparation, verification and use of a digital groundwater
simulation program 224 D . G . D E C O U R S E Y (United States). — Applications of computer technology to hydrologie
model building 233 J. Y . K W A N , J. P. R I L E Y and R . A . AMISIAL (United States). — A digital computer program
to plot isohyetal maps and calculate volumes of precipitation 240 G . G . S V A N I D Z E ( U S S R ) . — Use of digital computers for mathematical modelling of
hydrological processes 249 L. R . B E A R D (United States). — Hypothetical flood compution for a stream s y s t e m . . . . 258
G . S. R I S C H (United States). — Application of computerized operations research technique
for optimum economic sizing of the Middle Fork Eel River project 268 K . B O D Y , G . E R D Ô S and K . S Z E S Z T A Y (Hungary). — S o m e problems of streamflow forecasts
based on information theory 280
R. J. C . B U R N A S H and R . L . FERRAL (United States). — A n operational system for computer
preparation of short-term river forecasts on the north coast of California 300 J.G. W E L S H , H . M . FRAZIER and P. Bock (United States). — Computational analyses of
moisture flux over North America 307 V . P . S C H E R M E R H O R N and D . W . K U E H L (United States). — Operational streamflow fore-
casting with the S S A R R model 317 D . M . R O C K W O O D (United States). — Application of streamflow synthesis and reservoir
regulation—"SSARR"—program to the lower Mekong River 329
views of Unesco.
Le choix et la présentation du contenu de cet ouvrage et les opinions qui s'y expriment n'engagent que la responsabilité de l'auteur (ou des auteurs), et ne correspondent pas nécessairement aux vues de l'Unesco.
The use of analog and digital computers in hydrology is one of the areas of modern hydrol- ogy in which a great advance has been m a d e over the past ten years or so. T h e Coordi- nating Council for the International Hydrological Decade at its first session established several projects related to this subject: " Application of mathematical models for runoff prediction in various climatic and physiographic regimes"; "Automatic processing of hydrological data " ; " Methods of calculating and forecasting the regime of subterranean waters with the aid of mathematical statistics and computing devices".
In order to bring together the analog and digital specialists and the practising hydrolo- gists and to give each an opportunity to become acquainted with the other's views and problems, the Co-ordinating Council recommended the organization of this Symposium, one of the most important in the framework of the I H D
In keeping with the general policy of the I H D , the Symposium covers both applications to surface and groundwater studies and their interrelationships.
The presented papers consider the following aspects of the problem:
1. Analogue Computing Techniques;
2. Digital Computing Techniques;
3. Digital Data Handling Techniques;
4. Hybrid Computing Techniques;
5. Comparative Studies of Computing Techniques ; 6. Mathematics of Computing Techniques.
S o m e papers (Groups 5 and 6) discuss the general theoretical and philosophical aspects of modelling and computers, but most of them describe applications (three first groups).
The papers of the first series are mostly in relation with problems on groundwater, but some of them consider more specific problems: the influence of m a n is namely the subject of some of these papers. In the second group, papers are mostly in relation with problems on surface waters: floods, runoff, precipitation, water quality, etc.
The different fields of hydrology are represented in the third group.
The Symposium was organized at Tucson, Arizona, by I A S H , in cooperation with Unesco, the American Geophysical Union, the U . S. National Committee for the I H D and the University of Arizona.
The joint publication by the International Association of Scientific Hydrology and Unesco of the papers presented at the Symposium is another example of the fruitful cooperation that has been established between the I A S H , Unesco and the National Committees of the I H D
Avant-propos
L'emploi de calculatrices analogiques et numériques en hydrologie est l'un des domaines de l'hydrologie moderne dans lesquels de grands progrès ont été accomplis depuis une dizaine d'années. A sa première session, le Conseil de coordination de la Décennie hy- drologique internationale a élaboré plusieurs projets en ce domaine : «Utilisation de modèles mathématiques pour la prévision des débits dans diverses conditions climatiques et géomorphologiques», «Traitement automatique des données hydrologiques», «Calcul et prévision d u débit des eaux souterraines à l'aide des statistiques mathématiques et d'autres moyens de calcul».
C'est pour réunir des spécialistes du calcul analogique et numérique et des praticiens de l'hydrologie, et donner à chaque groupe l'occasion de connaître l'opinion et les problèmes de l'autre, que le Conseil de coordination a recommandé l'organisation de ce colloque, l'un des plus importants qui aient été convoqués dans le cadre de la D H L
Conformément à la politique générale de la D H I , ce colloque a porté sur les applications des techniques analogiques et numériques aux études sur les eaux de surface et les eaux souterraines et leurs interrelations.
Les communications présentées traitent les aspects suivants des problèmes : 1. Techniques des appareils par analogie;
2. Techniques des calculatrices pour prévision;
3. Techniques des ordinateurs;
4. Techniques hybrides;
5. Étude comparative des appareils des deux types;
6. Mathématiques des techniques de prévision.
Quelques-unes des études (dans les groupes 5 et 6) considèrent l'aspect général théorique et philosophique de l'emploi des modèles et des calculatrices, mais la plupart des c o m m u - nications présentent des applications (dans les groupes 1, 2 et 3). Les études de la première série se rapportent surtout aux problèmes des eaux souterraines, mais quelques-unes de ces communications considèrent des problèmes plus spécifiques c o m m e notamment l'action de l ' h o m m e .
D a n s le second groupe, les études se rapportent surtout aux problèmes des eaux de surface : crues, écoulement superficiel, précipitations, qualité des eaux, etc.
Par contre, les divers domaines de l'hydrologie sont représentés dans le troisième groupe.
Le colloque a été organisé à Tucson (Arizona) par l ' A I H S , en coopération avec FUnesco, l'American Geophysical Union, le Comité national des États-Unis pour la D H I et l'Université de l'Arizona.
L a publication conjointe par l'Association internationale d'hydrologie scientifique et l'Unesco des communications présentées à ce colloque est u n nouvel exemple de la fruc- tueuse coopération qui s'est établie entre l ' A I H S , l'Unesco et les comités nationaux pour
la DHL
ANALOGUE COMPUTING
TECHNIQUES
the groundwater table and the loss of river discharges
E . V a r r ó k , Research Institute for W a t e r Resources D e v e l o p m e n t Budapest, H u n g a r y
R É S U M É : L'article traite de prévision des niveaux des nappes phréatiques longeant les lits des cours d'eau à l'aide d'un modèle d'analogie électrique et d'un dispositif automatique.
O n a envisagé la construction d'usines hydroélectriques sur le D a n u b e entre les points kilo- métriques 1795-1868. L e tronçon d u fleuve en question suit la crête d'un cône de déjection, le fleuve exerce par conséquent une influence sensible sur le régime des eaux phréatiques des deux rives. Sur la rive droite la superficie de la zone d'influence se chiffre par à peu près de 800 k m2
(fig. 1). L e modèle d'analogie électrique de la couche perméable d'une épaisseur variable de 50 à 300 m de cette zone d'influence fut construit à l'échelle 1:25000. Le substratum imperméable fut formé en résine synthétique (figs. 2-4). O n tenait compte de la modification future de la pente superficielle des cours d'eau qui limitent ou traversent la région considérée, ainsi que l'anisotropie du sol. L e modèle permet la prévision du niveau de la nappe phréatique, des débits infiltrés dans le canal de drainage, et de la perte totale du débit du fleuve (fig. 5).
U n appareil automatique accouplé au modèle repère et suit les lignes équipotentielles choisies et les dresse à l'échelle 1:1 sur une feuille de papier (fig. 6-8).
S U M M A R Y : Groundwater levels o n riverside areas have been predicted by electrolytic tank models and automatic devices.
O n the 73 k m long stretch of the D a n u b e river between river stations 1795 and 1868 k m hydro- electric development has been contemplated. Here the river flows on the ridge of an alluvial depo- sit, and influences the water table on both sides. O n the right side an area of about 800 square kilometers is influenced (fig. 1). T h e gravel aquifer overlying the impermeable bottom is from 50 to 300 metres deep. T h e above area was reproduced in an electrolyte type model to 1:25 000 scale, with the bottom relief m a d e of synthetic resin (figs. 2 to 4). T h e slope of the water surface in the rivers bordering and crossing the area, and also the anisotropy of the aquifer were taken into consideration. This model w a s used to predict the position of water table, its depth under the terrain, the discharge filtering into the draining canals a n d the total seepage loss from the river (fig. 5).
For models of this type an automatic equipment has been developed (figs. 6 to 8) to find the preselected equipotential lines and follow them automatically, tracing their path o n an adjacent drawing board to the scale of the model.
M O D E L TESTS
Laboratory tests w e r e carried out in preparation for the hydroelectric development of the D a n u b e reach forming the border b e t w e e n H u n g a r y a n d Czecho-Slovakia. T h e tests and the e q u i p m e n t used are described in the present paper.
A h e a d of r o u n d 2 0 metres can b e developed over this stretch, w h e r e the river flows o n the ridge o f a n alluvial deposit, over a gravel layer o f great thickness a n d influences the g r o u n d w a t e r table u n d e r a large area.
A s regards the m o v e m e n t of u n d e r g r o u n d waters the bed of the D a n u b e f o r m s a divide;
the g r o u n d w a t e r m o v e s practically independently o n the right a n d left sides.
T h e investigations to b e described are concerned with the area o n the right-hand side of the D a n u b e (fig. 1). T o the west this area is b o u n d e d b y the l o w hills of the Parndorf Plateau a n d L a k e Ferto, to the south b y the H a n s á g C a n a l a n d the small R a b e a river.
This territory is crossed in its northern part b y the gate-controlled M o s o n D a n u b e branch. T h e terrain slopes moderately f r o m N W to S E . T h e soil is stratified; the thin
surface layer of silt is underlain by a sandy gravel aquifer which extends in s o m e places to great depths, as shown by the isometric lines of figure 1. In view of the fact that the toplayer is only of an insignificant thickness these lines represent also the depth of the impermeable bottom below the terrain.
F I G U R E 1
T h e development of the power potential of this D a n u b e reach will change the hydro- logical parameters of the river and the m o v e m e n t of groundwater under adjacent areas significantly so that the expected n e w situation cannot be forecasted on the basis of available observation data. A s the expected position of the groundwater table plays an important role in the relative evaluation of different project alternatives an approach of another kind was necessary for predicting it. Since d a m m i n g tends to equalize the flow of the river, the actual movement of groundwater m a y be approximated by steady flow conditions. T h e acceptance of this approximation permits the application of electric analogy.
In constructing the electric analogy model the variable thickness, anisotropy and boundaries of the aquifer, the slope of water surface, the form and dimensions of the river beds and lakes, bordering and crossing the area in question had to be taken into consideration. T h e model was built to the scale 1:25,000.
A pan of non-conducting material was m a d e with variable depth, corresponding to the variable thickness of the aquifer. The model under construction is shown in figure 2 . T h e paper strips of variable width were set on the contour lines. A layer of synthetic resin was poured between the strips u p to the height determined by the strips. The model, partly filled resin is shown in figure 3. T h e river beds were m a d e of isolator sheets covered in sections with copper o n one side. S o m e of these river-models are shown in figure 4 . These copper electrodes are on the lower face of the sheets and contact the surface of the electrolyte. Their vertical position was fixed by frames m a d e of Lucite. The slope of water surface w a s approximated by gradually reduced voltage. T h e canals which serve to prevent the extreme rise of groundwater table were also reproduced in the model.
Tap-water w a s used in the model as electrolyte. T h e highest voltage w a s 45 V , the frequency 500 H z . T h e equipotential lines were determined o n the surface of the electrolyte.
FIGURE 2
FIGURE 3
The equipotential lines obtained by the tests are presented in figure 5, and correspond to the contour lines of the groundwater table. T h e rate of seepage from the river bed could hereafter be computed on the basis of the D A R C Y - l a w with the k n o w n values of
iient, thickness of aquifer and the coefficient of permeability. T h e isometric lines
FIGURE 4
If Levtí of ground water table, elevation meter t forecasted}
'¿^.Deptf» at ground water table under the surface, merer (forecasted)
FIGURE 5
indicating the position of the groundwater table below the terrain were obtained as the difference of contour lines of the terrain and the groundwater table.
N u m e r o u s additional detail problems were solved with the help of electric analogy models: estimation of seepage intercepted by the canals and moving toward the protected land, the velocity of seepage emerging in the canal bed, the extent of an occasional
scouring of soil (the probable distortion of bed) and the drawdown surface around the construction pit, etc.
F r o m the result obtained for mean flow conditions it was concluded that the total seepage loss towards the right-hand side over the river stretch under consideration is 96 cu m/sec, corresponding to 6-7% of the m e a n river discharge. O f this total 15 cu m/sec feeds the groundwater, 45 and 27 cu m/sec are intercepted respectively by the two canals while 9 cu m/sec are lost by seepage under the downstream structure.
These investigations—involving the construction of the model, measurements and evaluation—were completed in three months.
THE MEASURING DEVICE
Electric analogy models have been used frequently for solving problems associated with the movement of fluids in porous media which can be solved not at all or with crude approximation only, by analytical methods.
Owing to the large number of similar problems and for reducing the time of measure- ments as well as for increasing the accuracy of the method, an automatic measuring device has been developed; the block diagram of which is shown in figure 6. The principal parts of the equipment are: a casing with electronic and supply units, transportable switch board, a table for models and a drawing board (figs. 7 and 8).
F I G U R E 8
A bridge with a moving carriage travels over the table and the drawing board. T h e probe is mounted on the carriage and it can m o v e in the X and Y directions and revolve about its vertical axis.
The operations of measurement are as follows:
- T h e probe is lowered until it immerses into the electrolyte.
- T h e desired percentage of voltage is adjusted.
- The switch of the " A N G U L A R S C A N N I N G " circuit is set, whereupon the probe revolves into a position, tangential to the equipotential line which crosses its m o m e n - tary position.
- The switch of the " L O C A T I O N S C A N N I N G " circuit is set, whereupon the probe starts to m o v e , and stops over the desired equipotential line.
- The switches of the circuits " M A P P I N G " and " D R A W I N G " are set, whereupon the probe follows the curve correcting its tangential position continuously and automatic- ally. Its path is traced on the drawing board to the scale 1:1.
The probe m a y be located by manual controls over any desired point of the model and the approximate end point of a particular line can be found; the accurate setting is accomplished automatically.
The probe traces the curves with the velocity of 0,5 cm/sec. The relative m e a n error of repeated scanning of a particular potential-value (converted to voltage and related to the total voltage) is 0,5 %0. T h e reliability of individual potential-steps depends o n the accuracy of the standard resistances. Those mounted into the device deviate from their nominal value by not more than ± 1%. By a suitable combination of resistances the accumulation of regular errors was avoided and the deviation was less than 1% at any division. A remarkable feature of the device is that the reror is slightly greater w h e n moving parallel to the coordinate axis, and the error decreases w h e n the probe follows a curve.
At the beginning of regular use minor irregularities were encountered in the electronic units of the automatic device. After the defects were corrected the equipment has operated without any trouble for more than 300 hours by n o w .
If justified by a further increase in the number of similar assignments, the equipment can be developed in a w a y to permit the whole net of equipotential and streamlines to be traced in a single model, without constructing its inverted counterpart.
computer and a physical model of a watershed
Professor Jaromir N ë m e c B . E n g . , C . Sc. '
H e a d , Department of Water Resources, Prague Agricultural University
SYNOPSIS: In order to be able to analyse the time element of flood hydrographs of surface runoff, use is made of a single-purpose electronic R C computer containing six R C units with a n o n - linearity element. The time lag constants of the computer are being selected on the basis of measured time lags from a physical scaled model of an experimental watershed o n which the floods are modelled with the help of a sprinkler.
The resulting hydrographs from the analogue computer and the physical model are compared, different intensities and different durations of rain being used.
The study is directed toward an interconnexion of the analogue computer and the physical model.
R É S U M É : Pour analyser l'élément du temps dans les hydrogrammes de l'écoulement de surface pendant les crues, un ordinateur électronique aux éléments R C est employé. Cet ordinateur, construit spécialement pour ce but, contient six unités R C avec une composante non-linéaire.
Les constantes du retardement de l'ordinateur sont sélectionnées d'après les retardements mesurés sur un modèle physique à l'échelle d'un bassin expérimental. Les crues sont simulées sur le modèle à l'aide d'un appareil de pluie artificielle.
Les hydrogrammes provenant de l'ordinateur et ceux du modèle physique, sont comparés, en tenant compte des différentes durées et intensités de la pluie.
L'étude s'efforce d'établir une interconnection entre l'ordinateur et le modèle physique.
1. Recent trends in the development of analysis a n d synthesis of the hydrograph for purposes of flood computation a n d forecasting, sometimes k n o w n as "parametric hydrology", have m a d e m o r e and m o r e evident the necessity of using models of hydro- logical processes ( N ë m e c , 1968). T h e data from natural basins does not often yield the needed detailed time and space information, although they will always remain the ultimate touchstone for verifying the proposed computation schemes. In our previous studies ( N ë m e c , 1967a, b) it w a s ascertained that the hydrograph analysis a n d synthesis m a y be considerably advanced by detailed examination of the time element of hydrograph formation.
2 . T h e electronic analogue computer, used for flood routing, is a very convenient tool for such examination, mainly due to the ease with which a multitude of cases can be reproduced a n d alternatively varied. T h e use of such a computer for this purpose w a s reported exhaustively be several authors (Ven T e C h o w , 1964; Kalinin G . P . , Levin A . G . , 1960; Shiklomanov A . , 1964) and also by us ( N ë m e c - M o u d r y , 19676).
3. O u r laboratory in the Water Resources Department of the Prague Agricultural University has, since April 1968, been working with a n e w non-linear R C single-purpose computer, the P R - 4 3 , using six R C units and a n automatic as well as m a n u a l input. T h e computer P R - 4 3 w a s designed by the Hydrometeorological Research Centre of the U S S R
1. Presently on leave of absence and serving as Chief, Division of Hydrometeorology, World Meteorological Organization, Geneva, Switzerland.
Hydrometeorological Service and is produced commercially in the U S S R . Its components are:
(a) Automatic input unit ; (6) M a n u a l input unit ; (c) C o m p u t i n g unit ;
(d) Precision tuning of time constants unit ; (e) Automatic time constant switch ; (/) Scale selection unit ;
(g) T w o registration units (potentiometers) for input a n d output.
T h e modelling principle in each R C unit is based o n the analogy of the following equation of approximated unsteady flow in o n e reach of the channel (or basin):
6Î = « ( l - e -
( , / t ))
where:
Q, discharge at the outflow of the reach;
q inflow (input) in the first reach or intensity of the rainfall excess of uniform intensity ; T "lag time" parameter of the reach;
with the equation of electric flow in a n R C unit:
U, = £(l-e
_,/RC)
where:
Ut output voltage of a n R C unit;
E input voltage of a n R C unit ; R resistance of the unit ; C capacitance of the unit.
It appears from this analogy that the "lag-time" x is represented b y the value R C T h e resultant "kernel" function (the instantaneous unit graph or time-area curve) is (Kalinin, 1964):
h{t)=—^— f - Y ' V ' "
T ( H - 1 ) W
where:
h(j) ordinate of the time-area curve;
n n u m b e r of transformation reaches ; x, t as above.
T o c o m p u t e the design hydrograph from a basin, the rain excess for intervals shorter than the concentration time and the unit hydrograph or the standard time-area curve m u s t be k n o w n . T h e parameter x can b e either selected as a constant for each reach or it can be variable x =f{Q) =/"(/). In this last case the best approach in computing the values of x for each reach is to proceed b y trial a n d error a n d c o m p u t e the right values using a " l o o p " approach. T h e computer P R - 4 3 is particularly suitable for this purpose 4 . In order to examine the influence of the different elements of the input a n d basin o n the hydrographs, the input data for the analogue computer were taken from a scaled physical m o d e l of a watershed. This m o d e l has three components:
(a) Rain simulator of the b o x type;
(b) 1:2000, 1:1330 a n d 1:1000 models of a small experimental basin;
(c) Measuring instrumentation.
The description of this type of model and the principles of physical models have been given in our previous work (Nëmec, 1967a; N ë m e c , 1968) and by others (Ven T e C h o w , 1967).
F I G U R E 1
5. O n figure 1 there are three hydrographs of runoffs yielded from the physical model 1:2000 with rains of the same duration of 20 sec and different intensities, namely l , 6 7 m m m i n_ 1, l , 1 4 m m m i n- 1 and 0 , 7 9 m m m i n- 1. The production of each hydro- graph was repeated twice with practically the exact same results. F r o m figure 1 it appears that the intuitive conclusion, which represents one of several reservations expressed about the unit hydrograph method is quite well-founded. This particular reservation is that rains of different intensities cannot produce the same distribution of volumes of the hydrograph and that the time of occurrence of m a x i m u m discharge cannot be the same for all of them. In fact, the difference of time of occurrence for the rain of 1,67 and 0,79 m m m i n- 1 differs by 2 0 % . The distribution of volumes of runoff, particularly for the falling limb of hydrograph is equally different for all three hydrographs.
6. Despite these discrepancies, a U . H . was derived from the three runoffs and it was compared with the hydrographs derived from a unitary input of the same duration to the analogue computer with several values of the parameters T . It was ascertained that the
closest similarity was achieved for a value of x = 4 seconds or for x„ = n. T = 24 seconds (see fig. 2).
The shape of the hydrograph produced by the analogue with x = const w a s fairly similar to that derived by the method of the unit hydrograph. B y comparison of hydro- graphs with different values for T it w a s also ascertained that the sensitivity of the shape of hydrograph on the value of x is less than that provoqued by the changes of the rain duration and intensity.
F I G U R E 2
7. These facts m a y permit us to suggest a first important conclusion. If the principle of unit hydrograph is used in any flood forecasting or design computation scheme, the type of I . U . H . (kernel function, area-time curve) is of less importance than the evaluation of input (rainfall intensity and infiltration losses).
8. T h e w o r k on interconnexion of the physical model with the analogue computer is continuing n o w to ascertain the characteristics of nonlinearity and functions of x in connexion with physical elements of the model basin and of the input.
ACKNOWLEDGMENTS
The author wishes to acknowledge his gratitude to his collaborators from the Water Resources Department of the Prague Agricultural University and in particular Professor M . M o u d r y and Assistant Professor F . Hrádek for the supervision and execution of experiments in the laboratory of the Department.
REFERENCES
K A L I N I N , G . P . , and L E V I N , A . G . (1960): Use of electronic analogue computers for forecasting of flood resulting from rainfalls, Meteorología i Gidrologia, N o . 12, Leningrad.
N Ë M E C , J., and M O U D R Y , M . (1967a): Peak discharge and time of concentration relation to rain intensity investigated by physical models of watersheds, Proceedings, International Symposium on Floods and their Computation, Leningrad.
N Ë M E C , J., and M O U D R Í , M . (19676): A contribution to analogue and physical modeling of surface runoff process in small basins, Proceedings, International Hydrology Symposium, Fort Collins, Colorado.
N Ë M E C , J. (1968): Models in Hydrology and physical models of surface runoff in basins, Gidrologia i Meteorología, N o . 4, Leningrad.
S H I K L O M A N O V , I. A . (1964): Use of electronic analogue computer for computation of flood hydrographs, Proceedings, Leningrad Hydrometeorological Teaching Institute, N o . 26, Leningrad.
V E N T E C H O W (1964): Handbook of Applied Hydrology, Sections 14 and 29, M c G r a w Hill & Co., N e w York.
V E N T E C H O W (1967): Laboratory study of watershed hydrology, Hydraulic Engineering Series, N o . 14, University of Illinois, Urbana.
in Tucson basin, Arizona, U . S . A .
1T . W . A n d e r s o n2
A B S T R A C T : T h e water supply for the area in the Tucson basin, Arizona, is derived entirely from ground water, and pumpage has caused water-level declines of as m u c h as 60 feet. A n electrical- analog model of the hydrologie system in the Tucson basin area was constructed to provide a hydrologie tool for determining the effects of possible ground-water management schemes.
Periodic water-level data, p u m p a g e , and transmissibility constants were compiled to allow the construction of the primary model. Preliminary analyses of the model showed where additional data or modifications in model design were needed. T h e final design, the most precise representa- tion of the actual data, was used to predict ground-water levels in 1985, assuming that p u m p a g e is stabilized at the present rate and distribution.
R É S U M É : L'alimentation en eau pour la région du bassin de Tucson, Arizona, se fait uniquement par eau souterraine et les pompages ont provoqué u n rabattement du niveau de l'eau d'au moins 60 pieds. U n modèle électrique du système hydrologique de la région d u bassin de Tucson a été construit pour fournir un instrument pour déterminer les effets de projets possibles d'aménagement des eaux souterraines. Les données sur les variations périodiques des niveaux d'eau, le p o m p a g e et les constantes de transmissibilité ont été rassemblées pour permettre la construction de ce modèle primaire. Des analyses préliminaires du modèle ont montré où des données additionnelles ou des modifications du plan d u modèle étaient nécessaires. Le projet final, la représentation la plus précise des données actuelles, a été utilisé pour prédire les niveaux de l'eau souterraine en 1985 en supposant que les pompages seraient stabilisés à leur taux et distribution actuelle.
INTRODUCTION
T h e ground-water reservoir provides the entire water supply for the Tucson basin, Ariz.
In recent years an average of 165,000 acre-feet of water per year has been withdrawn from the reservoir—an a m o u n t that is in excess of the natural recharge. T h e result has been large declines in water levels in the area. T h e economic development of this area is dependent u p o n a reliable source of water, and this study w a s undertaken to develop an electrical-analog model of the hydrologie system that could be used to predict water-level declines and other hydrologie effects caused by m a n a g e m e n t of the aquifer system.
T h e Tucson basin is an elongated northwest-sloping plain bounded by mountains on the east and west (fig. 1). T h e basin is 50 miles long, from 4 to 20 miles wide, and has an areal extent of about 750 square miles. T h e climate is semiarid, and the major drainages in the basin—the Santa Cruz River and Rillito Creek—are ephemeral streams that drain to the northwest.
The aquifer system consists of unconsolidated and semiconsolidated alluvial deposits ranging in size from gravel to clay. In the central part of the basin the deposits are m o r e than 2,000 feet thick. Along the flood plains of the Santa Cruz River, Rillito Creek, and their principal tributaries, younger deposits of unconsolidated sand and gravel overlie the thick alluvial deposits. T h e unconsolidated sand and gravel deposits are from 10 to about 100 feet thick.
1. Publication authorized by the Director, U . S . Geological Survey.
2. Hydraulic engineer, U . S . Geological Survey, Tucson, Arizona, U . S . A .
E X P L A N A T I O N
- 2 2 0 0 -
Measured altitude of water table in 1940 (contour interval, 100 and 500 feet;
datum is m o a n sea level) 2500
Altitude of water table in 19^0, as determined from the analog model
(contour interval, 100 feet;
datum is m e a n sea level)
M a p of United States of America, showing city of Tucson
and Slate of Arizona
F I G U R E 1. Altitude of the water table based on model data and field data, 1940
T h e analog-model design is based o n the similarity between the flow of ground water and the flow of electricity. The resistors in the model represent the transmissibility, and the capacitors represent the storage coefficient of the aquifers.
In this study the model analysis consisted of two phases—steady-state or equilibrium condition and transient or time-changing condition. T h e 1940 ground-water flow condi- tions were assumed to be near equilibrium in most of the ground-water system. T h e equilibrium conditions were simulated to determine the rates of recharge occurring in the basin prior to extensive development of ground water. T h e transient condition duplicated the effects of increased ground-water withdrawal and changes in recharge on the water levels. T h e electrical-analog model is assumed to be a workable pragmatic tool w h e n the ground-water declines synthesized by the model correspond to those measured in the field. After the analogy between the electrical and hydrologie systems has been proven, the m o d e l can be used to predict future water levels using any possible withdrawal- recharge program.
T h e analog-model analysis of the ground-water system is but one phase of the overall study of the hydrologie system currently being conducted by the U . S. Geological Survey in cooperation with the Bureau of Reclamation, the city of Tucson, and the University of Arizona.
HYDROLOGIC SYSTEM
T h e ultimate source of all water in the Tucson basin is from precipitation in the upper Santa Cruz drainage basin. Water enters the ground-water reservoir through infiltration from streamflow, as underflow from adjacent basins, or as return flow from irrigation water applied to the agricultural land. Recharge from direct precipitation on the valley floor is negligible. G r o u n d water generally occurs under unconfined conditions in the Tucson basin, and depths to water range from 0 to about 500 feet. T h e configuration of the water table prior to ground-water development generally conformed to the shape of the land surface—the direction of flow was generally from south to north through the basin (fig. 1). Water leaves the ground-water reservoir as underflow, through évapo- transpiration, or as a result of pumping. The outlet for underflow is in the northwest end of the Tucson basin at Rillito ; here, the basin is only 4 miles wide.
M o r e than 240 aquifer tests have been conducted in the Tucson basin by personnel of the University of Arizona Agricultural Engineering Department in an attempt to define the areal pattern of transmissibility (fig. 2). Values of transmissibility determined from individual pumping tests ranged from 300,000 gpd (gallons per day) per foot to less than 5,000 gpd per foot. T h e storage coefficient of the aquifer was estimated to be 15 percent.
Development and utilization of the ground-water resources in the area began in about 1900. T h e pumpage in 1940 was 48,300 acre-feet and steadily increased to 170,000 acre- feet in 1954; after 1954, pumpage decreased slightly and more recently has increased again. T h e percentage of the total p u m p a g e used for agricultural purposes has decreased from an average of m o r e than 80 percent prior to 1954 to the present value of 54 percent.
T h e a m o u n t of municipal and domestic p u m p a g e has increased gradually since 1940 and generally parallels the rate of population growth in the area. Industrial d e m a n d has increased greatly since 1958 owing to the development of large copper mining operations on the west side of the basin.
T h e total p u m p a g e from 1940 through 1964 was 3.14 million acre-feet. A b o u t 60 percent of this water was withdrawn from storage. Three major cones of depression—(1) in the southern part of the basin, (2) in the metropolitan Tucson area, and (3) near the conflu- ence of Rillito Creek and the Santa Cruz River—have resulted from p u m p i n g (fig. 3).
In the southern part of the basin along the Santa Cruz River, water levels have declined as m u c h as 70 feet, and, at the present time, the rate of decline is about 5 feet per year
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E X P L A N A T I O N
Aquifer transmissibilities, in gallons per day per foot 180
Approximate boundary where transmissibility is greater than 180, 000
Approximate boundary where transmissibility is greater than 50, 000
Approximate boundary where transmissibility is less than 100
Arbitrary boundary, extent of modeled area
F I G U R E 2. Regional transmissibility pattern and extent of modeled area
E X P L A N A T I O N 30
Approximate boundary of area where pumpage was m o r e than 30, 000 acre-feet per square mile
Approximate boundary of area where pumpc\ge was m o r e than 10, 000 acre-feet per square mile
Approximate boundary of area where pumpage was m o r e than 5, 000 acre-feet per square mile
- 0
Approximate boundary of area where pumpage was m o r e than 100 acre- feet per square mile
50
Boundary of area where decline was m o r e than 50 feet
Boundary of area where decline was m o r e than 25 feet
in the center of the cone. Before 1958 the rate of decline was about 3 feet per year. T h e cone is elongated along the axis of the river and has resulted from pumping. T h e water is used for irrigation of agricultural land along the flood plain of the river channel. T h e m o r e recent increase in the rate of water-level decline is due to increased withdrawal for industrial use.
T h e cone in the metropolitan Tucson area is the result of pumping for municipal use.
This area is not affected greatly by surface flow and receives n o recharge by infiltration ; however, a small amount of recharge enters the area as underflow. T h e m a x i m u m water- level decline w a s about 64 feet from 1940 to spring 1965. Recent decline rates have been as m u c h as 3.5 feet per year.
T h e other major cone of depression is northwest of Tucson near the confluence of Rillito Creek and the Santa Cruz River. F r o m 1940 to 1965 the m a x i m u m decline w a s about 60 feet. T h e rate of decline was as m u c h as 6 feet per year from 1950 to 1955 but m o r e recently the decline has been only about 2 feet per year. T h e water levels in the developed areas in the basin have been lowered an average of 30-35 feet since 1940, and the influence of pumping has extended throughout the entire basin.
T h e water-level decline in some areas, especially along streams, is greatly affected by recharge. T h e ground-water system receives recharge in m a n y ways, the most important being from streamflow losses during periods of surface flow. Estimates of the a m o u n t of annual streamflow losses have been m a d e from streamflow records and infiltration studies for the period 1940-64. T h e estimates provide an upper limit for the amount of recharge from streamflow, but évapotranspiration accounts for part of the losses; therefore, the net gain in stored ground water is u n k n o w n . Other sources of recharge m a y be as underflow from other basins, underflow from the peripheral hard-rock areas, or as return flow of irrigation water. The electrical-analog model will aid in determining the quantities of recharge. T h e amount of electrical-current input required to provide the best match of potential distribution in the electrical and hydrologie systems will indicate the approxi- mate amount of inflow into the hydrologie system.
ELECTRICAL-ANALOG SYSTEM
T h e purpose of this study w a s to duplicate the ground-water system in the Tucson basin by use of electrical-analog techniques and to develop a working model of the system.
T h e analysis consisted of steady-state and transient phases. T h e steady-state analysis served to verify the areal transmissive pattern determined from pumping tests and to estimate the general inflow-outflow conditions prior to extensive ground-water develop- ment in the basin. The transient analysis duplicated the changing conditions since 1940 in terms of pumpage, recharge, and water-level declines.
T h e model was constructed so that each grid width represented half a mile of aquifer.
T h e general technique used in the steady-state analysis was one of trial and error because m a n y of the quantities in the flow system were u n k n o w n . T h e objective w a s to obtain the best match of the 1940 water-level altitude m a p (fig. 1) and to determine the corresponding inflow-outflow values.
T h e underflow in and out of the basin was established on the basis of voltage gradients rather than current to allow the quantities of inflow and outflow currents to change freely to satisfy the requirements imposed by k n o w n hydraulic gradients in the aquifer. T h e recharge from the streams and mountain fronts was established through trial and error techniques. T h e current input from specific reaches along those boundaries w a s varied until an acceptable match of potential distribution was obtained.
T h e results of the steady-state analysis indicated that an average of about 64,900 acre- feet of water was entering and leaving the ground-water reservoir annually prior to 1940.
T h e distribution of inflow and outflow through the major boundaries is s h o w n on figure 4 .
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UN TA, Ns
PUMPAGE 47, 400 A C R E - F E E T
7800
ess
Underflow entering and leaving basin in acre -feet
E X P L A N A T I O N
' i
3100
Annual recharge at mountain fronts, in acre-feet
H—H
2200
Annual recharge along streams in acre-feet
F I G U R E 4 . Results of steady-state analysis, 1940 inflow-outflow conditions
T h e accuracy of these inflow and outflow values is dependent largely on the validity of the assumption that equilibrium conditions existed in 1940. Recharge along the mountain fronts was 28,100 acre-feet per year, and ranged from zero to as m u c h as 325 acre-feet per mile of mountain front per year. These rates were determined from electrical current inputs required to simulate the 1940 water level altitudes. Recharge from the streams w a s initially assumed equal to streamflow losses that were estimated for specific reaches.
Recharge from the streams was then modified in successive trials on the model to match the 1940 water levels. T h e model study indicated that recharge from streams ranged from 38 to 47 percent of the m e a n annual losses, which is equivalent to a range of 150 to 345 acre-feet per mile of channel in the selected reaches. The total input to the aquifer from stream channels was 19,000 acre-feet per year, which is 40.5 percent of the total m e a n annual losses. T h e model indicated that the amount of underflow into the basin w a s 17,800 acre-feet per year—an input of 10,000 acre-feet at the southern end and 7,800 acre- feet in the Canada del O r o area.
Underflow out of the basin was 17,500 acre-feet per year at Rillito. T h e discharge shown as p u m p a g e on figure 4 was leaving the system as évapotranspiration prior to 1900.
Large areas of s w a m p s and dense vegetation existed along some reaches of Rillito Creek and the Santa Cruz River prior to 1900. A s development in the basin progressed after 1900, the évapotranspiration losses were gradually converted to p u m p a g e in these areas along the streams. T h e total discharge, whether by évapotranspiration or by m a n ' s use, was probably fairly uniform through 1940.
T h e transient analysis duplicated the changes in the system since the assumed equilib- rium time (1940). T h e input consisted of increases in pumping rates that occurred since 1940 and estimated changes in recharge. The output of the model was changes in water levels with time. T h e model was verified through its duplication of measured changes in historic water levels. Four check periods were used to verify the continuous analogy of the electrical system for the period 1940-65. T h e pumping rates and their variation in time were simulated at each center of pumping in the basin. Recharge along the stream courses was put into the model as a variable dependent on the departure of annual streamflow above m e a n .
T h e analysis of the transient system was approached by trial and error because the input functions, such as pumpage, recharge, and storage coefficient, were based o n estimates. T h e results of the transient analysis indicated that a number of the hydrologie variables initially incorporated in the analog design required change. T h e storage coeffi- cient was charged from 15 to 4.5 percent in a 5-square-mile area near the center of the cone of depression in the metropolitan Tucson area. T h e model decline in this area w a s less than the actual decline by a fairly uniform percentage throughout the period 1940-65, and the storage coefficient was assumed to be the most probable source of error. T h e p u m p a g e was not altered because the municipal p u m p a g e data in this area were good.
Several minor changes in the simulated p u m p a g e pattern were necessary ; such changes involved centering current withdrawal points in the apparent center of pumping.
T h e model results indicated several areas where changes in recharge were required.
T h e d r a w d o w n indicated by the model was m u c h greater than the actual decline in t w o areas—along the Santa Cruz River from its confluence with Rillito Creek upstream for a distance of about 15 miles and along Rillito Creek. In these areas ground water occurred at very shallow depths during 1940, and the streams were perennial in these reaches during the early 1900's.
A change in the type of riparian vegetation has occurred since the early 1900's, probably owing to the increasing depth to water. This change could have two possible effects on the ground-water reservoir. O n e would be a decreased usage of ground water through évapotranspiration. The other possibility is that the declining water table has m a d e available a larger volume of unsaturated material ; therefore, m o r e of the infiltrated water could be stored, and the net result would also be an effective increase in recharge.
TORTOLITA
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E X P I. A N A T I O N 2500
Predicted altitude of water table in 1985 (contour interval, 100 and 500 feet,
datum is m e a n sea level) - 1 2 5 -
Boundary of area where decline is predicted to be m o r e than 125 feet
Boundary of area where decline is predicted to be m o r e than 100 feet
Boundary of area where decline is predicted to be m o r e than 75 feet
Boundary of area where decline is predicted to be m o r e than 50 feet
F I G U R E 5. Water-level declines for 1940-1985 and predicted water-table altitude in 1985
T h e recharge input along the stream channels finally derived from the model required an increasing amount of recharge with time. This increase in recharge w a s treated as a function of water-level altitudes, and was simulated as current flow through zener diodes.
T h e diodes have the characteristic of conducting current only if the voltage across the diode exceeds a certain value. Thus, flow of current to or from the model could be m a d e a function of voltage o n the resistor network, which represented change in water stage for the transient-flow condition. This is analogous to what probably happened in the hydro- logic system. A s water levels declined, the évapotranspiration from ground water gradually decreased to zero. T h e input along the stream channels in 1940 was 19,000 acre-feet; the input was increased to a rate of about 35,000 acre-feet per year in 1964. Additional recharge also was required in the model in the southern part of the basin, probably accounting for the return flow of irrigation water. T h e model indicated that prior to 1958, 25 percent of the total p u m p a g e in this area was being returned to the ground-water reservoir. After 1958 the total amount of return flow decreased, apparently as a result of the m o r e efficient use of irrigation water. Increased efficiency was assumed to be the solution to the problem in this area because the total p u m p a g e for irrigation has decreased, and there has been little change in irrigated acreage.
Future water-level conditions were predicted on the basis of past trends in p u m p i n g patterns because n o other management schemes have been proposed. Pumping w a s assumed to continue at the same rate and with the same areal distribution as existed in 1962-65. W h e r e high évapotranspiration occurred along the stream channels during 1940, recharge was continually increased through the projection period 1965-85. T h e rate of increase was regulated automatically in the model by the interaction between the aquifer net and the zener diodes. All other recharge conditions were projected at the s a m e rateas occurred during the period 1962-65. T h e model forecasts were m a d e to determine the possible water levels for spring 1985 (fig. 5).
Predictions indicate that the overall shape of the cones of depression will remain about the same. A large a m o u n t of lateral development in all cones is evident. This extrapolation represents but one of the possible pumping-recharge management situations that could be solved by use of the electrical-analog model. Little chance exists that this will be the actual future pumping situation, but it is used here to illustrate the utility of the analog model.
S U M M A R Y A N D CONCLUSIONS
The electrical-analog model of the ground-water system in the Tucson basin duplicated the actual conditions observed throughout the period of ground-water development. T h e model results indicate that the quantity of recharge entering the ground-water system has increased since 1940, perhaps owing to the lowering of the water table along the streambeds in s o m e areas. T h e increase in recharge resulted from a decrease in évapo- transpiration supplied from ground water and the larger volume of unsaturated material that w a s available for storage of intermittent streamflow losses. T h e model was used to determine possible future water-level conditions in 1985, based on the assumption that p u m p a g e would continue at its present rate and areal distribution. Recharge w a s con- sidered as continually increasing. T h e model will aid water management in predicting the future effects of any possible pumping-recharge scheme on the regional water table.
J. Paul Riley1, D u a n e G . C h a d w i c k2, and E u g e n e K . Israelsen3
A N S T R A C T : A S demands upon available water supplies increase throughout the world, there is an accompanying increase in the need to assess the downstream consequences resulting from changes at specific locations in a hydrologie system. However, because of the m a n y variables involved, this is an extremely complicated problem. At Utah State University the problem is being approached by electronic analog simulation. Under this concept, a model is developed for investigating the behavior or response of a dynamic prototype system subject to particular constraints and input functions. Simulation permits an examination of the composite system involving all processes occurring simultaneously. T h u s , a model is not only an excellent explor- atory tool, but also a direct aid to creative thinking. Potentially, it can provide answers regarding the sensitivity of the total system to changes in certain parameters, and the amount of change required to produce a desired result. A model can, therefore, greatly facilitate an appraisal of proposed changes within a prototype system.
A fundamental requirement of a computer model of a physical system is that it simulates on a continuous basis all important processes and relationships within the system that it represents.
So far as possible, the model is based on general relationships, and through the process of verification, equation constants are estimated which establish the model for a particular area or geographic region. T h e various functions and operations of the different parts of the system are interrelated by the concepts of continuity of mass and m o m e n t u m . M a n y of the processes which occur in hydrologie systems can be represented by time-dependent differential equations. For the solution of this equation form, the analog computer is particularly adept because it can integrate problem variables on a continuous basis.
Studies have been undertaken for several watershed areas and involving different time and space increments. Close agreement with observed outflow hydrographs has been achieved.
Analog computer simulation seems capable of making substantial contributions both in the area of basic waterrelated research, and also as a planning and management technique in seeking optimum use of existing water supplies.
R É S U M É : C o m m e la demande pour l'approvisionnement en eau augmente à travers le m o n d e , il y a concurremment un besoin croissant d'évaluer les conséquences résultant en aval des change- ments apportés en certains points d'un réseau hydrologique. Cependant ce problème est extrême- ment compliqué à cause du grand n o m b r e d'inconnues qu'il comporte. A « Utah State Univer- sity» le problème est étudié par simulation sur calculatrice analogique. Selon ce concept, un modèle est développé pour analyser le comportement d ' u n système dynamique soumis à des conditions particulières et à des fonctions données. L a simulation permet d'examiner le système complexe comportant des phénomènes qui se produisent simultanément. Ainsi, un modèle est non seulement un excellent instrument d'exploration, mais encore une aide directe à la pensée créative. Potentiellement, il peut fournir des informations concernant la sensibilité du système global aux variations de certains paramètres, et la grandeur de la variation nécessaire pour produire u n résultat désiré. U n modèle peut donc beaucoup faciliter l'évaluation d ' u n changement proposé dans un système.
Il est nécessaire que le modèle d ' u n système physique sur calculatrice électronique simule d'une façon continue tous les phénomènes importants et toutes les relations que comporte le système.
Autant que possible, le modèle est basé sur des relations générales, et dans le processus de vérification, les constantes des équations sont évaluées afin d'établir le modèle pour u n endroit particulier ou une région géographique. Les diverses fonctions et opérations des différentes parties du système vérifient l'équation de continuité et l'équation des quantités de m o u v e m e n t . Beaucoup
1. Associate Professor, Civil Engineering, Utah Water Research Laboratory, Logan, Utah.
2. Associate Professor, Electrical Engineering, Utah Water Research Laboratory, Logan, Utah.
3. Research Engineer, Utah Water Research Laboratory, Logan, Utah.
