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The use of models in solving agricultural development problems
Agriculture and Environment, 1 (1974) 17--37 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
THE USE OF MODELS IN SOLVING AGRICULTURAL PROBLEMS
DEVELOPMENT
N.A. DE RIDDER
International Institute for Land Reclamation and Improvement, Wageningen (The Netherlands) (Received January 18, 1974)
ABSTRACT De Ridder, N.A., 1974. The use of models in solving agricultural development problems. Agric. Environm., 1: 17--37. Agricultural development is a complex undertaking because of the numerous factors involved, including those of a physical and non-physical nature. Land and water have often been (and are nowadays sometimes still) regarded as a means to grow crops. This approach, based on the utility principle, may lead to dismal failures. Fertile lands were thus turned into a saline wilderness within a relatively short period. In the above approach the management problem, i.e. the problem of cause-and-effect relations has been neglected. More than is the case at present, proper planning must relate the physical, environmental, economical, and social factors involved. But the integration of all these factors encounters some major difficulties of which insufficient data and lack of an exact and comprehensive methodology are the most serious. But planning cannot be postponed indefinitely or until the last information has been obtained. Effective development of agriculture, of which water resources management forms an important part, is undoubtedly one of the greatest needs of to-day's world. The complexity of the problem has outgrown traditional problem-solving methods. The principal aim of this article is to describe in brief some recent developments in water resources management methods and water supply optimization techniques. Two models are discussed: a linear programming model for finding optimum solutions of water supply and a mathematical groundwater basin model, which is capable of simulating various extraction and replenishment flows and predicting the consequences of future engineering works. The unique feature of these two models is that the output of the linear programming model can be used directly on the groundwater basin model to test the physical validity of the economic solution.
INTRODUCTION In spite of major advances in agricultural science the world food situation is a t t h e m o m e n t c r i t i c a l . D u r i n g t h e last y e a r t h e p r o d u c t i o n o f f o o d d i d n o t i n c r e a s e a n d i n s o m e d e v e l o p i n g as w e l l as d e v e l o p e d c o u n t r i e s it d r o p p e d s h a r p l y . A p a r t f r o m t h e f a c t t h a t t h e ' g r e e n r e v o l u t i o n ' is l a g g i n g b e h i n d , a d e p r e s s i v e list c o u l d b e d r a w n u p o f a g r i c u l t u r a l d e v e l o p m e n t p r o j e c t s w h i c h have failed dismally d u e to d i f f e r e n t causes.
18 This proves that agricultural development, here defined as all the activities undertaken to increase agricultural productivity, is a much more complicated problem than is often thought. The problem takes even larger proportions if we think in terms of rural development which, in addition, includes all the non-agricultural activities, economic and non-economic with the objective to increase not only agricultural production but also the satisfactions of rural living (Mosher, 1972). Agricultural development and rural development cannot be strictly separated from each other as their activities are usually partly overlapping. Raising agricultural production causes the rural family income to rise and this in turn will increase the satisfactions of rural living, provided the rewards of the increased production are well divided among landowners, tenants, farm labourers, and urban consumers. Even if we limit our considerations to the problem of agricultural development -- and we shall do so here -- there is no denying that the problem is a complicated one. The numerous physical and non-physical factors ir,volved in increasing agricultural production are inextricably interwoven. It is not surprising therefore that there is a call for a more interdisciplinary and integrated approach to the problem. Such an approach means that all the various relevant factors and aspects will receive due consideration, separately as well as in their mutual relationships. Properly applied, an integrated approach may make us witnesses to a transition from the " a r t " of agricultural development -- an art based largely on unsubstantiated empirical methods -to a fully fledged engineering system designed to achieve the c o m m o n objective of raising agricultural productivity. The days have passed that one single person could solve the problem. Nowadays, the survey teams of agricultural development projects are staffed by members of very different disciplines: hydrologists, groundwater geologists, soil surveyors, agronomists, civil engineers, economists, and rural sociologists. Why then do so many agricultural development projects, even after several years of operation, give unsatisfactory results, show steadily decreasing crop yields, and in the worst cases even become complete failures? There is as yet no clear-cut answer to this question. But it is a distinctive feature of our normal approach to problem solving - including problems of agricultural development -- that the various aspects of the problem are investigated in relative isolation. Often too much time is spent on details at the expense of gaining an understanding of the overall problem. Obviously there is something missing in this approach. That 'something' is the factor relating cause-and-effect. The development of agriculture does not necessarily dictate that a single factor or a single component of the plant--soil--water system should be optimized, for example, water or soil. Besides such physical factors as climate, land, and water, non-physical factors such as economy and sociology play an equally important role. The integration of the data from these different disciplines in a logical, organized, and objective manner is a major problem. It requires a methodology which, as far as agricultural development is con-
19 cerned, is still largely lacking. Advances in science during the last decades, however, are making it possible to adapt and apply modern techniques to the problem, using computerized models and simulations. DEFINITION OF THE PROBLEM There are various approaches we can apply to the problem of raising agricultural productivity. We may, for example, regard land and water as a means of growing crops. In this approach we are interested in land and water only to the extent that they achieve some utility or purpose. Working along this line we apply laws established by science to predict the performance and reliability of the two resources, and we are concerned with the costs of construction, maintenance, operation, and life time of the facilities required to grow crops that give high yields. This approach has often led to failure. Taking water to the desert, for example, does not necessarily mean that the desert will blossom. It may blossom for a while, but will it continue to blossom? There are numerous examples where this approach, founded on the utility principle only, has turned the briefly blossoming desert into a land that is severely waterlogged and salinized and where crops can no longer be grown. The obvious reason for the failure is that the interrelationship existing between surface water and groundwater was overlooked or was thought to be of minor importance. Other examples of failures that have come from following the utility principle are overpumping of groundwater resources, resulting in steadily declining water tables and the intrusion of saline water; or cutting down all vegetation in areas with a windy climate, which results in severe wind erosion. In the above approach the management problem has been neglected. We must distinguish between the existing state and the future state of an area where agricultural production is to be raised. In the future state many things will have changed. For example, water will be supplied to areas where water was never supplied before; new conveyance systems will be built, either concrete lined or not; a more economic use of irrigation water is dictated, i.e., less water will be lost to the underground; well fields will be established in areas where such facilities did not exist before, and so on. Each of these improvement measures has its effect on the groundwater table and it is a major problem to determine their combined effect. The discrepancy between the existing state and some proposed state in fact defines the management problem: the problem of cause-and-effect relations. The greater the discrepancy between the existing and the future state, the greater the management problem will be, and the more difficult it becomes to solve this problem by conventional methods. Since the development of agriculture is thus a complex undertaking, including scientific, engineering, and management aspects, there is an urgent need for a more general approach to the problem. As we all know, there are usually alternative ways of doing things. The
20 fundamental question to be answered in developing agriculture is what is the " b e s t " way of doing so. Hence, it is possible to ask what is the best combination of crops that can be grown? This is the one that gives the highest net return per hectare or per cubic metre of irrigation water supplied. This is an economic problem whose solution requires a proper knowledge not only of soil quality, available water, water demands of crops to be grown, and farm size, but also of available inputs (material, manpower, machinery), water prices, and markets for farm products. All this information must be organized and objective tools applied to it to find the unique solution of the optimum cropping pattern. A similar problem arises when, in the area under study, surface water and groundwater of good quality are available for irrigation. To meet the water demands of agriculture, we could possibly supply surface water only, or groundwater only, but the supply can also be made in an almost infinite number of combinations of the two resources. Hence we may ask what is the best way of operating a groundwater basin or a surface water reservoir or integrated groundwater--surface water supply? Here we are again facing the problem of what is the best solution, the one that is the most economic. When working with traditional methods the solution to this problem can hardly be found, certainly not within a reasonable period of time. Or, having found a solution, how sure are we that there are not better solutions? Again there is a need for objective tools that allow optimal solutions to this and similar problems to be found. A SYSTEMS APPROACH In the preceding paragraphs we mentioned the word " s y s t e m " . What do we mean by a system? There are several definitions of the word and which definition is used depends on the types of problems investigated (Domenico, 1972; In 't Veld, 1972). For example, it can be defined as the whole of a number of related things that are organized in one way or another. All definitions, however, have two essential characteristics in common: a set of elements and the relation between these elements. A systems approach is a general approach aimed at a better understanding of the combination of elements which, taken together, form a complex that can be designated as a system. Characteristic of a systems approach is that it tries to distil the essence of a complex physical entity or system, to describe its structure, and to explain its internal cause-and-effect relations. A systems approach is not limited to physical entities; it can be applied equally well to non-physical phenomena, including those of an economic, biological, and sociological nature. Problems in management and planning involve systems too, e.g., planning irrigation water distribution and supply, farm management, etc. A system is composed of elements, also called objects or components. They can be of any nature; even feelings (in the sociological sense) can be regarded
21 as elements. The elements are the smallest parts which we wish to consider in a given study. Within the system they are interrelated, and, depending on what system is being considered, they may be related to elements outside the system: the environment, for instance. Within a system, we may distinguish subsystems, which are lumped elements. Within a subsystem, the interrelationships remain unchanged. Problems in raising agricultural productivity clearly involve systems. We must in the first place optimize the elements 'plant', 'soil', and 'water' of the plant--soil--water system (Fig.l). We have seen, however, that if we limit our dctivities to this optimization only, failures can be expected. The reason why this is so can also be seen from this figure: the plant--soil--water system is, what is called, an open system, i.e., water from it is interchanged with water from the underlying groundwater system and from the overlying atmospheric system. In fact, these systems are subsystems, representing parts of the main system, called the hydrologic cycle. As the name indicates, the hydrologic cycle is a closed system: no drop of water can be created or destroyed within this system. It will be clear that agricultural development involves more than merely optimizing certain subsystems or their component parts and then waiting to see what happens. The various subsystems must not only be studied separately, they must also be linked and their interrelations and cause-and-effect relations defined. Fig.2 shows a schematic representation of the various subsystems
Eva p o t r a n spi r a t ion
[
PLANT-SOIL-WATER Unsaturated
SUBSYSTEM zone
t Percolation
I
I Capillary
rise
I I GROUNDWATER SUBSYSTEM Outflow
Inflow Saturated
zone
Fig.1. Plant--soil--water subsystem linked with groundwater subsystem and atmospheric subsystem.
22
~
ecipitation
Surfacerunoff subsystem~
groundwattransfer er
Surface w a t e r [
- -
Surface water-
Flow rates Surface water quality subsystems
~tes Groundwater subsystem
Return
flow
Return
flow
[ quality
ty,
Agricultural prod. subsystems, croppinq patterns
-Output
I man power, material
Fig.2. The various subsystems of an agricultural development scheme and their interrelations.
and their interrelations to be considered in problems of developing irrigated agriculture. Developing agriculture thus means planning, management, and control, where control is the monitored state of the development system. A few things are now evident. Firstly, a system implies interrelated objects, actions, or procedures, rather than a collection of loose parts. A systems approach forces us to look at the entire problem, or in other words to look at the forest as well as the trees. And by doing so, we enrich our understanding of the major factors governing the problem of agricultural development. Secondly, the study and solution of the problem involve the development of models of some sort. W H A T IS A MODEL?
If we want to study a system -- the behaviour of a rural population, for instance, or the behaviour of a groundwater basin under modern irrigation
23 techniques or new pumping patterns -- we could make experiments. Often though, this is impossible because of the high costs, the great risks, or the long time required to make them. What we can do is to develop a model of the system in question, and use i t t o simulate certain actions, procedures, decisions, or even feelings. A model is a tool of exploration in which the chaos of facts has been properly organized. A model is a representation of reality, not reality itself, which allows certain actions, procedures, and decisions to be tested and their effects on the system to be predicted. The technique of modelling a certain system or subsystem m a y provide an objective standard by which all the relevant information of the various disciplines can be effectively processed and organized for study. Since a model is a simplification of reality, many people lose confidence in the technique of modelling: reality is too complex to be modelled. The art of modelling, however, is not to lose oneself in details, as is often seen in agricultural development projects, but to take into account those factors that really govern the process under study. In science, simplifications are commonly applied to find a solution to a specific problem. Simplification involves: (a) abstraction, (b) substitution, and (c) reduction. Abstraction means that certain elements or aspects of the system are left out of consideration as they do not greatly affect the validity of the results. For example, in developing a model of an extensive aquifer, a local clay lense occurring within such an aquifer can be neglected without causing severe validity problems. The procedure of abstraction makes the model less complex than reality and thus easier to study. Substitution involves replacing certain elements or aspects by others that have the same effect. To determine the proper size of an airplane wing in a laboratory, for instance, crew and passengers can be replaced by a piece of iron or lead, without causing validity problems. Reduction is another means of simplifying a complex reality. In some models, for example, the time is reduced. Simplification means that the simulation may look quite different from what is being simulated. Simplification is necessary if we want to avoid mathematical difficulties and arrive at solutions. It should, however, be done carefully and with professional judgement. Unjustified simplifications, or ones that are too far-reaching, will render the results obtained from the model unreliable. Agricultural development may be regarded as a system. The various elements of this system can be lumped in an organized manner to form a series of subsystems, as Fig.2 shows clearly. Because of the complex interdisciplinary interest in agricultural development, the models to be developed for each subsystem will differ markedly in purpose, information requirements, assumptions, usefulness, and even the kind of mathematics applied. The models can be used to simulate objects, actions, procedures, or agricultural improvement measures, and to predict the effect of these on other subsystems. For this purpose the relevant subsystems must be linked.
24 In the agricultural development system of Fig.2 two types of subsystems can be distinguished: deterministic subsystems, and probabilistic subsystems. A deterministic subsystem is one that is defined by definite cause-and-effect relations. For example, pumping from wells (a cause) is related to water table change (an effect) or canal seepage and field irrigation losses (a cause) are related to water table changes (an effect). These cause-and-effect relations become only meaningful if they are related to the geology of the subsystem in question. Deterministic cause-and-effect relations can be measured and modelled. A probabilistic subsystems allows no precise prediction, but may provide expected values within the limitations of the probability terms which define its behaviour. Rainfall and river flows, for example, are stochastic or random variables with a definite range of values, each one of which can be attained with a definite probability. Human behaviour, as we are told repeatedly, is unpredictable. But the problem of behaviour of a rural population to agricultural development measures may be studied in a probabilistic manner. The above approach is not new but it is still little applied to the problems of agricultural development. We should take advantage of the experience gained in other sciences, for example, physics or economics, where a systems approach is a c o m m o n approach to problem solving. This article is not intended to be a lesson on how to apply a systems approach ta the complicated problem of developing agriculture; we are just at the beginning. However, a few examples, related to some of the subsystems shown in Fig.2, will be given as an illustration. ECONOMIC OPERATION MODELS As mentioned before, there are usually alternative ways of doing things, and we prefer the " b e s t " way. Crops can be grown in any combination, and surface water and groundwater can be supplied in any combination to irrigate the crops, but how to find the " b e s t " combination? These problems are true economic optimization problems, which nowadays are c o m m o n l y solved by applying the technique of linear programming. Optimization is the problem of finding the best course of action from a set of alternatives. The above problem has as its basic conditions (constraints): the limitation of the available resources (land, water, manpower, machinery, etc.), the minimum water requirements of crops, the market for agricultural products; and as its objective: the maximization of the net return. A solution that satisfies both the conditions of the problem and the given objective is termed an optimal solution. Let us take as an example the problem of finding optimal solutions of water supply for various alternatives of agricultural development. It is assumed that in the semi-arid area under study both surface water and groundwater are available and that an optimal integrated use has to be made of the two resources. But the amounts of surface water available vary during the year and
25 also from ono year to another, though several consecutive dry and wet years can be detected from the records. Groundwater of good quality is available, but the depth to the water table varies from one part of the area to another. Such a situation is often found in alluvial fans which are huge bodies of sediments deposited where mountainous rivers debouch into a plain. In the apex of the fans the water table is considerably deeper than at their foot. In adjacent areas the groundwater is salty. The land resources (soil classes) are known from a soil survey. Sociological surveys have revealed the number of rural families living in the area, the number of cattle they possess, their present water rights and land use. There are chances that the present shortage of irrigation water can be alleviated in the future by importing treated waste water from nearby towns, or surface water from another catchment area. These waters are, of course, more costly than local water because purification plants, pipe lines, dams, and tunnels through mountainous areas must be built. But the price of local water also varies in different parts of the area, because a new conveyance system has to be built to distribute this water even to the remotest parts of the area. This network of irrigation canals may or may not be concrete-lined or partly lined to reduce seepage losses. The various depths at which the groundwater is found makes the price of groundwater differ from one part of the area to another. We are facing here extremely complex decision problems. Decisions must be taken as to how much land is to be supplied with water. Shall we supply all the existing farm lands with water or only the best lands? The latter decision involves resettlement of a number of farmers. What kind of water supply and delivery system has to be built? Is a certain period of overpumping the groundwater resources (mining) permitted to alleviate the shortage of surface water till foreign water is available from another catchment? To what extent can this imported water be used economically? Where can groundwater in the future best be abstracted and at what rate? Occasionally flooding of the river occurs; how can this water or part of it be used, for example, to recharge the groundwater artificially? What will be the best size of the farms? And finally, how has the envisaged water supply system to be operated so as to meet the water demands of agriculture in an optimal way without causing harmful side-effects? It will be clear that there are series of different possibilities which we may regard as alternative plans. De Ridder et al. (1969) applied the technique of linear programming to the problem of finding optimal solutions of irrigation water distribution and supply in a 100 000 hectares large agricultural area in Iran. Linear programming is a single-stage optimization technique by which several decision variables are simultaneously optimized. The complete mathematical statement of a linear programming problem for water supply includes a set of linear equations which represent the conditions (constraints) of the problem, and a linear function which expresses the objective of the problem.
26
The linear programming problem concerned is a maximization problem, i.e., a problem of maximizing the net income of a governmental agency which will take care of the distribution and supply of irrigation water, operation and maintenance of the water supply and delivery facilities. It will conduct its business as a non-profit agency. "Net income" is defined as the residual of the following transactions: receipts from selling water to the farmers minus all costs of water services from deep wells and surface water canals. By "maximization" is meant the economic criteria that marginal returns should be greater than or equal to marginal costs. The demand for water is considered as agricultural production activities in the distinguished sub-areas of the plain which yield different net returns per cubic metre of water. The activities compete in this way for the available limited water resources. The model comprises the following activities (see also Fig.3):
A C T I V I T I E S ~ Supply of river
water by cana s No costs assumed]
upstream of
diversion point
/ I
~
Annual costs of new canal system (investment, m a i ~ tenance, operation)
LINEAR
PRO
I Supply of ground I water by we s
Agricultural production
Annual costs of I Net return perI deep well system I cubic metre of (investment,main- water tenance,operation
RAMMING
MODEL~ f,
-~I PHYSICALCONSTRAINTS
ALTERNATIVEPLANS
Amount of river water available in a dry, wet, average
--
All the best soils are supplied
L
year
All existing farms are supplied
L~
Maximum water
All i r r i g a t i o n canals
|
requirements per ha
are lined
of crop
V g-
Irrigation canals are partly lined
Minimum water
__ requirements per ha
of c~op
Various river flows | (dry, wet, normal years)
F-
Computing optimal water supply system
Importation of water in various quantities
|
Mining and no mining of groundwater
|
F--
I
I
I solutions physicaland ...... qcal] with d i f f e r e n t alternatives
Fig.3. S c h e m e for the e c o n o m i c analysis of various alternatives of water supply to an irrigation area.
27 R I VER = Inflow o f river water at the main diversion dam at the head of the alluvial fan. iSRF = Supply of river water by a canal system to sub-area i. iWELL = Supply of groundwater from wells to sub-area i. iPRD = Agricultural p r o d u c t i o n in sub-area i. These activities have costs which were calculated. For example, iSRF costs represent the costs of maintenance, operation, and capital costs o f a new canal system, iWELL costs represent the cost of a well, 150 m deep, operation, maintenance, interest, depreciation. The cubic metre price of well water was differentiated for different parts of the plain on the basis of water table d e p t h and aquifer characteristics, iPRD costs were considered as negative costs (returns); th e y represent the net return per cubic metre of water, i.e., the net residual of the crop value after deduction of purchased input, including interest, all labour costs, and capital costs of land levelling. The activity iPRD was based on an o p t i m u m agricultural p r o d u c t i o n pattern and the respective water requirements of this crop pattern per hectare was determined. The constraints of the model are defined as follows: xRIVER xiPRD xiWELL Z xiSRF xiPRD
~< ~< 4 = =
MXRIV iMXD MXSFY + Z xiSRF xRIVER xiWELL + xiSRF
x R I V E R ~< MXRIV: the available river water in a dry, wet, and average year. The inequality xiPRD ~< iMXD defines a m a x i m u m water demand restriction in sub-area i, and the inequality Z xiWELL ~< MXSFY + Z xiSRF states th at the total well water abstraction is smaller than or equal to the sum of the net subsurface inflow into the basin and the net deep percolation in sub-area i. The equality Z xiSRF = x R I V E R states that all surface water distribution activities equal the total river flow, and the equality xiPRD = xiWELL + xiSRF defines the logical condition that any level of p r o d u c t i o n in sub-area i must be supplied by groundwater or surface water. The linear programming model then allows the o p t i m u m solution of water supply to be c o m p u t e d for each alternative agricultural devel opm ent plan. The results obtained f r om the model show what part of the plain should be supplied with surface water, what part by groundwater, what part by the t w o resources, and what part should n o t be supplied from either source because it is n o t economic to do so. Fo r each water supply solution the net return per cubic metre of water is calculated. The net return values of the alternative plans can then be com pared and ranked. Those plans t h a t show the highest net return can be selected for further study and eventually the best plan can be selected for final design.
28 GROUNDWATER BASIN MODEL As was mentioned before, a water supply solution, being a proposed state, may and often will differ considerably from the existing state. Hence a basic question to be answered is, how will the whole groundwater basin, meaning here in particular the water table, react to the total of all the changes that will be brought about in the future? The optimal water supply solutions, as obtained from the linear programming model, have to be tested as to their physical and technical feasibility. A tool that can be used to examine the response of the water table to new engineering works as suggested by the linear programming model is a digital model of the groundwater subsystem shown in Fig.1. The groundwater basin model used in the above studies has initially been developed by Mr. H.N. Tyson, Data Processing Division of IBM Corporation in Los Angeles, in cooperation with engineers of the California Department of Water Resources (Chun et al., 1963; Weber et al., 1968). The model is developed to simulate the dynamic behaviour of the groundwater basin under various plans of basin operation. It is based on the Darcy equation and the law of conservation of mass which combined yield a nonlinear partial differential equation. This equation represents a model of the flow rates associated with a unit area of aquifer, including the subsurface inflow ~tnd outflow rates, flow rates in or out of storage, and inward or outward flow rates external to the aquifer: ah
gP ~]k(x,y) h ~ h - S ( x , y ) ~- -Q(x,y,t) = 0 p
(1)
where k = permeability coefficient, h = water table height above a datum, S = storage coefficient, t = time, Q = net external input, including precipitation, evaporation, canal seepage, drainage flow, irrigation percolation losses, well flow, etc., g = acceleration of gravity, p = density of groundwater, p = viscosity of groundwater, x and y are cartesian coordinates, and V, = differential operator ( V,= a/ax + a/ay). The partial differential equation is approximated by a finite differences equation. The groundwater basin is therefore subdivided into a number of sub-areas (polygonal areas) by applying Tiessen's method (Fig.4). The size and location of the polygons is chosen on the basis of known variations in replenishment, extractions, transmission, storage, and water table heights. Each polygon has a nodal point, which is considered the control point for that particular area. In accordance with the theory of finite differences the flow rates in a polygonal area may be integrated. The finite difference equation for a given node reads:
i
Yi,B hi(tj+l)- hs(t]+l)
1
-
ABSB t
hB (t]+l) - hB(tj) ] + ABQB(t]+I)
(2)
1
2
3
4
5
6
'7
8
9
10
M I\////// 7.~i'1KA I --
X /
t
/
U
GHALEH BOtANO~ !
%%~
v!
IY
!
'
i,
\\ \\
Ilw
_ ...~127
/I I
iX
Y
L
i Z[_____
L
B
1( SIAH
1
2
3
4
5
6
KUH
7
~
9
10
Fig.4. A sample of a polygonal network. Varamin groundwater basin, Iran (After De Ridder et al., 1969).
Lb
.^
l
:: . . . . .
l
I
l
. .. . . . l
.
.
l.
. .
l
i
.
.
.
.
.
.*
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.
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:
:
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:
l
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.
l
l
cc r?I_._____‘_,____.____*---“l”“““‘~
58
.
.
.
l
+
l
Fig.5. Example of a digital computer output special polygon of the Mires Basin on Crete, groundwater levels are compared.
i
1 Ef I ! I’
i
I I I
I
I I I
~,__-_‘__‘_*__‘_-_-“
54
I
66
bb 7. LU ~~._.,.,.~..^_‘_._.,I-.I-__~‘I-_~~-,~~___~.~~~ ‘C
._
for the groundwater table elevations in a Greece. In this diagram computed and historic
.
.
.
.
‘.
*. .
^Y_ IF*,
se-: se:0
ai 5.5:4
61.4 61.‘) 60.5 60.1 59.7 59.5 59.5 59.4 59.7 49.R 59.9 b0.L 59.9 59.5
61.6
61.7
$3 b::b 60.6 60.5 ho.* 60.’ 60.4 60.6 6l.l 61.7
b3.D
.-
as-; &3:.5
LO.3 59.9 59*7 59.T 59.8 59.9 to.1 60.1 60.0 59.7
to.0
61.5 t2.4 62.8 62.9 62.8 62.6 62.2 Cl.4
:0,'p
0.
::*: .
t1.n
CL.7 62.3
63.0
HISI. 63.0 %?
31
where Y = a conductance factor made up of transmissivity width (W), and flow path length (L): Y=
wi, B Ti, B
(
Li,B
1
X
saturated (
(T), boundary
thickness
total thickness
1
A = area of polygon,
i,B = contiguous nodes and node in question, respectively, and the other symbols as defined above. A computer is used to solve the finite difference equations. The computer generates water table elevations for each polygon and for each time step (a period of two weeks or one month) using a Gauss-Seidel relaxation technique. For this, as for any other model, there is the problem of validity. The validity of the groundwater model can be tested by comparing the polygonal water table elevations generated by the computer and those measured in the field. To make it easier to compare computed and measured (historic) water table elevations, a plot programme is used. At the end of the computations these data are plotted graphically for each polygon (Fig.5). If the two hydrographs do not match satisfactory, such input values as aquifer transmissivity,
Mathematical water basin
qround model
I
Natural ground water basin
Groundwater basin simulation
Model
Historic
verification
water
Computed water table data
'
testing various alternative plans of groundwater basin
Fig.6. Scheme for developing groundwater basin computer models,
32
storage coefficient, or net deep percolation rates are adjusted as is required. This calibration process is repeated until the pairs of hydrographs for all polygons match satisfactorily (Fig.6). The model can then be used for simulating and testing alternative water supply solutions. The behaviour of the water table can be predicted for each polygonal area for any desired period of time. SIMULATING A L T E R N A T I V E WATER SUPPLY SOLUTIONS
We have seen in Fig.1 that the plant--soil--water subsystem is linked with the underlying groundwater subsystem. A change in the element 'water' of the plant--soil--water subsystem may result in a change in the element 'percolation', with which it is linked to the groundwater subsystem. A change in percolation will effect the groundwater subsystem, and this will be reflected by a change in water table height. Other factors that may affect the groundwater subsystem are: groundwater recovery by wells, artificial recharge of the groundwater basin, seepage from the conveyance subsystem, and field irrigation percolation. We have seen that in the groundwater model all the external flows (rainfall, evaporation, seepage, artificial recharge, if any) are lumped with the pumped extractions, if any, into a single term, called "net deep percolation" (AQ-term). For the existing state, the net deep percolation values for each polygonal area and for each time step (say, one month) are known. Hence, if in a proposed state groundwater extraction in a specific polygonal area will be increased by a rate of X mS/month, the monthly net deep percolation of this area must be reduced by the same rate, or a portion of it if a certain return flow occurs. Similarly, if in a proposed state canal seepage or field irrigation percolation in a particular polygonal area will be X% higher than in the existing state, the polygonal net deep percolation must be increased by this percentage. For testing linear programming solutions of water supply, two things are required: (1) the linear programming model must be grafted on the groundwater model; (2) the linear programming solutions must be translated into terms of polygonal net deep percolation values. As to item (1), all the activities of agricultural production, well water supply, surface water supply, etc., and their respective costs must be based on the polygonal areas as distinguished by the groundwater hydrologist in developing the groundwater basin model. As to item (2), a special computer programme is required to compute the net deep percolation values on a polygonal basis for each water supply solution as calculated by the linear programming model. By means of this programme, the polygonal water demands, quantities supplied b y surface water and/or groundwater, quantities lost in conveyance and at the field are listed at the end of the computations and the sum is formed of the polygonal field and conveyance losses and pumped extractions: the polygonal net deep percolation in the proposed state. These new net deep percolation values are then fed into the groundwater model. As shown in Fig.7, this model simulates these values and generates the water table heights for each polygonal area for any period of time, say 10 or 20 years, as is desired.
33
IMathematical ground L[ water basin model
Translation of linear programming solutions in terms of groundwater hydrology
i Groundwater basin simu ation
l
Computed future watertables
Alternative linear
[ programming solutions
I
Evaluationof the alternative solutions and selection of the best plan
YES Final design of water I delivery system and I water resources management plan
Fig.7. Scheme for feasibility analysis of linear programming results adapted to a groundwater basin computer model.
Table I shows an example of a water supply solution obtained from the linear programming model. The solution is based on the assumptions that there is an average river discharge of 245.106 m3/year; mining of the groundwater resources is not permitted; the canal system is completely lined; all farmers living in the plain will be supplied with irrigation water; each farmer will possess 3.85 hectares of land, which will be supplied with 3.85 × 10 440 m 3 = 40 194 m 3 of water. The solution shows that of the total maximum demand of 299.106 m 3, 203.1.106 m 3 will be supplied by the river and 95.9.106 m 3 by the groundwater. It can be seen from the table that all polygonal areas are supplied up to their maximum demand except polygon 16 whose demand is only partly met by supplying river water. The reason for this is that there is not sufficient water available from either source of water. The general solution also shows that river water should be supplied to the northern and middle areas of the plain, while the water demand of the southern and peripheral polygonal areas should be met by supplying groundwater (a transport cost minimizing solution). To examine the effect which the water supply solution, as presented in Table I, would have on the groundwater table in the plain if it were imple-
34
TABLE I Linear programming solution of irrigation water supply (106 m 3) Number of polygon
Maximum water demand
Supplied by river water
Supplied by well water
1 2 3 4 5 6 7 8 9 10 11 12 13 14
4.793 18.855 19.815 3.515 13.530 14.778 14.778 7.882 13.102 8.330 10.046 16.659 11.165 15.241
4.793 18.855 19.815 3.515 13.530 14.778 14.778 7.882 13.102 8.330 10.046 16.659 6.953 15.241
15
14.609
14.609
16 17 18 19 20 21 22 23 24
5.208 13.278 15.091 18.402 10.815 9.883 25.707 5.890 11.056
1.831 --18.402 ------
-13.278 15.091 -10.815 9.883 25.707 5.890 11.506
3.377 ---------
299.051
203.119
95.932
3.377
Total
---------4.212 --
Unsupplied demand
--
-------------
mented, the polygonal net deep percolation values corresponding to this solution are fed into the groundwater model. The model then simulates these v a l u e s a n d t h e r e s p o n s e o f t h e w a t e r t a b l e is p r e d i c t e d . T h e d i f f e r e n c e b e t w e e n the predicted water table after a certain period of operation and the initial water table elevation can be calculated. The polygonal water table differences a r e t h e n p l o t t e d o n a m a p a n d l in e s o f e q u a l c h a n g e a r e d r a w n ( F i g . 8 ) . I t c a n b e s e e n f r o m t h i s f i g u r e t h a t t h e w a t e r t a b l e in t h e m i d d l e o f t h e p l a i n ( p o l y g o n s 9, 1 0 , 1 1 , 1 2 , 1 4 , a n d 1 5 ) w o u l d rise c o n s i d e r a b l y in a p e r i o d o f 9 years. This area would become waterlogged within this period of time, the reason being t h e exclusive s u p p l y of river w a t e r to these areas a c c o m p a n i e d by r e l a t i v e l y h i g h p e r c o l a t i o n losses. O n t h e o t h e r h a n d , t h e h e a v y g r o u n d w a t e r a b s t r a c t i o n in s o m e p o l y g o n s ( n o . 1 7 , 2 0 , 2 1 , a n d 2 2 ) w o u l d c a u s e t h e w a t e r t a b l e t o d r o p a b o u t 1 6 m w i t h i n a p e r i o d o f 9 y e a r s . F o r p o l y g o n 1 7 t h e r e is a d a n g e r o f i n t r u s i o n o f s a l t y g r o u n d w a t e r f r o m a d j a c e n t areas. T h e m a i n c o n c l u s i o n is t h a t t h e w a t e r s u p p l y s o l u t i o n , t h o u g h e c o n o m i c a l l y s o u n d , is n o t f e a s i b l e f r o m a h y d r o d y n a m i c a l p o i n t o f v i e w ; i m p l e m e n t a t i o n
35
/
i I
\
/
/
Fig.8. Changes in water table after 9 years if the linear programming solution of irrigation water sup.ply as shown in Table I were implemented and operated. of t h e p l a n w o u l d cause severe g r o u n d w a t e r p r o b l e m s w i t h i n a relatively s h o r t period of time. In t h e s a m e w a y all t h e o t h e r a l t e r n a t i v e s o l u t i o n s can be tested. T h e s o l u t i o n , w h i c h is e v e n t u a l l y selected, m a y still s h o w u n a c c e p t a b l e w a t e r t a b l e changes in certain p a r t s o f t h e plain. A l t h o u g h it m a y n o t be e c o n o m i c a l , a d j u s t m e n t s can be m a d e . F o r e x a m p l e , in areas w i t h r a p i d l y rising w a t e r tables less surface w a t e r c o u l d be supplied a n d m o r e g r o u n d w a t e r e x t r a c t e d . T h e s e a d j u s t m e n t s m a y be r e g a r d e d as a p o s t o p t i m i z a t i o n o f t h e s o l u t i o n in q u e s t i o n . F o r this p r o c e s s t h e g r o u n d w a t e r m o d e l again can b e used to t e s t t h e e f f e c t s o f t h e s e a d j u s t m e n t s o n t h e w a t e r table.
36 CONCLUDING REMARKS In dealing with complex problems of agricultural development, a systems approach has great advantages over conventional approaches, as it allows the problem to be seen as a whole instead of in its details. Agricultural development involves planning, management, and control, and this should be effected in the best possible manner. A systems approach also allows certain subsystems or combination of subsystems of the main system to be examined, as we have tried to explain. A systems approach always involves some sort of model whose variables can be changed within the range of their possibilities. Once a model has been developed and verified it can be used to simulate almost infinite numbers of alternative plans, actions, procedures, assumptions, and allows their responses to be examined. This approach will enrich our understanding of the problem. Decisions can be taken on a much firmer basis than is possible with traditional methods. The example of rapidly rising water tables given above is not a hypothetical one; it comes regularly to our notice from semi-arid regions where irrigated agriculture is introduced. High investments must then be made to cure the problem of waterlogging and soil salinization, for example by installing an artificial drainage system or by changing cropping patterns and irrigation techniques. These and similar problems must be recognized beforehand, i.e., before an agricultural development plan is implemented. Agricultural development, of course, encompasses more than the few cases discussed in this article. Several factors of a non-physical nature -- those of sociology or politics, for instance -- play an equally important role. It is often heard that unsurmountable difficulties are encountered in their modelling. But the physical environment is no less complex than a human society. There is an urgent need for a rational approach to sociological and political problems related to agricultural development, which will allow the results of these fields of study to be effectively integrated in the whole system. To avoid misunderstanding, we must state that models are not the answer to all problems; they have their limitations too, and we should not expect miracles from them. However, in spite of their limitations we can say that any model is better than no model. They are very useful tools by which we can make more substantiated decisions than is possible by conventional methods. For further details of the techniques described in this paper and the results obtained from them for a case study in Iran, the reader is referred to a forthcoming publication on the subject matter in the Series of Bulletins of the International Institute for Land Reclamation and Improvement, Wageningen, The Netherlands
REFERENCES Chun, R.Y.D., Weber, E.M. and Mido, K., 1963. Computer tools for sound management of groundwater basins. Int. Assoc. Sci. Hydrol.,I~erkeley,Publ. No.14: 424--437.
37
De Ridder, N.A., Eres, A., Chun, R.Y.D. and Weber, E.M., 1969. A computer approach to the planning for optimum irrigation water supply development and use in the Varamin Plain, Iran. Report of the FAO, Rome, 28 pp. Domenico, P.A., 1972. Concepts and Models in Groundwater Hydrology. MacGraw-Hill, London, New York, N.Y., 405 pp. In 't Veld, J., 1972. Denken in systemen: systeembegrippen, systeem benadering, hi~rarchie van systemen. Ingenieur, 84(32/33): A 680--685. Mosher, A.T., 1972. Projects of Integrated Rural Development. The Agricultural Development Council, Inc., New York, N.Y., pp.l--8. Weber, E.M., Peters, H.J. and Frankel, M.L., 1968. California's digital computer approach to groundwater basin management studies. Symposium on Use of Analog and Digital Computers in Hydrology, Tuscon, Arizona, December 8--15, 1968, pp.215--223.
THE USE OF MODELS IN SOLVING AGRICULTURAL PROBLEMS
DEVELOPMENT
N.A. DE RIDDER
International Institute for Land Reclamation and Improvement, Wageningen (The Netherlands) (Received January 18, 1974)
ABSTRACT De Ridder, N.A., 1974. The use of models in solving agricultural development problems. Agric. Environm., 1: 17--37. Agricultural development is a complex undertaking because of the numerous factors involved, including those of a physical and non-physical nature. Land and water have often been (and are nowadays sometimes still) regarded as a means to grow crops. This approach, based on the utility principle, may lead to dismal failures. Fertile lands were thus turned into a saline wilderness within a relatively short period. In the above approach the management problem, i.e. the problem of cause-and-effect relations has been neglected. More than is the case at present, proper planning must relate the physical, environmental, economical, and social factors involved. But the integration of all these factors encounters some major difficulties of which insufficient data and lack of an exact and comprehensive methodology are the most serious. But planning cannot be postponed indefinitely or until the last information has been obtained. Effective development of agriculture, of which water resources management forms an important part, is undoubtedly one of the greatest needs of to-day's world. The complexity of the problem has outgrown traditional problem-solving methods. The principal aim of this article is to describe in brief some recent developments in water resources management methods and water supply optimization techniques. Two models are discussed: a linear programming model for finding optimum solutions of water supply and a mathematical groundwater basin model, which is capable of simulating various extraction and replenishment flows and predicting the consequences of future engineering works. The unique feature of these two models is that the output of the linear programming model can be used directly on the groundwater basin model to test the physical validity of the economic solution.
INTRODUCTION In spite of major advances in agricultural science the world food situation is a t t h e m o m e n t c r i t i c a l . D u r i n g t h e last y e a r t h e p r o d u c t i o n o f f o o d d i d n o t i n c r e a s e a n d i n s o m e d e v e l o p i n g as w e l l as d e v e l o p e d c o u n t r i e s it d r o p p e d s h a r p l y . A p a r t f r o m t h e f a c t t h a t t h e ' g r e e n r e v o l u t i o n ' is l a g g i n g b e h i n d , a d e p r e s s i v e list c o u l d b e d r a w n u p o f a g r i c u l t u r a l d e v e l o p m e n t p r o j e c t s w h i c h have failed dismally d u e to d i f f e r e n t causes.
18 This proves that agricultural development, here defined as all the activities undertaken to increase agricultural productivity, is a much more complicated problem than is often thought. The problem takes even larger proportions if we think in terms of rural development which, in addition, includes all the non-agricultural activities, economic and non-economic with the objective to increase not only agricultural production but also the satisfactions of rural living (Mosher, 1972). Agricultural development and rural development cannot be strictly separated from each other as their activities are usually partly overlapping. Raising agricultural production causes the rural family income to rise and this in turn will increase the satisfactions of rural living, provided the rewards of the increased production are well divided among landowners, tenants, farm labourers, and urban consumers. Even if we limit our considerations to the problem of agricultural development -- and we shall do so here -- there is no denying that the problem is a complicated one. The numerous physical and non-physical factors ir,volved in increasing agricultural production are inextricably interwoven. It is not surprising therefore that there is a call for a more interdisciplinary and integrated approach to the problem. Such an approach means that all the various relevant factors and aspects will receive due consideration, separately as well as in their mutual relationships. Properly applied, an integrated approach may make us witnesses to a transition from the " a r t " of agricultural development -- an art based largely on unsubstantiated empirical methods -to a fully fledged engineering system designed to achieve the c o m m o n objective of raising agricultural productivity. The days have passed that one single person could solve the problem. Nowadays, the survey teams of agricultural development projects are staffed by members of very different disciplines: hydrologists, groundwater geologists, soil surveyors, agronomists, civil engineers, economists, and rural sociologists. Why then do so many agricultural development projects, even after several years of operation, give unsatisfactory results, show steadily decreasing crop yields, and in the worst cases even become complete failures? There is as yet no clear-cut answer to this question. But it is a distinctive feature of our normal approach to problem solving - including problems of agricultural development -- that the various aspects of the problem are investigated in relative isolation. Often too much time is spent on details at the expense of gaining an understanding of the overall problem. Obviously there is something missing in this approach. That 'something' is the factor relating cause-and-effect. The development of agriculture does not necessarily dictate that a single factor or a single component of the plant--soil--water system should be optimized, for example, water or soil. Besides such physical factors as climate, land, and water, non-physical factors such as economy and sociology play an equally important role. The integration of the data from these different disciplines in a logical, organized, and objective manner is a major problem. It requires a methodology which, as far as agricultural development is con-
19 cerned, is still largely lacking. Advances in science during the last decades, however, are making it possible to adapt and apply modern techniques to the problem, using computerized models and simulations. DEFINITION OF THE PROBLEM There are various approaches we can apply to the problem of raising agricultural productivity. We may, for example, regard land and water as a means of growing crops. In this approach we are interested in land and water only to the extent that they achieve some utility or purpose. Working along this line we apply laws established by science to predict the performance and reliability of the two resources, and we are concerned with the costs of construction, maintenance, operation, and life time of the facilities required to grow crops that give high yields. This approach has often led to failure. Taking water to the desert, for example, does not necessarily mean that the desert will blossom. It may blossom for a while, but will it continue to blossom? There are numerous examples where this approach, founded on the utility principle only, has turned the briefly blossoming desert into a land that is severely waterlogged and salinized and where crops can no longer be grown. The obvious reason for the failure is that the interrelationship existing between surface water and groundwater was overlooked or was thought to be of minor importance. Other examples of failures that have come from following the utility principle are overpumping of groundwater resources, resulting in steadily declining water tables and the intrusion of saline water; or cutting down all vegetation in areas with a windy climate, which results in severe wind erosion. In the above approach the management problem has been neglected. We must distinguish between the existing state and the future state of an area where agricultural production is to be raised. In the future state many things will have changed. For example, water will be supplied to areas where water was never supplied before; new conveyance systems will be built, either concrete lined or not; a more economic use of irrigation water is dictated, i.e., less water will be lost to the underground; well fields will be established in areas where such facilities did not exist before, and so on. Each of these improvement measures has its effect on the groundwater table and it is a major problem to determine their combined effect. The discrepancy between the existing state and some proposed state in fact defines the management problem: the problem of cause-and-effect relations. The greater the discrepancy between the existing and the future state, the greater the management problem will be, and the more difficult it becomes to solve this problem by conventional methods. Since the development of agriculture is thus a complex undertaking, including scientific, engineering, and management aspects, there is an urgent need for a more general approach to the problem. As we all know, there are usually alternative ways of doing things. The
20 fundamental question to be answered in developing agriculture is what is the " b e s t " way of doing so. Hence, it is possible to ask what is the best combination of crops that can be grown? This is the one that gives the highest net return per hectare or per cubic metre of irrigation water supplied. This is an economic problem whose solution requires a proper knowledge not only of soil quality, available water, water demands of crops to be grown, and farm size, but also of available inputs (material, manpower, machinery), water prices, and markets for farm products. All this information must be organized and objective tools applied to it to find the unique solution of the optimum cropping pattern. A similar problem arises when, in the area under study, surface water and groundwater of good quality are available for irrigation. To meet the water demands of agriculture, we could possibly supply surface water only, or groundwater only, but the supply can also be made in an almost infinite number of combinations of the two resources. Hence we may ask what is the best way of operating a groundwater basin or a surface water reservoir or integrated groundwater--surface water supply? Here we are again facing the problem of what is the best solution, the one that is the most economic. When working with traditional methods the solution to this problem can hardly be found, certainly not within a reasonable period of time. Or, having found a solution, how sure are we that there are not better solutions? Again there is a need for objective tools that allow optimal solutions to this and similar problems to be found. A SYSTEMS APPROACH In the preceding paragraphs we mentioned the word " s y s t e m " . What do we mean by a system? There are several definitions of the word and which definition is used depends on the types of problems investigated (Domenico, 1972; In 't Veld, 1972). For example, it can be defined as the whole of a number of related things that are organized in one way or another. All definitions, however, have two essential characteristics in common: a set of elements and the relation between these elements. A systems approach is a general approach aimed at a better understanding of the combination of elements which, taken together, form a complex that can be designated as a system. Characteristic of a systems approach is that it tries to distil the essence of a complex physical entity or system, to describe its structure, and to explain its internal cause-and-effect relations. A systems approach is not limited to physical entities; it can be applied equally well to non-physical phenomena, including those of an economic, biological, and sociological nature. Problems in management and planning involve systems too, e.g., planning irrigation water distribution and supply, farm management, etc. A system is composed of elements, also called objects or components. They can be of any nature; even feelings (in the sociological sense) can be regarded
21 as elements. The elements are the smallest parts which we wish to consider in a given study. Within the system they are interrelated, and, depending on what system is being considered, they may be related to elements outside the system: the environment, for instance. Within a system, we may distinguish subsystems, which are lumped elements. Within a subsystem, the interrelationships remain unchanged. Problems in raising agricultural productivity clearly involve systems. We must in the first place optimize the elements 'plant', 'soil', and 'water' of the plant--soil--water system (Fig.l). We have seen, however, that if we limit our dctivities to this optimization only, failures can be expected. The reason why this is so can also be seen from this figure: the plant--soil--water system is, what is called, an open system, i.e., water from it is interchanged with water from the underlying groundwater system and from the overlying atmospheric system. In fact, these systems are subsystems, representing parts of the main system, called the hydrologic cycle. As the name indicates, the hydrologic cycle is a closed system: no drop of water can be created or destroyed within this system. It will be clear that agricultural development involves more than merely optimizing certain subsystems or their component parts and then waiting to see what happens. The various subsystems must not only be studied separately, they must also be linked and their interrelations and cause-and-effect relations defined. Fig.2 shows a schematic representation of the various subsystems
Eva p o t r a n spi r a t ion
[
PLANT-SOIL-WATER Unsaturated
SUBSYSTEM zone
t Percolation
I
I Capillary
rise
I I GROUNDWATER SUBSYSTEM Outflow
Inflow Saturated
zone
Fig.1. Plant--soil--water subsystem linked with groundwater subsystem and atmospheric subsystem.
22
~
ecipitation
Surfacerunoff subsystem~
groundwattransfer er
Surface w a t e r [
- -
Surface water-
Flow rates Surface water quality subsystems
~tes Groundwater subsystem
Return
flow
Return
flow
[ quality
ty,
Agricultural prod. subsystems, croppinq patterns
-Output
I man power, material
Fig.2. The various subsystems of an agricultural development scheme and their interrelations.
and their interrelations to be considered in problems of developing irrigated agriculture. Developing agriculture thus means planning, management, and control, where control is the monitored state of the development system. A few things are now evident. Firstly, a system implies interrelated objects, actions, or procedures, rather than a collection of loose parts. A systems approach forces us to look at the entire problem, or in other words to look at the forest as well as the trees. And by doing so, we enrich our understanding of the major factors governing the problem of agricultural development. Secondly, the study and solution of the problem involve the development of models of some sort. W H A T IS A MODEL?
If we want to study a system -- the behaviour of a rural population, for instance, or the behaviour of a groundwater basin under modern irrigation
23 techniques or new pumping patterns -- we could make experiments. Often though, this is impossible because of the high costs, the great risks, or the long time required to make them. What we can do is to develop a model of the system in question, and use i t t o simulate certain actions, procedures, decisions, or even feelings. A model is a tool of exploration in which the chaos of facts has been properly organized. A model is a representation of reality, not reality itself, which allows certain actions, procedures, and decisions to be tested and their effects on the system to be predicted. The technique of modelling a certain system or subsystem m a y provide an objective standard by which all the relevant information of the various disciplines can be effectively processed and organized for study. Since a model is a simplification of reality, many people lose confidence in the technique of modelling: reality is too complex to be modelled. The art of modelling, however, is not to lose oneself in details, as is often seen in agricultural development projects, but to take into account those factors that really govern the process under study. In science, simplifications are commonly applied to find a solution to a specific problem. Simplification involves: (a) abstraction, (b) substitution, and (c) reduction. Abstraction means that certain elements or aspects of the system are left out of consideration as they do not greatly affect the validity of the results. For example, in developing a model of an extensive aquifer, a local clay lense occurring within such an aquifer can be neglected without causing severe validity problems. The procedure of abstraction makes the model less complex than reality and thus easier to study. Substitution involves replacing certain elements or aspects by others that have the same effect. To determine the proper size of an airplane wing in a laboratory, for instance, crew and passengers can be replaced by a piece of iron or lead, without causing validity problems. Reduction is another means of simplifying a complex reality. In some models, for example, the time is reduced. Simplification means that the simulation may look quite different from what is being simulated. Simplification is necessary if we want to avoid mathematical difficulties and arrive at solutions. It should, however, be done carefully and with professional judgement. Unjustified simplifications, or ones that are too far-reaching, will render the results obtained from the model unreliable. Agricultural development may be regarded as a system. The various elements of this system can be lumped in an organized manner to form a series of subsystems, as Fig.2 shows clearly. Because of the complex interdisciplinary interest in agricultural development, the models to be developed for each subsystem will differ markedly in purpose, information requirements, assumptions, usefulness, and even the kind of mathematics applied. The models can be used to simulate objects, actions, procedures, or agricultural improvement measures, and to predict the effect of these on other subsystems. For this purpose the relevant subsystems must be linked.
24 In the agricultural development system of Fig.2 two types of subsystems can be distinguished: deterministic subsystems, and probabilistic subsystems. A deterministic subsystem is one that is defined by definite cause-and-effect relations. For example, pumping from wells (a cause) is related to water table change (an effect) or canal seepage and field irrigation losses (a cause) are related to water table changes (an effect). These cause-and-effect relations become only meaningful if they are related to the geology of the subsystem in question. Deterministic cause-and-effect relations can be measured and modelled. A probabilistic subsystems allows no precise prediction, but may provide expected values within the limitations of the probability terms which define its behaviour. Rainfall and river flows, for example, are stochastic or random variables with a definite range of values, each one of which can be attained with a definite probability. Human behaviour, as we are told repeatedly, is unpredictable. But the problem of behaviour of a rural population to agricultural development measures may be studied in a probabilistic manner. The above approach is not new but it is still little applied to the problems of agricultural development. We should take advantage of the experience gained in other sciences, for example, physics or economics, where a systems approach is a c o m m o n approach to problem solving. This article is not intended to be a lesson on how to apply a systems approach ta the complicated problem of developing agriculture; we are just at the beginning. However, a few examples, related to some of the subsystems shown in Fig.2, will be given as an illustration. ECONOMIC OPERATION MODELS As mentioned before, there are usually alternative ways of doing things, and we prefer the " b e s t " way. Crops can be grown in any combination, and surface water and groundwater can be supplied in any combination to irrigate the crops, but how to find the " b e s t " combination? These problems are true economic optimization problems, which nowadays are c o m m o n l y solved by applying the technique of linear programming. Optimization is the problem of finding the best course of action from a set of alternatives. The above problem has as its basic conditions (constraints): the limitation of the available resources (land, water, manpower, machinery, etc.), the minimum water requirements of crops, the market for agricultural products; and as its objective: the maximization of the net return. A solution that satisfies both the conditions of the problem and the given objective is termed an optimal solution. Let us take as an example the problem of finding optimal solutions of water supply for various alternatives of agricultural development. It is assumed that in the semi-arid area under study both surface water and groundwater are available and that an optimal integrated use has to be made of the two resources. But the amounts of surface water available vary during the year and
25 also from ono year to another, though several consecutive dry and wet years can be detected from the records. Groundwater of good quality is available, but the depth to the water table varies from one part of the area to another. Such a situation is often found in alluvial fans which are huge bodies of sediments deposited where mountainous rivers debouch into a plain. In the apex of the fans the water table is considerably deeper than at their foot. In adjacent areas the groundwater is salty. The land resources (soil classes) are known from a soil survey. Sociological surveys have revealed the number of rural families living in the area, the number of cattle they possess, their present water rights and land use. There are chances that the present shortage of irrigation water can be alleviated in the future by importing treated waste water from nearby towns, or surface water from another catchment area. These waters are, of course, more costly than local water because purification plants, pipe lines, dams, and tunnels through mountainous areas must be built. But the price of local water also varies in different parts of the area, because a new conveyance system has to be built to distribute this water even to the remotest parts of the area. This network of irrigation canals may or may not be concrete-lined or partly lined to reduce seepage losses. The various depths at which the groundwater is found makes the price of groundwater differ from one part of the area to another. We are facing here extremely complex decision problems. Decisions must be taken as to how much land is to be supplied with water. Shall we supply all the existing farm lands with water or only the best lands? The latter decision involves resettlement of a number of farmers. What kind of water supply and delivery system has to be built? Is a certain period of overpumping the groundwater resources (mining) permitted to alleviate the shortage of surface water till foreign water is available from another catchment? To what extent can this imported water be used economically? Where can groundwater in the future best be abstracted and at what rate? Occasionally flooding of the river occurs; how can this water or part of it be used, for example, to recharge the groundwater artificially? What will be the best size of the farms? And finally, how has the envisaged water supply system to be operated so as to meet the water demands of agriculture in an optimal way without causing harmful side-effects? It will be clear that there are series of different possibilities which we may regard as alternative plans. De Ridder et al. (1969) applied the technique of linear programming to the problem of finding optimal solutions of irrigation water distribution and supply in a 100 000 hectares large agricultural area in Iran. Linear programming is a single-stage optimization technique by which several decision variables are simultaneously optimized. The complete mathematical statement of a linear programming problem for water supply includes a set of linear equations which represent the conditions (constraints) of the problem, and a linear function which expresses the objective of the problem.
26
The linear programming problem concerned is a maximization problem, i.e., a problem of maximizing the net income of a governmental agency which will take care of the distribution and supply of irrigation water, operation and maintenance of the water supply and delivery facilities. It will conduct its business as a non-profit agency. "Net income" is defined as the residual of the following transactions: receipts from selling water to the farmers minus all costs of water services from deep wells and surface water canals. By "maximization" is meant the economic criteria that marginal returns should be greater than or equal to marginal costs. The demand for water is considered as agricultural production activities in the distinguished sub-areas of the plain which yield different net returns per cubic metre of water. The activities compete in this way for the available limited water resources. The model comprises the following activities (see also Fig.3):
A C T I V I T I E S ~ Supply of river
water by cana s No costs assumed]
upstream of
diversion point
/ I
~
Annual costs of new canal system (investment, m a i ~ tenance, operation)
LINEAR
PRO
I Supply of ground I water by we s
Agricultural production
Annual costs of I Net return perI deep well system I cubic metre of (investment,main- water tenance,operation
RAMMING
MODEL~ f,
-~I PHYSICALCONSTRAINTS
ALTERNATIVEPLANS
Amount of river water available in a dry, wet, average
--
All the best soils are supplied
L
year
All existing farms are supplied
L~
Maximum water
All i r r i g a t i o n canals
|
requirements per ha
are lined
of crop
V g-
Irrigation canals are partly lined
Minimum water
__ requirements per ha
of c~op
Various river flows | (dry, wet, normal years)
F-
Computing optimal water supply system
Importation of water in various quantities
|
Mining and no mining of groundwater
|
F--
I
I
I solutions physicaland ...... qcal] with d i f f e r e n t alternatives
Fig.3. S c h e m e for the e c o n o m i c analysis of various alternatives of water supply to an irrigation area.
27 R I VER = Inflow o f river water at the main diversion dam at the head of the alluvial fan. iSRF = Supply of river water by a canal system to sub-area i. iWELL = Supply of groundwater from wells to sub-area i. iPRD = Agricultural p r o d u c t i o n in sub-area i. These activities have costs which were calculated. For example, iSRF costs represent the costs of maintenance, operation, and capital costs o f a new canal system, iWELL costs represent the cost of a well, 150 m deep, operation, maintenance, interest, depreciation. The cubic metre price of well water was differentiated for different parts of the plain on the basis of water table d e p t h and aquifer characteristics, iPRD costs were considered as negative costs (returns); th e y represent the net return per cubic metre of water, i.e., the net residual of the crop value after deduction of purchased input, including interest, all labour costs, and capital costs of land levelling. The activity iPRD was based on an o p t i m u m agricultural p r o d u c t i o n pattern and the respective water requirements of this crop pattern per hectare was determined. The constraints of the model are defined as follows: xRIVER xiPRD xiWELL Z xiSRF xiPRD
~< ~< 4 = =
MXRIV iMXD MXSFY + Z xiSRF xRIVER xiWELL + xiSRF
x R I V E R ~< MXRIV: the available river water in a dry, wet, and average year. The inequality xiPRD ~< iMXD defines a m a x i m u m water demand restriction in sub-area i, and the inequality Z xiWELL ~< MXSFY + Z xiSRF states th at the total well water abstraction is smaller than or equal to the sum of the net subsurface inflow into the basin and the net deep percolation in sub-area i. The equality Z xiSRF = x R I V E R states that all surface water distribution activities equal the total river flow, and the equality xiPRD = xiWELL + xiSRF defines the logical condition that any level of p r o d u c t i o n in sub-area i must be supplied by groundwater or surface water. The linear programming model then allows the o p t i m u m solution of water supply to be c o m p u t e d for each alternative agricultural devel opm ent plan. The results obtained f r om the model show what part of the plain should be supplied with surface water, what part by groundwater, what part by the t w o resources, and what part should n o t be supplied from either source because it is n o t economic to do so. Fo r each water supply solution the net return per cubic metre of water is calculated. The net return values of the alternative plans can then be com pared and ranked. Those plans t h a t show the highest net return can be selected for further study and eventually the best plan can be selected for final design.
28 GROUNDWATER BASIN MODEL As was mentioned before, a water supply solution, being a proposed state, may and often will differ considerably from the existing state. Hence a basic question to be answered is, how will the whole groundwater basin, meaning here in particular the water table, react to the total of all the changes that will be brought about in the future? The optimal water supply solutions, as obtained from the linear programming model, have to be tested as to their physical and technical feasibility. A tool that can be used to examine the response of the water table to new engineering works as suggested by the linear programming model is a digital model of the groundwater subsystem shown in Fig.1. The groundwater basin model used in the above studies has initially been developed by Mr. H.N. Tyson, Data Processing Division of IBM Corporation in Los Angeles, in cooperation with engineers of the California Department of Water Resources (Chun et al., 1963; Weber et al., 1968). The model is developed to simulate the dynamic behaviour of the groundwater basin under various plans of basin operation. It is based on the Darcy equation and the law of conservation of mass which combined yield a nonlinear partial differential equation. This equation represents a model of the flow rates associated with a unit area of aquifer, including the subsurface inflow ~tnd outflow rates, flow rates in or out of storage, and inward or outward flow rates external to the aquifer: ah
gP ~]k(x,y) h ~ h - S ( x , y ) ~- -Q(x,y,t) = 0 p
(1)
where k = permeability coefficient, h = water table height above a datum, S = storage coefficient, t = time, Q = net external input, including precipitation, evaporation, canal seepage, drainage flow, irrigation percolation losses, well flow, etc., g = acceleration of gravity, p = density of groundwater, p = viscosity of groundwater, x and y are cartesian coordinates, and V, = differential operator ( V,= a/ax + a/ay). The partial differential equation is approximated by a finite differences equation. The groundwater basin is therefore subdivided into a number of sub-areas (polygonal areas) by applying Tiessen's method (Fig.4). The size and location of the polygons is chosen on the basis of known variations in replenishment, extractions, transmission, storage, and water table heights. Each polygon has a nodal point, which is considered the control point for that particular area. In accordance with the theory of finite differences the flow rates in a polygonal area may be integrated. The finite difference equation for a given node reads:
i
Yi,B hi(tj+l)- hs(t]+l)
1
-
ABSB t
hB (t]+l) - hB(tj) ] + ABQB(t]+I)
(2)
1
2
3
4
5
6
'7
8
9
10
M I\////// 7.~i'1KA I --
X /
t
/
U
GHALEH BOtANO~ !
%%~
v!
IY
!
'
i,
\\ \\
Ilw
_ ...~127
/I I
iX
Y
L
i Z[_____
L
B
1( SIAH
1
2
3
4
5
6
KUH
7
~
9
10
Fig.4. A sample of a polygonal network. Varamin groundwater basin, Iran (After De Ridder et al., 1969).
Lb
.^
l
:: . . . . .
l
I
l
. .. . . . l
.
.
l.
. .
l
i
.
.
.
.
.
.*
l
.
l l
:
:
.
.
.
:
l
1
.
l
l
cc r?I_._____‘_,____.____*---“l”“““‘~
58
.
.
.
l
+
l
Fig.5. Example of a digital computer output special polygon of the Mires Basin on Crete, groundwater levels are compared.
i
1 Ef I ! I’
i
I I I
I
I I I
~,__-_‘__‘_*__‘_-_-“
54
I
66
bb 7. LU ~~._.,.,.~..^_‘_._.,I-.I-__~‘I-_~~-,~~___~.~~~ ‘C
._
for the groundwater table elevations in a Greece. In this diagram computed and historic
.
.
.
.
‘.
*. .
^Y_ IF*,
se-: se:0
ai 5.5:4
61.4 61.‘) 60.5 60.1 59.7 59.5 59.5 59.4 59.7 49.R 59.9 b0.L 59.9 59.5
61.6
61.7
$3 b::b 60.6 60.5 ho.* 60.’ 60.4 60.6 6l.l 61.7
b3.D
.-
as-; &3:.5
LO.3 59.9 59*7 59.T 59.8 59.9 to.1 60.1 60.0 59.7
to.0
61.5 t2.4 62.8 62.9 62.8 62.6 62.2 Cl.4
:0,'p
0.
::*: .
t1.n
CL.7 62.3
63.0
HISI. 63.0 %?
31
where Y = a conductance factor made up of transmissivity width (W), and flow path length (L): Y=
wi, B Ti, B
(
Li,B
1
X
saturated (
(T), boundary
thickness
total thickness
1
A = area of polygon,
i,B = contiguous nodes and node in question, respectively, and the other symbols as defined above. A computer is used to solve the finite difference equations. The computer generates water table elevations for each polygon and for each time step (a period of two weeks or one month) using a Gauss-Seidel relaxation technique. For this, as for any other model, there is the problem of validity. The validity of the groundwater model can be tested by comparing the polygonal water table elevations generated by the computer and those measured in the field. To make it easier to compare computed and measured (historic) water table elevations, a plot programme is used. At the end of the computations these data are plotted graphically for each polygon (Fig.5). If the two hydrographs do not match satisfactory, such input values as aquifer transmissivity,
Mathematical water basin
qround model
I
Natural ground water basin
Groundwater basin simulation
Model
Historic
verification
water
Computed water table data
'
testing various alternative plans of groundwater basin
Fig.6. Scheme for developing groundwater basin computer models,
32
storage coefficient, or net deep percolation rates are adjusted as is required. This calibration process is repeated until the pairs of hydrographs for all polygons match satisfactorily (Fig.6). The model can then be used for simulating and testing alternative water supply solutions. The behaviour of the water table can be predicted for each polygonal area for any desired period of time. SIMULATING A L T E R N A T I V E WATER SUPPLY SOLUTIONS
We have seen in Fig.1 that the plant--soil--water subsystem is linked with the underlying groundwater subsystem. A change in the element 'water' of the plant--soil--water subsystem may result in a change in the element 'percolation', with which it is linked to the groundwater subsystem. A change in percolation will effect the groundwater subsystem, and this will be reflected by a change in water table height. Other factors that may affect the groundwater subsystem are: groundwater recovery by wells, artificial recharge of the groundwater basin, seepage from the conveyance subsystem, and field irrigation percolation. We have seen that in the groundwater model all the external flows (rainfall, evaporation, seepage, artificial recharge, if any) are lumped with the pumped extractions, if any, into a single term, called "net deep percolation" (AQ-term). For the existing state, the net deep percolation values for each polygonal area and for each time step (say, one month) are known. Hence, if in a proposed state groundwater extraction in a specific polygonal area will be increased by a rate of X mS/month, the monthly net deep percolation of this area must be reduced by the same rate, or a portion of it if a certain return flow occurs. Similarly, if in a proposed state canal seepage or field irrigation percolation in a particular polygonal area will be X% higher than in the existing state, the polygonal net deep percolation must be increased by this percentage. For testing linear programming solutions of water supply, two things are required: (1) the linear programming model must be grafted on the groundwater model; (2) the linear programming solutions must be translated into terms of polygonal net deep percolation values. As to item (1), all the activities of agricultural production, well water supply, surface water supply, etc., and their respective costs must be based on the polygonal areas as distinguished by the groundwater hydrologist in developing the groundwater basin model. As to item (2), a special computer programme is required to compute the net deep percolation values on a polygonal basis for each water supply solution as calculated by the linear programming model. By means of this programme, the polygonal water demands, quantities supplied b y surface water and/or groundwater, quantities lost in conveyance and at the field are listed at the end of the computations and the sum is formed of the polygonal field and conveyance losses and pumped extractions: the polygonal net deep percolation in the proposed state. These new net deep percolation values are then fed into the groundwater model. As shown in Fig.7, this model simulates these values and generates the water table heights for each polygonal area for any period of time, say 10 or 20 years, as is desired.
33
IMathematical ground L[ water basin model
Translation of linear programming solutions in terms of groundwater hydrology
i Groundwater basin simu ation
l
Computed future watertables
Alternative linear
[ programming solutions
I
Evaluationof the alternative solutions and selection of the best plan
YES Final design of water I delivery system and I water resources management plan
Fig.7. Scheme for feasibility analysis of linear programming results adapted to a groundwater basin computer model.
Table I shows an example of a water supply solution obtained from the linear programming model. The solution is based on the assumptions that there is an average river discharge of 245.106 m3/year; mining of the groundwater resources is not permitted; the canal system is completely lined; all farmers living in the plain will be supplied with irrigation water; each farmer will possess 3.85 hectares of land, which will be supplied with 3.85 × 10 440 m 3 = 40 194 m 3 of water. The solution shows that of the total maximum demand of 299.106 m 3, 203.1.106 m 3 will be supplied by the river and 95.9.106 m 3 by the groundwater. It can be seen from the table that all polygonal areas are supplied up to their maximum demand except polygon 16 whose demand is only partly met by supplying river water. The reason for this is that there is not sufficient water available from either source of water. The general solution also shows that river water should be supplied to the northern and middle areas of the plain, while the water demand of the southern and peripheral polygonal areas should be met by supplying groundwater (a transport cost minimizing solution). To examine the effect which the water supply solution, as presented in Table I, would have on the groundwater table in the plain if it were imple-
34
TABLE I Linear programming solution of irrigation water supply (106 m 3) Number of polygon
Maximum water demand
Supplied by river water
Supplied by well water
1 2 3 4 5 6 7 8 9 10 11 12 13 14
4.793 18.855 19.815 3.515 13.530 14.778 14.778 7.882 13.102 8.330 10.046 16.659 11.165 15.241
4.793 18.855 19.815 3.515 13.530 14.778 14.778 7.882 13.102 8.330 10.046 16.659 6.953 15.241
15
14.609
14.609
16 17 18 19 20 21 22 23 24
5.208 13.278 15.091 18.402 10.815 9.883 25.707 5.890 11.056
1.831 --18.402 ------
-13.278 15.091 -10.815 9.883 25.707 5.890 11.506
3.377 ---------
299.051
203.119
95.932
3.377
Total
---------4.212 --
Unsupplied demand
--
-------------
mented, the polygonal net deep percolation values corresponding to this solution are fed into the groundwater model. The model then simulates these v a l u e s a n d t h e r e s p o n s e o f t h e w a t e r t a b l e is p r e d i c t e d . T h e d i f f e r e n c e b e t w e e n the predicted water table after a certain period of operation and the initial water table elevation can be calculated. The polygonal water table differences a r e t h e n p l o t t e d o n a m a p a n d l in e s o f e q u a l c h a n g e a r e d r a w n ( F i g . 8 ) . I t c a n b e s e e n f r o m t h i s f i g u r e t h a t t h e w a t e r t a b l e in t h e m i d d l e o f t h e p l a i n ( p o l y g o n s 9, 1 0 , 1 1 , 1 2 , 1 4 , a n d 1 5 ) w o u l d rise c o n s i d e r a b l y in a p e r i o d o f 9 years. This area would become waterlogged within this period of time, the reason being t h e exclusive s u p p l y of river w a t e r to these areas a c c o m p a n i e d by r e l a t i v e l y h i g h p e r c o l a t i o n losses. O n t h e o t h e r h a n d , t h e h e a v y g r o u n d w a t e r a b s t r a c t i o n in s o m e p o l y g o n s ( n o . 1 7 , 2 0 , 2 1 , a n d 2 2 ) w o u l d c a u s e t h e w a t e r t a b l e t o d r o p a b o u t 1 6 m w i t h i n a p e r i o d o f 9 y e a r s . F o r p o l y g o n 1 7 t h e r e is a d a n g e r o f i n t r u s i o n o f s a l t y g r o u n d w a t e r f r o m a d j a c e n t areas. T h e m a i n c o n c l u s i o n is t h a t t h e w a t e r s u p p l y s o l u t i o n , t h o u g h e c o n o m i c a l l y s o u n d , is n o t f e a s i b l e f r o m a h y d r o d y n a m i c a l p o i n t o f v i e w ; i m p l e m e n t a t i o n
35
/
i I
\
/
/
Fig.8. Changes in water table after 9 years if the linear programming solution of irrigation water sup.ply as shown in Table I were implemented and operated. of t h e p l a n w o u l d cause severe g r o u n d w a t e r p r o b l e m s w i t h i n a relatively s h o r t period of time. In t h e s a m e w a y all t h e o t h e r a l t e r n a t i v e s o l u t i o n s can be tested. T h e s o l u t i o n , w h i c h is e v e n t u a l l y selected, m a y still s h o w u n a c c e p t a b l e w a t e r t a b l e changes in certain p a r t s o f t h e plain. A l t h o u g h it m a y n o t be e c o n o m i c a l , a d j u s t m e n t s can be m a d e . F o r e x a m p l e , in areas w i t h r a p i d l y rising w a t e r tables less surface w a t e r c o u l d be supplied a n d m o r e g r o u n d w a t e r e x t r a c t e d . T h e s e a d j u s t m e n t s m a y be r e g a r d e d as a p o s t o p t i m i z a t i o n o f t h e s o l u t i o n in q u e s t i o n . F o r this p r o c e s s t h e g r o u n d w a t e r m o d e l again can b e used to t e s t t h e e f f e c t s o f t h e s e a d j u s t m e n t s o n t h e w a t e r table.
36 CONCLUDING REMARKS In dealing with complex problems of agricultural development, a systems approach has great advantages over conventional approaches, as it allows the problem to be seen as a whole instead of in its details. Agricultural development involves planning, management, and control, and this should be effected in the best possible manner. A systems approach also allows certain subsystems or combination of subsystems of the main system to be examined, as we have tried to explain. A systems approach always involves some sort of model whose variables can be changed within the range of their possibilities. Once a model has been developed and verified it can be used to simulate almost infinite numbers of alternative plans, actions, procedures, assumptions, and allows their responses to be examined. This approach will enrich our understanding of the problem. Decisions can be taken on a much firmer basis than is possible with traditional methods. The example of rapidly rising water tables given above is not a hypothetical one; it comes regularly to our notice from semi-arid regions where irrigated agriculture is introduced. High investments must then be made to cure the problem of waterlogging and soil salinization, for example by installing an artificial drainage system or by changing cropping patterns and irrigation techniques. These and similar problems must be recognized beforehand, i.e., before an agricultural development plan is implemented. Agricultural development, of course, encompasses more than the few cases discussed in this article. Several factors of a non-physical nature -- those of sociology or politics, for instance -- play an equally important role. It is often heard that unsurmountable difficulties are encountered in their modelling. But the physical environment is no less complex than a human society. There is an urgent need for a rational approach to sociological and political problems related to agricultural development, which will allow the results of these fields of study to be effectively integrated in the whole system. To avoid misunderstanding, we must state that models are not the answer to all problems; they have their limitations too, and we should not expect miracles from them. However, in spite of their limitations we can say that any model is better than no model. They are very useful tools by which we can make more substantiated decisions than is possible by conventional methods. For further details of the techniques described in this paper and the results obtained from them for a case study in Iran, the reader is referred to a forthcoming publication on the subject matter in the Series of Bulletins of the International Institute for Land Reclamation and Improvement, Wageningen, The Netherlands
REFERENCES Chun, R.Y.D., Weber, E.M. and Mido, K., 1963. Computer tools for sound management of groundwater basins. Int. Assoc. Sci. Hydrol.,I~erkeley,Publ. No.14: 424--437.
37
De Ridder, N.A., Eres, A., Chun, R.Y.D. and Weber, E.M., 1969. A computer approach to the planning for optimum irrigation water supply development and use in the Varamin Plain, Iran. Report of the FAO, Rome, 28 pp. Domenico, P.A., 1972. Concepts and Models in Groundwater Hydrology. MacGraw-Hill, London, New York, N.Y., 405 pp. In 't Veld, J., 1972. Denken in systemen: systeembegrippen, systeem benadering, hi~rarchie van systemen. Ingenieur, 84(32/33): A 680--685. Mosher, A.T., 1972. Projects of Integrated Rural Development. The Agricultural Development Council, Inc., New York, N.Y., pp.l--8. Weber, E.M., Peters, H.J. and Frankel, M.L., 1968. California's digital computer approach to groundwater basin management studies. Symposium on Use of Analog and Digital Computers in Hydrology, Tuscon, Arizona, December 8--15, 1968, pp.215--223.