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Test of an Equation for Evaporation From Bare Soil Water Black, T. Andrew; Novak, M. D. 1982

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WATER RESOURCES RESEARCH, VOL. 18, NO. 6, PAGES 1735-1737, DECEMBER 1982  Test of an Equation for Evaporation From Bare Soil M.D.  NOVAK  AND  T.  A.  BLACK  Department of Soil Science, University of British Columbia, Vancouver, British Columbia, Canada V6T 2A2  An empirical equationdevelopedby Idso et al. (1979) at Phoenix, Arizona, to calculatedaily average evaporationrates during all three drying stagesof a bare soil was tested usingmeasurementsmade at Agassiz, British Columbia, and is discussedon the basisof available evaporationtheory. The results show that their expressionfor potential evaporationrate did not apply at Agassizdue to differencesin the advection regimes at the two locations. The Agassiz potential evaporation rate data was well representedby the Priestley-Taylor equationwith apt ('alpha') = 1.27 +- 0.1. It was concludedthat the Idso et al. equationfor potentialevaporationrate hasno greatergeneralitythan the Priestley-Tayloror other such semiempiricalapproaches.The conceptof expressingthe stageIII rate as proportional to the expressionfor potential evaporation rate worked marginally well at a culti-packed site and quite well at a disc-harrowedsite. It was concludedthat for soilswith stageIII rates much greater than 50% of potential evaporation rate, more complete proceduresare necessaryfor calculating evaporation rates during extended drying periods. INTRODUCTION  ldso et al. [ 1979]presentedthe following simpleempirical formulafor the 24-houraverageevaporationrate (latent heat flux density) from bare Avondale loam soil,  LEi,ii,iii = (3/8 + 5/8 •)(S N q- 1.56LN + 76)  (1)  where SN and LN are the 24-hour average net solar and net  Stage III, or soil moisture limited evaporation, occursfor /3 = 0. From (1) it is seenthat it takes place at a rate equal to 3/8 times the potential rate expression(3). ldso et al. [1979] show that expressingthe stageIII evaporation in this manner absorbed the seasonal variation in this rate at Phoenix. The  stage III rate is mainly a function of soil moisture content and will decrease in some manner as the soil dries. Theoreti-  cal arguments by Gardner [1959] as well as several field studies [Ritchie, 1972] show that the stage III evaporation rate for deeply wetted, homogeneoussoilsmay be described densities arein W m-2. The factor/3wasoriginallydefined by the relation by Jackson et al. [1976] as  longwave radiationflux densities,respectively,/3is the soil surface wetness partitioning factor, and all energy flux  13= (aa-  a)/(aa-  aw)  (2)  LEIII = Ct-1/2  (5)  where t is the time in days from the start of stage III evaporation, and C is a constant related to the hydraulic a is the daytimeaveragealbedoon any given day;/3 varies from 1 to 0 as the soil surfacechangesfrom wet to dry. The diffusivityof the soil. Accordingto Jacksonet al. [ 1976],C is a function of soil temperature and hence varies with season. Roman numeral subscriptsindicate that (1) applies to all As is implied by (5), the stage III rate eventually becomes three stagesof soil drying, as defined by ldso et al. [1974]. independent of the potential rate within a given drying The evaporation rate during stage I, or the potential period. This seems to be somewhat incompatible with (1) evaporationrate (PLE), occursfor/3 = 1 and is given by with /3 = 0, although since LN is generally a decreasing function of time during stage III due to increasing soil LEi = PLE = SN + 1.56LN + 76 (3) surface temperature, (3) could simulate some of the square The development of (3) for Avondale loam over all four root of time behavior of (5). seasonsat Phoenix as well as validation for crop and water Stage II, or the transition stageevaporation, occursfor 0 surfacesin Arizona and California are describedby ldso et </3 < 1. The model for this stageis a soil surfacepartitioned al. [1975, 1977].ldso et al. [1975]note that (3) is well adapted into patchesevaporatingat either stageI or stageIII rates, to remote sensingand suggestthat it shoulddescribeevapowith the partitioningdeterminedby/3. ration rates throughout the complete range of possible ldso et al. [1979] suggestthat (1) shouldbe tested on other advective conditions.Priestley and Taylor [1972] also presoils and in other climates. The purposeof this paper is to sented a simple semiempirical equation for the potential report on the evaluation of (1) using a data set obtained for a evaporation rate bare soil surface in the Lower Fraser Valley during the PLE = apT[S/(S+ T)](RN- G) (4) spring and early summer of 1978. Since the cool, wet, and cloudy climatic conditions of British Columbia contrasted  where aa is the dry soil albedo, aw is the wet soil albedo, and  wheres is the slopeof the saturationvapor pressurecurve, y sharplywith the mostlyclearskyconditions of Phoenixand is the psychrometricconstant, RN is the net radiation flux since two contrasting tillage treatments were studied (cultidensity, G is the soil surface heat flux density, and the packedversusdisc-harrowed),this was felt to be an opportucoefficient apt must be locally determined to account for nity for a demandingtest of (1). advection, although a value of 1.2 to 1.3 is considered appropriate to 'advection-free' conditions.  EXPERIMENTAL  PROCEDURE  The study was carried out at the Agriculture Canada Research Station at Agassiz, British Columbia, on a Monroe seriesloam/silt-loam soil (Eluviated Eutric Brunisol). A 145 x 175 m level field, kept bare for this study, was divided into  Copyfight 1982 by the American Geophysical Union. Paper number 2W1317. 0043-1397/82/002 W- 1317502.00 1735  1736  NOVAK AND BLACK: TECHNICAL NOTE  •,•240 4200O I.iJ  ß  is not inconsistentwith Figure 2 of Idso et al. [1974],which showsthat stagesI and III were definedby narrow rangesof a. The values of aw and ad used in (2) to calculate /3 at Agassizwere 0.065 and 0.173, respectively,which were the extreme values of measureddaily average albedo for both  e•,•,4 ,, • /1:1LINE_-  •' ß  • 160  ß•  sites.  *•*•  : 120 ß /  In Figure 1, daily average evaporationrates calculated from (1) are plotted againstmeasuredrates for both sites.It is evident that (1) did not agree with most of the measure-  o  ß  i  •  •  80  */  ß  ments at site 1 and all of the measurements  SITE STAGE  I 2  3 40u  0  0  80  •20  •60  200  at site 2.  Examination of the potential rate data (/3 > 0.8) shows clearly that (3) failed to describethese. This, as well as the agreementof (1) with someof the stageIII and near stageIII pointsfor site 1, showsthat the factor 3/8 in (1) cannotapply to the site 1 data.  240  MEASURED 24-HOURAVERAGE LE •Wm  Fig. 1. Plot of daily averageevaporationratescalculatedfrom (1) versusmeasuredratesfor sites1 and 2 at Agassiz,BritishColumbia, 1978.The dryingstageof eachday is indicated.The dashedline was fit by eye to the stageI data from both sites.  While (1) did not adequatelydescribethe measureddata,it was decidedto investigatewhether the conceptof expressing the stageIII rate asproportionalto the potentialevaporation rate, as done in (1), would still apply, i.e., whether  LEi,n,m = [8 + (1 - /5)/3]PLEAg  (6)  would describethe measuredLE. PLEAg,the expression two parts, which will be referred to as sites 1 and 2. The division  of the field was done with  consideration  of the  describingthe potential evaporationrate at Agassiz,can be determined from the dashed line in Figure 1 and is  prevailing wind direction and fetch requirements.Site 1 was disc-harrowed,then firmly packedwith a culti-packer,while site 2 was disc-harrowed only. The data collection periods were May 17 to July 21 and July 6 to July 21 at sites 1 and 2, respectively. The identical micrometeorologicalinstrumentation was centrally located at both sites. The average bulk  The value of/5 for each site was calculated using (6) after averaging[LEm/(SN + 1.56L/+ 7)] and/3 over the stageIII days (12 for site 1 and 7 for site 2). This was analogousto the graphicalprocedureusedby Idso et al. [ 1979].Stage!II rates  densities oftheupper10cmof soilwere1030and870kgm-3  at site 2 were about half of those at site 1. This led to/5 = 0.74  PLEAg= SN q- 1.56LN+ 7  (7)  for sites 1 and 2, respectively. Bulk densitiesbelow 10 cm  +- 0.2 for site 1 and/5 = 0.34 + 0.1 for site 2, which shows  werein therange1000-1300 kg m-3 at bothsites.  that this factor is a strongfunction of near-surfacesoil bulk density and/or structure. Comparisonof (6) with the measurementsfrom sites 1 and 2 is shown in Figure 2; the degree  Half-hour average evaporation rates were measured throughout the day by the energy balance/Bowen ratio technique, using the same instrumentation described by Black and McNaughton [1971]. Both reversing psychrometers (50-cm separation)were mountedwithin 1 m of the soil surfaces, which led to a fetch-height ratio of 80: 1. Net radiation flux densities were measured by Swissteco S-1 net  of scatter is similar for all three stagesand is about _+25W  Equation (7) differs from (3) for Phoenix by a constant69  W m-2. Jacksonet al. [1976]pointout that the coefficient apt was 1.41 for summer days when 24-hour totals of net  radiometers located 0.65 m above the soil surfaces. The RN  signaland both the wet-bulb and dry-bulb vertical temperature difference signalswere continuouslyintegrated using dual-ramping voltage integrators. Soil surface heat flux densitieswere calculated half hourly from soil temperatures measured at 30 depths down to 1 m and heat capacity profilescalculatedfrom bulk densitiesand gravimetricwater contents(sampledat least every 2 days) by usingthe nullalignmentmethod describedby Kimball and Jackson [1975]. Half-hour average solar irradiance was measured(continuous integration as above) by a Kipp and Zonen CM5 pyranometer, while the albedoswere spot measuredevery half hour usinginverted Kipp and Zonen CM5 pyranometers located 0.6 m above the soil surfaces. Net long wave  E  •,,•200 ,,, 160  >  O  120  80  i  Q  40  radiation flux densities were calculated from measured net  radiation flux densities, albedos, and solar irradiance according to LN = RN -- SN.  :  0  RESULTS AND DISCUSSION  Examination of the Agassiz data shows that the drying stagesI, II, and III were approximately delineatedby/3 > 0.8, 0.8 >/3 > 0.2,/3 < 0.2, respectively[Novak, 1981].This  Fig. 2. Plotof dailyaverageevaporationratescalculatedfrom(6) with 8 = 0.74 for site 1 and 8 = 0.34 for site 2 versus measured rates  for thesesitesat Agassiz,BritishColumbia,1978.The dryingstage of each day is indicated.  NOVAK  AND BLACK: TECHNICAL  160  1737  potential rate, such as for site 1, equationsof the form (6) will not work well over extended drying periods. In these cases, formulae such as (5) will have to be used to describe the stageIII evaporationrates, as is detailedby Jacksonet al. [1976]. It is noted that (5) did not describe the stage III evaporationratesat either site 1 or site2. This was attributed to the relatively shortdrying periods(typically 2-4 days with a maximum of 10 days) and variable cloudiness,the presence of a water table at a depth of 1-3 m, and the bulk density(and textural) variations with depth.  SITE 12 120  80  40  CONCLUSIONS  0  0  40  80  120  24- HOURAVERAGE s% (.REG) •.Wm-2) Fig. 3. Plot of measureddaily averagestageI (•3> 0.8) evaporation rates versus equilibriumrates for sites 1 and 2 at Agassiz, British Columbia, 1978. The solid line was fit to the data by eye.  radiation were used and soil surface heat flux densities were  assumednegligible. This indicates that some advective enhancement occurred at the Phoenix site. At Agassiz the average 24-hour value of aer (G not neglected)for the stageI days was 1.27 _ 0.1, as shown in Figure 3, indicating minimal advection on these days. This showsthat (3) is not applicable over the full range of atmospheric advective regimes. Therefore formulae such as (3) and (7) have no advantageover (4) except perhaps at a single site and after calibration. Furthermore, it is noted that (4) with apt in the range 1.0-1.3 describedthe half hourly evaporationrates on stage I days quite well, while (7) failed to do so at all (overestimatingby up to 120%). The +__ 30% variability in •i for each of the two Agassizsites is not inconsistentwith the scatter in Figure 1 of ldso et al. [1979]. However, for site 1 the variability is not random. Calculatingvalues of •i at site 1 for the first and last thirds of the experiment (there were no stage III days in the middle third due to cloudy and rainy weather) shows that •i decreased from 0.84 _ 0.1 in the first third to 0.62 _ 0.1 in the  last third. During the first third of the experimentthe average volumetric soil moisturecontentat site 1 in the upper 0.06 m of soil on the stageIII days was 0.27 - 0.01, whereasduring the last third this value was 0.23 _ 0.01. The average stage III evaporation rates correspondingto these moisture con-  tentswere119__20 and82 __10W m-2, respectively, while the corresponding valuesof PLEAggivenby (7) were 137__ 15and123__15W m-2, respectively. It is seenthatthe 10% decreasein PLEAg could not compensatefor the 31% decreasein stage Ill rate between the first and last thirds of the experiment. This suggests that had the experiment continued further into the drier summer weather, the calculated site 1 & would have decreased even more and (6) with & = 0.74 would not have described the data adequately. Whether  NOTE  this would  have been true for site 2 as well is  difficult to assesssince that site was monitored for only 16 days. However, the already low stage III rates observed at  this site (30-40 W m-2 or = 25% of the potentialrate) suggestthat (6) with & = 0.34 would have described site 2 evaporation adequately over a longer period. Therefore for soils with stage Ill rates initially well in excess of 50% of  Equation (3), developedby ldso et al. [1975] to describe potential evaporation at Phoenix, Arizona, did not apply at Agassiz, British Columbia. However, subtractingfrom it a  constant69 W m-2 gavegoodagreement. This valueaccounted  for the difference  in advection  between  the two  locations and demonstrates that formulae such as (3) and (7) have no greater genoralitythan the Priestley-Taylor formulation representedby (4).  Expressingthe stageIII evaporationrate as proportional to the expression for potential evaporation worked only marginallywell on the firmly packed site (/5= 0.74 _+0.2) and quite well at the disced site (/5 = 0.34 _+ 0.1). The results show that this concept is applicable to soils with stage III rates much less than 50% of potential rate, but that on soils with stage III rates (initially) much greater than 50% of potential rate, a more completeprocedureshouldbe usedfor extended drying periods. REFERENCES  Black, T. A., and K. G. McNaughton, Psychrometricapparatusfor Bowen-ratio determination over forests, Boundary Layer Meteorol., 2, 246-254, 1971.  Gardner, W. R., Solutionsof the flow equationfor the drying of soils and other porous media, Soil Sci. Soc. Am. Proc., 23, 183-187, 1959.  Idso, S. B., R. J. Reginato,R. D. Jackson,B. A. Kimball, and F. S. Nakayama, The three stagesof drying of a field soil, Soil Sci. Soc. Am. Proc., 38, 831-837, 1974.  Idso, S. B., R. D. Jackson,and R. J. Reginato, Estimatingevaporation: A techniqueadaptableto remote sensing,Science, 189, 991992, 1975.  Idso, S. B., R. J. Reginato, and R. D. Jackson, An equation for potential evaporationfrom soil, water, and crop surfacesadaptable to use by remote sensing,Geophys. Res. Lett., 4, 187-188, 1977.  Idso, S. B., R. J. Reginato, and R. D. Jackson, Calculation of evaporationduringthe three stagesof soil drying, Water Resour. Res., 15, 487-488, 1979.  Jackson, R. D., S. B. Idso, and R. J. Reginato, Calculation of evaporation rates during the transition from energy-limiting to soil-limiting phases using albedo data, Water Resour. Res., 12, 23-26, 1976. Kimball, B. A., and R. D. Jackson, Soil heat flux determination: A null-alignment method, Agric. Meteorol., 15, 1-9, 1975. Novak, M.D., The moisture and thermal regimes of a bare soil in the Lower Fraser Valley during spring,Ph.D. thesis, Univ. of B. C., Vancouver, 1981. Priestley, C. H. B., and R. J. Taylor, On the assessmentof surface heat flux and evaporation using large-scale parameters, Mon. Weather Rev., 100, 81-92, 1972. Ritchie, J. T., Model for predicting evaporation from a row crop with incomplete cover, Water Resour. Res., 8, 1204-1213, 1972.  (Received May 10, 1982; revised August 25, 1982' accepted August 25, 1982.)  

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