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Evapotranspiration From Douglas Fir Stands Exposed to Soil Water Deficits Black, T. Andrew Feb 28, 1979

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VOL. 15, NO. I  WATER RESOURCES RESEARCH  FEBRUARY 1979  Evapotranspiration FromDouglasFir StandsExposed to SoilWaterDeficits T. A. BLACK  Department of Soil Science,Universityof BritishColumbia,Vancouver, BritishColumbiaV6T 1W5  Therateofevapotranspiration fromthinned andunthinned stands ofDouglas firwasm6asured using energy andwaterbalance methods. At highvalues ofsoilwaterstorage intherootzonetheevapotranspirationratewasapproximately 80%oftheequilibrium evaporation rate.Belowa criticalvalueofsoilwater  storage theratioof theevapotranspiration rateto theequilibrium evaporation rate(E/Eeq) tended to decrease linearly withdecreasing soilwaterstorage. Thecritical values of soilwaterstorage intheroot zonewere11.8and8.3cmforthethinned andunthinned stand, respectively. Below these critical storage values, there wasapproximately 3.5cmofwater remaining inbothrootzones thatwasextractable bythe trees.The relationship between E/Eeqandthefractionof extractable waterin therootzonefor both  stands wasverysimilarfor sunny days.In thisrelationship, E/E•qbegan to decrease whentherewas approximately 40%of theextractable waterremaining in therootzonesof bothstands. INTRODUCTION  eithergreateror lessthan 1.26[e.g.,JuryandTanner,1975; andBlack,1973]. McNaughton an•lBlackfound A practicalapproach to describing howsupplyanddemand McNaughton factorsaffectwateruseby cropsandforestisto relatetheratio that in an 8-m tall Douglasfir forestwith no soilwatershortwasapproximately equaltoE•q.In thispaper,E/E•q of the actualto themaximumevapotranspiration rateto soil age,Emax and water content or potential of the root zone. Several workers ratioswill bereportedfor a rangeof soilwaterconditions willtherefore provideanindication of Em•/E• undercondistudying agricultural cropshavereported evapotranspiration (Thelatterratioisoftengiven datain thisform[e.g.,Denmead andShaw,1962;Gardner and tionsof highsoilwatercontent. a in themicrometeorological literature.) Ehlig, 1963;VanBayel,1967;Ritchieet al., 1972;Daviesand thesymbol Many workers have observedthat at a critical soil water  Allen, 1973].  Thisgeneralapproach is usedin thispaperto describe rates contentor matric potentialthe rate of evapotranspiration Denmead andShaw[1962]foundthatthis of wateruseby two WestCoastDouglasfir standsthat are beginsto decline. withincreasing atmospheric usuallyexposed to midsummer drought. Theobjectives of this criticalwatercontentincreased for water.Priestley andTaylor[1972]foundduring paperare to reportthe maximumratesof evapotranspirationdemand whenrootzonesoilwatercontentis highandto describe the the drying phase(i.e., for water contentslessthan the critical to belinearlyrelatedto rootzone variationin the evapotranspiration rate as the root zonesoil value)thatg/Emaxappeared  soilwaterstorage. In analyzing theresults of 24cropevapotranspiration experiments, Tannerand Ritchie[1974]con-  dries out. GENERAL CONSIDERATIONS  verted all soil water content data to fractional extractable The maximum rate of evapotranspirationrequired in the water in the root zone(0e) definedas follows: above approachhas beenobtained in severalways. Denmead Oe= (W- Wra)/(WF -- Wra) (2) and Shaw [1962] used the measuredrate at the field capacity value  of soil water content.  Some variations  whereW is therootzonewaterstorage,Wmis theminimum  of the Penman  [1948] equationhave beenusedby other workers[Tannerand water storageat whichthe rate of water extractionby the zero,and Wr is thewaterstorage at field Pelton, 1960; Van Bayel, 1967; Ritchie, 1973]. Priestley and plantsapproaches (whendrainage issmallin relation to evapotranspiraTaylor [1972] showed that for well-watered crops at several capacity experimentalsitesthe maximum24-hour rate of evapotranspi- tion). Theyfoundthat duringthedryingphase,E/Em,• was related to0,•Furthermore, theyfound thatwithnearly ration (Emax) was approximately equal to the equilibrium linearly evaporation rate multiplied by 1.26. The term equilibrium all of the data examined,thecriticalvalueof 0, wasbetween of thispaperwill be a reporton evaporationrate (Eeq) is usedby many micrometeorologists 0.25and0.35.An objective and is defined as follows [Slatyer and Mcllroy, 1961; how closelytwo Douglasfir foreststandsconformto these findings. McNaughton, 1976]:  Ee,•= [s/(s + 3`)](R,• - G - M)/L  (1)  EXPERIMENTAL PROCEDURE  wheres is the slopeof the saturationvapor pressurecurve,3' is  ExperimentalSites  the psychrometricconstant,Rn is the net radiationflux, G is Theresearch wascarriedoutin twolargestandsof Douglas the soil heat flux, M is the rate of canopyheatstorage,and L is fir (Pseudotsuga menziesii (Mirb.), Franco)treesof densities the latent heat of vaporizationof water. 1840 trees/ha (site 1, unthinned) and 840 trees/ha(site 2, There has been a good deal of experimentalsupportof the thinned)plantedin 1953.In the thinnedstand,over half the conclusionof Priestleyand Taylor from workersstudyinglowthinning(from 1470trees/ha) was donein 1974,and it was growing plant communitieswith no shortageof water [e.g., Davies and Allen, 1973; R. B. Stewart and W. R. Rouse, 1977]. However, other workers have found that while Emaxwas a  linear functionof E•, the proportionalitycoefficient couldbe  Copyright ¸ 1979by theAmerican Geophysical Union. Paper number 8W0992. 0043-1397/ 79/018 W-0992501.00  164  completed in May 1975.Bothsites(about1•km apart) were locatedat anelevationof 150m ongenerally flatterrainonthe  east coast of Vancouver Island about 27 km northwest of  Courtenay, BritishColumbia, onCrownZellerbach Company land.Furtherdescription of thesitesisgivenby TanandBlack [1976]andNnyamahandBlack[1977].  BLACK:EVAPOTRANSPIRATION  TABLE 1. Retention Properties of Dashwood Gravelly Sandy Loam  at Sites I and 2  Field  Permanent  Capacity (- • bar)  Wilting Point (-15 bars)  Available Water  Site I  0  0.215  W, cm  14.0  0.080  0.135  5.2  8.8  0.213  O. llO  0.103  W, cm  17.0  8.8  8.2  the entire root zone could be calculated [Nnyamah and Black, 1977]. Average values of the evapotranspirationrate E were calculated for successive 5- to 10-day intervals during drying periods of about 1-month duration (each drying period followed heavy rain) at each site. Calculationswere made using the following water balance equation: E = -AW/At-  Site 2  0  165  The averagevolumetricwater contentof the root zone (0) is equal to the root zone water storage (W) divided by the depth of the root zone. Root zone depths were assumedto be 65 and 80 cm at site I and site 2, respectively.  D + P  (3)  where AW is the changein root zone soil water storageover the time interval At, D is the averagerate of drainagefrom the root zone over the time interval (D was positive during only part of the first week following the end of the heavy rain that wetted the entire root zone), and P is the averagerainfall rate over the time interval.  Surface  runoff  was not observed  at  either site throughout the duration of the study. Half-hourly measurements of evapotranspiration were made using the energy balance/Bowen ratio method. The Trees at site 1 were 8-10 m tall, while those at site 2 were 7-9 Bowen ratio • was measuredusinga psychrometricapparatus m tall. There was almostno undergrowthat site l, but at site2 describedby Black and McNaughton [1971]. The separation there was considerablesalal (Gaultheriashallon,Pursh) underbetweenthe two psychrometricsensingheadswas 1 m at site 1 growth. The leaf area index at site 1 was between 7.5 and 8.0 and 3 m at site 2. The importance of the increasedhead (projectedleaf area basis),while at site 2 it was approximately separationwill be discussed later in the paper.The evapotrans6.6 (3.6 for Douglas fir and 3.0 for salal),[Tan et al., 1978]. piration rate was calculatedusing the equation The soil texture at both sitesis gravelly sandyloam of the Dashwood series.The soil is underlain by sandstoneat a E = (R. - G - M)/[L(1 + (4) maximum depth of 70 cm at site I and 85 cm at site 2. The physicalpropertiesof the soil are describedin detail by Nnya- Detailed descriptionof the measurementof Rn, G, and M at ,tab and Black [1977]. Soil water retentionpropertiesfor the the Courtenay sitesis givenby Tan andBlack [ 1976].At site l, root zonesat both sitesare given in Table 1. energy balance measurementsof E were made on 18 sunny  days between June 17 and August 14, 1974. After further examination of thesedata, values on 4 days were not considSite 1 was instrumented in the summer of 1974, and site 2 in ered in this paper becauseof their lower reliability. SinceR,• the summer of 1975. Soil water matric potential (•bm)was and Xt/rnwere measured throughout this period, E on the measuredat least 3 times daily usinga tensiometer-pressure remaining days was estimated from the relationshipbetween transducer systemand Wescor PT51-10 hygrometersat four LE/R• and XPmobtained from the 18 days of E measurements depthsat site I and five depthsat site 2. Using gradientsof the reported by Tan and Black [1976]. At site 2, E was measured total soil water potential at the baseof the root zone and the from June 30 to August 11, 1975,exceptfor July 8, 9, and 10, unsaturated hydraulic conductivity characteristic,Nnyamah when it was estimated as described above. and Black [1977] estimatedthe rate of vertical flow of water into or out of the root zonesat both sites.Weekly soil water RESULTS AND DISCUSSION content measurementswere made gravimetrically in the 0- to 10-cmlayer and by neutron moisturemeter (calibratedat each Energybalancemeasurements Figures 1, 2, and 3 show energybalancediagramsfor three site) down to the 50-cm and 75-cm depthsat site 1 and site 2, respectively.From these measurementsthe water storage in sunny days at different stagesof the main dry period of weather in 1975af site 2. June 30 was the secondday sincerain fell (June 28), and soil water mattic potentialsin the root zone Measurements  800  COURTENAY  varied from -0.1  Rn  600 ENERGY  bar. The sensible heat flux exceeded  Bowen ratios were observed on June 29. This is in contrast to  FLUX  DENSITY  to -0.4  the latent heat flux (i.e., •5 > 1) well into the early part of the afternoon and would have continuedthis way were it not for the occurrenceof midafternoon cloud. Very similar daytime  JUNE $0,1975  40(]  the energybalancediagramsof McNaughtonand Black [1973] for an 8-m tall Douglas fir forest at the University of British Columbia ResearchForest at Haney, British Columbia. In the latter case, by late morning the latent heat flux exceededthe sensibleheat flux, and by midafternoon the former considerably exceededthe latter. The energy balance diagrams for July 22 and July 28 showa progressiveincreasein the sensible  i" •" '•.,"-'t  (W m'•) 2O0  ,./?-..,  ;'\ .-x _•. \  .,,, ,/-//, ........ ,,.....  heat flux and a decrease in the latent heat flux as the soil wa-200  '  0  '  '  6  '  '  '  ,  12 HOURS  ,  '  18  ,  ,  '  24  (PST)  Fig. I. Energybalancediagramfor June30, thesecond dayof the main summerdryingperiodin 1975,at site 2 (thinnedstand)at Courtenay, British Columbia. The variablesare defined in the text.  ter content of the forest root zone decreased.On July 29 the stomatawere more closedthan on July 28, thuscausing•5to be even greater on July 29. On July 30 and 31, some stomatal opening causeda decreasein •5. Tan et al. [1978] have suggestedthat the stomatalopeningwasdue to a slightdecreasein  166  BLACK: EVAPOTRANSPIRATION 800  the vapor pressuredeficitof canopyair or an improvementin tree water statusas a result of marked stomatalclosureon July 29. The importanceof this variation in daily evapotranspiration will be further discussed later in the paper. Tan andBlack [1976] have reporteddaily net radiation and latent heat flux trends for site 1 studied in 1974.  near the end, it was between 0.75 and 1.75 mm d -•.  Comparisonof Energyand WaterBalance Estimatesof Evapotranspiration  Figure 5 showsthe trends of water balanceestimatesof evapotranspirationduring a summerdryingperiod at site 1 and site 2. Also includedin this figure is the averagevalue of for each of the intervals. Notice  JULY22,1975  that the  Rn  600 ENERGY FLUX  DENSITY  Figure 4 shows a graphical summary of daily (24-hour) valuesof energybalancemeasurementsof evapotranspiration rate made at site 2 in 1975. Also shownin this figure are daily (24-hour) valuesof the availableenergy(R,• - G - M) and the values of daily (24-hour) mean temperature.Toward the beginningof the main dry period, roughly50% of the available energy was used in evapotranspiration,while near the end (rain occurredon August 1), roughly20% was usedin evapotranspiration. Toward the beginningof the dry period the evapotranspirationrate was between3 and 4 mm d-1, while  the net radiation  COURTENAY  400  (Wm'a) 200  0  -.•00  0  '  ,  I  6  .  ,  I  '  I•  HOURS  18  -  ß  2•  (PST)  Fig. 2. Energybalancediagramfor July 22, the twenty-fourthday of the main summerdryingperiodin 1975,at site2 (thinnedstand)at Courtenay, British Columbia. The variables are defined in the text.  observedto be, for site 1, 0.12 and 0.08øC m-1, respectively, and, for site 2, 0.09 and 0.06øC m-1, respectively. Also plotted in Figure 6 are the averageenergybalanceand water balanceestimatesof evapotranspirationfor the Douglas fir standat the Universityof British Columbia ResearchForest over a 15-day period in 1970 reported by Black and McNaughton [1972]. Their reported uncertainty in the water  water balancevaluesof evapotranspiration at site2 agreewell with averagedvaluesof the energybalanceestimatesshownin Figure 4. The value of evapotranspirationat the beginningof balance estimate was +0.6 mm d -•. the dryingperiod in 1974was lower becausethe first 10 days following rain had considerablecloud and consequentlylow Effect of Soil Water andNet net radiation as shown in Figure 5. The ratios of latent heat Radiationon E/Eeq flux to net radiation for the first 10 daysfollowing rain at the Figures7 and 8 showthe ratio of E to E•q plotted against two siteswere similar (site 1, 53%; site 2, 49%). water storage(the equivalentdepth of water) in the root zone Energyand water balanceestimatesof evapotranspiration from both standsare comparedin Figure 6. The water balance for sites 2 and 1, respectively.The equilibrium evaporation valuesare the sameas thosein Figure 5. The energybalance rate E•q was calculatedfrom (1) using24-hour valuesof the valuesare averageevapotranspiration valuesfor all daysmak- available energy and mean temperaturewhich, for site 2, is shown in Figure 4. Becausethe analysisin Figure 6 suggests ing up eachwater balancetime interval.For site2 theseenergy that the energy balance data at site 1 overestimatedevapobalancevaluesare thoseshownin Figure 4. As can be seenin transpiration by about 10%,the evapotranspirationdata used Figure 6, there is goodagreementbetweenwater and energy balanceestimatesof evapotranspirationat site2. The regres- to calculatethe valuesof E/Eeqin Figure 8 werefirst decreased sionequationin Figure6 indicatesthat energybalancevalues by 10%. The values of the left-hand ends of the abscissaeof averaged1% higherthan the water balancevalues.The regres- Figures7 and 8 are the estimatedfield capacitywater storage sion equation for site 1 showsthat energy balancevalues valuesfor the respectiveroot zonesfrom Table 1. The general averaged12%higherthanwater balancevalues.Water balance shapeof Figures7 and 8 is similarto that of Figures3-5 of estimates for site 1 should be more accurate than those for site  2 becausethe unsaturatedhydraulic conductivitycharacteristic usedin calculatingverticalsoil water flux at both siteswas determinedon a soil samplefrom site 1 [NnyamahandBlack, 1977].The accuracyof energybalancemeasurements at site 1 was less than that at site 2 for two reasons.First, a forestry  accessroad passedwithin 50 m of the meteorologicaltower, and wind  direction  was from the road to the tower for a  COURTENAY  JULY 28,1975  Rn  600  ENERGY FLUX  DENSITY  400  (Win-a ) significantfraction of the time. Second,the 1-m separation distancebetweenthe sensingheadsof the Bowenratio mea2O0 surementapparatus,whenoperatingat site 1, wasa minimum acceptable distancein viewof the smallsizeof themeasured 0 :........-.v..--•, e..'..-..-...-...-..•..-.• verticalgradientsof temperatureand humidity.Increasingthis distanceto 3 m at site 2 proved most satisfactory,as can be seenin the stabilityof the latent and sensibleheatflux data in - 200 , , I , , I , , , ß , 0 6 12 18 24 Figures1-3. Sensorseparationat site 2 was increased,since HOURS (PST) gradientshad beenobservedto be smallat site 1 and were expectedto be smallerabovethe thinnedstandat site 2. Fig. 3. Energybalancediagramfor July28, the thirtiethdayof the During the daytimeon a sunnyday when soil water content main summer drying period in 1975, at site 2 (thinned stand) at was relativelyhigh, typical dry and wet bulb gradientswere Courtenay,British Columbia. The variablesare definedin the text.  BL^OC: EVAPOTRANSPIRATION  20  I  ''  ....  167  '- I  '  '  -8  15  6  Rn-G-M  Rn -G-M  L  (MJrn-=doy '•)  4 (mm day")  Io  o  'ø  LE  (MJm'=d=y '•)5 O'  I  ,,  •  io  JUNE  20  JULY  $:)  i(ram day")  i  1975  AUGUST  Fig. 4. Twenty-four-hour valuesof energybalancemeasurements of evapotranspiration rate(E) madeat site2 in 1975. Dottedvaluesof E wereestimatedfrom a plot of LE/R,, versussoilwatermatricpotentialusingdatameasured at site2. Also shownare 24-hourvaluesof the availableenergy(Rn - G - M) and the 24-hourmeanvalueof air temperature(T) above the stand.  PriestleyandTaylor[ 1972].In Figures7 and8, thereisa range cloudy days,especiallycloudy days followingrain, E/E,q is of soilwaterstoragebeginning at fieldcapacityin whichE/E,q significantlyhigherthan on sunnydays.Unfortunately,there is relativelyconstant,and there is a rangein whichE/E,q wereno cloudyday data whensoil waterstoragewashigh, so decreaseswith decreasingsoil water storage.Priestleyand little can be said about E/E,q under theseconditions.Other Taylorreferredto thelatterrangeasthedryingphase.If E/E,q workershave reportedthat at a given soil water contentthe had beenplottedagainstthe accumulated evapotranspiration ratio of actualto maximumevapotranspirationincreasedwith minusprecipitation (i.e.,f (E - P) dt),asit wasin Figures 3-5 decreasingmaximum evapotranspiration,the latter being of Priestleyand Taylor, the shapeof the graphswould be stronglydependenton the daily net radiation [Makkink and virtuallyunchanged. This is because theverticalflowof water Van Heemst, 1956;Scholte-Ubing,1961;Denmeadand Shaw, into or out of the root zone at Courtenayaveragedlessthan 1962]. It is interestingto note in Figure 7 that on the only 10%of the evapotranspiration. (It shouldbe notedthat Priest- sunnyday after rain at site 2 (June29, 1975),E/E,q was no sunnydayswhensoil waterstorage ley andTaylorwereusingf(E - P) dt asa meteorologicalhigherthan on subsequent estimateof the changein root zone water storageassuming was relatively high. that vertical soil water flow was usually small.)  Data in Figure 7 havebeenseparatedinto two categories: E/Eeqat High Soil WaterStorage: An Estimateof Emax/Eeq dayswith a 24-hourvalueofR,• > 12MJ m-•' d-• (sunnydays) In order to determinethe averagevalueof E/Eeq at site 2 and thosewith a 24-hour value of R,• < 12MJ m- •'d-• (cloudy appearednot to be limited by the days).Cloudy day data at site 1 were not consideredvery when evapotranspiration reliable for reasonsdiscussedearlier, and therefore all data in quantityof water in the root zone,the regression slopeof a Figure8 arefor sunnydays.Figure7 stronglysuggests that on plot of E againstEeqwas determinedfor all data for which 20  ,  i  !  i  !  COURTENAY  .. Rn,SITE  15  Rn &LE  Rn  -•- e,E  .  (MJm'a day'•)  Rn,SITE  (mmday '•)  IO  -4  E, SITE I  E,SITE 2 •-,  'i  øo  o DAYS AFTER JULY 17, 1974 (SITE I)  AND JUNE 30,1975 (SITE2)  Fig. 5. Average evapotranspiratio. n ratesdetermined fromwaterbalance measurements duringa summer dryingperiod at site 1 (unthinnedstand)in 1974and at site2 (thinnedstand)in 1975.Also shownare averagednet radiation(Rn) values.  168  BLACK;EVAPOTRANSPIRATION  '  I  I.O  ,  _L = 0.857  ßHANEY, 1970  ß COURTENAY, SITE ,,1974 X COURENAY. SITE 2,1975  ß /Eeq  1I .'"''";?•' /  0.8  e,,,".• •.o• z..' ,X•/• (SITE 2)  EEB  (mmday-I)  O.6  COURTENAY  0.4  Rnß 12Mdm-z doy-I  E Eeq  SITEI, 1974  (E doto corrected) 0.. n  -[---0. Eeq  0  , 14  I  I 12  ,  I I0  W (cm)  Fig.8. Corrected 24-hour energy balance values of evapotranspirationrate(E) at siteI dividedby theequilibrium evaporation rate (Eeq)plottedagainst waterstorage in therootzone(W). Thecorrec-  0  I  2:  3  4  tion, basedon resultsshownin Figure6, wasa 10%reductionin E.  Ewe(mmday-I)  Fig. 6. Comparison of average energybalance values(E•.•)and  From theirFigure2 it is possibleto estimatethe 24-hourvalue Waterbalance valuesare thesameas thosein Figure5. A point of E/E•, forthisforestfortwosunnydays,July7 and8, 1971, correspondingto the fourth water balancetime interval for site I in to be 0.6 and 0.7, respectively. waterbalance values (Ewe)of evapotranspiration ratesat sitesI and2.  Figure5 is missingbecause energybalancemeasurements werenot  7 and8 it isclearthatat Courtenay whensoil madethroughout thisinterval. Alsoshown areregression equations FromFigures lessthan 1.If it was andlinesforthedataforbothsites. A datapointfora 15-day periodat waterstorageis high,E/Ee, issignificantly theUniversity of British Columbia Research ForestatHaney,British notnecessary to correctthes,ite1data,thenE/E•, mightbeas Columbia,fromBlackandMcNaughton [1972]is alsoshown. highas0.9 for the thinnedstand.However,if thecorrection is valid,as is stronglysuggested by Figure6, thenthinnedand  standsat Courtenay havean E/E•, at highsoil W > 11.6cm.Thisvaluewasselected because valuesof E/Eeq unthinned of about0.8. The valuesof E/E•, reported for for largervaluesof W showedno tendencyto decreasein waterstorage responseto decreasingW. The plot of the data for these 15  days(sunnyandcloudy)andthecorresponding regression line is shownin Figure9. For thisrangeof W theaverage valueof E/Eeq wasfoundto be 0.797 and is shownas a horizontalline  the Courtenay sitesin this sectionare consideredreliableesti-  matesof Emax/Een, sinceon severaldays,rootzonesoilwater  matricpotentials weregreater than-0.2 barandoneday,with therootzoneat thisvalueof matticpotential,occurred imme-  in Figure7. In the caseof site1 the sameprocedure wasused diatelyafter a rainy day. on the threedatapointsfor whichW > 9 cm (seeFigure9). For this rangeof W the averagevalueof E/E•, (E data E/EeqDuringtheDryingPhase  corrected) was 0.837 and is shown as the horizontal line in Figure 8.  Therelationship between E andE•qfortheCourtenay forest standsis comparedto 1970data for the Universityof British ColumbiaResearchForeststand(replottedfrom Figure4 of McNaughton andBlack[1973])in Figure9. McNaughtonand Blackfoundthat for XI/m> -0.3 bar,E/E•, was1.05.As was indicatedearlierfor low-growing vegetation withadequate soil  Thestraight linedrawnthrough thedatain Figure7 forlow valuesof W istheregression linefor dayswhenRn> 12MJ m-•'d-1.Whilethereisconsiderable scatter atlowvalues of W, a straightline provides an approximate description of the  sunny daydata.Thevariation inE/Eeqat lowWisnotsimply experimental error in the energybalancemeasurements. Cal-  culations of evapotranspiration forJuly28,29,and30, 1975, usinga stomatalresistance-vapor pressure deficitmodel, veryclosely withenergy balance measurements [Tanet general,for foreststhe ratio appearsto be lessthan that for agreed al., 1978], values of E/Eoq being 0.22, 0.19, and 0.39, respeccrops.A goodexampleof this is the 16-m-tallpine forestat values of Wwere10.08,10.00, Thefiord, England,for which soil water matric potentials tively,whilethecorresponding water, values of this ratio tend to lie between 1.1 and 1.3. In  rarelyfall below-1 bar [J. B. StewartandA. S. Thom,1973]. ßA  1.0  ßA  1[=0.797  Eeq x  0.8  x  ß  ß  •  ©A  E 4  x  ( mmday -I)  3  0.6  COURTENAY  E__  Eeq  eCOURTENAY, HANEY, 1970 SITEI, 1974  •..-' //o•,t' ,•..-:  -/•'  "%•--E=0.797 ø/if9//•..ø/.•'• '" Eeq  0.4  0.2  x Rn> 12MOm-zday-• ß Rn< 12Mdm -zdOy -I A  DAY AFTER  RAIN  0  • =0.229(W-8.$0cm) Eeq 0  •"  o /•' .,-'•" E'1.05 Eeq •o///x .,'"  :7  SITE 2,1975  /  I I L?NE LINE (...... t.d) o ////•r.I xCOURTENAY, SITE 2,1975 •/,• x_./..'/  I 16  i  I 14  ,  I  12  I0  W (cm)  I 8  o  ;  i  •  ,  4  ,  5  Esq(ramday -I)  Fig.9. Twenty-four-hour energybalance valuesof evapotranspiration rate (E) beforethe start of the dryingphaseat sitesI and 2  Fig.7. Twenty-four-hour energy balance values ofevapotranspiplotted againstequilibriumevaporationrate. Also shownare data rationrate(E) at site2 divided bytheequilibrium evaporation rate from McNaughtonand Black [1973]for the Universityof British  (Eeq)plottedagainst thewaterstorage in therootzone(W).  ColumbiaResearchForestat Haney, BritishColumbia.  Bk^cl<: EVAPOTRANSPIRATION  TABLE 2. Summaryof Graphical AnalysisUsed to Estimatethe Extractable  169  i.o  Soil Water in the Root Zone at Sites I and 2  x Field  Zero  Capacity (-• bar)  Extraction Point  Extractable Water  0.215  W, cm  14.0  COURTENAY  Eeq  ßSITE I 1974  x  (corrected)  0.8x x .' ' x x  xSITE 2,1975  0.6  Rnß 12MJm-•' doy-m  ß  xxx.  œ  Site I  0  .L= 0.797  0.071  0.144  4.6  9.4  0.104  0.109  8.3  8.7  Eeq 0.4  E  • =1.990 Oe  Site 2 0  0.213  W, cm  17.0  0  The values of W at the zero extraction point (Wm) are shown in Figure 7 (site 2) and Figure 8 (site 1).  and 9.92 cm, respectively.Possiblereasonsfor this variability were discussed in the sectionon energybalancemeasurements. Becauseof a lack of data for site 1 it wasdecidedthat the slope of the line drawn through the data at low W (Figure 8) would be the same as that for site 2 shown in Figure 7 (i.e., 0.229 cm-•). This slopeappearsto describethe data of site 1 reasonably well. Extrapolationof the slopinglinesin Figures7 and 8 through E/Eeq = 0 provides an estimate of the point of zero water extraction, Wm (i.e., the minimum water storagewhen water extractionhaspracticallystopped).The intersectionof sloping and horizontallinesin thesefiguresprovidesan estimateof the criticalpoint, Wc(i.e., the water storagewhenE/Eeq beginsto decreasein responseto decreasingW). Tables2 and 3 list the valuesof Wmand Wc for both sites.Becauseroot zone depth and retentionpropertiesof the soil at the two sitesare slightly different(seeTable 1), it is not surprisingthat the value of W at the critical point and the zero extractionpoint are different. It is of interestto note that the critical point was reachedat both sites about 12 days after the dry period began. This similarity is quite fortuitous, sinceat site 1 the soil was about 2.5 cm lessthan field capacityat the beginningof the period and the net radiation at site 1 over the 12-dayperiod was 20% lessthan that at site 2. At sites 1 and 2 the quantity of water extractablebetween field capacity and the critical point is about 5.7 and 5.2 cm, respectively,while the quantity of water extractablebetweenthe critical point and the zero extraction point is about 3.7 and 3.5 cm, respectively(Tables 2 and 3). The latter figures compare with a value of 5 cm found by Priestleyand Taylor [1972] for variouscombinationsof agricultural cropsand soils. Figure 10 showsE/Eoq on sunnydaysfor both sitesplotted againstfractional extractablewater in the root zone (0e) as calculatedfrom (2). The correctedvaluesof the data from site 1 have beenusedin this figure.The two linesdrawn through the data are the sameas thosein Figure 7. The relationship  1.0  0.8  0.6  0.4  0.2  0  Oe  Fig. 10. A plot of sunnyday valuesof E/Eeq from Figures7 and 8 againstthefractionalextractablewaterremainingin the rootzone(0,).  betweenE/Eo• and soil water contentat the two sitesappears to be very similar when they are comparedon the basis of fractionalextractablewater. Figure 10suggests that the critical point at the two sitesoccurs when there is about 40% of the extractablewater left in the root zone, or Oec• 0.4 (seealso Table 3). Tanner and Ritchie [1974] concluded from their survey of crop water use experimentsthat a useful average value of Oecfor cropswas 0.3. How do the valuesof the soil water matric potential in the root zonecompareat the occurrenceof the critical point at the two sites?At site 1 they varied from - 1.1 bars near the bottom of the root zone to -3.4 bars near the top, while at site 2 the  valueswere- 1.2and -3.0 bars,respectively. Sincethesepairs of values are very similar, it would seemreasonableto compare valuesof E/Eo• at the two sitesfor given valuesof soil water matric potential. Several workers have related relative evapotranspirationratesto soil water potential [e.g., Van Bayel, 1967; Tan and Black, 1976]. One problem with this approachis that mattic potentialswithin the root zone are rarely constantwith depth. The problem is then characterizingthe root zone with a meaningfulaveragematric potential. Figure 11 shows24-hourvaluesof E/Eo• on sunnydays(from Figures 7 and 8) plotted against the range of •m values found in the root zone on the day for which each value of E/Eoq was determined.(The diurnal variation in •m at any depth was negligiblein comparisonto the rangesshownin Figure 11.) Consideringthe magnitudeof the rangesshownin Figure 11it COURTENAY 1.0 -  0.8  ......  SITE I, 1974 (corrected)  •  SITE 2,1975  Rn>17_ MJ m-•'doy-m  E  Eeq  0.6  TABLE 3. Critical Point Values of the Root Zone Water Storage (We), the Average Volumetric Water Content of the Root Zone the Fraction of ExtractableWater Remainingin the Root Zone and the Maximum  and Minimum  0.4  Values of the Root Zone Soil Water  Matric Potential (•m) 0.2  Xt/m,bars Wc, cm Site I Site 2  8.3 11.8  Oc 0.13 0.15  Oec 0.39 0.40  Maximum  Minimum  - 1.1 - 1.2  - 3.4 - 3.0  The valuesof Wc are taken from Figures7 and 8.  0  m I 0  -2  *  I -4  .  I -6  ,  I -8  I  I -I0  ß  , -12  ,  l -14  ¾m tbors) Fig. l I. A plot of sunnyday valuesof E/Eeq from Figures7 and 8 againstthe rangeof soil water matric potentials(XPm)observedin the root  zone.  170  BLACK: EVAPOTRANSPIRATION  is clear that an arithmetic averagexPmfor the root zone has limited meaning.The conceptof usinga total root zone water storageor fractional extractablewater to describethe water statusof the root zone appearsto be somewhatmore usefulin the empiricalapproachdescribedin this paper.Furthermore, W can be obtained by a simplewater balancemethod without the need to use soil water retention information. Figure 11 showsthat asE/Ee,• drops,matric potentialgradientsincrease in the root zone. Both sitesshowa similarpattern.In addition, Figure 11 confirms the earlier remark that when maximum root zone matric potentialsfall to slightly lessthan -1 bar,  Black, T. A., and K. G. McNaughton, AverageBowen-ratiomethods of calculatingevapotranspirationapplied to a Douglas fir forest, BoundaryLayer Meteorol., 2, 466-475, 1972. Davies, J. A., and C. D. Allen, Equilibrium, potential and actual evaporation from cropped surfacesin southernOntario, J. Appl. Meteorol., 12, 649-657, 1973.  Denmead, O. T., and R. H. Shaw, Availability of soil water to plants as affectedby soil moisturecontent and meteorologicalconditions, Agron.J., 54, 385-390, 1962. Gardner, W. R., and C. F. Ehlig, The influenceof soil water on transpirationby plants, J. Geophys.Res., 68, 5719-5724, 1963. Jury, W. A., and C. B. Tanner, A modificationof the Priestleyand Taylor evapotranspirationformula, Agron. J., 67, 840-842, 1975. Makkink, G. F., and H. D. J. Van Heemst,The actualevapotranspiraE/Ee,• beginsto declinebelowmaximumvaluesat both sites. tion as a function of the potential evapotranspirationand the soil moisturetension,Neth. J. Agr. Sci., 4, 67-72, 1956. CONCLUSION McNaughton, K. G., Evaporationand advection,I, Evaporationfrom extensivehomogeneous surfaces,Quart.J. Roy. Meteorol.Soc.,102, The analysis in this paper indicates that micro-  meteorologicalenergybalanceestimatesof forestevapotranspiration agreewell with water balanceestimates.The separation distance between the sensing heads of Bowen ,ratio measurementapparatusshouldbe no lessthan 3 m for reliable measurementsabove forest standsas aerodynamicallyrough as thosein this study. The maximum 24-hour rate of evapotranspirationunder sunnyconditionsat the two Courtenay siteswas lessthan the equilibriumrate of evaporation,evenon a day followingrain. In the caseof the thinned stand,the averagevalue of the ratio of the maximum rate of evapotranspirationto the equilibrium evaporation rate was 0.8 In the caseof the unthinned stand, this ratio was 0.9; however,water balancedata suggested that this was as much as 10%too high. During the dryingphaseat both sites,E/E•,• was,to a good approximation,a linear function of water storagein the root zone. Approximately 3.5 cm of water wasstill extractablefrom the root zone after the critical water storagevalue had been reachedat both sites.Both sitesexhibiteda very similar relationshipbetweenE/E•,• and soilwaterstoragewhensoilwater storage was expressedas a fraction of the extractable soil water. The critical point at both sitesoccurredwhenthere was approximately40% of the extractablewater remainingin the root zone.This appearsto be higherthan mostvaluesreported for agricultural crops. The critical point at both sitescorrespondedto a maximum root zone matric potential of a little less than - 1 bar.  Acknowledgments.This researchwas supportedby grants from the National  Research Council  of Canada  and the British Columbia  Department of Agriculture and by a contract from the Canadian ForestryService(Department of the Environment). I acknowledgethe advice and cooperation of H. Brix and M. Crown of the Canadian ForestryServiceand the forestersof the Crown ZellerbackCompany. I am gratefulto J. U. Nnyamah and C. S. Tan for makingavailableto me data obtainedduring their Ph.D. researchprojectsat the University of British Columbia.  181-191, 1976.  McNaughton, K. G., and T. A. Black, A studyof evapotranspiration from a Douglasfir forest usingthe energybalanceapproach,Water Resour. Res., 9, 1579-1590, 1973.  Nnyamah, J. U., and T. A. Black, Rates and patternsof water uptake in a Douglas fir forest, Soil Sci. Soc. Amer. J., 41, 972-979, 1977. Penman, H. L., Natural evaporationfrom open water, bare soil and grass,Proc. Roy. Soc. London,Ser. A, 193, 120--146,1948. Priestley,C. H. B., and R. J. Taylor, On the assessment of surfaceheat flux and evaporation using large-scaleparameters,Mon. Weather Rev., 100, 81-92, 1972.  Ritchie, J. T., Influenceof soil water statusand meteorologicalconditions on evaporationfrom a corn canopy,Agron. J., 65, 893-897, 1973.  Ritchie, J. T., E. Burnett, and R. C. Henderson,Dryland evaporative flux in a subhumidclimate, III, Soil water influence,Agron.J., 64, 168-173, 1972.  Scholte-Ubing,D. W., Solar and net radiation,availableenergyand its influenceon evapotranspiration from grass,Neth.J. Agr. Sci., 9, 81-93, 1961.  Slatyer,R. O., and I. C. McIlroy, Practicalmicroclimatology, report, 328 pp., Counc. for Sci. and Ind. Res., Plant Ind. Div., Canberra, Australia, 1961.  Stewart,J. B., and A. S. Thom, Energybudgetsin pine forest,Quart. J. Roy. Meteorol. Soc., 99, 154-170, 1973. Stewart, R. B., and W. R. Rouse, Substantiationof the Priestleyand Taylor parametera = 1.26 for potential evaporationat high latitudes,J. Appl. Meteorol., 16, 649-650, 1977. Tan, C. S., and T. A. Black,Factorsaffectingthe canopyresistance of a Douglas-firforest,BoundaryLayer Meteorol., 10, 475-488, 1976. Tan, C. S., T. A. Black, and J. U. Nnyamah, A simplediffusionmodel  of transpiration appliedto a thinnedDouglas-fir stand,Ecology, 59, in press,1978. Tanner,C. B., and W. L. Pelton, Potentialevapotranspiration by the approximateenergybalancemethod of Penman,J. Geophys.Res., 65, 3391-3413, 1960.  Tanner, C. B., and J. T. Ritchie, Evapotranspiration:Empiricismsand modeling, paper presentedat Annual Meeting, Amer. Soc. of Agron., Chicago, Ill., Nov. 1974. Van Bavel, C. H. M., Changesin canopy resistanceto water lossfrom alfalfa inducedby soil water depletion,Agr. Meteorol.,4, 765-176, 1967.  REFERENCES  Black, T. A., and K. G. McNaughton, Psychrometricapparatusfor Bowenratio determinationover forests,BoundaryLayer Meteorol., 2, 246--254, 1971.  (ReceivedJune 13, 1978; revisedAugust 25, 1978; acceptedSeptember18, 1978.)  


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