The Derived Demand for Irrigation Scheduling Services · scheduling service. Since this paper focuses on an economic evaluation of the adoption of irrigation scheduling services under

The Derived Demand forIrrigation Scheduling Services

Daniel J. Dudek, Gerald L. Hornerand Marshall J. English

Scientific irrigation scheduling is a technique for systematically determining theproper date and quantity of each irrigation in individual fields. This technique ispresently being used by government agencies and private companies in the WesternUnited States to assist farmers in planning irrigations. This paper presents the results of acase study of the regional economic effects of scheduling in the A & B District in Idaho.The analysis indicated that substantial reductions in total water use resulted fromimplementation of the service. However, the acreage of scheduled irrigation activity wasfound to be sensitive to the cost of the service and the cost of irrigation water.

In recent years a new approach to irriga-tion has emerged in which a computer isused, in combination with trained personnelworking in the field, to determine the appro-priate timing and amount of each irrigationfor individual fields. The computer is used tomodel soil moisture conditions and forecastthe required date and amount of upcomingirrigations. Field personnel interpret thecomputer outputs, periodically check soilmoisture in the fields, and advise the farmeron his irrigation schedule. This schedulingprocedure is based upon principles of soilscience, agronomy, meterology, and engi-neering and is often referred to as scientific

Daniel J. Dudek and Gerald L. Horner are AgriculturalEconomists, Natural Resource Economics Division, Ec-onomic Research Service, U.S. Department of Agricul-ture stationed at the Department of Agricultural Eco-nomics, University of California, Davis. Marshall J. En-glish is an Assistant Professor in the Department ofAgricultural Engineering at Oregon State University.

Giannini Foundation Paper 628. This research was sup-ported by the Robert S. Kerr Environmental ResearchLaboratory, Office of Research and Development, U.S.Environmental Protection Agency, Ada, Oklahoma, Ar-thur G. Hornsby, Project Officer for EPA-IAG D60121.

This paper has benefited from the reviews and com-ments of Charles V. Moore, Kent D. Olson and threeanonymous reviewers. As is customary, we alone areresponsible for the contents of the paper.

irrigation scheduling. It was originally de-veloped by Dr. Marvin Jensen [1975] of theU.S. Agricultural Research Service between1968 and 1971; was modified and developedby the Water and Power Resources Service(WPRS), the Soil Conservation Service, andothers [Gear, et al.; Buchheim and Ploss];and is now being supplied as a commercialservice to farmers throughout the WesternUnited States.

It is generally held that the potential bene-fits of an irrigation scheduling service (ISS)may include:

a. Reduced water use, with attendant re-ductions in drainage problems and re-duced salinity of downstream flows,

b. Increased crop yields,

c. Reduced production costs for water,fertilizer and pesticides, and

d. Improved farm operating efficienciesdue to the ability to plan irrigationswell ahead of time.

In practice, however, these benefits areoften disputed. Given the legislative man-date (Public Law 92-500) to control nonpointsources of pollution from irrigated agricul-ture through the imposition of "Best Man-agement Practices," considerable attentionhas been focused on irrigation scheduling as apotential control measure. Against this back-

217

Western Journal of Agricultural Economics

ground, then, the specific objectives of thisresearch were to:

a. Develop a method of assessing the re-gional environmental and economicbenefits and costs of an irrigationscheduling service,

b. Apply that method to a case study forthe purposes of evaluating the methodand developing some perspective onthe factors which affect the benefits andcosts of a scheduling service.

Only those results pertaining to the econom-ics of scheduling services are reported in thispaper.

Study Area and Data

The analysis was conducted in the contextof a case study involving the A & B IrrigationDistrict, 76,800 acres located on the SnakeRiver in Southern Idaho. An irrigationscheduling service has been in use there forten-years. The principal reasons for choosingthe A & B District are: first, the area isrelatively homogenous in physical character-istics, and second, substantial data and re-search have been compiled by various agen-cies in the area. The district is supplied withwater pumped both from the Snake Riverand from wells, with a lift of approximately200 feet in either case. One important char-acteristic of farmers in the A & B District isthat their irrigation operations are relativelyefficient for gravity systems in SouthernIdaho. It was estimated in this study thatdistribution system losses account for approx-imately 10 percent of water delivered to thefarm while surface runoff and deep percola-tion account for 39 percent of water appliedto the fields. During the ten-year periodfrom 1958 to 1968, annual district deliveriesaveraged 3.18 acre feet per acre which wasconsiderably less than the 4.1 and 5.09 acrefeet per acre in two adjacent districts.

Between 1964 and 1968, six typical farmsin the A & B District encompassing approxi-mately 600 acres participated in a U.S.Bureau of Reclamation (USBR) study of irri-gation water use [USBR]. An exhaustive data

218

collection program was conducted in eachfield during each of those years. The dataincluded climatic variables, soil conditions,and agronomic and irrigation practices. In anearlier interagency study conducted from1958 to 1963, 40 farms covering 4,340 acreswere evaluated for irrigation water use andefficiency. Data collected on those 40 farmsincluded water deliveries, runoff, weatherdata, and crop yields. However, the datacollection effort during the 40-farm study wasneither as comprehensive nor as complete asthat of the six-farm study.

Physical Analytical Subsystem

The analytical system employed for thisresearch is composed of a physical analyticalsubsystem and a regional economic model(Figure 1). The physical analytical subsystemestimates crop yields, irrigation water useand frequency, and salt and sediment loads ofreturn flows on a per acre basis. This infor-mation is used in the regional economic mod-el to estimate changes in regional farm in-come, water use, scheduled acres, and theamount and quality of irrigation return flowsthat could result from the use of an irrigationscheduling service. Since this paper focuseson an economic evaluation of the adoption ofirrigation scheduling services under alterna-tive implementation strategies, only a briefdescription of those models relevant for theestimation of water use and crop productionrelationships will be presented. For a de-tailed description of the models comprisingthe physical analytical system see English, etal.

Water use and crop production coefficientsunder irrigation scheduling were estimatedfrom a two-stage simulation process. The firststage involves the interaction of soil moistureand irrigation models in order to simulatemoisture stress and seasonal evapotranspira-tion. The soil moisture model estimatesevapotranspiration and soil moisture for eachcrop by calculating soil moisture budgets forthe active root zone and a lower zone intowhich the root system will eventually move.The soil moisture content, Sijt, expressed as a

December 1981

Dudek, Horner and English

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219

Demand for Irrigation Scheduling


percent by volume in field i for crop j at timet is given by:

(1) Sijt = s(RZjt, mi, EETijt, DPit)t

where:

RZjt is active root zone depth for crop j attime t.

mi is soil moisture holding capacity in fieldi.

SETit is cumulative evapotranspiration int field i for crop j at time t.

DPit is deep percolation in field i at time t.

Evapotranspiration and percolation, primarydeterminants of soil moisture, are dependentupon the size of the active root zone. Thisdynamic area is explained as:

(2) RZjt = r(RZmax, kijt)

where:

RZmax is the estimated maximum depth forthe active root zone.

kijt is a measure of relative evapotranspira-tional demand for crop j in field i attime t. 1

This equation describes a model developedby Jensen that relates root zone size to thecrop growth stage [Jensen, 1979].

In turn, deep percolation in field i at time tis of the form:

(3) DPit = h(Sijt, RZjt, Ci, sdi)

where:

Ci is the conductivity of soil comprisingfield i.

sdi is the depth of the soil profile in field i.

This empirical model of soil drainage rates isbased upon work by Nielsen, et al. It wascalibrated for local soils using data suppliedby Jensen [1976].

1This variable is more commonly known as a crop coeffi-cient. It serves as an index for the growth and develop-ment of the crop.

220

The calculation of evapotranspiration alsofollows methods proposed by Jensen, et al.The basic relationship may be generally ex-pressed as:

(4) ETijt = n(Sijt, kijt, Wt, dt, Wit, ot, Yt)

where:

Wt is average wind velocity during time t.

dt is average mean daily temperature dur-ing time t.

fit is soil surface moisture conditions offield i at time t.

Ct is average solar radiation during time t.

Yt is relative humidity at time t.Procedurally then, when the calculated soilmoisture budget reaches a crop-specific criti-cal level, the required water diversion isdetermined by the irrigation model:

(5) qijt = f(fit, Sijt, e)

where:

qijt is irigation water to be diverted.fit is nominal field capacity in the root zone.

e is the overall efficiency of irrigation in-cluding all losses.

These models were then interacted throughtime to simulate the crop season.

The second stage in the estimation of cropproduction coefficients under irrigationscheduling is comprised of the crop produc-tion model. This model is based uponStewart, et al., Stewart and Hagan, andDowney; however, the model itself is empiri-cal. The crop production model may be gen-erally represented as:

(6)Yj = V(EETijt, ETdij, smti, qijt, P, Iij)

where:

Yij is the yield per acre of crop j in field i.

ETdij is the evaporanspirational deficit suf-fered by crop j in field i.

smti is average soil moisture tension infield i.

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lqijt is the quantity of irrigation water ap-t plied.

P is net rainfall.

Iij is the number of irrigations applied tofield i to raise crop j.

These soil moisture, irrigation and schedul-ing, and crop production models were usedto estimate yield and water use coefficientsfor each crop under irrigation scheduling.

The Regional Economic Model

A scheduling service can be made availableto farmers either by a private company or apublic agency. The public agency maychoose to offer such a service for manyreasons, such as to promote more efficientwater use in order to increase the size of theirrigated area served from a fixed supply ofwater or to reduce irrigation return flows.The purpose of this analysis is to project theamount of irrigation activity that would bescheduled if a private company or publicagency provided the service. Linear pro-gramming was used to determine optimalwater application rates so as to maximize netreturns to land and management under thedistrict cropping pattern that existed in the1973-75 period. While the relevant decisionunit in this analysis is the firm, substantialinterest in irrigation scheduling is vested inits impact upon externality production. Sincefirms are assumed to be profit maximizers,and lacking firm-specific economic informa-tion, it is presumed that the maximization ofnet returns under the aggregate district crop-ping pattern adequately simulates aggregategrower behavior.

The LP model was optimized for three setsof assumptions. The first solution was con-strained to unscheduled operations to esti-mate the level of returns to producers, re-source use, and irrigation return flows as-suming a scheduling service did not exist.This solution served as a basis from whichother solutions could be compared. The sec-ond model configuration required all waterapplications to be determined by a schedul-ing service. The difference between the solu-

tions derived in the first and second modelconfigurations served as an estimate of thepotential change that could be possible froma scheduling service. The third configurationwas not restricted to scheduled ornonscheduled water applications. Therefore,the optimal solution represented the level ofscheduling that would probably exist if theservice were offered on an elective basis. Thecost of the scheduling service and the cost ofwater were parameterized in the third modelconfiguration to determine the effect on thenumber of scheduled acres.

Input Data

The USBR information provided a set ofdata describing water use, crop yields, andirrigation return flows. These data withprices and costs were used to derive thecoefficients detailing unscheduled operationsin the linear programming model. Threelevels of observed irrigation water applica-tion rates were defined as low, medium, andhigh on the basis of observed water use bycrop in 443 unscheduled field operations inthe A & B District. Ranges for the threelevels were determined by ordering theseobserved application rates and inspectingtheir distribution. The medium level wasdefined as the typical rate for that crop plusvariations that could be explained by differ-ences in the precision of applying water.Extreme application rates were placed in thehigh and low classifications.

The 443 observations were taken from thesix-farm study (204 cases) and the 40-farmstudy (239 cases) and included correspondingcrop yields. Table 1 contains the specificwater application rates and the proportion ofcases in each rate. As an example, the rangebetween 25 and 35 acre-inches of appliedwater was defined as medium water use forbarley. Less than 25 acre-inches and morethan 35 acre-inches were defined as low andhigh water use respectively. The averageirrigation labor per acre set and the averagenumber of irrigation sets for each crop wereestimated from the six-farm study and used

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Dudek., Horner and English


TABLE 1. Definition of Low, Medium and High Water Use for Each Crop (UnscheduledIrrigation Regime) and Proportion of Irrigated Cases in Each Categorya.

Crop Low Medium High

------------------------------------ Acre-inches per acre----------------------------------------Alfalfa <35.1 35.1 - 50.0 >50

(0.243) (0.457) (0.300)Barley <25.03 25.0 - 35.0 >35.0

(0.541) (0.360) (0.099)Beans <25.0 25.0- 37.0 >37.0

(0.255) (0.568) (0.177)Peas <27.0 27.0-42.0 >42.0

(0.452) (0.474) (0.074)Potatoes <30.0 30.0 - 45.0 >45.0

(0.115) (0.499) (0.386)Sugar Beets <40.1 40.1 - 50.0 >50.0

(0.346) (0.414) (0.240)Wheat <25.0 25.0- 35.0 >35.0

(0.544) (0.364) (0.092)

aThe numbers in parentheses represent the proportion of irrigated fields observed with application rates within theindicated class.

to compute the average total irrigation laborper acre by crop for each water applicationrate.

Crop yields observed in the 443 water usecases were used to estimate yields for eachcrop for the three levels of unscheduled wa-ter use. Crop yields had to be adjusted toreflect technologic changes that have causedgradual increases in productivity since theUSBR studies. Crop yields under scheduledwater regimes were estimated from the cropproduction model calibrated for each cropwith data from the 204 cases of the six-farmstudy. The resulting estimates of scheduledcrop yields were modestly higher than theirunscheduled counterparts for beans,potatoes, and sugar beets. In the remainingcases, scheduled yield estimates were withinthe range of yields associated with alternativewater use rates.

Crop prices used in the analysis were dis-trict average prices paid to farmers in the A &B District during the years 1973 through1975, the most recent data available at thetime of the analysis. Water prices were based

222

upon actual District prices during those sameyears. Production costs per acre for alfalfa,barley, potatoes, sugar beets, and springwheat were based on variable preharvestcosts taken from budgets derived by Kuntz.Harvest costs were adjusted proportionallyfor the differences between the yield per acreused in the budget and the yield per acreadjusted for trend.

Regional Effects of anIrrigation Scheduling Service

Potential Impacts of aScheduling Service

Basic economic information was estimatedfor each irrigation regime under alternativepolicies (Table 2). The changes in averageannual returns to land and managementunder alternative implementation schemesare described in Table 3. Changes in theannual returns to land and management areattributable to adjustments in the crop andresource use mix and, therefore, productivity

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TABLE 2. Estimated Average Annual Results of the Irrigation Scheduling Analysis in the A &B Districta.

Voluntary VoluntaryScheduling Scheduling

Base Mandatory No Charge $5.00 PerVariable Units No Scheduling Scheduling Per Acre Acre Charge

Returns to Land $1,000,000 14.118 14.390 14.518 14.456and Management

Irrigation Water:Acre-

Use 1,000 Feet 216.865 144.013 167.711 205.078Cost $ 1,000 841.013 655.767 721.628 838.553

Irrigation Labor:Use 1,000 Hours 120.539 86.476 97.625 114.681Cost $ 1,000 416.469 298.759 335.807 395.349

aThese results are averaged from annual estimates for 1973, 74 and 75. The average area irrigated in this periodwas 65,132 acres.

TABLE 3. Changes InAnalysis.

Average Annual Net Returns Per Acre By Policy From the Base


Mandatory No Charge $5.00 PerComponent Change Scheduling Per Acre Acre Charge

----------------------------------- Dollars Per Acre ---------------------------------Increase inValue of Production -0.32 3.07 4.83Decrease inIrrigation Water Cost 2.69 1.83 0.04Decrease inIrrigation Labor Cost 1.81 1.24 0.32Increase in Net Returns 4.18 6.14 5.19

differences as well as changes in irrigationcosts. 2 The average per acre value of produc-tion declines from the unscheduled baseanalysis under the mandatory scheduling re-gime since alfalfa yields for the high wateruse alternative were greater than those es-

2 Note that this formulation of the linear programmingmodel employs the expected values of yields and prices.The costs of risk management associated with yieldand/or price variability are not included.

timated to be obtained under scheduling.3

Under the two voluntary adoption analyses,regional crop production and resource use iscompletely optimized given the scheduling

3It should be emphasized that these results are basedupon the perfect implementation of recommendationsfrom the ISS. For an assessment of the impact ofdepartures from the schedule see English, et al. Conse-quently, under such stringent conditions, these esti-mates represent an optimistic upper bound of participa-tion.

223



service charges. Under fully subsidizedvoluntary scheduling, an average of 48,230acres were scheduled annually. Table 4 indi-cates that the production of beans, potatoesand sugar beets was increased throughscheduling when compared against the baseanalysis. Despite production declines for al-falfa and barley, the average per acre value ofproduction under subsidized scheduling in-creased by $3.07. When a $5.00 per acrecharge for scheduling is levied, however,scheduled acreage declines to 21,550 acres.At this charge level, alfalfa, barley, peas, andsugar beets are no longer scheduled (Table4).4 Thus, the bulk of the change in netreturns per acre is associated with changes inthe value of production; i.e., irrigation-associated cost savings are no longer accruingto the grower.

The average annual per acre reduction inwater and irrigation labor costs ranged from$0.36 to $4.50 depending upon the particularimplementation policy (Table 3). In aggre-gate terms, water costs were reduced 22percent under mandatory scheduling, 14.2percent under voluntary subsidized schedul-ing services, and 0.3 percent under a $5.00per acre scheduling service. These cost re-

4 Under the no-charge implementation policy, alfalfa wasscheduled in 1974 and 75, but not in 1973. With a $5.00per acre charge, alfalfa is not scheduled at all. Sugarbeets are scheduled in 1975 under the charge policy,but not in 1973 or 1974.

ductions belie the reductions in water useaccomplished through irrigation scheduling.Water use was reduced 33.6, 22.7, and 5.4percent under the mandatory, subsidized,and priced alternatives, respectively.5 Thedisparity between water cost and use reduc-tions is due to the water pricing schedule ofthe A & B District, which stipulates a fixedrate for the first three acre-feet of water use.The economic incentive to reduce water useand for the adoption of a scheduling servicewould be proportionately greater if the unitcost of water varied directly with use.

Voluntary Adoption of aScheduling Service

The foregoing analysis indicated that thedistrict as a whole would profit from univer-sal irrigation scheduling. However, it shouldbe noted that in some situations a farmermight be better off not to use a schedulingservice for some crops but instead to adoptone of the three levels of unscheduled wateruse because it would be more profitable. Asan example, the highest profit for alfalfagrowers in 1973 was realized with high wateruse and no scheduling, rather than withscheduling. The most profitable strategy

5Note that the water saved under each of the implemen-tation strategies is not explicitly valued in its availabilityfor other uses. To the extent that such opportunitiesexist, there are further potential benefits associatedwith the implementation of irrigation scheduling.

TABLE 4. Average Annual Crop Production by Policya.


Base No Mandatory No Charge $5.00 PerCrop Units Scheduling Scheduling Per Acre Acre Charge

Alfalfa tons 92,423 86,558 88,646 92,423Barley bushels 1,385,959 1,378,342 1,378,342 1,385,959Beans cwt 105,983 111,309 111,309 111,309Peas cwt 42,239 37,425 42,239 42,239Potatoes cwt 1,288,035 1,337,890 1,337,890 1,337,890Sugar Beets tons 190,370 192,698 192,698 191,822Spring Wheat bushels 797,806 773,354 797,806 797,806

aNote that crop acreages are constant by policy. Consequently, production changes are due to variations inaverage yields resulting from changes in the optimal mix of activities.

224

December 1981


would depend upon the cost of water andscheduling and the value of any yield differ-entials. Therefore, the analysis was repeatedallowing the LP to select the optimum irriga-tion regime for each crop given a set of waterand scheduling costs.

The cost of scheduling was parametricallyvaried in the LP model from zero to $5.00 toestimate average annual changes in the num-ber of acres scheduled and the amount ofreturn flows. The cost of scheduling affectedthe number of acres scheduled differently ineach year. However, the composite resultsfrom the three-year analysis indicates that anincrease in the price of scheduling from zeroto $5.00 per acre would reduce the numberof scheduled acres from approximately48,000 acres to 22,000 acres (Figure 2). Thegeneral relationship of price to scheduledacres can be captured by estimating the elas-ticity of demand in order to assess the sen-

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sitivity of scheduled acres to cost for specificranges of the demand function. Elasticitieswere estimated from the linearized demandfunction for various scheduling costs. Thesevalues are presented in Table 5. At less than$3.00, response is inelastic, but as the costapproaches $5.00, it becomes substantiallymore elastic. Therefore, if the schedulingservice were supplied in the A & B District atcurrent market cost ($5.00 per acre) about25,000 acres or 38 percent of the total irri-gated acreage would be scheduled.

Varying scheduling costs would not affectregional returns to a great extent. The aver-age net return for 1973, 74, and 75 without ascheduling service was $14.118 million or$216.76 per acre. This return was increasedrelative to the unscheduled regime by a zerocost scheduling service to $14.518 million or$222.90 per acre. An increase in the cost ofscheduling to $5.00 per acre would decrease

II

LI

0.00 I 1 I I I I- 1 I I10 20 30 40 50 60 70

SCHEDULED ACREAGE, (1,000 ACRES,(404.7 HA))

Figure 2. Estimated Scheduled Acreage and Scheduling Cost, A & B District, 1973, 1974 &1975.

225

Dudek,, Horner and English

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I-

-


TABLE 5. Estimated Elasticity of Demand for Irrigation Scheduling Services.

Scheduling Cost Elasticity($/Acre) of Demand

$1.00 -0.1222.00 -0.2803.00 -0.4894.00 -0.7785.00 -1.208

average annual returns to $221.95 per acre.As reported earlier, the estimated annualwater use in the A & B District without ascheduling service was 216,865 acre-feet and144,013 acre-feet if a scheduling system wasimposed (Table 2). In the case of a voluntaryscheduling service charging $5.00 per acre,the estimated average annual water use was205,078 acre feet. This amount was reducedto about 167,711 acre-feet if the service wasoffered at no charge (Figure 3).

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Conclusions

Irrigation scheduling could be an effectivetool in irrigation management since the pro-gram objective is to keep soil moisture higherthan the permanent wilting point and belowsoil moisture holding capacity with aminimum number of irrigations. This resultsin a minimum of return flows without re-ducing acreage or yields. The main problemof course is the ability of each farmer toimplement each scheduling order with suffi-

IIII

r- lI

I

I

.iI

40 80 120 160 200 240 280

IRRIGATION WATER USE (1,000 ACRE-FEET (1233 x 103 cm3)

Figure 3. Estimated Water Use and Scheduling Cost, A & B District, 1973, 1974 & 1975.

226

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December 1981

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cient precision. Errors in timing and applica-tion amounts can negate most of the cropyield or return flow benefits.

To summarize the effects of the schedulingprogram, water use resulting from the vari-ous scheduling policies in the A & B Districtwere compared with the results of noscheduling service. The results from the re-gional economic model indicate that schedul-ing and the degree to which it is implement-ed has a dramatic effect. Water use wasestimated at 216,865 acre-feet withoutscheduling and 144,013 acre-feet with re-quired scheduling. Water use varied be-tween these amounts for voluntary schedul-ing with costs ranging from zero to $5.00 peracre.

Scheduling cost proved to be a significantfactor in determining the aggregate amountof irrigated acreage that will be scheduled.This is true in the A & B District sinceirrigation practices normally applied in theDistrict are reasonably efficient, and increas-ing the charge for scheduling services willmake it less profitable than normal irrigationpractices.

Many irrigation districts hold water rightsin excess of ET and percolation requirementsand do not charge farmers on the basis ofwater use. This promotes inefficient wateruse and opportunities for large amounts ofreturn flows to be generated. An imposedscheduling service in these areas would havea substantial effect on water use and bypassthe more compelx legal and institutionalquestions involving water pricing and alloca-tion.

References

Buchheim, Jerry H. and L. F. Ploss. "ComputerizedIrrigation Scheduling Using Neutron Probes." Paper77-2004. ASAE Annual Meeting. Raleigh, N.C. June26-29, 1977.

Downey, L. A. "Water Yield Relations for Non-ForageCrops." Journal of the Irrigation and Drainage Divi-sion, ASCE, 98(1972): 107-15.

English, Marshall J., Gerald L. Horner, Gerald T. Or-lob, Joseph Erpenbeck, Michael Moehlman, RichardH. Cuenca, and Daniel J. Dudek. A Regional Assess-ment of the Economic and Environmental Benefits ofan Irrigation Scheduling Service, EPA-600/2-80-063,Robert S. Kerr Environmental Research Laboratory,Ada, OK, April, 1980.

Gear, R. D., A. S. Drausfield and M. Campbell. "Ef-fects of Irrigation Scheduling and Coordinated Deliv-ery on Irrigation and Drainge Systems," Natural Re-sources and Ocean Engineering Convention, SanDiego, CA, April 5-8, 1976.

Jensen, M. E. Scientific Irrigation Schedulingfor Salin-ity Control of Irrigation Return Flows, EPA-600/2-75-064, U.S. Environmental Protection Agency, Ada,OK, 1975.

Jensen, M. E. Snake River Conservation Research Cen-ter, Kimberly, ID., Personal Communication, 1976.

Jensen, M. E. Snake River Conservation Research Cen-ter, Kimberly, ID., Personal Communication, 1979.

Jensen, M. E., J. L. Wright and B. J. Pratt. "EstimatingSoil Moisture Depletion from Climate, Crop and SoilData," Transaction of the American Society of Agricul-tural Engineers, Paper No. 69-941, 1969.

Kuntz, B. Ted. Unpublished Crop Production Budgetsfor the A and B District, ERS, USDA, Corvallis, OR,1976.

Nielsen, D. R., J. W. Biggar and K. T. Erh. "SpatialVariability of Field Measured Soil Water Properties,"Hilgardia, 42(1973): 215-60.

Stewart, J. I. and R. M. Hagan. "Development of Evap-otranspiration-Crop Yield Functions for ManagingLimited Water Supplies, Seventh Congress, Interna-tional Commission on Irrigation and Drainage, Mex-ico City, 1969.

Stewart, J. I., R. M. Hagan, W. O. Pruitt and W. A.Hall. "Water Production Functions and IrrigationProgramming for Greater Economy in Project andIrrigation System Design and for Increased Efficiencyin Water Use," University of California, March. FinalReport 14-06-D-7229, USDI, USBR E&R Center,Denver, CO., 1973.

U.S. Bureau of Reclamation. "Use of Water on FederalIrrigation Projects, Minidoka Project, NorthsidePumping Division, Unit A, Idaho Summary Report,"USBR Region 1, Boise, Idaho, 1971.

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Documents

The Derived Demand for Irrigation Scheduling Services · scheduling service. Since this paper focuses on an economic evaluation of the adoption of irrigation scheduling services under