Research Reports

IWMI’s mission is to improve water and land resources management for food, livelihoodsand nature. In serving this mission, IWMI concentrates on the integration of policies,technologies and management systems to achieve workable solutions to realproblems¾ practical, relevant results in the field of irrigation and water and land resources.

The publications in this series cover a wide range of subjects¾ from computermodeling to experience with water users associations¾ and vary in content from directlyapplicable research to more basic studies, on which applied work ultimately depends.Some research reports are narrowly focused, analytical, and detailed empirical studies;others are wide-ranging and synthetic overviews of generic problems.

Although most of the reports are published by IWMI staff and their collaborators,we welcome contributions from others. Each report is reviewed internally by IWMI’s ownstaff and Fellows, and by external reviewers. The reports are published and distributedboth in hard copy and electronically (www.iwmi.org) and where possible all data andanalyses will be available as separate downloadable files. Reports may be copied freelyand cited with due acknowledgment.

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Research Report 48

Predicting Water Availability inIrrigation Tank Cascade Systems:The Cascade Water Balance Model

International Water Management InstituteP O Box 2075, Colombo, Sri Lanka

C. J. JayatilakaR. SakthivadivelY. ShinogiI.W. MakinandP. Witharana

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The authors: C. J. Jayatilaka is a Research Engineer/Civil Engineer and was aConsultant at the International Water Management Institute (IWMI). R. Sakthivadiveland Ian Makin are Senior Irrigation Specialist and Head, Sri Lanka National Program,respectively, at IWMI. Y. Shinogi was Irrigation Specialist at IWMI and P. Witharana

is an Engineer at the Department of Agrarian Services, Sri Lanka.

This report draws from a study conducted as part of a collaborative research programbetween the International Water Management Institute (IWMI) and Japan InternationalResearch Center for Agricultural Sciences (JIRCAS), based on the Thirappane tankcascade system in Anuradhapura, Sri Lanka. This project was funded by JIRCAS.The authors gratefully acknowledge the useful comments provided by reviewers. Thesupport received from Mr. Lal Muthuwatte in preparing figures and tables and from Ms.Gayathree Jayasinghe and Mr. A. D. Ranjith with data analysis and interpretations areacknowledged with thanks.

Jayatilaka, C. J.; R. Sakthivadivel; Y. Shinogi; I. W. Makin; P. Witharana. 2001.Predicting water availability in irrigation tank cascade systems: The cascade waterbalance model. Research Report 48. Colombo, Sri Lanka: International WaterManagement Institute.

/ water management / irrigation systems / tank irrigation / mathematical models /calibration / water balance / water use efficiency / water availability / forecasting /runoff / indicators / agricultural production / Sri Lanka /

ISBN 92-9090-422-4

ISSN 1026-0862

Copyright Ó by IWMI. All rights reserved

Please send inquiries and comments to: iwmi-research-news@cgiar.org

IWMI receives its principal funding from 58 governments, private foundations, andinternational and regional organizations known as the Consultative Group onInternational Agricultural Research (CGIAR). Support is also given by theGovernments of Pakistan, South Africa, and Sri Lanka.

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Contents

Summary v

Introduction 1

The Study Area and Field Measurements 3

Model Development 5

Calibration of the Model 10

Discussion on Calibration 22

Application of the Model 23

Results and Discussion 30

Conclusions 31

Appendix A 33

Literature Cited 41

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v

Summary

In the dry zone of Sri Lanka and in other similarregions, better water management in irrigationtank cascade systems is vital in achieving higherproductive use of available water. To develop andimplement management practices aimed atimproving effective use of water, studies leadingto the development of models that can predictavailable tank water in irrigation tank cascadesystems are invaluable.

This report presents a water balance modelCascade that can predict tank water availability inthe Thirappane tank cascade system inAnuradhapura, Sri Lanka. The model determinestank water availability on a daily basis, for thepurpose of improving productive use of the waterresources in a tank cascade system. It representsthe physical system using a node-link systemconfiguration, and incorporates water balancecomponents of different types of irrigation tanksincluding rainfall runoff, rainfall on tank, evaporationof tank water, tank seepage and percolation,irrigation water release, spillway discharge andreturn flow from upstream tanks. An importantfeature of the Cascade model is that it employs amodified runoff coefficient method for estimatingrunoff from rainfall, which incorporates anAntecedent Precipitation Index (API) function asan indicator for catchment wetness, providing asimplified method for the representation of thenonlinear runoff-generation process. The modelcalculates tank seepage and percolation based onfunctions derived from an analysis of theobserved tank water reduction during time periodswithout rainfall.

The Cascade model was calibrated usingfield data collected at four tanks over a periodof 21months, which represented differentagrometeorologic conditions encountered at theThirappane tank cascade system under bothmaha (wet) and yala (dry) growing seasons. Themodel was applied over a 10-year period forpredicting tank water availability for rice crops inthe Thirappane tank cascade system.

The results demonstrated the applicabilityof the model for evaluating feasibility of acropping scenario, and thus the potential useof the model in the development ofmanagement options for minimizing theeffects of water shortage on crops. The modelprovided valuable insights into the processesthat determine tank water balance, and clearlymanifested the relative magnitudes of the tankwater balance components and their temporalvariations. Further, it demonstrated theavailability of water from upstream tanks asreturn flow in the immediately downstreamtanks, and thus the increased potential usageof water resources facilitated by the tankcascade system.

Using a relatively modest input and a simplewater balance modeling approach, the Cascademodel provides a valuable means to determinewater availability in the Thirappane tank cascadesystem. The model has shown its potential tobecome a useful tool in the process of optimizingusage of the limited water resources in tankcascade systems for improving agriculturalproduction.

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Predicting Water Availability in Irrigation TankCascade Systems: The CascadeWater Balance Model

C. J. Jayatilaka, R. Sakthivadivel, Y. Shinogi,I.W. Makin, and P. Witharana

Introduction

With the increasing demand for improved agriculturalproduction to sustain growing population, the needto maximize the productive use of the limitedwater resources has been widely recognized. Inthe dry zone of Sri Lanka and in other similarregions, better management of water stored inirrigation tanks (reservoirs) is vital to achieve this.

Thousands of irrigation tanks have sustainedagricultural production over more than 2000 yearsin the dry zone of Sri Lanka, providing aneconomical means for surface storage of runoffduring the rainy season for subsequent releaseas irrigation water according to the requirementsof rice and other crops. Many of the irrigationtanks are interconnected forming cascades,allowing surplus flow from the upstream tank(s)and return flow from the upstream commandarea(s) to reach the tank that is immediatelydownstream. This facilitates reuse of water in thecommand area of the downstream tank, and ineffect, increases available water for irrigation.Several hundreds of such tank cascade systems(TCSs), with small tanks in the cascadenumbering from 3 to 30, have been identified inthe dry zone of Sri Lanka (Tasumi et al. 1999),which occupies about 60 percent of the island,where rainfall is less reliable.

To develop and implement managementpractices aimed at improving effective use ofwater, studies leading to the development ofmodels that can predict required tank water in

cascade systems are invaluable. It is imperativethat any such model developed should be of acomplexity commensurate with the generallyavailable data, in order to provide a practical toolfor improving effective water usage in tankcascade systems.

The report presents a simple water balancemodel Cascade developed to predict tank wateravailability in the Thirappane tank cascadesystem, in Anuradhapura, Sri Lanka (figure 1).The report includes calibration of the model andits application to predict tank water availability forrice crops over a 10-year period.

This report draws from a study conducted aspart of a collaborative research program betweenthe International Water Management Institute(IWMI) and the Japan International ResearchCenter for Agricultural Sciences (JIRCAS). Theaim of the study was to develop a model with thecapability to account for the dynamic hydrologiccomponents of the tank cascade systems similarto that of the Thirappane TCS commonly found inthe dry zone of Sri Lanka. It was intended to keepthe model structure as simple as possible and thedata requirement to be minimal for increasing thepotential practical use of the model. The expectationwas that the Cascade model would provide thebasis for the development of a useful practicaltool with the capability to predict tank wateravailability in similar tank cascade systems inSri Lanka and in other countries.

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FIGURE 1.Location of the Thirappane tank cascade system.

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The Study Area and Field Measurements

(October–December) of the year, average monthlypotential evapotranspiration exceeds averagemonthly rainfall. During the growing season maha(October–March), total rainfall is 1,036 mm andthe potential evapotranspiration is slightly higher,1,084 mm. The difference is much greater in theyala season (April–September), during which thetotal rainfall is only 454 mm while the totalpotential evapotranspiration is 1,369 mm.

It is clear that much of the rainfall occursduring the maha season. The rainfall eventsnormally tend to be of high intensity and shortduration resulting in rapid runoff. In order tosustain crops during no-rainfall periods, the runoffproduced during rain events need to be stored intanks, and subsequent water issue for irrigationshould be regulated ensuring optimum usage ofwater available in the tank cascade system.

The field measurements to obtain importanthydrological and physical characteristics of theThirappane TCS have been carried out based onan observation network since 1997 (Shinogi et al.1998). These measurements have provided vitalobserved data required for this study on dailyrainfall and pan evaporation, tank water height,and water issue for irrigation. Initially, this studyutilized the observed data recorded from 22 July1997 to 21 February 1998. As more data becameavailable, the data set was extended to 18 April1999, thus 21 months of observed daily data werefinally used. However, the data sets obtained atthe head-end tanks in the cascade, Vendarankulamaand Bulankulama, were not complete asrehabilitation work was carried out.

Except during the rehabilitation work, the tankwater levels were observed twice a day, manuallyin all four tanks considered in this study. Thevolume of water released for irrigation was measuredat Parshall flumes located downstream of the tanksluices. The daily rainfall measurements weremade at each tank with the use of manually

The Thirappane TCS, the focus of this study, islocated about 20 km south of Anuradhapura inSri Lanka (figure 1). It is typical of hundreds ofirrigation tank cascade systems that are found inthe dry zone of Sri Lanka. The Thirappane TCS issituated within the catchment area of the muchlarger Nachchaduwa reservoir, which was built inthe ancient times. There are six inter-linked tanksin this TCS and the distance from the mostupstream to the most downstream tank is only8 km (Itakura 1995).

The Cascade model was developed consideringfour tanks in the TCS namely, Vendarankulama,Bulankulama, Meegassagama and Alisthana(figure 1), where field measurements have beencollected as reported by Shinogi et al. (1998). Asmall tank named Badugama, which was notfunctioning during the period considered in thisstudy (P. Witharana, personal communication),was included as part of the catchment area of theimmediately downstream tank Bulankulama.

Rice, the staple food of Sri Lanka, is themain irrigated crop during both maha (wet) andyala (dry) growing seasons in the Thirappane TCS,in common with much of the agricultural land inthe North Central Province of Sri Lanka. Althoughthe command areas of minor tanks in smallcascades such as the Thirappane TCS are small(less than 40 ha), each command area isimportant for sustaining the livelihood and the vitalagricultural production of the village that formspart of the tank system.

The rainfall and evaporation statistics for thestudy area based on the meteorological data fromthe Maha Illuppallamma Agricultural ResearchStation, located about 13 km from the study siteis used in this study (Shinogi et al. 1998). Theaverage annual rainfall for this area is about1,490 mm, and the average annual potentialevapotranspiration is estimated to be muchhigher, 2,453 mm. Except during three months

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FIGURE 2.The study area and locations of field measurements.

recorded rain gauges and the pan evaporation datacollected at the Meegassagama tank was used inthis study. The points of above field measurementsat each tank in the TCS are shown in figure 2.

The field measurements also included soilsurveys, which allowed classification of the soil

series. The main soil types commonly found inthe North Central Province, Reddish Brown Earth(RBE) and Low Humic Gley (LHG), cover most ofthe area in the Thirappane TCS (table 1). Thetypes of land use and the physical characteristicsof the catchment areas are also given in table 1.

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TABLE 1.Thirappane tank cascade system: Catchment area description.

(a) Catchment area, average slope and aquifer thickness.

Tank Catchment area Average slope Average thickness(%) of the aquifer

(m2) N-S E-W (meters)

Vendaramkulama 2.40E06 2.97 0.36 8.2

Bulankulama 1.13E06 0.30 0.36 5.0

Meegassagama 3.33E06 0.69 0.41 5.0

Alisthana 3.25E06 0.85 0.91 6.0

(b) Land use (percentage area).

(c) Soil type (percentage area).

Model Development

The development of the Cascade model wasinitiated considering the structure and the processesincluded in the Reservoir Operation Simulation(Extended) Systems (ROSES), a software packagedeveloped by Usgodaarachi et al. (1996) to simulate

the operation of water resources systems on dailybasis. The Cascade model was formulated basedon a simple structure, incorporating the dynamichydrologic processes associated with a set of fourtanks in the Thirappane TCS.

Tank Cropped Dense Scrub Degraded Barren Teakland* forest land forest land plantation

Vendaramkulama 2 40 6 0 5 47

Bulankulama 6 57 8 7 11 9

Meegassagama 27 40 16 11 1 5

Alisthana 16 50 11 20 4 0

*Includes paddy land, homestead gardens, and chena land.

Tank Well drained, Moderately to imperfectly Poorly drained Rockreddish brown drained reddish brown low humic outcrops

earth soils earth soils gley soils

Vendaramkulama 62 22 10 6

Bulankulama 63 15 8 13

Meegassagama 67 16 17 1

Alisthana 78 9 9 4

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Representation of the Physical System

The configuration of the tank cascade system isrepresented in the model using a commonlyaccepted node-link system configuration that candelineate relative positions of tanks and theirinterconnections (figure 3). The nodes indicatetanks and the links indicate the interconnectionbetween tanks. The links do not necessarilyrepresent any physical link such as a canal orstream; they indicate the direction of flow betweenthe tanks.

As the initial step in setting up the model fora given cascade, each tank should be assigned anode number and tank type depending on itsrelative position within the cascade. Three typesof tanks are identified—Start tank (ST): a tank

with no inflow from upstream tanks; Normal tank(NT): a tank with inflow from one upstream tank;and Confluence tank (CT): a tank with inflow frommore than one upstream tank.

In the Thirappane TCS, Vendarankulama andBulankulama have been identified as STs, andMeegassagama and Alisthana were assigned asCT and NT, respectively (figure 3). The nodenumbering begins with the STs in the upstreamend of the cascade and continues sequentiallytowards the downstream end. The CTs shouldalways have a node number higher than those ofthe upstream tanks linked to them. The NTshould be assigned a node number greater thanthat of the tank located immediately upstream.The last node number in the cascade should beequal to the number of tanks in the cascade.

FIGURE 3.Representation of the Thirappane tank cascade system in the model.

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Tank Water Balance Components

The effective water balance components of thetank cascade system simulated by the Cascademodel are shown in figure 4. In start tanks, whichare normally located in the upstream end of thecascade, runoff from the catchment, and rainfallon the tank water surface, form the ‘inflow’components. The ‘outflow’ components include:evaporation of tank water, seepage through the

FIGURE 4.Schematic of the tank water balance components.

tank embankment and percolation through the tankbed, which is referred to as ‘tank seepage,’ waterissue for irrigation, and spillway discharge.

In normal and confluence tanks, in addition tothe runoff generated in their own catchments andthe rainfall on tank water surface, a fraction of theoutflow from the immediately upstream tank(s) canflow in, increasing the total available tank water(figure 4). This additional inflow is treated as twodifferent components: return flow due to seepage

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and water issue, and return flow due to spillwaydischarge. In normal tanks, these flowcomponents occur from the immediately upstreamtank, whereas, in confluence tanks, inflow fromthe immediately upstream tanks (more than one)that are linked to the confluence tank needs to beincorporated. The outflow components of normaltanks and confluence tanks are similar to those ofstart tanks. In all three types of tanks, the fractionof outflow can only reach the immediatelydownstream tank as return flow.

The relevant information on the node-linksystem configuration needs to be specified as partof the input to the model that describes thephysical system. Based on the survey data ateach tank, mathematical expressions forrepresenting (1) tank area, (2) tank water volumeas functions of the tank water height, and (3) tankwater height as a function of tank water volumeneed to be formulated. The cubic expressionsderived for the Thirappane TCS depicting aboverelationships are given in Jayatilaka et al. (2000).

Simulation of Daily Tank Water Balance

The components of the tank water balancerepresent complex hydrological processesassociated with the tank cascade system. Forexample, generating runoff from rainfall on acatchment is a complex process that involvesinteraction of effective climatic, geologic, andtopographic factors; vegetation characteristics;and the antecedent conditions of the catchment.Accurate simulation of these complex processescan impose a substantial input data requirementand a detailed mathematical representation of thephysical system and the relevant processes onthe model. The Cascade model approximates thephysical system and the effective water balancecomponents with the use of several expressionsand assumptions as described in Appendix A.

Starting from the most upstream end of thetank cascade, the model performs water balancecomputations for each tank on a daily basis based

on the processing procedure illustrated in theflowchart presented in figure 5. The model inputconsists of meteorological data and water releasefor irrigation on a daily basis and information onthe physical system. In the process of calibrationof the model, water released for irrigationmeasured in the field is used as the model input.In using the model for predictions, the requiredwater release needs to be estimated consideringthe water requirements for land preparation andthe crop water requirements during the growingstage, based on cultivation extents of differenttypes of crops in the command area. In eithercase, through the daily water balance computations,the model allows release of the required irrigationwater when the storage is adequate. If the storageis insufficient, the model calculates the allowablewater release, and it will be less than the measuredwater release for the day (when calibrating themodel) or the estimated water release requirementof the day (during predictions). The water releaseallowed by the model is denoted as the waterissue (model), when presenting the results. Inaddition to the allowable water issue, the modelprovides output at the end of each day includingthe tank water height, tank storage, and informationon the tank water balance components.

An important feature of the Cascade model isthat it employs a modified runoff coefficientmethod for estimating runoff from the catchment.As runoff generation is a complex processinfluenced by several factors, the use of either aconstant or a simple seasonal variation (eg., asused by Itakura 1995 or Kachroo and Liang 1992)for representing the runoff coefficient is notadequate. The method adopted by the Cascademodel incorporates an Antecedent PrecipitationIndex (API) function, which in an indirect way,acts as an index of the wetness of the catchment.This allows variation of the runoff coefficient,providing a simplified method for the representationof the nonlinear runoff-generation process. As theeffect of the antecedent soil moisture level onrunoff yield is accommodated through the methodadopted, the requirement for detailed field

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FIGURE 5.Flowchart of the Cascade model.

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measurements on soil moisture levels and theneed for complex mathematical techniques in themodel for simulating flow in the unsaturated soilzone are eliminated.

The runoff generation in response to rainfallcan be delayed after a prolonged dry period, asthe soil moisture needs to be replenished beforerunoff can occur. The model handles the initialloss of rainfall that occurs in such conditions withthe use of a delay parameter. The delay and therunoff coefficient (RCF), which represent thecombined effect of the factors affecting runoffgeneration in the catchment, such as the soil type,topographic slope and vegetation, are the twoparameters used in the model that need calibration.

The model calculates the tank seepage basedon functions derived from an analysis of theobserved tank water loss during time periodswithout rainfall (Appendix A). Normally, the tankseepage is estimated as a certain percentage ofthe tank volume (e.g., 0.5 percent of the tankvolume per month used by Ponrajah 1984; 2.4percent of the tank water volume per day as givenin Tasumi et al. 1999). Based on the resultsobtained at all four tanks in the Thirappanecascade, this study clearly indicated a greaterpercentage of tank water volume would leave as

seepage, when the tank water level is low, thanwhen the tank water level is high. Similarobservations have also been made at theWalagambahuwa village tank as reported byDharmasena (1985). The observed trend invariation of the seepage rate is consistent with thelarger head difference that can occur between tankwater and the groundwater in the surrounding areawhen the water table is low under dry conditions inthe cascade. In contrast, in wet conditions whenthe tank water level is high and the water table isnear the surface, the resulting head difference canbe comparatively low resulting in low percentagereduction of tank water due to seepage.

The analysis on the tank seepage also led tothe derivation of a function (Appendix A) that canbe used for seepage and percolation calculationsin similar small irrigation tanks in the absence ofobserved measurements to obtain parametersrelevant to each tank. This function can befurther improved by extending the seepageanalysis further involving more field data underdifferent agrometeorological conditions in thecascade. The option to use such a function forthe tank seepage estimation would furtherenhance the potential application of the model.

Calibration of the Model

The process of calibration of the model was basedon two stages, involving field measurementscollected as described by Shinogi et al. (1998) atfour tanks of the Thirappane TCS. The initialcalibration (stage1) was based on the data setavailable at the time, which included daily recordsof the field measurements from 22 July 1997 to21 February 1998. In the second stage (stage 2),calibration was extended until 18 April 1999,involving 21 months of observed data. Theextended data set spanned over two maha and

one yala growing seasons, thus representing bothdry and wet conditions in the tank cascadesystem. The use of the entire data set facilitatedthe model to be calibrated under different seasonalfield conditions in the tank cascade.

The functions used in the Cascade model forthe estimation of the tank water reduction due toseepage have been derived utilizing relevantinformation from the data set used in stage 1 ofthe calibration process. The parameters of theseseepage functions kept unchanged as the model

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calibration was extended to stage 2. This, to adegree, allowed verification of the applicability ofthe seepage functions over the changing fieldconditions in the tank cascade.

Model Input and Initial Condition

In the process of calibration of the model, initialcondition in the tank cascade was assigned basedon the measured tank water levels at 8 am on22 July 1997. During the calibration stage 1,the model input including daily measurements ofrainfall and pan evaporation, tank water height,and tank water released for irrigation were basedon the field data recorded over the period 22 July1997–21 February 1998. The user-definedcoefficient, fp, which converts pan evaporationrate to tank water surface evaporation, was takenas 0.8. The user-defined coefficients fr (return flowcoefficient), fs (return flow fraction due to upstreamtank spilling), and the two model parameters RCFand delay that need to be calibrated were initiallyassigned values as recommended in Appendix A,and were later adjusted during calibration.

The model performed daily water balancecomputations for each tank in the cascade andcalculated water balance components and the tankwater height at the end of each day over thecalibration period. The simulated tank water heightat the end of each day was compared with thetank water height measurements taken at thebeginning of the following day. The calibration wasfinalized in stage 2 involving field data collectedover 21 months (until 18 April 1999), based on aqualitative comparison of the match between theobserved and simulated tank water heights overthe calibration period. This was considered to bemore appropriate for comparing simulated resultswith the measured data than using a numericalcriterion due to the lack of a complete data setover the periods of rehabilitation work and itseffects over the following periods at the two head-end tanks. The model input, user-definedcoefficients, and the parameters of the calibrated

model are given in table 2. The observed data andthe simulated results are presented in figures 6–9.The first graph in each figure shows the observedand predicted tank water height along with themodel input on daily rainfall, pan evaporation data.The second and third graphs illustrate tank waterbalance components. The fourth graph includesthe predicted and observed tank water volume,and the measured tank water issue along with thewater issue allowed by the model, which isdenoted as water issue (model). The temporalvariations of the water balance components arealso presented in figures 6–9. The total waterbalance over the 21-month calibration period ispresented in figure 10 and table 3.

Model Simulations

The modeling results presented in this study spana 21-month period, which represented differentagrometeorologic conditions encountered at thetank cascade system under both maha and yalagrowing seasons. The simulations started on 22July 1997, when the rainfall in the yala seasonended, and dry conditions prevailed in the tankcascade system until the rainfall in mid-September.The field observations indicated low initial storagein all tanks corresponding to tank water heightsranging from 0.48–1.21 m (table 2). The waterlevels decreased and tanks became empty duringthis no-rainfall period. The model simulations overthis dry period agreed well with the fieldobservations as shown in figures 6–9.

The generation of runoff in response to rainfallfollowing the dry period was delayed due todepleted soil moisture levels in the catchments atthe end of the long dry spell. This condition wasclearly visible from the tank water level measurementsparticularly in tanks downstream of Vendarankulama.The model accounted for the delay in runoffgeneration in catchments by adjusting the delayparameter in the runoff calculation procedure, thefinal values of which are given in table 2. Thegradual increase of the tank water height in the

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TABLE 2.The Cascade model input parameters.

a. User-defined coefficients.

fp fr fs

0. 8 0.10 0.5

b. Input data on tanks.

Tank Node Tank type Effective Length of the Initial tank RCF Delayno: spill level spillway water height

(m) (m) (m) (mm)

Vendarankulama 1 ST (Start Tank) 3.00 30.0 1.21 0.21 80.0

Bulankulama 2 ST (Start Tank) 2.50 30.0 0.48 0.30 290.0

Meegassagama 3 CT (Confluence Tank) 2.75 55.0 0.97 0.132 240.0

Alisthana 4 NT (Normal Tank) 3.75 30.0 0.81 0.31 260.0

TABLE 3.Model calibration: Tank water balance components.

a. Inflow components as percentage of the total inflow to the tank during the calibration period.

Tank Rain on tank Runoff Return flow from Inflow from upstreamsurface upstream tanks tank spilling

(%) (%) (%) (%)

Vendarankulama 17.4 82.6 0.0 0.0

Bulankulama 15.3 84.7 0.0 0.0

Meegassagama 26.0 60.1 12.5 1.4

Alisthana 25.2 70.6 2.8 1.4

b. Outflow components and net storage increase as percentage of the total inflow to the tank during the calibration period.

Tank Evaporation Seepage Spill discharge Water issue Storage increase

(%) (%) (%) (%) (%)

Vendarankulama 11.0 75.2 2.9 4.4 6.5

Bulankulama 8.0 83.9 0.0 7.9 0.3

Meegassagama 22.6 41.6 5.3 16.1 14.4

Alisthana 20.4 46.8 0.0 21.8 11.0

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FIGURE 6.Model calibration: Observed and simulated tank water height, volume, and simulated tank water balance components–Vendarankulama.

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FIGURE 7.Model calibration: Observed and simulated tank water height, volume, and simulated tank water balancecomponents—Bulankulama.

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FIGURE 8.Model calibration: Observed and simulated tank water height, volume, and simulated tank water balancecomponents—Meegassagama.

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FIGURE 9.Model calibration: Observed and simulated tank water height, volume, and simulated tank water balancecomponents—Alisthana.

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FIGURE 10.Total water balance of the tank cascade system over the calibration period.

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maha (97/98) season and the changes in tankstorage in the following periods in response torainfall variations were simulated by adjusting therunoff coefficient (RCF), which is also included intable 2.

During the 97/98 maha season, the simulatedtank water height showed a close agreement withthe observed data in all the tanks, particularly inthe early part of the rainfall period (figures 6–9).Towards the end of the maha season rainfallperiod, the model underestimated the tank waterheight at the Bulankulama tank. This conditionwas commonly observed at the Bulankulama andVendarankulama tanks towards the end of the97/98 maha season.

The agreement of the model simulations withthe field observations over the rest of the calibrationperiod was considerably better in the downstreamtanks when compared with the upstream tanks. Theapparent discrepancy between the model results andthe field measurement can be explained byconsidering the field conditions and physicalattributes of the catchments (table 1) and theassumptions associated with the Cascade model.

Vendarankulama Tank

This tank is located at the foot of a hill in theupstream end of the cascade. The catchmentarea of the Vendarankulama is relatively steep(slope of 2.7 percent in the N-S direction)compared with other catchments within thiscascade (table 1). Cultivated land in thiscatchment accounts for a small fraction of thetotal area (2%) in comparison with othercatchments (6–27%). Teak plantations cover47 percent of the area. This indicates a markeddifference compared with other catchments, inwhich the teak plantations cover only 0–9 percentof the area. The predominant soil type in thecascade, well-drained reddish brown earth, covers62 percent of this catchment.

The delay in runoff generation in responseto the maha 97/98 rainfall was simulated atthe Vendarankulama tank with the use of adelay parameter (80 mm) that was considerablylow compared with the range of the values(240–290 mm) used at the other tanks in thecascade. The RCF value used at the Vendarankulamatank (0.21) is well within the range of values usedfor the downstream tanks (0.132–0.31).

Given the catchment area is accurate, thevalue of RCF would reflect the resulting effects ofthe factors influencing runoff generation such asvegetation, slope, and soil type. The initial loss ofrainfall after the prolonged dry spell indicated bythe delay parameter would also be influenced bythese factors. The steeper slope could haveinfluenced the low delay in runoff generationobserved in this catchment. The larger area withteak plantations and the smaller cropped areacould have influenced both RCF and delayparameters, as discussed by Dharmasena (1994)in studying the effect of land use on rainfall–runoffrelationships and runoff threshold values.

The simulated tank water height at theVendarankulama tank agreed well with theobserved data until February 1998. The modelsimulated spillway discharge at the end of therainfall period in January 1998. The fieldobservations over this period also indicated tankspilling. However, the agreement of the modelresults with the observed data shown in figure 6was obtained with the use of a weir crest level of3 m in the model. This is slightly higher than thecrest level indicated by the survey data (2.9 m).In all the tanks considered, with an exception ofthe Alisthana tank, it was necessary to use spillcrest levels different from those indicated by thesurvey data. It can be envisaged that the fieldpractices such as the use of sand bags to raisethe spill level, and in some cases, extension ofthe sections of the spillway, and other fieldconditions could have contributed to the changesin the effective spill crest level. In addition, it is

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not clear whether the survey data used in thisstudy represent the existing physical conditionsaccurately.

From February to June 1998, the modelunderestimated the tank storage. This could bedue to an inadequacy of the function used for theestimation of tank seepage, which was derivedusing the observed data until February 1998.

On 26 June 1998, the tank was emptied forrehabilitation work as indicated by the measuredwater issue in figure 6. There has been anuncontrolled water issue over the rehabilitationperiod, and the tank remained dry until the end ofDecember 1998. As the water issue data was notsupplied to the model over this period, the modeldid not allow any water release, but simulated anincrease in tank storage in response to rainfall.Therefore, a direct comparison of the simulatedand measured tank water height is not possibleover the period during and after the rehabilitationwork. However, the trend shown in the simulatedtank water height agreed well with the observedtrend since the end of the rehabilitation work inDecember 1998 (figure 6).

Tank water balance

As a start tank, Vendrankulama received inflowonly due to rainfall on the tank surface (17.4%) andrunoff from its catchment (82.6%), as shown intable 3, which illustrates the total tank waterbalance over the calibration period. The seepageloss dominated the outflow from the tank, andaccounted for the 75.2 percent of the total inflowto the tank. The evaporation was low particularlyduring low storage conditions; nevertheless, theevaporation was estimated to be 11 percent of thetotal inflow. The water issue allowed by the modelagreed well with the available measured data, andaccounted for 4.4 percent of the total inflow. Thetotal spillway discharge and the net storageincrease over the simulation period were 2.9 and 6.5percent of the total inflow, respectively.

Bulankulama Tank

The Bulankulama tank is also located near theupstream end of the cascade and it containedanother small tank, Badugama, within itscatchment. The area with rock outcrops (13%) islarger in this catchment compared with that of theother catchments (1–6%). This could promoteadditional runoff generation, and thus, would haveinfluenced the RCF values used at this tank(0.30), which is towards the higher end of therange of the values used (0.132–0.31) in thecascade. The slope of the catchment is milder(0.30% in the N-S direction) than that of the otherthree catchments, and cropped area is small (6%),compared with the downstream catchments. Thisattribute, together with other attributes of thiscatchment (table 1) may have influenced both theRCF and the delay parameters (290 mm) used insimulating runoff.

The simulated water height at theBulankulama tank showed a reasonable agreementwith the measured data until the tank waterreached the highest level indicated by themeasured data during the maha (97/98) rainfallperiod (figure 7). The simulated results were basedon an effective spillway crest level of 2.5 m. Thespill level of 2.2 m as indicated by the surveydata will not allow tank water level to reach 2.4 mas indicated by the observed data. The requirementto use a higher effective crest level could be anindication of the existing field conditions of thespillway, or the effect of the field practices toraise the spill level, or an inconsistency in thefield measurements.

The Bulankulama tank was kept dry when therehabilitation work was carried out from 5 October1997 to 1 May 1998. With the exception of someindication of water accumulation in July 1998, thetank remained empty until July 1998. Due to theincomplete water issue information supplied to themodel, it is not feasible to compare the modelresults with the observed data during this period.

20

The model simulations over the rest of thecalibration period did not show a close agreementwith the measured data. The reasons for theapparent discrepancy are not clear. It is possiblethat the changes resulting from the rehabilitationwork were not adequately represented in themodel. And the possibility of inconsistency in thedata used in formulating expressions such as thetank height vs. tank capacity relationship cannotbe ruled out. In addition, it can be envisaged thatthe inadequacy of the seepage function could alsohave contributed to the apparent differences.

Tank water balance

As a start tank, Bulankulama received inflow dueto runoff from its catchment (84.7%) and rainfallon the tank water surface (15.3%). The tankseepage loss dominated the outflow and wasestimated to be 83.9 percent of the total inflow.The total water release for irrigation allowed by themodel accounted for 7.9 percent of the totalinflow. The model indicated drying up of the tankin February 1998, earlier than what was indicatedby the field data. As a result, the water issueallowed by the model was less than that wasindicated by the field measurements (figure 7). Theevaporation component accounted for 8 percent ofthe total inflow. In this tank only 0.3 percent of thetotal inflow was added to the net storage increase.

Meegassagama Tank

The confluence tank Meegassagama is locateddownstream of the Vendarankulama andBulankulama tanks. Therefore, it received returnand spill flows from both upstream tanks asinflow, in addition to the rainfall on the tank andrunoff from its own catchment. The catchmentarea of this tank is fairly large compared to thetwo tanks upstream, and is even slightly largerand higher than that of the Alisthana tank which islocated immediately downstream (table 1). Thecropped area is relatively large—27 percent of the

catchment area, and rock outcrops represent asmall area (1%) of this catchment. The slope inthe N-S direction of this catchment is greater thanthat of the Bulankulama, but is milder than that ofthe other two catchments.

At this tank, the parameter used for simulatingthe delay in runoff generation in the 97/98 mahaseason was 240 mm. A close agreement betweenthe model results and the measured data wasobtained using RCF as 0.132, which is the lowestin the range of values used in the tank cascade(table 2). As noted earlier, the catchment area ofthis tank is the largest amongst the four tanksconsidered. The need for a low RCF value couldbe a consequence of the effects of the factorsaffecting runoff generation. Another plausibleexplanation is that the low RCF value may havecompensated for an overestimation of thecatchment area that is effective in contributingrunoff to the Meegassagama tank. In improvingthe model, it would be useful to re-draw the effectivecatchment area of this tank and to check thevalidity of the survey data in determining tankcapacity from tank height.

The overall match between the model resultsand the field measurement was considerablyclose; however, over the relatively dry period frommid-June to November 1998, the model simulationsdeviated from the measured data (figure 8). Thismay have resulted from underestimating the tankseepage rates by the seepage function used inthe model. The seepage function, which has beenderived using relevant data from July 1997 toFebruary 1998, indicated unrealistic (negative)values when the tank storage was near its fullcapacity. Under such conditions, a very lowseepage rate (0.1%) was assumed in the model.This assumption needs to be used until theseepage function is improved involving more dataon tank seepage components under high tankstorage conditions.

The model simulated spillway discharge withan effective spill crest level at 2.75 m, which islower than that was indicated by the survey data(2.9 m). It is possible that field conditions at the

21

spillway or an inconsistency in survey data couldhave contributed to this difference in the spillcrest level.

Tank water balance

Based on the simulated results the inflowcomponents of the Meegassagama tank were:Runoff (60.1%), rainfall on tank water(26%), return flow due to upstream tank seepageand water issue (12.5%), and return flow due toupstream tank spilling (1.4%). This shows thatover the calibration period, return flow and spillflow from the upstream tanks accounted for a totalof 13.9 percent of the total inflow into thisconfluence tank. This highlights the concept ofreuse of water in the tank cascade.

Except in the dry period in the beginning ofthe simulations, this tank had a considerablestorage throughout the calibration period. Due tothis condition, rainfall on tank water surfacerepresented a significant component of the totalinflow (26%).

The seepage component dominated theoutflow, accounting for 41.6 percent of the totalinflow, but was considerably lower than that of thetwo upstream tanks. The evaporation in this tankaccounted for 22.6 percent of the total inflow.This can be attributed to the tank water surfacearea corresponding to the relatively high tankwater storage over most of the calibration periodcompared with the previous two tanks, which weredry or had very little storage over considerablylong time periods. The water release allowed bythe model was estimated to be 16.1 percent of theinflow. This agreed well with the measured dataexcept at the beginning of the calibration periodwhen the model indicated an empty tank earlierthan that was indicated by the field data. The netstorage increase in this tank accounted for14.4 percent of the total inflow, whereas spillwaydischarge was estimated to be 5.3 percent of thetotal inflow.

Alisthana Tank

The Alisthana tank is located downstream of theMeegassagama tank, and is the last nodeconsidered in this study. The predominant soiltype, red brown earth, covers a relatively largearea of this catchment (78%). Cropped landaccounts for 16 percent of the area and there areno teak plantations. The slope of the catchment ismuch smaller than that of the Vendarankulamacatchment, but it is higher than the other twoupstream catchments (table 1).

The delay in runoff generation in response tomaha (97/98) rainfall was simulated with a delayparameter of 260 mm. A close agreement betweenthe simulated tank water height and the observeddata was obtained throughout the calibration period(figure 9) with RCF set at 0.31, the highest in therange values used in the cascade.

Tank water balance

As a normal tank, Alisthana received returnflow from the immediately upstream tank(Meegassagama) in addition to the inflow fromits own catchment and rainfall on tank surface.Runoff from its catchment was estimated to be70.6 percent of the total inflow. As this tankhad considerable storage during most of thecalibration period, rainfall on tank surfaceaccounted for 25.2 percent of the total inflow.Return flow due to water release and seepageat the upstream tank was estimated to be2.8 percent and, return flow from upstream tankspilling was 1.4 percent.

The seepage dominated the outflow and wasestimated to be 46.8 percent of the total inflow.However, in this tank and in the Meegassagamatank, the seepage component was considerablylow compared with the two upstream tanks. Thehigh storage conditions were often observed atthese downstream tanks, and as indicated by theseepage functions, seepage under suchconditions will be relatively low.

22

The high storage conditions also promote tankwater reduction due to evaporation, and at theAlisthana tank the evaporation was estimated tobe 20.4 percent of the total inflow. Except in theearly part of the calibration period, tank storage

between the observed data and the simulatedresults over the calibration period can be regardedas an indication of the applicability of the simplewater balance modeling approach used in theCascade model.

The increase in the simulated tank waterlevel in response to rainfall events over thecalibration period agreed well with fieldobservations, providing confidence in the methodadopted in simulating runoff yield from catchment.The runoff coefficient (RCF) and delay parameterscould reflect the combined effect of the factorssuch as land use, soil type, and slope of thecatchment. This was clearly evident at theVendarankulama tank where a distinctly low delayparameter was required to simulate runoff generationin its catchment area that was relatively steep. Bycomparing simulations with additional observeddata at Thirappane and at other similar tankcascade systems, it may be possible to gainfurther insights into the effect of catchmentcharacteristics on parameters such as RCF anddelay. As shown by Dharmasena (1994) bystudying the effect of land use on rainfall–runoffrelationships and runoff threshold values, suchstudies may enable derivation of the values of thedelay and RCF parameters based on catchmentcharacteristics. This can eliminate the calibrationrequirement of the model.

The model simulations clarified the relativemagnitudes of the water balance components ateach tank. The results showed that tank inflowwas mainly comprised of runoff from thecatchment (60–85%). The significance of

was sufficient to provide for the water issuerequirements at this tank. The water issueallowed by the model was 21.8 percent of theinflow. The net storage increase was equal to11 percent of the total inflow.

Discussion on Calibration

Except for the apparent differences in the latterpart of the simulation period at the two head-endtanks, a reasonable overall agreement wasobtained between the simulated results and themeasured data. However, a close match betweenthe observed data and model simulations is anindication of the combined accuracy in simulatingthe different hydrologic components by the model.For example, if rainfall runoff is underestimatedwhile the tank seepage is also underestimated,the simulated tank water height may still show aclose agreement with the observed data. Therefore,it is important, whenever possible, to verify thevalidity of the simulated results considering thefield evidence and understanding of the physicalsystem.

The apparent discrepancy between themodel results and the observed data can beattributed to several factors. At least in part, theobserved differences highlight the need for furtherimprovement of the seepage functions involvingadditional data representing different seasonalconditions at the tank cascade. The simulatedresults also depend on the validity of the modelinput in representing field conditions. There isuncertainty concerning the degree to which themodel input is representative of the fieldconditions. Siltation and other problemsassociated with village irrigation tanks can affectthe water-holding capacity of tanks. As such, thevalidity of the mathematical relationships in themodel used for estimating tank capacity and tankarea can change. Given the uncertainty caused bythe above factors, the agreement obtained

23

tank seepage became clearly evident, as itaccounted for 42–84 percent of the total inflowto the tank. The lower values were observed inthe downstream tanks, which had considerablyhigh tank storage over most of the calibrationperiod. In comparison, the total water release forirrigation was relatively low, and was within therange 4–22 percent. The results confirm tankseepage as the main outflow component, which,in an indirect way, supplements the waterrequirement of vegetation in the surrounding and

13 km from the Thirappane tank cascade system.This was part of the long-term data set preparedby filling in the missing data using records atanother met station, Maradankadawala, situated6.4 km from the study site, as described byJayatilaka et al. (2000). For the estimation ofirrigation water release requirement, a procedureappropriate for the type of crops and fieldpractices of the model application should beadopted. The method adopted for estimating therequired daily irrigation water release based onpaddy cultivation extents is given in the followingsection.

Irrigation Water Requirement

The irrigation water requirement at each tankneeds to be estimated considering the fieldpractices of the two growing seasons maha(relatively wet season from October to March) andyala (relatively dry season from April to September).The water issue requirement in each season isestimated based on three stages: (1) landpreparation; (2) growing stage of the crop; and(3) ripening period of the crop.

In the maha season, land is prepared usingrainfall in October, and therefore, tank water is not

command areas of a tank. The results indicatedthat about 14 percent of the total inflow to theconfluence tank Meegassagama was derivedfrom the return and spill flows from the upstreamtanks, and thus, demonstrated the reuse of waterfrom upstream catchments in the immediatelydownstream tanks facilitated by the tank cascadesystem. Thus the simulated results showed thecapability of the model to provide valuableinsights into the water balance at each tank.

Application of the Model

Using the model parameters obtained through thecalibration process, the Cascade model wasapplied to predict water availability for rice cropsin the Thirappane TCS over a 10-year period. Theextent of paddy cultivation in the Thirappane TCSfrom 1988 yala to 1997 yala given in table 4 wasused to estimate the demand for irrigation waterrelease in each tank. The model was then usedto predict whether the available tank waterstorage would be sufficient to provide for the time-varying irrigation water requirement at each tank.

This application of the Cascade modelprovides an example of how the model can beutilized to evaluate the feasibility of providing therequired irrigation water for a cropping scenario,and thus illustrates a vital initial step in theprocess of improving effective water usage in atank cascade system.

Model Input

The model input includes daily meteorological dataand the water release required for irrigation. Thedaily rainfall and pan evaporation data over thetime period considered in this model applicationwas taken from the records at the Maha IluppallamaResearch Station, which is situated at about

24

TABLE 4.Paddy cultivation extents (area in ha) of the Thirappane tank cascade system.

SeasonPaddy cultivation extent (ha)

Vendarankulama Bulankulama Meegassagama Alisthana

Yala 88 0.0 0.0 6.1 0.0

Maha 88 10.1 8.1 28.3 18.2

Yala 89 0.0 0.0 0.0 0.0

Maha 89 8.1 6.1 28.3 16.2

Yala 90 0.0 0.0 0.0 0.0

Maha 90 6.1 6.1 28.3 14.2

Yala 91 0.0 0.0 6.1 0.0

Maha 91 12.1 8.1 28.3 16.2

Yala 92 0.0 0.0 2.6 2.0

Maha 92 19.0 10.1 28.3 24.3

Yala 93 0.0 0.0 0.0 6.1

Maha 93 19.0 14.6 28.3 20.2

Yala 94 0.0 0.0 0.0 0.0

Maha 94 0.0 0.0 0.0 0.0

Yala 95 0.0 0.0 0.0 0.0

Maha 95 0.8 0.0 0.0 0.0

Yala 96 0.0 0.0 0.0 0.0

Maha 96 10.1 3.2 6.1 0.0

Yala 97 0.6 8.1 6.1 5.5

required. In the yala season, tank water isreleased for land preparation in April. The volumeof water released and the time period could vary.It is assumed that a 15-day period starting from16th of April and a total of 125 mm of water wouldgenerally indicate the land preparation waterrequirement in the yala season. The irrigationwater release requirements during the growingstage of the crop (stage 2), which is considered tobe a 90-day period, is determined according to thecrop water requirements as indicated in theprocess described below. During the third stage,the ripening period of the crop (15 days), irrigationwater is not required.

Irrigation water demand in the growing stage

Using daily rainfall and pan evaporation data, thedaily net irrigation water requirement (WR in m/day)at the paddy field is calculated using equation (1).

WR = cf1.E – cf2. R …….. (1)

where, E is pan evaporation (m/day), R is rainfall(m/day), cf1 is pan coefficient for paddy fields andcf2 is the coefficient to convert rainfall to effectiverainfall. cf1 was assigned the values suggested byKitamura (1984) for the pan coefficient for thepaddy fields in the dry zone of Sri Lanka, taking

25

rice-growing period as 90 days in both seasons(table 5). cf2 was taken as 0.8 in the yala seasonand 0.65 in the maha season as used in theROSES model (Usgodaarachi et al. 1996).

If WR, calculated using equation (1), is lessthan or equal to zero, then the required DailyIrrigation Water Issue (WI) is taken as zero. IfWR > 0.0 then, WI is calculated (in m3/day) fromequation (2).

WI = WR.PA / IE ……………… (2)

where, PA is the paddy cultivation area (m2), IE isthe irrigation efficiency (assumed as 0.6) and WRis the daily net irrigation water requirement (m).

on the 1 August 1987, leaving a considerable timeperiod before the start of predictions in yala 1988.

Considering the relatively dry period normallyobserved in the cascade towards the end of theyala season, a small tank water height, 0.1 m,was assumed in each tank. It was expected thatthe model simulations during the last two monthsof the 87 yala season and the 87/88 maha seasonwould adjust tank water height to a realistic valueby the start of predictions in yala 1988.

Model Predictions

Using the model parameters and the user-defined coefficients of the calibrated Cascademodel, tank water availability in the Thirappanecascade was predicted based on the dailywater balance computations over a 10-yearperiod, from 1 August 1987 to 30 September1997. The results obtained are presented infigures 11–14.

The model simulated the delay in runoffgeneration at the beginning as a prolonged dryspell was assumed in the cascade at that time,and predicted the subsequent increase in tankstorage and its changes in response to rainfall. Inaddition to the initial period, the delay in runoffgeneration was simulated after a prolonged dryspell, which was assumed when two conditions,(1) no rainfall and (2) empty tank, occurredsimultaneously over 50 consecutive days at agiven tank.

In general, the model predictions indicatedthat two upstream tanks became dry moreoften (almost every year) during the predictionperiod compared with the two downstream tanks.After the initial dry spell, delay in the generationof runoff occurred only once at the Bulankulamatank when a prolonged dry spell occurred inApril in 1992. This condition however, did notoccur in the other tanks, as conditions forprolonged dry spells were not satisfied.

TABLE 5.Pan coefficient for paddy fields in Sri Lanka( Kitamura 1984).

Growing Pan coefficientperiod day Wet season Dry seasonnumber (Maha) (Yala)

11 0.8 0.9

21 0.8 0.9

31 0.9 0.9

41 1.1 1.0

50 1.2 1.1

60 1.4 1.2

70 1.4 1.2

80 1.4 1.2

90 1.4 1.2

Initial Condition

The Cascade model was to be set up forpredictions from the beginning of the yala seasonin 1988. There were no observed tank height dataavailable to assign water level in tanks, andtherefore, the initial condition had to beapproximated. In order to minimize the effect ofany errors in the assumed tank water height onmodel predictions, initial condition was assigned

26

FIGURE 11.Predicted tank water height, volume, and tank water balance components—Vendarankulama.

27

FIGURE 12.Predicted tank water height, volume, and tank water balance components—Bulankulama.

28

FIGURE 13.Predicted tank water height, volume and tank water balance components—Meegassagama.

29

FIGURE 14.Predicted tank water height, volume, and tank water balance components—Alisthana.

30

Results and Discussion

the calibration period as indicated in figure 13.Low tank water and dry tank conditions wereapparent during 1989. During the rest of theprediction period, this tank had considerablestorage. The available tank water was sufficient toprovide for the estimated irrigation waterrequirements. It appears that this tank had thepotential to meet even greater irrigation waterdemand than that was estimated based on thepaddy cultivation extent.

The normal Alisthana tank received returnflow from the upstream Meegassagama tank inaddition to the rainfall runoff from its catchmentand direct rainfall on the tank. The tank storageremained high over a considerable part of thesimulation period and became relatively low only afew times during the prediction period (figure 14).Spill discharge was predicted several times asindicated in figure 14. At this tank, available tankwater was sufficient to meet the estimatedirrigation water demand during all the cultivationseasons considered. As observed in theMeegassagama tank, this tank also showed thepotential to meet even greater irrigation waterdemand.

In general, the application of the Cascademodel illustrates how it can be used to predictwater availability in the Thirappane TCS under agiven cropping scenario. It was not feasible todirectly compare the model predictions with fielddata due to insufficient field records. Although thecultivation extents were based on field data, theestimated water issue data (supplied as input tothe model) may not have represented the actualwater issue as this depends on various fieldpractices. However, the model predictionsindicated the feasibility of supplying the estimatedirrigation water requirement at each tank, andclearly indicated the periods in which tank watershortages occurred. The results also manifestedthat, in comparison with the head-end tanks, thetail-end tanks in the cascade have a greater

The Vendarankulama start tank was filled to itscapacity several times during the time periodconsidered, and spilling occurred a few times,most noticeably in the 93/94 maha season. Themodel predictions indicated low tank storageconditions over the relatively dry period 88/89. Thetank storage was only sufficient to provide part ofthe required irrigation water release in the 88/89maha season, and a water shortage was predictedfrom mid-November 1988 to mid-January 1989 inthe fourth graph of figure 11. The tank storagewas adequate to release the required irrigationwater during other cultivation periods. The modelpredictions also indicated that inflow to the tankwas dominated by rainfall runoff and the greaterportion of the inflow was lost due to tank seepage.The irrigation water release was smaller incomparison with the other outflow componentsfrom the tank.

The predictions at the Bulankulama tank,which is the other start tank in the cascade, weresimilar to those at the Vendarankulama (figure 12).The Bulankulama tank was also filled to its fullsupply level several times and tank spillingoccurred in maha 93/94 and in November 1995.The tank became empty at the end of every yalaseason. The model predicted a delay in thegeneration of runoff due to prolonged dryconditions in April 1992. The tank storage wassufficient to provide only part of the demand forirrigation water in 88/89 maha. The tank becameempty during the growing stage of rice, andtherefore, a water shortage was predicted frommid-November 1988 to mid-January 1989. Thetank water shortage was also apparent in the97 yala season and towards the end of the 96/97and 92/93 maha seasons.

As a confluence tank, Meegassagamareceived return flow from the two upstream tanksand this helped to maintain high tank waterstorage during the greater part of the predictionperiod. Tank spilling occurred several times during

31

potential than indicated by the cultivation extentdata to meet the irrigation water demand andirrigate larger areas. In particular, the application ofthe model highlighted the potential use of the

model for evaluating water use scenarios thatwould allow the optimum use of the available tankwater, minimizing water shortage during criticalgrowth stages of the crop(s) in the command area.

Conclusions

more observed data that represent differentagrometeorological conditions in thecascade.

2. An independent verification of the modelshould be carried out involving a new data setat the Thirappane TCS. This would allowfurther verification of the validity of thecalibrated model parameters. Until asatisfactory independent validation of themodel is completed, calibration of the modelshould be further extended involving moredata collected at the site.

3. The model should be calibrated using datafrom similar cascades. This process can helpeliminate the calibration requirement of themodel by formulating suitable guidelines topre-determine the values of the delayparameter and the runoff coefficient (RCF)based on the physical characteristics of thecatchment.

4. The model needs to be further developed to beable to incorporate other features of tankcascade systems such as diversion weirs andfeeder canals, which are not present in cascadesystems such as the Thirappane TCS.

5. The model code should be further improved byincorporating the dynamic array capabilityavailable in Lahey Fortran.

The reasonable overall agreement between thesimulated results and the measured data over thecalibration period provided a degree of confidencein the calculation procedure adopted by theCascade model for simulating water balance of thedifferent types of tanks in the cascade system.Although it was not feasible to carry out acomplete verification of the model, the calibrationprocess that was based on two stages allowedverification of the applicability of the seepagefunctions over the changing field conditions at thetank cascade system. The apparent differencesbetween the model simulations and field data canbe attributed to several factors including theinadequacy of the seepage functions, theassumptions used in the model, validity of themodel input, and the uncertainty of field data.

The model simulations provided valuableinsights into the water balance at each tank anddisplayed inter-connections of the tanks within thecascade system. The application of the model forpredicting availability of tank water for rice cropsin the Thirappane TCS demonstrated the potentialuse of the model in the vital initial steps of theprocess aimed at optimizing the usage of thelimited water resources in tank cascade systemsfor improved agricultural production.

The Cascade model can be further improvedby using additional field observations at theThirappane TCS and in other similar tank cascadesystems. The areas of the model that needmodifications or further improvement are:

1. The seepage function derived for each tankand for the general use in tank cascadesystems needs to be improved involving

32

With further improvements as suggestedabove, the Cascade model may provide abasis for the development of a valuable tool forevaluating different cropping scenarios andwater management options in similar irrigation

tank cascade systems in Sri Lanka and inother countries. The present version of themodel has shown its potential use in thisrespect within the Thirappane tank cascadesystem.

33

Appendix A

Mathematical Representation of the Tank Water Balance Components

CAj is the catchment area (m2), and APIj isAntecedent Precipitation Index. API, at node jdepends on the number of days since the last daywith rainfall (n). Depending on n, APIj can beestimated as:

The method adopted by the Cascade modelprovides a means to account for the effect of soilmoisture depletion over no-rainfall periods onrunoff yield. It accommodates both (1) the effectof field conditions more favorable for runoffgeneration when there has been rainfall raising soilmoisture levels and thus the catchment wetness,and (2) the effect of decreasing soil moisture(or the catchment wetness), which would graduallydecrease the runoff yield. The effect of decreasingsoil moisture on runoff yield would decrease asthe number of days without rainfall increases.Similarly, the increase in API and its effect ofrunoff yield decreases with the increasing numberof days without rainfall once that exceeds acertain limiting value. In the model this limit istaken as 11 days. Therefore, when the number ofdays without rainfall is greater than 11 days(n > 11), API corresponding to n = 11 is used inthe model.

The above process allows estimation of runofffrom rainfall on the catchment on a daily basisunder normal conditions. However, when there areprolonged dry spells without rainfall, soil moisturemay decrease to a very low level, and runoff maynot be produced in response to rainfall until thesoil moisture is replenished. Particularly at the endof the yala season, during the months of July andAugust, such prolonged dry spells can occur andthe tanks may dry up completely. This conditioncan cause a delay in the generation of runoff

)a1.A......(....................).........1k/(1APInk

0kj

+= ∑=

=

The mathematical expressions and assumptionsused in representing the effective tank waterbalance components in the Cascade model arepresented in this section.

Inflow Components

Runoff from rainfall on catchment

The process of runoff generation in catchments iscommonly approximated by the use of simplemodels based on the runoff coefficient method.The runoff coefficient of most linear systemmodels is assumed to be a constant. However, aspointed out by Xia et al. (1997), the runoffcoefficient is by no means a constant, and itsvariability (due to the influence of factors such asevaporation, catchment wetness, and rainfallintensity) cannot be explained in terms of simpleseasonal variation. The nonlinearity of the runoffgeneration process can be approximated through atime-varying runoff coefficient, facilitated by theuse of an Antecedent Precipitation Index functionindicating the degree of catchment wetness (eg.,Xia et al. 1997). The Cascade model estimatesrunoff from rainfall on the catchment of each tankon a daily basis by adopting a modified runoffcoefficient method, which allows the runoffcoefficient to vary daily depending on anAntecedent Precipitation Index (API), as describedby equations A.1 and A.1a. On a given day, runoffcontribution to the tank denoted as node ‘j’, isexpressed as:

)1.A.....(..............................API/CARRCFROjjjjj

=

where, ROj is runoff yield (m3/day), RCFj is runoffcoefficient, Rj is rainfall on the catchment (m/day),

34

when rainfall arrives, as the soil moisture levelhas to rise before runoff can occur. The modelaccounts for the above condition by using aparameter named delay, which is assigned to eachnode (tank) to act as an indicator of the ‘initialloss’ of rainfall before runoff can occur in itscatchment after a long dry spell. In suchconditions, the model would not allow generationof runoff, until the cumulative rainfall since aprolonged dry spell exceeds the value of delay,which is also given in mm. If a simulation startsfollowing a long dry period, which has causedtanks in the cascade to dry up, this condition isassumed at the beginning of the simulation. Inaddition, if the number of consecutive days (1)without rainfall, and (2) tank being dry, exceeds aset “upper limit,” the model activates the conditionrelated to long dry spells so that runoff generationwill be delayed until rainfall exceeds the initial lossindicated by the delay parameter. The upper limitis assumed as 50 days, limiting the effect of thedelay in generating runoff from rainfall only forperiods that follow extended dry spells.

The parameters RCF and delay, which aredependent on catchment characteristics such assoil type, vegetation, land slope etc., and need tobe determined through calibration, are generallyexpected to be in the range: delay, from 0 to 300mm; and RCF, from 0 to 0.35. This range can beused in assigning values for the parameters at thestart of a simulation.

Rain on tank water surface

Rainfall on the tank water spread area isdetermined as:

where, RTj is rainfall on tank (m3/day), Rj is thedaily rainfall (m/day), TAj is the tank waterspreadarea (m2), which is updated based on the latesttank water height at the beginning of each day.

)2.A..(....................RTARTjjj

=

Outflow Components

Evaporation

The reduction of tank water due to evaporation iscomputed as:

where, EVj is evaporation (m3/day), fp is pancoefficient for converting pan evaporation to tankwater evaporation, Ej is pan evaporation (m/day)and TAj is tank waterspread area (m2).

Seepage and percolation

The seepage and percolation of tank water throughthe tank bed and the embankment (referred to asthe tank seepage) represents a significantcomponent of the tank water reduction. Theseepage depends on the hydraulic conductivity ofthe tank bed and the embankment, and thedifference between the tank water level and thewater table in the surrounding area. Theestimation of the seepage requires fieldmeasurements on the spatially varying hydraulicconductivity of the tank bed and flanks, and thetime-varying tank water height and groundwaterlevels.

In the absence of such measurements,seepage has been assumed as a percentage ofthe water stored in the tank. For example, themonthly seepage from tanks has been commonlytaken as 0.5 percent of the tank water volume asreported in the manual on the design of irrigationheadworks for small catchment in Sri Lanka(Ponrajah 1984). Tasumi et al. (1999) pointed outthat seepage of 0.5 percent of the tank volumeper month is based on the seepage measurementsof large tank systems constructed with moderntechnology and cutoff trenches, and therefore,would not be representative of the seepage insmall irrigation tanks. Further, the analysis carried

)3.A.......(....................TApEEVjjj

f=

35

out by Tasumi et al. (1999) indicated that anirrigation tank completely filled with water with noinflow into the tank and outflow from sluices canloose about 75 percent of its volume due toseepage within two months of filling. Thisrepresents a seepage rate of 2.4 percent of thetank water volume per day.

In the development of thc Cascade model,the seepage in the Thirappane TCS wasestimated using the observed data from 22 July1997 to 21 February 1998, the data set that wasinitially available for the study. The decrease intank storage during time periods without rainfalloccurs as a result of the tank water issue forirrigation, evaporation of tank water, and the waterremoval due to seepage. Therefore, the seepageduring no-rainfall periods can be estimated on adaily basis from the difference between theobserved tank storage decrease (which can beestimated from the tank water height measurements)and the total of evaporation and the volume ofwater issued for irrigation. The detailed analysisperformed using the estimated seepage at eachtank (Jayatilaka et al. 2000) indicated that dailyseepage as a percentage of tank water volume(%SP) is relatively high when the tank waterheight is low when compared with the dailyseepage when tank water height is high. Thistrend is commonly observed in all four tanksconsidered, and the trend line obtained forpercentage SP as a logarithmic function of thetank water height for each tank is shown infigure A.1.

This analysis indicated that tank seepage ratecan be even higher than 20 percent of the tankwater volume when the tank water height is low,and when the tank volume is large it can decreaseto a very small rate close to zero. The high dailyseepage rates during periods with small volumesof tank water observed in this study is muchgreater than that indicated by the monthly rateused by Ponrajah (1984) and the daily ratereported by Tasumi et al. (1999). A monthly ratewould not reflect the variations in the dailyseepage rate under changing tank water storage

conditions. Unless a study has been conductedincluding different tank water conditions, even thefigure derived for the daily rate may not representthe possible range of variations in the seepagerate.

The daily seepage rate, 2.4 percent of thetank volume, derived by Tassumi et al. (1999) isbased on an analysis on a tank cascade systemin the Anuradhapura District. However, the tanksin this cascade system receive water from afeeder canal in addition to the rainfall runoff fromtheir own catchment, and therefore, the tanksremain full most of the time. The storage underwhich the seepage rate has been derived wasgreater than 50,000 m3. Therefore, it is not clearwhether the daily seepage rate of 2.4 percent ofthe tank volume would be representative of theseepage under low tank water storage conditions,which commonly occur in tank cascade systemsthat do not receive water from other sources suchas feeder canals.

The seepage rate variation observed at theThirappane TCS agrees with the results of a waterbalance study at a village tank, Walagambahuwa,in the dry zone of Sri Lanka conducted byDharmasena (1985). The seepage interpreted as apercentage of tank storage at the Walagambahuwatank decreased as the head increased. Inaddition, the observed seepage rate variation inthe Thirappane TCS is consistent with the effectsof different field conditions on the tank waterreduction due to seepage. During periods whenthe tank has water at or near its capacity at thefull supply level, the ground water table in thesurrounding area can be high. The water volumereduction due to seepage in this condition maynot be a high percentage of the tank watervolume. On the contrary, during dry periods whenthe tank storage is small, water table in thesurrounding area can be low, resulting in a greaterhead difference between tank water and thegroundwater level. This can cause a significantreduction in the volume of water due to seepageas dry conditions could prevail over a considerablearea around the tank. Given that the tank water

36

FIGURE A.1.Percent seepage as a function of the tank water height.

37

volume is low, reduction in water due to seepagecan be a relatively large fraction of tank watercompared with the fraction of water reduction dueto seepage when the tank water volume is high.

The seepage functions derived for the tanks inthe Thirappane TCS presented in figure A.1indicate a common trend consistent with thepossible variations of the seepage rate asdiscussed above. Although the R2 values obtainedare not very high (0.28-0.48), the logarithmicfunction derived for each tank was considered torepresent the generally observed trend in variationin the seepage rate. Based on these functions,the tank water reduction due to seepage throughthe tank embankment and percolation through thetank bed, referred to as ‘tank seepage’ in theCascade model, is estimated using equation (A.4):

)4.A.......(....................100/TV]b)hln(a[SPjjjjj

+=

where, SPj is tank seepage (m3/day), TVj is tankwater volume (m3), hj is tank water height (m),and aj, bj are parameters of the seepage functiongiven in figure A.1 (in which, daily seepage as apercentage of tank volume (y) is represented asa logarithmic function of tank water height (x) inthe form “y = aj ln (x) + bj” for tank j. At the startof the simulation, TVj, is determined using thecubic expression representing tank water volumeas a function of tank height given in Jayatilaka etal. (2000a). Subsequently, TVj is estimated at theend of each day as part of the water balancecalculations.

In many field situations the required data todetermine parameters of the seepage functionrelevant to the tank(s) may not be available. Theanalysis performed in this study has beenextended to derive a function that canapproximate the tank water reduction due toseepage in similar tank cascade systems. Theseepage functions of the Thirappane TCS can bepresented based on a common horizontal axisrepresenting relative tank water height defined as

tank water height/tank water height at the fullsupply level (figure A.2). Based on the averagevalue of the SP percentage corresponding to thefour expressions, a logarithmic function can bederived as presented in figure A.2. This functioncan provide a means to estimate seepage inirrigation tank cascades such as the ThirappaneTCS, when the required information to determinethe relevant parameters of the seepage function isunavailable.

Water issue for irrigation

The water released for irrigation (WQj) is a dailyfield measurement, which is part of the inputrequired for model calibration. When the model isused for predictions, the irrigation water issuerequirement needs to be estimated based on aprocess appropriate for the crops and fieldpractices of the model application.

Spillway discharge

When the tank water height is greater than theweir crest level, initially, the spillway discharge iscomputed assuming it can be approximated withthe equation A.5, which is generally applicable forbroad crested weirs (French 1994).

( ) )5.A......(....................hVL.fdSL 5.1jjjj

−=

where, SLj is spillway discharge (m3/s), Lj is thelength of the spillway (m), Vj is the spill level (m),and hj is the tank water height (m) and fd is thedischarge coefficient taken as 1.7 m1/2/s (French1994). SLj is then converted to a daily rate toobtain the upper limit of the spillway dischargeallowed by the model on a given day. The actualdischarge is determined by the lower of thefollowing two quantities: (a) estimation based onthe equation A.5, and (b) tank water volume inexcess of the full supply level (tank capacity atthe spill level).

38

FIGURE A.2.Percent seepage as a function of the relative tank water height.

39

Additional inflow components

The return flow from upstream tanks, which formsadditional inflow components to normal andconfluence tanks is estimated as follows.

Return flow due to seepage and water issue

During Maha, return flow due to seepage andwater issue from upstream tanks is estimatedfrom equation A.6:

and irrigation release) at each tank in thecascade. The coefficient fr in the Cascade modelis expected to provide a simple means to providea reasonable estimate of the return flow fraction,which would be generally applicable to the tankcascade. Initially fr can be set to be in the range0.1–0.4, and this can be refined through calibrationof the model.

Return flow due to spillway discharge

The return flow due to spillway discharge atupstream tanks is estimated as:( )[ ] )6.A......(..........SPWQfr

mk

nRF

kkj+

== ∑

where, RFj is return flow at tank j (m3/day), k isthe contributing upstream node number, m is thefirst contributing upstream node, n is the lastcontributing upstream node, WQk is water issue atthe upstream node k (m3/day), SPk is the seepageat upstream node k (m3/day), fr is a user-definedcoefficient (0 ≤ fr ≤ 1).

It is assumed that the water released forirrigation during the yala season would be justadequate to provide for the requirements in thecommand area, and as such, part of the irrigationrelease would not arrive as return flow at thedownstream tank. The return flow component inyala is therefore, estimated from equation A.6 withWQ set to zero. fr denotes the fraction of theseepage and water issue in the upstream tankthat would become available as inflow at thedownstream tank. Ponrajah (1984) noted that 20percent of the irrigation release for cultivation inthe immediately upstream tank is available asdrainage for reuse in the downstream tank.

It is difficult to assign a return flow fractionthat would be applicable for both flow components(seepage and irrigation release) in each tank,under the spatially and temporally varyingconditions in a cascade system. On the otherhand it is not feasible to determine different returnflow fractions for the two components (seepage

( ) )7.A........(.....................SO.fsmk

nSI

kj ∑=

=

where, k is the contributing upstream nodenumber, m is the first contributing upstream node,n is the last contributing upstream node, SIj isinflow at tank j due to spillage at upstream tank(m3/day), SOk is spill discharge at upstream nodek (m3/day), and fs is a user-defined coefficientthat determines the fraction of spill discharge thatarrives at the downstream tank. In the studyconducted by Shinogi et al. (1998), this fractionwas taken as 0.57 and 0.67 for the Vendarankulamaand Bulankulama tanks, respectively. Although ingeneral, fs could vary from tank to tank, in theCascade model it is assumed to be a commoncoefficient and can be set to a value in the range,0 ≤ fs ≤ 1. In the absence of field measurementsto determine fs, it is assumed that 0.5 would be areasonable value.

It should be noted that the above computationsof return flow are based on the assumption thatpart of the water released for irrigation, tankseepage, and spillway discharge from theupstream tank can arrive at the downstream tankwithin the same day. As the model was designedfor cascades with small irrigation tanks withrelatively small command areas this assumption isconsidered to be reasonable.

40

Processing Procedure

The daily water balance for tank ‘j’ in the cascadecan be written in the form of equation A.8.

Ij – Oj = DSj..............................................(A.8)

where, Ij is total inflow and is Oj outflow and DSj

is the change in storage determined from thedifference between tank storage at the beginning

and the end of the day. Tank storage at the endof the day is taken as the storage at the beginningof the next day. Inflow components and outflowcomponents of the tank water balance aresubstituted in equation A.8 in the order explainedin the processing procedure illustrated by theflowchart presented in figure 5. It provided thebasis for the Cascade-model code, which iswritten as a Lahey Fortran program.

41

Literature Cited

Dharmasena, P. B. 1985. System loss studies of village tanks. Tropical Agriculturist 141: 95-108.

Dharmasena, P. B. 1994. Conservation farming practices for small reservoir watersheds: A case study from Sri Lanka.Agroforestry Systems 28: 203 – 212.

French, R.H. 1994. Open-channel hydraulics, McGraw-Hill., Inc. pages 739. International Editions, 1994.ISBN 0-07-113310-0.

Itakura, J. 1995. Water balance model for planning rehabilitation of a tank cascade irrigation system in Sri Lanka.IIMI Working Paper No. 3. Colombo: Sri Lanka: International Irrigation Management Institute.

Jayatilaka, C. J.; R. Sakthivadivel; Y. Shinogi; I. W. Makin; and P. Witharana. 2000. Simulation of the ThirappaneIrrigation Tank Cascade System based on the Cascade water balance model. International Water ManagementInstitute. Working Paper. Colombo, Sri Lanka: International Water Management Institute.

Kachroo, R. K.; and G. C Liang. 1992. River flow forecasting. Part 2. Algebraic development of linear modellingtechniques. Journal of Hydrology 133 (1-2): 17-40.

Kitamura, Y. 1984. Consumptive use of water for paddy field irrigation in the dry zone areas of Sri Lanka. NekkensiryoNo. 63. Japan: Tropical Agricultural Research Centre.

Ponrajah, A. J. P. 1984. Design of Irrigation Headworks for small catchments (up to catchments of 20 square miles)Colombo, Sri Lanka: Department of Irrigation.

Shinogi, Y.; I. W. Makin; and P. Witharana. 1998. Simulation of the water balance in a dry zone tank cascade. Paperpresented at the National Conference of The status and Future Direction of Water Research in Sri Lanka,Nov. 4-6, 1998, at BMICH, Colombo, Sri Lanka.

Tasumi, M.; Y. Matsuno; Y. Otsuki; W. Van der Hoek; and R. Sakthivadivel. The role of return flows in a tank cascadesystem in Sri Lanka. Submitted for publication to the International Journal of Water ResourcesDevelopment (IJWRD).

Usgodaarachi, T.; A. D. Weerasinghe; and R. Sakthivadivel. 1996. Reservoir Operation Simulation (Extended)Systems, ROSES, version 3.00. User Manual. Colombo, Sri Lanka : International Water Management Institute .

Xia, J.; K. M. O’Connor; R. K. Kachroo,; and G. C. Liang. 1997. A non-linear perturbation model consideringcatchment wetness and its application in river flow forecasting. Journal of Hydrology 200: 164-178.

Research Reports

35. Modernizing Irrigation Operations: Spatially Differentiated Resource Allocations.D. Renault and I. W. Makin, 1999.

36. Institutional Change and Shared Management of Water Resources in Large CanalSystems: Results of an Action Research Program in Pakistan. D. J. Bandaragoda,1999.

37. Farmer-Based Financing of Operations in the Niger Valley Irrigation Schemes. CharlesL. Abernethy, Hilmy Sally, Kurt Lonsway, and Chégou Maman, 2000.

38. An Assessment of the Small-Scale Irrigation Management Turnover Program inIndonesia. Douglas L. Vermillion, Madar Samad, Suprodjo Pusposutardjo, SigitS. Arif, and Saiful Rochdyanto, 2000.

39. Water Scarcity and the Role of Storage in Development. Andrew Keller, R. Sakthivadivel,and David Seckler, 2000.

40. Using Datasets from the Internet for Hydrological Modeling: An Example from theKüçük Menderes Basin, Turkey. Martin Lacroix, Geoff Kite, and Peter Droogers, 2000.

41. Urban-Wastewater Reuse for Crop Production in the Water-Short Guanajuato RiverBasin, Mexico. Christopher A. Scott, J. Antonio Zarazúa, and Gilbert Levine, 2000.

42. Comparison of Actual Evapotranspiration from Satellites, Hydrological Modelsand Field Data. Geoff Kite and Peter Droogers, 2000.

43. Integrated Basin Modeling. Geoff Kite and Peter Droogers, 2000.

44. Productivity and Performance of Irrigated Wheat Farms across Canal Commands inthe Lower Indus Basin. Intizar Hussain, Fuard Marikar, and Waqar Jehangir, 2000.

45. Pedaling out of Poverty: Social Impact of a Manual Irrigation Technology in SouthAsia. Tushaar Shah, M. Alam, M. Dinesh Kumar, R. K. Nagar, and Mahendra Singh,2000.

46. Using Remote Sensing Techniques to Evaluate Lining Efficacy of Watercourses.R. Sakthivadivel, Upali A. Amarasinghe, and S. Thiruvengadachari, 2001.

47. Alternate Wet/Dry Irrigation in Rice Cultivation: A Practical way to save water andcontrol malaria and Japanese encephalitis? Wim van der Hoek, R. Sakthivadivel,Melanie Renshaw, John B. Silver Martin, H. Birley, and Flemming Konradsen, 2001.

48. Predicting Water Availability in Irrigation Tank Cascade Systems: The CascadeWater Balance Model. C. J. Jayatilaka, R. Sakthivadivel, Y. Shinogi, I. W. Makinand P. Witharana, 2001.