COMPARISON OF POTENTIAL EVAPOTRANSPIRATION MODELS ANDSOME APPLICATIONS IN SOIL WATER MODELING

R. de Jong1 and P. M. Higwood2

1Land Resource Research Institute, Agriculture Canada, Ottawa, Ont. K1A 0C6; and25 AmethystRd., Agincourt, Ont. M1T2E6

Contribution no. LRRI-85-51, received 29 April 1986, accepted 25 August 1986

de Jong, R. andP. M. Ttogwood. 1987. Comparison ofpotential evapotranspiration models and some applications insoil water modeling. Can. Agric. Eng. 29: 15-20.

Potentialevapotranspiration (PET) estimates from adjustedClass A pan data, from three physically based combinationmodels and from several versions of an empirical model were compared for selected regions in Canada. Both the Penmanand the Monteith model provided reasonable PET estimates at all stations when compared to the adjusted Class A pan data.The size of the convective term at stations with large vapor pressure deficits and high windspeeds suggests that a constantproportionality factor of 1.26 in the Priestley-Taylor model is inappropriate.The empirical Baier-Robertson model appearsto require regional calibrationfor improvedPETestimates. Actualevapotranspiration (AET), as calculated with a diffusionbased soil-water model and with a soil-water budget model, was insensitive to PET input, suggesting that the imposed soiland crop characteristics played a larger role in controlling AET than the PET regime.

INTRODUCTION

The concept of potential evapotranspiration (PET), defined by Penman (1956) as"the amount of water transpired in unittime by a short green crop, completelyshading the ground, of uniform height andnever short of water" has proven to be auseful one in agriculture and hydrology.Irrigation scheduling procedures, soil-water models and crop growth modelsgenerally first estimate PET from meteorological factors and then compute theamount of the potential that is utilized bythe actual evapotranspiration (AET) process, given the current status of the plant,and soil-water related characteristics.

Hydrologic models, concerned with streamflow forecasting, also require PET data.The effects of different PET estimatesas input to crop growth models and hydrologic models have been addressed byParmele (1977) and Dugas and Ainsworth(1985).

Direct measurements of PET from afull-cover, well-watered green crop can bemade with either lysimeters (Harrold1966) or with micro-meteorological techniques (Fritschen 1966; Goddard andPruitt 1966). However, because these methods are time consuming and/or expensive,PET is generally estimated from standardmeteorological data.

Measured evaporation from a standardClass A pan is one of the most commonmethods for estimating PET. Becauseevaporationfrom a pan is generally higherthan that from a well-watered surface(Pruitt 1966), empirically derived coefficients(Kp) are requiredto adjustpanevaporation to PET. Although specific Kpvalues for application to any given situation or pan may have to be found by cal

ibration, representative values from otherstudies can provide satisfactory results(Doorenbos and Pruitt 1977).

Physically based evapotranspirationmodels which incorporate both energy balance and aerodynamic principles are generally known as combination methods.Penman (1948, 1956) developed the firstcombination equation to calculate potential evaporation from an open water surface. With suitable refinements his model

now represents one of the most reliabletechniques for estimating PET from climatic data (Baier 1968; Shouse et al. 1980;Saxton and McGuinness 1982). Monteith(1965) generalized the Penman equationby specifying two resistances: (i) an aerodynamic resistance through the air to areference height and (ii) a physiologicalresistance from evaporating surfaces(stomates) to the air. The aerodynamicresistance is related to windspeed and surface roughness parameters (Szeicz et al.1969; Rijtema 1970) while the physiological resistance depends on factors suchas crop species, soil moisture availability,irradiance, humidity, etc. (Ziemer 1979).

Priestley and Taylor (1972) presented asimplified combination model by assuming that the radiant energy term of theoriginal Penman formula is, by itself,equivalent to an equilibrium rate of evaporation and proportional to PET. Experimental evidence (Davies and Allen 1973;Clothier et al. 1982) has shown that theaverage proportionality constant in non-advective, potential conditions is 1.26.

Meteorological data required for physically based evapotranspiration models isoften incomplete. Therefore, Baier andRobertson (1965) and Baier (1971) proposed a model for estimating daily PET

CANADIAN AGRICULTURAL ENGINEERING, VOL. 29, NO. 1, WINTER, 1987

from standard climatological observationsusing multiple-regression type equations.The regression coefficients in the modelwere derived from six stations located in

central and western Canada. Although nomaritime stations were included in the der

ivation of the coefficients, the model isextensively used throughout Canada,especially formula I.

The objective of this paper is to presenta comparison among computed PETvalues from (i) Class A pan data, (ii) thephysically based combination models and(iii)the empirical Baier-Robertson equations. Long-term climatic data fromselected regions in Canada will be used toanalyze differences in the models. Theeffect of the PET model upon the estimation of actual evapotranspiration (AET),i.e. under soil water stress conditions, willbe evaluated using a physically based soil-water diffusion model (Hayhoe and de Jong1982) and a more empirical based soil-water budget model (Baier et al. 1979).

METHODOLOGY

Eight meteorological stations representing the main climatic regions as well as theagricultural areas of Canada (Fig. 1) wereselected for this study. For each stationmean daily Class A pan evaporation valueswere extracted from the Monthly Recordof Meteorological Observations in Canadafor the period 1962-1980. Monthly averages were multiplied by pan coefficients,selected following guidelines presented byDoorenbos and Pruitt (1977). Seasonaltotals were then calculated for Maythrough September.

Complete climatological records asrequired to calculate PET according tovarious models were not available for

Figure 1. Map showing sites selected for this study.

TABLE I. SEASONAL CLIMATOLOGICAL CHARACTERISTICS AT THE STATIONS

Station

Climatologicalcharacteristic

Vancouver

UBC BeaverlodgeSwift

Current Winnipeg Harrow Ottawa Cookshire Truro

Map unit G1017 B2011 A1008 A3107 G1007 G1002 D3137 C2114

Class A pan evaporation(mm day ~') 3.9 5.2 7.4 6.3 5.7 4.8 3.7 3.8

Global solar radiation (W m ~ 2) 227.6 211.6 237.6 228.7 219.6 220.8 210.3 212.0

Mean air temperature (°C) 14.7 12.3 15.5 15.4 18.7 16.9 14.6 14.5

Vapor pressure deficit (1^) 260 390 600 480 500 490 280 290

Windspeed at 2 m height (km day~l) 188.8 239.0 377.9 290.9 224.6 192.9 206.6 212.5

Net radiation, Eq. 1 (Wm~2) 127.9 119.0 133.9 129.3 126.7 125.7 118.6 119.4

many stations. Therefore, monthly climatic normals (1951-1980) of solar radiation, maximum and minimum air temperature, vapor pressure and windspeed wereobtained from the Land Potential Data

Base (LPDB) (Kirkwood et al. 1983).Since all records in the LPDB are identi

fied by the soil map unit designations asfound on the Soils Map of Canada(Clayton et al. 1977), only the data fromthose map units whose geographical centerwas within 50 km of the meteorologicalstation were considered (Table I). Daily

16

values of global solar radiation, air temperature, vapor pressure and windspeedwere generated from the monthly normalsusing the Brooks (1943) sine wave interpolation technique for use in the modelsdescribed below.

The net radiation flux, which is arequired input for the physically basedevapotranspiration models, was calculatedfrom the radiation balance equation

Rn = (1 - r) Rs - Rln (1)

where Rs is the incoming global solar radi-

ation flux (obtained from the LPDB), Rlnis the effective outgoing longwave radiation flux and r is the surface reflection

coefficient (albedo). The latter was estimated to be 0.23, based on observed normal global solar and normal reflected solarradiation data (Environment Canada1982).

The net longwave radiation flux wasestimated using the empirical relationship(Jensen 1973)

Rln i'<rTk4(\ARs/Rso - 0.1) (2)

CANADIAN AGRICULTURAL ENGINEERING, VOL. 29, NO. 1, WINTER, 1987

where a is the Stefan-Boltzmann constantand Tk the air temperature indegrees Kelvin. Assumingthat the emittanceof a vegetated surface is 0.98 (Fuchs and Tanner1966), then the difference in emittancebetween surface and atmosphere, e\ wascalculated using Brutsaert's (1975) equation for atmospheric emissivity

e' = 0.98 - \.2A(e/Tk)in (3)

where e is the vapor pressure, obtainedfrom the LPDB.

The global solar radiation flux expectedon a perfectly clear day, Rso, was computed as

Rso = 221.2 + 162.1 sin(0.017 J + 4.956) (4)

where J is the Julian date and the argumentof the function is in radians. Equation 4was derived from data collected byDriedger (1969) at Winnipeg.

Potential Evapotranspiration Models

Penman ModelPenman (1948) combined the energy

balance and the aerodynamic equationsinto a combination model

PET •i[-A (Rn - G) + 7L£a

A + y(5)

where L is the latent heat of vaporization, 7is the psychrometerconstant, Rn is the netradiation flux (Eq. 1),and G is the soil heatflux. The latter was assumed to be negligible over the course of the growing seasonand was ignored in the calculation of PET.The aerodynamic term, £a, wascalculatedaccording to

£a = 0.26 (1.0 + 0.0062 Vim) (e* - e) (6)

where Vim is the windspeed at 2 mheight. Windspeeds at 2 m were approximated from recorded ones at 10 m in theLPDB, using U2m = 0.725 UlOm.Teten's equation (Murray 1967) was usedto calculate the saturated vapor pressure,e*, and its derivative, the slope of thesaturation vapor pressures - mean airtemperature curve, A.

Monteith model

Monteith (1965) modified Penman'smodel by including an aerodynamic and aphysiological resistance

PET -i[A(/?n - G) + pc(e* - e)/

HA + 7d + rjra)

where pc is the volumetric heat capacity ofdry air, ra is the aerodynamic diffusionresistance and rs is the physiological resistance assumed to be 40 s m~'. The aerodynamic resistance was calculated usingthe method proposed by Thorn and Oliver(1977)

(7)

ra = [4.72 (In 200/z0)2] / (1.0 + 0.54 U) (8)

wherez0, the surface roughness, wassetat1.0 cm and U is the windspeed expressedin ms"1.

Priestley-Taylor modelThe Priestley and Taylor model (1972)

was employed as a third method to compute potential evapotranspiration fromcombination theory

PET 4[« A + 7(Rn - G) (9)

where the constant a was assigned a valueof 1.26.

Baier and Robertson model

Baier and Robertson's (1965) multipleregression equations were used to calculatelatent evaporation. Eight formulas provided the estimates which were based on

extraterrestrial radiation, maximum airtemperature and air temperature range(formula I) and also on wind, vapor pressure and solar radiation, if data for anyone, two or three of these latter variableswere available (formulas II-VIII). Inthis way, efficient use was made of allavail

able meteorological data. A factor of0.0094cm cm-3, suggested by Baier(1971), was used to convert the results toPET.

Calculation of Actual

EvapotranspirationDaily potential evapotranspiration rates,

calculated from the various PET models,were used as input to a diffusion-basedsoil-water model (Hayhoe and de Jong1982) and a soil-water budget model (Baieret al. 1979). Daily precipitation data from 1May till 30 Sept. for 1975 at Swift Current,for 1976 at Harrow and for 1952 at Truro,obtained from the Monthly Record ofMeteorological Observations in Canada,were also used as input.

In the diffusion-based model a 100-cm

homogeneous soil profile was assumed tohave the soil characteristics of a clay loamas described by Clapp and Hornberger(1978). A unit hydraulic gradient (freedrainage) was applied across the basalboundary. Crop cover was assumed to be95% throughout the season, and the rootdensity function, RDF, was described by

RDF = 0.0051 exp (-0.02 Z) (10)

where Z is the depth in centimetres belowthe soil surface. The initial volumetric

water content of the profile was 40%,which corresponded to a soil water suctionhead of 16 kPa.

The Versatile Soil Moisture Budget

CANADIAN AGRICULTURAL ENGINEERING, VOL. 29, NO. 1, WINTER, 1987

(VSMB) was run with six standard zonesand a total available soil-water-holdingcapacity of 165 mm. Empirical cropcoefficients for brome grass were used. Inthe VSMB available soil water and theratio of actual to potential evapotranspiration (AET/PET) were related by standardempirical curves. In this studycurveGwasselected, which assumed that the ratioAET/PET remained at unity from 100 to70% available water, and reduced linearlyfor drying below this point to the permanent wiltingcondition. The soilprofile wasassumed to be at field capacity on 1 May,the date the runs were started.

RESULTS AND DISCUSSIONThe climatological conditions at the sta

tions, averagedover the period 1May to 30Sept., are presented in TableI. Class A panevaporation varied from 3.7 mm day~l atCookshire to 7.4 mm day_' at Swift Current. Variations in the radiation data(global solar and net radiation flux, as calculated per Eq. 1) were relatively smallamong the stations, but larger variationsoccurred in mean air temperature, vaporpressure deficit and windspeed data. Thestations on the prairies are characterized byhigh evaporation rates, large vapor pressure deficits and high windspeeds,whereas the maritime stations are charac

terized by low evaporation rates and smallvapor pressure deficits.

In the Penman and Priestley-Taylormodels, PET is solely determined bymeteorological features, whereas in theMonteith model surface factors or cropcharacteristics also play a role. As the surface roughness, which is considered to beproportional to crop height (Tanner andPelton 1960), increases, the aerodynamicresistance, ra, decreases and consequentlythe potential evapotranspiration rateincreases. Influencing this relationship arethe meteorological conditions themselves,as exemplified in Fig. 2 by the data fromthe stations at Vancouver UBC and Winni

peg, as well as the physiological resistancers. For wet canopies rs is thought to benegligible, but for a dry canopy, evenwhen the crop is well supplied with water,a minimum physiological resistanceshould be introduced to avoid overestima-

tions in PET (Bailey and Davies 1981).Apart from the soil moisture conditions, rsis dependent upon crop species, stage ofdevelopment and numerous environmentalfactors (Ziemer 1979). For grass well supplied with water,rs values range from 26 to60 sec m_1 (Szeicz and Long 1969;Russell 1980; De Bruin and Holtslag1982). For this study an rs value of 40 secm_1 was selected. At this resistance the

TABLE H. ACCUMULATED POTENTIAL EVAPOTRANSPIRATION (IN MILLIMETRES FROM 1MAY TO 30SEPTEMBER)

Station

Vancouver SwiftModel UBC Beaverlodge Current Winnipeg Harrow

649

Ottawa

552

Cookshire

422

Truro

Adjusted Class A pan 443 578 790 696 437

Penman 525 550 111 661 644 598 493 525

Monteith 510 549 801 661 660 604 474 501Priestley-Taylor 537 488 590 559 578 555 503 496

Baier-Robertson I 516 513 687 624 633 629 572 586

Baier-Robertson II 504 477 626 579 582 572 509 518

Baier-Robertson III 437 510 703 602 581 597 492 516

Baier-Robertson IV 455 509 863 693 602 573 532 598

Baier-Robertson V 523 532 702 619 630 608 505 524

Baier-Robertson VI 465 475 788 643 582 525 477 523

Baier-Robertson VII 407 510 832 658 589 559 477 531

Baier-Robertson VIII 428 483 780 647 560 524 445 497

1000

900-

800-

Q.

700-

D

2DOo<

600-

500

400

WINNIPEG

VANCOUVER

1 1 1

0.5 1.0 1.5

ROUGHNESS LENGTH (cm)

Figure 2. Potential evapotranspiration calculatedwith the Monteith model as a function of

roughness length and physiologicalresistance (rs).

-60

—i

2.0

accumulated PET increased at a rate of

23 mm per centimetre increase in roughness length at Vancouver and at 65 mm percentimetre at Winnipeg (Fig. 2).

At all stations the monthly variation inpan coefficient (Kp), which was selected

according to guidelines (Doorenbos andPruitt 1977), was small. Seasonal mean Kpvalues varied from 0.70 at Swift Current,0.73 at Beaverlodge and Winnipeg to 0.75at the remaining stations. Consequentlythe adjusted PET values from the Class A

pan data varied less among the stationsthan the Class A pan data themselves.

Seasonal accumulated PET data calcu

lated from the models are presented inTable II. Compared to the adjusted Class Apan, Penman's model estimated PET towithin 5% at the drier stations where the

daily average Class A pan evaporationexceeded 5.0 mm day ~l. Overestimationsof approximately 20% were found at themaritime stations. The results from the

Monteith model were similar to those from

the Penman model, although the overestimates at Vancouver UBC, Cookshire andTruro were not as large. The differences inaccumulated PET between Penman's and

Monteith's model were small, varyingfrom 24 mm at Truro to - 24 mm at Swift

Current.

The Priestley-Taylor model predictedaccumulated PET values which were at

least 15% below adjusted Class A panevaporation data at Beaverlodge, SwiftCurrent and Winnipeg and 15% above theadjusted Class A pan data from VancouverUBC and Cookshire. The Priestley-Taylormodel is a simplified combination modelwith a proportionality constant a = 1.26.It assumes that the radiant energy term

(at^(*"-G))accounts for 79% of the potential evapotranspiration, while the convective energyterm accounts for only 21%. In contrast, inthe Penman formulation the convective

energy term

u A + 7(LEa)\

is not a constant proportion of PET, butdependent upon temperature, vapor pressure and windspeed. At Vancouver,Cookshire and Truro the convective

CANADIAN AGRICULTURAL ENGINEERING, VOL. 29, NO. 1, WINTER, 1987

energy term in the Penman modelaccounted for, respectively, 20, 22 and24%ofthe potential evapotranspiration, orapproximately a similar percentage as inthe Priestley-Taylor model. On the otherhand, at Beaverlodge, Swift Current,Winnipeg, HarrowandOttawa,all stationswith relatively large vapor pressure deficits and high windspeeds, the convectiveterm accounted for, respectively, 30, 34,33, 29 and 28% of PET. This caused significant differences in accumulated PETbetween the Penman and Priestley-Taylormodelsand supports evidenceby Jury andTanner (1975) and Shouse et al. (1980) thata constant proportionality factor of 1.26 inEq. 11 is inappropriate at stations wherelarge-scale advection can be anticipated.

The results from the Baier-Robertson

model were highly variable. The difference in largest and smallest estimatedaccumulated PET from the eight formulasexceeded 100 mm at all stations, except atBeaverlodge and Harrow. Compared toadjusted Class A pan evaporation bothunder- and overestimations of PET

occurred at Vancouver UBC, Swift Current and Ottawa. All eight formulas underestimated PET at Beaverlodge, Winnipegand Harrow, while they overestimated atCookshire and Truro.

Formula I of the Baier-Robertson

model, which uses only air temperaturedata as a meteorological variable, predicted the largest or second largest PET atall stations, except at Swift Current andWinnipeg where formula IV producedconsiderably larger PET values. The differences in accumulated PET between the

Penman model and formula I varied from

90 mm at Swift Current to -66 mm at

Cookshire.

Formula V, which uses air temperature,global solar radiation and vapor pressuredeficit data, gave the best agreement withthe Penman model, except at Swift Currentand Winnipeg where the higher wind-speeds (see Table I) play an important rolein the potential evapotranspiration process.The average difference with the Penmanmodel, when Swift Current and Winnipegwere excluded, was less than 7 mm.

Formula VIII, which uses the samemeteorological variables as the Penmanmodel, was in good agreement with Penman's result at Swift Current, Winnipegand Truro. However at the remaining stations the accumulated PET was at least

60 mm lower than the one calculated with

the Penman model.

While PET is largely controlled bymeteorological conditions, actual evapotranspiration (AET) is subject to the samemeteorological conditions plus soil and

TABLE III. ESTIMATED ACTUAL EVAPOTRANSPIRATION FROM 1 MAY TO 30SEPTEMBER WITH DIFFERENT PET MODELS AT SWIFT CURRENT, HARROW

AND TRURO

Actual evapotranspiration

Rainfall PET Diffusion model VSMB

Station (mm)

239

Model (mm) (mm) (mm)

Swift Current Penman

Priestley-TaylorBaier-Robertson I

777

590

687

355

348

353

367

346

359

Harrow 339 Penman

Priestley-TaylorBaier-Robertson I

644

578

633

407

394

406

385

367

382

Truro 395 Penman

Priestley-TaylorBaier-Robertson I

525

496

586

459

454

468

430

417

450

crop conditions. Therefore, models whichestimate AET generally use PET input ascalculated by the various models.

As was shown in Table II, PET estimatesvaried largely among the different models.However similar large variations did notshow up in AET estimates (Table III). Forexample, at Swift Current where the PETestimate from the Priestley-Taylor modelwas 24% below Penman's estimate, thediffusion model predicted an accumulatedAET which was only 2.0% lower than thePriestley-Taylor PET input as compared tothe Penman PET input. Similar small differences in AET among PET input modelsare noted for Harrow and Truro. The dif

ferences in AET predicted by the VSMBwere also small at any of the three stations,although they were somewhat larger thanthe relative differences predicted by thediffusion-based model.

In both soil water models, actual evapotranspiration was controlled to a largedegree by the imposed soil and crop conditions and to a much smaller extent by PETconditions. In the diffusion-based model

AET was governed by a sink term specified as

S = K(Q)(Vr - iK8))RDF (11)

where K(Q) is the hydraulic conductivityfunction, ^r is the suction head at the root-soil interface (= 1500 kP&) and i|i(8) is thesoil water suction head function. The

model assumed that the crop will attemptto meet the evaporative demand (PET).When water was available both near the

surface and deep in the profile, the modelassumptions implied that the crop wouldfirst use the readily available water near thesurface. As water was depleted, uptakefrom the surface zones decreased rapidlydue to the rapid decrease in hydraulicconductivity.

In the VSMB water was withdrawn

simultaneously from different depths ofthe soil profile in relation to the rate of

PET, the rooting pattern of the crop, thedrying characteristic of the soil and theavailable water in each of the zones ofspecified water-holding capacities. Thedrying characteristic of the soil, whichis afunction of available soil water, limitedevapotranspiration in the VSMB in thesame way as the hydraulic conductivityfunction, AT(6), limited evapotranspirationin the diffusion-based model.

CONCLUSIONS

Long-term measurements of PET,as defined by Penman (1956), are not availablein Canada. Measured evaporation from aClass A pan must be multiplied by anempirical coefficient, thereby making theadjusted Class A pan data themselves anestimate of PET. Only an intercomparisonof PET models was attempted in this paper.

The results from the PET models varied

widely at any one station. None of themodels estimated consistently either highor low PET values. The Penman and theMonteith model produced similar resultsand in comparison with the adjusted ClassA pan data provided reasonable estimatesof PET at all stations. The results from the

Priestley-Taylor model were similar toPenman's at Vancouver, Cookshire andTruro, but significantly lower at the otherstations, suggesting that a (Eq. 11) is not auniversal constant. Formula I of the Baier-

Robertson model predicted larger PETvalues than the other formulas of the

model, except at Swift Current and Winnipeg. If air temperature, global solar radiation and vapor pressure deficits wereincluded (formula V) good agreement withthe Penman model was obtained, except atSwift Current and Winnipeg where wind-speed should be included as well. It isthought that derivation of regional coefficients instead of country-wide ones wouldimprove PET estimates from the Baier-Robertson model.

CANADIAN AGRICULTURAL ENGINEERING, VOL. 29, NO. 1, WINTER, 1987 19

Actual evapotranspiration, as calculatedwith a diffusion-based model and a soil-

water budget model, was insensitive toPET input. The imposed soil and cropcharacteristics played a much largerrole incontrolling AET than did the PET regime.Dugas and Ainsworth (1985) also reportedcumulative seasonal AET values when the

Priestley-Taylor model was substituted bythe Penman model in three crop-growth/soil-water models in the southern U.S.

With the Penman model as input, theyfound that the simulated yields were significantly reduced; other water-relatedmodel outputs, except phenology, werealso affected by the change in PET model.The climate, soil and crop conditions inthe southern U.S. are different from the

ones reported in this study. Further investigations should be undertaken to elucidatethe effects of changing the PET model incrop-growth and/or soil-water models fora variety of soil and crop conditions.

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