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Estimating the effects of understory removal from a Douglas Fir forest using a two-layer canopy evapotranspiration… Price, D. T.; Black, T. Andrew; Kelliher, F. M. 1986

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WATER RESOURCES RESEARCH, VOL. 22, NO. 13, PAGES 1891-1899, DECEMBER  1986  Estimating the Effects of Understory Removal From a Douglas Fir Forest Using a Two-Layer Canopy Evapotranspiration Model F. M. KELLIHER 1 AND T. A. BLACK Departmentof Soil Science,University of British Columbia, Vancouver D. T. PRICE  Faculty of Forestry, University of British Columbia, Vancouver  W. J. Shuttleworth's(1979) developmentof the Penman-Monteith evaporationequation for multilayer, partially wet forest canopieswas modified for application to the hypostomatouscanopiesof Douglas fir and salal. This theory was combined with standard hourly micrometeorologicalmeasurements,eddy diffusive,boundary layer and stomatal resistancefunctions, and canopy and root zone water balance equationsto calculateevapotranspirationrates (E) from a Douglas fir forest with salal understoryover extendedperiodsduring two growing seasons.Calculatedvaluesof E agreedto within 0.2 mm d-• of values determined using Bowen ratio-energy balance measurements.The coursesof average root zone volumetric water content (0) calculated for two extended periods agreed well with neutron probe measurements. Salal understoryremovalresultedin measuredvaluesof 0 beingonly 0.01-0.03 m3 m -3 higher over the two periods, in close agreementwith calculations.This correspondedto calculated tree  transpirationratesbeing0.4 mm d- • higheron average,during the secondhalf of both periods.These higher rates were confirmed by stomatal resistancemeasurements.  INTRODUCTION  The Penman-Monteith equation [Monteith, 1965] has provided usefulinsightinto the physicaland physiologicalfactors affecting forest evapotranspiration [Stewart and Thom, 1973; Tan and Black, 1976]. A further developmentof the equation for multilayer, partially wet forest canopies has provided a practical one-dimensional model [Shuttleworth, 1978, 1979], despite the simplifying assumptionsregarding within canopy turbulent transfer [Jarvis et al., 1976; Raupach and Thom, 1981; Finnegan, 1985]. With standard hourly micrometeorological measurements and stomatal resistance character-  where E[ is the difference between the water vapor flux density above and below the layer (i.e., Ei- Ei-•); R.i and Di are the net radiation flux density and vapor pressuredeficit above layer i, respectively; G is the soil heat flux density; L is the  latentheatof vaporization; p is thedensityof air; cv isspecific heat of air; s is the slope of the saturation vapour pressure curve; 7 is the psychrometricconstant, and  (•i= [S(Rni-•-- G)(rt, i/(2ai))+ (s + 7)LEi_ •rai]/(pcv)  (2)  The total aerodynamicresistance(r,•i) [Thom, 1972] is given by  istics, the model can be combined with a root zone water  balance model [e.g., Spittlehouseand Black, 1982] to provide estimatesof forest evapotranspiration over extended periods. This paper (1) describesthe evapotranspiration model as modified for use in hypostomatouscanopies,(2) tests the model using energy and water balance measurements,and (3) uses the model to explain the effects of salal (Gaultheria shallon Pursh.) understory removal on tree transpiration rates in a Douglas fir (Pseudotsugamenziesii(Mirb.) Franco) forest.  Using Shuttleworth's[1979] evapotranspiration theory, assumingthe similarity of sensibleheat and water vapor aerodynamic transfer resistancesand neglecting canopy energy storage, it can be shown that the water vapour flux density from layer i(E[) with leaf area (one side)index (ai) within a multilayer forest canopy of hypostomatous leaves can be expressedas (see the avpendix)  (1)  •Now at Forest ResearchInstitute, Private Bag, Rotorua, New Zealand.  (3)  and the canopyresistanceof layer i(rcOis expressedas  w,  1-Wi ]-•  rci-- (1+ s/7)rt, i/(2ai)rsi/a i + (2+ •--•)rb,/(2a)  -- (1 + s/7)%i/(2ai)  (4)  whererai is the eddy diffusiveresistanceabovelayer i, r•i and  THEORY  Ei'--s(Rni - G)+ pcv(D i --6i)/ra, L[s + 7(1 + rci/rAi)]  rAi = rai q- rt•i/(2ai)  rs•are the boundary layer and stomatal resistancesof one side  of the leavesin layer i, respectively,and W•is the fraction of leaf area in layer i that is completelywet. Stomatal resistances of hypostomatousleavesof Douglas fir and salal on a onesided basishave been related to light, leaf and soil water potential, and vapor pressuredeficit [Tan et al., 1977, 1978]. Equation (1) is recognizedas the Penman-Monteith equation with an additional  term which accounts for the net radi-  ation, latent and sensibleheat flux densitiesbelow layer i. Black et al. [1970] used(1) as an evapotranspirationmodel for a dry snapbeancanopywherer•i <<rsiwasassumedso that was equal to the soil evaporationrate multiplied by  + 7)/(pcv). If r•i is assumed to be zero,then(1) reduces to the Copyright 1986 by the American GeophysicalUnion. Paper number 6W4433. 0043-1397/86/006W-4433505.00  Penman-Monteithequationappliedto the layer (i.e.,usingthe vapor pressuredeficit and the available energy flux density (R.- R._ •) within the layer). Equation (4) givesthe canopy 1891  1892  KELLIHER ET AL.: TwO-LAYER  CANOPY EVAPOTRANSPIRATION  resistanceof a partially wet layer assumingthat the individual leavesare either completelywet or completelydry so that the wet and dry leaveshave different temperatures.Equation (4) differs slightly from Shuttleworth's[1978] (32) because his derivation was for amphistomatousleaves. When W•= 0, rci = rsi/ai + rbi/(2ai) comparedto rci = rsi/(2ai)for an amphistomatousleaf canopyas in (24) of Shuttleworth.As expected, when W•= 1, rci = 0 in both hypostomatousand amphistomatous cases.Making use of Shuttleworth'stheory it can be shown that the rate of evaporation of interceptedwater from layer i(Eu') is given by (seethe appendix) E,'W•[(2 + s/?)%,+ 2rs,]  Eli'--(1 +s/7)r• + W•(r• +2rs• )  (5)  The vapor flux densityabove layer i(E•) is given by summing (1) from 0 to i, so that for a canopy of n layers the evapotranspirationrate is  MODEL  model S-1 radiometer (Swissteco Pty. Ltd., Victoria, Australia), while R, below the tree canopy (R,) was measuredin one plot using one net radiometer above the salal canopy and another above the forest floor surface, where salal had been  removed. In 1982, R, was estimated,prior to August, from solar irradiance measurementsfollowing Gates [1980]. During August 1982, R, was measuredas in 1981, but R, was measured using an S-1 net radiometer mounted on a tram traveling at the 1-m height along a 10-m path where salal along one half of the path had been removed [Kelliher, 1985]. The  tram traveled at 0.5 m min-x and automaticallyreversed when it reached each end. The net radiometer output voltage was measuredevery 10 s. These resultsshowed that R.b was  approximately0.16 R, and 0.14 R, for uncut and cut subplots, respectively.In 1982, these relationshipswere used to estimateR, prior to August. In both years, R, below the salal canopy was estimated using R, = ((s + 7)/s)LEo + G  whereLEO was 2 W m-2 (measuredusingsmall lysimeters  describedlater). The soil heat flux densityat the 50-mm depth in each subplot of one plot was measuredduring 1981 and in August 1982 using three soil heat flux plates (100 mm where E o = Eo' is the evaporation rate from the forest floor long x 25 mm wide x 3 mm thick), made following the design with 6o - O and rcobeing the forest floor diffusiveresistance of Fuchs and Tanner [1968], connected in seriesand corrected [Denmead, 1984; Shuttleworth and Wallace, 1985]. In this for the rate of change of heat storage in the upper 50 mm of study the forest canopy was divided into two layers (n- 2), soil. On the basis of these measurements, G was estimated as where the Douglas fir subcanopywas designatedas layer 2 0.02 R, and 0.03 R, for uncut and cut subplots,respectively, and the salal subcanopyas layer 1. in 1982.  E= • E[ i=0  "(6)  In both years,air temperature(Tair)and vapor pressuredeficit (D) were estimated below the tree canopy using hourly Site Description average values at the 6-m height with the relationshipsrair r (øC)(6 m height)+ 1.2 and The site was a 31-year-oldDouglas fir stand with about 800 (øC) (0.5 m height)= 0.93Tai D(kPa) (0.5 m height)= 0.89 D(kPa) (6 m height)- 0.03 treesha-•, approximately 27 km northwestof Courtenayon the eastern coast of Vancouver Island (49ø 50'N, 125ø 14'W, (based on 33 hourly average measurementsof Tair and D at 150 m above sealevel).At the end of the 1982 growing season, both heights on July 24 and 25, 1981). Hourly Assmann psystand(excludingunderstory)basalarea was 16 m2 ha-•, and chrometer measurementsconfirmed the validity of these reaverage tree height was 14 m. Average tree and salal under- lationshipson severaldays in August 1981 and June 1982. story leaf area indices on a one-sided leaf area basis, were Diffusive ResistanceFunctions about 6 and 3, respectively,in 1982. The soil, an Orthic Humo Ferric Podzol, is a gravelly sandy loam with a volumetric Stomatal resistances (rs) of Douglas fir and salal were esticoarse fragment (> 2 mm diameter) content of 10-45%. It is mated usingaverageroot zone soil water potential(Ws)and D coveredwith a layer of organic forestfloor material 10-20 mm for the layer followinginterpolationof the functionsin Tan et thick and is about 700 mm deep over sandstonebedrock. The al. [1978] [Kelliher, 1985]. When R, was negative(i.e., 1900siteis on a slopeof lessthan 10%, with a northeastaspect. 0700 hours PST), rs of both specieswas set to 105 s m -x. The model was tested using stand energy balance measure- Boundary layer resistances (r•) were estimatedusinga function ments made in 1982 and soil water content and potential for artificial leaves in the work by Spittlehouseand Black measurements made in 1981 and 1982 in four circular plots [1982] and a shelter factor of two [Landsberg and Powell, about 7 m in diameter, each containing two subplots,one with 1973;Jarviset al., 1976].The functionro(sm-•) = 2 x 184 salal understorypresentand the other with it cut and removed (dt/u)ø'5was used,wheredt is leaf diameter(m) (0.001m for on May 21, 1981. Each subplot containedone tree which was Douglas fir and 0.06 m for salal) and u is the wind speed(m similar in size to the one in the adjacent subplot. The root s-x) nearthe leaf(0.5ux5 mfor Douglasfir and0.13u•5mfor zones of all eight trees were isolated by a vertical plastic barsalal, where ux5m is the wind speedat the 15-m height). In rier consisting of two sheets of 0.15-mm-thick polyethylene 1982(prior to August),ux5mwasestimatedto be 3 m s- x for extending down to bedrock [Kelliher, 1985; Price et al., 1986]. 1100-2000hoursPST and 1.5 m s- x for the restof the day. Dividing thesevaluesby 2a• gavemean boundarylayer resistMicrometeorological Measurements ances similar to those estimated following the relationships Routine measurements of solar irradiance above the stand, given by Garratt and Hicks [1973]. The eddy diffusiveresistair temperature, and relative humidity in a Stevensonscreen ance above the Douglas fir layer, required when the air temat the 6 m height, wind speedat the 15 m height, and precipi- perature and relative humidity measuredat the 15-m height in tation above the stand were made throughout the 1981 and August1982 were used,was estimatedassuminga logarithmic 1982 growing seasons.Data were recorded as one hour wind profile [Jarvis et al., 1976] with a zero-plane displaceaveragesor totals usinga data logger (model CR21, Campbell ment height of 8.5 m I-Szeiczet al., 1969] and a roughness Scientific Inc., Logan, Utah). length of 1.5 m [Stanhill, 1969]. The correspondingresistance In 1981, Rn above the forest (Rna)was measuredusing a above the salal layer was roughly estimatedassumingan exMETHODS  KELLIHER ET AL..' TwO-LAYER CANOPY EVAPO•RANSPIRATIONMODEL  ponential eddy diffusivity profile from the top of the trees to the salal layer [Thom, 1975; Shuttleworthand Wallace, 1985] with an attenuation  coefficient  of 2. This value was based on  1893  lowing water balanceequationappliedto the stand and its single-layerroot zone  Ok= Ok-1 + (Pk- Ek -- Fk)At/•  (8)  the ratio of the below to above tree canopy windspeedsbeing about 0.13. Daytime eddy diffusive resistancesabove the salal  wherePk,Ek,and Fk are the ratesof rainfall,evapotranspira-  layer were calculatedto be about 40 s m -x comparedto approximately20 s m -x for the 600 trees ha-x Thefiord  tion, and root zone drainage at time k, respectively;At is the time interval between k and k- 1 (1 hour except for when  [Shuttleworth, 1979; Roberts et al., 1980] and the 400 trees  W•>0 and then At is 15 rain); and • is root zonedepth.  ha-x Jadraas[Lindroth,1984] forests.For the cut subplots, Evapotranspiration rates were calculatedusing (1) through (7) valuesof raiestimatedfor the salal layer were used. Forest floor diffusiveresistances (rco)for 10 daysin July and August 1981 were determinedby choosinga value which resulted in agreement between daily total values of measured and calculated Eo on each day. Measurementsof E o were made in the cut subplot of plot 2 using plastic-walledlysimeters 150 mm in diameter and 120 mm deep, which were weighed every 1-2 hours. The undisturbed soil cores in the lysimeterswere replacedevery 1-2 days. The values of r½o were related to average root zone water content (see Results and Discussion)for calculationsof forest floor diffusiveresistanceson other days. For each Douglas fir tree in a subplot, leaf area was estimated from the diameter at the 1.37-m height usinga function in the work by Spittlehouse[1981]. Ground area occupiedby the tree was estimated using a tree location map and the  with the canopydivided into two layers(tree and understory). Drainagefrom the root zonewascalculatedas a functionof 0  (F(mm d -a) --- 100 (0/0.3)l•) [Spittlehouse and Black, 1981a•. During most of the summer,drainage was a small term in the root zone water balance equation so that 0 was largely determined by rainfall and evapotranspiration. Testing the Evapotranspirationand Root Zone Water Balance Equations  During July to September 1981 and May to July 1982, 0 was measured at 1- to 2-week intervals using the neutron moderation techniquewith a calibrated [Kelliher, 1985] probe  (model CPN 503, CampbellPacificNuclear Corp., Pacheco, Calif.) being lowered into aluminum accesstubes. There were 3 or 4 tubes in each subplot. Thermocouple psychrometers and tensiometerswere usedto measureWsevery 2-7 days. A  "polygonof occupancy" [Santantonio et al., 1977].Tree leaf pair of psychrometers and a tensiometei' wereinstalledat 150 area divided by the polygon of occupancywas taken as the mm depthintervalsdownto bedrockin eachsubplotof plot 2. value of leaf area index (a) for each of thesetrees(i.e., for the  Measured valuesof 0 and Ws were compai'edduring the two  Douglasfir layer).For the salallayer, 1-me samplemeasure- summer periods with calculatedvalues obtained using (8) and mentsmadein eachof the cut subplotson May 21, 1981,were a soil water retention curve determined using neutron probe, used to estimate  a.  tensiometer,and thermocouplepsychrometermeasurementsat  The leafwetness variablefor eachlayerwasestimatedusing thesite(Ws(MPa)= --0.005(0/0.3)-6'5). the ratio of the layer water storage(C) to the maximum water Forest evapotranspiration was measured on 4 days in storageof the layer (S). The value of S for the Douglas fir layer August1982 usingthe Bowenratio-energybalancetechnique. was determined by plotting 24-hour throughfall (above the Half-hourly measurementsof the Bowen ratio (/•) were made salal) against the correspondingrainfall using data of Spittle- using a de-powered rotating psychrometric apparatus dehouse [1981] for 1978. Rutter et al. [1971] showed that the scribedby Spittlehouse and Black [1981b]. The apparatuswas negative intercept of the line of unit slope along the upper located at the top of a 15-m-tall tower adjacent to the four limit of the throughfall data gives the value of S. This wag plots, with the vertical separationbetweenthe two psychromfound to be 0.6 mm. Since the value of a of the Douglas fir etersbeing 3 m. The lower psychrometerwas about 1 m above layer in 1978 was 5, the averagedepth of water on the leaves the tops of the trees. Forest evapotranspiration was calculated was 0.12 mm. This was very close to the depth of water after using drainage on a foliated Douglas fir branch sprayedin the laboratory [Spittlehouseand Black, 1982]. The value of S for the (9) E -- (Rna-- G - M)/(L(1 + t•)) salal layer was approximated by multiplying salal a by 0.12. The value of C was calculatedfor each time j usingthe follow- where M is the rate of canopy heat storageestimatedfollowing Stewart and Thom [1973]. This measurement of E was ing water balanceequation for each layer: consideredto include tree and understory transpiration and C• = C•_1 + [-(1-- p)P•- E,f-- Q•JAt (7) soil evaporation,since the area where understoryhad been  whereAt is 1/5min,andP• and Q• aretheratesof rainfalland drainage of interceptedwater respectivelyfor the interval between j- 1 and j. The free throughfall coefficientp was calculated by taking the averageof the ratio of 24 hour throtighfall (above salal) to rainfall for /5 days from Spittlehouse[-1981J, where P < S [-Rutter et al., 1971•. It was found to be 0.6.  removed was small and 20 m from the tower in a direction at  right angles to the prevailing wind direction. These measure-  mentsof E werecompared to calculated valuesobtainedusing (1)-(8) (W•= 0) appliedto a two-layercanopy(treesand understory)plus soil evaporation. Stomatal resistancemeasurementswere made using a venti-  Drainage wasassumed to bezerountilC•exceeded/9. At this lated diffusionporemeterdescribedby Tan et al. [1977]. point drainage was calculatedas the amount by which ((1  --p)P•--E•f)At exceededthe remainingwater storagecapacityof theleaves(S -- C•_ Root Zone Water Balance Equation  The courseof averageroot zone volt•metricwater content (0) during two summer periods was calculated using the fol-  Hourly measurementswere made on the two trees and salal in one plot from sunriseuntil late afternoon on Augfist 12 and 20, 1981, and on the two trees only on June 9, 17, 23, and 30,  1982. These measurements were used to check the applicability of the rs functionsmentioned earlier to the trees and salal in 1981 and 1982 and to assessthe accuracyof the rates of tree and understorytranspirationcalculatedusing(1).  1894  KELLIHER ET AL.' TwO-LAYER CANOPY EVAPOTRANSPIRATION MODEL  TABLE 1. Daily (24-hour)Net RadiationFlux DensityAbovethe Forest(R,a) and Daily Measuredand CalculatedValuesof  i  was0.16m3 m -3 (qJs- -0.3 MPa)  1600  Date (August, 1982)  Rna Measured  Calculated  25  26  11.6  12.6  1.8  2.2  1.8  0.2  1.9  2.0  2.0  0.3  E  O\  O_ø .... 9.0.  1.4  Rnaare givenin MJ m-2 d-x andE in mm d-x. Rootmeansquare  ,i  00%  -  27  11.5 E  i  3ZOO •øo• I  Evapotranspiration Rate (E) Following Initialization of Calculations on August 20, 1982, When Measured 0  24  i  I  o  I  0.16  I  I  .I  0.18  0.20  O (m3m'3) Fig. 2. Relationshipbetweenforest floor diffusiveresistance(rco)  errors in measuredand calculated E were approximately 0.2-0.3 mm  and average root zone soil water content (0) in the cut subplot of plot  d-x for August24-26 and 0.1 mm d-x for August27.  2 for 10 daysin July and August1981.For 0 lessthan 0.185,rco(s m-X)= -83000 0 + 16100 (R2 =0.96) as shown by the solid line. For 0 greaterthan 0.185,r•o was800 s m-x, on average,as shownby  RESULTS AND DISCUSSION  the dashed line.  Measuredand CalculatedDaytimeEvapotranspiration Rates There was generally good agreement between daily values of E measured during the 4-day test period using the energy balance-Bowen  ratio and values calculated  for the stand with  understory present (Table 1). Agreement was not as good when comparing the daytime coursesof measuredand calculated E (Figure 1). However, both measuredand calculatedE was highestfor the 2-hour period prior to noon on August25, 1982. Calculated Douglas fir rs increasedmarkedly after 1400 hours (>6000 s m -x) owing to the high values of D, and calculated salal E was highestfor the period 1100-1400 hours  (•0.1 mm h-:). Measurementerror accountsfor someof the disagreement,since Bowen ratios were high (_>2) on August 24-26 and wet and dry bulb gradients small on August 27 [Spittlehouseand Black, 1980].  Forest Floor EvaporationAfter Salal Removal For 0 less than 0.185, forest floor diffusive resistance was  linearly related to 0 (Figure 2). On 3 days when 0 > 0.185, rco 600  2.4  4OO  was 700 s m-: (0 = 0.189),and 900 s m-: (0 = 0.200 and 0.203). This meant that E o was limited by a dry surfacelayer whose thickness(la) can be related to rco using [Denmead, 1984; Novak and Black, 1985]  Ia = rcofa(%-- Oa)• %  (10)  wheref• is a "tortuosity"factor (0.66); % and 0dare the poros-  ity and volumetricwatercontentof the dry layer;and •%is the moleculardiffusivityfor water vapor (24.9 x 10-6 m2 s- • at 25øC). For the forest floor, eaand 0awere taken from Pla-  toondon[1972] as 0.88 (i.e., bulk density= 150 kg m -3, organicmatter density- 1300 kg m-3 [Van Wijk and De Vries, 1963], and 0.20 (i.e., matric potential =-  1.5 MPa).  Usingthesevaluesandrco= 700s m- • in (10)resultsin la- 8 mm. Field observationssupport this calculation. At about midday on the day following an eveningirrigation equivalent to 100 mm of rain, the forest floor surfaceof a cut area (i.e., salal cut and removed)adjacent to the four plots was observed to be dry. The abovevalue of la suggests that the top 8 mm of forest floor consistedof rapidly draining litter (i.e., undecomposed leavesand twigs), while the bottom 2-12 mm was humifled with some water storage capacity. The interface between  the organiclayerand mineralsoil wasmoistuntil rcoreached  2:00 300  I•  •--  '• 200  •  .... :"'-l'4o. lZ [ 0l'ø I I0 LU 6  12  18  hour (PST) Fig. 1. Courses of net radiation flux density and vapor pressure deficit above the forest (Rn• (solid lines) and D (dashedlines),respectively) and measured(solid lines)and calculated(dashedlines)forest evapotranspiration rate (E) (with understory) on August 25, 1982, a clear day when averagezone soil water potential 0Ps)was about -0.7 MPa. Errors in measuredE were approximately0.02-0.04 mm h-x [Spittlehouseand Black, 1980]. Root-mean-squareerrors in calculated E were 0.04-0.06 mm h -x as determinedby differentiationof (1) applied to two layers and soil. A 10% error was assumedfor D s, a 20% error for (Rni-- G), and a 30% error for the transferresistances, LE Oand Rno.  I  I  I  I  I24  ..r"  • ,oo o  60  • 4O  0.08  -. I  18  .......  i'• .......... •"  0  6  .._c..•] E I  12  /  18 ¸  hour (PST)  Fig. 3. Coursesof net radiation flux density and vapor pressure  deficitabovethe forestfloor (R,o (solidlines)and Do (dashedlines), respectively)and measured(solid lines)and calculated(dashedlines) forestfloor evaporationrate (Eo)in the cut subplotof plot 2 on July 2•25, 1981, two clear days when averageroot zone soil water poten-  tial (•s) wasabout -0.05 MPa. Standarddeviations for measured Eo values were typically 0.004 mm h -• at night and 0.015 mm h -• duringthe daytime.Root-mean-square errorsfor calculatedEo values were similar. These errors were determinedby differentiationof (1) with rio= 0. A 20% error wasassumed for (R,o - G) and r•o, a 10% error for Do,and a 30% error for r•o.  KELLIHERET AL.' TwO-LAYERCANOPYEVAPOTRANSPIRATION MODEL  /  %.  '  r  I  I  I  i  I  =-i  TABLE 2.  0 'r.•_  1895  Average Values of the Minimum Measured and  CalculatedAverageRoot Zone Water Content(m3 m-3) in the Cut (C) and Uncut (U) Subplots August 27, 1981  June 25, 1982  0.16  Subplot  o  •  z•.....:............... •"  • -o.8 -16  ,  i  I  JUL 30  i  AUG 7  I"  AUG 15  AUG 23  AUG :31  Measured  1U 1C 2U 2C 3U 3C  Calculated  Measured  Calculated  0.14 0.13 0.13 0.15 0.14 0.17  0.14 0.14 0.13 0.15 0.13 0.15  0.14 0.15 0.12 0.14 0.14 0.17  0.12  4U  0.16  4C  0.17  0.14 0.16  0.16  0.13 0.15  U  0.14  0.13  0.14  0.12  C  0.16  0.15  0.16  0.14  0.14  0.12 0.14 0.12 0.14  0.16  Means  1981  Fig. 4. Courses of measured (symbols) and calculated (lines) averageroot zone soil water content(0) and soil water potential(Ts) in the cut (open trianglesand dashedcurves)and uncut (closedtriangles and solid curves) subplots of plot 2 for the period July 24 to September3, 1981. Standarddeviationsfor measured0 and tPs were  For plots 2 and 3 (but not plots 1 and 4) the difference between measured values in cut and uncut subplotswas statistically significant (95% probability)in both years.  0.01-0.02m3 m -3 and 0.1-0.2, MPA, respectively. Also shownis the daily rainfall rate (P).  850-1500s m-• (0 = 0.184-0.176). For 0 = 0.125(Ws= --1.5 MPa), ldwas 68 mm so that the top 48-58 mm of soil wasdry.  calculated differencesin 0 between paired subplots.Salal understory removal resulted in slightly higher values of 0 and  muchhighervaluesof •s. Becauseof the largevalueof A•s/ A0 for this gravelly sandy loam soil at low valuesof 0, a small  For July 24-25, 1981,two consecutive clear dayswhenWs to a largedecrease in Ws(Figures4 was about -0.05 MPa, settingre0- 900 s m -• provided decreasein 0 corresponded agreement between calculated and measured daily values of  E0 (0.6 mm d-•). Hourly valuesof calculatedE0 generally agreedwith lysimetermeasurementsin the cut subplot of plot 2 (Figure 3). Eddy diffusive resistancesvaried from 10-50 s  and 5).  Effect of assumingrAi = 0 and r,i = 0. Considerablesimplification of the evapotranspirationtheory is achievedwhen W• = 0 by using the limit rAi-• 0 in the theory so that El=  whererc•= rsi/a•. Workingin the samestandas in m-• andwerehighestfor theperiod0200-0600hourson July pcpD•/rc•,  this study, Tan et al. [1978] obtained good agreement between energy balance-Bowen ratio evapotranspiration was due to sun fleckswhich were generallycommon to the net measurementsand values calculated using the above proradiometer and lysimeters.About 16% of the daily measured cedure in 1975 following heavy thinning of the stand. Use of E 0 occurredat night (2200-0600 hours Figure 3), while for the this procedurein the cut subplot of plot 2 (salal understory calculations the value was 10%. cut and removed)for the rainlessperiod July 30 to August 18,  25. The high variabilityin the measuredvaluesof R,0 and E0  Measured and CalculatedCoursesof Average Root Zone  Volumetric  Water  Using equations (I)  Content  to (4).  0.20  i  I  i  Calculations of the courses of  0 usingthe completeevapotranspirationtheory and water balance equations were made for the eight subplots for the  0.16  _  --  _  --  periodsJuly 24 to September3, 1981, and May 27 to July 1, 1982. There was good agreementbetween measuredcoursesof  0 in cut and uncut subplots(Figures4 and 5 and Table 2). In particular, there was excellentagreementin the measuredand  .5  o.o  .  ,  ,  I'-1  EO.12 0.20  o•  0.16  ...  0.16  e.  0.12  0.12  o0o8 -!.6  MAY 25  JUN 2  JUN I0  JUN 16  JUN 26  ,JUL 4  1982  Fig. 5. Same as for Figure 4 exceptfor May 27 to July 1, 1982, (open circles and dashed curves) for cut and (solid circles and solid curves)for uncut subplots.  JUL 30  AUG 7 1981  AUG 15  Fig. 6. Courses of measured(symbols)and calculated (curves) average root zone soil water content (0) in the cut (open circles)and uncut (closedcircles)subplotsof plot 2 for the rainlessperiod July 30 to August 18, 1981. Values of 0 were calculatedwith eddy diffusive and leaf boundary layer resistances(solid lines), without eddy diffusive resistances(long-dashedlines), and without eddy diffusiveand leaf boundary layer resistances(short-dashedlines). For the cut subplot there was no significantdifferencebetween calculationswith both sets of resistancesand without eddy diffusive resistances.Error bars are one standard  deviation.  1896  KELLIHER ET AL.' TwO-LAYER  TABLE 3.  CANOPY EVAPOTRANSPIRATION MODEL  Average Calculated Values of Total Evapotranspiration  was for the period August6-19, 1981,in plot 2 when the water  (E), Transpiration (Er'), Evaporation of InterceptedWater (E/), and balance values of E were 2.4 and 1.1 mm d- • for the uncut Forest Floor Evaporation(E0) in the Cut (C) and Uncut (U) Subplots for Periods July 24 to September3, 1981, and May 27 to July 1, 1982  E T'  Subplot  E  Fir  U  88  39  C  81  51  U  63  21  C  59  32  E l'  Salal  Fir  Salal  15  3  E0  1981  28  15  3 15  1982 20  17  2  17  3  10  Values are given in millimeters.  1981, resulted in only slightly higher calculated 0 values than those obtained when r,•i was not assumedto be negligible (Figure 6). This is to be expected,since r,•i is much smaller than rsi for Douglas fir so that rs•/a• is a good approximation of the Douglas fir canopy resistance[Tan et al., 1978]. The reason  for the small  difference  between  calculated  0 values  (with r,•i included)in Figure 6 and thosein Figure 4 is due to the difference in the starting dates for calculations in the two  figures.For salal, the magnitudesof r,• and rctare similar so that neglectingr,•t for salal and Douglas fir layers resultedin much lower calculated 0 values in the uncut subplot of plot 2 for the samerainlessperiod (Figure 6). A reasonableassumptionfor many standsis that the eddy  diffusiveresistances (r,•) within and abovethe tree canopyare small compared to stomatal and boundary layer resistances [Stewart, 1984]. Writing the theory with rat-- 0 is furtherjustified in view of the doubt in the validity of concept of eddy  diffusiveresistance within the plant canopy[Raupachand Thom, 1981]. This assumptiondoesnot limit the theory to dry leaf canopiesas was the casewith r,•- 0. As expected,the former assumptionresulted in 0 in the uncut subplots being slightlylowerthan whenratand r•t are included(Figure6). When r,•t for both layerswas included,calculatedtree transpiration in the uncut subplot for this 20-day period was 25 mm. The correspondingvalue was 20 mm when r,• for both  and cut subplots,respectively,compared to calculatedaverage  valuesof 1.7and 1.5mm d- • respectively. Calculated transpiration rates of the trees in the cut subplots were slightlyhigher than thosein the uncut subplotsfor the first 19 days of the 1981 period and first 11 days of the 1982 period but were considerablyhigher during the rest of the respectiveperiods(Figure 7). On August 12, 1981, calculated tree transpirationrateswere 1.5 and 1.1 mm d- • in the cut and uncut subplots of plot 2 (leaf area index was 5 for both trees)respectively.The correspondingvalueson August  20 were1.1 and 0.5 mm d-•. Using(1) and rs measurements made at about the midcrown height of the treesin plot 2, tree transpirationrates were estimatedto be 1.4 and 1.1 mm d- • on August 12 and 0.8 and 0.6 on August 20, 1981, in cut and uncut subplots,respectively.There was not as good agreement betweencalculatedand estimatedtree transpiration rates in plot 2 for June 9, 17, 23, and 30, 1982; however, the differences betweenthe cut and uncut subplotswere in good agreement. During the 1981 and 1982 periods, salal removal resulted in an averageincreasein calculatedtree transpirationrate of 31 and 52%, respectively,in the four plots. Calculationsindicated that the increasein tree transpirationrate was greatestin plot 3 where salal leaf area index (3 and 2.4 in 1981 and 1982, respectively)was highest and was least in plot 4 where salal leaf areaindexwaslowest(2.1 and 1.7in 1981and 1982). Calculated values of total salal transpiration plus forest floor evaporation below the salal were about twice those of forest floor evaporation after salal removal in the 1981 and 1982 periods.This largely accountsfor the increasedtree transpiration following salal removal, since Douglas fir interception in adjacentsubplotswas identical and salal interception was a small term in the water balance. McNaughton and Jarvis [1983] expressedthe evapotranspirationrate in terms  of the equilibriumevaporationrate (Eel= [S/(S+ 7)](Rn -G)/L) and'theequilibrium vaporpressure deficit(D•[s/(s+ y)]Yrc(R n-G)/p%). For the salal,smallcanopyresistances[Tan et al., 1978]resultedin D• < D abovethe salal canopy and the ratio of the 24-hour averagesalal transpira-  layers were neglected.The difference between these two values resultedfrom more salal understorytranspiration being calculated using the latter procedure.Since salal stomatal resistance  2.4  characteristicsand leaf area index remained relatively con-  E1.6 "•1 "r•L•.• 1981  stant from 1975-1981, it appears that the reduction in salal transpirationfrom 1975-1981 resultedfrom forestcanopyclosure leading to a reduction in the ratio of below to above tree canopywind speedand an increasein r,• for the salal layer.  "  '•  .-!  i ;'•.r•.....  ?..'  a: 08  -  z  Calculatedtree transpirationfor the 20-dayperiodwith r•i = 0 was 24 mm, only slightlylessthan with the eddy diffusive resistance included.  n  Partitioning of Evapotranspirationin Cut and Uncut Subplots  m  Table 3 gives the calculated values of total evapotranspiration, transpiration and interception of Douglas fir and salal, and forestfloor evaporation for cut and uncut subplotsfor the periods shown in Figures 4 and 5. Calculated values of total E for the uncut subplotswere slightly larger than those for the cut subplots in both years. Throughout these periods, calculated values of E of the uncut subplots were also slightly higher than in the cut subplots.This was also found using a simple water balance analysisof the 0 and P data which used the approximation E ,•-(AO/At)• + P. The only exception  JUL 30  AUG7  Z  •  A•  15  •  AUG23  '  AUG31  -  0 • E  • 1.6  ""•  20E  0  J•  2  •  I0  JUN 18  JUN 26  Fig. 7. Courses of calculated tree transpiration rates in the cut (dashedlines)and uncut (solid lines)subplotsof plot 2 for the periods July 24 to September 3, 1981, and May 27 to July 1, 1982. Root-  mean-squareerrorsweretypically0.2•.4 mm d- • whencalculatedas describedin the Figure 1 caption. Also shown is the daily rainfall rate (P).  KELLIHER ET AL.' Two-LAYER  CANOPY EVAPOTRANSPIRATION  tion and forest floor evaporation rate to the corresponding  valueof Eeqbeing2.0-2.7duringtheperiodJuly24 to August 20, 1981. For the forest floor after salal removal, large surface  diffusiveresistances generallyresultedin Deq> D abovethe forest floor and the ratio of the 24-hour average evaporation  rateto Eeqbeing 0.5-1.0duringthesameperiod. The evapotranspirationtheory was developedfor extensive homogeneoussurfacesso that its application in the cut subplots included the use of below-tree canopy values of D and Tair largely determinedby the presenceof salal in the surrounding forest.Values of below-treecanopy D and Tair would be expected to be higher following extensive salal removal; however, it is difficult to estimate the magnitude of the increase.McNaughton and Jarvis [1983] show that the D above a conifer forestcanopy is likely to be well coupled to the outer mixed portion of the planetary boundary layer. Consequently, they argue that a 50% reduction in forest leaf area index would not result in an increase in above-forest  D and therefore  would result in a significantreduction in forest evapotranspiration. Since D below the tree canopy in this study was well correlated to that above (in agreementwith the resultsreported by Stewart [1984] for Thefiord forest),it is likely that only a slight increasein below-tree canopy D would result from extensivesalal removal. Further researchinvolving understory removal over an extensive area is required to answer this question.  MODEL  1897  LEi  Hi  eiI Di'Rn i Ti ravi r•rv•ø•TeTe ' Tj-IrøHi ei-I IDi-•,Rni-• e'(si)  si  LF'i.I  Hi.I  Fig. 8. Electrical analogue for the vertical transfer of latent and sensibleheat fluxesabovecanopylayer i (LE i and H) where T• • is the "effective" surfacetemperature of the layer (i.e., wet and dry portions), and other symbolsare defined in the text.  boundary layer. This equation givesthe water vapor flux density from an equivalent extended isothermal one-sided leaf with boundary layer resistancesr• i and rva• to sensibleheat and vapor transfer, respectively,and a surfaceor canopy resistancerc•to vapor transfer.The water vapor flux densityon a ground area basis from a canopy layer of hypostomatous leaveswith a projectedleaf area index (a) and a fraction of the leaf area wet (W•)can be written as  I•(s q-7rvi/rtli) El'= Wiai[S(Rni --Rni_ •)/ai +pcvDi_ •/(rui/2).] +(1-Wi)aiI'S(Rni-Rni-•)/ai +pcrDi-•/(rui/2) (A2) The first bracketed term of (A2) is the evaporation rate from the average wet leaf on a projected leaf area basisin layer i, the second bracketed term is the transpiration rate from the averagedry hypostomatous leaf on a projectedleaf area basis  CONCLUSIONS  Shuttleworth's [1979] evapotranspiration theory with canopy and root zone water balance models proved to be reasonably accurate and practical in calculating the coursesof in layer i, r• is the leaf stomatalresistanceof the side with 0, •, and tree transpiration during extendedperiods in the stomata,and rm and rvi are leaf boundarylayer resistances on growing season. The difficulty in using the theory is in estione side. In order that (A2) can be rewritten in the form of mating the transfer resistances(r•i, r•,i, rai, and forest floor (A1) by making rci a functionof W/,we requirern.i = rtti/(2ai) diffusive resistance),although r• is often available from and physiological studies. Simplifying the evapotranspiration theory by neglecting%i above and within the canopy resulted in very small decreasesin the coursesof 0 and tree transpiration rate. Further simplification for dry canopy conditions s + ?(rv•i/rui)(1 + (rci/rv•i)) (W•- 0) by assumingrA• -- 0 causedan overestimationof Wi 1- Wi = (A3) understory transpiration which resultedin an underestimation s + 7rvi/rm s + 7(rvi+ r•)/(rm/2) of the coursesof 0, •, and tree transpiration in uncut subplots. This simplification resulted in little change in cut sub- Solvingfor rciwe have plots, sincerA•is much smallerthan r• for Douglas fir. Calculations showed that the slightly higher values of 0 as a rc'= (s/7)rnai•rv,/2a ' result of understory removal correspondedto higher tree transpiration rates. During early (June 1982) and late (August 1981) growing seasondrying periods,most of the differencein tree transpiration occurred during the second half of the period due to the large value of A•P•/A0 of the soil water wherervai = rvi/(2ai)whichreduces to (4) whenrvi andrm are retention curve for low values of 0 and stomatal closure by assumedto be equal and written as Douglas fir where salal remained. Increase in tree transpiraSince(A2) can be written in the form of (A1), the canopy tion as a result of understory removal was greatest where layerhasan effectiveleaftemperature (Tsie) [Campbell,1977]. understory leaf area index was highest.  w/  +(s/v)rn, i1-W• +(rvi q-rsi)/a i]-•--(s/v)ru, i--rv, i (A4)  ApplyingOhm'sLaw to the electricalanalogueof the model for canopy layer i shownin Figure 8, the relationshipsbe-  APPENDIX: DERIVATION OF EQUATIONS  (1), (4), AND (5) The Penman-Monteith equation for a canopy layer i neglecting energy storageis  E[ =  s(Rni- Rni 1)q-pcrDi 1/ruai  L(s q- 7rv•i/ru•i(1 q- (rci/rv•i)))  (A1)  where R.e_• is the net radiation below the layer, and D i_ • is the vapor pressuredeficit within the layer but outside the leaf  tween fluxes and resistancescan be written as [Shuttleworth, 1979, p. 321]  Ti -- Ti- 1 = -- HiraHi/P%  (AS)  Ti_I -- Tsie --- --(H i -- H i_ •)(rHi/2ai)/PC v  (A6)  ei -- e*(Tsi e): -- LEiraviY/p % -- L(E,- E•_•)(rci+ (rv•/2a•))7/pc v  (A7)  1898  KELLIHER ET AL.' TwO-LAYER CANOPY EVAPOTRANSPIRATION MODEL  where H is the sensibleheat flux density; e is the vapor pressure; and e*(rsie) is the saturation vapor pressureat the effective leaf temperature. Using the Penman transformation, we have  ei- e*(Tsie) = Di + s(Ti-- Ti-1) -it-s(T/- 1 -- Tsie)  (A8)  where, since T•ie-- T• is not large, the same value of s is used for both temperature differences.The energy balance equation for all layers 1 to i (neglectingenergystorage)is Rni- G = H i + LEg  (A9)  where LE• is the latent heat flux density above layer i. Substituting (A5), (A6), and (A7) into (A8), using (A9) and dividing by L, we have  of leaves subject to mutual interference,Agric. Meteorol., 12, 169184, 1973.  Lindroth, A., Seasonal variation in pine forest evaporation and canopy conductance, Ph.D. thesis, Univ. of Uppsala, Uppsala, Sweden, 1984. McNaughton, K. G., and P. G. Jarvis, Predicting effectsof vegetation changeson transpiration and evaporation, in Water Deficits and Plant Growth,vol. 7, edited by T. T. Kozlowski, pp. 1-47, Academic, Orlando, Fla., 1983. Monteith, J. L., Evaporation and environment, in The State and Movement of Water in Living Organisms,Symp. Soc. Exp. Biol. No. 19, edited by G. E. Fogg, pp. 205-234, Academic, Orlando, Fla., 1965.  Novak, M. D., and T. A. Black, Theoretical determination of the  surfaceenergy balance and thermal regime of bare soils, Boundary Layer Meteorol., 33, 313-333, 1985. Plamondon, A. P., Hydrologic properties and water balance of the forest floor of a Canadian west coast watershed, Ph.D. thesis, Univ.  s(R,- G) + pcp(D i + •Si')/r,• m  of B.C., Vancouver, 1972.  D. T., T. A. Black, and F. M. Kelliher, Effects of salal underEi=L(s +7(r,•vi/r,•m)(1 +(rci/r,•vi)))(A10)Price, story removal on photosynthesisrate and stomatal conductanceof where  •5/ = [LE i_ •[(rci + (rv•/2a•))7+ (rm/2a•)s]  -- s(Rni_x -- G)(rm/2ai)]/p%  (All)  with r,•m = rm/2ai + ram and r,•vi = rw/2a i + ray•. Equation (A10) is the same as (9) in the work by Shuttleworth [1979]. Subtracting Ei_ x from (A10) and assuming similarity (i.e., rHi -- rvi : rbiand raili -- ravi: rai) give (1). The rate of evaporation of intercepted water from layer i(E•/) is obtained by multiplying the fraction of leaf area (one side) that is completely wet (W•) by (A1) with rci: 0 which gives  young Douglas-fir trees, Can. J. For. Res., 16, 90-97, 1986. Raupach, M. R., and A. S. Thom, Turbulence in and above plant canopies,Ann. Rev. Fluid Mech., 13, 97-129, 1981. Roberts, J., C. F. Pymar, J. S. Wallace, and R. M. Pitman, Seasonal changes in leaf area, stomatal conductance and transpiration from bracken below a forestcanopy,J. Appl. Ecol., 17, 409-422, 1980. Rutter, A. J., K. A. Kershaw, P. C. Robins, and A. J. Morton, A predictive model of rainfall interception in forests, 1, Derivation of the model from observations in a plantation of Corsican pine, Agric. Meteorol., 9, 367-384, 1971. Santantonio, D., R. K. Herman, and W. S. Overton, Root biomass  studiesin forest ecosystems,Pedobiol.,17, 1-31, 1977. Shuttleworth, W. J., A simplified one-dimensional theoretical description of the vegetation-atmosphereinteraction, Boundary Layer Meteorol., 14, 3-27, 1978.  Shuttleworth, W. J., Below-canopy fluxes in a simplified onedimensional theoretical description of the vegetation-atmosphere interaction, BoundaryLayer Meteorol., 17, 315-331, 1979. Shuttleworth, W. J., and J. S. Wallace, Evaporation from sparse crops--An energy combination theory, Q. J. R. Meteorol. Soc., 111,  E1 i,= gi[s(Rni --Rni1)-11pcpDi1/rHai](A12) L(s + 7(rvai/raai)) Dividing (A12) by (A1), assumingsimilarity (i.e., rHai = rvai = %i/2a0, making useof (4) and rearranginggive (5). Acknowledgments. This research was supported by a grant from the Natural Science and Engineering Research Council of Canada and a contract from the British Columbia Ministry of Forests. We appreciate the assistanceof D. Beames,R. Adams, R. Emerson, and the staff of the University of British Columbia Research Farm at Oyster River. We are grateful to D. L. Spittlehouseand M.D. Novak for valuable discussionson the paper. REFERENCES  Black, T. A., C. B. Tanner, and W. R. Gardner, Evapotranspiration from a snap bean crop, Agron. d., 62, 66-69, 1970. Campbell, G. S., Introductionto EnvironmentalBiophysics,SpringerVerlag',New York, 1977. Denmead,O. T., Plant physiologicalmethodsfor studyingevapotranspiration: Problems of telling the forest from the trees, Agric. Water Manage., 8, 167-189, 1984. Finnegan,J. J., Turbulent transport in flexibleplant canopies,in The Forest-AtmosphereInteraction, edited by B. A. Hutchison and B. B. Hicks, pp. 443-480, D. Reidel, Hingham, Mass., 1985.  839-855, 1985.  Spittlehouse,D. L., Measuring and modelling forest evapotranspiration, Ph.D. thesis, Univ. of B.C., Vancouver, 1981. Spittlehouse,D. L., and T. A. Black, Evaluation of the Bowen ratio/ energy balance method for determining forest evapotranspiration, Atmos. Ocean, 18, 98-116, 1980.  Spittlehouse,D. L., and T. A. Black, A growingseasonwater balance model applied to two Douglas-fir stands, Water Resour.Res., 17, 1651-1656, 1981a.  Spittlehouse,D. L., and T. A. Black, A comparisonof reversingpsychrometric Bowen ratio measurement systems,Atmos. Ocean, 19, 372-379,  1981b.  Spittlehouse,D. L., and T. A. Black, A growing seasonwater balance model usedto partition water usebetweentrees and understory,in Proceedingsof CanadianHydrology Symposium82, Processesin ForestedAreas, Fredericton,New Brunswick,Canada, pp. 195-214, Associate Committee on Hydrology, National Research Council, Ottawa, 1982.  Stanhill, G., A simple instrument for the field measurement of turbulent diffusion flux, J. Appl. Meteorol., 8, 509-513, 1969.  Stewart,J. B., Measurementand predictionof evaporationfrom forested and agricultural catchments,Agric. Water Manage., 8, 1-28, 1984.  Fuchs, M., and C. B. Tanner, Calibration and field test of heat flux plates,Soil Sci. Soc.Am. d., 32, 326-328, 1968.  Stewart,J. B., and A. S. Thom, Energybudgetsin pine forest,Q. J. R.  Garratt, J. R., and B. B. Hicks, Momentum, heat and water vapor transferto and from natural and artificial surfaces,Q. J. R. Meteo-  Szeicz,G., G. Endrodi, and S. Tajchman,Aerodynamicand surface  rol. Soc., 99, 680-687, 1973.  Gates, D. M., BiophysicalEcology,Springer-Verlag,New York, 1980. Jarvis, P. G., G. B. James,and J. J. Landsberg,Coniferousforest, in Vegetationand the Atmosphere, vol. 2, editedby J. L. Monteith, pp. 171-240, Academic, Orlando, Fla., 1976.  Meteorol. Soc., 99, 154-170, 1973.  factorsin evaporation, Water Resour.Res.,5, 380-394, 1969. Tan, C. S., and T. A. Black, Factors affectingthe canopyresistanceof a Douglas-fir forest,BoundaryLayer Meteorol., 10, 475-488, 1976. Tan, C. S., T. A. Black, and J. U. Nnyamah, Characteristicsof stomatal diffusionresistancein a Douglas-fir forestexposedto soil water  deficits, Can. J. For. Res., 7, 595-604, 1977. Kelliher, F. M., Salal understory removal effects on the soil water regime and tree transpiration rates in a Douglas-fir forest, Ph.D. Tan, C. S., T. A. Black, and J. U. Nnyamah, A simple diffusion model thesis,Univ. of B.C., Vancouver, 1985. of transpiration applied to a thinned Douglas-fir stand, Ecol., 59, 1221-1229, 1978. Landsberg,J. J., and D. B. B. Powell, Surfaceexchangecharacteristics  KELLIHER ET AL.: TWO-LAYER CANOPY EVAPOTRANSPIRATION MODEL  Thom, A. S., Momentum, massand heat exchangeof vegetation,Q. J. R. Meteorol. Soc., 98, 124-134, 1972.  Thom, A. S., Momentum, mass and heat exchangeof plant communities, in Vegetation and Atmosphere,vol. 1, edited by J. L. Monteith,  F. M. Kelliher, Forest ResearchInstitute, Private Bag, Rotorua, New  Zealand.  D. T. Price, Faculty of Forestry, University of British Columbia, Vancouver, British Columbia V6T lW5.  pp. 57-109, Academic, Orlando, Fla., 1975.  Van Wijk, W. R., and D. A. De Vries, Periodic temperature variation, in Physicsof Plant Environment,edited by W. R. Van Wijk, pp. 102-143, North-Holland, Amsterdam, 1963.  T. A. Black, Department of Soil Science,The University of British Columbia, 139, 2357 Main Mall, Vancouver, British Columbia Canada  V6T  2A2.  1899  (ReceivedFebruary 4, 1986; revisedAugust 5, 1986; acceptedAugust 5, 1986.)  

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