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Study of Evapotranspiration from a Douglas Fir Forest Using the Energy Balance Approach McNaughton, K. G.; Black, T. Andrew 1973

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VOL. 9, NO. 6  WATER RESOURCES RESEARCH  DECEMBER  1973  A StudyofEvapotranspiration froma Douglas Fir Forest Usingthe EnergyBalanceApproach K. G. McNAUGHTON AND T. A. BLACK Department o! Soil Science, University of British Columbia Vancouver, British Columbia, Canada Energy balance measurements of evapotranspiration from a young Douglas fir forest are  reported for a period of 18 days in July 1õ70when soil water was not limiting. Peak daily evapotranspirationrates characteristicallyoccurred 2-3 hours after solar noon, and evapotranspiration showed a short-term independence from net radiation. This behavior is interpreted as being a consequenceof the large forest roughnes.s.Daily evapotranspirationand net radiation were, however, well correlated. Values of surface diffusion resistance calculated  from Monteith's combinationformula are presented.Daytime values showedsignificant day-to-day diff•renc.es, and an attempt to define g potential evapotmnspirationrate by assum-  ing a constantdaytimesurfaceresistance wasnot successful. Comparisonof evapotransp{ration measurementswith a potential evaporation formula for wet surfacesdeveloped by Priestley and Taylor suggeststhat evaporation of intercepted water proceeds20% more rapidly than evgpotranspiration from the nonwetted canopy.  In July and August, 1970, energy balance/ establishedby the experimentalwork of Van ' "• .... Bowen ratio measurementsof evapotranspira- Bavel[1.966].In modern reslstancq •e•nunology tion from a.youngDouglasfir forestwere made this exp.ression canbe written as  as part o]•a hydrologic balanceexperimen.t on a site in the University of British Columbia (UBC) ResearchForest. Examination of the energy balances com-  Eo = (1/L)[s/(s nt- '•)](RN-  G-  7  M)  -[- [p%(ez*-- ez)]/[(s q- 'y)r.L]  (1)  pu•tedfrom the measurements revealsseveral where theaerodynamic resistanc,e• raisgiven by  clear patterns in the results.This paper presents the results for the initial 18-day period of the experimentand discusses these patterns and someof the implicationsof the results.As a basis for interpreting the results,Monteith's [1965] canopy transpiration model has been used for part of the analysis.  when a similarity is assumedbetweenthe transfer coefficientsfor momentum, heat, and water  MONTEITI-I'S EQUATION  water vapor. The quantity Eo, definedby (1), will be called the free evaporationrate in this  =  ,  Penman [1948] has shown that energy balance and aerodynamic equations for evaporation can be combined to give an expression for evaporationfrom extensivewet surfacesin terms of easilymeasurableparameters.Businger [1956] has' developeda rational expression basedon measuredwind profilesfor the original empiricalwind function. The accuracy of the resulting combination formula for calculating evaporation from wet surfaceswith small roughness lengthshas been Copyright (•) 1973 by the American Geophysical Union  (2)  vapor and whenthe virtual sink.formomentum is taken to be also a virtual source for heat and  paper.  Monteith [1965] introducedthe effect of diffusive resistanceto vapor flow of the stomata of the vegetative canopy by consideringthe  canopyas a singleextensiveisothermalleaf. In his model,transpirationfrom this leaf is expressedas  E = (p%/L'y)[(eo*-- eo)Ir.]  (3)  where the subscript zero refers to values at the canopy surface obtained by extrapolating the temperatureand humidityprofilesdownto (zo+ D). Followinga proceduresimilarto that  1579  McNAUGHTON  1580  AND BLACK'  i•OREST EVAPOTRANSPIRATION  /  of Pent, an [1948], Monteith derived the ex-  AE/E--  (st•-  'Y) Ara  pressio n for transpiration + [(s -• 'y)(ra-• Ar•) -• r,'),]  = +  Eo  +  (4)  (5)  where the Bowen ratio fi has been introduced for convenience. It can be seen that E is inde-  where the surface resistance rs is formally  pendentof ra when fi -- y/s, as has been noted previously by Monteith [1965]. of the leaves of the canopy acting in parallel. Anticipating the results of this paper, for a Total evapotranspirationcan be considered forest we can take ra • 5 secm -•, rs • 75 as entirely transpiration with small error for secm-•, and fi • 1 and assumethat T -- 18øC forestswher•interceptedwater is not present, an,d s - 1.29 mb K -•. An overestimateof r• by since soil evaporationhas been found to be 50% introduces only a 2x•/2% overestimate in small by man,yworkers [e.g., Rutter, 1966]. the calculatedvalue of E. Further, if we let r• approach zero, (4) becomes  identified  as the resistan,ce of all the stomata  SURFACE AND AERODYNAMIC P•ESISTANCES  E -- (p%/L'yrs)(ez*-- ez)  (6)  The one-layermodel is a considerablesimplification of real plant canopiesand has attracted with only 5% underestimate. This result indistrong criticism [Phillip, 1963, 1966; Tanner, cates that a forest transpiring in accordance 1963; T•dn)terand Fuchs, 1968]. These criti- with (4) is little affected by wind speed and cismsarise from the observationthat the simple that radiation is important indirectly through one-layer model ignores leaf boundary layer its effect on stomatal resistance and on temdiffusion:resistancesand aerodyn,amicdiffusion perature and therefore on vapor pressuredeficit. resistances between different levels of the Both stomatal resistance and vapor pressure canopY.An examination showsthat transpira- deficit are expectedto show a slow responseto tion from each individual leaf surface can be changesin radiation, and therefore (6) predicts summedto producean expressionfor transpira- poor correlation between changesin transpiration from the whole canopy that is in, the form tion and radiation over periods of less than a of (3) only under the assumption that these few hours.In addition, (6) suggeststhat diurnal resistancesare indeednegligible.In general,the tren,dsin the cvapotranspiration rate will tend surfaceresistancecannotbe rigorouslyidentified to follow the trend of the atmosphericvapor with the stomatal resistance of all the leaf sur-  pressure deficitif the daytimetrend5f stomatal  facesacting in parallel, and such interpretation resistanceis not too large. Stewart and Thom must be justified by examiningthe assumptions [1973] have also examined forest transpiration for each canopy studied. and have independently derived 5 relationship From the results of Rutter [1967] for a Scots (their equation 32) that is easily shown to be pine plantation it can be seen that stomatal equivalent to (6). Hinckley and' Scott [1971] have found n,o resistanceswere large in comparison with the aerodynamic and boundary layer resistances significantcorrelation between solar radiation within the canopy. There is some expectation, and sap velocity in Douglas fir trees under therefore, that surfaceresistancemay be closely conditionsof high atmosphericdemand. Mearelated to stomatal resistancein that case and, surements of transpiration by Parker [1957] by implication, also in the present analysis. made by quick-weighingexcisedleavesof openGood wind profile data for calculatingra are grown oak and white pine showno shor•-term frequently unavailable. For this reason a con- responseto changesin sunlightmeasuredwith sideration of the errors introduced into the 5 pyrheliomctcr.Comparisonsof transpiration values of E calculated from (4) causedby an estimated from sap velocity with wind speed error of estimate in ra is appropriate here. and light intensity made by Lade[oged[1963] An error formula can be derived by differen- showedlittle correlation and also support this tiating (4) with respect to ra and then inteconclusion.Ladefogcdfound, on the other hand, grating overt'herange of errorfromr• to ra q- a dependenceon relative humidity. Inspection Ar•. Thus of his Figures 10-13 suggestsa strong correla-  McNAUGI-ITONAND BLACK: FORESTEVAPOTRANSPIRATION  tion between vapor pressuredeficit and trans-  piration in agreementwith (6). In this paper r8 is computedfrom Monteith's equation (4). The effect of an error in ra on the value of r8 calculatedfrom (4) can be found by transforming (4) to make r, the subject of the equation and then differentiating with respect to Pa.Integration of the resulting expressionover the rangeof error from ra to r• -]- Ara then gives  At, = [(•s/7)-  1] Ara  (7)  When the values above are substituted, (7) showsthat a 50% error in r• introducesonly a 3% error into the value of r,. Cowan [1968] and Thom [1972] have examined the assumptionof similarity of the aerodynamicdiffusionresistancefor momentumand the aerodynamic diffusion resistancesfor heat and vapor. Both investigatorsconsiderthat the assumptionof similarity may not be appropriate for exchange within canopies. Stewart and Thom [1973] have included a discussionof this problem for a forest. However, in view of the insensitivity of forest transpiration and surface resistance values calculated from (4) to errors in r•, this aspectwill not be examined here. In calculatingr.• for forests from (4), the major uncertainty will usually be caused by errors in the measuredvalues of transpiration,.  1581  Measurements of net radiation,wind speed at 8.75 meters,and wet and dry bulb temperatures at 8.1 and 9.1 meters,respectively[Black and McNaughton, 1971], were made with instruments supported above the canopy on a meteorological tower. A thermometer and a dewcell were located in a small slatted screen 3 meters above the forest floor. Two soil heat  flux plates were placed at a depth of 5 cm in the soil, and the mean temperature of the surface 5-cm layer was determined with two in.te-  grating thermometers.Samplesof the top 5 cm of the soil were collecteddaily for determination of the heat capacity of the layer. A tensiometer-transducer system was used to monitor soil water potential at depths from 30 to 150 cm at 30-cm  intervals.  The  tree  root  zoneextendedto a depth of 60 cm. Visual observation of a wind vane at the top of the tower indicated that wind was predominantly from the southerly quarter during the daytime. At n.ighta valley wind systemproducednortheasterly winds.  Duringthe monthof Junepreceding the experiment, 9.4 cm of rain were recorded at a  permanent Weather stationabout400 meters from the experimentalsite. Of this total, 6 cm were recorded during the period June 26-29. No  rain  fell between June 29 and the comof detailed measurements.  mencement  Sites with satisfactoryfetch for micrometeorological measurementsare rare in the mounThe experimentalsite was located in a Doug- tainous Canadian west coast region.In spite of las fir plantation growingon a glacial outwash the nonidealconditionsfor the presentstudy, it terrace in the UBC ResearchForest at Haney, is felt that the older regrowthforest beyondthe British Columbia, at an altitude of 250 meters. plantation boundary should have had very The plantation was of a fairly uniform height similar surface temperature and fluxes of heat of about 7.8 meters with some differences in and vapor and that little adjustment of the stand spacing i• the southern section. Fetch boundary layer properties would have been EXPERIMENTAL  SITE  was between 200 and 400 meters in all direc-  tions from NNE through E-SW but was limited in the remaining directionsby a river cutting adjacent to the site. The plantation area sloped down •t about 5% towards the southwest. Beyond the plantation, about 200 meters to the east, was older regrowth forest about 25 meters tall on a slopeof about 10% gradingupward to the east. Land in all directionswas predominantly forest covered for more than 2 km. It is unlikely that advectedenergyhad any significant effect on the evaporation processesnear the experimentaltower.  necessary.  RESULTS AND DISCUSSION  Energy balance. From the data collected during the period July 8-25, 1970, average values of the terms of the familiar energy balance equation  R•v = H + LE + G+  M  (8)  were evaluated for each half hour. Photosynthetic energystoragerate and horizontal energy flux divergenceterms were assumednegligible.  1582  McNAUGHTON  AND BLACK: FOREST EVAPOTRANSPIRATION  Soil heat flux was calculated by correcting  1968] and error introducedby ignoringphoto-  the 5-cm flux plate reading for heat storage syntheticenergy storage (• 5%) do not affect changesin the top 5-cm layer. It was not pos- the comparisonsmade in this paper. Errors sible to evaluate the canopy volume heat due to horizontal flux divergenceare not amenstoragerate term M with precision,and values used in this analysisare estimated from the air temperature and vapor pressure within and above the canopy and estimates of biomass volume and heat capacity of the trees. In the results the quantity (RNGM) usually decreasedto zero in the evening after the wet bulb gradient diminishedto zero, and it was thus indicated that the rate of heat releasedby the canopywas larger than the calculatedvalue  able to this type of analysisbut do not appear to be large.It is expectedthat the 24-hourtotals of evapotranspirationare accurate to within  Little error has been introduced in smoothing values at thesetimes by eye before making the daily (24 hour) totals of evapotranspiration reported in this paper. Resultsfor selecteddays presentedin FiguresI and 2 are unsmoothed. Summationof possibleerror from all sources except that introduced by ignoring photosynthesis and horizontal divergenceterms indicates that individual values of E through most of the day have an uncertainty of 20%. However, consistencyof the resultsindicatesthat random errors are usuallyless.Possiblesystematicerror  (6).  15%.  Energy balanceresultswere found to showa consistentpattern with two distinctivefeatures that differentiate them frdm typical balances for low agricultural crops. Short-term fluctuations in radiation did not producecorresponding proportional changesin the latent heat flux. at that time. A method used to estimate the An exampleis shownin Figure 1 for a partly error in the daily values of evapotranspiration cloudy day, July 23. This pattern may be contrasted with, for example,an energy balanceof due to uncertainty in the values of G and M suggeststhat errors in the daily values from irrigatedalf•fa-bromegrasson a partly cloudy this source are negligible [Black and Mc- day measuredby Tanner and Pelion [1960], where changesin net radiation and latent heat Naughton, 1972]. flux are stronglycoupled.Secon. dly, peak evapoThe Bowen ratio techniquewas used to partitranspiration rates consistentlyoccurred 2-3 tion the available energy between H and LE. An exampleof the energy balance for one day hours after solar noon. This behavior is shown from this period has been presentedpreviously in the energy balancespresentedfor July 8, [Black and McNaughton, 1971]. (Sincethe dry 10, 15, and 18 in Figure 2. Gay [1972] has bulb temperature gradient above the forest is reported a nearly identical pattern for a clear small, correctionfor the adiabatic lapse rate July day energybalanceof a taller Douglasfir (--0.01øC/m) is significantand has been ap- forest at Cedar River, Washington.Fritschen plied to the calculationsfor the present and and Doraiswamy [1973] have made lysimetric preceding papers [Black and McNaughton, measurementsof evapotranspirationfrom a 1971, 1972]. Equation I of Black and McsingleDouglasfir tree in early May 1972 on Naugton [1971] is suitable only for error esti- the site used by Gay. Their results also show mation.) When the Bowen ratio is near --1, that the daily evapotranspi•ration maximums large errors in the computedfluxesmay occur. occur several hours after the net radiation In this study values of the Bowen ratio in the maximums. These results show that forest range --1.5 • fi • 0.5 were rare, except for evapotranspirati0n is not directly 'driven' by two or three values about 1800 PST each afternet radiation in accordancewith the approximanoon when total energy exchangewas small. tion of Monteith's equation for rough surfaces  in net radiation  tion (2«%)  measurement  due to calibra-  and sampling (3%)  [Federer,  Surface resistance. When the results of the measurements and calculations described above  were taken, only ra remainedto be evaluated to solve (4) for  Wind profilessuitablefor use in calculating aerodynamicresistancera were not measured. Wind profileshave been estimatedfrom wind at one height and temperature gradient measurementsusing diabatic profile theory and assumedvalues of surface roughnessand displacement height [Black and McNaughton, 1972]. By using the similarity of heat, vapor, and momentum transport, these profiles suc-  MCNAUGHTON  AND BLACK' FOREST EYAPOTRANSPIRATION I  I  U B.C.  RESEARCH  HANEY,  FIR  2.4 M x 2.4 M 7.8  500  400  M  FOREST  B.C.  DOUGLAS  600  1583 !  SPACING  HIGH  PLANTE  D  ß  1959  -  •500  200  0 -100  -200 0  I  I  I  I  I  I  I  I  I  2  4  6  8  I0  12  14  16  18  dULY  1970  HOURS  PST  2•5  i  I  I  20  22  24  Fig. 1. Energy balance diagram for a day with variable net radiation. The latent heat flux density is largely independent of the short-term changesin net radiation. The Bowen ratio at 1900 PST  was--0.97.  cessfullypredictedthe diurn.alvariationof the eddy diffusivity and were used by Black and McNaughtonto computelatent heat flux with about 34% overestimation.Values of the fric-  that, in a worst-case daytime situation, r, derives an uncertainty of ñ8 sec m-• from this source.This uncertainty is small in comparison with the diurnal and day-to-day differencesin  tion velocity and wind speedat 8.6 meters were calculatedfrom the same synthetic profilesand used to calculate r• from (2). These values are  the calculated values of rs.  Typical daytime r, trends are shownin Figure 2. Nighttime and late-afternoon values, probably systematically underestimated by when the Bowen ratio was near --1, were erratic and frequentlynegative.Daytime trends about 30%. Daytime trends of wind speed and aerody- for each day from July 8 through 13 generally namic resistancecalculated from the synthetic followedthe pattern observedfor July 10 (Figprofileswhen constantzo and D are assumed ure 2b). Of the 13 days followingJuly 13, six are shownfor the four sampledaysin Figure 2. had surface resistancesnotably higher than Aerodynamic resistance exhibited a marked those for the period, two had notably lower diurnal pattern with a definite decreaseand values, and the remainder had similar values. increaseat about 0600 and 173.0PST, respec- On the six days with higher surface resistances tively, when reversalsin the sen. sible heat flux the early-morningvalueswere about 60 secm-•, occurred. Daytime values of r• usually were as was observedfor the days prior to July 13, between 5.5 and 7.5 secm -• and showed less but increasedmore rapidly during the day. This variatio• than the wind speed. $zeicz et al. behavior is illustrated in Figures 2c and d for [1969] have noted a similar small variation July 15 and 18, respectively. in daytime valuesof r• in their analysisof wind Interpreting this behavior as an increasein stomatal resistanceon those days indicatesthat profiles measuredabove a 27-meter-high Northere was water-stress-induced stomatal closure. way spruceforest in Germany. Using (7) to estimate the error in rs calcu- The result is unexpected, since there was a lated from (4) due to uncertain.tyin r• shows plentiful supply of water in the root zone held  McNAUGHTON  1584  600A  AND BLACK: FOREST EVAPOTRA•TSPIRATION  ERGY BALANCE  ENERGY BALANCE  •øø• •oo  o  zo  2.0  .,  .  .,  ••  •  z0  o.•-  .  2.0  ß  0.5  .  .  .  WIND  .  40  ......  e:  40  •z  •,o  SPEED ,  I,  i  ,,  o  0 •  20  •  I0  0 ["•-  ......  I  •RESlSTA•C,E  •  o  I  I  i  0  I  I  I  - f  VAPOR PRESSURE I  DEFICIT  FREEEVAPORATION I  u•  RE-ql-qT_aNCE  20  •  •  A•RODYN•MIC  , ,  ,I  I  _  zoo  e) I00  I  _ _-  z  -  0  o  m 9  HOURS  12  PST  15  18  [_.  06  ,  ,SURFACE  ,.... 12  9  HOURS  15  18  PST  Fig. 2. Daytime trends of meteorological parameters and the derived surface diffusion resistanceof a 7.8-meter-highDouglas fir forest at Haney, British Columbia. The free evaporation rate is shown as the equivalent latent heat flux density. Errat,•c values of the sensible and the latent heat flux and consequently the surface resistance near 1800 PST are due to Bowen ratios near --1 at those times. (a) July 8, 1970. (b) July 10, 1970. (c) July 15, 1970. (d) July 18, 1970.  MCNAUGHTON AND BLACK' FORESTEVAPOTRANSPIRATION  C  600  ENERGY BALANCE600 D  1585  ENERGY BALANCE  •0-  õ00  400  ? 400  300  ß  •OC  • 200  •00 •00  0• 2.0  2.0  WIND 0.5  i  I  WIND  SPEED I  ß  ,I  I  SPEED I  I  40  40  20 0  ,  I  0  AERODYNAMIC RESlSTA•ICE  I  AERODYNAMIC RESlSTA[qCE  30  20  20 I0  I0 VAPOR  0  I  PRESSURE  •  DEFICIT  0  I  I  VAPOR PRESSURE DEFICIT i  I  i  2•  FE[[ [V•POE•TI• •T[  FREE EVAPORATIONRATE I  I  I  i  I  .,oo g  HOURS  12  15  18  E[SlST•NC[ i  HOURS  PST  Fig. 2.  SUEF•C[  PST  (continued)  at relatively high soil water matric potentials. July 25 had not reached60 cm at the time of Soil water mattic potentialsat the 60-cmdepth the recording. are shownfor 0600 PST each day in Table 1. On July 21 very light rain fell for about 2 The wetting front from the heavy rainfall on hours, commencing at 0930 PST, and the  McNAUGHTON  1586 TABLE  1.  AND BLACK' FOREST EVAPOTRANSPIRATION  Summary of Daily Evapotranspiration Data from a Douglas Fir Forest at the UBC Research Forest, Haney, British Columbia  Date,  E,*  Eo,*  E75,*  1970  mm  mm  mm  mm  mm  øC  8 9 10 11 12 13 14 15 16 17 18 19 2O 21  4.34 4.39 4.03 4.20 4.15 4.08  4.07 4.15 4.50 4.40  4.34 4.15 3.74 4.19  6.73 6.46 5.93 6.71  18.3 16.4 15.5 15.6  0.053 0.062 0.064 0.069  4.26  4.10  6.51  16.3  0.074  3.98  4.09  6.53  15.9  0.080  5.45  4.16  6.45  18.4  0.089  7.66 3.11 3.74  4.22 2.10 4.07  6.29 3.20 6.45  22.0 17.3 15.9  0.098 0.110 0.119  22  3.18  23 24 25  2.56 1.75 1.49  July  4.65  4.80 2.40 3.84 4.29 3.61 3.10 1.46  19  15  20 70 22 59 23 91 25 27 22 33 26.77 33 04 18 57 18 89 26 64 22 21 i3 06 7 29 14 52 15 52 9 38  ! .56  [s/(s -]- •)](RN -- G),*  RN,*  T,l  Rain,  --i•,•:  mm  bars  5.88  4.13  6.33  19.9  0.132  4.94  3.50  5.31  19.8  0.148  2.97  2.51  3.90  16.9  1.16  1.01  1.47  12.0  2.89 3.23  3.05 2.59  4.99 4.19  14.2 15.0  1.96  1.64  2.63  13.6  0.5  0.261  0.43  1.26  2.05  12.3  33.5  0.297  &.168 0.25  0.189  0.203 0.230  * 24-hour totals expressedas equivalent depths. I 24-hour arithmetic mean of half hourly temperatures above the forest. •: MeasUrementat 60-cm depth in the soil at 0600 PST.  weather station recorded 0.01 in. (0.25 mm) of precipitation.The rain was almosttotally intercepted by the canopy,and the forest floor was not noticeablywetted. Surfaceresistancevalues immediately fell to about 15 secm -• and remained near this value for 3• hours. During this period of lower surface resistances,energy balance  results  show that  0.31 mm  of water  evaporated. The period of low surface resistance, therefore, correspondedto the period during which interceptedwater was probablypresent on the foliage. July 25 was a day of continuousrain, and surfaceresistancevalueswere closeto zero all day. Elsewhere in the coastal Douglas fir region Phillips [1967] has studied the daily trends of stomatal resistanceof a dominant Douglas fir tree in a closedstand at La Grande, Washington. Using a pressureinfiltration technique,he found daily trends of stomatal resistanceconsistent with those shown in Figure 2. Phillips  leavesacting in parallel and if a leaf area index of about 10 is assumedfor the UBC forest, a typical stomatal resistancefor morn,ingsof about 700 sec m-• is indicated. Phillips' results show150 secm-• as a typical morningvalue. As was noted previously, the simple canopy model expressedby (4) shouldbe treated with caution. Nevertheless, it does seem that the day-to-day differences in surfaceresistanceare unlikelyto be artifactsof the model,sincewind  speedand net radiationwere quite similar on days when resistances were significan.tly different, as is illustratedby the sampledaysin Figure 2. Furthermore, the trends of r8 are generally consistentwith Phillips' measurementsof stomatal resistance made on similar trees.  It seemslikely, therefore,that the observed short-termindependence of the measuredforest evapotranspiration and net radiation., is a result of the roughness of the forest canopyand that the meteorological factor most directly controlalso noted that smaller stomatal resistances ling forestevapotranspiration is the vapor preswere observedon days of lower vapor pressure sure deficit. This hypothesisshouldbe readily multideficit as indicated by hygrothermographmea- testableby useof the moresophisticated surementsat groundlevel. If the surfaceresist- layered canopy model of Waggoneret al. anceis simply the stomatalresistanceof all the [1969], in which aerodynamicresistanceabove  McNAuGHTON AND BLACK: FORESTEVAPOTRANSPIRATION  1587  approaches to the estimationof potentialevap-  attenuated.With the prevailinglow cloudbase, long-wave balance is thought to have been small, and, further, any errors introduced into R• entered almost equally into the calculation of E and Eo. The closeagreementbetween E and Eo suggeststhat (1) can be usedto calculate evaporation from wet forests. However, the agreementis far better than expectedin view of the small temperaturegradients,and hence the large possibleerrors in Bowen ratio  otranspiration. The formula for the free evaporation rate  determinations used to calculate E. This result should not be considered definitive.  the canopy,net radiation,vapor pressuredeficit, and stomatal resistan.ce parameterscan all be manipulatedindependently. Potential evapotranspiration estimates. Since water was plentifulin the root zonethroughout the periodJuly 7-25, actual forestevapotranspiration shouldhave beenat the potentialrate. The estimatesof evapotranspirationfrom the UBC forest can therefore be used to test several  An alternative approach to the estimation of potential evapotranspirationis to attempt vective term. Accurate determination of Eo is to determine representativevalues of the surrei•tivelyeasyfor lowagricultural cropssince face resistancefor various surfaces [Szeicz and the energyterm predominates,and the aerody- Long, 1969] so that these may be used in (4) namic resistancecan be determinedwi•h suffi-. to calculateevapotranspiration.We have thereeient accuracysincethe convectiveterm is in fore examined our results to see if a single day-  (1) hastwo additivetermsthat canbe called  for conveniencethe energy term and the con-  the nature of a correction. For the UBC forest the convective term was as much as seven times  time value of r8 could be found that would  representthe typical behavior of the forest  greaterthanthe energytermowingt0 smallra when it was not short of water. Such a value, values, and consequentlythe uncertainty in ra leadsto a probableoverestimatein Eo of about 25%. Both vapor pressuredeficit an.d Eo are presentedfor the sampledaysin Figure 2. The free evaporationrate has been expressedas the latent heat flux density equivalent (LEo), so that the measuredevapotranspirationand free evaporationrates can be compareddirectly. In spite of the uncertaintyin Eo, a comparison of the measured evapotranspiration rate with the free evaporation rate is instructive. Values of E and Eo for the period July 8-25 are givenin Table 1. It canbe seenthat Eois many times greaterthan E on all days but July 25. This, plus the difficultyof accuratelymeasuring rs and thereforeof calculatingEo, indicatesthat E0 has little practical significanceas a potential evapotranspirationmeasurefor forests. Or. July 25, rain fell continuously,commencing at 0130 PST. The canopywas already wet from a light shower at about 1800 PST the previousevening.The assumptionof a saturated surfacein the derivation of (1) was satisfied. Error in the calculation of Eo was small  on July 25 since all but two of the half-hour values of the vapor pressuredeficit were less than 0.5 mb, and the energy term predominated. The net, radiometer hemisphereswere wet throughout the day, so that the long-wave componentsof the measurementmay have been  it was hoped, would representthe forest with the normal number of stomata open to a nor-  mal degreefor stress-freeconditions. Since the rise in surface resistance was no-  ticed after July 13, only the first six days were used to determine the value. It was found that  values of evapotranspirationfor the first six  days plus three later days couldbe calculated to within 10% by rather arbitrarily setting r8 equalto 75 secm-• in the daytimeperiodfrom 0700 to 1800 PST and 500 secm -• for the re-  maininghours.Daily valuesof evapotranspiration calculatedby this method,denotedby the symbolErs, are plotted againstthe measured 24-hour totals of evapotranspirationin Figure  3. Two points lie significantlybelow the line and are for days when rain fell. Sevenpoints fell significantlyabovethe line. As a potential evapotra:nspiration measure,E?•may have some merit, but on half the days the differencebetween E,• and E was greater than 10% and on July 15 was 40%, even though there was a plentiful supply of water in the root zone throughoutthe period. Where adveeted energy is not an important  sourceof energy for evapotranspiration and soil water is adequate,a closerelationshipbetween net radiation and daily evapotranspiration is expected.Examinationof the data from the UBC forest reveals that daily evapotrans-  1588  McNA•sGX-ITONAND B•,ACK' FORESTEVAPOTRANSPIRATION DATA  and Taylor [1972].They havesurveyed several  FOR  ,JULY 8-  25,  experimentsover surfaceswhere surface resist-  1970  _  ancewas expectedto be negligiblysmall and E0  wasexpected to be equalto the actualevaporation rate. They examined both terrestrial and oceanic data from locations where the  effectsof advectionwereexpected to be negligible. They usedthe data to determinea coefficienta to satisfythe equation  A  4  =  +  -  (s)  where the energyflux density terms are here  24-hourintegrals with unitsof equivalent depth in millimetersof water evaporatedand s is cal-  ••  culated from the mean surface temperature. The bestvalueof a was fo.undto be 1.26.  HANEY, BC•  i  i  I  I  I  I  2  3  4  5  DAILY  EVAPOTRANSPIRATION  (aa)  Fig. 3. Comparison of calculated 24-•hour evapotranspiration values assumingconstant daytime, surface resistance of 75 secm -• with measured  values. Dashed lines represent 10% deviation from the 1'1 line.  piration and net radiation were highly correlated. Energy used in daily evapotranspiration was generally about two thirds of net radiation. Before such a correlation  Measuredevapotranspiration rates from the UBC forestsite plottedagainst(l/L) [s/(s q7)] (R• -- G) are shownin Figure 4. When July 21 and25, on whichrain fell, are neglected, a vaiue for a of 1.05 is found.  When the possibleerrorsin determiningeach value of a are considered,these values are not riecessarilysignificantly different. However, it  doesseempro.bable that evaporationfrom the UBC forest, when it is wet, would proceed I  I  I  I  DATA FOR  2  JULY 8 - 25, 1970  can bo used with  confidence as a basisfor estimating evapotranspiration, further work must be done to determine the influenceof other factors,suchas tree phen, ology and presenceof intercepted water on the canopy,on the partitioningof the available energy between sensibleand latent heat fluxes. Examination  of the  UBC  forest data  allowsus to make someestimateof the importance of interception.In the absenceof advection the maximum possiblerate of evapotranspiration is given by (R• -- (7). With typically small G values for the forest, this equation implies that the maximum possiblerate of evaporationof interceptedwater after general rain could not be more than 50% faster than the observed rates.  ß  _  --  ß  ß  U B C RESEARCH  HANEY,  FOREST  B.C.  • ' •' 2 4M x 2.4M SPACING-] (u•,\.o•O DOUGLAS FIR  78MHIGH1 PLANTE D  i  I  2  i  $  1959  1  4  5  ¾ S'•"•RN-G (MM)  Fig. 4. Measured daily values of evapotmnspiration in comparison with (1/L)[s/(s q- v)] (R• -- G). Data for July 21 and July 25, when  Perhapsa more realisticestimateof the influrain fell, are shown as triangles and have not been ence of interceptedwater can be obtainedby used to determine the line of best fit. The availcomparingthe result from the dry transpiring able energy R• -- G is expressedas an equivalent canopywith a relationship. found by Priestley depth of water evaporated.  McNAuGHTON  AND BLACK: FOREST]•VAPOTRANSPIRATION  at a rate 20% faster than the expectedevapo-  transpirationfrom the same canopywhen it is well suppliedwith water but not wet. On July 25, a was1.18,whichis closeto the value foundby Priestleyand Taylor for wet surfaces and tendsto supportthe validity of this comparison.Data from July 21 are not suitablefor usein this comparison sincethe high value of a for this day (a ----1.45) is a resultof a clear sky beforedawn,and thus the 24-hourradiation total is unrepresentativeof the daytime period. During the period when the canopy was wet on this day, LE was about three quarters of RN.  An estimateof the importanceof interception lossesby the forest can now be made. GrossinterceptionlossI is the amountof pre-  1589  lated. By comparing the UBC forest results with a relationshipdevelopedby Priestleyand Taylor to predict evaporationfrom wet sur-  faces,it is tentativelyinferredthat intercepted water evaporates 20% more rapidly than transpiredwater and that thereforeonly 17% of grossinterception lossesat the UBC forest are to be consideredas net interceptionlosses. NOTATION  D, zero plane displacement,meters; E, evapotranspirationrate, kg m-•- sec-•; E0, free evaporationrate, kg m-2 sec-•;  E7,, total 24-hour evapotranspirationassuming daytime ro = 75 secrn-•, mm; G, soil heat flux density,w m-•'; H, sensibleheat flux density, w m-•; I, L,  grossinterception loss,mm; latent heat of vaporization of water, joules  kg-•; cipitationontothe forest.that is caughtby the M, rate of heat storagein the canopyvolumeon canopyand reevaporates withoutreachingthe an area basis,w m-•-; ground.However,becausethe leavesare wet, P, potential evapotranspiration,ram; transpirationis at the sametime suppressed, R•r, net radiation flux density, w m-•';  and not all of the grossinterceptionlossrepresents a loss in the hydrologicsense.The net  interceptionlossis the difference betweengross interception lossand the reductionin transpiration causedby the presenceof the intercepted water. From the above result, only 17% of the  T,  temperature, øC;  c•, specificheat of moist air, jouleskg-• K-•; e0, water vapor pressureat the canopysurface, mb; e0*, saturation water vapor pressure at the canopysurfacetemperature,mb; e•, water vapor pressureat height z, mb;  e•*, saturationwater vapor pressureat height z, grosslosscan be considered to be net loss. mb; Perhapsthe bestpotentialevapotranspiration ra, aerodynamicdiffusionresistanceat height z relationshipthat can be suggestedfrom the (assumedequal to u•/u.•'), secm-•; to, surfacediffusionresistance,secm-•; s, slopeof the saturationwater vapor pressure curve, mb K -•; P = (1.05/L)[s/(s-]-y)](R•G) -]- 0.17I u•, wind velocity at height z, m sec-•; (10) u., friction velocity, m sec-•; wherethe energyflux densityterms have been z, height above soil surface,meters; z0, roughnesslength, meters; integratedover 24-hourperiods,as in (9). ß ,•, soil water matric potential, bars; CONCLUSIONS a, empirical coefiqcient; t], Bowen ratio, identically equal to H/LE; Measurementsof evapotranspiration made at % psychrometric constant, equal to 0.66 mb the UBC Research Forest showed that peak K-•; p, density of moist air, kg m-•. evapotranspirationrates occurred 2-3 hours Acknowledg•nents. We would like to thank after solarnoo.nand that.evapotranspirationwas not stronglyaffectedby short-termchangesin Mr. John Walters, Director of the UBC Research Forest, for his cooperation in the measurement net radiation..On the basis of a simplified anal- phase of this research.This researchwas supported ysis using Monteith's combination canopy by grants from the National ResearchCouncil of model it is hypothesizedthat this is a direct Canada and the Canada Department of the En-  presentstudy is  effect of the large canopy roughnessand that vironment (NACWRR). vapor pressuredeficitis the dominantmeteoroP•EFERENCES logical factor directly controllingforest evapo- Black, T. A., and K. G. McNaughton, Psychrotranspiration. metric apparatusfor Bowen-ratio determination On a daily basis,measurements of net radiaover forests,Boundary Layer Meteorol., 2, 246254, 1971. tion and evapotranspirationwere highly corre-  1590  McNAUGHTON AND BLACK: FORES? EVAPOTRANSPIRATION  Black, T. A., and K. G. McNaughton, Average Bowen-ratio methods of calculating evapotranspiration applied to a Douglas-fir forest, Boundary Layer Meteorol., 2, 466-475, 1972. Businger,J. A., Some remarkson Penman'sequation for evapotranspiration,Neth. J. Agr. Sci., 4, 77-80, 1956. Cowan, I. R., Estimation of evaporation using meteorologicaldata, in Land Evaluation Papers o] CSIRO Symposium Organized in Coopera. tion with UNESCO, edited by G. A. Steward, pp. 291-311, Macmillan, New York, 1968. Federer, C. A., Spatial variation of net radiation albedo and surface temperature of forests, J. Appl. Meteorol., 7, 789-794, 1968.  Fritschen,L. J.,_and P. Doraiswamy,Dew: An  Phillips, R. A., Stomatal characteristics throughout a tree crown, M.F. thesis, 67 pp., Univ. of Wash., Seattle, 1967. Priesfiey, C. It. B., and R. J. Taylor, On the assessment of surfaceheat flux and evaporation using large-scale parameters, Mon. Weather Rec., 100, 81-92, 1972. Rutter, A. J., Studies on the water relations on  PinusSylvestries in plantation condition, s, J.  Appl. Ecol., 3, 393-405, 1966. Rutter, A. J., An analysis of evaporation from a stand of Scotspine, in International Symposium on Forest Hydrology, edited by W. E. Sopper and It. W. Lull, pp. 403-417, Pergamon, New York, 1967. Stewart, J. B., and A. S. Thom, Energy budgets  addition to the hydrologic balance of Douglas in pine forest, Quart. J. Roy. Meteorol. Soc.,99, fir, Wc•terResour.Res., 9(4), 891-894, 1973. 154-170, 1973. Gay, L. W., Energy flux studiesin a coniferous Szeicz, G., and I. F. Long, Surface resistanceof forest ecosystem,in Proceedings--Researchon Co,ni]erousForest Ecosystems--A Symposiu.m,  edited by J. F. Franklin, L. J. Dempster,and P•. H. Waring, pp. 243-253, Pacific and North-west Forest and Range Experimental Station, Portland, Oreg., 1972.  Hinckley, T. M., and D. R. M. Scott, Estimates of water loss and its relation to environmental  parametersin Douglas-firsaplings,Ecology,52, 520-524, 1971.  Ladefoged,K., Transpirationof forest trees in • closedstands,Physiol.Plant., 16, 378-414,1963. Monteith, J. L., Evaporation and environment, Symp. Soc. Exp. Biol., 19, 205-234, 1965. Parker, J., The cut-leaf method and estimations of diurnal trends in transpiration from different heights and sides of an oak and a pine, Bot. Gaz. Chicago, 199, 93-101, 1957.  Penman, I-I. L., Natural evaporation from open water, bare soil and grass, Proc. Roy. Soc. London, Ser. A, 193, 120-145, 1948.  Phillip, J. R., Commentson paper by Monteith, in Enviror•mer•tal .Control o• Plant Growth, edited by L. T. Evans, p. 111, Academic, New York, 1963. Phillip, J. R., Plant water relations: Some physical aspects,Ann. Rev. Plant Physiol., 17, 245268, 1966.  crop canopies, Water Resour. Res., 5(3), 622633, 1969.  Szeicz, G., G. Endrodi, and S. Tajchman, Aerodynamic and surface factors in evaporation, Water R esour. R es., 5(2), 380-394, 1969.  Tanner, C. B., Energy relations in plant communities, in Environmental Control o] Plant Growth, edited by L. T. Evans, pp. 141-148, Academic, New York, 1963. Tanner, C. B., and M. Fuchs, Evaporation from unsaturated surfaces, J. Geophys. Res., 73, 1299-1303, 1968.  Tanner, C. B., and W. L. Pelton, Potential evapotranspiration by the approximate energy balance method of Penman, J. Geophys. Res., 65, 3391-3413, 1960. Thom, A. S., Momentum, massand heat exchange  of vegetation,Quart. J. Roy. Meterol. Soc.,98, 124-134, 1972.  Van Bavel, C. I-I. M., Potential evaporation:The combinationconceptand its experimentalverification,Water Resour.Res.,2(3), 455-467,1966. Waggoner, P. E., G. M. Furnival, and W. E. Reifsnyder, Simulation of the microclimate in a forest, Forest Sci., 15, 37-45, 1969. (Received January 3, 1973; revised July 27, 1973.)  

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