TEXAS WATER DEVELOPMENT BOARD

REPORT 141

A COMPARISON OF MASS-TRANSFER AND CLIMATIC-INDEX

EVAPORATION COMPUTATIONS FROM

SMALL RESERVOIRS IN TEXAS

By

R. O. HawkinsonU.S. Geological 5U1vey

Prepared by the U.S. Gedogical Surveyin cooperation with the

Texillli Water Owelopmenl BOllrd

Febnlarv 1972

TABLE OF CONTENTS

ABSTRACT

INTRODUCTION

METHODS OF DETERMINING EVAPORATION

Water· Budget Method

Energy-Budget Method

Pan-ta·Lake Coefficients.

Mass-Transfer Method

Climatic-Index Method

COLLECTION OF DATA

ANALYSES OF DATA

Method of Analyses

Results of Analyses .

SUMMARY AND CONCLUSIONS

REFERENCES.

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TABLES

Period During Which Climatic Data Were Collected for theEvaporation Study on Each Subwatershed Reservoir ....

Mass·Transfer Coefficient, Intercept, and Standard Error of Estimate of theMass-Transfer Coefficient for Each Reservoir Utilized in the Study ..

Results of the Analyses by 2·Month Periods for the Comparison of Mass-Transfer andClimatic· Index Evaporation Data From Seven Small Reservoirs in Texas .

FIGURES

Graph Showing lake Evaporation Relations Used by theTexas Water Rights Commission in Climatic-Index Computations

Map of Texas Showing location of the EightWatersheds Where Evaporation Data Were Collected

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TABLE OF CONTENTS (Conl'd.)

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3. Photographs of Climatologicallnslruments That ProvideData for Use in Mass-Transfer Computations .................................. .. 7

4. Photograph of a Typical Gage Installationat a Floodwater·Retarding Reservoir ..... .....•....•.......•......................•. 8

A COMPARISON OF MASS-TRANSFER ANO CLIMATIC-INDEX

EVAPORATION COMPUTATIONS FROM

SMALL RESERVOIRS IN TEXAS

ABSTRACT

The mass-transfer method of determiningevaporation is utilized as the control method in anevaluation of climatic-index evaporation data providedby the Texas Water Ri!flts Commission for eightfloodwater-retarding reservoirs in Texas. Data werecollected at each reservoir at various times during theperiod 1960-68 by the U.S. Geological Survey.

A t·test for the comparison of means of two setsof independent observations was used to determine if asignificant diHerence existed between monthlyevaporation rates for bimonthly periods beginning withJanuary as computed by the mass-transfer method andby the c1imatic·index method. No significant differenceat the 5 percent level was found between the two sets ofdata during any of the 2-month periods.

Exclusion of the inconsistent Calaveras Creek dataincreased the correlation coefficient betweenmass-transfer and climatic-index evaporation data from0.81 to 0.86.

Because the t-tests showed no significantdifferences between the mass· transfer and dimatic-indexdata, both methods are assumed to provide an equallygood estimate of evaporation from small reservoirs.Therefore it is concluded that the climatic-indexevaporation data, as supplied by the Texas Water RightsCommission, provide a reliable estimate of evapofationfor use in hydrologic studies of small reservoirs in Texas.

A COMPARISON OF MASS-TRANSFER AND CLIMATIC-INDEX

EVAPORATION COMPUTATIONS FROM

SMALL RESERVOIRS IN TEXAS

INTRODUCTION

The purpose of this report, which was prepared bythe U.S. Geological Survey in cooperation with theTexas Water Development Board. is to compare monthlyevaporation by 2-month periods beginning withJanuary-February as computed by the empiricalclimatic-index method, Eel, (furnished by the TexasWater Ai~ts Commission) to evaporation as calculatedby the mass-transfer method, EMT. The comparisonswill show whether or not Eel is significantly differentfrom EMT. In the keeping with this purpose, this reportpresents:

1. the mass· transfer coefficients and standardelTor of each as determined for eightfloodwater-retarding reservoirs;

2. the results of I-tests used to compare Eeland EMT; and

3. recommended coefficients if necessary toadjust Eel to EMT.

As of September 30, 1969. the Soil ConservationService of the U.S. Department of Agriculture hadcompleted 1,355 floodwater-retarding structures inTexas. Definition of the hydrologic effects of thesestructures is requisite to the development of practicalwater.planning and management pmgrams. Definition ofthe hydrologic effects is dependent upon an accurateevaluation of the following variables: 111 net inflow,(2) outflow. 131 rainfall on the pool, (4) change instorage, and (5) consumption.

Consumption includes evaporation from the freewater surface, evaporation from the soil surface adjacentto the pool. transpiration, and percolation to theground·water reservoir. Generally, percolation to theground·water reservoir is not considered as consumption.However, in the study areas of this investigation, thewater table normally does not intersect the surfacestreams any\'Vhere near the floodwater-retardingresel'\loirs. Therefore, percolation to the ground-waterresel'\loir is not recoverable as a "surface-water resource"

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in the basin and is considered as a loss. Becauseconsumption includes components that are difficult tomeasure, it is the variable most difficult to evaluate.Gilbert and Sauer (1970, p. 31-37) present data andanalyses which show consumption fromfloodwater·retarding reservoirs to exceed evaporationlosses associated with the surface storage of water.

METHODS OF DETERMININGEVAPORATION

There are five basic methods that can be used toestimate evaporation from lake surfaces. These fivemethods are discussed briefly in the following sectionsof this report.

Water-Budget Method

The water·budget method results in thedetermination of evaporation from a reservoir bymeasuring inflow, outflow, seepage, and change instorage. The results of water·budget studies made onlake Hefner in Oklahoma (Marciano and Harbeck,1954) indicate that this method yields realistic resultsprovided that inflow, outflow, change in storage, andseepage are measured accurately. In instances wheretranspiration, "bank" storage, or ground·water storageaffects the water loss from a reservoir, the water·budgetmethod may not provide accurate evaporation data.

Energy·Budget Method

The energy·budget method is based on theprinciple of conservation of energy. Incoming, outgoing,and stored energy are measured over some finite periodand related to the amount of energy required for theevaporation process. Anderson (1954) used theenergy·budget method to compute evaporation fromLake Hefner. Harbeck and others (195B) used theenergy·budget method as a control for calculations madeduring the lake Mead studies.

The energy-budget method, from a physical pointof view, appears to be the most accurate method ofcomputing evaporation. Use of the method, however, isgenerally limited to the calibration of other methods ofdetermining evaporation because of the relatively highinstrumentation cost.

Pan-to-Lake Coefficients

The evaporation pan is currently the most widelyused instrument to determine evaporation. Reservoirevaporation is determined by application of pan-to-Iakecoefficients to the pan-evaporation values. The methodis simple to use, required data are generally available,and the results are reasonably accurate on an annualbasis.

The primary objectives of evaporation studies bythe U.S. Weather Bureau are the development ofimproved methods for estimating lake evaporation froma network of climatological observations (Kohler andParmele. 1967). Monthly values of pan-to·lakecoefficients vary considerably, depending on lakecharacteristics and local climate. Unless the effects ofadYected energy into the lake and the effects of heattransfer through the pan are taken into account,appreciable error can be introduced by the use of thecustomary 0.7 annual coefficient.

eo • saturation vapor pressure, in millibars,corresponding to water-surface temperature,and

ea '" vapor pressure of the air, in millibars.

Harbeck (1962) states that the mass-transfercoefficient, N, generally represents a combination ofmany variables. such as the size of the lake; roughness ofthe water surface; manner of variation of wind withheight; atmospheric stability; barometric pressure; anddensity and kinematic viscosity of the air. Gilbert andothers (1964) and Harbeck (1962) present threemethods that can be used to determine the mass·transfercoefficient.

An evaporation-seepage technique presented byHarbeck and previously described by Langbein, Hains,and Culler 119511 is used in this report to determine N.Application of the technique is based on the followingassumptions:

1. The decline in reservoir stage during periodswhen there is no surface inflow or outflowis composed of two parts. evaporation andseepage.

2. When the product uleo - eal is zero,evaporation is negligible.

Mass-Transfer Method

The following quasi-empirical mass·transferequation (Harbeck, 1962) was used in this study as thecontrol method to determine evaporation from a freewater surface:

The mass· transfer method of deriving evaporationequations is based on the concepts of discontinuous andcontinuous mixing applied to the transfer of mass orwater vapor in the boundary layer. Nearly allmass-transfer equations have one common factor-thatevaporation is directly proportional to the product ofvapor· pressure difference and wind speed. Wind speed, insome of the equations, has been assigned an exponentbetlNeen 0.75 and 1.00. Marciano and Harbeck (1954)present a physical and mathematical review ofmass-transfer equations.

EMT '" Nu leo - eal 111

The evaporation·seepage technique is applied asfollows in the determination of a composite N for areservoir. Determine the change in stage 16HI and theaverage values of wind speed and vapor pressuredifferences for 3· to 5-day periods of no inflow oroutflow. The values of these variables are then plottedwith 16Hl, in feet per day, as the ordinate, and theproduct of u(eo - ea). where u is expressed in miles perhour and (eo - ea) in millibars, as the abscissa. Aleast-squares line is then fitted to the data. The slope ofthis line is the mass· transfer coefficient.

Initially, an attempt was made to determine amass-transfer coefficient for each 2·month period ateach reservoir. However, the lack of data prevented aleast-squares determination of N for the 2-monthperiods. Consequently, a composite N based on all datawas calculated for each reservoir. Had it been possible todetermine a mass· transfer coefficient for each 2-monthperiod, any seasonal variation in the intercepl, which isindicative of other consumptive losses such as seepage,lIIIOuld have been shown.

where EMT '" evaporation in inches per day.

N • the mass-transfer coefficient, a coefficientof proportionality.

The composite N value with the humidity,temperature, and wind speed data were used in equationIII to compute monthly evaporation from eachreservoir.

u • wind speed, in miles per hour. at 2 metersabove the ,wter surface,

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Climatic-Index Method

Veihmeyer (1964) presents a summary of selectedevaporation equations based on Dalton's Law, which isthe basis of most empirical equations. Other than thevapor-pressure differential, wind movement is generallythe most important factor in the equations.

Use of pan·to-Iake coefficients, withoutaccounting for advected energy into the lake and heattransfer through the pan, can introduce considerableerror into estimates of evaporation. Kohler, Nordenson,and Fox (1955) developed the "theoretical" panconcept, in which sensible heat transfer through the panand the part available for use in the evaporation processis determined. The Texas Water Rights Commission hasadopted the method presented by Kohler, Nordenson,and Fox (19551. The method, as applied by theCommission is entitled the climatic-index method.

The Texas Water Rights Commission utilizes thecomposite relation between air temperature, dew-pointtemperature, wind movement, and solar radiation asshown. in Figure 1 for the determination of monthlylake-surface evaporation (ECI). Figure 1 is based onequation 10 in the U.S. Weather Bureau Research PaperNo. 38 by Kohler, Nordenson, and Fox (1955).

COLLECTION OF DATA

The data necessary to compute mass-transferevaporation values were collected on onefloodwater-retarding reservoir in each of the eightwatersheds shown on Figure 2. The subwatershedreservoirs and the periods during which data werecollected are given in Table 1.

The data used in this study are wind movement,mean daily air and water temperatures, relativehumidity, rainfal', and change in stage. A raft supportinga 28-day thermograph and a totalizing anemometer wasanchored at midlake. The thermograph providedwater·surface temperature data and the anemometerprovided wind-movement data at 2 meters above thewater surface (Figure 3). Air-temperature andrelative-humidity records were obtained weekly fromhygrothermograph installations IFi!PJre 3) near eachreservoir.

ANALYSES OF DATA

Method of Analyses

The monthly evaporation data for all reservoirswere plotted prior to statistical evaluation to determineif inconsistencies existed. ECI was plotted against EMT.The points were random about the line of equalevaporation for all reservoirs except the Calaveras Creekreservoir, where EMT was consistently greater than ECI.The Calaveras Creek data were omitted from thestatistical evaluation except in computing a correlationcoefficient to show the effect of the inconsistent data.

Change in stage and wind·speed records onCalaveras Creek were generally poor during the studyperiod. New equipment was tried, but was notdependable (written communication, Kennon, 1965).The reservoir also contained a luxuriant growth ofweeds. These circumstances provided sufficient reasonsto question the accuracy of the evaporation data.

A t·test for the comparison of means of two setsof independent observations was used to determine ifany significant difference exists between the monthlyevaporation rates of ECI and EMT- Statistical evaluationof the monthly data was made for the 2·month periods.

Wine (1964) gives the following formula for thecomputation of the t statistic:

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where te is the value used to judge statistical significanceor insignificance when compared to a t·value table,

X is the mean of the monthly mass· transferevaporation data for a 2·month period,

Y is the mean of the monthly climatic-indexevaporation data for a 2·month period,

sp is the pooled standard deviation for samplesof equal size computed as

Change in stage and rainfall data were provided bya continuous·stage recorder and a recording rain gage.Figure 4 shows part of a typical well and gage house usedto obtain stage and rainfall records (note receiver forrecording rain gage on top of the gage house).

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Climatic· index data were obtained from theEnvironmental Science Services Administrationflrst·order synoptic stations. Values of the climatic dataat a specific reservoir site are determined byinterpolation of the data from surrounding stations.

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where s2 MT and s2CI are the variances of themass-transfer and climatic-index data, respectively,

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EXPLANATION

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A. Standard R.ft with Thermograph and Totalizing Anemomete-r

, .8 Hygrothe'mograph. Young Screened Pan. and Nonrecord,,'9 Rain Gq

Figure 3

Climatological Instruments That Provide Data for Use In

Moss.Tronsfer Computations .

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Figure 4.-Typical Gage Installation at a Floodwater-Retarding Reservoir

"1 and "2 are the sample sizes of the mass-transferand climatic-index data, respectively.

The 95 percent confidence interval was computedto show the magnitude of the difference in means ofEMT and Eel that could be expected for any 2-monthperiod. The limits of the confidence interval of twomeans are given by li (1964) as follows:

The t-test provides a valid comparison of the twosets of evaporation data because the variables used forcomputation of Eel and EMT are derivedindependently. There is no common measurement ofany climatic factor. Coefficients (K) to adjust theclimatic-index data to the mass-transfer data for each2·month period were computed as the ratio ofXMT/YCI.

Results of Analyses

The mass· transfer coefficient, intercept, and thestandard error of estimate of the mass·transfercoefficient for each reservoir are shown in Table 2. Theaverage standard error expressed as a percentage(excluding data from the Calaveras Creek reservoir) is 10percent. The range is 5 percent to 17 percent. Thecorrelation coefficients bet'Neen EMT and Eel with tiledata from tile Calaveras Creek reservoir included andexcluded were 0.81 and 0.86, respectively.

where t,025 is the 2.5 percent point of the t distributionwith (n1 + n2· 2) degrees of freedom. Definitions of theother terms are as given previously.

The results of the t·test between the two sets ofdata, tile adjustment coefficients, and the 95 percentconfidence intervals for the difference in means are givenin Table 3 for each 2-month period. There is nosignificant difference between EMT and ECI at the 5percent level. The confidence intervals given in the lastcolumn of Table 3 show the range within which thedifference in monthly mean evaporation, as determinedby the two methods, falls 95 percent of the time.

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Table 2.-Mass-Transfer Coefficient Intercept, and Standard Error of Estimate ofthe Mass-Transfer Coefficient for Each Reservoir Utilized in the Study

MASS-TRANSFER STANDARD ERROR. Sb. OF Sb EXPRESSED ASWATERSHED AND RESERVOIR COEFFICIENT INTERCEPT MASS·TRANSFER COEFFICIENT PERCENT

Elm Fork Trinity River. '0 2.66'10-4 3.0'10-3 2.97'10.5 "Honey Creek. " 2.27,10-4 2.8'10.3 2.66.10.5 "Green Creek. , 2.62'10.4 2.5'10.3 1.79'10.5 ,Cow Seyou. 4 1.90'10-4 1.1'10.2 3.23'10-5 "Mukeweter Creek. , 2.39'10-4 6.0'10.3 1.21'10-5 ,Deep Creek. , 2.29'10.4 4.5'10-3 1.17'10.5 ,Calaveru Creek. , "4.43'10-4 1.2.10.2 2.74.10.5 ,Escondido Creak. " 2.22'10.

4 2.1'10.2 3.27'10.5 "Kennon Iwrll1an communication. 19651 computed a mus·transfer coefficiant of 2.28 X 10-4 by weighting the bimonthly

coefficients. Secause of this and other discrepancies, Calaveres Creak dan ware not uH'd in tha study.

Table 3.-Results of the Analyses by 2-Month Periods for the Comparison of Mass-Transferand Climatic-Index Evaporation Data From Seven Small Reservoirs in Texas

±t.025 wilh (nl+n2'21 degrees AdjUStment coefficientof freedom (df! hhat value (climale·index evaporation

Computed which computed t value must times coefficient· rTIaS$'Period t value exceed to show significance) transfer evaporation)

Jan. ·Feb. 1.63 b.oO with 56 df 1.11

Mar. ·Apr. 0.32 ±:2.00 with 56 df 1.03

May ·June ·0.65 b.oO with 54 df 0.96

July ·Au~ -1..87 ±:2.00 with 56 df 0.92

Sept. ·Oct. 0.'" ±2 .01 with 50 df 1.03

Nov. ·Dec. 0.73 ±:2.00 with 60 df LOO

!I X is the mNn of EMT. Y is the mNn of ECI.

95 percent confidence interval(95 percent of the time the

difference in means lieswithin this interval)

Units· feet per month

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REFERENCES

Anderson, A. E., 1954. Energy-budget studies, inWater-loss investigations-lake Hefner studies.technical report: U.S. Geol. Survey Prof. Paper 269,p.71.119.

Gilbert. C. R., Commons, G. G., Koberg. G. E., andKennon, F. W" 1964. Hydrologic studies of smallwatersheds, Honey Creek basin, Collin and GraysonCounties. Texas, 1953-59: U.S. Gro!. SurveyWater·Supply Paper 1779-F. 98 p.

Gilbert, C. R.. and Sauer, S. P., 1970, Hydrologic effectsof floodwater-retarding structures on Garza-littleElm Resenmir, Texas: U.S. Geol. SurveyWater·Supply Paper 1984, 95 p.

Harbeck, G. E.• Jr., 1962. A practical field techniquefor measuring reservoir evaporation utilizingmass-transfer theory: U.S. Geol. Survey Prof.Paper 272-E, p. 101·105.

Harbeck. G. E.. Jr., Kohler, M. A., Koberg, G. E., andothers, 1958. Water·loss investigations-Lake Meadstudies: U.S. Geol. Survey Prof. Paper 298, 100 p.

Kohler, M. A., Nordenson, T. J., and Baker. D. R., 1959,Evaporation maps for the United States: U.S.Weather Bureau Technical Paper 37,13 p.

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Kohler, M. A., Nordenson, T. J., and Fox. W. E., 1955,Evaporation from pans and lakes: U.S. WeatherBureau Research Paper 38, 21 p.

Kohler. M. A.• and Parmele, L. H., 1967. Generalizedestimates of free·water evaporation: Water ResourcesResearch. v. 3. no. 4, p. 997-1005.

Langbein, W. B., Hains, C. H.• and Culler, R. C., 1951.Hydrology of stock-water reservoirs in Arizona.progress report: U.S. Geol. Survey Circ. 110, 18 p.

Li, J. C. R., 1964, Statistical inference I: Ann Arbor,Michigan, Edwards Brothers, Inc.• 658 p.

Marciano, J. J., and Harbeck, G. E., Jr., 1954,Mass·transfer studies, in Water·lossinvestigations-Lake Hefner studies, technical report:U.S. Gee!. Survey Prof. Paper 269, p. 46-70.

Viehmeyer. F. J., 1964. Section 11,Evapotranspiration,in Handbook of applied hydrology, Ven Te Chow:New York. McGraw· Hill Book Co.• Inc:.

Wine. R. L., 1964, Statistics for scientists and engineers:Englewood Cliffs, New Jersey. Prentice-Hall, Inc.,671 p.