a method for estimating pan evaporation for · 2009-08-18 · a method for estimating pan...

southeastern geographer, 48(2) 2008: pp. 149–171

A Method for Estimating Pan Evaporation forInland and Coastal Regions of the Southeastern U.S.

WILLIAM H. COOKE III, KATARZYNA GRALA, CHARLES L. WAXDepartment of Geosciences, Mississippi State University

Regression models that estimate daily pan evap-

oration for inland and coastal regions of South-

eastern U.S. were developed using observations

of wind speed, solar radiation, minimum rela-

tive humidity, and maximum temperature. These

weather elements are collected in numerous lo-

cations where measured pan evaporation records

are not available, allowing an estimation of pan

evaporation across large regions with higher

point pattern density than is available using pan

evaporation sites only. Sixteen models were devel-

oped and tested. An innovative model selection

metric was developed, employing R square, Pear-

son’s correlation coefficient, average difference

between estimated and measured evaporation,

root mean-squared error, and mean absolute er-

ror. Models selected included two validated for use

in inland environments and one validated for use

in coastal environments.

key words: climate model, pan evaporation,

water balance, weather

introduction

Daily pan evaporation is an importantfactor in landscape-level water budget cal-culations. It is also an important dynamicvariable that should be considered whenmodeling fire potential, making crop man-agement decisions, and in other projectsfocusing on water management and con-servation. Acquisition of pan evaporation

data suitable for water budget calcula-tions is a challenge because the datamust be easily accessible, spatially welldistributed, and collected regularly overextended time periods.

The predominant pan evaporationmeasurement method utilizes a ∂∫-inchdiameter pan that sits above ground,known as the Class-A evaporation pan.Exclusive adoption of these pans by theNational Weather Service is considered tobe the first attempt to unify evaporationdata collection throughout the U.S. (Jones∞ΩΩ≤). Evaporation pans and associatedautomated measurement devices are ratherexpensive and are located at a limitednumber of weather stations around theU.S. and the world. For example, in Mis-sissippi evaporation pans are maintainedat only nine locations and most of themare in the northern two-thirds of the state(Bell ≤≠≠∂).

In addition to the relative scarcity ofcollected pan evaporation data, the ac-curacy of pan evaporation estimates hasbeen questioned by numerous researchers(Bruton et al. ≤≠≠≠a; Sumner and Jacobs≤≠≠∑). For example, precipitation eventsinterfere with accurate measurement ofpan evaporation (Lindsey and Farnsworth∞ΩΩπ). Generally, the pan evaporation rec-ord must be corrected for any additionsof rainfall to the pan. However, errors in

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V0 20 40 60 8010

Miles

Solar Radiation Data S recorded

! not recorded R

Weather Stations in Mississippi

Figure ∞. Map showing weather stations in Mississippi;

stars indicate stations recording solar radiation.

A Method for Estimating Pan Evaporation 151

rainfall measurement and inconsistencyin rainfall capture add error to recordedpan evaporation data (Sumner and Ja-cobs ≤≠≠∑). Finally, pan evaporation rec-ords are often acquired seasonally, withmore comprehensive data available in thesummer months and during the growingseason.

All these obstacles make good-qualitydaily evaporation data difficult to obtainat many locations across large regions. Inorder to fill this void, this study presentsa method for estimating pan evaporationbased on data from existing pan evapora-tion stations in Mississippi, Alabama, andLouisiana and other meteorological datathat are readily available at numerousweather stations.

Many attempts have been made to de-velop empirical formulas that estimatepotential evaporation and evapotranspi-ration. Thornthwaite (∞Ω∂≤) stated, ‘‘Thelack of a direct measure of losses by evap-oration from natural surfaces has led tothe development of many empirical for-mulas for expressing the effectivenessof evaporation.’’ Historical formulas com-monly used in the southeastern U.S. in-clude Thornthwaite (∞Ω∂∫), Blaney andCriddle (∞Ω∑≠), Penman (∞Ω∑∏), and Poteand Wax (∞Ω∫∏). These formulas havevarying degrees of complexity and somewere developed for application at specificlocations. Often, data necessary for for-mula calculations are simply not available.For example, the Penman equation, a com-monly used estimator of evaporation fromthe free surface of a body of water (Pen-man ∞Ω∂∫; Penman ∞Ω∏≥; Shuttleworth∞ΩΩ≥), requires measurement of net radia-tion, soil heat flux, air temperature, rela-tive humidity, wind speed, vapor pressure,and other environmental variables (Sum-

ner and Jacobs ≤≠≠∑). A complete set ofthese input elements at locations thatare spatially well distributed over largegeographic regions is rare. For example,Figure ∞ shows the spatial distributionof weather stations in Mississippi withonly ∞π of ∞π∫ stations recording solarradiation.

With recent increased availability ofhourly and daily meteorological data froma variety of observing networks, estima-tors of evaporation have been developedusing ‘‘proxy’’ weather elements as inputs.Hanson (∞Ω∫Ω) used daily solar radiation,daily mean temperature, and wind run(daily average wind speed) to model class-A daily pan evaporation for southwestIdaho. Cahoon et al. (∞ΩΩ∞) used mea-sured pan evaporation data to determinelocal coefficients for existing equationsthat estimate pan evaporation using datafrom ∞≥ stations in the mid-south andsoutheastern U.S. Bruton et al. (≤≠≠≠b)developed artificial neural network (ANN)models to estimate daily pan evaporationusing multiple measured weather vari-ables as inputs. The ANN model included∞∂ different meteorological variables andresulted in r≤ of ≠.π∞π. ANN models werealso developed by Terzi and Keskin (≤≠≠∑)to estimate evaporation for the Lake Dis-trict in western Turkey using air tempera-ture, water temperature, solar radiation,air pressure, wind speed, and relative hu-midity. Another recent method employedfuzzy logic models to estimate daily panevaporation using air and water tempera-tures, sunshine hours, solar radiation,air pressures, relative humidity, and windspeed for Lake Egirdir in Turkey (Keskin etal. ≤≠≠∂).

While it is certainly possible to estimatepan evaporation at selected locations us-

152 william h. cooke, katarzyna gr ala and charles l. wax

ing any of these methods, the goal of thisstudy is to estimate pan evaporation re-gionally, using numerous locations thatmeet four basic criteria: ∞) data are readilyavailable and easy to obtain; ≤) data arespatially well distributed; ≥) estimates aresensitive to regional climatic heterogene-ity; and ∂) data are easily implemented forinterpolation of statistical surfaces withinGeographic Information Systems (GIS).

While the simplest evaporation esti-mation methods are temperature based(Thornthwaite and Mather ∞Ω∑∑), andthese data are widely available acrossthe Southeastern U.S., the dependence ofmore sophisticated evaporation estima-tion methods (Penman ∞Ω∂∫) require netradiation, which is available at only ap-proximately ∞≠ percent of stations in Mis-sissippi. Evaporation estimates derivedfrom data obtained at the coarse resolu-tion represented by stations that record netradiation are less likely to be sensitive toregional climatic variations. This coarsepoint resolution is less likely to captureenvironmental variability when data areinterpolated using GIS (Hijmans et al.≤≠≠∑). Consequently, none of the existingmethods for calculating pan evaporationmet all four criteria.

Pan evaporation estimates derived froma dense network of sites can play an impor-tant role in assessment of water budgetsin areas frequently impacted by hurri-canes. Environmental assessments willbenefit from water budget calculations asthey relate to fire hazard, water resourcemanagement, and rates of oxidation thataffect vegetation decomposition and plantcommunities’ recovery. Hurricanes fre-quently impact Gulf Coast weather stationdata streams (Graumann et al. ≤≠≠∑). Inthe aftermath of Hurricane Katrina, many

of the existing weather observation siteswere impacted, indicating the need for aspatially dense network of stations thatmeasure pan evaporation or record datanecessary for estimating pan evaporation.

materials and methods

Study Area andPreliminary AnalysisThe study focuses on areas of the south-

ern region of the U.S. in the states of Loui-siana, Mississippi, and Alabama that main-tain pan evaporation stations (Figure ≤).As shown in Figure ≤, there are only a fewstations in the region that record pan evap-oration, and current daily pan evaporationdata at these locations are not consistentlyavailable.

Because of the deficiency of actualdaily pan evaporation data, substitutingcalculated daily historic average values foractual daily pan evaporation is an optionfor water budget applications and is cur-rently used as an input in various mod-els (Cothren et al. ≤≠≠∞; Ruley and Rusch≤≠≠∂; Enciso and Wiedenfeld ≤≠≠∑). Onedrawback of using historic averages is theremoval of short-term variability in evap-oration via the averaging process.

In general, measured pan evaporationin the region was found to have total dailyvalues ranging from a minimum of ≤.∑∂mm to maximum of π.∏≤ mm over the pe-riod of the study (July–October). There-fore the overall mean values for historicand actual evaporation should be similarwithin this small range most of the time.Furthermore, evaporation is more spa-tially homogeneous than precipitation, sodaily variability across the region is likelyto be small (Bell ≤≠≠∂). The daily variationof precipitation is much more controlling


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Alabama

Mississippi

Arkansas

Florida

Jennings

Milton

Hope

Rolling Fork

Crowley

Catfish Point

Newton

Woodworth

St. Joseph

Fairhope

State University

LSU Ben Hur

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Calhoun

Red River

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weather stationrecording evaporation models developed basedon the inland station datamodels developed based on the coastal station data

0 25 50 75 10012.5MilesG u l f o f M e x i c o

Figure ≤. Map showing weather stations recording evaporation and locations

for which evaporation models were created.

in a daily moisture assessment. Accordingto Bell (≤≠≠∂), the average daily precipi-tation for July ∞∑th in the southern regionis ∂.∑π mm, and pan evaporation has analmost identical average of ∂.∫≤ mm onthat same day. However, the standard de-viation of the precipitation data is Ω.≥Ωmm, while the pan evaporation data havea standard deviation of only ∞.∑≤ mm. Pre-cipitation is therefore over ∏ times as vari-able on a given day as evaporation in theregion. Nevertheless, the sparse coverageof pan evaporation stations makes it dif-ficult to characterize small differences inevaporation, particularly during summermonths when convective rainfall eventscan modify the microclimate and local wa-ter budgets. In addition, accurate char-

acterization of the evaporation gradientand decay of coastal influences on evap-oration is difficult to measure due to thelimited number of pan evaporation sta-tions that exist in both coastal and inlandenvironments.

An initial comparison of actual mea-sured and historic average records indi-cated numerous drawbacks. Figure ≥ illus-trates a comparison of the ≤≠≠≥ measuredactual pan evaporation with the long-termhistoric average daily pan evaporation foran inland station (Stoneville, MS) and acoastal station (Houma, LA). The graphclearly illustrates that the derived averagedaily pan evaporation does not conformwell to actual measured pan evapora-tion. It is apparent that the average pan


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1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101

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(mm

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actual evaporation Stoneville 2003 historic average evaporation Stoneville

July October

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1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101

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actual evaporation Houma 2003 historic average evaporation HoumaJuly October

Figure ≥. Comparison of actual measured (Stoneville ≤≠≠≥; Houma ≤≠≠≥) and historic average

evaporation data (Stoneville ∞Ωππ–≤≠≠≤; Houma ∞Ωππ–≤≠≠≤).

evaporation fluctuates slightly around themean value of ∑ mm with a small declineat the end of the study period, while theactual measured pan evaporation is muchmore variable. Range and variance valuesare considerably different for historic aver-age and actual pan evaporation, signifyingthe fact that average pan evaporation de-picts neither low nor high pan evaporationvalues accurately (Table ∞). This indicatesthat the average daily pan evaporation rec-

ord poorly expresses the specific variabilityof actual daily pan evaporation as dictatedby fluctuating weather conditions.

Estimation error can be significantwhen daily differences between historicaverages and actual measured pan evap-oration are cumulatively summed over anumber of days. The cumulative differ-ences are important criteria for identifica-tion of continuous dry periods that are as-sociated with drought conditions.


Table ∞. Comparison between actual and historic pan evaporation for coastal and inland

stations (mm).

Stoneville, MS Houma, LA

Actual ≤≠≠≥ Historic Actual ≤≠≠≥ Historic

Mean ∑.≤∑ ∑.∑≤ ∂.≠∏ ∂.∑∂

Minimum ≠.π∏ ≤.πΩ ≠.≤∑ ≤.π∞

Maximum ∞≠.∞∏ π.≥π ∞≠.∞∏ ∏.∫≠

Range Ω.∂≠ ∂.∑π Ω.Ω≠ ∂.≠Ω

Std. Deviation ∞.∫∑ ∞.∞∞ ∞.∫≠ ≠.π≤

Variance ≥.∂∂ ∞.≤∑ ≥.≤≥ ≠.∑≤

Finally, an important aspect of the panevaporation estimation technique adoptedin this research is the recognition of differ-ences in pan evaporation rates between in-land and coastal environments. In general,pan evaporation rates are higher inlandthan in the coastal zone (Wax and Pote∞ΩΩ∏). This fact was initially confirmed byvisual comparisons of means for actual andhistoric pan evaporation at Houma, Loui-siana (coastal) and Stoneville, Mississippi(inland) stations (Table ∞). In addition,vapor pressure deficits were calculated forGulfport (coastal) and Tupelo (inland),MS, using ≥:≠≠ pm observation each July∞∑ from ∞ΩΩ∂ to ≤≠≠∏. The average vaporpressure deficit at the coastal location was∞∂.∂≤ mb, and at the inland location was≤∞.∏≠ mb, indicating that evaporation po-tential at coastal location is only about ∏πpercent of that at the inland location.

MethodsThe study was carried out in three

major stages. The first stage focused onthe development of simple, representativeregression models, capable of estimat-ing daily pan evaporation for inland andcoastal environments in the study region.

The second stage included the selection ofthe ‘best inland model’ (BIM) and the ‘bestcoastal model’ (BCM). The third stage in-volved resolving whether modeled panevaporation rates are more accurate thanavailable historic averages. These threemajor stages are illustrated in more detailin the methodology flowchart (Figure ∂).Finally, each selected ‘‘best’’ model wasvalidated through an assessment of thesemodels’ accuracy when compared to ac-tual measured pan evaporation.

Stage One: Model Development. Weatherdata used to develop and validate regres-sion models were obtained from obser-vation networks of the National WeatherService, the Louisiana Agriclimatic Infor-mation Center (http://www.lsuagcenter.com/weather/), the Mississippi StateUniversity Extension Service (http://ext.msstate.edu/anr/drec/), and the Univer-sity of Utah ‘Meso West’ weather service(http://www.met.utah.edu/mesowest/).Data collected included daily observationsof pan evaporation (inches), maximumtemperature (Fahrenheit degrees), mini-mum relative humidity (percent), solarradiation (langleys), and wind speed

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(miles per hour) from July ∞ through Oc-tober ≥∞ for ≤≠≠≤, ≤≠≠≥, and ≤≠≠∂. Datafrom these three years provided the mostcomplete record of combined meteorologi-cal data and pan evaporation data avail-able at the most sites in the region. Therelatively short analysis period (July–October) was selected to represent peri-ods of highest evaporative demand in theregion. During the months from Julythrough October irrigation demands, cropyield, fire hazard, and ground water de-pletion/replenishment are impacted mostseverely and this is the period when esti-mating pan evaporation is most useful.While it would have been advantageous toinclude data from a longer time period,thereby increasing the number of observa-tions used to fit the models, these datawere considered representative of the nor-mal range of conditions expected in thesouthern gulf region. According to the Na-tional Climatic Data Center Mississippi,Alabama, and Louisiana experienced arange of conditions, slightly below orabove normal in terms of temperature andprecipitation between ≤≠≠≤ and ≤≠≠∂.The limited availability of complete dataalso re-emphasizes the problem addressedby this study; lack of a consistently avail-able source of evaporation data.

The accuracy of pan evaporation esti-mation depends greatly on the quality ofmeasured pan evaporation data as well asthe statistical properties of the other mete-orological variables used to develop mod-els. Even though the data acquired for themodeling period were the most spatiallyand serially complete, numerous problemswere still evident. For this reason, thedata obtained were carefully examined be-fore the modeling was attempted. The ma-jor data drawback observed was that seri-

ally complete and homogeneous data wereoften not available—weather stations inthe study area do not consistently ob-serve and archive similar elements. Also,daily pan evaporation records did not corre-spond with other measured meteorologicalvariables due to difference in time of obser-vation. Finally, numerous daily observa-tions were either missing or incorrect.

Therefore, prior to the analysis, threedata quality and variable properties issueswere addressed. First, daily pan evapora-tion records were modified to correspondwith other measured meteorological vari-ables that differ in time of observation. Forexample, observations for temperature andminimum relative humidity usually occurthe day before morning observations, notat the time of observation. Total solar radi-ation is summed over the period from mid-night to midnight on the same day thatmaximum temperature, minimum relativehumidity, and maximum wind speed arerecorded. Also, evaporation is recorded atsome sites over a ≤∂-hour period from mid-night to midnight on the day following theday of record for the other meteorologicalobservations. Consequently, prior to mod-eling, pan evaporation measurements atthese sites were shifted back by one day toinsure consistency of observation period.Second, missing or obviously incorrectmeteorological values (these not fittingwithin the range of normals) were identi-fied and replaced with an average valuecalculated using records for the precedingand the following day. In general, less than∂ percent of pan evaporation data requiredediting (Wax and Pote ∞ΩΩ∏). Third, fourmajor assumptions of multiple linear re-gression were tested. These assumptionsincluded normal distribution of variables,assumption of a linear relationship be-


tween independent and dependent vari-ables, variable measurement reliability,and assumption of homoscedasticity.

Using the corrected data sets, multiplelinear regression (MLR) was used to de-velop evaporation models. Daily pan evap-oration data for the years ≤≠≠≤ and ≤≠≠∂were used as the dependent variable;≤≠≠≥ data were used later for validation.Maximum air temperature, minimum rel-ative humidity, and solar radiation for thecorresponding years were used as inde-pendent variables. An ‘all possible com-binations’ approach was used to assessvariable relationships and variable inter-actions’ contribution to pan evaporationpredictions. From this approach, the opti-mal variable set was chosen on the basisof evaluation of adjusted R-square (RSQ)values and tests of assumptions for MLR.R-square is the coefficient of determina-tion and is the proportion of variability ina data set that is accounted for by a statis-tical model. Adjusted RSQ is a modifica-tion of RSQ that adjusts for the number ofexplanatory terms in a model. Unlike RSQ,the adjusted RSQ increases only if thenew term improves the model more thanwould be expected by chance. For, the op-timal set of variables, outlier analysis wasperformed by assessing the values of thestandardized residuals (e.g. values ] ≤.≠and values [ –≤.≠) and using Cook’s Doutliers were removed from the data sets(Fox ∞ΩΩπ).

Models were created for Louisiana sta-tions (Ben Hur, Houma, Calhoun), Missis-sippi stations (Stoneville, Newton), andone Alabama station (Fairhope). Theseweather stations measure and archivedaily pan evaporation that could be usedfor model fitting and cross-validation (Fig-ure ≤). These locations were also selected

on the basis of weather data availability forthe years ≤≠≠≤, ≤≠≠≥, and ≤≠≠∂, and to sat-isfy the spatial requirements for selectivelyestimating pan evaporation for both inlandand coastal environments. Inland modelswere developed using Stoneville, Newton,Calhoun, and Ben Hur data, while coastalmodels were developed with Houma andFairhope data.

Many weather stations only record asubset of the potential independent vari-ables (Figure ∞). In order to select the opti-mal combination of weather elements forboth inland and coastal locations, two dif-ferent ‘‘modeling approaches’’ were used.Approach A incorporated the optimal vari-able set selected on the basis of evaluationof adjusted RSQ. Approach B integratedonly the two most commonly available ele-ments as input variables—minimum rela-tive humidity and maximum air tempera-ture. Solar radiation was not included inthe approach B models, since it is availableonly at a limited number of weather sta-tions. Approach B requires the fewest num-ber of variables, and models developedunder this approach were compared withactual pan evaporation values to assess po-tential model under-fitting problem. Aslightly under-fit model can be imple-mented at many locations that would notbe used due an incomplete suite of explan-atory variables.

Stage Two: Model Selection. Ultimately, thebest inland and coastal models were se-lected to estimate pan evaporation forthese two distinctively different environ-ments. Modeled and historic evaporationrates were then tested against the actual≤≠≠≥ measured pan evaporation in orderto determine the most accurate method ofestimating evaporation.


Table ≤. Model performance measures, description, ranking, weights, and standardized values.

Performance

measure Description Rank Weight

Ideal

value

Standardized

value

RSQ Explains the variance in the data.

The higher the RSQ value the more

versatile the model is.

∞ ≠.∑ ∞ RSQ

CC Indicates trend agreement (model

conformity) between actual and

modeled evaporation.

The higher the CC value the better

model conforms with actual.

Can have trend agreement, but

different value range.

≤ ≠.∞≤∑ ∞ CC

AVG Overcomes CC limitations of range

value.

≤ ≠.∞≤∑ ≠ ∞-|AVG*∞≠|

RMSE Accepted standard model accuracy

evaluation measure.

≤ ≠.∞≤∑ ≠ ∞-RMSE*∞≠

MAE Accepted standard model accuracy

evaluation measure.

≤ ≠.∞≤∑ ≠ ∞-MAE*∞≠

The second stage of the research in-volved the selection of the best inlandmodel (BIM) and the best coastal model(BCM). Inland and coastal models wereevaluated separately. Each potential modelwas evaluated by comparing the predic-tion results against actual pan evaporationmeasured in ≤≠≠≥. Inland models wereevaluated against Stoneville ≤≠≠≥ panevaporation data and coastal models wereevaluated against Houma ≤≠≠≥ pan evap-oration data. Both of these datasets werethe most complete in the analyzed period.

The following performance measureswere used to compare the predicted andmeasured pan evaporation. RSQ was usedto measure how well each linear model un-der consideration fit the weather data tothe measured pan evaporation data. Pear-

son’s correlation coefficient (CC), averagedifference (AVG), root mean-squared error(RMSE), and mean absolute error (MAE)were used to measure how modeled pre-dictions departed from the actual panevaporation measurements. These per-formance measures were employed for allmodels in the initial inland and coastalscreening groups and were used to com-pare each model to a hypothetical ‘‘per-fect’’ model described with the followingattributes: RSQ value = ∞, RMSE and MAEvalues = ≠, CC value = ∞, and AVG value =≠. The performance measures were ordi-nated and weighted according to their per-ceived significance, and actual values werestandardized (scaled between ≠–∞) to rep-resent uniform value ranges as shown inTable ≤. The perfect model for stage two


(PM≤) can therefore be expressed with thefollowing formula:

PM≤=≠.∑ (RSQ) + ≠.∞≤∑ (CC) +≠.∞≤∑ (∞-∞≠|AVG|) + ≠.∞≤∑ (∞-∞≠RMSE) + ≠.∞≤∑ (∞-∞≠ MAE) = ∞ (∞)

The model RSQ that describes howwell the predicted ‘line’ fits the data wasconsidered the most important measureand assigned a weight of ≠.∑. The othermeasures (CC, |AVG|, RMSE, and MAE)measure the departure of the predictedpan evaporation values from the actualpan evaporation values. Individually, each‘departure’ measure is assigned a weightof ≠.∞≤∑ and collectively are weightedequally (sum = ≠.∑) to RSQ. The totalscore for the perfect model is equal to ∞,and scores for other models were calcu-lated according to the same formula asshown above using the standardized mea-surement values (Table ≤). The calcu-lated scores were then compared, andmodels with highest scores were selectedfrom inland and coastal screening groupsrespectively.

Stage Three: Model Comparison with His-toric Average. The third stage evaluatedwhether modeled pan evaporation ratesmore accurately track actual pan evap-oration than available historic averages.While it is expected that modeled daily panevaporation rates should track actual dailypan evaporation rates better than historicaverages, historic pan evaporation is cur-rently used as an input in various models(Cothren et al. ≤≠≠∞; Ruley and Rusch≤≠≠∂; Enciso and Wiedenfeld ≤≠≠∑).

Values for the performance measuresfrom the best-selected models and per-formance measures calculated for the his-toric averages were used to validate the

premise that modeled pan evaporationvalues are better estimates of daily evap-oration than historic average values forpan evaporation. Determination of the hy-pothetical ‘‘perfect’’ model for stage three(PM≥) did not include RSQ since historicdata are actual pan evaporation measure-ments and not estimated by fitting a modelto the data. All performance measureswere weighted equally in stage three, andthe following formula was used:

PM≥ = ≠.≤∑ (CC) + ≠.≤∑ (∞-∞≠|AVG|)+ ≠.≤∑ (∞-∞≠ RMSE) + ≠.≤∑ (∞-∞≠MAE) = ∞ (≤)

The estimation method (modeled oraverage historic values) that yielded thehighest overall score and therefore themost accurate substitute for measured panevaporation was selected.

Model ValidationThe final phase of the study examined

how closely model-estimated pan evap-oration from the ‘best’ coastal and inlandmodels approximated actual measuredpan evaporation. To accomplish this, ac-tual ≤≠≠≥ measured pan evaporation wascompared with estimated pan evaporationderived from the ‘best’ models for valida-tion. Modeling output units are inches andwere later converted to millimeters for thepurpose of this study.

results and discussion

Stage One: Model DevelopmentMultiple linear regression is a paramet-

ric analysis technique that was used to pre-dict pan evaporation. While several as-sumptions that should be considered whenusing MLR were evaluated, it should benoted that moderate violations of para-


metric assumptions have little or no effecton substantive conclusions in most in-stances (Cohen ∞Ω∏Ω).

The Kolmogorov-Smirnov test (K-S)enables comparison of each independentvariables’ distribution with the theoreti-cal normal distribution. The test statistic(Smirnov Z) is computed from the largestdifference (in absolute value) between theindependent variables distribution andthe normal distribution. This test assesseswhether the observations of the indepen-dent variable could reasonably have comefrom the normal distribution. Solar radi-ation showed evidence of a negativelyskewed distribution and the K-S test re-sulted in confirmation of a non-normaldistribution. Transforming solar radiationusing a standard variable normalizationtechnique (Equation ≥) for the Ben Hur≤≠≠≤ and ≤≠≠∂ data sets resulted in in-creases of approximately ≠.≠∞ in adjustedRSQ value and consequently, the decisionwas made not to transform solar radiation.K-S variable normality tests for maximumtemperature and minimum relative hu-midity revealed that both variables werenormally distributed with one exception;the Newton ≤≠≠∂ dataset where all threevariables (maximum temperature, mini-mum relative humidity, and solar radia-tion) were determined to be non-normal.

newvalue = �((max value + ∞) – SRi)(≥)

An Analysis of Variance (ANOVA) testof linearity was performed for all pairwisecombinations of pan evaporation and eachindependent variable. The hypothesis thatthe relationship between each variableand pan evaporation was linear was notrejected for all datasets at all locationsfor solar radiation, maximum tempera-

ture, and minimum relative humidity. Thehypothesis was rejected for wind speed forall datasets at all locations. The lack of alinear relationship between wind speedand pan evaporation is further evidencedby examination of the simple scatter plots.The scatterplot for the Newton ≤≠≠∂ dataset (Figure ∑) is typical of the relationshipbetween wind speed and pan evaporationfor all datasets at all locations.

A useful coefficient for assessing inter-nal consistency of a variable’s measure-ment scale is Cronbach’s alpha (Cronbach∞Ω∑∞). Cronbach’s alpha was estimatedfor standardized variable scales. Nunnally(∞Ωπ∫) has indicated values of ≠.π andabove are an acceptable level of reliability.Measurement scale reliability was gener-ally high (near or above the ≠.π threshold)for solar radiation, maximum tempera-ture, and minimum relative humidity forall datasets at all locations with a few ex-ceptions. Cronbach’s alpha values werebelow ≠.π for maximum temperature atBen Hur ≤≠≠∂ (≠.∑∂), and Calhoun ≤≠≠∂(≠.∏∞). Cronbach’s alpha values were be-low ≠.π for minimum relative humidity atFairhope ≤≠≠∂ (≠.∂Ω) and Houma ≤≠≠∂(≠.∏∂).

Homoscedasticity assumes that thevariance of errors is the same across alllevels of the Independent Variable (IV). Ex-amination of plots of the standardized re-siduals (y-axis) by the regression standard-ized predicted value (x-axis) indicatedthat, in general, residuals were randomlyscattered around ≠ providing a relativelyeven distribution and no evidence of het-eroscedasticity. Plots for solar radiation de-viated slightly from a random scattering,probably due in part to the negative skewof the variable.

Multicollinearity in regression models

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Table ≥. Simple Linear Regression (SLR) R square (RSQ) values and all possible regression combinations for

Multiple Linear Regression (MLR) with adjusted R square (ARSQ) listed.

Ben Hur Stoneville FairhopeModel name/

model

combinations ≤≠≠≤ ≤≠≠∂

Calhoun

≤≠≠∂

Newton

≤≠≠∂ ≤≠≠≤ ≤≠≠∂ ≤≠≠≤ ≤≠≠∂

Houma

≤≠≠∂

Temp RSQ ≠.∂≥≤ ≠.∞≥∑ ≠.∞Ω∞ ≠.∞∫π ≠.∑∫≤ ≠.≤≤∑ ≠.∂≥∫ ≠.∑≠Ω ≠.≤∑π

RH RSQ ≠.∂∫∏ ≠.∂π∞ ≠.∞∏∏ ≠.∂∞∫ ≠.∂ΩΩ ≠.≤∏∞ ≠.∂≠≥ ≠.∞∑∫ ≠.≤∏∑

SRad RSQ ≠.∏Ω∂ ≠.∏≤π ≠.∑∫∫ ≠.π∂π ≠.∏∑∑ ≠.∑∂∂ No data No data ≠.≥≠∞

Wind RSQ ≠.≠≠≥ ≠.≠≤∑ ≠.≠≠∑ ≠.≠≠≠ ≠.≠≠≠ ≠.≠≠∂ No data No data ≠.≠≥∂

Temp/RH ARSQ ≠.∏∞∏ ≠.∂∫∏ ≠.≥π≤ ≠.∑∞∑ ≠.∏π∑ ≠.∂≤∞ ≠.∑∏∞ ≠.∑∫Ω ≠.≥π∏

Temp/Srad ARSQ ≠.∏Ωπ ≠.∏≤π ≠.∏∞∫ ≠.π∑≤ ≠.∏Ω∫ ≠.∑∂≠ No data No data ≠.∂≠≤

RH/SRad ARSQ ≠.∏∫∏ ≠.∏≤∑ ≠.∑∫π ≠.π∂∂ ≠.∏∫∑ ≠.∑∫∫ No data No data ≠.≥∞≠

Temp/RH/SRad ARSQ ≠.∏Ω∑ ≠.∏≤π ≠.∏∞∑ ≠.π∑≠ ≠.π≤≥ ≠.∑Ω∑ No data No data ≠.∂≠∫

is evidenced by a high level of intercorre-lation among independent variables. TheVariance Inflation Factor (VIF) is oftenused as a measure of the degree multi-collinearity of a particular independentvariable. As a rule of thumb, a VIF greaterthan ∂.≠ indicates when multicollinearityof a particular independent variable be-comes problematic (Belsley ∞ΩΩ∞). Forthis study, VIF values for all full models(maximum temperature, minimum rela-tive humidity, and solar radiation) werecalculated and evaluated. All VIF valuesfor independent variables were less than∂.≠ with one exception, Ben Hur ≤≠≠≤. Forthis dataset the VIF for solar radiation was∑.∏Ω. On the basis of these results, multi-collinearity was not determined to be anoteworthy problem.

Four independent variables were ini-tially considered as independent variablesfor modeling pan evaporation. The hy-pothesis that the relationship betweenwind speed and pan evaporation was lin-ear was rejected for every location andevery year. These results indicate that, forthese stations and these data, wind speed

has a random effect on pan evaporation.This finding coupled with low RSQ forwind speed (e.g. ≠.≠≥∂) led to the conclu-sion that wind speed should be eliminatedas a potential independent variable.

Using the three remaining indepen-dent variables, the ‘‘all possible combi-nations’’ analyses enabled assessment ofrelationships between each variable andvariable combinations with pan evapora-tion (Table ≥). Solar radiation and maxi-mum air temperature showed strong posi-tive relationships with evaporation. Theanalyses also confirmed an inverse rela-tionship between minimum relative hu-midity and measured pan evaporation.

Solar radiation had the highest RSQamong all variables and this result is con-sistent with previous studies (Sumner andJacobs ≤≠≠∑). Marginal improvementswere noted when maximum temperatureor minimum relative humidity were com-bined with solar radiation. In general,highest adjusted RSQ values were ob-tained when all three variables were in-cluded. On the basis of these analyses, itwas determined that when all three vari-


Table ∂. MLR results of inland and coastal models (the highlighted models were further evaluated).

Station App. Year Rsq B Temp. Rel. hum. Solar rad.

Stoneville A ≤≠≠≤ ≠.π≥≠ –≠.≠∂∞≤πΩ∫ ≠.≠≠≤π∑∂ –≠.≠≠∞∂≠∫ ≠.≠≠≠≤π≥

Stoneville B ≤≠≠≤ ≠.∏∫∞ –≠.≠∑∫≠∂π ≠.≠≠∂∏≥π –≠.≠≠≤≥≥∂ not used

Stoneville A ≤≠≠∂ ≠.∏≠∏ ≠.≥≤∏ ≠.≠≠∞∂π∑∞∏ –≠.≠≠∞∂∂∞∫ ≠.≠≠≠≤∫

Stoneville B ≤≠≠∂ ≠.∂π∑ –≠.∞≥Ω ≠.≠≠∏ –≠.≠≠≥ not used

Newton A ≤≠≠∂ ≠.π∑∏ –≠.≠πΩ∞≤ ≠.≠≠∞∞≠∂ ≠.≠≠≠≠π ≠.≠≠≠≥∏Ω

Newton B ≤≠≠∂ ≠.∑≤≥ ≠.≠≤π∫∫ ≠.≠≠≥∑∫∏ –≠.≠≠≥≤≥∏ not used

Calhoun A ≤≠≠∂ ≠.∏≤∑ –≠.∞∏≥ ≠.≠≠≤ ≠.≠≠≠≠∏Ω ≠.≠≠≠≥∫

Calhoun B ≤≠≠∂ ≠.≥∫≥ –≠.∞∏π ≠.≠≠∑ –≠.≠≠≥ not used

Ben Hur A ≤≠≠≤ ≠.π≠π –≠.∞∞≥∞πΩ ≠.≠≠∞Ω∏∑ –≠.≠≠≠∂≥∏ ≠.≠≠≠≥≤∂

Ben Hur B ≤≠≠≤ ≠.∏≤∏ –≠.∞∞π∑≤∫ ≠.≠≠∑∞∂π –≠.≠≠≤π≤≥ not used

Ben Hur A ≤≠≠∂ ≠.∏≥π –≠.≠∞π∑∂≥π ≠.≠≠∞≤∞Ω –≠.≠≠∏∑∫∑ ≠.≠≠≠≥∂∫

Ben Hur B ≤≠≠∂ ≠.∂Ω∑ ≠.∞∫∞ ≠.≠≠≤∂≥∑≥ –≠.≠≠≥∫ not used

Fairhope B ≤≠≠≤ ≠.∑∏Ω –≠.∞≤∫ ≠.≠≠∑ –≠.≠≠≤ not used

Fairhope B ≤≠≠∂ ≠.∑∫π –≠.∑∞ ≠.≠≠Ω –≠.≠≠≤ not used

Houma A ≤≠≠∂ ≠.∂≤π –≠.∂≠≤ ≠.≠≠π –≠.≠≠∞ ≠.≠≠≠≤≥

Houma B ≤≠≠∂ ≠.≥∫Ω –≠.≤∫∂ ≠.≠≠π –≠.≠≠≥ no data

ables are available, they should be usedfor modeling pan evaporation. However,when solar radiation is not available, com-bining temperature and relative humidityresulted in adjusted RSQ values that in-dicate both variables should be includedin the model. These results led to the de-velopment of tests of model efficacy fortwo different modeling approaches, withsolar radiation (Approach A) and with-out solar radiation (Approach B). Oncevariable combinations were determined,model comparisons were made using RSQrather than adjusted RSQ, since adjustedRSQ was only used to account for artificialinflation of potential variable combina-tions during the variable selection process.

Stage Two: Model SelectionInland and coastal models were initially

screened by RSQ values to reduce the totalnumber of models for evaluation (Table ∂).From all inland models, the followingsix were selected for further evaluation:Stoneville approach A ≤≠≠≤, Stoneville ap-proach B ≤≠≠≤, Newton approach A ≤≠≠∂,Newton approach B ≤≠≠∂, Ben Hur ap-proach A, and Ben Hur approach B ≤≠≠≤.From this group the best inland model(BIM) was selected using equation ∞. Per-formance measures calculated for thesemodels are shown in Table ∑. The initialscreening process for coastal models re-sulted in the selection of three models:Fairhope approach B ≤≠≠≤, Fairhope ap-


Table ∑. Decision-making calculations carried out to select best inland model (BIM);

weights (wght.) and standardized values (st.val.) are multiplied and then summed together (formula ∞);

values of performance measures are highlighted.

Performance measures

RSQ value CC AVG RMSE MAEInland

Models wght. st.val. wght. st.val. wght. st.val. wght. st.val. wght. st.val.

Total

score

w

Stoneville

app. A ≤≠≠≤

≠.π≥ ≠.∏≤ –≠.≠∑π ≠.≠∫≤ ≠.≠π≠

≠.∑ ≠.π≥ ≠.∞≤∑ ≠.∏≤ ≠.∞≤∑ ≠.∂∂ ≠.∞≤∑ ≠.∞∫ ≠.∞≤∑ ≠.≥≠ ≠.∑∑∫

Stoneville

app. B ≤≠≠≤

≠.∏∫ ≠.∂∑ –≠.≠≥∏ ≠.≠π∏ ≠.≠∏≥

≠.∑ ≠.∏∫ ≠.∞≤∑ ≠.∂∑ ≠.∞≤∑ ≠.∏∑ ≠.∞≤∑ ≠.≤∂ ≠.∞≤∑ ≠.≥π ≠.∑∑∂

Newton app.

A ≤≠≠∂

≠.π∏ ≠.∏∏ ≠.≠∞∂ ≠.≠∑∏ ≠.≠∂∞

≠∑ ≠.π∏ ≠.∞≤∑ ≠.∏∏ ≠.∞≤∑ ≠.∫∏ ≠.∞≤∑ ≠.∂∂ ≠.∞≤∑ ≠.∑Ω ≠.∏ΩΩ

Newton app.

B ≤≠≠∂

≠.∑≤ ≠.∂≤ ≠.≠∞∞ ≠.≠π∞ ≠.≠∑∑

≠.∑ ≠.∑≤ ≠.∞≤∑ ≠.∂≤ ≠.∞≤∑ ≠.∫Ω ≠.∞≤∑ ≠.≤Ω ≠.∞≤∑ ≠.∂∑ ≠.∑∞∏

Ben Hur

app. A ≤≠≠≤

≠.π∞ ≠.∏∑ –≠.≠∞π ≠.≠∑∫ ≠.≠∂≥

≠.∑ ≠.π∞ ≠.∞≤∑ ≠.∏∑ ≠.∞≤∑ ≠.∫≥ ≠.∞≤∑ ≠.∂≤ ≠.∞≤∑ ≠.∑π ≠.∏∏∂

Ben Hur

app. B ≤≠≠≤

≠.∏≥ ≠.∂∑ –≠.≠≠≥ ≠.≠∏Ω ≠.≠∑∏

≠.∑ ≠.∏≥ ≠.∞≤∑ ≠.∂∑ ≠.∞≤∑ ≠.Ωπ ≠.∞≤∑ ≠.≥∞ ≠.∞≤∑ ≠.∂∂ ≠.∑∫∏

proach B ≤≠≠∂, and Houma approach A≤≠≠∂ model. Performance measures deter-mined for these models are shown in Table∏. These measures, highlighted in Tables ∑and ∏, were used directly in the process ofselecting the best inland models (BIM)and best coastal (BCM) models.

The best inland and coastal modelswere selected based on performance mea-sure metrics using formula ∞. In gen-eral, the best model was specified bya combination of the following char-acteristics: high RSQ and correlationcoefficient values, low values of errormeasures, and a low value of average dif-ference. Tables ∑ and ∏ show the decision-making calculations and total scorescomputed for selected inland and coastalmodels.

The highest total score among inlandmodels was achieved by Newton approachA ≤≠≠∂ model (≠.∏ΩΩ). The optional model

(Ben Hur approach B ≤≠≠≤, ≠.∑∫∏ score)was selected for use at locations where so-lar radiation data are not available. There-fore, the following models are recom-mended for use at inland sites:With solar radiation: BIM=–≠.≠πΩ∞≤+≠.≠≠∞∞(maxT)+≠.≠≠≠≠π(minRH)+≠.≠≠≠≥π(SR)Without solar radiation:OBIM=–≠.∞∞π∑≤∫+≠.≠≠∑∞∑(maxT)–≠.≠≠≤π≤(minRH)

The highest total score among evalu-ated coastal models was achieved by Fair-hope approach B ≤≠≠∂ model (≠.∑πΩ). Anoptional coastal model was not selectedsince solar radiation was not available atany sites with pan evaporation records.For use in all coastal sites (no solar radia-tion data required), the following model isrecommended:BCM=–≠.∑∞+≠.≠≠Ω(maxT)–≠.≠≠≤(minRH)


Table ∏. Decision-making calculations carried out to select best coastal model (BCM); weights (wght.) and

standardized values (st.val.) are multiplied and then summed together (formula ∞);



RSQ value CC AVG RMSE MAECoastal

Models wght. st.val. wght. st.val. wght. st.val. wght. st.val. wght. st.val.

Total

w

Fairhope ≠.∑π ≠.∑∂ –≠.≠∂≤ ≠.≠π∂ ≠.≠∏≥

app. B ≤≠≠≤ ≠.∑ ≠.∑π ≠.∞≤∑ ≠.∑∂ ≠.∞≤∑ ≠.∑∫∑ ≠.∞≤∑ ≠.≤∏ ≠.∞≤∑ ≠.≥π ≠.∑≠∂

Fairhope ≠.∑Ω ≠.∑≠ –≠.≠≠Ω ≠.≠∏π ≠.≠∑∑

app. B ≤≠≠∂ ≠.∑ ≠.∑Ω ≠.∞≤∑ ≠.∑≠ ≠.∞≤∑ ≠.ΩΩ∞ ≠.∞≤∑ ≠.≥≥ ≠.∞≤∑ ≠.∂∑ ≠.∑πΩ

Houma app. ≠.∂≥ ≠.∑Ω –≠.≠π∞ ≠.≠Ω∂ ≠.≠∫≤

A ≤≠≠∂ ≠.∑ ≠.∂≥ ≠.∞≤∑ ≠.∑Ω ≠.∞≤∑ ≠.≤Ω∑ ≠.∞≤∑ ≠.≠∏ ≠.∞≤∑ ≠.∞∫ ≠.≥∑∏

Stage Three: Model Comparisonwith Historic AverageThe two best inland models and one

best coastal model were evaluated to de-termine whether modeled pan evapora-tion rates more accurately track actual panevaporation than available historic aver-ages. Table π shows performance measuresfor best-selected models versus historicaverage records as well as final scores cal-culated using formula ≤. The results indi-cate that for the best inland and coastalmodels, modeled estimates represent ac-tual pan evaporation better than historicaverages. These calculations indicated thatfor all ‘‘best’’ models, predicted pan evap-oration is superior to historic averages.

Model ValidationEach ‘‘best’’ model was compared to ac-

tual ≤≠≠≥-measured pan evaporation forvalidation purposes. Figure ∏A illustratesvalidation results of the best inland model(created based on Newton ≤≠≠∂ data us-ing approach A) by plotting model re-sults against pan evaporation measured atStoneville in ≤≠≠≥. This inland model uti-

lizes three variables: maximum air tem-perature, minimum relative humidity, andsolar radiation. If solar radiation dataare unavailable, the Ben Hur ≤≠≠∂ ap-proach B model, which utilizes only maxi-mum air temperature and minimum rela-tive humidity, should be used. Figure ∏Bshows the validation results of this op-tional inland model. The best coastalmodel was created based on Fairhope≤≠≠∂ data using approach B. This modeluses maximum air temperature and mini-mum relative humidity data only. Figure∏C illustrates validation results of themodel results plotted against pan evapora-tion measured at Houma in ≤≠≠≥. Overall,mean pan evaporation decreases duringthe fall months when daily temperaturebegins to decline. Since these models weredeveloped for periods when temperatureis high and precipitation is low, it is pos-sible (when temperature is low and mini-mum relative humidity is high) to estimatea negative value for pan evaporation. Thissituation occurred twice in the selectedcoastal model (Figure ∏C). To prevent thisoccurrence, negative model estimation


Table π. Evaluation calculations carried out to compare results of the best-selected models and historic averages;

weights (wght.) and standardized values (st.val.) are multiplied and then summed together (formula ≤);



CC AVG RMSE MAESelected

models/

Historic wght. st.val. wght. st.val. wght. st.val. wght. st.val.

Total

w

Newton ≠.∏∏ ≠.≠∞∂ ≠.≠∑∏ ≠.≠∂∞

app. B ≤≠≠∂ ≠.≤∑ ≠.∏∏ ≠.≤∑ ≠.∫∏ ≠.≤∑ ≠.∂∂ ≠.≤∑ ≠.∑Ω ≠.∏≥∫

Ben Hur ≠.∂∑ –≠.≠≠≥ ≠.≠∏Ω ≠.≠∑∏

app. C ≤≠≠≤ ≠.≤∑ ≠.∂∑ ≠.≤∑ ≠.Ωπ ≠.≤∑ ≠.≥∞ ≠.≤∑ ≠.∂∂ ≠.∑∂≤

Historic ≠.∂≤ –≠.≠∞≠∑ ≠.≠∏∫ ≠.≠∑∂

inland ≠.≤∑ ≠.∂≤ ≠.≤∑ ≠.∫Ω∑ ≠.≤∑ ≠.≥≤ ≠.≤∑ ≠.∂∏ ≠.∑≤∂

Fairhope ≠.∑≠ –≠.≠≠Ω ≠.≠∏π ≠.≠∑∑

app. C ≤≠≠∂ ≠.≤∑ ≠.∑≠ ≠.≤∑ ≠.ΩΩ∞ ≠.≤∑ ≠.≥≥ ≠.≤∑ ≠.∂∑ ≠.∑∏π

Historic ≠.≤≠ –≠.≠∞∫π ≠.≠π∂ ≠.≠∏≤

coastal ≠.≤∑ ≠.≤ ≠.≤∑ ≠.∫∞≥ ≠.≤∑ ≠.≤∏ ≠.≤∑ ≠.≥∫ ≠.∂∞∂

was constrained to equal zero, since nega-tive evaporation is not possible.

Validation of model results confirmedinitial expectations that pan evaporationrates predicted using selected models aresuperior to historic pan evaporation esti-mates. Modeled pan evaporation for bothinland and coastal models reflected actualchanges in daily weather conditions, whilehistoric averages did not (compare Figure≥ to Figures ∏A, B, and C).

conclusions

The goal of this research was to esti-mate daily pan evaporation using readilyavailable data at numerous locations forthe southeastern region of the U.S. wheresuch data are not routinely and consis-tently available. Although there is a largebody of literature that indicates wind iscorrelated to pan evaporation, these re-sults indicate a poor relationship for thesedatasets. This unexpected result might be

explained by the fact that in these south-ern regions, wind is often accompanied byhigh humidity and rainfall.

The multiple regression models devel-oped for this study combined actual mea-sured solar radiation, maximum tem-perature, and minimum relative humidityto estimate pan evaporation. Pan evap-oration estimations based on the best-selected models proved superior to avail-able historic average pan evaporationdata. As the number of input variables wasreduced, the accuracy of the models wasalso reduced. However, inclusion of allvariables as inputs significantly loweredthe number of stations that have the po-tential for such estimation due to dataavailability. It was concluded that mini-mum relative humidity and maximum airtemperature are the minimum requiredvariables necessary to create satisfactorymodels. Even though reducing the numberof input variables decreased model accu-racy, it increased the number of stations

0

2

4

6

8

10

12

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101

105

109

113

117

121

Evap

orat

ion

(mm

)

actual evaporation Stoneville 2003 estimated evaporation (based on Newton app. B 2004 model)

July October

-4

-2

0

2

4

6

8

10

12

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101

105

109

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121

Evap

orat

ion

(mm

)

actual evaporation Houma 2003 estimated evaporation (based on Fairhope app. C 2004 model) July October

0

2

4

6

8

10

12

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 101

105

109

113

117

121

Evap

orat

ion

(mm

)

actual evaporation Stoneville 2003 estimated evaporation (based on Ben Hur app. C 2004 model)

July October

A

B

C

Figure ∏. A. Comparison of actual measured (Stoneville ≤≠≠≥) evaporation and evaporation estimated

for Stoneville ≤≠≠≥ using best inland model (Newton approach B ≤≠≠∂); B. Comparison chart of

actual measured evaporation (Stoneville ≤≠≠≥) and evaporation estimated for Stoneville ≤≠≠≥ using

optional best inland model (Ben Hur approach C ≤≠≠∂); C. Comparison chart of actual measured

evaporation (Houma ≤≠≠≥) and evaporation estimated for Houma ≤≠≠≥ using best coastal model

(Fairhope approach C ≤≠≠∂).


with weather data available for modelingpan evaporation. Maintaining a greaternumber of stations is considered of criticalimportance to the overall project goal, asit assures a large number of points areavailable for interpolation of evaporationacross the entire region—important forthe creation of dynamic water budgetlayers useful in GIS-based water budgetapplications. Regional climatic heteroge-neity associated with coastal and inlandprocesses are better characterized withthese ‘best’ models. It is likely that withthe increased number of stations availablefor interpolation, climatic heterogeneitydue to landscape characteristics will bebetter measured.

The best pan evaporation predictionmodels were selected using a combinationof different performance characteristics,as neither RSQ values nor error measuresalone were determined to be satisfactoryindicators of the best model. The decision-making process, as validated by compari-son of predicted and actual pan evapora-tion rates, produced three easily-appliedmodels—two inland and one coastal—thatappear to provide reliable and useabledaily pan evaporation estimates. Modelchoice depends on whether or not solarradiation data are available for use at aninland site. These selected best models aresimple to use since they require minimalinputs and they are easy to update on adaily basis. Thus the models offer theopportunity to effectively estimate dailypan evaporation at multiple locations overa broad region using the best available in-put data.

The number of metrics employed in cre-ating, testing, and validating selectedmodels yields results that provide rigorousand credible estimates of pan evaporation.

Use of these models results in pan evapo-ration estimates comparable to measuredpan evaporation. In fact, it is possible thatthe predicted pan evaporation rates mayproduce a more useful regional assessmentof evaporation because they are relativelyfree from recording errors or missing val-ues, issues commonly found in measuredand recorded pan evaporation data.

There are several model limitationsand potential improvements that shouldbe considered. The performance of coastalmodels could be improved by expand-ing the analysis region to include moreweather stations that record solar radia-tion and develop more Approach A modelsfor coastal environments. Also, it is notknown how well the models will performover time. The models should be continu-ously validated over time with actual panevaporation data where available. Avail-able records of actual pan evaporationthat extend beyond the July–October timeperiod should be compared with model-based estimates of pan evaporation to as-sess the precision of pan evaporation es-timates that are extrapolated beyond themodel development time period.

Evaporation derived from the Penmanmethod could be used for further evalua-tion of the selected models’ performance.The basic relationships between these vari-ables and pan evaporation are not ex-pected to undergo significant change overtime; however, the coefficients couldchange in response to changing climaticconditions. Consequently, models shouldbe recalibrated as more quality pan evap-oration and weather station data becomesavailable. Additional analyses are plannedthat examine vapor pressure deficit as apossible substitute for minimum relativehumidity in the models and for determin-


ing the extent of coastal influences overthe inland environment. Analyses are alsoplanned to compare predicted values athigher spatial densities with interpolatedvalues from pan evaporation stations only.

Results of this study indicate that evap-oration can be predicted at numerous loca-tions with a few easy-to-obtain variables.This method of estimating missing or spa-tially deficient daily pan evaporation datashould prove useful in regional GIS-basedapplications where a well-distributed pat-tern of stations used to estimate evapo-ration helps characterize the influence ofconvective precipitation events and coastalprocesses on evaporation.

references

Bell, C.L. ≤≠≠∂. Synthesis of a serially complete

and homogeneous evaporation data set for

the Southeastern region of the United States.

Department of Geosciences, Mississippi

State University.

Belsley, D.A. ∞ΩΩ∞. A guide to using the

collinearity diagnostics. Computer Science

in Economics and Management ∂:≥≥–∑≠.

Blaney, H.F., and W.D. Criddle. ∞Ω∑≠.

Determining water requirements in irrigated

areas from climatological and irrigation

data. ed. USDA, ∂∫. Washington, D.C.: U.S.

Soil Conservation Service.

Bruton, J.M., G. Hoogenboom, and R.W.

McClendon. ≤≠≠≠a. A comparison of

automatically and manually collected pan

evaporation data. Transactions of the Asae

∂≥:∞≠Ωπ–∞∞≠∞.

Bruton, J.M., R.W. McClendon, and G.

Hoogenboom. ≤≠≠≠b. Estimating daily pan

evaporation with artificial neural networks.

Transactions of the Asae ∂≥:∂Ω∞–∂Ω∏.

Cahoon, J.E., J.A. Ferguson, and T.A. Costello.

∞ΩΩ∞. Estimating evapotranspiration using

limited meteorological observations.

Agricultural and Forest Meteorology ∑∑:∞∫∞–

∞Ω≠.

Cohen, J. ∞Ω∏Ω. Statistical power analysis for the

behavioral sciences. New York: Academic

Press.

Cothren, G.M., S. Chen, M. Rahman, and

R. Malone. ≤≠≠∞. Hydrologic modeling of

aquatic plant treatment systems polishing

dairy lagoon effluents. Journal of

Environmental Science and Health Part

a-Toxic/Hazardous Substances &

Environmental Engineering ≥∏:∞Ω≠∑–∞Ω∞π.

Cronbach, L.J. ∞Ω∑∞. Coefficient alpha and the

internal structure of tests. Psychometrika

∞∏:≤Ωπ–≥≥∂.

Enciso, J., and B. Wiedenfeld. ≤≠≠∑. Irrigation

guidelines based on historical weather data

in the Lower Rio Grande Valley of Texas.

Agricultural Water Management π∏:∞–π.

Fox, J. ∞ΩΩπ. Applied regression analysis, linear

models, and related methods. Thousand

Oaks, Calif.: Sage Publications.

Graumann, A., T. Houston, J.H. Lawrimore,

D. Levinson, N. Lott, S. McCown,

S. Stephens, and D. Wuerts. ≤≠≠∑.

Hurricane Katrina Climatological

Perspective. Preliminary Report ∞-≤∫.

Asheville, NC NOAA’s National Climatic

Data Center.

Hanson, C.L. ∞Ω∫Ω. Prediction of Class A pan

evaporation in southwest Idaho. J. Irrig.

Drain. Eng. ASCE ∞∞∑(≤):∞∏∏–∞π∞.

Hijmans, R.J., S.E. Cameron, J.L. Parra, P.G.

Jones, and A. Jarvis. ≤≠≠∑. Very high

resolution interpolated climate surfaces for

global land areas. International Journal of

Climatology ≤∑:∞Ω∏∑–∞Ωπ∫.

Jones, F.E. ∞ΩΩ≤. Evaporation of water: with

emphasis on applications and measurements

Chelsea, Michigan: Lewis Publishers.

Keskin, M.E., O. Terzi, and D. Taylan. ≤≠≠∂.

Fuzzy logic model approaches to daily pan

evaporation estimation in western Turkey.


Hydrological Sciences Journal-Journal Des

Sciences Hydrologiques ∂Ω:∞≠≠∞–∞≠∞≠.

Lindsey, S.D., and R.K. Farnsworth.∞ΩΩπ.

Sources of solar radiation estimates and

their effect on daily potential evaporation

for use in streamflow modeling. Journal of

Hydrology ≤≠∞:≥∂∫–≥∏∏.

Nunnally, J.C. ∞Ωπ∫. Psychometric theory. New

York: McGraw-Hill.

Penman, H.L. ∞Ω∂∫. Natural evaporation from

open water, bare soil, and grass. In Proc.

Roy. Soc. London ∞≤≠–∞∂∏.

———. ∞Ω∑∏. Estimating Evapotranspiration. Trans

American Geophysical Union ≥π:∂≥–∂∏.

———. ∞Ω∏≥. Vegetation and hydrology. In Tech.

Comm., ∞≤∑. Harpenden, England:

Commonwealth Bureau of Soils.

Pote, J.W., and C.L. Wax. ∞Ω∫∏. Climatological

Aspects of Irrigation Design Criteria in

Mississippi. In Mississippi Agricultural and

Forestry Experiment Station Technical

Bulletin Mississippi State University:

Mississippi State, MS.

Ruley, J.E., and K.A. Rusch. ≤≠≠∂. Development

of a simplified phosphorus management

model for a shallow, subtropical, urban

hypereutrophic lake. Ecological Engineering

≤≤:ππ–Ω∫.

Shuttleworth, W.J. ∞ΩΩ≥. Evaporation. In

Handbook of Hydrology, ed. D. R.

Maidments. McGraw-Hill.

Sumner, D.M., and J.M. Jacobs. ≤≠≠∑. Utility

of Penman-Monteith, Priestley-Taylor,

reference evapotranspiration, and pan

evaporation methods to estimate pasture

evapotranspiration. Journal of Hydrology

≥≠∫:∫∞–∞≠∂.

Terzi, O., and M.E. Keskin. ≤≠≠∑. Modeling of

Daily Pan Evaporation. Journal of Applied

Sciences ∑:≥∏∫–≥π≤.

Thornthwaite, C.W. ∞Ω∂≤. Measurement of

evaporation from land and water surfaces,

Washington, D.C.: U.S. Dept. of Agriculture.

∞∂≥ p.

———. ∞Ω∂∫. An approach toward a rational

classification of climate. New York:

American Geographical Society.

Thornthwaite, C.W., and J.R. Mather.∞Ω∑∑. The

Water Balance. Publications in Climatology

VIII (∞):∞–∞≠∂.

Wax, C.L., and J.W. Pote. ∞ΩΩ∏. The influence

of climate on design of systems for land

application of wastewater. Climate Research

∏:π∞–π∫.

william h. cooke iii is an Assistant

Professor in the Department of Geosciences

and GeoResources Institute at Mississippi

State University, Mississippi State, MS ≥Ωπ∏≤.

Email: whc∑@geosci.msstate.edu. His research

interests include remote sensing, GIS

multicriteria analysis, fire potential

modeling, and vector-borne diseases.

katarzyna grala is a Research Associate

in the Department of Geosciences and

GeoResources Institute at Mississippi State

University, Mississippi State, MS ≥Ωπ∏≤. Email:

[email protected]. Her research

interests include GIS multicriteria analysis,

natural resources management, fire potential

modeling, and vector-borne diseases.

charles l. wax is a State Climatologist and

Professor of Geography in the Department of

Geosciences at Mississippi State University,

Mississippi State, MS ≥Ωπ∏≤. Email:

[email protected]. His research

interests include climatology, meteorology,

hydrology, and natural resources.

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