309

WATER MANAGEMENT AND TECHNOLOGICAL CHANGE: VILLAGE DAMS IN SRI LANKA

S. Mahendrarajah and P. G. Warr*

This. paper studies the intertemporal allocation of monsoonal water storage in village dam-based irrigation systems in the Dry Zone of Sri Lanka. The traditional water management practices observed in these villages are based on common property access and serve to minimise social conflict over water rights. They are also acceptably efficient in economic terms, given the water demands of the traditional rice production technology. Adoption of high-yielding variety ( H I " ) rice technology produces a dramatic increase in rice output, but the traditional water-management practices then become less efficient. The paper demonstrates a method for determining the nature of an efficient water-management system and for estimating the economic magnitude of the inefficiency arising from the traditional practices. In the case study, eficient water management increases the gains available f rom H W adoption by a further one fourth.

1. Introduction The traditional systems of water allocation found in the semi-arid agricultural regions of developing countries have been formed over many centuries. They arose within the context of relatively unchanging agricultural technologies and were designed to satisfy the twin objectives of economic efficiency and avoidance of conflict among users. The traditional systems often achieve these objectives in ingenious ways, reconciling the seasonal nature of water supply and the competing demands placed by diverse agricultural and non-agricultural water usage.

A consequence of rapid changes in agricultural technology associated with the green revolution is that the economic or scarcity value of water has changed radically, and this can also imply drastic changes in the economic efficiency of traditional allocation systems. An example of this henomenon is the adoption of high-yielding and short-age varieties of rice &YVs) and the package of associated fertilisedpest-control inputs and modified cropping calendars. The technological change increases output and raises the value of marginal product of water. It also alters the interseasonal pattern of water scarcity. These * Dr. Sinniah Mahendrarajah is a Senior Lecturer in Economics, Faculty of Commerce and

Administration, Victona University of Wellington, Wellington, New Zealand, and Peter G. Warr is John Crawford Professor of Agricultural Economics, The Australian National University, Canberra, Australia. This paper has benefited from the helpful suggestions of two anonymous referees. The authors are responsible for all views presented and for any errors.

310 S. MAHENDRARAJAH AND P. G . WARR

changes can have important implications for the economic efficiency of the traditional institutional mechanisms for water usage. Systems of management of water storage and allocation that were well-adapted to the traditional technology and its associated pattern of water scarcity may not be efficient when the technology changes.

In this paper we study these issues uantitatively within the context of village

area irrigated by village dams. Nevertheless, although improved irrigation practices have been adopted in some areas, most villages still retain traditional water allocation systems (IDRC, 1988). Sri Lanka provides a clear example of the way that changing technology can cause traditional water storage and allocation systems, previously acceptably efficient, to become inefficient. In such circumstances, pressures for adaptation of the institutions of water allocation can be expected. Such pressures are already evident in Sri Lanka, where the government has recognised the potential implications of HYV technology for the efficiency of traditional water allocation systems and has begun to intervene to speed up the process of reform.* The process of institutional reform may be slow, and in the Sri Lankan case it is likely to be socially disruptive and costly in economic terms. Economic analysis can be helpful in this context by providing estimates of the economic cost of any inefficiency which arises from traditional water-allocation practices and the likely economic gains available from reform. That is the purpose of this paper.

In Section 2, we use theoretical arguments to show that the traditional systems of water allocation seen in Sri Lanka may result in inefficiencies which may be accentuated by technical advances such as HYV adoption. In Section 3 , an empirical economic model is developed to reveal the magnitude of any such inefficiencies using a simulation and dynamic programming model of the irrigation system. Section 4 summarises our quantitative results, and Section 5 draws out the central conclusions from our analysis.

dams in Sri Lankan agriculture. H Y3 s have been adopted on almost all of the

2.

This section presents a simplified analytical representation of the water storage and allocation problem. The analysis is intentionally stylised so as to draw out the economic issues involved. We first describe the way the traditional allocation system operates, and then show the inefficiency that results when the traditional allocation system is combined with the new HYV technology.

Interseasonal Storage, Common Property Access and Area Rationing

The Traditional Technological Environment of Water Allocation The one dam - one village system has existed in Sri Lanka for hundreds of years (Codrington, 1938). The village rice land is a single block lying immediately below the dam. Families have private property rights over individual holdings, which are usually in the form of a number of scattered small parcels separated by shallow bunds. The block of rice land has two components: the central portion, known as Purana land and the boundary section at a relatively higher elevation, known as Akkara land. Purana land has Drioritv in water allocation. Irrigations are made via a single channel that * See, for example, the Sri Lanka - IDRC Cropping Systems Project Proposal, Government of Sri

Lanka, 1974; the Sri Lanka - USAID Cropping Systems Program Agreement, Government of Sri Lanka, 1976; and Panabokke, 1976.

WATER MANAGEMENT AND TECHNOLOGICAL CHANGE 31 1

traverses the block from top to bottom. The control structures such as sluices and spills remained primitive until the 1940s, when a ‘Villa e Tank

several improvements to the engineering efficiency of the water control system but left the basic allocative practices intact. In-field distribution of water uses plot-to-plot flood irrigation. The rainfall during the two monsoons, the major one from September to December and the minor one from April to mid-May, provides a significant supplementary source of water to meet crop demand, apart from contributing to storage in the dam.

The traditional water allocation system is based on the implicit premise that crops have a unique water requirement and that water has little if any substitutability with ather inputs in rice production. In the traditional cropping pattern, primary importance is attached to the Wet Season crop, which utilises local rice varieties* belonging to the 4-4% month age-class. These varieties exhibit poor response to the use of modern inputs and possess a low yield potential. Cultivation operations begin only in November and planting activities could extend up to mid-December. Water storage in the dam is used first for land pre aration and subse uently for generous irrigations of rice,

April. For the Dry Season cultivation, a similar water management is adopted to grow a short-age traditional variety of rice, which is planted in a portion of the rice land, usually in May.

Modernisation’ programme was launched (see Arumugam, 1959). -A is made

maintaining stan B ing water in the fie 9 d. The Wet Season rice is harvested in

Institutional Arrangements Water release from a dam is administered by an elected village-level body known as a Cultivation Committee (CC). This Committee also takes the leading role in steering the cultivation programmes of the village, by convening pre-season meetings. It arbitrates all dis Utes among villagers related to

the light of expected water availability. In the Wet Season, all the Purana land is generally cultivated, but in the Dry Season only one third to one half of this land is normally cultivated. After planting, the sluice will be opened by the CC for irrigation whenever the standing water reaches an unacce tably low level

opened, each farmer will receive as much water for irrigating his cultivated land as he wishes.

The convention that each farmer is entitled to receive as much water as he wishes whenever the sluice is opened is equivalent to treating the water as a common property resource. We shall see that this fact has important implications for the inter-seasonal allocation of water at an aggregate level. This management practice has clear social benefits. The ease of olicing any

and which could be used to divert water to land not approved for cultivation, minimises irrigation-related conflicts. Interpersonal conflict over water allocation is thus reduced to the single decision at the beginning of each season as to how much of the total land area is to be both cultivated and irrigated in that season, given the water available in the darn at the beginning of that season and expected rainfall. This management practice is known as Berhrna. Inter- personal conflicts that could potentially arise under such a water-scarce * Varieties grown in the Wet Season include local varietiessuch as Hathili and Karuppan. A select

hybrid, H4, released in the 1950s is perhaps the most popular 4 4 month variety. In the Dry Season, a 3-’h month traditional variety known as Pachchaipperurnal has been in wide use.

irrigation and cultivation. The area to be cu P tivated is determined by the CC in

on any part of the cultivated area. On each such occasion t R at the sluice is

breaches in the water distribution system which are not approve 8 by the CC,

312 S. MAHENDRARAJAH AND P. G . WARR

situation are avoided by the Bethma system. Potential conflict is further minimised by the fact that each family owns a number of parcels of land scattered in the block, usually at least a parcel in each of the proximal, middle and distant end of the block (Abeyratne, 1956).

Simple Analytics of Water Allocation In the traditional interseasonal allocation process, the rice crops of the two seasons are not treated by villagers as competing bidders for the storage in the dam. The Dry Season’s cultivation is relegated to secondary importance and receives only the residual storage. In combination, the late lanting and the use

Interseasonal allocation is a potential source of inefficiency of water use. Further inefficiencies occur in intraseasonal allocation, at least in part in mitigation of interpersonal conflicts. Villagers are permitted to apply generous or even wasteful amounts of irrigation water on each occasion that the sluice is opened, such that the value of marginal roduct (VMP) is zero. In economic terms, this practice could be justified on P y if this Wet Season water had zero opportunity cost.

Under the traditional rice technology, which we shall subsequently call the ‘old technology’, any inefficiencies arising under the traditional water allocation system of villa e dams have been judged to be acceptably small (Abeysinghe, 1982; Cham % ers, 1977). The advantages of the traditional system in avoiding social conflict over water access are considered to outweigh any such loss in productive efficiency. More recently, Sri Lankan sources have recognised the possibility of significantly increased inefficiency arising under the greater water demands of HYV technology (Somasiri, 1976). The source of this increased inefficiency is that HYV adoption raises the opportunity cost of water applied in the Wet Season. That is, the persistence of the biased interseasonal mechanism and the potentially wasteful intraseasonal allocation is thought to reduce the economic gains available from the adoption of HYV technology. One of the main objectives of the government’s Cropping Systems Improvement Program is to achieve a more efficient allocation of water (Panabokke, 1976), though little is known of the possible magnitude of the economic gains available.

The salient features of the water allocation problem can be demonstrated with the aid of Figure 1, where the two vertical axes represent the net benefits per unit of water use in each of the two seasons, while the horizontal axis measures the stock of water. Water allocation for the Wet Season is measured from left to right and that of the Dry Season from right to left. For simplicity, we assume that the quantity of water storage is given at the beginning of the Wet Season, that it is not subject to evaporative losses, and that water is not required for any other household or community purposes.* Under the traditional allocation, water use in the Wet Season proceeds until the VMP of water is zero. Given that the cost of extraction is zero and the assumption that the market for the final product (rice) is undistorted, this also corresponds to the point where marginal net social benefit (MNSB) is zero. This is shown in Figure 1, where the MNSB curve for the Wet Season, using the old technology, Mz , cuts the horizontal axis at point A. The residual storage is allocated to an appropriate area of rice in the Dry Season. The area of land both cultivated and irngated in the Dry Season is chosen to be just sufficient to exhaust the stock of

All three of these simplifying assumptions are relaxed in the simulations we report later in the

of long-age varieties of rice in the Wet Season rein P orces this feature.

paper.

WATER MANAGEMENT AND TECHNOLOGlCAL CHANGE 313

Traditional and ERicient Interseasonal Allocation of Water

__* Water Storage (Ac-ft) (Wet Season) t

(Dry Season)

water remaining after the Wet Season. The Dry Season - old technology MNSB curve Mi corresponding to this restricted amount of land thus intersects the horizontal axis also at A. The areas bounded by the two MNSB curves and the horizontal axis measure the total net social benefit accruing to villagers: the areas EAM plus AGN.

The effect of the adoption of HYV technolo y is represented in Figure 1 as shifts in the MNSB curves: Mito ML in the Wet sg eason; and Ml to M,in the Dry Season. In our diagram, Milies outside Miand the amount of water remaining after the Wet Season is less under the HYV technology than the old. The amount of land which can be irrigated in the Dry Season under the tradition?l water-allocation system, is thus correspondingly reduced. The position of M,, inside M:, reflects this. It is important to realise that these two schedules correspond to different amounts of land. Thus points A and B capture the nature of the traditional system of allocation for the old and the HYV technologies respectively. The relative positions of points A and B is an empirical issue. Under efficient water allocation within season, further shifts in both MNSB curves would become possible. The traditional water allocation system restricts Dry Season cultivation to an area that exhausts the available water stock -the residual after Wet Season use - at zero VMP. If this system were abandoned it would be possible to cultivate and irrigate more land in the Dry Season by applying the greater conservation from the Wet Season to,a larger area and at positive VMP. Attainment of the higher MNSB curve M, , lying above Mi, would then become feasible,

314 S. MAHENDRARAJAH AND P. G . W A R R

Efficiency in interseasonal allocation will prevail only when the VMPs for water in the two seasons are equated. The efficient interseasonal allocation occurs with positive VMP for water and corresponds to point C. The gain attributable to the adoption of HYV technology, but retaining the traditional water allocation system, is equivalent to the area ABDE less area ABFG. This difference must be positive, or the new technology would not be adopted. The further gain attributable to the efficient allocation of water under HYV technology corresponds to the area BCHF. The total gain from both, corresponding to the movement from A to C, is given by the area DEAGHC.

Three other significant aspects of water storage and allocation require consideration. First, the volume of storage is not all given at the beginning of the agricultural year, that is in September, but depends on rainfall throughout the Wet Season. Second, stored water is subject to significant losses due to evaporation especially from February onwards and intensifying in the driest months of June, July and August. Third, there is also village demand for a quantity of ‘dead’ storage for washing and other non-depleting uses. The evaporation of storage plays the role of a ‘discount factor’ and hence can favour early or Wet Season extraction relative to conservation for use in the Dry Season. Also, efficient intraseasonal distribution of storage in each of the seasons is a necessary condition for overall efficiency. A static two-period model has limitations for dealing adequately with such complications, which can be more readily incorporated within a dynamic or multi-period framework. The components and operation of such a framework is outlined next in the context of a specific dam which constitutes the basis for the empirical conclusion drawn in this paper.

3. In this section, we first outline a statistical water storage model which belongs to a class of time series models developed in the context of hydrological systems and discussed in Young (1984). The model is applied to a selected dam in the North Central Province of Sri Lanka.* Second, we summarise a simulation model of the irrigation system describing the atmosphere-soil-crop complex and the effect of irrigation decisions. A dynamic programming (DP) routine is em loyed to find the sequence of optimal water-allocation decisions within

aggregate village net income - i.e. the value of output less the cost of inputs other than water. Our analysis considers weekly sub-periods. The weeks are numbered beginning 1 Se tember which marks the beginning of both the cropping year and the Wet sp eason.

Intertemporal Storage and Allocation Model

eac K season. The optimal allocation is defined as the one which maximises

Water Storage Model and Forecasts The storage of water is governed by the rainfall characteristics and the evaporation pattern. The annual rainfall distribution is bimodal, but varies from year to year. For the case study area, rainfall records are available from 1960 to 1983. Data on the weekly distribution of storage was available for only one of these years, 1976/77, as documented in Mahendrarajah (1978). It was * In terms of area, this is the largest of the nine provincesof Sri Lanka. It belongs to the Dry Zone,

the region receiving an annual rainfall of less than 1900mm and covering three quarters of the island. The articular province receives an average rainfall of approximatel 1400mm, of which rough& 80 per cent is experienced in heavy storms during a penod of 100 lays or so from September to December under the influence of the North-East monsoon and the balance is received during the South-West monsoon from April to May. Details can be found in Panabokke and Kannangara (1975).

WATER MANAGEMENT AND TECHNOLOGICAL CHANGE 315

necessary for the present study to generate storage forecasts for the other 22 years. This was accomplished first by estimating a water storage model by relating the weekly storage level in the dam to rainfall in the catchment and then, on the basis of the results, by developing a stochastic simulation model capable of forecasting storage levels for various rainfall histories. The procedures involved are discussed in detail in Mahendrarajah and Warr (1989). We shall provide a brief sketch.

The storage and depletion process was approximated as a linear dynamic system driven by ‘effective’ rainfall, that is rainfall modified for ambient temperature and antecedent soil moisture conditions in the catchment. Version of a recursive instrumental variable-approximate maximum likelihood approach, elaborated in Young (1984), were used to identify and to estimate the parameters. Fundamentally, the approach decomposes the observed storage, Yk, in week k into a system component, xk, and a noise component, e k ,

generated by ek, a serially uncorrelated sequence of random variables with zero mean. However, parameters in the system and noise models are estimated in co-ordination (Young, 1984).

The estimated model for storage in the dam can be summarised as:

x k = 0.938 Xk-t + 0.556 uk (0.003) (0.01 8)

where uk represents the ‘effective’ rainfall in millimeters. The storage is measured in megalitres (1 MI = 0.81 ac-ft). The figures in parentheses represent the standard errors of estimates and the covariance estimate of the two system parameters in (1) is 4.98 x lo-’. The stochastic simulation follows the general approach described in Anderson (1958), making use of the parameter estimates to make forecasts of the storage pattern in the dam for any one year’s rainfall scenario.

Simulation of Rice Irrigation A major difficulty in the efficient allocation of limited water for agriculture arises from the problems of estimating suitable dated water response functions for crops (see Minhas et al., 1974; Yaron, 1971). There have been several attempts to estimate response functions for rice using various empirical indices at the field level (Small and Chen, 1984; Wickham and Sen, 1978). Among other problems, the explanatory variables in these functions cannot be translated into quantities of irrigation water and are therefore of limited value for the scheduling of limited stocks of irrigation water such as the problem under consideration.

We have employed a simulation model encom assing the atmosphere-soil

inputs such as rainfall and evaporation on soil moisture and, in turn, on crop complex. It is capable of accounting explicitly for t fl e influences of atmospheric

316 S. MAHENDRARAJAH AND P. G . W A R R

yield. This is an important consideration where irrigation is supplementary. The irrigation system simulation has two components, viz., a soil-moisture budgeting routine and a crop-response routine.

The role of the soil moisture budgeting routine is to compute the soil moisture level in the root zone of rice on a daily basis according to the relation

N, = Nt-l + F, + I, + A, - E, - D, (4)

where N, represents the available soil moisture in the evapotranspiration zone in mm or inches in day t; F, the rainfall; I, the depth of irrigation; A, the available moisture in the additional depth of soil into which the roots extended; E, the evapotranspiration; and D, the runoff from the surface and deep percolation.

The soil moisture at the beginning of day t is treated as that found at the end of the previous day. The soil moisture content as a percentage of the total water holding capacity of the root zone (R,) gives the soil moisture level. The root growth of rice is assumed to be linear and the root zone deepens at the same rate to reach the maximum of 30cm. It is assumed that the soil is homogeneous with a water-holding capacity (or field capacity) of 50mm per 30cm of depth, which is the accepted figure for the soil type in the locality.

When no irrigation is applied, the moisture level is driven chiefly by incident rainfall and surface evapotranspiration. The quantity of water in each irrigation is designed to restore the soil moisture within the depth of the rootzone to field capacity.

Crop Growth Response The crop growth rate is a function of soil moisture and atmospheric conditions. The potential evapotranspiration reflects the demand placed by the latter on a crop in the field. The fundamental premise is that the crop is stressed if the actual evapotranspiration (Ea) made feasible by the available soil moisture is below the potential evapotranspiration ( E p ) and that it does not grow on any 'stress' day. The EP also depends on the stage of the crop and has been computed from open-pan evaporimeter records and 'crop sensitivity' factors. Crop sensitivity factors for the various stages of rice are obtained by fine-tuning values reported for cereals by Flinn (1968). The E" itself is determined jointly by N, and EP. Coefficients (Ea/EP) for various combinations of N, and EP for high evaporative regions provided by Fleming (1964) were used in the computation of E".

The number of stress days in various stages of the crop were used as explanatory variables in the actual specification of the response function. Irrigation and rainfall reduce the number of such days and result in increased growth and yield. Similar specifications have been applied elsewhere (Hall and Butcher, 1968; Dudle et al., 1971; Hanks, 1974; Minhas et al., 1974; and Yaron and Dinar, 19827. The response function has the form:

where Gp is the maximum potential yield per acre that can be obtained under non-stress conditions for the crop variety and management package, whereas

WATER MANAGEMENT AND TECHNOLOGICAL CHANGE 317

Week number 1 7 14 6

G represents the actual yield; d, and F, are the number of stress days and the reduction in yield in kg er hectare per stress day during stage k. The F, values have been computed P rom relative yield reduction figures associated with moisture stress at various stages of rice reported by De Datta et af. (1973). The relative yield reduction percentage of a stage of crop growth reflects the importace of growth in that stage in determining total yield. Weekly stages have been considered and the corresponding F, values are given in Mahendrarajah and Warr (1989).

Given the climatic conditions and irrigation policy, the simulation routine determines the final grain yield according to the above function. Under the traditional water allocation, the soil moisture is maintained at saturation throughout the growing seasons and a yield of G , is realised. On the other hand, under the efficient water allocation, crops may be subjected to moisture stress selectively during certain times resulting in a yield G (<G,).

52

Cropping Calendars Given the role that climatic factors play in crop response functions, the cropping calendar is an important ingredient in the simulation model. Besides, one of the features qistinguishing the old and HYV rice technologies is the difference in their cropping calendars. Under the old technology, the Wet Season’s crop has an irrigation season of 16 weeks roughly extending from November 25 to March 24, or weeks 14 to 29 inclusive. Old varieties grown in the Dry Season belong to the 3 to 3-’/2 month age-class with an irrigation season of 13 weeks, roughly from April 21 to July 27 (i.e. weeks 34 to46).

HYVs bred and recommended for both seasons in village dams belong to the 3-’/2 month age-class with an irrigation season of 13 weeks. An important feature of the improved crop ing system is the early planting of the first crop with the onset of the Wet !! eason rains. On the basis of rainfall analysis, Panabokke and Walagama (1974) have recommended mid-October (week 7) and late February (week 25) as the most suitable planting times for the Wet and the Dry Seasons respectively. These times were also found to be optimal by a subsequent study considering patterns of both the rainfall and the water storage (Mahendrarajah etal., 1982). In between the two crops, there is a turn- around period of five weeks from week 20 to 24 inclusive. A long fallow period extends from week 38 to 52. Figure 2 provides a diagram of the cropping calendars under the two technologies.

Both of the simulation routines are readily adaptable to accomodate the various technology and water allocation situations. Simulating the traditional water allocation to determine the maximum net social benefit and the associated inter and intraseasonal distribution of storage is now straightforward.

318 S. MAHENDRARAJAH AND P. G. W A R R

Dynamic Programming Water distribution under the efficient system also entails the application of discrete dynamic programming (DP) routines, one each for the two irrigation seasons. In the past, DP has been applied to water resources and irrigation systems to find optimal operation policies (see Bras and Cordova, 1981; Dudley and Burt, 1973; Flinn, 1968; Hall and Butcher, 1968; Yaron and Dinar, 1982; Yakowitz, 1982). The main feature of our work is the generation of a water response function for each season taking into account optimal areas of crop and optimal intraseasonal allocation of water. This constitutes the basis for determining the efficient intertemporal allocation and the scarcity value of water.

Deterministic DP models comprising 13 weekly decision stages covering each of the irrigation seasons proved adequate. The state variables are yr and N,. The single decision variable is the terminal soil-moisture percentage (Wk), which is defined as the moisture level to which the root zone is allowed to dry in a decision stage k before being restored to field capacity. The soil moisture percentage, N,, and irrigation decision, Wk, take seven decile values, viz. 40,. . . ,100. The state on day t and the decision taken determine the states of soil moisture and water storage in day t+ l , and the gain. The immediate gain consists of the value of growth if the crop was not stressed on day t. The core of the DP routine follows a recursive relation and the solution procedure begins in the last stage of the D v Season’s DP, and proceeds by backward induction. The objective is to maximise the cumulative gain for each of the two seasons, subject to the crop acreage, dead storage and state transition relations, considering all possible discrete state values for storage and soil moisture. Further details are provided in Mahendrarajah and Warr (1989).

The fixed cost of the input package is set off against the gross benefit to obtain the Net Social Benefit (NSB). The labour cost of irrigation is disregarded. NSB functions were then generated for various allocations of water. ‘Frontier’ NSB functions were derived making use of the NSB functions obtained for different cro -areas in the two seasons. The frontier NSB functions for the seasons s E ow the NSBs accruing to various interseasonal allocations of stora e, while ensuring optimality in both crop areas and intraseasonal water Jstributions.

4. Empirical Results In the village under study, there are 12.15 hectares each of Purana and Akkara lands, roughly equally distributed among 45 families. The dam has a storage capacity of over 125 MI (>lo0 ac-ft). Interviews with villagers indicated that a dead storage of 4.94 MI (4 ac-ft) would be preferred for unimpaired non- imgation uses. In 1976/77, the year for which actual storage data were available, the water level rose from a low 10.5 MI in mid-October to a maximum of 77.1 MI in early December. Our results pertain to this year and the twenty-two others for which climatic data were available.

Traditional Land and Water Allocation, and Social Benefits The simulation model described above was used to simulate the patterns of water use, areas of cro ping and resulting net social benefits obtained under the traditional system o P water allocation, which is equivalent to maintaining wk

= 100 (that is, an’ imgation is implemented whenever soil moisture falls to 94%). The optimal areas of cultivation for the two seasons were determined by

Tab

le 1

Si

mul

ated

Inte

rsea

sona

l Allo

catio

n of

Lan

d an

d W

ater

and

Net

Soc

ial B

enef

its U

nder

the

Tra

ditio

nal System

of W

ater

Allo

catio

n A

llora

lion

of W

afer

(MI)

A

rea of R

ice

Cro

p N

et S

ocia

l Ben

efits

(R

upee

s)

1960

16 1

1961

I62

1962

63

1963

164

1964

165

1965

166

19W

67

1967

168

1968

/69

1969

flO

197o

n1

1971

fl2

1972

n3

1973

/74

1974

fl5

1976

n7

1977

fl8

197W

9 19

7918

0 19

8018

1 19

8118

2 19

8283

A

vera

ge

i975

n6

‘99.

07

70.5

7 87

.31

88.8

5 46.90

93.5

2 78

.94

64.5

1 51

.00

88.4

1 23

.41

67.1

8 38

.30

64.8

7 51

.98

36.9

3 69

.33

53.1

3 72

.97

45.6

7 58

.27

37.2

5 41

.41

62.1

6

10.0

3 2.

41

16.6

2 0 38

.82

15.0

9 0 3.

26

6.75

5.

84

34.6

8 0 0 10

.48

43.5

8 24

.72 0

7.45

10

.33

7.13

6.

84

14.2

1 10

.87

11.7

0

41.0

7 40

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42.7

3 35

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43.8

5 43

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40.1

4 48

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40.9

6 34

.52

2.58

45

.11

29.6

6 47

.84

34.5

9 42

.74

62.2

5 47

.57

41.6

7 29

.81

38.4

9 52

.98

38.2

2 40

.20

45.7

6 26

.72

43.9

4 35

.82

63.8

8 48

.70

28.9

5 21

.07

20.5

4 50

.92

41.6

0 22

.43

6.33

32

.03

46.6

2 44

.31

13.7

6 17

.33

43.0

2 21

.85

25.8

8 17

.48

23.7

2 32

.29

24.3

2.

8 17

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0.6

24.3

4.

1 22

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0.0

10.9

9.

3 24

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3.7

19.9

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24

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14.6

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39

62,3

70

56,1

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28,0

68

62,3

62

50,9

29

40,0

05

32,2

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70

13,6

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80

22,8

72

38,9

73

34,3

17

20,8

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40,5

33

31,1

84

45,1

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23,3

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38,6

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5,64

2 1.

211

8,02

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238 0

1,62

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2,80

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0

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244

3,21

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619

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625

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133,

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133,

652

133,

652

133,

652

133,

652

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61

Und

er Ir

riga

tion

(ha)

Tech

nolo

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Tech

nolo

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Tech

nolo

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Tech

nolo

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Tech

nolo

gy

Tech

nolo

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Year

O

ld

HW

O

ld

HW

O

ld

HW

Wet

D

ry

We:

D

ry

Wet

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ry

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D

ry

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ry

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ry

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ary

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are

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= 2

.47

acre

s.

320 S. MAHENDRARAJAH AND P. G . W A R R

search subject to the dead storage constraint. This exercise was performed separately for each of the 23 years from 1960/61 to 1982/83 and was conducted for both the old and HYV technologies. The simulation for each year used data from that year, specifying: initial water storage levels; actual incident rainfall throughout the year on a weekly basis; and evapotranspiration rates.

The fixed costs per hectare of growing rice under the old technology in the Wet and Dr Seasons are estimated in 1983 prices at Rs 4,817 and 2,470 respectively hzumi and Ranatunge, 1973). The respective potential yields per hectare are assumed to be 2.5 and 1.5 tonnes. The cost of production per hectare of rice under the HYV technology for each season is estimated at Rs 6,175 in 1983 prices, and the potential yield levels in either season is taken as 4 tonnes per hectare (Mahendrarajah, 1978). The price of unhusked rice is Rs 3,000 per tonne in 1983 prices.

Under the old technology, on average the estimated land and water allocation in the two seasons amount to 18. I ha and 73.9 MI respectively, the Wet Season’s share being 84 per cent (see Table 1). The average annual NSB for the village is Rs 44,521. Under the HYV technology, the average water allocation in the Wet and Dry Seasons works out to 40.2 and 32.3 MI respectively. Even with the traditional water allocation practice, the HYV technology appears to make efficient use of water storage, minimising evaporative losses with the aid of its shorter growing season and earlier cropping calendar.

Efficient Water Allocation and H W Technology Next, the principles of efficient water allocation were applied to the HYV technology. The DP and simulation routines were used to estimate the optimal patterns of water and land allocation under HYV technology, again for each of the above 23 years. The frontier response functions generated for the two seasons to find the optimal land and water allocation are discussed in Mahendrarajah and Warr (1989). The following two conditions are satisfied at the optimum: the additional gain in NSB for a small increase in water allocation in the Wet Season is exactly offset by the corresponding loss in NSB in the Dry Season; and the total of the NSBs for the two seasons is the largest. Irrigating the whole rice land was found to be optimal in all Wet Seasons with the exception of 1970171, which had one of the driest Wet Seasons in the recent history. Even in the Dry Seasons, it was found optimal to irrigate the whole block in 12 out of 23 years. The results obtained when water and land are allocated according to the efficiency principles are summarised in Table 2.

The pattern of interseasonal allocation clearly shows the greater diversion of storage for use in the Dry Season under the efficient system. Only a small proportion of the simulated annual water-use is allocated to irrigating Wet Season rice, when compared with the figures for the traditional system in Table 1. On average, the simulated volumes of water applied in the Wet and the Dry Seasons are 19.2 and 36.2 MI respectively. Clearly, the diversion of a larger amount of water enables the cultivation of a larger area of rice in the Dry Season under the efficient allocation system.

The main sources of annual variation are differences in the rainfall patterns *and in the patterns of crop demand for water during the Wet and Dry Seasons. Broadly, the traditional system of water allocation uses too much water in the first (Wet) Season and conserves too little for the second (Dry) Season. Reflecting this, NSB achieved in the Wet Season under the traditional system is

WATER MANAGEMENT AND TECHNOLOGICAL CHANGE 321

typically greater than the corresponding NSB achieved under an efficient allocation. Nevertheless, when water is allocated efficiently, the additional NSB achieved in the Dry Season more than compensates for the shortfall.

The last column of Table 2 gives the scarcity value of water at the end of the Wet Seasons implied by the parameter values of the model for the respective years. These scarcity values should be interpreted as the increase in total net social benefit that would have been obtained under an efficient system of water allocation if one more acre-foot (or one cubic metre) of water had been available at that time. Under the traditional system of water allocation, this implied shadow price of water is zero because water is used up to the point where its marginal net social benefit is zero.

Table 2 Emcient Intertemporal Allocation for the HYV RiceTechnology: 1960/61- 1982/83

Wet Season Dry Season Total Scarcity Net Value

Water Area NetSocial Water Area NetSocial Benefit Rain Water (Mi) (ha) Benefit(Rs) (MI) (ha) Benefit(Rs) (Rs) (mm) (RslMI)

1960161 17.90 24.3 131,660 43.39 24.3 131,976 263,637 1,573 1,061 1961162 10.98 24.3 132,814 36.16 24.3 128,830 261,644 1,337 1,132 196263 17.03 24.3 130,299 44.23 24.3 131.660 261,959 1,728 1,132 1963164 15.49 24.3 129,668 40.03 24.3 117,825 247,493 1.835 1,079 1964165 20.30 24.3 131,976 62.23 24.3 132,814 264,790 1,386 970 1965166 21.54 24.3 128,308 49.78 24.3 130,299 258,607 1,929 1.292 1966167 19.56 24.3 132,814 35.85 24.3 94,239 227,053 1,559 1,044 1967168 19.32 24.3 121,700 28.14 24.3 120,000 241.700 1,419 1,213 1968169 26.77 24.3 103,882 20.94 8.9 42,910 146,792 1,295 1,515 1969170 8.21 24.3 132,814 54.44 24.3 132,814 265,628 1,377 905 1970171 10.92 5.3 29,236 41.09 24.3 131,147 160,383 1,092 2,952 19716'2 18.82 24.3 102,631 32.19 24.3 125,118 227,749 1,353 3,586 197373 16.97 24.3 92,453 10.80 4.1 21,230 113,683 1,084 1,447 1973f74 22.40 24.3 130,518 38.80 23.5 107,323 237,841 1,268 1,736 1974/75 22.03 24.3 131,138 43.93 16.2 88,340 219,478 1,273 1,296 19756'6 20.98 24.3 131,334 45.63 17.1 90,963 222,297 907 1,402 1976/77 41.04 24.3 131,138 18.53 8.1 36.166 167,304 1,480 1,235 19776'8 22.52 24.3 125,478 21.72 11.0 63,216 188,694 1,548 690 1378/79 16.97 24.3 131,660 45.89 24.3 131,976 263,636 1,066 959 1979/80 15.67 24.3 97,797 23.81 10.5 54.226 152,023 1,195 2,100 1980181 8.58 24.3 131,660 34.74 18.3 78,130 209,790 1.347 1,155 1981182 30.79 24.3 124,846 26.45 18.3 92,231 217,077 1,013 857 198383 14.26 24.3 129,668 32.94 16.2 70,663 200,331 1,036 1,277 Mean 19.19 23.5 120,238 36.16 19.3 98,004 218,242 1,352 1,393 Note: All monetary (rupee) values are based on 1983 prices.

Year Social Annual of

Gains from H W Technology and Efficient Allocation of Water The adoption of HYV rice technology in itself raises the net social benefits derived, whether water is allocated efficiently or in the traditional manner. The relative magnitudes of NSBs derived in each case can be ascertained by comparing the benefits of H W technology under efficient and traditional allocations. These results are summarised inTable 3.

322 S. MAHENDRARAJAH AND P. G. WARR

Table 3 A Summary of Simulated Water Allocation and Gain: 1960/61 to 1982/83 H W Technology

Old Technology and Traditional Efficient Period Traditional Allocation Allocation Allocation Mean NSB (Rs) 44,521 175,403 218,242

(0.32) (0.22) (0.20)

(0.26) (0.22) (0.21) Mean Water Use (MI) 73.9 72.5 55.3

Irrigation Area (ha) 18. I 31.9 42.8 (0.32) (0.221 (0.17) . , . I . ,

Note: Monetary values are based o n 1983 prices. Figures in parentheses are coefficients of variation.

The transition from the system with old rice technology and traditional allocation of the water resource to the HYV technology and efficient water allocation results in a striking increase, nearly five-fold, in the net benefits to the village. Of this, three quarters are due to HYV adoption alone, and a quarter to efficient intertemporal allocation of the water resource once HYVs are adopted.

Whether the gains from adopting an efficient system of water allocation are ‘large’ depends on the costs that must be incurred in achieving them. These costs would include social disruption, additional administrative inputs, and any increased risk associated with the new system. In the Sri Lankan context, i t is possible that the social costs incurred in moving from traditional water allocation systems to more efficient ones would exceed the economic gains derived. Such a claim could not be made lightly, however. Our results show that once HYVs have been adopted, as they have been throughout the irrigated rice lands of Sri Lanka, the further gains available from an efficient water allocation system are significant. In this respect, our case study lends support to Sri Lankan government initiatives in reforming the system of water management practised in village dams.

5. Summary and Conclusions This study has analysed the efficient allocation of water in a village dam based imgation system by taking an example in the Dry Zone of Sri Lanka. The principal focus is on the interseasonal allocation of water. Water stored in the dam is a common property resource used for irrigating rice grown in two seasons and for domestic uses. Dams exhibit an annual dynamic storage- depletion behaviour, influenced by monsoonal rains and arid climatic conditions. The traditional water allocation system developed over many centuries in the context of relatively static agricultural technology, but it leads to an inefficiency arising from its treatment of water stored in the dam as a common property resource.

Individual land holders have no way of storing water privately for future use. The public dam is the only storage device available. Whenever water is released from the dam for irrigation purposes, each land holder is entitled to draw as much water as desired. Once the sluice is opened, it is left open until all such demand is satisfied. Social conflicts over water access are minimised by this system but it encourages the use of water on individual plots of land up to the point where its value of marginal product is zero. In aggre ate, too much of the water stock is used when it is plentiful (the Wet Season! and too little is stored for future use when it is more scarce (the Dry Season).

WATER MANAGEMENT AND TECHNOLOGICAL CHANGE 323

The inefficiency of this system of demand management arises not from the collective decisions on when to release water from the dam but from the system of common access that operates once the decision is made to open the sluice. The inefficient pattern of exploitation that this system of property rights induces is familiar from other examples of common property resources, such as fisheries, forests, oil, and groundwater reserves (Dasgupta and Heal, 1979; Milliman, 1956). In the case of water stored in village dams, the resource is replenished annually by rainfall, but common property access results in an inefficient interseasonal allocation.

The pattern of water demand arising when traditional varieties of rice are cultivated, as they have been for centuries in Sri Lanka, apparently leads to little inefficiency under the common property water access system. Although too little water is stored from the Wet Season to the Dry Season, total demand in the Dry Season is restricted by limiting the area of land that can be irrigated. This system serves to minimise conflict over water access within the village. When HYVs are adopted, however, the inefficiency of this system is accentuated. The performance of HYVs is highly sensitive to water management and their adoption increases the economic cost of sub-optimal water storage from the Wet Season to the Dry. This paper has focussed on measurement of the economic magnitude of the gains potentially available from more efficient management of the water resource. Under the traditional water allocation system, a four-fold increase in village net benefits can be achieved by switching from old rice technology - traditional varieties and low fertliser useage - to modern HYV technology - improved short-age varieties and higher levels of fertiliser application. Not surprisingly, the HYV technology is becoming widely adopted.

Our results show that on average the gain from HYV adoption can potentially be increased by a further one fourth when HYVs are combined with an improved water allocation system. This improved system consists of a judicious rationing of the water storage to various stages of each crop intraseasonally, depending on their relative importance to final yield, and interseasonally between the two crops. Improved rice technology is now widely adopted in the Dry Zone of Sri Lanka, and the government has announced the policy of encouraging the adoption of more efficient irrigation practices. The results of this study provide information on the economic gains potentially available from improved irrigation practices. Our qualitative results may also have application to other societies practising monsoonal rice cultivation.

References Abeyratne, E. F. L. (1956). Dry Land Farmingin Ceylon, TropicafAgriculrurist, 62,191-229. Abeysinghe, A . (1982). Minor Irrigation in the Agricultural Development of Sri Lanka, Peoples

Bank of Sri Lanka Economic Review, 8 (6), 25-29. Anderson, T. W. (1958). An Introduction to Multivariate Statistical Analysis. New York: John

Wiley &Sons. Arumugam, S. (1959). Deve[opment of Village Irrigation Works. Colombo: Government Press. Bras, R . L. and Cordova, J . R . (1981). lntraseasonal water allocation in deficit irrigation, Water

Resources Research, 17,866-74. Chambers, R. J . (1977). On Substituting Political and Administrative Will for Foreign Exchange:

The Potential for Water Management in the Dry Zone, in Samarasinghe. S. W. R. de A . (ed.) Agriculture in the Peasant Sector of Sri Lanka. Colombo: Wesley Press.

Codrington, H . W. (1938). Ancient Land Tenure and Revenue in Ceylon. Colombo: Ceylon Government Press.

Dasgu ta, P. and Heal, G . M. (1979). Economic Theory and Exhaustible Resources. New York: Zambridge Universit Press.

DeDatta, S. K . , Abila d P . and Kalwar, G . N. (1973). Waterstress Effectsin FloodedTropical Rice, in IRRI &I.) Wate! Management in Philippine Irrigation Systems: Research and Operatiom. Los Banos, Philippines: International Rice Research Institute.

324 S. MAHENDRARAJAH A N D P. G. WARR

Dudley, N. J., Howell, D. T. and Musgrave, W. F. (IY71). Optimal lntraseasonal Water Allocation, Wafer Resources Research. 7,770-788.

Dudley. N. J. and Burt, 0. R. (1973). Stochastic Reservoir Management and System Design for Irrigation, Water Resources Reseach. 9 (3), 507-22.

Fleming, P. A. (1964). A Water Bud et Method to Predict Plant Response and Irrigation Requirements for Widely Varying 8vaporative Conditions. in Proc. of [he VIth Inf. Congress of Agricultural Engineering, Lausanne, Suisse. 21-27 September 1964.

Flinn, J. C. (1968). Allocation of Water Resources: A Derived Demand Funcfion for Irrigation Wafer and Efficiency of Allocafion. Agricultural Economics Bulletin I , Armidale. University of New England, Australia.

Hall, W. A. and Butcher, W. S. (1968). Optimal Timing of Irrigation, Journal ofthe Irrigafion and Drainage Division of ASCE, 94-IR2: 267-75.

Hanks, R . J. (1974). Model for Predicting Plant Yield as Influenced by Water Use, Agronomy Journal, 66.660-65.

IDRC (1988). Crop and Animal Production Sysfems Program. AFNS Division Publication. International Development Research Centre, Ottawa, Canada.

Izumi, K. and Ranatunge, A. S. (1973). Cost of Production of Paddy. Research Studies Series No. I Agrarian Research andTraining Institute. Colombo.

Mahendrarajah. S. (1978). Resource Characteristics and Utilisation in Small Tank Settlements in fhe Dry Zone of Sri Lanka: A Case Study of the Village Walagambahuwa. Mimeo. Sri Lankan Department of Agriculture, Maha Illuppallama.

Mahendrarajah, S., Young, P. and Jakeman, A. (1982). Stochastic Time Series Analysis and the Village Dam Management Problem in Sri Lanka, in Optimal Allocafion of Wafer Resources, Publication 135, International Association of Hydrological Sciences. UK.

Mahendrarajah, S. and Warr. P. G. (1989). Efficient Water Allocation andTechnological Change: Village Dams in Sri Lanka. Working Papers in Trade and Development, 89/10, The Australian National University. Canberra.

Milliman, J. M. (1956). Commonality, the Price System and the Use of Water Supplies, Soufhrrn Economic Journal, 22,426-437.

Minhas, B. S . , Parikh, K . S. and Srinivasan, T. N. (1974). Towards the Structure of Production Function for Wheat Yield with Dated Inputs of Irrigation Water. Water Resources Research,

Panabokke, C. R. and Walagama, R. (1974). The Application of Rainfall Confidence Limits to Crop Water Re uirements in Dry Zone Agriculture, Journal of the NationalScience Council ofSriLanka. 2.35-113.

Panabokke, C. R. and Kannangara, R. (1975). The Identification and Demarcation of the Agro- Ecolo@cal Regions of Sri Lanka. Proceedings of Annual Sessions, Section B. Sri Lanka Association for Advancement of Science, Colombo.

Panabokke, C. R. 1976). The Need for Research in Crop ing Systems in Sri Lanka, in

Department of Agncuiure, Maha Illuppallama, Sri Lanka, 20-21 Aprif1976. Small, L. E. and Chen, C. L. (1984). A n Approach to Estimating Potential Benefits from Improved

Irrigarion Wafer Management for Rice. New Jersey Agr. Exp. Stat. Publication No. P-02119484, Rutgen-The State University of New Jersey.

Somasin, S. (1976). Efficient Utilisation of Physical Agricultural Resources in the Dr Zone of Sri Lanka, in Proceedings of the Cropping Systems Workshop: IDRC-Sri Lanla Cropping Systems Project, Department of Agriculture, Maha Illuppallama, Sri Lanka, 20-21 April 1976.

Sri Lanka (1974). IDRC-Sri Lanka Cropping Systems Project Proposal. Government Department of Agriculture, Peradeniya.

Sri Lanka (1976). Sri Lanka - USAID Cropping Systems Program Agreement, Government of Sri Lanka, Colombo.

Wickham, T. H. and Sen, C. N. (1978). Water Mana ement for Lowland Rice: Water Requirements and Yield Response, in IRRI (ed.) S o i i and Rice. Los Banos, Philippines: International Rice Research Institute.

Yakowitz, S. (1982). Dynamic Programming Applications in Water Resources, Water Resources Research, 18 (4), 673-96.

Yaron, D. (1971). Estimation and Use of Water Production Functions in Crops, Journal of the In'igation and Drainage Division of ASCE. 97-IR2.291-303.

Yaron, D. and Dinar, A. (1982). Optimal Allocation of Farm Irrigation Water During Peak Seasons, American JournalofAgricuIrural Economics, 64,681-89.

Youn , p. c. (1984). Recursive Estimation and TimeSeries Analysis: An Introduction. New York: tpringer-Verlag .

.

10,383-93.

Proceedings of I I, e Cro ping Systems Workshop: IDRC-Sri &nka Cro ping Systems Projecf,