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Evapotranspiration and surface conductance for a high elevation, grass covered forest clearcut Adams, Ralph S. 1990

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E V A P O T R A N S P I R A T I O N A N D S U R F A C E C O N D U C T A N C E F O R A H I G H E L E V A T I O N , G R A S S C O V E R E D F O R E S T C L E A R C U T . By Ralph S. Adams B. Sc. (Agr.), University of British Columbia, 1981 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF SOIL SCIENCE We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 1990 © Ralph S. Adams, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Soil Science The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: Abstract Evapotranspiration from a forest clearcut was measured over two growing seasons as part of a larger study of the microclimate of forest clearcuts and microclimate modification by site preparation. Pinegrass is the dominant species on clearcuts in the dry southern interior and is the major competitor with coniferous seedlings. This paper examines the water use of a pinegrass dominated clearcut and the response of surface conductance to environmental variables. Evapotranspiration was derived from eddy correlation measurements of sensible heat flux and measurements of net radiation and soil heat flux. 419 hours of daytime energy balance data from the summers of 1987 and 1988 were analyzed. A rearranged form of the Penman-Monteith equation was used to calculate hourly mean surface conductances for the clearcut. Leaf area measurements were used to calculate stomatal conductance from surface conductances. Stomatal conductance was modelled using boundary-line and non-linear optimization techniques. The most successful model (R2 = 0.71) was obtained using non-linear op-timization with stomatal conductance as a non-linear function of saturation deficit at the leaf surface (Do) and solar irradiance. DQ was calculated from measured evapotran-spiration and surface conductance. Response of stomata to saturation deficit would be expected to be better correlated to D0 than D measured at a reference height above the canopy. Stomatal conductance was also modelled as a function of D (measured at 1.3 m) and solar irradiance. The resulting model (R2 = 0.50) was poor compared to that based on Do. Saturation deficit and temperature were found to be highly correlated both at 1.3 m i i above the canopy and at the leaf surface. Use of air temperature in the conductance model caused R2 to decrease. No relationship between stomatal conductance and volumetric soil water content was found. Hourly evapotranspiration rates calculated using modelled surface conductances agreed well with measured rates.(R2 — 0.89). Evapotranspiration was also modelled using the Priestley-Taylor approach. The mean hourly a for all daylight data was found to be 0.81. This simple model was found to give comparable results to the stomatal conductance based model (R2 = 0.85). i n Table of Contents Abstract ii List of Tables vi List of Figures vii Acknowledgement viii 1 introduction 1 2 Theoretical Considerations 3 2.1 The Penman-Monteith Equation 3 2.2 Stomatal Conductance 4 2.3 Surface Conductance 5 2.4 Evapotranspiration Models 7 3 Experimental Procedures 8 3.1 Site Description 8 3.2 Measurements 9 3.2.1 Climate Station Measurements 9 3.2.2 Energy Balance Measurements 10 3.2.3 Soil Moisture and Leaf Area 12 3.2.4 Data Analysis 13 3.2.5 Testing of Models 17 i v 4 Results and Discussion 19 4.1 Diurnal Energy Balance 19 4.2 Modelling Surface Conductance 23 4.2.1 The Technique of Boundary Line Analysis 23 4.2.2 The technique of NLLS Optimization 27 4.3 Modelling Evapotranspiration 33 5 Conclusions 37 Bibliography 39 v List of Tables 4.1 Daytime mean surface conductances and leaf area indices for grassland without soil water limitation 22 4.2 Parameters for multiplicative model of gs determined by BLA 25 4.3 Results of testing models of gs with parameters determined by BLA. . . 26 4.4 Parameters for multiplicative model of gs determined by NLLS optimization. 29 4.5 Results of testing models of gs with parameters determined by NLLS op-timization 31 4.6 Results of testing models of \E using different models of gs, using the combined data set 35 v i List of Figures 4.1 Diurnal energy balance and trends in environmental variables for July 1, 1987 20 4.2 Mean canopy stomatal conductance plotted against saturation deficit, strat-ified by solar irradiance. Hourly mean data from 1987 and 1988, • = •S >200Wm" 2, o = S < 200 Wm~ 2 24 4.3 Functions in multiplcative model of gs plotted with data used to determine parameters 28 4.4 Regression analysis of models of gs with parameters determined using NLLS optimization. A , Model of gs based on D0 and S. B , Model of gs based on D and S 32 4.5 Regression analysis of models of \E. A , P M equation with model of gs based on D0 (calculated from measured values of \E) and S. B , P M equation with model of gs based on D0 (Iterated). C, P M equation with model of gs based on D and S. D , PT equation with a = 0.89. Solid line is the 1:1 line, dotted line is regression equation given in Table 4.6. . . . 34 vn Acknowledgement In historical order I would like to acknowledge those people who I think have helped most over the years in inspiring and then supporting my scientific interests: my parents, for answering questions no parent should have to endure, the late Dr. S. H. Skaife of Hout Bay, South Africa, for writing Dwellers in Darkness which inspired an 11 year old to study entomology. To various high school teachers, Mr. Jukes and Mr. Cunningham in particular, who always found time to answer questions, and my wife Colleen for putting up, even if under protest, with a graduate student in the house. This research project has had much help from other people. My fellow students in the Biometeorolgy group have also made considerable contributions, in particular I would like to thank Rob Fleming (Elwood) for teaching me all that I know about trees and how to grow them. Various summer students have helped with things in the field, Laura Koch, Scott Mitchell, Isobel Simpson and Maureen Scott in particular. Norm Eldridge helped with compilation of climate station data and soil water contents. The members of my committee, Dr. Tim Ballard and Dr. Mike Novak have always been ready to help and supply encouragement. Finally, but far from least, I must acknowledge the debt I owe to my supervisor Dr. T.A. Black. Andy has been a constant source of knowledge, skill, and encouragement through my programme. Without his patience and faith in my abilities this thesis would not have been written. Following in the footsteps of Dr. Dave Price who has acknowledged our debt to the Intel corporation, I would like to thank Donald Knuth for finding time to write TgK and to Leslie Lamport for making it accessible to the rabble through his lATgX programme. viii Chapter 1 Introduction In the dry southern interior of British Columbia, clearcutting of native stands of lodge-pole pine (Pinus contorta) and Douglas-fir (Pseudotsuga menzeizii var. glauca) results in large areas dominated by grass and shrub species. Native pinegrass (Calamagrostis rubescens) invades the clearcuts soon after cutting and is a major competitor with conif-erous seedlings planted into these sites. In 1985, the Forest Resource Development Agree-ment (FRDA) between the federal and provincial governments was initiated to reduce the amount of insufficiently regenerated land in British Columbia. In addition to replanting, research was conducted into all aspects of forest regeneration. One of the projects was an intensive biometeorological study of clearcut microcli-mate, seedling water relations, and the microclimatic impact of site preparation treat-ments (Black et al. 1989). Since soil water deficits are one of the major factors limiting seedling growth on these sites, micrometeorological measurements of evapotranspiration were made to determine water use by the pinegrass clearcut. Models of evapotranspiration are required to assess the effects of removing competing vegetation, to determine optimum seedling planting dates and to investigate plantation failures. Evapotranspiration models are also required in hydrological studies of forested watersheds containing increasing areas of clearcut land. Furthermore, current global cir-culation models require accurate estimates of evapotranspiration from different vegeta-tion types (Dickinson and Sellers 1988). The Penman-Monteith (PM) equation (Monteith 1981) has been used in all of these situations. In addition to weather variables, the PM 1 Chapter 1. Introduction 2 equation also requires estimates of the surface conductance of each vegetated surface and the response of surface conductance to environmental variables. The objectives of this thesis are (i) to determine the response of the surface conduc-tance of a high elevation grass covered forest clearcut to environmental variables, (ii) to compare several techniques for determining the parameters used in modelling this re-sponse and (iii) to compare the effectiveness of the P M equation and the simpler Priestley and Taylor (1972) equation for estimating evapotranspiration. Chapter 2 Theoretical Considerations 2.1 The Penman-Monteith Equation The Penman-Monteith equation, which describes the isothermal, big leaf model of evap-otranspiration from an extensive vegetated surface, is given by XE = 3 { R n ~ G ) + pCffa (2.1) s + >y{l + ga/g.) V ' where (Rn — G) is the available energy flux density (net irradiance — soil heat flux density (Wm~ 2)), s is the slope of the saturation specific humidity curve at air temperature (kgkg - 1 ° C _ 1 ) , p is the density of air at air temperature (kgm - 3), cp is the specific heat of air ( J k g - l o C _ 1 ) , A is the latent heat of vaporisation at air temperature (Jkg - 1 ) , E is the flux density of water vapour from the surface (kgm - 2 s _ 1 ) , 7 is the psychrometric constant (cp/X) ( °C _ 1 ) , Da is saturation specific humidity deficit (kgkg - 1), ga is the aerodynamic conductance between the effective canopy surface and the reference height at which air temperature and Da are measured (ms - 1 ) , and g3 is the surface conductance (ms- 1). Assumptions in equation 2.1 are that (i) all leaf stomatal conductances can be com-bined in parallel to give the surface conductance, i.e. n g. = YtLi9si (2.2) «=i where X, is the leaf area index of element i and gsi is the stomatal conductance of element i and (ii) all leaf boundary-layer conductances and the eddy diffusive resistance above the Chapter 2. Theoretical Considerations 4 canopy can be combined to give a single aerodynamic resistance (Thorn 1972). Although equation 2.1 is a simplification (Monteith 1981, Raupach and Finnegan 1988), in practice it has been found to succesfully represent the surface conductance of real canopies (Black et al. 1970, Tan and Black 1976). 2.2 Stomatal Conductance Stomatal conductance is known to respond to changes in quantum (0.4-0.7 //m) irradiance (Q), leaf temperature (To), leaf surface saturation deficit (Do), leaf water potential (\&/), soil water potential (^ a), and ambient C O 2 concentration (C). The relationship between gs and an environmental variable, when others are held constant at non-limiting levels, is similar in many plant species and families (Jones 1983). It has not been possible to produce a mechanistic model of stomatal conductance. A phenomenological model was proposed by Jarvis (1976) to determine gs as a function of a number of environmental variables. He proposed that gs responds to each environmental variable independently and the value of gs resulting from any combination of variables is given by 9s = 9smax f(Q) 9(D0) h(T0) i(%) j(C) (2.3) where gsmax is the maximum stomatal conductance which would occur if none of the environmental variables were limiting. The individual functions, with values between 0 and 1, are determined when all the other variables are not limiting. Equation 2.3 is referred to as the Jarvis or multiplicative model of stomatal conductance. Jarvis suggested that, for application to porometer data taken under field conditions, functions determined in controlled environment chambers be used and the parameters be empirically fitted to the field data. Two methods can be used to determine the values of the individual parameters. Webb (1972) and Jarvis (1976) observed that the upper edge of a scatter plot of gs against an environmental variable would indicate the response Chapter 2. Theoretical Considerations 5 to the variable when no other variables are limiting. By fitting a function, the form of which was determined in controlled environment studies, to the upper boundary of the data the values of the individual parameters can be determined. Unfortunately, as the upper points contain errors, judgement must be used to determine the most probable location of the boundary line. Also, it is not possible to describe the resulting function statistically. Boundary line analysis (BLA) has been successfully used by Livingston and Black (1987) to determine the parameters in a multiplicative model describing the stomatal conductance of conifer seedlings. They used solar irradiance (S), saturation deficit and temperature of the air, and soil water potential. They also found that time since sunrise had a significant effect on stomatal conductance. Jarvis (1976) used non-linear least squares optimization to determine values for the parameters in the multiplicative model applied to shoots of Sitka spruce and Douglas-fir. This technique has also been applied to porometer measurements of stomatal conductance of a bracken understory (Roberts and Pitman 1984). 2.3 Surface Conductance As surface conductance depends on the stomatal conductance of the vegetation, it would be expected that similar techniques could be used to model the response of surface con-ductance to environmental variables. The technique of stratification has been used by Stewart and de Bruin (1985), Callender and Woodhead (1981) and Black and Kelliher (1989). In this technique two environmental variables are assumed to control surface conductance. One variable is stratified into ranges. A family of curves is then developed to determine surface conductance as a function of the second variable, each curve corre-sponding to one of the ranges of the first variable. This technique is difficult to implement if surface conductance is to be related to more than two environmental variables. The Chapter 2. Theoretical Considerations 6 range of values assumed by one of the variables is discontinuous. Stewart (1988) extended the Jarvis multiplicative model to the canopy of a pine forest. Stewart's equation was 9> = 9smaxf(D)g(S)h(Ta)i(66) (2.4) where S is the solar irradiance, D is the saturation specific humidity deficit at the ref-erence height, Ta is the air temperature at the reference height, and 89 is the soil water storage deficit in the upper 1 m of soil. As the variation in C is small during outdoor experiments, it was neglected. The forms of the functions used were similar to those of Jarvis (1976). The parameters for each function were determined by non-linear least squares (NLLS) optimization. This approach has been used by Gash et al. (1989) for a stand of maritime pine and by Stewart and Gay (1989) for prairie grassland. Price and Black (1989) also used the multiplicative model to estimate surface con-ductance of a Douglas-fir stand. The parameters were determined using boundary line analysis. They found that surface conductance was better modelled by substituting a limiting factor model for the multiplicative model. In their model, gs was estimated from 9s = 9smaxF (2.5) where F is the minimum of f(D), g(S), h(Ta), «(£#), and j(t), where t is time since sunrise. Monteith (1990) points out that stomata respond to saturation specific humidity deficit at the leaf surface (Do) rather than that at a reference height above the canopy (D). Do as denned by the big leaf model is given by Do = — (2.6) P9s From equation 2.1, it can be shown that when E is equal to the equilibrium evaporation rate, Eeq = (s/(s + -y))(Rn - G), D = D0 . When E < Eeq, D0 > D. When the surface Chapter 2. Theoretical Considerations 7 is rough and ga is high, the two deficits will also be similar due to the large degree of coupling between the canopy and surface layer. Similarly, stomata must respond to the temperature of the leaf rather than to that at a reference height. The temperature of the effective canopy surface (To) is given by To = Ta + — (2.7) pcPga where H is the sensible heat flux density. 2.4 Evapotranspiration Models Evapotranspiration can be estimated using equation 2.1, climate station data, and a model of surface conductance (Price and Black 1989, Dolman 1988). Evapotranspiration is usually estimated more accurately than surface conductance is modelled (Stewart 1988, Gash et al. 1989, Stewart and Gay 1989). This is because E in equation 2.1 depends only in part on gs. The sensitivity of E to gs for forests is expected to be greater than for agricultural crops because ga is greater than for agricultural crops (Raupach and Finnegan 1988). Priestley and Taylor (1972) proposed a model of regional evapotanspiration for veg-etated surfaces with no shortage of soil water in the form XE = a ~— (Rn - G) (2.8) where a is an empirical constant. They found that a value of a — 1.26 fit data from several sources. McNaughton and Spriggs (1989) showed that for surfaces with values of g3 > 17-20mms_1, equation 2.8 with this value of o; gives estimates of evapotranspiration, in the absence of advection, that agree with equation 2.1. This model has been applied to vegetation which was not well supplied with water, resulting in values of a less than 1.26. Chapter 3 Experimental Procedures 3.1 Site Description The site is at an altitude of 1220 m and is located at 50° 40'N, 120° 54'W on the Thompson plateau in the southern interior of British Columbia, Canada. The Thompson plateau is a large area approximately 900 x 400 km formed by lava flows from fissures and shield volcanoes during the Tertiary period. The landscape consists of rolling terrain with 300 to 900 m deep river valleys cut into the plateau. The soil on the site is an Orthic Grey Luvisol derived from a morainal blanket composed of mixed volcanic materials. The upper 30 cm has a loam texture with a high stone content (Mitchell et al. 1981). A layer with high bulk density (1700-2200 kgm - 3 ) is found below 40cm. The closest station at which long term weather records are available is 15 km to the south west at a similar altitude and with similar topography. The mean annual rainfall is 390 mm, and the mean rainfall in the growing season (May-August) is 164 mm. In the two years of this study, the growing season rainfall measured at the experimental site was 163 mm in 1987 and 275 mm in 1988. Frequent frosts occur throughout the growing season. In 1987, there were 37 nights with air temperatures (measured at 15 cm) below 0°C. These frosts were frequently below —5°C and caused significant damage to planted conifer seedlings. The natural vegetation consists of coniferous forest composed of lodgepole pine and interior Douglas-fir with an understory dominated by pinegrass. The 10 ha experimental 8 Chapter 3. Experimental Procedures 9 site was clearcut logged in 1982 and scarified with a crawler tractor brush blade in 1984 leaving a large number of stumps and coarse woody fragments. The predominant vegeta-tion in the clearcut during the experiment was pinegrass, prickley rose (Rosa acicularis), dwarf blueberry (Vaccinnium c&spitosum) and arctic lupine (Lupinus arcticus). Visually pinegrass, which grows to a height of 15-30 cm, appears to dominate the site due to the large biomass of standing dead material that remains from year to year. 3.2 Measurements 3.2.1 Climate Station Measurements An automated climate station using a Campbell Scientific 2IX datalogger has been used since May 1986 to collect hourly mean microclimate data. The sensors are read at 10 s in-tervals and means calculated at the end of each hour. Solar irradiance was measured with a Licor silicon cell pyranometer. This unit was calibrated in the field annually against a Moll-Gorczynski pyranometer, manufactured by Kipp and Zonen. The calibration of the second instrument was traceable to a national standard. Air temperature and relative humidity (RH) were measured with a Fenwall UUT-51J1 thermistor and a Phys Chem sulphonated polystyrene sensor respectively, housed in a Stevenson screen at a height of 1.3 m. The sensors were regularly checked with an aspirated Assmann psychrometer. For a 6 week period in each year an automated aspirated psychrometer (Spittlehouse and Black 1981) was used to measure wet and dry bulb temperatures at 1.3 m. Due to the power requirements of this instrument, aspiration was applied only for the 5min preceding a spot measurement every 30 min. Excellent agreement was found between the hourly mean values from the thermistor and RH sensor and the mean of the three 30 min spot readings taken each hour with the aspirated psychrometer. The saturation deficit values used in the analysis were taken from the thermistor and RH sensor. Wind speed Chapter 3. Experimental Procedures 10 was measured at a height of 1.3 m with a Met-One cup anemometer with a stall speed of 0.47 m s _ 1 . Wind speed during the day tends to be high (hourly mean 2.73 ms - 1 ) and examination of the data revealed no mean wind speeds that were suspect due to stalling. Wind direction was monitored with a Met-One windvane mounted at 1.3 m. Air temper-ature at a height of 15 cm was measured using a Fenwall UUT-51J1 thermistor potted in epoxy and mounted in a radiation shield consisting of two horizontal square aluminum plates 20 cm wide. The upper surface was covered with aluminized mylar and all other surfaces were allowed to oxidise. Tests with fine-wire thermocouples showed that the radiation error was less than 0.1 °C. Rainfall and soil temperature were also measured at the climate station. 3.2.2 Energy Balance Measurements An area was set aside for energy balance measurements to prevent destruction of vege-tation. The site chosen was flat with changes in topography of no more than 0.5 m in height. However, no stumps or large slash were removed. It was estimated that approx-imately 5% of the area was covered by stumps or coarse woody fragments. The fetch extended approximately 100 m downwind to the forest edge. Due to the location of site preparation treatments and a small depression, only data collected with the wind in the sector from 90° to 200° was used in analysis. In 1988, poplar saplings began to grow in this area and were manually removed. Net irradiance was measured with a Swissteco SI net radiometer mounted at a height of 1 m over vegetation considered to be characteristic of the area downwind. The ra-diometer was inflated by a flow of dry nitrogen gas from a compressed gas cylinder. A shortwave calibration by shading outdoors was performed before the radiometer was taken into the field. The domes were frequently checked for condensation or rain droplets and any data taken when the domes were wet were discarded. In August 1988, another Chapter 3. Experimental Procedures 11 SI net radiometer was used in an experiment to determine the spatial variation of net radiation at the site. It was run for two days within 30 cm of the fixed radiometer for calibration. It was then moved to various positions in the clearcut to determine the vari-ation in net irradiance caused by slight changes in vegetation and the presence of slash. It was found that Rn varied by less than 5% even near large pieces of slash and so no attempt was made to correct values measured with the fixed radiometer. Soil heat flux was measured with a pair of Middleton heat flux plates buried in the area below the net radiometer. The plates were inserted at the interface between the organic and mineral horizons at a depth of 3 cm. Correction for heat storage in the organic layer was done using a pair of integrating thermometers made by winding 30 gauge Nickel resistance wire on a 5 mm diameter glass rod and coating with epoxy. Sensible heat flux was measured using the eddy correlation method with three Camp-bell Scientific one-dimensional sonic anemometers and fine-wire (0.013 mm diameter) thermocouples. The instruments were read at a frequency of 10 Hz and the mean co-variance of vertical wind velocity and air temperature was recorded every 30 min using a Campbell Scientific 21X datalogger. The three instruments were mounted at a height of l m on masts 10m apart, arranged as an equilateral triangle. At intervals during the growing season, the three instruments were mounted at a height of 1 m around a single tower. Each sensor being separated from its nearest neighbour by at least 80 cm. It was found that all anemometers agreed to within 10% of the mean value for the three. Due to the variability of the site and the minimum separation required to prevent cross-talk, this was considered good agreement. When mounted on the three towers, the instruments agreed to within ± 25% of the mean value. The mean value was used in the energy bal-ance analysis. Another test was conducted in which the three instruments were mounted on one tower at three heights: 0.5, 1, and 1.5 m. There was no significant variation in heat flux observed, which indicated that fetch was adequate for the 1 m height used. Chapter 3. Experimental Procedures 12 A 3-day run was made with a reversing Bowen-ratio apparatus using aspirated psy-chrometers with silicon diode temperature sensors (Spittlehouse and Black 1981). The separation of the sensors was l m with the lower sensor at a height of 0.5 m. 3.2.3 Soil Moisture and Leaf Area Volumetric soil water content was determined at weekly intervals through the growing season. Gravimetric sampling was used in the upper 10 cm and a calibrated neutron probe (Fleming 1990) at the 19, 30, 45, 60, and 90 cm depths. Three shallow (60 cm) and three deep access tubes were installed. If necessary, the value of 8 was interpolated to determine the value for a particular day. The volumetric water content in the upper 5 cm was used to determine the volumetric heat capacity of the organic layer required in correcting soil heat flux measurements. The mean value of 0 from 0 to 30 cm was used in the modelling of surface conductance. Leaf area index was measured at 2-4 week intervals during the experiment. A square meter of vegetation was selected which did not contain large pieces of slash or atypical species composition. All vegetation was removed at the soil surface and stored in a refrigerator. The samples were later sorted into grass and herbaceous components. The senesced grass was removed from the sample. Leaf areas were then measured using a Licor leaf area meter. Due to the large spatial variability in vegetated cover and the difficulty in separating the living from senesced grass, measurements from three years were combined and a quadratic fitted to the data to give an estimate of total L as a function of Julian date (J). This was found to be L = -4.66 + 0.0556J - 0.00014J2 (3.9) Although the clearcut appeared to be dominated by pinegrass, the other species con-tributed up to 45% of the leaf area. This was due to the large amount of standing dead Chapter 3. Experimental Procedures 13 grass and because a small amount of broadleaved vegetation significantly affected the value of L. The total leaf area index never exceeded 1 and the growing season mean was 0.56. The maximum leaf area index occurred in mid July. This is similar to the re-sults reported by (Nicholson 1989, and Stout &: Brooke 1985) for pinegrass in the central interior of B.C. 3.2.4 Data Analysis After removing eddy correlation data collected when fetch was inadequate or the surface was wet with dew or rain, 419 hours of data remained. The 30 min mean values were averaged to give hourly mean values, this was necessary in order to combine hourly data from the climate station. Covariance measurements were converted to sensible heat fluxes assuming a constant air pressure of 87.5 kPa. The latent heat flux (XE) was then calculated using the energy balance equation \E = Rn-G-H (3.10) The energy stored in the canopy and used in photosynthesis was assumed to be negligible. After correcting for variations in the psychrometric constant due to elevation and the changes in air density due to fluxes of heat (Webb et al. 1980), it was found that the Bowen ratio apparatus overestimated mean 30 min values of the Bowen ratio compared to the Bowen ratio calculated from Rn, G and the eddy correlation measurement of H. This resulted in \E determined from the Bowen ratio/energy balance method being up to 30% less than that from the eddy correlation/energy balance method. A similar phenomenon was observed by Leuning et al. (1982) over a rice stubble surface. The errors in the Bowen ratio/energy balance method were likely due to (i) the lower sensor of the Bowen ratio apparatus being within the wake zone of the surface elements and (ii) marked differences in the locations of sources of sensible and latent heat in the sparse pinegrass canopy, which Chapter 3. Experimental Procedures 14 tend to invalidate the similarity assumption used in the Bowen ratio/energy balance method (Thurtell 1987, Raupach 1989). A comparison was made between estimates of evapotranspiration based on the eddy-correlation/energy balance technique, and weekly measurements of soil water content. Daytime values of a were calculated for the days on which eddy-correlation data were available. These values were then extrapolated to days when no eddy-correlation data were available. Measured daytime mean air temperature and net radiation were used with equation 2.8 to estimate evapotranspiation over the growing season. The estimates based on the eddy-correlation/energy balance technique agreed well with the soil water balance indicating that the Bowen ratio apparatus was in error. Aerodynamic conductance for neutral conditions was calculated using (Verma 1989) where d is the zero plane displacement height, z™ and ZQ are the roughness lengths for momentum and heat transfer respectively, k is von Karman's constant and u is the windspeed at the reference height z. d was assumed to be 2h/3, where h is the height of the vegetation, while the roughness lengths were calculated using z™ — h/10 and zo = ^ c T A O (Verma 1989). No correction for stability was made. The surface conductance gs was then calculated using a rearranged form of equa-tion 2.1. Mean stomatal conductance was calculated using D0 and To were calculated from equations 2.6 and 2.7 respectively. Data was analysed and investigated for each day to determine if all values appeared reasonable. On two days, extremely high values of gs in the morning indicated that the surface was wet, although it appeared dry. These data were removed. Data were also removed if the value (3-11) (3.12) Chapter 3. Experimental Procedures 15 of (Rn — G) was less than 25 W m - 2 because, under these conditions, estimates of XE were erratic. All hourly data were then combined into three data sets: 1987, 1988 and both years combined. A total of 419 hours of data was used in the modelling. Modelling Mean Stomatal Conductance Boundary line analysis. The maximum value of gs observed in the two years of data was 42 mm s _ 1 , this was used as the maximum in both years. The functions used in the BLA were selected from controlled environment studies if possible. The function used for the response of gs to Do was /(A>)= 0<Do<K2 = 1 - KXK2 - K3D0 Do > K2 This is similar to the function used by Stewart (1988) except that the lower arm was horizontal in that case. The function is a linear approximation of the exponential decay function given by Jarvis (1976) and Jones (1983). Jones showed that an exponential decay function is produced by a negative feedback model of stomatal response to saturation deficit, while a linear decrease is produced by a feedforward response. The choice of two linear segments was made in this case to avoid rounding errors, which caused the software to abort when many exponential functions were used in the NLLS optimization. The function used for the response of gs to solar irradiance was g(S) = 1 - eK*s This is the form given by Jones (1983). The function used for the response of gs to temperature was Chapter 3. Experimental Procedures 16 K5 = (Tmax-K6)/(K6-Tmin) where Tm,„ was taken as 0 °C and Tmax was taken as 42 °C. This is the function presented by Jarvis (1976). is the temperature at which the function reaches its maximum. In this study Tm,„ and Tmax were considered to be constants. The response of gs to the soil water regime was described by a function relating gs to the volumetric soil water content (6) in the upper 30 cm _ (A ~ -KV)(flmai ~ flm.n) #max((# — Kl) + 9min) At very low 6, gs approaches 0. It increases rapidly with increasing 0 until it reaches a level where increasing 6 has little effect. Price and Black (1989) and Livingston and Black (1987) found that there was a response by gs to time since sunrise. There is a relationship between time since sunrise and Do, as saturation deficit usually increases during the daytime; however, there is evidence (Zang and Davies 1988) that gs responds to abscisic acid transported from the roots to the leaf epidermis during the day. It is possible that this effect is independent of the daytime trend in saturation deficit. The function used to model the response of gs to time since sunrise (hours) was j(t) = 1 0 < t < K8 = 1-K9(t-K8) t>K8 Delucia (1987) found that photosynthesis and stomatal conductance of conifer seedlings was decreased after being subjected to short periods of low temperature. As the exper-imental site is subject to frequent summer frosts, a response of gs to the minimum air temperature the previous night was investigated. The minimum air temperature at a height of 15 cm was determined for the night before each day of eddy correlation measure-ments. Al l hourly mean conductance data were paired with the minimum temperature Chapter 3. Experimental Procedures 17 for the previous night. No boundary line relationship could be determined and it was concluded that the vegetation in the clearcut did not show a response in conductance to exposure to freezing temperatures. The starting values for the parameters were chosen by inspection and the functions were plotted onto the scatterplots using a commercial plotting routine (Wilkinson 1989). The parameters were refined until it was judged that that the BLA curve had been achieved. The parameters were then tested in the multiplicative model. This was re-peated for each year individually and then with both years combined. Non linear least squares optimization The maximum value of gs and the same functions described above were used except the function used to describe the response of gs to S was This is the function used by Stewart (1988), and approximates the exponential function described above. It was chosen to avoid rounding errors during optimization. The op-timization was performed using SYSTAT, a commercial statistical package containing a general non linear modelling unit and an integrated graphics capability (Wilkinson 1989). These functions were used in the multiplicative model of mean stomatal conductance in the form where the maximum mean stomatal conductance gsmax w a s 42 mm s 1 for all years and models. 3.2.5 Testing of Models Models of gs and XE were tested using the same data set used to determine the values of the parameters. The success of the models was determined using linear regression with g(S) = (1000 + K4)S 1000(^ 4 + S) 9s = gsmaxf(Do)g(S)h(To)i(t)j(0) (3.13) Chapter 3. Experimental Procedures 18 intercepts. The measured and modelled values were the independent and dependent vari-ables respectively. Wilkinson (1989) and Kvalseth (1985) point out that the algorithms used to determine the coefficient of determination (R2) are not equivalent when inter-cepts are not calculated. Many statistical programmes use different algorithms, which makes the comparison of R2 from different workers impossible if intercepts are not used. Chapter 4 Results and Discussion 4.1 Diurnal Energy Balance Figure 4.1a shows the diurnal energy balance for July 1, 1987. The maximum hourly mean solar irradiance was 880 W m - 2 . At this point in the growing season, leaf area index was approaching maximum (0.7) and no mineral soil surface was visible. Volumetric soil water content on this day was estimated to be 0.08 in the upper 30 cm of soil. This was the lowest value of 9 for this layer observed in both years. The saturation deficit was high and followed the characteristic trend through the day as shown in Figure 4.1b. Although saturation deficit was high and soil moisture content was low, the latent heat flux was high. The Bowen ratio reached a maximum for the day of only 0.8 by late morning. This suggests that the vegetation of the clearcut was adequately supplied with water. This is probably mainly due to the deep rooting characteristics of pinegrass (Fleming, 1990). Volumetric soil water content in the 19 to 60 cm zone was 0.24 on this day. There was little variation in 9 at the l m depth during both of the growing seasons. The response of H and XE to changes in the available energy flux shown in Figure 4.1a display characteristics of both aerodynamically rough surfaces such as forests and aerodynamically smooth surfaces such as grass or short crops. Above a rough surface, XE tends to respond to changes in D rather than to available energy flux. This is shown in Figure 4.1a by the tendency for XE to remain high as the available energy flux drops in the afternoon. Above a smooth surface, XE tends to follow the available energy flux. 19 Chapter 4. Results and Discussion 20 HOURS (PST) Figure 4.1: Diurnal energy balance and hourly mean environmental variables for July 1, 1987. A , the hourly mean values of energy balance components. B , The diurnal trend in saturation deficit. D was measured at 1.3m and Do was calculated with equation 2.6. C, Diurnal trend of g8 and ga, ga calculated with equation 3.11, gs calculated with a rear-ranged form of equation 2.1 and ga. D , diurnal trend in a calculated with equation 2.8, and Q, calculated with equation 4.14. Chapter 4. Results and Discussion 21 This behaviour is shown in Figure 4.1a by the decrease in XE and Rn at noon as a cloud moved past. Figures 4.1a and b show that this was not accompanied by a decrease in D. McNaughton and Jarvis (1983) defined the coupling coefficient (fi) to describe the coupling between XE and the saturation deficit of the mixed layer of the atmosphere as Rough surfaces such as forests are well coupled to the mixed layer and have values of 0 less than 0.5. Smooth surfaces are not well coupled to the mixed layer, show a marked response to available energy flux and have values of fl greater than 0.5. Figure 4.1 d shows the diurnal trend in hourly mean fi. Hourly fi varied between 0.65 and 0.35, and the mean value for the period 07:00-18:00 PST was 0.52. Hourly values of 0 varied from 0.2 to 0.7 during the growing season; however, the daytime mean values only varied between 0.3 and 0.6. Characteristically was higher in the morning and decreased through the day. This reflects the diurnal trend in ga and ga shown in Figure 4.1 c. Surface conductance tends to decrease in the afternoon in response to increasing saturation deficit. Wind speed often increases in the afternoon resulting in ga increasing. The surface conductances shown in Figure 4.1 c are similar to those reported for other grass surfaces. Table 4.1 lists daily mean values of gs from several studies selected for days when soil water was not considered to be limiting evapotranspiration. The value from Stewart and Gay (1989) was the daytime mean of nine days of data, all other values were calculated from data for a single day. For species with similar stomatal characteristics, gs would be directly related to L. This would indicate that the pinegrass clearcut has a high surface conductance relative to the low leaf area index. Stewart and Gay (1989) and Parton et al. (1981) did not observe the characteristic decrease in gs in the afternoon as was observed in this and the other reported studies; however, as they do not show the diurnal trend in D this may be due to unusual conditions. The mean hourly gs over the (4.14) Chapter 4. Results and Discussion 22 Table 4.1: Daytime mean surface conductances and leaf area indices for grassland without soil water limitation. Vegetation ga (mm s x) £ ( m 2 m - 2 ) Shortgrass steppe" 0.5 Agropyron-Koeleriab 9.1 1.45 Tussock grass0 5.7 -Tallgrass prairie^ 10.1 -Pinegrass clearcute 6.7 0.75 "Parton et al. (1981). bRipley and Redmann (1976). cCampbell (1989). ^Stewart and Gay (1989). e Present study. ^This study did not separate gs and ga, but as wind speeds were high ga was small. Chapter 4. Results and Discussion 23 419 hours of this experiment was 6.14 mms 1 with a standard deviation of 3.53 mms 1 . The maximum and minimum values were 24.9 mms - 1 and 1.02 mms - 1 , respectively. 4.2 Modelling Surface Conductance As indicated earlier, here L is considered to be known, so that modelling surface con-ductance depends on the success in modelling stomatal conductance. Figure 4.2 shows the relationship between gs calculated using equation 3.12 and the saturation specific humidity deficit at the leaf surface calculated using equation 2.6, stratified by solar ir-radiance. A clear response to DQ and S is indicated. Idso (1990) suggests that many of the reported responses of gs to Do are due to changes in leaf environment following enclosure in porometer chambers. These data for pinegrass were determined from energy balance measurements and are free of enclosure effects, but show a marked response to saturation deficit. Similar results have been obtained in other studies, (Black and Kel-liher 1990, Stewart 1988, Gash et al. 1989, Stewart and Gay 1989). McNaughton and Jarvis (1983) point out that as most grasses evolved in arid conditions, such a response would be advantageous and not unexpected. 4.2.1 The Technique of Boundary Line Analysis The values of the parameters for the functions described above determined using the BLA technique are listed in Table 4.2. These parameters were used with equation 3.13 to estimate gs with the three data sets used in the determination of the parameters. The results of the models are listed in Table 4.3. The models were tested by successively adding functions to the multiplicative model given by equation 3.13 to determine the response of gs- Tables 4.2 and 4.3 show that there is little difference between the two years in both the values of the parameters and value of R2 for the various models. The Chapter 4. Results and Discussion 24 Figure 4.2: Mean canopy stomatal conductance plotted against saturation deficit, strat-ified by solar irradiance. Hourly mean data from 1987 and 1988, • = S >200Wm~2, o = S < 200 W m - 2 . Chapter 4. Results and Discussion Table 4.2: Parameters for multiplicative model of gs determined by BLA. Parameter Data set used 1987 in analysis 1988 Combined #i 0.069 0.052 0.052 K2 11 14 14 K3 0.006 0.006 0.008 IU 0.004 0.006 0.004 K6 15 20 21 KJ 0.075 0.075 0.075 K8 0 4 4 I<9 0.052 0.08 0.08 Chapter 4. Results and Discussion Table 4.3: Results of testing models of gs with parameters determined by BLA. Variables used R2 Intercept (mms x) Slope 1987 data set D0,S 0.39 10.04 1.07 D 0 , S, T 0 0.22 5.01 1.07 D0, S, TO, t 0.26 1.57 0.87 Do, S, To, t, 9 0.28 1.08 0.84 1988 data set D0,S 0.41 9.64 0.81 Do, S, To 0.32 7.44 0.82 Do, S, To, t 0.27 3.71 0.72 D0, S, T0, t, 0 0.28 3.21 0.69 Combined data set D0,S 0.41 11.32 0.84 Do, S, TQ 0.27 9.80 0.86 Do, S, To, t 0.26 4.41 0.83 DQ, S, TQ, t, 0 0.23 3.70 0.79 Chapter 4. Results and Discussion 27 most successful models with all three data sets were those which included only functions of Do and S. Inclusion of any other functions produced a significant decrease in R2. This indicates that the vegetation mainly responded to changes in DQ and S during the two years of this experiment. The lack of response to 9 is not surprising as 9 did not change significantly at depths below 30 cm and pinegrass is known to have roots extending well below 30 cm. The lack of a response to T0 is due to the strong correlation between DQ and T0. Livingston and Black (1987), Stewart (1988), and Gash et al. (1988) all found that stomatal or canopy conductance responded to air temperature (T was used, not To). The limiting factor approach of Price and Black (1989) was also tested but the value of R2 was found to be only 0.03. Figure 4.3a and b show the boundary line functions derived from the three data sets plotted onto the combined data set. There is a more distinct boundary to the scatter plot of gs plotted against Do than to that plotted against S. This indicates, as shown in Figure 4.2, that S limits gs less frequently than Do-The above results indicate that the best model for mean stomatal conductance was of the form gs = <7sm<lx f(Do) g{S). This model, with parameters determined using boundary line analysis, explained 40 % of the variance in gs-4.2.2 The technique of NLLS Optimization The values of the parameters determined using the technique of NLLS optimization are listed in Table 4.4. Parameters K6 • • • K9 could not be determined using NLLS optimiza-tion for any of the data sets. As indicated above, there was a strong correlation between Do and T0. The NLLS optimization showed that there was no response in gs to the environmental variables To, t, and 9. If these variables were used, the optimization model did not converge or gave unreasonable values for all parameters. The SYSTAT software used in this analysis also indicated if correlations existed between variables in the model being tested; however, it did not indicate which variables were correlated. Casement Chapter 4. Results and Discussion 28 40 'WJ «> 20 0 40 a 20 -0 0 10 20 30 0 D 0 ( g k g 1 ) 400 S (W m2) 800 Figure 4.3: A and B , Functions with parameters determined by BLA for the response of gs to D0 and S respectively. C and D, Functions with parameters determined by NLLS optimization for the response of gs to D0 and S respectively. Dotted lines = 1987, dashed lines = 1988, and solid lines = combined data sets. Chapter 4. Results and Discussion 29 Table 4.4: Parameters for multiplicative model of gs determined by NLLS optimization. Parameter Data set used in analysis 1987 1988 Combined Modelled using DQ and S. Kx a0.110 (0.0019) 0.0810 (0.0035) 0.084 (0.0026) K2 6.56 (0.077) 7.73 (.35) 8.15 (0.27) Kz 0.0079 (8.0E-4) 0.016 (1.9E-3) 0.011 (0.00099) K4 421 (44) 730 (156) 758 (97.4) Modelled using D and S. 0.16 (0.0041) K2 4.44 (0.100) K3 0.011 (0.0013) IU 268 (45.4) "value (standard error) Chapter 4. Results and Discussion 30 plots of the data sets showed that Do, T0, and t were correlated. NLLS optimization was also used to determine the parameters for a multiplicative model substituting the saturation deficit measured at the reference height (D) for the saturation deficit at the leaf surface (D0). The model was optimized using the same functions as above and the combined data set was used. The values of the parameters are listed in Table 4.4. The models were tested and the results are listed in Table 4.5. These results indicate that, as with the results of the BLA analysis, there is little variation in the it!2 between years. The model using the variables Do and S explained 71% of the variance in gs when the two years were used in the analysis. This is significantly higher than that explained by the model when the parameters were determined using BLA. The value is similar to that found by Stewart and Gay (1989) working over a short grass prairie. Their model used the variables D and S, and the R2 was 0.73. As they did not compute the intercept, a direct comparison is impossible. Using definition 7 of Kvalseth (1985) for R2 with an intercept of 0, the R2 in this model increases to 0.94. The higher R2 for the model using Do suggests that mean stomatal conductance should not be related to D except in instances when D is similar to D0 (Monteith 1990). The forms of the functions are plotted on the combined data set in Figure 4.3c and 4.3d. Models produced by both techniques tended to underestimate gs at high values of gs- The model using the parameters determined by NLLS optimization tended to understimate more than that using parameters determined by BLA (Figure 4.4). This can be seen by comparing the slopes of the regression lines given in Tables 4.3 and 4.5. This effect is due to the form of the multiplicative model. Any points which lie above the functions shown in Figure 4.3 must be underestimated by the model. The functions used in the relationship between gs and Do tend to fall below the edge of the scatterplot at low values of Do-Chapter 4. Results and Discussion 31 Table 4.5: Results of testing models of gs with parameters determined by NLLS opti-mization. Variables used R? Intercept (mms l ) Slope 1987 data set D0,S 0.65 1988 data set D0,S 0.73 Combined data set D0,S 0.71 Combined data set D,S 0.50 3.9 3.74 3.22 4.38 0.68 0.611 0.63 0.50 Chapter 4. Results and Discussion 32 Figure 4.4: Regression analysis of models of gs with parameters determined using NLLS optimization. A , Model of gs based on D0 and S. B , Model of gs based on D and S. Chapter 4. Results and Discussion 33 4.3 Modelling Evapotranspiration Evapotranspiration models using the P M equation and the Priestley-Taylor (PT) equa-tion were compared. The combined data set was used in all cases. The first model used a model of gs based on D0,S given in Table 4.4 and 4.5. It uses values of Do calculated from measurements of XE to estimate gs- Clearly, this model cannot be used to estimate evapotranspiration from routine climate station data in which only D was available. The second model used the same model for gs as above, but iteratively calculated D0 and XE. D was used as the initial estimate of DQ. The third model used the model of gs based on D and S. Finally, the mean hourly a defined by the PT equation, equation 2.8 and Table 4.6 was determined to be 0.89 with a standard deviation of 0.29. XE was then estimated using this value of a and equation 2.8. Values of s and 7 were determined from the mean hourly T measured at the reference height. The resulting regression analysis of these models is shown in Figure 4.5 and Table 4.6. The most successful model was that using the P M equation and the first model of gs based on Do and S with an R2 of 0.92. However, when this model was run iteratively, the R2 fell to 0.81. This is less than the model using the P M equation and the model of of gs based on D and S. These two results indicate that although the two models of gs explained only 71 and 50 % of the variance respectively (Table 4.6) in gs, when used with the P M equation to estimate XE, a higher proportion of the variance in XE is explained. This reflects the sensitivity of equation 2.1 to changes in gs in a partially coupled system (Raupach and Finnegan 1988). Even in a 20m tall forest Stewart (1988) and Gash et al. (1989) found substantially better agreement between modelled and measured XE than between modelled and measured gs. This indicates that in an apparently highly coupled system there is still a significant dependence of XE on available energy flux (Rn — G). The model using the PT equation and a hourly mean value of a explained 85% of Chapter 4. Results and Discussion 34 Figure 4.5: Regression analysis of models of on Do (calculated from measured values of gs based on Do (Iterated). C, P M equation equation with a = 0.89. Solid line is the 1:1 in Table 4.6. \E. A, P M equation with model of gs based \E) and S. B, P M equation with model of with model of gs based on D and S. D, PT line, dotted line is regression equation given Chapter 4. Results and Discussion 35 Table 4.6: Results of testing models of XE using different models of gs, using the com-bined data set. R2 Intercept (W m- 2) Slope PM equation with gs = f(D0,S) 0.919 22.55 0.877 PM equation with gs = f(D0,S) iterated. 0.81 43.46 0.85 PM equation with gs = f(D,S). 0.88 21.67 0.89 PT equation with a = = 0.89. 0.85 8.2 1.02 Chapter 4. Results and Discussion 36 the variance in \E. This is higher than the iterative model using the P M equation and very similar to the two other P M based models, and it does not tend to underestimate at high evapotranspiration rates. For estimates of evapotranspiration using climate station data, the Priestley-Taylor approach produces very similar results to the more complex P M equation combined with a model of surface conductance. McNaughton and Spriggs (1989), using a mixed-layer model with the P M equation, show that values of a of 0.9 would be observed for a surface with values of g8 in the range 4 to 10 mm s _ 1 . Figure 4.2 shows that most of the observed values of ga for this site fell between 3 and 10 mms - 1 . The mean value of gs was 6.18 mms - 1 with a standard deviation of 3.52 mms - 1 . Even though the vegetation appeared to be adequately supplied with water, the low L of the surface causes gs and a to be lower than expected for a well watered grass. Although the P M equation describes the physical processes of evapotranspiration and can be used to determine the response of a surface to environmental variables, XE must be measured with great accuracy in order to determine the gs response functions. Chapter 5 Conclusions Although the area in which this study took place is considered to be subject to drought, evapotranspiration rates were generally 0.9 of the equilibrium evaporation rate. The max-imum daily evapotranspiration was as much as 4.1mm. Surface conductance responded to changes in saturation deficit and solar irradiance, but no response could be found to soil water content in the upper 30 cm. The mean hourly value of fl over the two years of the study was found to be 0.45, a value intermediate between those typical of forests and short grass. Calculated values of surface conductance were similar to those found by other workers for unmanaged grasslands where soil water was not limiting. The generally low values of surface conductance at this site are attributable to the low leaf area index (maximum of 0.8). The NNLS technique was superior to the BLA technique for determining the pa-rameters in the Jarvis multiplicative model of surface conductance. The limiting factor approach was unsuccessful. The model produced using NLLS optimization explained a greater proportion of the variance in surface conductance than that produced with the BLA technique. NLLS optimization has several other advantages. It does not require subjective judgement in setting the position of the boundary line curves. Most statisti-cal software used for NLLS optimization will automatically detect interactions between variables, and will provide standard errors for each parameter. It is significantly faster to carry out because the repeated plotting used in BLA to refine the estimates of the parameters is not required. 37 Chapter 5. Conclusions 38 Due to the large variation in leaf area index through the season, it was necessary to separate mean canopy stomatal conductance and L. Models of the response of mean canopy stomatal conductance to environmental variables explained more of the variance than models of the response of surface conductance, (i.e. without L removed). The best model for gs required only DQ and S as inputs. Soil water content, air temperature, and minimum air temperature the previous night, did not improve the model. Soil water content did not effect ga because the soil water content below 30 cm did not vary signifi-cantly during the growing season (pinegrass roots extend below 70 cm). Air temperature was highly correlated with saturation deficit. The addition of temperature to the mul-tiplicative model decreased the explained variance of gs due to interaction between D0 and To. The lack of improvement in the estimation of evapotranspiration when using a model based on DQ rather than D is due to the errors in calculating gs from energy balance measurements and the Penman-Monteith equation, and to the fact that a large proportion of the observed evapotranspiration rates were near Eeq. The mean hourly value of the Priestley-Taylor a was found to be 0.89 with a standard deviation of 0.29. This is similar to values found for coniferous forests and is consistent with the observed values of surface conductance of the clearcut. 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