M fj 3 Lt 'World Bank Reprint Series: Number 334 Gerald T. O'Mara and John H. Duloy > VI I q q Modeling Efficient Water Allocation in a Conjunctive u se Regime The Indus Basin of Pakistan Reprinted with permission from Water Resources Research, vol. 20, no. 11 (November 1984), pp. 1489-98, copyright by the American Geophysical Union. WATER RESOURCES RESEARCH, VOL. 20, NO. I1, PAGES 1489-1498, NOVEMBER 1984 Modeling Efficient Water Allocation in a Conjunctive Use Regime: The Indus Basin of Pakistan GERALD T. O'MARA AND JOHN H. DULOY Agricultuiral and Rural Development Department, The World Bank, Washington, D. C. Efficient resource use where ground- and surface waters are used conjunctively may require special policies to rationalize the interaction between water use by farmers and the response of the stream aquifer system. In this paper, we examine alternative policies for achieving more efficient conjunctive use in the Indus Basin of Pakistan. Using a simulation model which links the hydrology of a conjunctive stream aquifer system to an economic model of agricultural production for each of 53 regions of the basin together with a network model of the flows in river reaches, link canals, and irrigation canals, we have studied the joint effect of various canal water allocation and associated private tube well tax or subsidy policies on overall system efficiency. The results su ggest that large gains in agricultural pro- duction and employment are possible, given more efficient policies. 1. INTRODUCTION reviews of the state of the art in modeling groundwater and The objective of this paper is to present some simulation stream-aquifer systems are found in the work of Bachinat et al. results on a efficient conjunctive use for the irrigated agricul- [1980] and Gorelick [1983]. Modeling that incorporates more ture of the Indus Basin of Pakistan. The Indus Basin has been real world detail has uncovered potential conflicts between the subject of a number of studies in the past several decades, public and private interests stemming from the physical link- as the long run effects of the introduction of large-scale canal age between operations by individual well operators created irrigation to the flat, slowly draining Indus plains, i.e., water- by reliance on a common aquifer, i.e., a physical external dis- logging and salinization, became increasingly troublesome economy or simply externality. This has led to a [e.g., Chaudry et al., 1974; Fiering, 1965; Greenman et al., characterization of the problem as a hierarchial or multilevel 1967; Irrigation and Agricultural Consultants Association one [Yu and Haimes, 1974]. One device for closing the gap (IACA), 1966; Lieftinck et al., 1968; Revelle, 1964; Tipton and between public and private interests caused by the externality Kalmbach Inc., 1967; Water and Power Development Authority is some form of tax and/or quota on pumping, and this solu- (WAPDA)-Harza Engineering Co., 1963; WAPDA, 1979]. tion has been explored in a number of studies [e.g., Bredehoeft The studies of WAPDA-Harza, Revelle, IACA, Tipton and and Young, 1970; Maddock and Haimes, 1975; Feinerman and Kalmbach, and Lieftinck et al. were unanimous in recom- Knapp, 1983]. The present study utilizes a static deterministic mending large-scale public tube well development for vertical formulation, multilevel structure, and a tax/subsidy instru- drainage and to achieve efficient conjunctive use, although the ment in analyzing efficient conjunctive use. long-term need for horizontal drainage to remove salt accu- This study had its origin in the World Bank's involvement mulations was recognized. These recommendations were in- as executing agent of a United Nations Development Program corporated in the government's investment program of the (UNDP) funded "Master Planning" effort by the Water and 1960's and 1970's. In retrospect, these studies underestimated Power Development Authority (WAPDA) of Pakistan to pre- both the strength of the incentives for private tube well invest- pare a "Revised Action Programme" (RAP) for irrigation in- ment and the difficulties in implementing and managing a vestments in the basin. This would update the "Action Pro- massive public tube well operation. These difficulties and the gramme" set out by a similar planning effort in the 1960's. Pakistani response have been carefully documented by John- The resulting Indus Basin family of models has demon- son [1982]. At present, about three quarters of tube well with- strated a capacity for providing answers to a variety of policy- drawals are by private agents, and the problem of achieving relevant questions, for example, issues of mechanization, tech- efficient conjunctive use has been completely transformed nical change, and agricultural price policy, as well as irrigation from that envisioned by the scenarios of the 1960's [WAPDA system management and evaluation of investment projects 1979]. and programs. To date these models have been used in three The problem of efficient conjunctive use is inherently dy- project appraisals in the bank, and there are several more namic, and much of the early work was explicitly dynamic prospective applications of this type. However, these models [e.g., Buras, 1963; Burt, 1964, 1966, 1967; Bredehoeft and may well have more potential utility to Government of Paki- Young, 1970; Brown and Deacon, 1972; Noel et al., 1980]. stan policy makers than to the World Bank. This possibility However, dynamic optimization suffers from the curse of di- was noted by the Planning Division of WAPDA, and a team mensionality, and necessarily dynamic models must simplify of WAPDA programmers and systems analysts was trained at to the point that significant aspects of real world applications the bank to effect the transfer of this modeling technology to must be suppressed. This dilemma has led to modeling meth- Pakistan. ods that are not explicitly dynamic, e.g., static "steady state" The outline of the paper is as follows: the next section models, such as that of Rogers and Smith [1970]. Excellent presents a description of the Indus model family structure, followed by a review of model validation. These are followed Copyright 1984 by the American Geophysical Union. by some results from simulation experiments which analyze Paper number 4W1019. conjunctive use in the Indus irrigation system and assess some 0043-1397/84/004W-1019$05.00 alternative policies. 1489 1490 O'MARA AND DULOY: MODELING EFFICIENT WATER ALLOCATION IN CONJUNCTIVE USE iTarela oChenob River R|servotr Madhopur 9-3 M. A.F) M~ang laBarg warsaw 17 ~~~Reservoir c ,4-arg e KabuC 53M.A.F) Marola AS -A \Oel Kaebul R veX 0 5 0 r ~ ~ R u fS Jina 0.R., o1 (Konbgh aaJo >., Barrage rr .9ithadirt. d Reevi *. t F;uoze9org an 6 0rrorr g rnn ~ Barrage denBaAgFS discharg SUtsKIJIn thousand cusecs. F. cre on Tuso - U. ' a sa / F SEAg, Fig.1. Sructre o theIndu bsiphrigtonsytm O'MARA AND DULOY: MODELING EFFICIENT WATER ALLOCATION IN CONJUNCTIVE USE 1491 NWFP Fig. 2. Pakistan: Indus basin agroclimatic zones. 2. MODEL STRUCTURE matic zones (ACZ's), and the mapping of polygons into ACZ's In the past, many economic models concerned with policy is given in Figure 2. The data for the differentiation of the and planning have been straightforward optimizing models. basin into ACZ specific cropping technologies were largely While admirably direct, this approach neglects an important derived from the 2000 farm sample of the Master Planning aspect of the economic policy environment. Models designed Agroeconomic survey. Table 1 gives average cropping patterns for policy analysis normally involve two kinds of agents: for the several ACZ's as some evidence of the appropriateness policy makers and policy receivers. If the policy receivers are of the partition. optimizing agents, one is faced with a hierarchical decision- The surface water distribution system must be superim- making problem. In the case of the Indus Basin models the posed on the complex mapping of groundwater areas (i.e., government plays the role of the policy maker, while the farm- polygons), canal commands, and ACZ's. This is done by ers play the role of the policy receivers. The government de- means of a network formulation. All of the flows of the sche- cides on water-related investments and surface water allo- matic for the Indus Basin Irrigation System are represented as cations and sets (some) agricultural prices, taxes, and/or sub- directed flows along segments, which are the arcs between one sidies. The farmers, in turn, react to the setting of these policy control point or node and another. instruments by using water (both surface and groundwater) In addition to the above-mentioned water constraints, each and other inputs, making private investments in tractors, tube polygonal model has embedded in it a single farm-level model wells, etc., and choosing cropping patterns so as to maximize to characterize the agricultural production system of the area. their own welfare. Generally speaking, the strategy of the Such a farm-level model simulates the resource allocation Indus family of models is to separate analytically the two choices of a single representative farmer who determine the types of decision makers by simulating the response of the production and disposition of 11 crops and four livestock policy receivers to the actions of the policy makers int the commodities. Exogenous resource limitations are imposed on model per se and to represent the actions of the policy makers land and labor. The water supply and demand constraint of by changes in model structure and/or parameters. However, each farm-level model includes estimates of water available there are exceptions to this rule, particularly in the instance of from rainfall, evapotranspiration from the aquifer, and canal policy constraints due to physical externalities (e.g., surface and tube well water. When used to evaluate water allocatiQn water-groundwater interactions) that are not recognized by policies, canal water allocations are endogenous, as is the policy receivers. volume of private tube well pumping. The model maximizes The basic structure of the Indus Basin model can be visual- the objective function, which is the sum of polygonal farm ized as follows. The entire basin is partitioned into 53 irrigated incomes less polygonal risk premium terms. The risk term regions, referred to as polygons. Each polygon is essentially essentially linearizes a nonlinear mean standard deviation of homogeneous with respect to groundwater and preserves income trade-off surface. Moreover, farm income enters into boundaries that are significant to the groundwater-aquifer linear family consumption constraints, and it can be shown system. Linkages in water supply that arise from seepage of that this formulation is equivalent to maximizing a nonlinear surface water to the aquifer and withdrawal of groundwater utility or weighting function that places grcat emphasis on via tube wells or capillary action, as well as underflows be- meeting family consumption needs. tween polygons, are explicitly modeled for each polygon, All polygonal models have a groundwater balance con- thereby interlocking the polygons. Each polygon also receives straint, which may be deleted in certain solutions. Briefly put, surface water on a monthly basis from one or more control this constraint forces equality between additions to and with- points of the surface water delivery system. Figure 1 presents drawals from the aquifer. The presence of this constraint is the schematic diagram of the Indus Basin Irrigation System, crucial to the solutions of the basinwide model with endogen- which identifies the control points where diversions to individ- ous canal water allocation. Without it the solution is not an ual canal commands are made. equilibrium in the sense that it would be indefinitely sus- In order to embed those differences in soils, climate, etc. tainable. As individual farmers do not recognize their individ- that create regional comparative advantage in different crops, ual effects on groundwater equilibrium which must be main- model cropping technologies were specialized to nine agrocli- tained over the long run, the government must take into ac- 1492 O'MARA AND DULOY: MODELING EFFICIENT WATER ALLOCAnON IN CONJUNCTIVE USE TABLE 1. Cropping Patterns of Major Crops, Average of 1972-1973 and 1975-1976 Cropping Years: Percent of Cropped Area Agroclimatic Zone Punjab Sind Sind Sind Sind Northwest Mixed Punjab Punjab Punjab Cotton- Rice- Cotton Rice- Frontier Crops- Cotton- Sugarcane- Rice- Wheat Wheat Wheat Wheat Province Wheat Wheat Wheat Wheat North North South South Total 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 100.0 Rice 0.4 2.5 5.2 5.0 30.7 12.5 54.8 8.8 51.0 14.0 Wheat 34.4 52.0 38.5 42.1 41.8 36.3 21.2 41.7 20.5 38.4 Cotton 0.5 8.9 26.2 13.3 2.7 25.8 3.3 30.0 14.8 17.3 Corn for grain 35.0 1.0 1.3 4.1 1.3 0.3 0.1 1.5 0.5 2.5 Gram 0.1 7.3 1.5 1.3 0.8 5.1 10.8 0.1 0.6 2.5 Sugar 18.7 5.0 3.6 8.4 1.9 3.6 0.4 3.7 5.4 4.6 Rape and mustard 0.6 5.1 3.2 1.9 1.4 5.7 3.4 2.6 2.2 2.9 Kharif fodder 3.6 10.0 11.0 10.6 7.0 3.8 0.4 5.4 1.6 8.3 Rabi fodder 6.7 8.3 9.4 13.4 11.1 7.1 5.6 6.2 3.4 9.4 Area cropped, ha x 103 336 757 4,745 2,043 1,604 837 931 636 345 12,231 Cropping intensity 158 107 113 121 134 105 106 91 83 114 Sources: 1972-1973 from Agricultural Census Organization, Government of Pakistan, Pakistan Census of Agriculture, 1972; 1975-1976 from provincial reports on cropped acreages. count the long-term consequences of any water allocation period should be used to generate model solutions that can be scheme and the impact of water-related investments on equi- compared with an average of actual producer responses in the librium. This expresses precisely the two-level aspect of the base period, on the assumption that producer responses on Indus Basin model, where some constraints are not formally the whole are close to long-run equilibrium. recognized by the farmers (the policy receivers) even though Two time periods were considered for validation runs, the the government (the policy maker) requires that they be satis- periods of 1967-1975 and 1975-1980. The former period in- fied. How the government might accomplish this task is ex- cludes responses that are subsequent to both the introduction plained in detail by Bisschop et al. [1982]. Briefly stated, the of the new green :.~volution varieties of wheat and rice and the main result is that if groundwater balance is imposed, the dual initiation of use of Mangla Reservior and are prior to the variable (i.e., shadow price) corresponding to this constraint is initiation of the use of Tarbela Reservoir. The latter period the tax or subsidy which would induce farmers to pump tube contains the history of post-Tarbela producer responses. wells at the level required for groundwater balance. The experiments reported are actually experiments to select The original Indus Basin model was a linear programming a set of water loss parameters that permit the model to accept- problem with more than 20,000 constraints, with an objective ably reproduce important aspects of both production re- function for the basinwide model that is simply the sum of the sponse, e.g., the cropping patterns and intensities of Table 1, objective functions of the polygonal submodels. A model of and the state of the groundwater aquifer. This procedure pre- this size exceeds the capability of existing software for linear supposes prior calibration of the specification of agricultural programs, and it was apparent early on that a special sim- technology and producer behavior, which was done previously plification would be needed. By converting the height of the on a polygon by polygon basis. The procedure for calibrating water table in each polygon to a policy instrument. structural single-farm-level models is well known and need not be dis- simplifications could be made such that the entire model con- cussed here. tains less than 8000 constraints, which is solvable using a large The existence of significant uncertainty with respect to the machine and commercial software. loss characteristics of the surface water system was unantici- The above introduction has been brief and has ignored pated. Perhaps somewhat naively, it had been assumed that many details. Despite this brevity, the reader will have gotten these characteristics, which are subject to measurement, would some impression of the site, structure, and complexities that be known with some precision by the operators of a system are captured by the system. Readers desiring a complete de- with as long a history as the surface water irrigation system of scription of the model structure may obtain this from the the Indus Basin. This assumption turned out to be incorrect. authors. Our response to the existence of significant uncertainty with respect to loss characteristics of the surface water system was CARACTEIO STIMATN OFLWATEOs to test the model with several specifications of system loss S Acharacteristics representing a spectrum of plausible scenarios The Indus Basin Model is a comparative statistical model concerning system performance. In order to keep the number that simulates producer response to policy intervention. That of validation experiments within reasonable bounds, these sce- is, it can be used to compare producer resporse to different narios were restricted to specification of a limited number of environments where the environmental change is wrought by cases covering the range of likely loss characteristics. The de- policy intervention in the sense of complete producer adjust- tails of the specification of these cases are given in Table 2. ment (i.e., long-run response) to environmental change. There- Note especially that the high efficiency assumption with re- fore the important function of model validation is not appro- spect to watercourse and field losses is at the level specified in priately accomplished when actual historical conditions on a the Indus Special Study [Lieftinick et al., 1968], which presents year by year basis are used to simulate a dynamic path of in detail the planning exercise behind the appraisal of the producer adjustment. Rather, average conditions in some base Tarbela Dam project in the mid 1960's. In contrast, the low O'MARA AND DULOY: MODELING EFFRIciENT WATER ALLOCATION IN CONJUNCTIVE USE 1493 efficiency assumption with respect to watercourse and field TABLE 3. Annual Rim Station Inflows, Indus Basin, 1967-1968 to losses is at the level specified in the recently completed Re- 1979-1980 vised Action Programme [WAPDA, 1979]. Solutions to the model configured for historical simulation Based on Based on Monthly Mean, Seasonal Median, wYith surface water diversions and reservoir capacity appropri- 1975-1976 to 1967-1968 to ate to the base periods 1967-,1975 and 1975-1980 were ob- RIM Station 1979-1980 1979-1980 tained for the six cases specified in Table 2. The validation experiments specify exogenously the level of the watertable Swat at Chakdara 5.651 5.785 and the surface water allocation for each polygon. Thus one Kabul at Warsak 18.737 19.460 important validation test is whether or not a given water loss Haro at Gariala 0.973 0.771 specification of the model acceptably reproduces the observed Soan at Dhok Pathan 1.759 1.322 production response of farmers to the historically given gross Jhelum at Mangla 28.350 27.978 Chenab at Marala 35.774 29.763 canal water supplies. Another is whether or not the calculated Ravi at Balloki 15.471 7.617 net recharge is consistent with available evidence on the state Sutlej at Ferozepur 7.804 8.558 of the aquifer. Important aspects of farmer response include cropping patterns, cropping intensities, and live3tock holdings. Total above 186.692 174.179 Considering both production response and the state of the Toal less Ravi 163.417 158.004 aquifer, our tests clearly pointed to case B2A2, i.e., high canal and Sutlej losses, medium efficiency for watercourse delivery and field Measurements in m3 x 109. application, as the scenario with the best estimate of water loss parameters among those considered. Thus the water loss permits the investigator to pose penetrating questions with parameters of the B2A2 case were accepted as specifying this respect to system efficiency. Of course, any effort to assess the aspect of the system. efficiency of resource allocation must specify a criterioii by To summarize, the method employed was essentially to which efficiency is to be measured, and this criterion must be impose a rigorous consistency test of model solutions, with acceptable to the people of the country concerned if the as- consistency defined as conformity with the observed aspects of sessment is to be meaningfuIl. It is proposed here that the the Indus Basin Irrigation System in a base period. Given the criterion of efficiency be maximization of the sustainable level logical consistency specified by model structure, the additional of agricultural production from available water, given a vector requirement of empirical consistency with observations from of prices. The qualification with respect to prices is necessary many independent sources is a stringent test. In fact, the se- because agricultural production is quite sensitive to relative verity of this test permitted estimation of unobserved loss pa- prices and the model does not provide solutions that are opti- rameters when no other method of estimation was available. mized with respect to prices. 4. AN APPLICATION TO SYSTEM MANAGEMENT 4.1. Analytical Framework One of the major virtues of modeling of any economic Clearly, a complicated, large-scale simulation model pre- system is the capacity that it creates to simulate counterfactual sents problems of interpretation if model solutions incorporate scenarios of system performance. In particular, this capacity multiple changes. For this reason the sequence of system man- agement experiments has b.'en designed to incorporate only TABLE 2. Cases for Sensitivity Analysis of Estimates of Water Loss single changes (from some reference case) in each experiment. Parameters A number of the specifications of the experimental sequence are essentially imposed by the choice of efficiency criterion, Specification of Losses i.e., maximization of the sustainable level of agricultural pro- duction from available water given a vector of prices. For A, low canal losses, set at approximately 50% of high losses A2 high canal losses, set at 21 percent of pre-Tarbela diversions example, the water endowment of the system from rim station B1 high efficiency at watercourse and field level, set at level ap- inflows must be specified in terms of the best available esti- proximating that of Lieftinck Report, i.e., 0.65 mates of long run supply (in terms of some appropriate mea- B2 medium efficiency at watercourse and field ievel, set at level sure of central tendency). For this reason the water en- approximately 0.50 dowment at rim stations for the sequence of experiments is B3 low efficiency at watercourse and field level, set at level ap- specified as the monthly flows of the median season over the proximating that of RAP, i.e., 0.395 period from 1967-1968 through 1979-1980 at each of the rim S* stations, with Ravi and Sutlej flows deleted since title to these Canal__System_Efficiencies*__ was given to India in the Indus Waters Treaty of 1960. The Case Efficiency, % resulting estimates (for annual flows) are presented in Table 3. For convenience the vector of prices prevailing in 1976- A1BI 56.8 1977, the period for which much of the data base was col- A1B2 43.9 lected, was chosen as the exogenous price vector. Comparison A2B2 39.2 established that relative prices in other years were similar to A1B3 34.4 those prevailing in 1976-1977 except for petroleum products A2B3 30.7 and one agricultural commodity whose world price has a very large variance. In order to provide a test of model sensitivity Definitions: A, are levels of canal losses, i = 1, 2; Bi are levels of to the price vector used as well as an indication of the long combined watercourse and field efficiencies, j= 1, 2, 3. Cases: A1B1, run equilibrium effects of the large increase in the relative A12, AB3, A,2B 1,2 2,A2B . *Assumes diversions of 109.9 x 109 m3 ard highl canal losses (en- price of petroleum that occurred in 1979-1980, several experi- clusive of link canals) of 23.2 x 109 m3. ments employed the price vector prevailing in 1980-1981. 1494 O'MARA AND DULOY: MODELING EFFICIENT WATER ALLOCATION IN CONJUNCTIVE USE TABLE 4. System Management Experiments Pre-Tarbela Allocation as Lower Pre- No Bound to Canal 'Water Allocation Tarbela Distributional Income Constraints Polygonal Provincial as Lower Water Endowment Bound to With Without and Loss Parameters Prices Month Sear.n Month Season Farn Inc. GWB GWB Monthly flows based on 1976-1977 J Q S T M 0 P 1967-1980 seasonal median without Ravi and Sutlej Monthly flows based on 1980-1981 K 1967-1980 seasonal median without Ravi and Sutlej Monthly flows based on plus 50% L 1967-1980 seasonal median energy inc. without Ravi and Sutlej Monthly flows based on 1976-1977 R 1967-1980 seasonal median without Ravi and Sutlej plus WC loss adjustment The sequence of experiments that provide the framework groundwater balance constraint. Strictly speaking, experiment for the analysis of system management are laid out categori- P does not provide meaningful long-run water allocation, but cally in Table 4. Experiment J is the base case in the analysis it is included to show the effect of dropping the groundwater of system management. The experiments listed to the right of balance constraint. The experiments listed below experiment J experiment J constitute the main sequence of single step vari- in the third column of Table 4 retain J's specification of long- ations in water allocation policy. Thus, experiments J, Q, S, run rim station inflows and the historic water rights constraint and T all specify a minimum water allocation based on his- in the form of a monthly polygonal lower bound on canal toric water rights, where these are defined operationally as the diversions but vary prices or water loss characteristics. Experi- mean diversion over the pre-Tarbela (but post-Mangla) ments K and L substitute 1980-1981 prices for 1976-1977 period, 1967-1975. However, experiments J and Q specify his- prices, and in addition, L increases energy prices by 50% and toric water rights in terms of each polygon, while S and T drops the subsidy on fertilizer use. Experiment R differs from specify historic water rights only at the provincial level. Simi- experiment J in that losses along water courses have been larly, J and S specify monthly and Q and T specify seasonal adjusted to reflect watercourse improvement and/or rehabili- water rights. Experiment M substitutes the level of farm tation, as specified by the On Farm Water Management Proj- income derived from a pre-Tarbela model solution as a lower ect, a credit to Pakistan which was recently approved by the bound to farm income in place of the historic water rights World Bank. constraint. Experiments 0 and P drop all explicit distri- butional constraints, with 0 including and P excluding the 4.2. System Management Experiments The experiments specified in Table 4 were completed with TABLE 5. Real Agricultural Value Added, Indus Basin the model configuration in a water-optimizing mode, i.e., solved for an endogenous water allocation. Since the experi- Fresh Saline mental solutions maximize farm income subject to farmer Groundwater Groundwater preferences with respect to family subsistence requirements Experiment Total Areas Areas and risk aversion, these solutions represent the maximum Value Added agricultural production that can be obtained given model D 100.0 100.0 100.0 specification and farmer preferences and hence correspond to J 116.6 101.9 155.1 the efficiency criterion adopted. In all experiments, existing OM 119.7 103.31 162.2 stocks (i.e., 1975-1976) of private tube wells and tractors are P 120.1 103.1 164.5 given as initial conditions, and these stocks can be augmented Q 118.4 102.4 159.9 by endogenous private investments. The groundwater balance R 120.5 104.4 162.4 constraint is imposed in all experiments except P. This implies S 119.3 102.9 162.1 that the value of the dual variable corresponding to this con- T 119.5 103.1 162.2 straint (i.e., shadow price) is the implicit tax or subsidy that is Employment required to induce farmers to pump their tube wells at the D 100.0 100.0 100.0 level required for aquifer equilibrium. This tax or subsidy J 113.6 103.2 144.6 J 115.1 103.7 149.4 must actually be imposed, at least indirectly, for the model O 115.1 103.7 149.4 solution ts be meaningful. Similarly, in the saline groundwater P 116.1 103.6 153.8 areas the objective function of the polygonal submodels in- Q 114.3 102.9 148.6 cludes a term for drainage costs. The interpretation is that R 115.9 104.5 150.0 farmers in these areas demand that amount of canal water S 1 15.1 103.6 149.3 . . . .. . T 115.1 103.7 149.4 diversions which maximizes their utility, given public drainage costs for which they expect to pay in the form of some kind of Measurements as percent of post-Tarbela level. tax. Since the government controls the canal water diversions, O'MARA AND DULOY: MODELING EFFICIENT WATER ALLOCATION IN CONJUNCTIVE USE 1495 it is not actually necessary that this tax be imposed in oruer to TABLE 7. Water Supply per Hectare (at Ront Zone) iluuce the desired level of agricultural production. It is neces- sary, however, that drainage costs be taken into account in SGW Areas FGW Areas determining the efficient water allocation.. Tn the model this is Public- Public- Private done by assuming that the government has social welfare ob- Experiment Supplied Total Supplied Tubewells Total jectives which are completely consistent with maximizing farm output subject to farmer preferences. In this fashion the two- D 0.579 Indus Basin 0.348 0.857 level programming problem discussed by Bisschop et al J 0.786 1.046 0.381 0.366 0.881 [1982] can be solved in a linear programming model, i.e., the M 0.774 1.039 0.372 0.351 0.860 physical externality imposed by the groundwater aquifer can 0 0.759 1.024 0.372 0.348 0.857 be internalized via a tax or subsidy. P 0.774 1.042 0.390 0.326 0.857 Q 0.753 1.024 0.390 0.354 0.881 4.3. Effects of System Management Policies R 0.860 1.131 0.418 0.332 0.893 4.3.roducti Effacs te Utianationt s 0.786 1.055 0.375 0.351 0.863 on Production and Factor Utlization T 0.759 1.024 0.375 0.351 0.863 Production is measured in terms of value added, and sinice Punjab our concern is efficiency, i.e., relative performance, production D 0.357 0.451 0.326 0.372 0-814 is measured relative to experiment D, which approximates J 0.494 0.631 0.326 0.390 0.838 actual post-Tarbela conditions. In additon, results from exper- M 0.537 0.686 0.332 0.381 0.835 iments K and L are not presented here in order to confine 0 0.537 0.686 0.329 0.378 0.832 discussion to policies directed toward changes in water distri- P 0.561 0.719 0.338 0.372 0.835 bution. The effect of the several such policies specified in Table R 0.533 0.692 0.360 0.363 0.850 4 on agricultural value added and employment is given in S 0.537 0.686 0.329 0.381 0.832 Table 5. Note that while the overall gains range from 17% to T 0.537 0.686 0.329 0.381 0.832 20% above the post-Tarbela level for value added and from Sind 14% to 16% for employment, the gains are markedly different D 0.750 1.006 0.744 0.235 1.192 between fresh groundwater (FGW) areas and saline gr>;-d- J 1.012 1.366 0.780 0.226 1.222 water (SGW) areas. The former show increases of only 2% to M 0.957 1.314 0.710 0.171 1.091 0 1.006 1.286 0.710 0.171 1.094 P 0.942 1.292 0.820 0.046 1.055 TABLE 6. Labor and Land Input Intensity by Groundwater Q 0.924 1.280 0.796 0.186 1.201 Quality area R 1.110 1.472 0.881 0.143 1.247 S 0.982 1.341 0.710 0.171 1.091 Labor Intensitya Land Intensityb T 0.930 1.286 0.710 0.171 1.094 Experiment FGW Areas SGW Areas FGW Areas SGW Areas Measured in meters. The number given is the delta, or height of total water applied per unit of level land. Thus a delta of one implies Indus Basin an application of 10,000 m3 ha-' (measured at the root zone). D 431 276 138 101 J 445 399 141 138 M 447 413 140 143 O 447 413 140 144 4% for both measures, while the latter have gains of 55% to P 446 425 140 144 65% in value added and from 45% to 54% in employment. Q 443 410 140 142 The striking difference between the output responses of R 450 414 142 144 FGW and SGW areas clearly signals similar shifts in resource T 447 413 140 144 utilization, and Table 6 presents some results on the intensity of use of labor and land. Note that the data from the post- Ptinjab Tarbela simulation (experiment D) show divergent levels of D 4471 3237 137 180 input intensity for both inputs between FGW and SGW areas. M 444 375 138 125 At the level of the entire basin the effect of alternative system O 444 375 138 125 mangement policies is to bring the levels of input intensity P 445 404 138 130 much closer to equality between the two groundwater quality Q 439 368 1378 126 regions, with this being accomplished by large increases in S 443 374 138 125 intensities for the SGW areas and relatively small increases in T 444 375 138 125 the FGW areas. However, when these data are disaggregated Sitid by major provinces, the picture is somewhat different. In D 396 308 154 117 Punjab, while the trend remains the same, the SGW areas lag J 415 440 158 154 significantly behind the FGW areas in input intensity under M 405 442 149 158 all policies. On the other hand, in Sind the SGW areas show O 407 442 149 158 greater input intensities under most policies. Thus the SGW Q 418 435 141 154 areas of Sind show much higher input intensities than do the R 418 450 160 158 SGW areas of Punjab. S 405 442 149 158 The reason for these divergent patterns becomes clearer T 407 442 149 158 when relative water supplies are taken into account, and these data are shown in Table 7. As might be expected, water supply aDefined as man-hours Of labor input per acre. 'Defined as cropping intensity or cropped acres per acre of irri- per acre also shows a pattern of large increases in the SGW gated land, normalized to a percentage scale, where 100 denotes each areas and small increases in the FGW areas under all water irrigated acre is cropped once a year. allocation policies. However, the quantity available per acre in 1496 O'MARA AND DULOY: MODEUNG EFICIENG T WATER ALLOCATION IN CONJUNCTIVE USE TABLE 8. Public Costs of Aquifer Control Under Groundwater Balance Cost Per Caput of Farm Private Tube Well Annual Cost Total Population, Experiment Tax (-) or Subsidy (+) of Drainage Public Cost rupees J 828.4 374.0 1,202.4 50.3 M 612.6 417.2 1,029.8 43.1 0 665.7 418.0 1,083.7 45.3 Q 425.7 411.6 837.2 35.0 R 807.0 290.2 1,097.2 45.9 S 687.9 415.8 1,103.7 46.2 T 684.4 418.1 1,102.5 46.1 Costs in 1977 rupees x 106. Sind SGW areas is almost twice as large as in Punjab 5GW with increases ranging from 2% to 13%, in the FGW areas areas. In fact, both the FGW and SGW areas in Sind show and from 46% to 84% in SGW areas. Unlike the current significantly greater total water supplies than the correspond- post-Tarbela situation, per capita incomes are greatest in Sind ing areas in Punjab under all policies. This is a surprising SGW areas under all policies, and incomes in Punjab SGW outcome since it is often argued that the interprovincial distri- areas are slightly greater than in Punjab FGW areas under bution of surface water is skewed toward Sind because of most policies. Thus, although the objective was more efficient political factors. Yet these experiments, which include some resource utilization, the alternative policies have significant which release all distributional or equity constraints, show the income distributional implications by water quality zone, with same pattern of relatively greater distribution of surface water something close to equality between zones achieved in Punjab in Sind. It might be argued that the physical capacities of the and a reversal of the present situation in Sind. Note, however, irrigation system for diversion at various points have con- that in absolute terms, every zone gains in per capita income. strained the model solutions to this outcome. However, when In addition, the public costs of aquifer control per head of the shadow prices on capacities of link and main canals are farm population, which range from 35 to 50 rupees, are small examined, this turns out not to be true to a significant degree. in relation to the gains in per capita incomes. Part of the difference in available annual supplies is due to Of course, the impact of the alternative policies on the in- significantly greater subirrigation in Sind, which is an uncon- comes of the several groups within a region may be adverse. trollable (by farmers) source that peaks in months when farm- Some information on income distributional impacts by class is ers have relatively little land under crops. Yet canal diversions available in the form of the shadow prices on the land and to SGW areas are significantly greater in Sind, and this cir- water constraints. These data are summarized in Table 10. cumstance argues for greater marginal productivity of water Note the very large increases in the implicit land rents in the there. One factor contributing to high productivity in this SGW areas under all of the alternative policies and the corre- region of Sind is its comparative advantage in rice cultivation, sponding sharp decreases in water prices in these areas. A which has benefited importantly from the introduction of the similar pattern occurs in the FGW areas, but as expected the high-yielding new varieties. Thus the high productivity of magnitudes of the changes are much smaller. It seems clear inputs in the water-intensive rice crop has resulted in signifi- that landowners, especially in the SGW areas, are well posi- cantly higher optimal diversions to the SGW areas of Sind. tioned to capture much of the increase in farm incomes. The extent to which tenants and landless laborers benefit from the 4.4. Etftcts o 'System MIanayg'nient Policies increase in aggregate farm production depends oni the relative oni Farm Incomies, Public Aqcuifer Conitrol Costs chanige in the demand for and supply of farm labor. at(1d Resource Prices The results from experiments K and L, which were run Since per capita income is a useful and frequently used using 1980-1981 prices, were very similar to the results from measure of economic development, albeit an imperfect one, a experiment J, which differs from them only in the price param- review of the impact of the system management experiments on per capita farm incomes has considerable interest. Note, however, that the necessary existence of transfer payments due TABLE 9. Per Capita Income (Adjusted) to the implicit tax or subsidy on tube well pumping somewhat complicates the concept of farm income. Thus a distinction Punjab Sind must be made between income from farm operations proper, Indus FGW SGW FGW SGW i.e., unadjusted income, and income that allows for the impact Experiment Basin Areas Areas Areas Areas of the tax or subsidy, i.e., adjusted income. The annual public D 1,081 1,125 708 1,473 1,222 costs of aquifer control for each of the system management D 1,284 1,188 1,129 1,623 1,780 experiments are given in Table 8. These costs, which are large- M 1.307 1.196 1.230 1,613 1,816 ly subsidy costs, range from 800 to 1200 x 106 rupees per 0 1,309 1,197 1,231 1,620 1,816 year. Adjusted per capita incomes by provinces and ground- P 1,288 1,151 1,305 1,585 1,800 water quality zones are given in Table 9, which shows that Q 1,323 1,216 1,209 1,664 1,837 Sind incorfies are greater than Punjab incomes for both S 1,308 1,195 1,230 1,643 1,816 groundwater quality zones and under all policies. Basin wide T 1,309 1,196 1,231 1,650 1,816 adjusted per capita incomes show increases of 19%, to 22'%, Income in 1977 rupees. O'MARA AND DULOY: MODELING EFFICIENT WATER ALLOCATION IN CONJUNCTIVE USE 1497 TABLE 10. Annual Shadow Prices of Land and Water tube well withdrawals in the fresh groundwater areas by means of some combination of taxes, subsidies, quotas, fees, Punjab Sind prices, etc. These steps can be regarded as adjustment costs in Indus FGW SGW FGW SGW a transit.ion toward more efficient resource utilizations. The Experiment Basin Areas Areas Areas Areas subsidy costs (shown in Table 8) might be unnecessary in practice, since simulation experiments have shown that im- Land, 15977 rupeesha proved agricultural technology shifts the optimal control from J 892 904 289 1,213 1,065 a subsidy to a tax. However, large drainage investments will M 993 892 588 1,233 1,405 be required 'to achieve the gains shown, since these depend on O 983 877 588 1,230 1,403 large increases in canal diversions to saline groundwater areas. p 904 810 590 1,072 1,225 Until such drainage investments are in place, only limited Q 931 865 462 1,253 1,242 gains are possible from increases in canal diversions. Control R 993 926 420 1,272 1,400 S 983 874 583 1,230 1,400 over private tube well pumping is not needed at present since T 986 877 585 1,230 1,400 subsidies to encourage greater pumping are unnecessary until Water, 1977 rupees/in3 significant increases in drainage capacity exist; and with pres- D 1.671 1.233 3.299 0.895 2.583 ent depths to water table of less than 20 feet (6 meters) In J 0.997 0.952 2.178 0.525 0.874 almost all fresh groundwater areas, a need for taxation to M 0.884 1.030 1.543 0.605 0.448 discourage excessive withdrawals does not yet exist. O 0.870 0.993 1.544 0.609 0.457 P 0.999 1.112 1.403 0.822 0.701 Acknowledgments. The views and interpretations in this paper are Q 0.953 1.033 1.802 0.457 0.683 those of the authors and should not be attributed to the World Bank, R 0.799 0.873 1.748 0.438 0.483 to its affiliated organizations, or to any individual acting on their S 0.861 1.007 1.553 0.612 0.454 behalf. T 0.860 0.993 1.544 0.610 0.459 REFERENCES Annual shadow prices are sums of shadow prices of respective Agricultural Census Organization, Pakistan: Census of Agriculture, 5 monthly constraints of polygonal submodels aggregated into weight- vols., Government of Pakistan, Lahore, 1972. ed averages for the areas shown. Bachmat, Y., J. Bredehoeft, B. Andrews, D. Holtz, and S. Sebastian, Groundwater Managemnent: The Use of Numnerical Models, Water Resour. Monogr. Ser., vol. 5, AGU, Washington, D C., 1980. eters. The important change in relative prices (and only these Bisschop, J., W. Candler, J. H. Duloy, and G. T. 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Bennett, Groundwa- estimates. ter hydrology of the Punjab, West Pakistan, with emphasis on problems caused by canal irrigation, U.S. Geol. Surv. Water Supply 5. SummARY Pap. 1608-H, 1967. Irrigation and Agricultural Consultants Association, Programme for Large gains in agricultural production and employment for the Development of Irrigation and Agriculture in West Pakistan, 23 the Indus Basin are possible given more efficient allocation vols., Lahore, Pakistan, 1966. and management of surface and ground waters (i.e., 17%-20% Johnson, S. H., III, Large-scale irrigation and drainage schemes in in output and 14%-16% in employment). These gains were Pakistan: A study of rigidities in public decision making, Food Res. Inst. Stud., 18(2), 149-180, 1982. estimated holding everything else constant and under conser- Lieftinck, P., A. R. Sadove, and T. Creyke, Water and Power Re- vative assumptions with respect to water supply. 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