Energy and Agriculture in Utah:Responses to Water Shortages

John E. Keith, Gustavo A. Martinez Gerstl,Donald L. Snyder, and Terrence F. Glover

Variability in water supplies is perceived as a major impediment to economic growthin both agricultural and energy sectors in the Intermountain West. A chance-constrained programming model of water allocations among agricultural, energy,municipal and industrial, and environmental activities for the Upper Colorado RiverBasin and the Great Basin in Utah was developed to analyze economically optimalwater use as energy production increases. Estimates of the probabilities of variousamounts of water production, representing different drought conditions, were used asright-hand sides in the model. Results indicate that water is not a constraining factorand that little, if any, water development is warranted, even during relatively intenseperiods of drought.

Key words: water allocations, chance-constrained programming, energy, irrigation,Intermountain West.

Water availability has been identified by manyindividuals and government agencies as a ma-jor constraint on energy and agricultural de-velopment in the Upper Colorado River andthe Great Basins. Earlier studies (see, for ex-ample, Keith et al.) indicate that average an-nual water availabilities are sufficient for sig-nificant growth for both irrigated agricultureand energy production in Utah. However, ithas been argued that the variability of precip-itation and consequent stream flows causes se-vere water shortages for all users. In fact, muchof water planning and development is targetedat increasing water availability during low-flowand/or drought periods to reduce the uncer-tainties of water dependency. This study ex-amines the economically efficient allocationsof water in the two basins for the average caseand for cases in which high probabilities of

The authors are, respectively, an associate professor, a researchassistant, an associate professor, and a professor, Department ofEconomics, Utah State University.

The work upon which this paper is based was supported in partby funds provided by the U.S. Office of Water Research and Tech-nology and by the Utah State University Agricultural ExperimentStation. Utah Agricultural Experiment Station Journal Paper No.3050.

This paper benefited greatly from comments by Oscar Burt andanonymous reviewers. The authors are solely responsible for anyerrors.

water production could be assigned represent-ing various drought conditions.

Modeling Approach

The approach used in this study involved con-structing a chance-constrained programmingmodel of the Upper Colorado and Utah's por-tion of the Great Basin. The model was de-veloped in two steps. First, an existing linearprogramming model of water allocations in thebasins (Snyder et al.) was modified to includea two-season water flow (January through Juneand July through December) with potentialstorage for interseasonal redistribution. Next,the probability distributions of water produc-tion for each major drainage in the basins wereestimated using existing water production andgage data from U.S. Geological Survey datatapes. These data had varied periods of record.The water production consistent with selectedprobabilities (85%, 90%, and 95% certainty)from the estimated distributions was then usedas the right-hand side for the water constraintsin the model, following Taha as suggested byCharnes and Cooper (1959, 1963); Wagner;Hillier and Lieberman; and Bishop and Na-rayanan. This approach does not reflect an ex-

Western Journal of Agricultural Economics, 14(1): 85-97Copyright 1989 Western Agricultural Economics Association

Western Journal of Agricultural Economics

OBJECTIVE FUNCTION

Maximization Gross Revenue Cost of Inputs Cost of Air And/Or Land And/OrOf From Agriculture Other Than Water, Transportation Water Abatement Water

Net Revenue and Select Energy Transportation or And/Or Cost DevelopmentIndustries Pollutant Related Transmission Cost

SUBJECT TO THE FOLLOWING CONSTRAINTS:

Agricultural Energy Surface Miscellaneousurrnt rfaWater Quantity Surface/Ground + Ground Water sEnergye Water _

t e mCut

t erGundWace

Water Requirement Requirement Requirementsutf ow t ora e

Availabilities

Salinity Load SalinityMaximumWater Quality and Redction

<Allowable Salt

Concentration n Concentration

Land Quantity Old/New Land OldNewandQuantityIn < Landand Quality In Land

Agriculture Availabilities

Coal Zone Coal Mined For Coal ZoneCapaciElec y Capacities Electricity Capacities

Coal To Coal Required, Coal MinedElectricity * Electricity And

Conversion (Decreasing TransportedFunction)

SO, NO, TSP SO,, NO,, and MaximumAir Quality Produced by - TSP < Allowable SOx

Energy Industries Removal NO xand TSP

Internal External Transmissionlectricity Electricity . Electrical < Line

Transmission Transmission Transmission Capacities

Return Gross Variable ReturnTo : Electrical - Electrical < On

Investment Revenue Production Cost - Investment

Figure 1. General economic feasibility model

pected value of the objective function; the so-lutions do not include consideration of theomitted tail of the distribution of water. Thus,the allocation results and the shadow valuesof the constraints suggest only the value ofwater at a given level of availability.

The Programming Model

The programming model has been describedpreviously in Keith et al.; Snyder et al.; andKeith and Snyder, which includes a very de-tailed discussion of each of the constraints andthe objective function. Figure 1 is a schematicdiagram of the model for a "low-flow" season(storage is added to, rather than subtractedfrom, the right-hand side availabilities). Figure2 and table 1 indicate the drainages (hydrologicsubunits, or HSUs) for which the model wasdeveloped. The following brief description ofthe model highlights its important features andprovides an overview of the modeling ap-proach.I The model included agricultural and

A complete model description and program are available fromthe authors.

energy sectors requiring water. The objectivefunction consisted of profits (net returns) toboth sectors. All costs and prices were adjustedto a base year of 1980, using appropriate in-dices where no direct cost data were availablefor 1980. The structure of the model was suchthat water rights were assumed to be freelytransferable even among states. Alternativeconstraint sets were used to reflect cases inwhich rights were transferable only within astate, only within HSUs, or restricted in otherspecific institutional ways.

Agricultural Sector

Within the agricultural sector are existing andpotential irrigated and dryland production onfour land classes in each HSU. These classi-fications are based on the U.S. Soil Conser-vation Service classifications and include soiltype, productivity, slope, irrigability, andgrowing season. Only variable costs were con-sidered for land currently in production,whereas new land involves both a develop-ment cost (a 20-year annualized investment inclearing, leveling, and providing on-farm water

86 July 1989

Water Shortages 87

Figure 2. Topography of Utah's hydrologic units

delivery systems using a 10% interest rate) andvariable costs.

The crops considered were those crops whichare currently grown in the HSU and whichmight reasonably (environmentally and eco-nomically) be considered by local farmers.Crops included alfalfa, irrigated barley, irri-gated wheat, corn for both grain and silage,fruits (apples, cherries, and peaches), sugarbeets (although sugar beet crops currently arenot grown in Utah), irrigated pastureland, dry-land beans, and dryland wheat. 2 When the costsof transportation of sugar beets to distant pro-cessors in Idaho were included in the variablecosts, the sugar beet activity was unprofitable.

2 For perennial crops, part of the rotations included either a"nurse" crop associated with establishment (e.g., barley for alfalfa)or young plants with reduced output (e.g., immature fruit trees).The proportion of each "nurse," or young, crop was based on therelative life of the main crop (e.g., one-fifth to one-seventh of therotation was a nurse crop for alfalfa, which is replanted each fiveto seven years). Costs of planting were annualized; all water re-quirements and production levels were adjusted according to av-erage yield data.

Each crop was assigned a seasonal consump-tive use water requirement per acre for thespecific soil type and HSU based on currentirrigation practices. Alfalfa and irrigated smallgrain production could take place with eitherfull or partial irrigation in each season withappropriate changes in production. Corn andfruit production had a fixed requirement forboth seasons, since lack of water in any seasonresults in a very low or no yield. The modelcould select crops and water use based on theprofits from the sale of each crop at fixed pricesnet of production costs other than water andland development (U.S. Department of Agri-culture).

Energy Sector

The energy sector consists of coal mining, coaltransportation activities, and the productionand transmission of electrical power. Using anair quality model developed by Wooldridge(1979a, b) and existing air quality constraints

Keith et al.

Western Journal of Agricultural Economics

Table 1. Hydrological Study Units in Utah

HSU No. Basin Name Drainage

1 Western Desert Great Basin2 Bear River Great Basin3 Ogden River Great Basin4 Jordan River Great Basin5 Sevier River Great Basin6 Cedar-Beaver Great Basin7.1 Green River Colorado River7.2 Uintah River Colorado River7.3 Lake Fork Colorado River7.4 Rock Creek Colorado River7.5 Headwaters of Straw- Colorado River

berry and DuchesneRivers

7.W White River in Utah Colorado River8.1 Price River Colorado River8.2 West of Colorado and Colorado River

East of Wasatch includ-ing the Colorado Riverinflows to Utaha

9 South and East of Colo- Colorado Riverrado River

10 Virgin River Colorado River

WY Wyoming Inflow Colorado RiverCY Colorado Yampa Colorado RiverCW Colorado White Colorado River

a Modeling the upper main stem would have required extensivedata collection and was beyond the scope of this study.

for sulfur dioxide, nitrogen oxides, and partic-ulates, the zones for potential coal-fired elec-trical power generation in Utah were identified(fig. 3). Other generation zones currently beingconsidered by public utilities and/or other re-searchers included Kemmerer, Wyoming; StarLake, New Mexico; Harry Allen at Las Vegas,Nevada; and two zones in California-Bar-stow and Cadiz.

Existing and potential coal fields, coal qual-ity (sulfur, nitrogen, and BTU content) andcosts of production were identified from U.S.Department of Interior and U.S. Departmentof Energy (1979a, b) publications as were al-ternative forms and routes by which coal istransported from mine sites to generationzones. There are significant increasing efficien-cies in coal use as the size of the boiler unitsof a generation plant increases. The decliningfeed rates for each coal (tons of coal per mega-watt hour produced) were estimated by Snyderet al., and separable constraints were used toapproximate this feed rate for each coal source/generation site combination.

Pollutants--sulfur oxides, nitrogen oxides,and particulates-were produced jointly with

electricity; the quantity of each depended uponthe quality of coal and boiler efficiencies. Am-bient air standards and the air quality modelswere used to establish the maximum emissionsof each pollutant within each zone (Woold-ridge 1979a, b).3 Treatment activities and costsfor each pollutant were based upon existingtechnologies (U.S. Department of Energy pub-lications 1978a, b, 1979a, b; Utah Division ofPublic Utilities). Variable costs of treatment(labor, material, etc.) were included directly inthe objective function. However, the fixed costs(plant construction and investments in treat-ment facilities) were treated in constraints re-quiring that at least the average return to in-vestment allowed by public utility commissions(roughly 13%) be earned, as indicated by the"profitability" or "return to" constraint in fig-ure 1.4 Water requirements included both di-rect (primarily for cooling purposes) and in-direct (the growth of municipal demandsrelated to the levels of energy production). Atotal containment policy for blowdown waterwas assumed for electrical generation. 5

Maximum demand for electricity was takenfrom U.S. Department of Energy estimates fornorthern and southern California, Nevada,Idaho, Wyoming, and Utah (the demand cen-ters supplied by the production zones whichwere examined). These demands were not pricedependent; prices for energy production wereexogenous. Several sets of 1980 "real" priceshave been examined in previous studies. Newpower production came "on-line" only at"real" bus-bar prices of 4¢ per kilowatt hour,which was about double the 1980 price. (SeeUtah Consortium for Energy Research and Ed-ucation for a discussion of price levels, pro-jected demand for, and production of energy.)Net profits from the energy sector, includingboth the coal and generation activities, werepart of the objective function.

Synfuel production in Utah and Colorado

3 Other approaches to air quality regulations including mandatedtreatment practices (NEPA's Best Practical and Best AvailableTechnologies) also were examined using the model; the results didnot differ substantially from the ambient air standards with respectto efficient water allocations.

4 Public utility regulatory agencies establish maximum profitrates and set prices accordingly. For this model, energy prices wereexogenously determined, so that a minimum profit constraint wasused, which implicitly suggests that generation facilities are builtif, and only if, they can achieve at least the "maximum" profitallowed at a given price.

5 Point sources of effluents are required to have secondary ortertiary treatment facilities which are prohibitively expensive com-pared to total containment approaches.

88 July1989

Water Shortages 89

Q Potential Siting Zones

Figure 3. Potential electric power generating zones

(including oil shale, tar sands, and coal gasi-fication) was also included in the model, eventhough none of these activities would havegenerated positive profits. The model usedproduction projections for each of these activ-ities from the U.S. Department of Energy andthe State of Utah (Utah Consortium for EnergyResearch and Education). Projected water re-quirements for each of these activities is sub-stantial, so that results from the model wouldoverstate demands for water in the specificHSU in which the activity occurs if synfuelsproduction does not occur.

Water QuantityThe water activities included water productionin each HSU for each season, availablegroundwater, return flows from agriculture toboth ground and surface water, outflows from

one HSU to another, and evaporation. Sinceeach "season"-the high runoff period fromJanuary to the end of June and the low runoffperiod from July to the end of December-isaggregated, it is implicitly assumed that somestream regulation occurs within each season.Because much of the early runoff occurs duringthe growing season (April through June), theintraseasonal regulation is probably of mini-mal importance. However, late season flowmay be more crucial than the model indicatesin any given month, week, or day, as a resultof this implicit intraseasonal regulation. Be-cause the model was large (approximately10,000 variables and 4,000 constraints) andbecause each additional water "season" woulddouble its size and require water availabilitydata which was already sparse, further seasonaldivision of the model was not undertaken.

Keith et al.

Western Journal of Agricultural Economics

The model used a simple mass balance ap-proach to calculate water availability in eachHSU. The water quantity constraint for a givenHSU included outflow activities from each up-stream HSU (if any) and calculated the out-flows from the given HSU from inflows, waterproduction, consumptive use, evaporation, andreturn flows within the HSU. The right-handside of each water quantity constraint was thelocal water production in each HSU. Outflowfrom the Upper Colorado River Basin at Lee'sFerry, Arizona (HSU 8.2), was constrained toa minimum of 7.5 million acre-feet per year(the current outflow minimum under the Col-orado River Compact). This minimum out-flow is based upon average annual water pro-duction in the Upper Basin and may beadjusted as long-term water productionchanges.

Costs of water included current (1980) op-eration, maintenance, and delivery costs forexisting facilities (variable costs of use) anddevelopment costs for new storage (including50-year annualized investment costs at 7.75%for both storage and main delivery systems;note that the discount rate was assumed to belower than the private rate of interest for ag-ricultural development, consistent with WaterResource Council guidelines). Storage linkedearly season flows to late season flows in eachHSU; the variable and fixed costs associatedwith new storage were taken from existing Bu-reau of Reclamation and state water devel-opment agencies' cost estimates for variousproposed projects adjusted to 1980 prices bythe Construction Cost Index (Prentice-Hall).

Water Quality

The water quality analysis was limited to sa-linity, the most significant water quality prob-lem in the Upper Colorado River Basin (UtahState University). Salt loading from both nat-ural sources and irrigation was included. Thelatter was dependent on the characteristics ofsoil and runoff in each HSU and reductions insalt loading from available treatment activi-ties. These treatments included canal liningand conversion to sprinkler irrigation systems,both assumed to be privately owned activities,although Franklin has suggested some publicinvestment in salt treatment facilities might beeconomically justified. The costs for each typeof treatment were included in the objectivefunction. Current variable costs were included

directly; fixed costs of investment were an-nualized also using a 7.75% interest rate (seeFranklin; Keith et al. for a detailed listing ofthe costs). Reduced irrigation in regions of highsalt loading (such as the Grand Valley region)also could result in reduced salinity. The max-imum allowable concentration has been estab-lished for outflows of the Upper Basin by theColorado River Basin Salinity Control Act (PL92-320). In the model, concentration was con-verted to a variable constraint on salt loadingrelative to levels of outflow.

Probabilistic Water Availability

Two approaches may be used to examine theallocation effects of variability in water pro-duction: stochastic dynamic or chance-con-strained programming. Stochastic dynamicprogramming characterizes the entire distri-bution of water availability. However, it re-quires a relatively large set of variables for eachwater source. Given the size and complexityof the study's linear programming model, thestochastic dynamic approach was infeasible.Chance-constrained programming, consider-ing the water production right-hand side ineach HSU as stochastic (as described in Taha,for example) was a more feasible alternative.

The amount of water produced in each HSUat given probabilities was estimated. Existingsimulation models for the flow in each reachof the Basin which use historical flow data ad-justed to account for consumptive use (suchas the U.S. Bureau of Reclamation models)have been developed. These flow data are syn-thetic but have been calibrated using historicdata. These flows generally are related to main-stem water flows and include upstream out-flows as well as local water production. Giventhe structure of the programming model andthe consumptive use and other adjustments inthe simulation models, water production ineach HSU was estimated directly. The pro-gramming model generated downstream totalflows internally. The Bureau models were usedto compare average seasonal water productionwithin each HSU to the statistical estimationsused in the study.

If seasonal flows are assumed to be inde-pendent (that is, water flow in one HSU isindependent of climatic conditions in otherHSUs), then the probability of the water pro-duction in the entire basin is a multiple of theprobabilities in each HSU of the basin. Thus,

90 July 1989

Water Shortages 91

a 90% probable seasonal water flow in each ofthe eleven HSUs in the Upper Colorado Riverwould yield a probability of approximately 30%for the outflow from the basin. Conversely, abasin outflow representing a 90% probabilitywould require a 99.1% probability of outflowin each of the upper basin HSUs, assumingequal probabilities in each HSU. Further, thereare infinitely many combinations of droughtevents in the HSUs that would generate anygiven probable outflow.

The assumption of independence of droughtconditions among HSUs seems unwarranted.Although no statistical study was made, thegeneral historic meteorological and hydrolog-ical patterns for the past 40 years suggest thatdroughts in the Upper Colorado Basin tend tobe general over all HSUs. However, it is alsotrue that the variability of precipitation andwater production over all HSUs does not ex-hibit perfect correlation. In order to be accu-rate, the correlations of water productionamong all HSUs and seasons would be re-quired which was beyond the scope of the re-search. It was assumed, therefore, that climaticevents in the Upper Basin were perfectly cor-related; that is, a drought of a given severity(for example, water production consistent witha 90% certainty) would occur in every HSU.The approach used was to determine thedrought events with given probabilities in eachHSU, treat the associated water production asthe right-hand side of the water availabilityconstraint, and allow the model to solve forthe optimal allocation of water. The term "90%probability" in this paper means that waterproduction in each HSU would be equaled orexceeded with a 90% probability, yielding adrought condition of that severity. In effect,the distribution for each HSU was used to gen-erate a "parameterization" of the constraintsconsistent with the given probabilities.6

In order to obtain the levels of water pro-duction for various probable events, an esti-mation of the distributions of water produc-tion for each HSU was required. Most of thegaged flows are not indicative of the variabilityof water production due to existing regulationand consumptive use upstream from the gage.

6 The use of the probabilistic water production as right-hand-side values in the model is essentially a sensitivity analysis. Chance-constrained programming does not generate the expected valuesof losses or changes in allocations; rather, the solutions representallocations under specifically constrained conditions.

In addition, because meteorologic data gen-erally do not conform to an HSU's boundaries,rainfall data cannot be used to estimate waterproduction and its variability for each HSU.Thus, it was necessary to apply the distribu-tions of the gaged headwater flows (above anyimpoundments or consumptive use) to the to-tal water production in an HSU. This "nor-malization" required knowing the mean sea-sonal water production for the entire HSU,finding the distribution of the headwater flows,determining the relationship between meanseasonal water production and the gaged head-water flows, and applying the headwater dis-tributions to the total seasonal production fromwhich the right-hand sides of the seasonal waterquantity constraint could be obtained. Esti-mating distribution of water production at theheadwaters was accomplished by using theUSGS WATSTORE (1979) data tapes. Sea-sonal flow data were obtained for each HSUfor the gaging stations above either storage fa-cilities or significant human-related consump-tive use for each stream in the HSU from theUSGS tapes. For several of the streams in theregion, only a limited number of years (threeto five) of observations were available. Thegaged flows, termed "headwater" flows (hi k),were summed over all j streams to obtain theheadwater flows for the HSU (THk):

(1)m

THik = Z hikj=

1

where i is the HSU, k is the season, and j isthe stream.

Several forms of the distribution functionhave been used in hydrologic modeling: nor-mal, log normal, Weibull, and Gumbel distri-butions. In general, Haan suggests that theWeibull and Gumbel distribution functionsperform best for extreme values, and the Wei-bull is particularly suited for minimum values.The gamma form of the Weibull distributionwas used for this study. The two parametersof the density function associated with the in-complete gamma distribution function,7 a and3, were estimated using the method of mo-ments. There were no HSUs with an observedzero minimum flow; therefore, the minimum

7 The incomplete gamma density function is:

f(x; a, ) = xa -le - x/ for x

> 0; a > 0; > 0.

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Western Journal ofAgricultural Economics

Table 2. Average Seasonal Surface WaterProduction by HSU (acre/feet x 103)

Season 1 Season 2HSU January-June July-December

1 424.85 188.152 519.37 413.633 445.78 320.064 273.00 265.695 196.60 213.406 41.30 37.707.1 2,216.60 1,148.807.2 166.74 92.917.3 685.39 360.097.4 314.08 168.817.5 296.85 286.647.W 21.00 9.008.1 122.45 79.458.2 4,829.70 1,820.209 1,427.70 714.25

10 173.49 70.12WY 1,114.23 682.97CY 967.00 483.50CW 345.20 177.15

Source: King et al.

observed seasonal flow in each HSU was usedas the third parameter (lower bound) in thegamma function which gave the best overallfit for every HSU.

Then, the mean headwater values were nor-malized to the total seasonal flow for each HSUusing the expected value of THk (obtained fromKing et al. and listed in table 2) and a param-eter, 6i, which accounts for the unmeasuredheadwaters and other runoff produced in theHSU:

(2) E(SF,) = (1 + i)E(TH,) = E(1 + 6i)TH,,

where E(.) is the expected value operator, andSFj is the seasonal water production. In thebest of cases, bi is low. For this study, i did notexceed 1.0 and was generally less than .25.Given equation 2, 'the variance of the seasonalwater production is

(3) V(SF) = E{(1 + bi)TH - E[(1 + ,)THJ} 2

= (1 + bi)2E[TH, - E(THi)] 2,

where V(.) is the variance operator.Using the first two moments of seasonal

water production, the distribution functionsfor water production in each HSU were esti-mated and the seasonal surface water produc-tion in each HSU for given probabilities wascalculated, as indicated in table 3. In HSU 1,the data were insufficient to predict water pro-duction with any accuracy. The streams in HSU4 (the Jordan River) are already highly regu-lated, and, given a normal carry-over in stor-age from the preceding year, there is sufficientwater to provide the average flow even at a95% probability. For these reasons, the twoHSUs were omitted from table 3. In HSUs 3,5, and 6, and in HSU 7.1 at the 90% and 95%probabilities, the "low" flow season producedmore water than the "high" flow season. Theseasonal average flows in HSU 5 followed asimilar pattern, and the flows in each seasonfor HSU 6 were almost equal. For HSU 3 and7.1, these results were not expected; the anom-alies are probably due to limited data for the

Table 3. Probabilistic Seasonal Surface Water Production by HSU in Utah (Acre/Feet)

Season 1 (January-June) Season 2 (July-December)

HSU 85% 90% 95% 85% 90% 95%

2 337,210 285,143 261,619 280,956 256,891 223,9073 216,960 183,642 141,265 238,393 222,640 200,6335 103,440 89,154 70,651 154,378 142,215 127,7096 16,898 13,731 9,869 18,660 15,858 12,2787.1 13,663 10,337 6,579 12,410 10,815 8,7267.2 117,229 108,039 95,351 67,859 63,092 56,4567.3 542,198 513,427 427,734 230,242 207,615 177,0117.4 194,441 174,025 146,612 68,496 55,550 39,7917.5 199,298 181,741 157,739 214,183 200,920 181,4667.W 11,835 10,366 8,433 5,489 4,796 4,1038.1 59,580 51,440 40,880 21,234 16,086 10,2638.2 1,231,670 893,040 52,280 1,160,030 1,045,240 890,0609 658,370 550,310 414,540 342,368 288,769 220,949

10 51,922 39,144 34,769 43,679 39,149 33,060WY 640,798 563,848 462,177 403,930 357,742 296,340CY 357,608 283,685 194,773 169,435 132,694 89,594CW 101,305 75,536 46,891 58,409 54,077 29,686

92 July1989

Table 4. Irrigated Acreages by HSU in Utah (Acres)

85% NSC 90% NSC 95% NSCChange Change Change

Base Base NSC From Base From Base From Base

HSU Total Acres Total Acres NSC NSC NSC

1 Western Desert 13,803 40,0002 Bear River 212,000 237,5483 Ogden River 144,366 144,3664 Jordan River 179,478 179,4785 Sevier River 272,200 282,701 [6,800]a [26,700]

6 Cedar-Beaver 71,500 75,866 [3,120] [3,120] [3,120]

7.1 Green River 4,600 4,6007.2 Uintah River 20,000 20,0007.3 Lake Fork 21,000 21,0007.4 Rock Creek 36,000 36,000 (6,220)b

7.5 Strawberry and Duchesne Rivers 27,911 27,911

7.W White River, Utah 0 0

8.1 Price River 17,944 18,000 [700] [1,100]

8.2 West of Colorado and East of Wasatch 51,510 62,5009 South and East of Colorado River 9,585 11,442

10 Virgin River 20,300 20,300 [3,400] [3,400] [3,400](659)

WY Wyoming 184,116 251,185CY Colorado Yampa 36,374 36,374CW Colorado White 5,753 22,371 (5,099) [200] [1,500]

(5,503) (8,664)

a [acres] = acres reduced from full to partial irrigation.b (acres) = acres eliminated from production.

gaging stations. The calculated water produc-tion was then used as the right-hand-side val-ues for the surface water constraints for eachHSU in the allocation model to determine theeffect of drought on economically optimal wateruse.

Allocation Effects of Water Availability

In order to provide a base to examine the ef-fects of drought, a solution for the average sea-sonal availabilities was obtained. Results forirrigated acreages are listed in table 4 underthe column "Base." A small amount of salttreatment (conversion to sprinkler systems)^wasindicated in HSU 6. The model generated pos-itive but relatively small shadow values forwater (less than $10 per diverted acre-foot) inHSUs 1, 5, 6, 8.1, 8.2, 9, WY, and CW. Thesevalues are the result of insufficient flows toirrigate all available land and meet the non-degradation requirement imposed on salinity.The shadow values represent the marginal val-ue of water in irrigation, as it is constrainedby the limits on the salinity concentration. Inthe other HSUs, water quantity is not a con-straining factor on either irrigation or salinitylevels.

Next, the seasonal availabilities for the 85%probability level (the amount of water pro-duced which would be equaled or exceededwith a probability of 85%) were used as right-hand sides for each HSU. The solution wasinfeasible because salinity concentrations in thebasin outflows exceeded the quality con-straints. There was insufficient water availablein the Upper Colorado Basin to dilute the nat-ural load, primarily because salt loading fromnatural sources does not decrease proportion-ately with water availabilities (Jeppson et al.).As less water was available (those flows asso-ciated with probabilities of 90% and 95%), thesalinity standards became constraining.

A solution for a base case with no salinityconstraint (NSC) was generated to provide analternative and consistent comparison with re-duced water availabilities. Given that PL 92-320 requires only a long-term average annualsalinity level, the relaxation of these con-straints in periods of low water productionseems reasonable. There are some importantdifferences between the Base NSC solution andthe Base solution. The agricultural land pres-ently under irrigation (Classes I, II, III, andirrigated pasture) was increased in most casesto existing (1979) maximums, and the amount

Water Shortages 93Keith et al.

Western Journal of Agricultural Economics

Table 5. Shadow Price of Water ($ per Acre Foot)

Season 1 (January-June) Season 2 (July-December)

Base Base

HSU Case 85% 90% 95% Case 85% 90% 95%

5 Sevier Rivera 4.41 5.27 5.27 5.27

6 Cedar-Beavera 6.13 6.13 6.13 6.137.5 Headwaters of Strawberry and 0.00 0.74 7.78 9.14

Duchesne Rivers7W White River, Utah 0.00 0.00 6.34 19.87

8.1 Price River 1.40 2.26 2.26 2.26 1.40 26.28 34.08 34.09

10 Virgin River 0.00 0.00 0.00 4.77

CW Colorado White 0.00 0.00 6.34 19.87

a Note that since water availability is least in the early or "high" flow season in HSUs 5 and 6, the shadow price is positive in that

season.

of water application (partial irrigation to fullirrigation) was also increased (table 4). Thesedifferences imply that, as energy developmenttakes place, a nondegradation salinity con-straint will require some reductions in irrigatedagriculture, assuming no major public involve-ment in salinity management. Accompanyingthe increases in irrigation was a drop in theshadow price of water to zero in all HSUs ex-cept 5, 6, and 8.1 (table 5). Energy production,with its relatively high marginal value of water,remained the same for both Base NSC andBase solutions (table 6). One implication ofthese results is that marginal agriculture can-not generate profits sufficient to pay for treat-ment of the associated increased salinity. A

second is that, as energy production or otherwater-using activities increase, water quality(salinity in the case of the Upper ColoradoRiver Basin) may be far more constraining thanwater availability.

With reductions in surface water production(to 85%, 90%, and 95% probabilities), therewas no decrease in irrigated acres with the ex-ception of HSUs 6, 7.4, 10, and CW. Otherthan in HSU CW, the reduced acreage was inirrigated pasture (the least profitable, least pro-ductive activity). The remaining reduction inwater use resulted from changes in water ap-plications (full to either partial irrigation fortwo seasons or irrigation for only one seasonon alfalfa and irrigated grain) instead of re-

Table 6. Electrical Production (MWH)

85% NSC Change 90% NSC Change

Plant Base Total MWH From Base From Base

East Juab 10,735,200 46,800 46,800

East Uintah Basin 665,780Sanpete Sevier 2,690,040Warner Valley 2,817,149 (309,223)a (72,006)

Western Box Elder 1,752,000 (1,687,016) (1,687,016)

Northwest Box Elder 3,832,398 243,532 6,305

Northeast Millard 5,693,816Milford-Black Rock 2,944,668Iron 864,578Southeast Emery 750,887West Carbon 2,295,393East Carbon 1,721,545Southwest Emery 1,147,696East Grand 210,220Harry Allen 723,440Star Lake 34,063 (124) (124)

Barstow 419,629 979,134 979,134

Cadiz 6,590,086 707,564 707,564

Kemmerer 3,190,997 19,228 19,228

a () Indicates production decrease.

94 July 1989

Water Shortages 95Keith et al.

duced acreages (table 4). Profits forgone in-crease as a result of decrements in water avail-ability in the HSUs in which water quantitybecomes constraining, as evidenced by the in-creases in shadow prices (table 5), although thevalues are relatively low in all but one HSU.

As surface water production was reduced,the potential for storing any excess early seasonrunoff was available in the model. Storage en-tered the solution only in HSU 8.1 (Price Riv-er) at 90% and 95% probabilities. These resultsindicate that, in general, agriculture is not prof-itable enough to justify the development ofnew storage. In HSU 8.1, the existence of coal-fired electrical production (East and West Car-bon) and a coal gasification plant reduced wateravailability so that only the highest valuedcrops (particularly corn) and best available landwere in production in the Base NSC case. Thus,the shadow value of water was correspondinglyhigh in that HSU. Even with the best land,only 620 and 6,443 acre-feet of storage wereindicated at the 90% and 95% probabilitylevels, respectively. Clearly, as energy or otherhigh-valued users of water develop, water vari-ability likely will result in transfers of waterfrom irrigation of small grains, hay, and pas-ture to the developing uses so long as thosetransfers are permitted. Typical irrigated cropsin the Intermountain West are not sufficientlyvaluable to pay for storage developments toinsure water supplies, particularly at the mar-gin. Water rights sales from irrigators to theIntermountain Power Project in the SevierRiver Basin support this conclusion.

Electrical production was redistributed aswater availability changed (table 6). For the85% probability level, a shift of electrical pro-duction occurred from Western Box Elder inUtah to the Barstow and Cadiz sites in Cali-fornia. Some smaller shifts also occurred with-in the Utah sites. Only minor shifts occurredwith the reduction of water availability to the90% probability, and none occurred with fur-ther reductions of water production. Theseshifts resulted from the very small differencein electrical generation profitability among thevarious generation sites and coal-source com-binations coupled with changes in the profit-ability of irrigated agriculture (the opportunitycost of water in energy production). It is notcertain that shifts in electrical production sitesactually would occur; rather, the similarity ofproduction costs is itself of interest. The modelresults suggest that variables other than water

likely will be the significant influences on thelocation of new electrical generation plants inthe Upper Colorado River Basin.

Solutions were obtained for the case in whichno interstate transfers of water were allowed(the current legal situation). This was accom-plished by limiting water use in each state tothat prescribed by the Colorado River Com-pact and the judicial decrees pertaining to it.No significant changes in allocations occurredunder the reduced water production scenarios.Thus, while the prohibition of interstate trans-fers is currently the legal standard (recent courtaction in Colorado prohibited storage rights inColorado to be sold to California demanders),such restrictions are not likely to cause seriousproblems for energy development in the UpperColorado River or Great Basins. This is gen-erally the result of the local transfer of waterfrom irrigation to energy.

In an effort to determine those conditionsunder which added storage capacity would bedeveloped in the Colorado River Basin in Utah,an examination of proposed storage develop-ment on the White River in Utah was under-taken. The White River in Utah has no irri-gation from which to transfer water and hasbeen frequently labeled one of the most "watershort" river basins in Utah. Storage would pro-vide water for proposed oil shale production,for which water provision was a predeter-mined requirement. 8 Only under the moststringent of circumstances did this storage en-ter the solution; when water production wasreduced to six times the smallest monthly flowin each season, interstate water transfers wereprevented, and water sales from Native Amer-ican water rights were prohibited, a significantamount of new storage (20,000 acre-feet) en-tered the solution. The water availability usedrepresents a more conservative estimate thana 100% probability level of water production.Thus, storage development seems unwarrant-ed, even under relatively stringent circum-stances, as long as institutions provide evenlimited flexibility of water rights transfers. Itis highly likely that similar results would befound in all other HSUs, since all containedirrigation water which could be transferred,and cropping included considerable acreage insmall grains, hay, and pasture.

8 There is little or no data on which to estimate values of themarginal profit for oil shale or any of the included synfuels.

Western Journal of Agricultural Economics

Conclusions and Recommendations

The results from the chance-constrained mod-el indicate that, in general, water quantity isnot a significant constraint in regional eco-nomic growth in the Upper Colorado RiverBasin and the Utah portion of the Great Basin,particularly if water rights are relatively freelytransferable. Even under the most severe caseexamined, where water production was con-sistent with a 95% probability, only marginalchanges in irrigated agriculture were evidencedwhile major production increases in energysectors were indicated. The Sevier River andColorado portion of the White River were theonly basins with reductions in irrigation onmore than a few thousand acres and on landsof more than the lowest productivity classes.

Water quality constraints appear to have asignificant impact on agriculture as energy de-velopment occurs, particularly since privatesalinity treatment programs appear to be eco-nomically infeasible. Only a publicly financedsystem could be expected to counteract theconcentrating effects of energy development,and it appears from the model results that thoseprograms probably are not economically jus-tifiable.

The development of new storage also ap-pears to be unwarranted because the water userwith the lowest marginal value, irrigated ag-riculture, cannot afford to pay the costs of con-struction and operation. If water rights trans-fers between agriculture and energy are severelyrestricted, it is possible that storage would beindicated for cases in which some reduction inenergy production or high-valued crops mightoccur.

Results appear to indicate that, at least inthe near term, other impediments to large scaleenergy development are more important thanwater availability in the Upper Colorado andGreat Basin regions even under drought con-ditions. If water markets or water banks wereimplemented, it would be likely that irrigatorswould sell or lease water rights to energy pro-ducers at more than the water's marginal valuein irrigation (as was the case in the Sevier Basinfor the Intermountain Power Plant). Alterna-tive water applications, such as partial irriga-tion, might be expected to mitigate some ofthe water transfer. Given that the types of cropsgrown in the river basins studied are typicalof many areas in the Intermountain West, it

is likely that these results could be generalizedto most of the Intermountain West.

A closer examination of the effects of waterquality standards, particularly nondegradationrules, on economic growth in the Upper Col-orado and Great Basins appears to be war-ranted. Model results appear to indicate thatsalinity constraints are more binding than wateravailability in the base case (using averageavailabilities) and would become even morebinding as water production is reduced, if qual-ity standards are not adjusted to flows.

[Received May 1987; final revisionreceived November 1988.]

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