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Measuring and modelling evapotranspiration from Douglas-fir stands Spittlehouse, David Leslie 1981

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MEASURING AND MODELLING EVAPOTRANSPIRATION FROM DOUGLAS-FIR STANDS by DAVID LESLIE SPITTLEHOUSE ( B . S c , U n i v e r s i t y of Not t ingham, Eng land , 1969) ( M . S c , U n i v e r s i t y of Saskatchewan, 1975) A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department o f S o i l Sc ience) We accept t h i s t h e s i s as conforming to the requ i red s tandard THE UNIVERSITY OF BRITISH COLUMBIA March 1981 c~") David L e s l i e S p i t t l e h o u s e , 1981 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a llowed without my w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 Date DE-6 (2/79) / i i ABSTRACT Methods of measuring forest evapotranspiration are reviewed and evaluated. Measurements on Douglas-fir stands indicated that eddy correlation, Bowen ratio/energy balance, stomatal diffusion resistance and s o i l water balance methods agreed with each other to within their respective measurement errors. A detailed error analysis of a Bowen ratio/energy balance system indicated that i t could give estimates of evapotranspiration to within ± 15% and ± 40% when evapotranspiration was high and low, respectively. The accuracy of this system was due to the use of a high s e n s i t i v i t y monitoring system, and the periodic reversal of well-matched sensors which results in the cancelling of certain systematic errors. The effects of certain non-cancelling errors are also i l l u s t r a t e d . Approaches to modelling forest evapotranspiration are reviewed and two approaches chosen for further study. Data obtained using the Bowen ratio/energy balance, stomatal diffusion resistance and s o i l water balance methods are used in the development and testing of two forest evapotranspiration models. These models are combined with simple interception and drainage relationships to produce two forest water balance models. In the energy/soil limited (E.S.L.) model, which is used on a daily basis, the d a i l y evapotranspiration rate (E) for dry foliage is assumed to be the lesser of either energy (demand) or s o i l water (supply) limited rates. The energy limited rate (E ) i s equal / i i i to o £ . where a is a constant (0.8) and E is the equilibrium eq ' eq ^ evapotranspiration rate, a function of the net radiation (Rn)- The soil limited, rate (Es) is equal to b6g, where b is a constant (8.6) and 9 is the fraction of extractable water in the root zone. On e rainy days, E = E m o v + g l , where I is the daily rainfall interception and g is a constant (0.6). Transpiration occurs when E > I and is the lesser of (E - I) and E . If I > E then (I - E) up to the saturated interception capacity of the foliage (S) is left until the next day. A water deficit is calculated that is the difference between the sum of E m g x and E, for dry foliage, for a given period. An average root zone matric potential {ty ) is used as a stress indicator. An hourly, physiologically based evapotranspiration model, the stomatal diffusion resistance (S.D.R.) model, is also presented. Transpiration is calculated, using an approximation of Fick's Law, from the vapour pressure deficit of the air (vpd), leaf stomatal resistance (r s ) , leaf boundary layer resistance (r^) and leaf area index (LAI) of the trees and the understory treated as two separate layers. Leaf temperature is assumed equal to air temperature. Stomatal resistance is calculated as a function of hourly vpd, average root zone ty and solar radiation (K4-). Evaporation from completely wet foliage is calculated using only the value of r^  while that from partially wet foliage is calculated using a wetness parameter (w = I/S), where I is depleted as water is evaporated and S, the saturated interception capacity, equal to 0.2 LAI mm. Tree water stress is indicated by times of low ty or high r . rm 3 s / i v D a i l y I i s c a l c u l a t e d as a f u n c t i o n of d a i l y r a i n f a l l (R) and 0 6 LAI from I = 0.08 LAI P ' . The roo t zone i s t r ea ted as a s i n g l e l a y e r t ha t i s u s u a l l y budgeted on a d a i l y b a s i s . Runoff d i d not occur and r a i n reach ing the f o r e s t f l o o r i n f i l t r a t e d immediately in the coarse s o i l s cons idered here. Drainage i s approximated by the h y d r a u l i c c o n d u c t i v i t y a t the average root zone water content (0). The average roo t zone s o i l water r e t e n t i o n c h a r a c t e r i s t i c i s used to g ive the average va lue o f f o r the root zone. The c h a r a c t e r i s t i c s o f the e v a p o t r a n s p i r a t i o n models were determined from measurements made i n 1975 on a th inned D o u g l a s - f i r {pseudotsuga menzesii (M i rb . ) Franco) s tand ,w i th a s a l a l {Gaultheria shaiion, Pursh) unders tory*1ocated on the east coast o f Vancouver I s l a n d . The c o e f f i c i e n t s f o r the i n t e r c e p t i o n and dra inage models were determined f o r the same s i t e i n 1978. Retent ion c h a r a c t e r i s t i c s were determined f o r each s i t e from f i e l d measurements. The water balance models were t es ted on the th inned stand dur ing the growing seasons of 1978 and 1979 and a nearby unthinned stand in 1974. The d a i l y , E . S . L . model we l l s imu la ted the seasonal course of 0 and t r ee water s t r e s s . The 1979 s imu la t i ons used d a i l y t o t a l K4-and average a i r temperature to c a l c u l a t e d a i l y R . The model i n d i c a t e d tha t over 20% of the summer's r a i n f a l l was l o s t through i n t e r c e p t i o n . In g e n e r a l , the h o u r l y , S .D .R . model adequate ly s imu la ted the course o f 0 through the summer, though there was a tendency to underest imate 0 and overes t imate s t r e s s as the summer p rogressed . Model led hour ly / v D o u g l a s - f i r and s a l a l t r a n s p i r a t i o n agreed we l l w i th porometer measurements i n 1975 and 1978. The s i z e o f the unders tory r b was important i n c o n t r o l l i n g unders tory t r a n s p i r a t i o n . The r s ~ c h a r a c t e r i s t i e s o f the D o u g l a s - f i r remained r e l a t i v e l y constant between 1975 and 1978 and between the th inned and unthinned stands wh i l e minimum o f the s a l a l may have decreased by 1978. The model i n d i c a t e d tha t the s a l a l unders tory used almost 40% of the a v a i l a b l e water dur ing the growing season. R e l i a b l e ten to twenty day es t imates o f E were obta ined in 1974 and 1979 wi th hour ly vpd s imula ted by f i t t i n g a s i ne wave to the d a i l y maximum vpd (mid a f ternoon) and minimum vpd (dawn). The two models are compared and eva lua ted . In g e n e r a l , both agreed w i th each o ther i n s i m u l a t i n g the t rend i n the growing season e v a p o t r a n s p i r a t i o n . However, the_S.D.R. model tended to g ive up to 15% h igher evapo t ransp i r a t i on r a t e s . P o s s i b l e reasons are presented f o r the r e l a t i v e constancy of a and i t s r e l a t i o n s h i p to the p h y s i o l o g i c a l c h a r a c t e r i s t i c s o f the vege ta t ion and the weather c o n d i t i o n s . A p p l i c a t i o n s o f the two models are cons ide red . Suggest ions f o r f u r t h e r f i e l d s tud ies and f o r improvement o f the model are presented . / v i ACKNOWLEDGEMENTS Funding f o r t h i s work was prov ided through grants from the Natura l Sc iences and Eng ineer ing Counc i l o f Canada and the U n i v e r s i t y o f B r i t i s h Columbia and c o n t r a c t s from the B .C . M i n i s t r y o f F o r e s t s . Support was a l s o prov ided by a research a s s i s t a n t s h i p and U . B . C . s c h o l a r s h i p s and teach ing a s s i s t a n t s h i p s . Research s i t e s were prov ided by the U . B . C . Research F o r e s t , Haney and by Crown Z e l l e r b a c h , Courtenay D i v i s i o n . Dur ing my study a t U . B . C . I have been helped i n a v a r i e t y o f ways by many peop le . In genera l , I wish to thank the f a c u l t y , s t a f f and s tudents o f the Department o f S o i l Sc ience the t h e i r help and f r i e n d s h i p . In p a r t i c u l a r , I wish to acknowledge the help o f my s u p e r v i s o r , Dr . Andy B l a c k , whose s u g g e s t i o n s , c r i t i c i s m s , support and f r i e n d s h i p con t r i bu ted g r e a t l y to my research and i t s p r e s e n t a t i o n . Also,many thanks to Andy f o r doing a l l the wo r r y i ng . Thanks a l s o t o : D rs . B a l l a r d , de V r i e s , L a v k u l i c h and Oke f o r t h e i r help and i n s p i r a t i o n ; Mike G o l d s t e i n f o r h i s help w i th the f i e l d s t u d i e s and p r o v i d i n g s o i l water and s o i l r e t e n t i o n d a t a ; Pat Wong and Paul Tang f o r t h e i r e l e c t r o n i c s ^ w i z a r d r y ; D rs . McNaughton, Tan and Nnyamah who's research l a i d the foundat ions (a t t imes somewhat shakey) f o r the research repor ted he re ; the s t a f f of the Oyster R i v e r Farm ( p a r t i c u l a r l y F r a n ) , f o r he lp ing preserve my s a n i t y dur ing the 1978 f i e l d season ; and l a s t , but not l e a s t , Joyce Ho l lands f o r pe rseve r ing w i th the t yp i ng o f t h i s t h e s i s and Nad in ia and J u l i e f o r d r a f t i n g the d iagrams. / v i i TABLE OF CONTENTS Page ABSTRACT i i ACKNOWLEDGEMENTS vi TABLE OF CONTENTS vii LIST OF TABLES x LIST OF FIGURES xii NOTATION xvii INTRODUCTION 1 CHAPTER 1 MEASURING AND MODELLING FOREST EVAPOTRANSPIRATION: A REVIEW 5 1. Introduction 5 \ 2. Measuring Forest Evapotranspiration 6 1. Eddy Correlation Methods 7 2. Aerodynamic Method 9 3. Bowen Ratio/Energy Balance Method 11 4. Methods using Stomatal Resistance Measurements 14 3. Modelling Forest Evapotranspiration 16 1. Thornthwaite Approach 18 2. Energy/Soil Limited Approach 18 3. Penman Approach 21 4. Approaches using Stomatal Resistance Characteristics. 22 4. Conclusions 24 CHAPTER 2 A SIMPLE FOREST WATER BALANCE MODEL 26 1. Introduction 26 2. Basis of the Model 27 1. The Evapotranspiration Sub-model 28 2. The Interception Sub-model 37 3. The Soil Water Balance Sub-model 38 / v i i i Page 3. Testing the Model 43 1. Site Description 43 2. Performance of the Model 44 4. Discussion 49 5. Conclusions 56 CHAPTER 3 A PHYSIOLOGICALLY BASED APPROACH TO EVAPOTRANS-PIRATION ESTIMATION IN A FOREST WATER BALANCE MODEL 58 1. Introduction 59 2. Theory 60 1. Evapotranspiration 60 2. Interception 69 3. Soil Water Balance 70 3. Site Description and Procedure.... 71 4. Results 76 5. Discussion 84 6. Conclusions 90 DISCUSSION AND CONCLUSIONS: THE TWO EVAPOTRANSPIRATION MODELS COMPARED 93 1. Performance of the Models 93 2. Further Considerations of the Theoretical Bases of the Two Models 97 3. Use of the Models in Water Balance Calculation 101 4. Suggestions for Further Studies 104 BIBLIOGRAPHY 106 APPENDIX I DETERMINATION OF FOREST EVAPOTRANSPIRATION USING BOWEN RATIO AND EDDY CORRELATION MEASUREMENTS 122 / i x Page APPENDIX II EVALUATION OF THE BOWEN RATIO/ENERGY BALANCE METHOD FOR DETERMINING FOREST EVAPOTRANS-PIRATION I* ..129 APPENDIX III ERROR ANALYSIS FOR THE REVERSING PSYCHROMETER 148 1. Calibration and Measurement Errors for the Reversing Psychrometer 148 2. Analysis of the Effect of Mismatched Diode Sensitivity on the Measurement of a Temperature Difference by the Reversing Psychrometer 181 3. Systematic Measurement Errors in the Reversing Psychrometer......... 185 4. Comparison of Reversing Psychrometers in the Laboratory and Field 189 5. Laboratory Experiment to Determine the Influence of External Radiation on the Temperature of the Reversing Psychrometer Heads 201 APPENDIX IV DATA COLLECTION AND ANALYSIS FOR THE THINNED SITE IN 1978 AND 1979 206 1. Site Description 206 2. Micrometeorological Instrumentation and Data Storage 238 APPENDIX V CALCULATIONS AND DATA USED IN CHAPTER 2 263 1. Determination of the Formula for the Effective Emissivity of the Sky (e ) 263 a 2. Normalizing the E versus 6 g Relationship.. 268 3. Field Soil Water Retention Characteristics for the Courtenay Unthinned and Thinned Sites in 1974 and 1975, respectively 273 4. Seasonal Change in Water Stored in the Trees in the Thinned Site 276 /x LIST OF TABLES Table Page 1.1 Comparison of micrometeorological methods of measur-ing the evapotranspiration rate (E). (a) Ratio of eddy correlation and aerodynamic measurements of (H + LE) to the available energy (Rn - G - M). (b) Ratio of the measurement of E, using various methods, to the Bowen ratio/energy balance measurement of E 10 1.2 Typical relative probable errors in the evapotrans-piration rate (6E/E) obtained with a reversing psychrometric system (psychrometer vertical separation 3 m), for two Bowen ratio (B) ranges and large and small potential temperature and height-corrected vapour pressure gradients d0/dz and deQ/dz, respectively. Relative error in the available energy was ± 7%. (From Spittlehouse and Black, 1980, see Appendix II.) 13 2.1 Coefficients and site parameters used in the calculation of the forest water balance of two Douglas-fir stands. See text for explanation of symbols . . . . . . . . . 42 3.1 Coefficients used to determine the stomatal resistance (rg) of the Douglas-fir and salal. (a) r -characteristics for vapour pressure deficit (vpd in p kPa), r = exp(a + b vpd ), for four matric potential ) ranges (modified from Tan et al., . 1978). (b) ^-characteristics for above-canopy solar radiation (K+) (modified from Tan et al., 1977). The equations give a multiplier (M ) to increase r g predicted by the characteristics in (a) Site parameters for the thinned and unthinned stands. Symbols explained in the text / x i i LIST OF FIGURES F igure Page 2.1 Components o f the f o r e s t water balance model 29 2.2 D a i l y e v a p o t r a n s p i r a t i o n ra te (E) f o r dry f o l i a g e versus the f r a c t i o n o f e x t r a c t a b l e water i n the root zone (6 ) f o r f i v e ranges of the e q u i l i b r i u m e v a p o t r a n s p i r a t i o n ra te (E ). C r i t i c a l water r eq content ( 9 e c ) i s i n d i c a t e d 35 2 .3 Comparison o f measured and model led 5-day average d a i l y e v a p o t r a n s p i r a t i o n (E) and mean roo t zone water content (6) f o r the th inned D o u g l a s - f i r s tand in 1975. Bars i n d i c a t e the probable e r r o r i n the measured d a t a . A l s o shown are model led d a i l y d ra inage (D) , t r a n s p i r a t i o n (E^) and i n t e r c e p t i o n ( I ) components o f model led d a i l y E and d a i l y r a i n f a l l ( P ) . On days w i thout r a i n E = E T 45 2.4 Comparison o f measured and model led mean roo t zone water content (8) f o r the unthinned D o u g l a s - f i r s tand in 1974. The bar i n d i c a t e s the probable e r r o r i n the measured d a t a . A l s o shown are model led d a i l y d ra inage (D) , t r a n s p i r a t i o n (E^) and i n t e r c e p t i o n ( I ) components o f the model led 5-day average d a i l y e v a p o t r a n s p i r a t i o n (E) and d a i l y r a i n f a l l ( P ) . On days w i thout r a i n E = E x 47 / x i i i F igure Page 2.5 As f o r F igu re 2.4 but f o r the th inned stand in 1978 48 2.6 Measured roo t zone m a t r i c p o t e n t i a l ) a t th ree dep ths , w i th bars (only one arm shown) i n d i c a t i n g range o f d a t a , and model led average ^ m o f the root zone 50 2.7 As f o r F igure 2.4 but f o r the th inned stand i n 1 9 7 9 . . . 51 2.8 E f f e c t on the model led average root zone water content (8) o f changing a by 25% f o r the th inned D o u g l a s - f i r s tand i n 1978. Measured 6 a l s o shown w i th the bar i n d i c a t i n g the probable e r r o r 53 2.9 Measured and model led root zone water content (9) f o r a m i c r o s i t e w i th a 1.05 m root zone , l oca ted 50 m from the main s i t e i n the th inned D o u g l a s - f i r s t a n d , 1979. Bar i n d i c a t e s probable e r r o r i n measured data 55 3.1 Comparison o f model led and measured 5-day average d a i l y e v a p o t r a n s p i r a t i o n (E) and mean roo t zone water content (0) f o r the th inned stand i n 1975. Bars i n d i c a t e probable e r r o r i n the measured da ta . A l s o shown are r a i n f a l l ( P ) , the model led D o u g l a s - f i r and s a l a l t r a n s p i r a t i o n and i n t e r c e p -t i o n (E j ) components o f d a i l y e v a p o t r a n s p i r a t i o n and the model led d a i l y dra inage (D) 77 / x i v F igu re Page 3.2 The upper diagram shows h o u r l y , daytime stand t r a n s p i r a t i o n ( E ) , model led ( s o l i d l i n e ) and measured w i th the Bowen r a t i o / e n e r g y balance method (x) and the porometer ( o ) , f o r the th inned s t a n d , 30 June , 1975. The lower diagram shows D o u g l a s - f i r and s a l a l t r a n s p i r a t i o n ( E T ) , model led ( s o l i d and dashed l i n e s , r e s p e c t i v e l y ) and measured w i th the porometer ((A) and ( « ) , r e s p e c t i v e l y ) . Measured data mod i f i ed from Tan e t al. (1978) w i th e r r o r bars i n d i c a t i n g ±10% f o r the Bowen r a t i o and ±20% f o r the porometer data ( S p i t t l e h o u s e and B l a c k , 1980). Only one arm o f the e r r o r bar i s shown. S o i l ma t r i c p o t e n t i a l , i n MPa, p r e d i c t e d by the model i s g iven 78 3.3 As f o r F igu re 3.2 but f o r 29 J u l y , 1975, w i th ±30% e r r o r f o r the porometer data 79 3.4 Comparison o f model led and measured mean root zone water content (6) f o r the th inned stand in 1978. The dashed l i n e i n d i c a t e s the s i m u l a t i o n s t a r t i n g on J u l y 18. The bar i n d i c a t e s probable e r r o r i n the measured d a t a . A l so shown are the d a i l y r a i n f a l l ( P ) , the model led D o u g l a s - f i r and s a l a l t r a n s p i r a t i o n and i n t e r c e p t i o n (E j ) components o f 5-day average d a i l y e v a p o t r a n s p i r a t i o n (E) and the model led d a i l y d ra inage (D) 80 / x v F igure Page 3.5 Model led and measured (porometer) h o u r l y , daytime t r a n s p i r a t i o n (Ey) from the D o u g l a s - f i r ( s o l i d l i n e and (A), r e s p e c t i v e l y ) and the s a l a l (dashed l i n e and (®) , r e s p e c t i v e l y ) f o r four days in 1978 f o r the th inned s tand . The bars (only one arm shown) i n d i c a t e the range of the measured d a t a . A l s o shown in the upper h a l f o f each quadrant are the hour ly above-canopy vapour pressure d e f i c i t (vpd) and s o l a r r a d i a t i o n ( K i ) as s o l i d and dashed l i n e s , r e s p e c t i v e l y . S o i l ma t r i c p o t e n t i a l s , i n MPa, p red i c ted by the model are g iven 82 3.6 As f o r F igu re 3.4 but f o r the unthinned stand i n 1974 and no s a l a l t r a n s p i r a t i o n 85 3.7 Ten to twenty day average d a i l y e v a p o t r a n s p i r a t i o n ra tes (E) f o r the unthinned stand in 1979. Measured data are from the s o i l water balance (S .W.B. ) method, w i th bars (on ly one arm shown) i n d i c a t i n g a ±5 mm or ±10 mm (when dra inage was l a rge ) e r r o r i n the change in s torage measurement. Model led E i s separated i n t o tha t from the D o u g l a s - f i r , the s a l a l and i n t e r c e p t e d water ( E j ) . D a i l y r a i n f a l l (P) i s a l s o shown 86 Ten to twenty day average daily evapotranspiration rate (E) for the unthinned Douglas-fir stand in 1974, simulated by the energy/soil limited (E.S.L.) model and the stomatal diffusion resistance (S.D.R.) model and calculated with the soil water balance (S.W.B.) method. Error bars (only one arm shown) are for the S.W.B. method. Daily rainfall (P) is also shown As for Figure 4.1 but for the thinned Douglas-fir stand in 1978 As for Figure 4.1 but for the thinned Douglas-fir stand in 1979 \ / x v i i NOTATION B A a r e a .of the s tem,at b reas t he ight (m 2) C heat c a p a c i t y of the a i r a t constant p ressure (= pCp) (J n f 3 0 C " ] ) C. i n t e g r a t o r output (counts) D dra inage ra te (mm d ^) DBH t r ee d iameter a t b reas t he igh t (mm) DT change in mean p r o f i l e temperature between two t ime per iods (°C) -2 -1 E e v a p o t r a n s p i r a t i o n ra te per u n i t ground area (kg m s , mm h~^, mm d"^) s u b s c r i p t s B, e , SR and WB i n d i c a t e E determined by the Bowen r a t i o , eddy c o r r e l a t i o n , stomatal d i f f u s i o n r e s i s t a n c e and s o i l water ba lance method, r e s p e c t i v e l y , i n Appendices I and II -2 -1 E e m p i r i c a l v e n t i l a t i o n term in Penman equat ion (kg m d ) a -2 -1 -1 E e q u i l i b r i u m e v a p o t r a n s p i r a t i o n ra te (kg m d , mm d ) E.p d a i l y evapora t ion ra te from the f o r e s t f l o o r (mm d ^) -2 -1 -1 Ej evapora t ion ra te of i n t e r cep ted water (kg m s , mm h , mm d b -2 -1 E^ t r a n s p i r a t i o n ra te per u n i t l e a f area (kg m s ) E energy l i m i t e d e v a p o t r a n s p i r a t i o n ra te (mm d ^) max -2 -1 E Penman es t imate of E m „ „ (kg m d ) p max E g s o i l water supply l i m i t e d e v a p o t r a n s p i r a t i o n ra te (mm d ^) -2 -1 Ey t r a n s p i r a t i o n ra te per u n i t ground area (kg m s , mm h ^) / x v i i i -2 -1 EQ evapora t ion ra te w i th leaves comple te ly wet (kg m s ) G s o i l heat f l u x d e n s i t y (W n f 2 , MJ rn"2 d " 1 ) -2 H s e n s i b l e heat f l u x d e n s i t y (W m ) s u b s c r i p t s 3 and e i n d i c a t e H determined by the Bowen r a t i o and eddy c o r r e l a t i o n methods, r e s p e c t i v e l y , i n Appendices I and I I I i n t e r cep ted r a i n f a l l (mm) -2 -2 -1 K+ shortwave r a d i a t i o n f l u x dens i t y (W m , MJ m d ) -2 -1 K 4 - M A X maximum p o s s i b l e d a i l y shortwave r a d i a t i o n ( M J m d ) 2 -1 eddy d i f f u s i v i t y f o r heat (m s ) 2 -1 Ky eddy d i f f u s i v i t y f o r water vapour (m s ) L l a t e n t heat o f v a p o u r i z a t i o n of water ( J kg ^) -2 -1 L* d a i l y net longwave r a d i a t i o n ( M J m d ) 2 LA l e a f area (m ) 2 2 L A I l e a f area index (m lea f /m ground) _o LE l a t e n t heat f l u x dens i t y (W m ) M r a te of s torage of energy i n the canopy on a ground area bas i s (W m" 2 ,MJ m" 2 d " 1 ) M^ m u l t i p l i e r to ad jus t r $ f o r l i g h t (d imens ion less ) P r a i n f a l l ra te (mm d~^) P c maximum value of P f o r which d a i l y I = P (mm d~^) R runo f f ra te (mm d~^) ~2 _2 - l R n net r a d i a t i o n f l u x dens i t y (W m , J m d ) S i n t e r c e p t i o n s torage c a p a c i t y o f the vege ta t i on (mm) S r i n t e g r a t o r s e n s i t i v i t y (counts (mV 10 min /xix diode s e n s i t i v i t y (mV °C ^) S-j-(n) spectral energy in T! (°C2 s) 2 -1 S (n) spectral energy in w1 (m s ) w Sw-p(n) w'T1 cospectral energy (m °C) T a i r temperature (°C) subscripts D and W indicate dry and wet bulb, respectively T daily average a i r temperature (°C) in Chapter 2 T1 turbulent fluctuation in a i r temperature (°C) leaf temperature (°C) T m a x daily maximum a i r temperature (°C) T -n daily minimum a i r temperature.(°C) T Q intercept of diode c a l i b r a t i o n equation (°C) V diode junction voltage (mV) subscripts c and m indicate c a l i b r a t i o n and measurement, respectively integrator input voltage (mV) Vp diode power supply voltage (V) W water storage capacity of the root zone (mm) W c r i t i c a l water content (mm) c W W at f i e l d capacity (mm) max K W .-n W at which transpiration v i r t u a l l y ceases (mm) Z sensing head separation in the reversing psychrometer system (m) a solar radiation r e f l e c t i o n c o e f f i c i e n t of the vegetation (dimensionless) b r a t i o of E g to e g (mm d ^) /xx c o e f f i c i e n t in daily cloudiness factor (dimensionless) s p e c i f i c heat of the a i r at constant pressure (J kg ^ °c -1) c o e f f i c i e n t in d a i l y cloudiness factor (dimensionless) vapour pressure of the a i r (kPa) saturated vapour pressure of the a i r (kPa) subscripts i and £w indicate e* at dry and wet leaf temperatures, respectively, and W indicates wet bulb temperature vapour pressure in leaf stomatal c a v i t i e s (kPa) height-corrected vapour pressure of the a i r (kPa) co e f f i c i e n t in the interception of r a i n f a l l equation (dimensionless) error term in Appendix I I I . l (counts) error term in Appendix I I I . l (°C) co e f f i c i e n t in the equation for the daily evaporation of intercepted water (d~^) co e f f i c i e n t in the interception of r a i n f a l l equation (dimensionless) von Karman's constant in Chapter 1 (dimensionless) s o i l hydraulic conductivity (mm d ) reference value of k in k(e) char a c t e r i s t i c (mm d ^) co e f f i c i e n t in the interception of r a i n f a l l equation (dimensionless) exponent in the s o i l water retention ch a r a c t e r i s t i c (dimension!ess) / x x i f requency in Appendix I ( s~^ ) , e l sewhe re , number of data po in t s (d imens ion less ) t u r b u l e n t f l u c t u a t i o n in the s p e c i f i c humidi ty of the a i r (kg water /kg a i r ) c o r r e l a t i o n c o e f f i c i e n t (d imens ion less ) l e a f boundary l a y e r r e s i s t a n c e (s n f ^ ) canopy o r su r f ace r e s i s t a n c e (s m~^) aerodynamic r e s i s t a n c e to heat t r a n s f e r (s nf ^) d a i l y i so thermal or c l i m a t o l o g i c a l r e s i s t a n c e (kPa(MJ m l e a f stomatal d i f f u s i o n r e s i s t a n c e (s nf" ' ) aerodynamic r e s i s t a n c e to vapour t r a n s f e r (s m ^) s lope o f the s a t u r a t i o n vapour p ressure curve (kPa °C ^) s a t wet bu lb temperature (kPa °C ) s tandard d e v i a t i o n of the mean ( v a r i a b l e ) s tandard d e v i a t i o n o f the d i f f e r e n c e between means ( v a r i a b l e ) t ime (d) wind speed (m s ^) f r i c t i o n v e l o c i t y (m s~^) vapour p ressure d e f i c i t o f the a i r (kPa) wetness parameter (d imens ion less ) t u r b u l e n t f l u c t u a t i o n i n the v e r t i c a l wind speed (m s ^) he igh t above the ground (m) roughness leng th (m) dry a d i a b a t i c lapse ra te (°C n f^ ) d i f f e r e n c e in a s s o c i a t e d parameter (d imens ion less ) \ / x x i i potential temperature ( C) r a t i o of E m a x to E g q (dimensionless) Bowen r a t i o (dimensionless) psychrometric constant (kPa °C ^) error in associated parameter (dimensionless) error term in Appendices II and III (°C) with subscripts indicating diode and location effective longwave emissivity of the sky (dimensionless) longwave emissivity of the vegetation (dimensionless) depth of the root zone (mm, m) net radiation extinction c o e f f i c i e n t (dimensionless) 3 3 volumetric water content (m water/m s o i l ) average volumetric water content of the root zone 3 3 (m water/m s o i l ) f r a ction of extractable water in the root zone (dimensionless) 3 3 value of 6" at f i e l d capacity (m water/m s o i l ) 3 3 value of 6 at which transpiration ceases (m water/m s o i l ) c r i t i c a l value of e g (dimensionless) reference value of e in k(e) and ^ ( s ) characteristics 3 3 (m water/m s o i l ) r e l a t i v e error term in Appendix III (dimensionless) density of the a i r (kg m ) absolute humidity of the a i r (kg m ) Stephan-Boltzman constant (MJ m~2 d~^ °K~^) wind speed s t a b i l i t y parameter (dimensionless) s o i l matric potential (MPa) / x x i i i ^ s s o i l water p o t e n t i a l (MPa) ^ t tw ig water p o t e n t i a l (MPa) an overbar i n d i c a t e s an average va lue /I INTRODUCTION R e l i a b l e methods of measuring and c a l c u l a t i n g f o r e s t e v a p o t r a n s p i r a t i o n are e s s e n t i a l f o r the management o f our water r esou rces . They are a l s o requ i red to determine t ree water requirements and, t h e r e f o r e , a i d i n the management o f f o r e s t s as a renewable resou rce . Many of the techniques f o r measuring and mode l l i ng ev apo t ransp i r a t i on have been developed f o r a g r i c u l t u r a l s u r f a c e s , and much i s known about the hydrology of these s u r f a c e s . However, f o r e s t s are s i g n i f i c a n t l y d i f f e r e n t s u r f a c e s . For example, they are aerodynamica l l y rougher , r e s u l t i n g in lower wind speeds and sma l l e r temperature and humidi ty g rad ien ts above the canopy, they have a lower r e f l e c t i v i t y o f s o l a r i r r a d i a n c e and d i f f e r e n t l e a f stomatal r e s i s t a n c e c h a r a c t e r i s t i c s . ( D e n m e a d , 1969; J a r v i s et a i . , 1976; Rauner, 1976; S i l v e r s i d e s , 1978). I t i s o f ten d i f f i c u l t to ob ta in adequate f e t ch in f o r e s t e d t e r r a i n to apply many o f the techniques f o r measuring e v a p o t r a n s p i r a t i o n . Mode l l i ng must f r equen t l y be done w i th a l i m i t e d amount o f data f o r l a rge heterogeneous a reas . R e l i a b l e measurements o f evapo t ransp i r a t i on must be ob ta ined f o r the development o f r e a l i s t i c evapo t ransp i r a t i on models. Measurement techniques such as eddy c o r r e l a t i o n and aerodynamic methods, the Bowen r a t i o / e n e r g y balance method and methods us ing stomatal r e s i s t a n c e measurements are b r i e f l y reviewed and eva luated i n Chapter 1. The Bowen r a t i o / e n e r g y balance method i s f u r t h e r reviewed and eva luated in d e t a i l i n Appendices TI and I I I s i nce t h i s method prov ided / 2 e v a p o t r a n s p i r a t i o n data used i n deve lop ing the models desc r ibed i n t h i s t h e s i s . The stomatal r e s i s t a n c e measurement method and the s o i l water balance method are f u r t h e r eva luated in Appendix II s i nce data obta ined us ing these methods were a l s o used in the model development. A b r i e f rev iew o f evapo t ransp i r a t i on models i s presented in the second par t o f Chapter 1. There are s t i l l many conceptual problems i n the p lan t water r e l a t i o n s requ i red i n these models. Gardner et al. (1974) comment tha t there i s , as y e t , no un i ve rsa l r e l a t i o n s h i p and tha t use fu l models w i l l r e q u i r e c a l i b r a t i o n f o r d i f f e r e n t c l i m a t e s , s o i l s and v e g e t a t i o n . However, Monte i th (1978) warns tha t there i s an important d i f f e r e n c e between s i m p l i f i c a t i o n and s imp l i sm. With these comments i n mind, two f o r e s t evapo t ransp i r a t i on models are f u r t h e r developed and desc r i bed in d e t a i l i n Chapters 2 and 3. The c r i t e r i a f o r these models were tha t they should be based on the phys i ca l processes i nvo l ved and the p lan t responses to the envi ronment, but be ab le to operate w i th a l i m i t e d amount o f weather and s i t e i n f o rma t i on . Chapter 2 presents a model r e l a t i n g d a i l y f o r e s t e v a p o t r a n s p i r a t i o n . to the root zone water content and the d a i l y net r a d i a t i o n f l u x . Th is model i s combined w i th s imple roo t zone water balance and r a i n f a l l i n t e r c e p t i o n models to prov ide a growing season f o r e s t water balance model tha t i s a p p l i c a b l e to many f o res ted a reas . Such models may be adequate f o r r ou t i ne water balance c a l c u l a t i o n s ; however, t h e i r empi r i c isms may do l i t t l e to e l u c i d a t e / 3 the ways tha t the p lan t s respond. to t h e i r phys i ca l environment (Mon te i th , 1978). For example, the model i n Chapter 2 t r e a t s the vege ta t ion as a s i n g l e evapo t ransp i r i ng u n i t , but i t i s important to know how the a v a i l a b l e water i s p a r t i t i o n e d between the t rees and the unders to ry . F u r t h e r , mode l l i ng o f water use and s t r e s s dur ing the daytime should a i d in understanding CC^ uptake and t ree growth. Chapter 3 cons ide rs the a p p l i c a t i o n o f a s imple d i f f u s i o n model (Tan et al., 1978) tha t determines hour ly evapo t ransp i r a t i on from the t rees and unde rs to ry , s e p a r a t e l y , over the growing season. Evapot rans-p i r a t i o n i s c a l c u l a t e d from the stomataT r e s i s t a n c e c h a r a c t e r i s t i c s and l e a f area index o f the vege ta t ion and the vapour pressure d e f i c i t of the a i r . The model i s combined w i th the above-mentioned root zone s o i l water balance and r a i n f a l l i n t e r c e p t i o n models to produce a second growing season f o r e s t water balance model. Obv ious ly computer models should not be cons idered an end in themselves. They encourage the syn thes i s o f o b s e r v a t i o n , hypothes is and theory (Mon te i t h , 1978). However, t h e i r assumptions and l i m i t a t i o n s should not be f o rgo t t en (Waggoner, 1977) , so tha t they should h i g h l i g h t c r i t i c a l po in ts and areas of ignorance . Monte i th notes tha t progress in b iometeorology r e q u i r e s a balance between measurement and mode l l i ng . Areas f o r model improvement, and thus f o r f i e l d measurement, are cons idered in D i s c u s s i o n . The two evapo t ransp i r a t i on models are::oompared and t h e i r i m p l i c a t i o n s f o r understanding the processes o f f o r e s t e v a p o t r a n s p i r a t i o n are d i s c u s s e d . /4 The chapters in the thesis are written in paper format. Thus, there is a certain amount of unavoidable duplication, though some repetition has been avoided by providing a single bibliography. Chapter 1 was presented at the First National Heat Transfer Symposium held in Edmonton, October 19-22, 1980 (Spittlehouse and Black, 1981). A summary of Chapters 2 and 3 was presented at the Interior West Watershed Management Symposium held in Spokane, April 8-10, 1980 (Black and Spittlehouse, 1980). Appendices T and II have been published, Spittlehouse and Black (1979) and (1980), respectively. /5 CHAPTER 1 MEASURING AND MODELLING FOREST EVAPOTRANSPIRATION: A REVIEW ABSTRACT Micro-meteorological methods of measuring and modelling forest evapotranspiration are reviewed and evaluated. Measurement, methods include eddy co r r e l a t i o n , aerodynamic, Bowen ratio/energy balance and stomatal diffusion resistance techniques. Modelling approaches include a model relati n g the daily evapotranspiration rate to the root zone water content and the dai l y net radiation .flux, the Penman equation, and vapour diffusion models requiring stomatal resistance characteris-t i c s of the stand to calculate hourly evapotranspiration. 1. INTRODUCTION Evapotranspiration i s an important part of the water balance of forested areas. The water balance equation can be written as P = E + D + R + AW/At (1) where P is the precipitation rate, E i s the evapotranspiration rate of the forest, D i s the drainage rate out of the root zone, R i s the rate of runoff and AW is the change in water content in the root zone over time At. The rate at which energy i s used in evapotranspiration, / 6 the l a t e n t heat f l u x ( L E , i . e . the l a t e n t heat o f v a p o u r i z a t i o n , L, m u l t i p l i e d by E ) , i s an important term in the f o r e s t energy ba lance , R n = LE + H + G + M (2) where R n i s the net r a d i a t i o n f l u x , H i s the s e n s i b l e heat f l u x , G i s the s o i l heat f l u x and M i s the ra te o f s torage o f energy ( s e n s i b l e , l a t e n t and pho tosyn the t i c ) i n the canopy. Changes to the f o r e s t , e . g . t h i n n i n g or c l e a r c u t t i n g , not on ly a l t e r the m ic roc l ima te through changes to (2) but may s i g n i f i c a n t l y a l t e r the water ba lance . Thus, the a b i l i t y to c o r r e c t l y measure or iriodel E a ids i n determin ing these changes as par t o f watershed - and f o r e s t management programmes. 2. MEASURING FOREST EVAPOTRANSPIRATION In 1970 Federer reviewed the theory and problems of measuring E. S ince then there have been many s i g n i f i c a n t advances i n measurement techniques and a l a rge quan t i t y o f in fo rmat ion on f o r e s t e v a p o t r a n s p i r a t i o n has been accumulated, e . g . J a r v i s et al. (1976) , Rauner (1976) , us ing mic rometeoro log ica l and non-micrometeoro log ica l techn iques . Some examples o f the l a t t e r i nc lude the s o i l water balance method where E i s obta ined as the r e s i d u a l term i n (1) ( C a l d e r , 1976; S c h o l l , 1976; Nnyamah and B l a c k , 1977). Th is method i s sometimes used to eva lua te m ic rometeoro log ica l procedures ( B l a c k , 1979; S p i t t l e h o u s e n and B l a c k , 1980, see Appendix I i ) , However, accura te measurements o f AW/At, D and R are o f ten more d i f f i c u l t to make than those o f E. The use o f l y s i m e t e r s , e . g . F r i t s c h e n et al. (1977) , i s l i m i t e d by the s i z e o f the ins t rumenta t ion and the need f o r an adequate sample s i z e . Measurement o f the f low o f water through t ree t runks w i th heat pu lse v e l o c i t y meters (Lasso ie et a i . , 1977; Running, 1980a), or r a d i o a c t i v e t r a c e r s (Waring and Robe r t s , 1979) , may r e q u i r e c a l i b r a t i o n w i th E determined by o ther methods. Sever ing t r ee t runks and p l a c i n g the cut t r ees i n water (Rober t s , 1977; Running, 1980a) may g ive anomalously h igh va lues o f E due to the reduc t i on in r e s i s t a n c e to water f l ow . However, the method may be use fu l f o r c a l i b r a t i n g heat pu lse v e l o c i t y and r a d i o a c t i v e t r a c e r methods and as a check on the stomatal d i f f u s i o n techniques desc r ibed l a t e r . The remainder o f t h i s s e c t i o n dea ls w i t h m ic rometeoro log ica l t echn iques . 1. Eddy C o r r e l a t i o n Methods D i r e c t measurement off E requ i res f a s t response sensors to measure the t u r b u l e n t f l u c t u a t i o n s o f the v e r t i c a l wind speed (w 1) and s p e c i f i c humid i ty ( q 1 ) above the f o r e s t canopy. The mean va lue of E over the sampl ing per iod i s g iven by E = p w ' q ' (3) where p i s the dens i t y o f a i r and the overbar represents the t ime average. The method i s s u i t a b l e f o r determin ing 30 to 60 minute average /8 values o f E. S i m i l a r l y , H i s g iven by H = C w ' T 1 (4) where T' i s the t u rbu len t f l u c t u a t i o n i n a i r temperature and C i s the heat c a p a c i t y o f the a i r . The sum o f LE and H obta ined us ing (3) and (4) should equal the net a v a i l a b l e energy (R - G - M). Such agreement has been obta ined above f o r e s t s f o r mean wind speeds, (u) above 2 m s " 1 (H icks et al., 1975; Moore, 1976; G a r r a t t , 1.978a; Thompson, 1979) (Table l . ' l ) . Webb et al. (1980) d i s c u s s p o s s i b l e c o r r e c t i o n s to (3) tha t depend on how humidi ty i s measured. Because i t . i s d i f f i c u l t t o - d i r e c t l y measure q ' , F r i t s c h e n (.1970) proposed an eddy c o r r e l a t i o n / e n e r g y balance method i n which E i s c a l c u l a t e d as the r e s i d u a l term i n ( 2 ) , H being obta ined from (4) and R n , G and M being measured or c a l c u l a t e d (see Stewart and Thorn, 1973). The method has been used w i th va ry ing degrees of success (McNeil and S h u t t l e w o r t h , 1975; M i l n e , 1979; S p i t t l e h o u s e and B l a c k , 1979, see Appendix I) (Table 1 ,1 ) . A l a c k o f s u i t a b l e i ns t rumen ta t ion f o r the long- term measurement o f E has been a major l i m i t a t i o n of eddy c o r r e l a t i o n methods. M i c r o -bead the rm is to rs adequate ly measure T ' ; however, humidi ty senso r , e . g . thermocouple wet bulb thermometers, are d e l i c a t e and e a s i l y contaminated. A l s o p r o p e l l e r anemometers may s e r i o u s l y underest imate w' and are l i m i t e d by low wind speeds (Moore, 1976; McNeil and Shu t t l ewo r t h , 1975; M i l n e , 1979; S p i t t l e h o u s e and B l a c k , 1979). /9 Recent improvements in i n f r a r e d h y g r o m e t r y ( H i c k s et ai., 1975; Hyson and H i c k s , 1975) and son ic anemometry (Campbell and Unsworth, 1.979) may .so lye many o f these problems. 2. Aerodynamic Method The d i f f u s i o n o f water vapour to and from the canopy can be desc r ibed by F i c k s Law, E = - ( C K v / Y L ) ( d e / d z ) (5) where y i s the psychromet r ic cons tant and (de/dz) i s the vapour pressure g rad ien t a t he ight z obta ined from p r o f i l e s above the canopy. However, the eddy d i f f u s i v i t y f o r water vapour (Ky) at z cannot be d i r e c t l y measured and must be c a l c u l a t e d from the wind p r o f i l e and an atmospher ic s t a b i l i t y parameter (4>v), i . e . Ky = k u* z/<j>^ , where k i s von Karman's cons tant and u* i s the f r i c t i o n v e l o c i t y . S t a b i l i t y co r rec ted wind p r o f i l e measurements or d i r e c t measurements o f the shear ing s t r e s s are requ i red to c a l c u l a t e u* . However, the c o r r e c t form o f these s t a b i l i t y parameters under a wide range o f s t a b i l i t i e s i s unce r ta i n f o r f o r e s t s (P ie rson and Jackson , 1975; Thorn et ai., 1975; G a r r a t t , 1978a,b; Raupach, 1979). Large d i s c r e p a n c i e s have been repor ted between aerodynamic and energy balance measurements o f E from f o r e s t s (Stewart and Thorn, 1973; Thorn et al., 1975; B lack and McNaughton, 1972; McFarlane and B l a c k , 1976, unpubl ished d a t a ; Raupach, 1979) (Table Tl.)l). Thorn et al. (1975) TABLE 1.1: Comparison o f m ic rometeoro log ica l methods of measuring the evapo t ransp i ra t i on ra te ( E ) . (a) Ra t i o o f eddy c o r r e l a t i o n and aerodynamic measurements o f (H + LE) to the a v a i l a b l e energy (R n - G - M). (b) Ra t io o f the measurement o f E, us ing var ious methods, to the Bowen r a t i o / e n e r g y balance measurement o f E. (a) Time per iod Method Source* (min) (H + L E ) / ( R n - G - M) Eddy c o r r e l a t i o n 1 30 0.8 - 1.1 2 20 0.7 - 1.4 3 30 0.8 - 1.0 Aerodynamic 4 60 0.3 - 0.5 5 30 0.4 - 1.0 (b) Time per iod Method Source* (min) E (Method)/E (Bowen) Eddy c o r r e l a t i o n / 6 60 1 - 1.4 energy balance 7 54 0.5 - 1.0 Aerodynamic 8 30 0.3 - 0.5 9 30 1.1 - 1.5 Stomatal r e s i s t a n c e 10 60 0.8 - 1,3 measurements S o i l water balance 1 1 weekly 0.9 - 1.2 monthly 0.9 - .1.0 * ! . . H icks et al. (1975) , Moore (1976) ; 2. Thompson (1979); 3. Ga r ra t t (1978a); 4 . Stewart and Thorn (1973) ; 5. McFarlane and B lack (unpubl ished data 1976); 6. McNeil and Shut t lewor th (1975); 7. S p i t t l e h o u s e and B lack (1979 ; ; 8. Thorn et al. (1975); 9. Black and McNaughton (1973) , w i th one anemometer; 10. Tan et al. (1978) ; 11 . Black (1979). /II pos tu la ted tha t wake d i f f u s i o n and thermal seeding e f f e c t s ac t as a d d i t i o n a l t r a n s f e r mechanisms over f o r e s t s . They concluded tha t "...aerodynamic equations ought not to be used to give independent flux estimates close to aerodynamically rough surfaces". G a r r a t t (1978a,b) shows tha t the aerodynamic method can be used f o r measurements at Z /ZQ > 50 to 90 , depending on s t a b i l i t y , where z Q i s the roughness leng th o f the v e g e t a t i o n . In G a r r a t t ' s s t ud ies the minimum z was about 44 iii i n uns tab le c o n d i t i o n s f o r an 8 fri t a l l , open canopy, f o r e s t . He suggests tha t the t u r b u l e n t wakes do not penet ra te above t h i s he igh t . Grant (1975) concluded tha t the Bowen r a t i o / e n e r g y balance method desc r ibed n e x t , would u s u a l l y g i ve more r e l i a b l e measurements o f E than the aerodynamic method. 3. Bowen Ra t i o /Ene rgy Balance Method The Bowen r a t i o / e n e r g y balance method has been s u c c e s s f u l l y used to measure E in many f o r e s t s tud ies (B lack and McNaughton, 1971; McNaughton and B l a c k , 1973; Droppo and Hami l ton , 1973; Gash and S tewar t , 1975; McNeil and S h u t t l e w o r t h , 1975; J a r v i s et al., 1976; McCaughey, 1978; Tan et a l . , 1978; Munro, 1979; S p i t t l e h o u s e and B l a c k , 1979; Tajchman.et al., 1979). The Bowen r a t i o (3) i s the r a t i o o f s e n s i b l e to l a t e n t heat t r a n s f e r from the f o r e s t canopy, i . e . 3 = H/LE. S u b s t i t u t i o n o f t h i s exp ress ion i n t o (2) to e l i m i n a t e H g ives E = ( R n - G - M ) / : t ( l + 3 ) L ] (6) /12 Express ing H and LE i n the form o f ( 5 ) , t ak i ng the r a t i o and assuming the eddy d i f f u s i v i t i e s f o r heat (K^) and water vapour (Ky) to be equal g ives 3 = y (dO/dz ) / (dep /dz ) . Here dQ/dz andde^/dz are the measured v e r t i c a l g rad ien t s above the canopy of p o t e n t i a l temperature and h e i g h t - c o r r e c t e d vapour p r e s s u r e , r e s p e c t i v e l y (Thorn, 1975). The assumption o f s i m i l a r i t y appears to be .accep tab le f o r neu t ra l to moderately uns tab le c o n d i t i o n s (Dyer , 1967) a l though there i s ev idence tha t > Ky in s t a b l e cond i t i ons (Verma et al., 1978). Assuming t ha t there i s no h o r i z o n t a l advec t ion below the top measurement h e i g h t , i . e . adequate f e t c h , nor net v e r t i c a l mass f low o f a i r , the r e l i a b i l i t y o f the Bowen r a t i o / e n e r g y balance method depends on the accuracy and r e s o l u t i o n o f d 0 / d z , de^/dz and (R - G - M) measurements. Sensors w i th high accuracy and r e s o l u t i o n are requ i red to measure the smal l temperature and humidi ty g rad ien ts above f o r e s t (Table 1 .2 ; J a r v i s et a i . , 1976, Table 9 ) . Measurement o f d0/dz andde 0 / dz d i f f e r e n t i a l l y w i th a p a i r o f psychrometers , t ha t reverse p e r i o d i c a l l y to remove sys temat ic e r r o r s , i s more accura te than determin ing the g rad ien ts from p r o f i l e s measured us ing f i x e d sensor systems (McNeil and S h u t t l e w o r t h , 1975; S p i t t l e h o u s e and B l a c k , 1980). T y p i c a l measure-ment e r r o r s f o r a r e v e r s i n g system are shown in Table 1 .2 , e x t r a c t e d from the more d e t a i l e d e r r o r a n a l y s i s i n Appendices II and I I I . Good agreement o f h o u r l y , weekly and monthly t o t a l s between t h i s method and o ther methods are shown i n Tab le 1.1 and Appendix I I . Webb et al. (1980) desc r i be p o s s i b l e c o r r e c t i o n s to (6) t ha t depend on howdeq'dz i s / 13 TABLE 1.2: T y p i c a l r e l a t i v e probable e r r o r s i n the e v a p o t r a n s p i r a t i o n ra te (o'E/E) ob ta ined w i th a r e v e r s i n g psychromet r ic system (psychrometer v e r t i c a l sepa ra t i on 3 m), f o r two Bowen r a t i o (3) ranges and l a rge and smal l p o t e n t i a l temperature and h e i g h t - c o r r e c t e d vapour p ressure g rad ien ts dG/dz and d e o / d z , r e s p e c t i v e l y . R e l a t i v e e r r o r i n the a v a i l a b l e energy was ± 7%. (From S p i t t l e h o u s e and B l a c k , 1980, see Appendix I.I.) 3 0.66 3.96 d9/dz °C m" 1 0.10 0.02 0.12 0.03 |de p/dz Pa m" 1 10 2 2 0.5 6E/E {% 3 > 0 10 15 54 3 < 0 12 38 24 90 /14 measured. The correction i s negligible for the case of a vapour pressure difference from two psychrometers (equation (34) in Webb et al.). 4. Methods Using Stomatal Resistance Measurements The transpiration rate of a leaf per unit leaf area (E|) i s E £ = C ( e A - e ) / Y L ( r s + r f a) (7) where e^ i s . the vapour pressure in the stomatal cavities of the leaf , e i s the vapour pressure of the a i r surrounding the l e a f , r s i s the leaf stomatal di f f u s i o n resistance and r^ i s the boundary layer resistance of the leaf. In principles the total canopy transpiration rate can be obtained from the summation of E for each canopy layer. Equation (7) has been simplified for needle leaf trees, where leaf temperature (T ) i s close to a i r temperature (T) and rb < r s ^ a n e t a 1 ' ' ^978). The transpiration rate per unit ground area (Ey) can be obtained with an error of about ± 20% (Spittlehouse and Black, 1980) from E T = f (C vpd L A I . / l y L 7 .-] ) (8) where r .' i s the mean stomatal resistance of the i t h layer of the si J canopy with leaf area index (LAI^), subject to an a i r vapour pressure d e f i c i t (vpd^. = e*^- e. ), where e*. i s the saturated yapour pressure /15 at a i r temperature. Determining forest f l o o r evaporation i s d i f f i c u l t , but i t could be estimated following PTamondon (1972) and Tanner and Jury (1976). However, when the forest f l o o r i s .dry or with a complete understory cover,, forest floor ••-'eyiporatton- i s 'small and E ~ Ej. Under such conditions Tan et al. (1978) found that hourly values of E from (8) and the Bowen ratio/energy balance method- agreed to within +10% for moist s o i l conditions and to within ±30% for dry s o i l conditions (Table 1)1). The method i s useful for indicating where the major transpiring surfaces are located within the canopy. However, i t can only be applied in dry canopies. For canopies where T^  i s s i g n i f i c a n t l y different from T, and measurement of T^  i s not feasible, the Penman-Monteith equation (Monteith, 1965; Thorn, 1972; and Stewart and Thorn, 1973; Shuttleworth, 1978) can be used to calculate E, i.e. E = [ s ( R n - G - M) + (C v p d / r ^ ) j / ( L [ s + y ( l + r c / r v ) j ) ) (9) where :• r H - r v - ( u / u i ) and l / r c =_I (LA I . / r g . ) . In (9) r^ and r^ are the aerodynamic resistances to sensible heat and water vapour transfer between the canopy and the above-canopy measurement height z, r £ i s the canopy or surface resistance, s i s the slope of the saturation vapour pressure curve at T and vpd i s evaluated at z. In this approach the canopy i s considered as a single isothermal leaf. /16 Shu t t lewor th (1976b, 1978, 1979) has de r i ved more r i go rous fo rmu la t i ons f o r r^, r^, and r c > In dry needle l e a f canopies r^ i s smal l compared to the s i z e o f r . Beven (1979) d i scusses the s e n s i t i v i t y o f (9) to i t s va r i ous parameters. Equat ions (7) to (9) can be used to c a l c u l a t e evapora t ion from f u l l y wet leaves by l e t t i n g r g = 0 i n ( 7 ) , F . = F^ in (8) and r c = 0 i n ( 9 ) . These equat ions cannot be d i r e c t l y used i n p a r t i a l l y wet canopies ( S h u t t l e w o r t h , 1976a,b, 1978, 1979). The m o d i f i c a t i o n s proposed by Shu t t l ewor th f o r p a r t i a l l y wet canopies are probably more s u i t a b l e f o r mode l l i ng ra the r than measuring e v a p o t r a n s p i r a t i o n . I t should be emphasized tha t use of the equat ions in t h i s s e c t i o n f o r measuring E from wet or p a r t i a l l y wet canopies should be avoided where p o s s i b l e . Equat ions (7) to (9) are t ime consuming to use as they r equ i r e many manual measurements w i th a porometer (Kanemasu, 1976; Tan et a l . , 1977, 1978) to ob ta in r . , and ex tens i ve sampl ing to ob ta in L A I . . However, they may be s u i t a b l e f o r smal l stands where f e t ch l i m i t a t i o n s prec lude the use o f p r e v i o u s l y d i scussed methods. 3. MODELLING FOREST EVAPOTRANSPIRATION There are two major requirements tha t should be met i n the development o f f o r e s t e v a p o t r a n s p i r a t i o n models. F i r s t , the models should be based on the p h y s i c a l processes i n v o l v e d , and the p lan t /17 responses t o , the environment (Mon te i th , 1978). Second, f o r p r a c t i c a l use , the models should r e q u i r e on l y a l i m i t e d amount o f b a s i c c l i m a t e and s i t e i n f o r m a t i o n . Often these requirements c o n f l i c t w i th one another . Many p h y s i c a l l y based models are complex and r e q u i r e a l a r g e amount o f i n fo rma t ion on weather , vege ta t i on and s o i l c o n d i t i o n s , e . g . Waggoner and Re i f snyde r (1968) , Cowan (1968) , Murphy and Knoerr (1972) , Thorn (1972), Shu t t l ewor th (1976b, 1979) , Federer (1979). These models are use fu l f o r research but are not o f immediate use to the f o r e s t h y d r o l o g i s t o r f o r e s t manager f o r general water balance c a l c u l a t i o n s . However, some models t ha t r e q u i r e a minimal amount o f i n fo rmat ion (Thornthwai te et ai., 1957; C u l l e r et ai., 1976) o f ten con ta in excess i ve emp i r i c i sm and are u s u a l l y a p p l i c a b l e on ly to the reg ion i n which they were developed (Webb, 1975; M o n t e i t h , 1978). In t h i s s e c t i o n some e m p i r i c a l l y and p h y s i c a l l y based models o f evapo t ransp i r a t i on are b r i e f l y rev iewed. Models f o r es t ima t i ng E f o r l a r g e reg ions from upper atmosphere d a t a , e . g . Mawdsley and B ru t sae r t (1977) , are not cons i de red . D i s c u s s i o n ' , o f canopy i n t e r c e p t i o n o f p r e c i p i t a t i o n , r u n o f f , i n f i l t r a t i o n and water movement i n the s o i l are beyond the scope of t h i s rev iew (though they are b r i e f l y d e a l t w i th i n Chapters 2 and 3 ) . The use o f o p t i m i z a t i o n techn iques to f i t model parameters i s d i scussed in Chapman and Dunin (1975) and Johnson and P i l g r i m (1976). D i scuss ions on mode l l i ng the water r e l a t i o n s o f watersheds can be found i n Chapman and Dunin (1975). /18 1. Thornthwaite Approach This method uses daily or monthly mean T to estimate E -, max the daily or monthly mean maximum evapotranspiration rate when soil moisture is not limiting evapotranspiration (Thornthwaite et al., 1957; Culler et a l . , 1976; Linacre, 1977). This relationship is assumed because T is related to Rn, and E m a x is usually well correlated with Rn (Priestley and Taylor, 1972; Tanner and Ritchie, 1974). The actual evapotranspiration (E) is usually obtained in one of three ways, (a) E = E m a x until all P and the available water in the root zone are evaporated; (b) E / E m a x decreases as available soil water decreases; (c) a consumptive use coefficient that is a function of vegetation cover is defined empirically. The advantage of the Thornthwaite approach is that it requires a minimum amount of data, i.e. T, P, and the available water storage capacity of the root zone. However, the correlation between T and Rn (and therefore E ) is not well defined and this approach often shows v max poor agreement with more accurate measurements (van Wijk and de Vries, 1954; McNaughton et a l . , 1979) especially for periods of less than a month long. 2. Energy/Soil Limited Approach -:• The equilibrium evapotranspiration rate (E^) is the expected rate of evapotranspiration from a moist surface of infinite extent (McNaughton 1976a,b; McNaughton et al., 1979). It is expressed as E e q = (s / (s + y ) ) ( R n - G - M)/L (10) / 19 where '('.R - G ---M) i s determined on a 24 hour b a s i s . Many researchers have found tha t d a i l y E m g x i s we l l c o r r e l a t e d w i th (10) and P r i e s t l e y and T a y l o r (1972) proposed tha t E = aE (11) max eq v ' where a i s an emp i r i ca l c o e f f i c i e n t . For a wide range of su r faces w i th smal l roughness and n o n - l i m i t i n g s o i l water c o n d i t i o n s a = 1.26 ± 0.2 ( P r i e s t l e y and T a y l o r , 1972; Tanner and R i t c h i e , 1974). McNaughton (1976b) has suggested tha t a > 1 represen ts mesoscale advec t i ve enhancement o f E. Values of a < 1 represent advec t i ve suppress ion o r s t rong su r face con t ro l through r . Strong su r face con t ro l appears to be the case f o r f o r e s t s where, f o r dry f o l i a g e , a v a r i e t y o f s t u d i e s have g iven 0.6 < a < 1.1 (McNaughton and B l a c k , 1973; J a r v i s et al., 1976; Moore, 1976; B l a c k , 1979; Munro, 1979; Shut t lewor th and C a l d e r , 1979; Tajachman e t a l . , 1979) a l though l a r g e r va lues have been repor ted (McCa.ughey, 1978). Below some c r i t i c a l va lue o f the roo t zone water s torage (W), E becomes s o i l water supply l i m i t e d . There are two e m p i r i c a l methods o f es t i m a t i ng e v a p o t r a n s p i r a t i o n under these c o n d i t i o n s . The f i r s t i s to cons ide r the r e l a t i v e e v a p o t r a n s p i r a t i o n ra te ( E / E m a x ) a f u n c t i o n o f the f r a c t i o n o f e x t r a c t a b l e water i n the root zone, 9 g = (W - W • )/ (W , - W . ) , where W , i s the maximum storage (W at f i e l d c a p a c i t y ) max min max • r J and W .^ ' . i i s . ther .s torage at which t r a n s p i r a t i o n v i r t u a l l y ceases . In /20 this method both l inear and nonlinear relationships have been used. In the former, E / E m a x is assumed equal to one until the c r i t i c a l value of 9 e ^ 9ec^ ^ s r e a c^ i e c '> below which E/Emax declines l inearly to zero (Zahner, 1976). However, i t appears that 8 is dependent on E ec r max (Black, 1979; McNaughton et a l . , 1979) and evapotranspiration estimates can be incorrect when using a single value of 8 (Appendix V.2). The second method assumes that at any value of 8 g there is a maximum rate of supply of water (E g) to the plant that the soil can maintain. A l inear decrease in E g with 8 g is usual Ty assumed, i .e . E s = b e e (12) I where b is experimentally determined. A c r i t i ca l value of 8 g is the value of Qn at which E p = E m = l v (Cowan, 1969; McNaughton et a l . , 1979). e s max In this two-phase model only meteorological or soi l factors (but not both) determine E so that for days without rain E = . [ l e s s e r of E m a x > E $ ] (13) Similar methods have been used with E m , „ calculated by the Thornthwaite max J approach and b determined by optimization techniques (Boughton, 1967; Federer and Lash, 1978), or E„,„ from (15) and b a function of soi l max matric potential (Item, 1974, 1978). Much larger values of a are found when the foliage is wet, and this can be accounted for by the lack of surface control (r - 0) /21 and mesoscale adyection (McNaughton and Black, 1973; Stewart, 1977; Shuttleworth and Calder, 1979). For rainy days, when soi l water is not l imiting transpiration, McNaughton and Black (1973) and Shuttleworth and Calder (1979) suggested that E can be calculated from E = E m a v + gl (14) max 3 where I is the daily intercepted ra infa l l and g is an experimentally determined constant. If E > I then (E - I) is transpired by the vegetation. However, i f E g < (E - I) then transpiration equals E g (Chapter 2). Gash (1978) has demonstrated the theoretical basis of (14), 3. Penman Approach Penman (1948) was the f i r s t to combine the surface energy balance and the heat and mass transfer equations, to produce an equation that linked daily evaporation from natural surfaces to the net radiation flux at the surface and the effective ventilation of the surface by the a i r . The form of Penman's equation that is currently widely used to obtain a dai ly Penman estimate of E m g x (Ep) is E p = ( s R n / L + Y E a ) / ( s + Y ) (15) where (G + M) is assumed zero on a 24 hour basis and E 3 is an empirical a function of wind run and mean dai ly vpd at 2 m above the canopy. An empirical constant is frequently used to reduce E n to the actual E 722 that occurs as the soi l dries (Thorn and Ol iver , 1977; Howard and Lloyd, 1979). The coefficients in the expression for E were empirically a obtained for a small water surface. Thus, no allowance is made in (15) for the effect on E of the greater roughness of vegetated surfaces and surface control , through r^ and r , respectively. The Penman-Monteith equation (9) is a more exact form of (15) that allows for variations in r^  and r . Thorn and Oliver (1977), by considering (9), show how (15) can be modified to allow for variations in r^  and r c due to seasonal and vegetational changes. Evaporation of intercepted rain can be accounted for by an equation of the form of E = E + gl r (Gash, 1978). Brutsaert and Strieker (1979) have proposed an approach that combines equations (10), (11) and (15). 4. Approaches Using Stomatal Resistance Characteristics This approach to determining evapotranspiration is the same as that discussed in Section 2.4, except that stomatal resistance characteristics are used rather than actual measurements of r . The characteristics are experimentally determined relationships between r g and environmental variables that influence the degree of opening of the stomata (Running et a l . , 1975; Jarv is , 1976; Gash and Stewart, 1977; Calder, 1977, 1978; Tan et al., 1977, 1978; Federer, 1979; Hinkley et a l . , 1979; Singh and Szeicz, 1979, 1980). Varying degrees of complexity of these relationships have been used to generate r s for calculating hourly or daily E. /23 If vpd is re lat ively constant with height in the canopy and T - T, (8) can be reduced for dry leaves (Tan et al., 1978) to E = C v p d / [ Y L r c ] (16) This also follows from (9) in well ventilated canopies where r y -* 0 (McNaughton and Black, 1973; Shuttleworth, 1979), and (16) has been used in such canopies, when dry, by Running et al. (1975) and Tan e t ai. (1978). If r^ is signif icant compared t o T , r c should be calculated from r g and r^. Equation (9) has been used in canopies that are relat ively isothermal but with T^ f T (Swift e t ai., 1975; Gash and * Stewart, 1977; Calder, 1977, 1978; Luxmoore e t al., 1978; Federer, 1979; Singh and Szeicz, 1979, 1980). Shuttleworth (1979) has modified (9) to allow the separate calculation of evapotranspiration from the understory. The evapotranspiration rate from a fu l ly wet canopy, E Q , can be calculated from (9) with r £ = 0 (Rutter e t al., 1971; Gash and Stewart, 1977; Calder, 1977, 1978; Singh and Szeicz, 1979; Gash, 1979) or from (16) by replacing r c with r^. In this situation the evaporation rate of intercepted water (Ej) is E Q . A good approximation to Ej for a part ia l ly wet canopy is Ej = EQ ( I /S) , where S is the saturated storage capacity of the canopy (Rutter e t a l . , 1971; Hancock and Crowther, 1979; Gash, 1979). Shuttleworth (1976b, 1978, 1979) has derived a wetness parameter that is used to adjust r for part ia l ly wet-conditions. Gash 724 and Stewart (1977) used an equation similar to (14) with E and gl on an hourly basis and E m a x from (9) for dry fol iage. Equations.(9) and (16) may be suitable for general water balance modelling. Equation (16) may be easier to use than (9) for dry, open canopies in that i t does not require net radiation or aerodynamic measurements. In the wet and part ia l ly wet case they both require a good estimate of the canopy wind speed to obtain r^. Forest f loor evaporation could be estimated as in Plamondon (1972) and Tanner and Jury (1976). A question requiring_.fyrther study is:- In what way do the ^ -charac ter is t ics ^change as the stand ages? 4. CONCLUSIONS Measurement of the daily evapotranspiration rate from forests over long periods of time is d i f f i c u l t . Maintenance of equipment above high stands, the small vert ical temperature and humidity gradients and low wind speed above the canopy l imit the methods that can be successfully used at the present time. It appears l ike ly that routine, direct eddy correlation measurements of evapotranspiration wil l be achieved in the near future. The Bowen ratio/energy balance method with reversing sensors is one of the best methods currently available to measure forest evapotranspiration. However, with the irregular topo-graphy of many forested watersheds l imit ing fetch, researchers may have to.resort to methods that use stomatal diffusion resistance or heat pulse velocity measurements, at least where canopies are dry for /25 signif icant periods. The soi l water balance procedure can be used only where flow through the base of the root zone is small or can be rel iably determined. Useful evapotranspiration models appear to be of two kinds. The energy/soil limited approaches .based on • the principle that evapotranspiration is well correlated with net radiation and root zone water content. It may be well suited to give daily estimates of evapotranspiration where data is l imited. This approach is tested in Chapter 2. The stomatal diffusion resistance or surface resistance approach uses the principle that the environment affects the process of water vapour diffusion through the stomata and through the canopy. This approach may be suitable for calculating evapotranspiration through the day and for partitioning transpiration between the trees and the understory. The method is tested in Chapter 3. /26 CHAPTER 2 A SIMPLE FOREST WATER BALANCE MODEL ABSTRACT A model that calculates the daily growing season forest water balance is presented. Input parameters are daily solar radiation, maximum and minimum ai r temperature, precipitat ion, soi l water retention and drainage functions and an estimate of s i te leaf area index. Evapotranspiration is calculated as a function of the equilibrium evapotranspiration rate and the fraction of extractable water in the root zone. Water def ic i ts and the matric potential of the root zone are used to indicate tree water stress. The model is tested on thinned and unthinned Douglas-fir stands. The same coefficients in the evapotranspiration sub-model were found to apply to both stands and to the thinned stand after a 20% increase in leaf area index. . Interception is over 20% of the growing season r a i n f a l l . 1. INTRODUCTION Practical procedures for estimating changes in soi l water storage, drainage and evapotranspiration in forests are required for the proper management of forested watersheds. A knowledge of the soi l water balance aids the determination of water y i e l d , the assessment of the growing conditions of trees and estimation of forest f i r e hazard. /27 Forest water balance models also can be used as a tool in the evaluation of forest management treatments. It would be advantageous i f the water balance could be calculated from routinely collected climate data, thus reducing the need for an extensive soi l water measurement programme. This Chapter presents a forest water balance model that requires only routine climate data and a limited amount of s i te information. The model calculates daily evapotranspiration, soi l water content and drainage for a forest stand. The main aims of the model are to provide an estimate of the water available to the trees and the length of periods of severe moisture stress experienced by the trees during the growing season. The model is tested on an unthinned Douglas-fir (pseudotsuga menziesii (Mirb.) Franco) stand •in - 1974 and a separate, thinned stand .in 1975, 1978 and 1979. 2. BASIS OF THE MODEL Detailed climate data and site information are not expected to be regularly available for most forested s i tes ; however, a certain amount of data is required to produce rea l is t ic water balances. The climate data required here are: (a) daily net or solar radiation; (b) daily ra infal l and (c) daily maximum and minimum a4r temperature. The s i te information required i s : (a) slope, aspect and lat i tude; (b) soi l prof i le descript ion, e .g . root zone depth, soi l texture; (c) root zone soil water retention characteristics and hydraulic conductivity character ist ics,or a drainage versus water content /28 function,measured or inferred from the soi l prof i le description; (d) i n i t i a l root zone water content; (e) measured or inferred leaf area index and (f) the coefficients in the evapotranspiration function. The model is composed of three sub-models: (1.) evapotranspir-ation; (2) interception of r a i n f a l l ; (3) soi l water balance. The components of the model are i l lustrated in Figure 2.1. The simulated soil water content and a tree st ress/soi l water relationship are used to determine the periods of tree water stress. Currently the model is not designed to.handle conditions of a snow pack or conditions when low temperatures may influence soil water movement or uptake by trees. 1. The Evapotranspiration Sub-model A variety of evapotranspiration models have been reported in the l i terature and are reviewed in Chapter 1. The model used here makes use of the relationship of evapotranspiration to the energy available to evaporate, water (the net radiation) and the average water content of the root zone. This approach has been chosen rather than physiolo-gical ly based models of evapotranspiration , e .g. Calder (1977), Thorn and Oliver (1977), Tan et a l . (1978), Federer (1979), since these models require a knowledge of the stomatal or canopy resistance characteristics of the vegetation, information that is not readily available for forests. Non-limiting Soil Water. The daily evapotranspiration from a surface with an adequate soi l water supply depends mainly on the net radiation /29 RAINFALL EVAPOTRANSPIRATION _ M A STORAGE * DRAINAGE FIGURE 2.1: Components of the forest water balance model. 730 received by the surface. The expected relationship for such a surface, with no advective effect is (McNaughton, 1976a) E e q = ( s / ( s + Y ) ) ( R n - G - M)/L (1) where E is the equilibrium evapotranspiration rate, R is the net eq n radiation f lux , G is the soi l heat f lux, M is the rate of storage of energy in the canopy (R n , G and M are on a 24 hour basis) , s is the slope of the saturation vapour pressure curve at the daily average air temperature ( T ) and y and L are the psychrometric constant and the latent heat of vapourization of water, respectively, at T. Many researchers have found that the maximum daily evapotranspiration rate ( E m = ) is well correlated with (1) and Priestley and Taylor (1972) max proposed that Em a x " « E e q <2> where a is an empirical coeff ic ient . A wide range of aerodynamically smooth surfaces, e .g. agricultural crops, have been shown to have a = 1.26 ± 0.2 (Priestley and Taylor, 1972; Tanner and Ritchie, 1974). McNaughton (1976b) has suggested that a > 1 represents mesoscale advective enhancement of evapotranspiration, and a < 1 represents advective suppression .. or strong surface control through the stomatal resistance of the leaves. In the case of forests strong surface control /31 is indicated by values of a, for dry canopies, of between 0.6 and 1.1 (McNaughton and Black, 1973; Gay and Stewart, 1974; Moore, 1976; Jarvis et al., 1976; Black, 1979; Munro, 1979; Shuttleworth and Calder, 1979; Tajchman et ai., 1979), though values greater than this have been reported (McCaughey, 1978). McNaughton and Black (1973) and Gay and Stewart (1974) found a - 1 for Douglas-fir stands on moist sites near Vancouver and Seattle, respectively. However, at Courtenay, on the east side of Vancouver Island, a rain shadow area where severe water def ic i ts occur regularly every summer, a was approximately 0.8 (Black, 1979). Some authors have reported a on a daytime basis, i .e . Rn > 0, rather than for 24 hours. Daytime values of a may be 10% smaller than 24 hour; values, depending upon sky conditions at night. This approach to calculating E m a x has been chosen since approaches involving correlations between daily or weekly mean air temperature and evapotranspiration, e .g. Thornthwaite et ai. (1957), Zahner (1967), Culler et ai. (1976), Federer and Lash (1978), can be quite inaccurate due to the relat ively poor correlation between temperature and net radiation (van Wijk and de Vries, 1954; McNaughton et ai., 1979). Approaches using the Penman equation, e .g. Zahner (1967), Boughton (1969), Item (1974, 1978)^require more weather data than the model described here, and tend to overestimate ^ m x as the region dries (Morton, 1978). Values of a much greater than those l is ted above are found when the foliage is wet. This is due to the lack of surface control of evapotranspiration and mesoscale advective enhancement (McNaughton and Black, 1973; Stewart, 1977; Shuttleworth and Calder, /32 1979). Evaporation of intercepted rainfal l is considered below, in a separate subsection. Equation (1) can be simplified by neglecting (G + M) since (G + M) < 0.05 Rn for forests on a daily basis (Jarvis et al., 1976). The value of 7 can be obtained with suff icient accuracy from ^Tmax + T m i n ^ 2 ' w h e r e Tmax a n d Tmin a r e t h e daily Maximum a n d minimum air temperatures, respectively. Direct measurement of Rn is d i f f i c u l t ; however, i t can be calculated from measurements of the daily solar radiation (Kl) , canopy reflection coeff icient for solar \ radiation (a) and net longwave radiation (L*) calculated from the a i r temperature (Jensen et a l . , 1971; Jury and Tanner, 1975) as follows: R n = (1 - a)K+ + L* (3) where L* = (c + d KVKi „ - e , ,)aT 4 . In (3) K*v is the maximum possible (clear sky) K4- for the day, c and d are constants, a is the Stefan-Boltzman constant, T is in Kelvin, e is the apparent a emissivity of the atmosphere and e y is the emissivity of the vegetation, assumed to be 0.96. Measurements in cloudy and clear conditions gave daily values of a = 0.12 ± 0.02 for the unthinned stand in 1974 and the thinned stand in 1975 and 1978, a typical value for coniferous forests (Jarvis et al., 1976). Unlike the fraction of daytime hours that have bright sunshine, K+/K+ has a minimum around 0.2 rather than zero. Thus, c and d were set equal to 0.1 and 0.9, respectively, rather 733 than the often used value of 0.2 and 0.8. This improves the estimation of low values of Rn and does not s igni f icant ly affect the higher values. Daily mean vapour pressure is not often available so that a formula based on a i r temperature, the Idso-Jackson formula (Aase and Idso, 1979) is used to calculate e as follows: a e = 1 - 0.261 exp (-7.77E-4(T-273)2) , where T is in Kelvin, a Concurrent measurements of Ki and R were available during the n 3 summer of 1975 and 1978. It was found that (3) consistently overestimated Rn by about 10% for Rn > 8 MJ m"2 d - 1 (Appendix V . l ) . Idso (1980) notes that formulae for e= determined for clear skies in a continental environments,overestimate e g by about 7% in coastal -2 -1 environments. Reduction of e g by 8% for R '> 8 MJ m d corrected the systematic overestimation of R n > A least-squares l inear regression of modelled Rn (with corrected e a ) on measured Rn had a correlation 2 -2 -1 coef f ic ient , r = 0.81 and a standard deviation, s = ±0.92 MJ m d , y 'X n = 169 (Appendix V . l ) . Equation (3) can be adjusted for slope angle and aspect by adjusting Ki (Buffo et a l . , 1972) and for view factor by adjusting L*. Storr (1972) i l lustrates how an average value of Rn for a small watershed can be obtained from a single site measurement. Limiting Soil Water. For any value of the fraction of extractable water in the root zone (9^) there is a maximum rate of supply of water (E c) to the plant that the soil can maintain (Cowan, 1965; 734 McNaughton et a l . , 1979). A l inear relationship between E g and 0 e is assumed, i .e . E s - b e e (4) where b is experimentally determined and 0 g = (9 - 9 m i n ) / ( 6 m a x ~ ^ m i n ^ ' The average, volumetric content of the root zone (0) is calculated from© = ( 9(z)dz)/£ where c . i s the root zone depth and 9(z) is the o^  volumetric water content of the soi l as a function of depth z. The symbols 0"max and 0 m i n are the values of 9 at f ie ld capacity, i .e . where drainage is small, and at which transpiration vir tual ly ceases, respectively (Tanner and Ritchie, 1974). In the gravelly sandy loam in this study the matric potentials corresponding to 0~ „ and 6". were UlaX ill 1 n approximately -0.01 MPa and1-2.0 ± 0.5 MPa, respectively. If at a particular 0 e, E s < E m a x , then E = E g , whereas, i f E g > E m a x , then E = E m a x . The c r i t i ca l value of 6 e (9 e c ) is where E $ = ^ - m x - This is i l lustrated in Figure 2.2 using data from Black (1979) for a 22 year old thinned Douglas-fir stand. Evapotranspiration was obtained during July and August 1975 from Bowen ratio/energy balance measurements above the canopy and soil water content by neutron soil moisture probe and gravimetric sampling. In this two-phase approach either meteorological or soi l factors (but not both) determine the evapotranspiration rate (McNaughton et al., 1979). Dividing both axes of Figure 2.2 b y - E m = v collapses the data" onto a ITIaX single curve with a single c r i t i c a l point (Federer, 1979 ; Appendix V.2). 735 D O U G L A S - F I R . COURTENAY, B.C. 29/6 /75 - 11/8/75 FIGURE 2.2: Daily evapotranspiration rate (E) for dry foliage versus the fraction of extractable water in the root zone (ep) for five ranges of the equilibrium evapotranspiration rate (E ). Critical water content (6 ) is indicated. /36 The value of 0 g for a day is obtained from the water balance at the end of the previous day (see Section 2.3). On days when 0 g may change signi f icant ly due to heavy rain or signif icant drainage, E wil l be limited by R . Evaporation of Intercepted Rainfa l l . During and shortly after a rainstorm the evapotranspiration rate ••for a wet canopy may be greater than the net radiation flux (Rutter, 1975; Stewart, 1977). McNaughton and Black (1973) and Shuttleworth and Calder (1979) proposed that the evapotranspiration rate on rainy days be calculated from E = E m a v + gl (5) max 3 where I is the daily interception.calculated from an interception model described in the next sect ion, and g is an experimentally determined coeff ic ient . If E > I then the lesser of (E- - I) and E g is the transpiration rate. If I > E there is no transpiration loss and (I - E ) up to the saturated interception capacity of the canopy is le f t until the next day. Shuttleworth and Calder use g = 0.93 for a = 0.72, while McNaughton and Black give g = 0.17 for a = 1.05. A value of g = 0.6 is indicated by ra infal l and evapotrans-piration data during 1975. Gash (1978) has demonstrated the theoretical basis of (5). /37 2. The Interception Sub-model Interception of ra infal l by the forest canopy is an important part of the forest water balance. Over 25% of the ra infa l l may be intercepted by and evaporated from the canopy surface (Rutter et a i . , 1971; Rutter, 1975; Shuttleworth and Calder, 1979; Gash, 1979). Most interception models are complex requiring ra infal l data input in time steps of as short as 5 minutes, e .g. Calder (1977), Gash (1979). However, with general climate data co l lect ion, ra infal l i s , at best, available on only a daily basis. The interception capacity (S) of the canopy is a function of the leaf area index (LAI) (projected area basis). The amount of water present at saturation can be considered as a layer of water 0.2 mm thick over the upper surface of the foliage (Rutter, 1975), i .e . S = 0.2 LAI (mm), assuming storage on trunks and branches is small. Since intercepted water evaporates during a rainstorm, I can greatly exceed S. It has been found that I is a function of intensity and length of the storm (Rutter et a l . , 1971; Gash, 1979). Daily interception is calculated from I = ffP^, for r a i n f a l l , : P, greater than some c r i t i c a l value, P , where f.and % are experimentally determined coefficients with I < 1, and I = P for P < P c (Zinke, 1967; Periera, 1973; Rutter, 1975; Ford and Deans, 1978; Shuttleworth and Calder, 1979). The coefficients used here were obtained for a Douglas-fir stand during 1978 using five below-canopy and one above-canopy rain gauges (Appendix IV. l ) . To apply this /38 formula in other years,change in LAI was empirically accounted for by setting f = h LAI, where h is a constant. The stand LAI was measured in 1975 (Tan et a l . , 1978) and 1978 (Appendix IV.1) (Table .2.1). Relationships between LAI and easily measured variables, e .g. Kinerson and Fritschen (1971), Gholz et al. (1976), would be adequate considering the accuracy of this simple interception model. 3. The Soil Water Balance Sub-model Root Zone Water Balance. The root zone is treated as a single layer ; (Figure 2.1). A multilayered root zone is not used because root water extraction functions and information on root distr ibution and variations of soi l hydrologic properties with depth in the prof i le are not expected to be available for most forest s i tes . However, a two layered root zone would probably be required for a forest where the root zone consists of layers with signi f icant ly different hydrologic properties, e .g. a thick litter-humus layer over the mineral s o i l . Signif icant horizontal var iab i l i ty in the soi l prof i le could be accommodated by considering area fractions of the site to be occupied by soi ls with di f fer ing hydrologic characteristics and obtaining the total water balance by summing each fract ion. Peck et a l . (1977) and Sharma and Luxmoore (1979) indicate that where the var iabi l i ty is not substantial , average soil properties can be used with minimal error. The two sites modelled here had surfaces covered by vegetation, slopes of < 10% and soi ls with high in f i l t ra t ion 739 rates so that runoff was negligible. Horizontal var iab i l i ty in the ra infa l l at the soi l surface due to the canopy concentrating the precipitation is not considered. The average root zone volumetric water content at the end of day i (6^) is calculated from e. = e._., + ( P . - E . - D . ) A t A (6) where 6. -j is the average water content at the end of the previous \ day, P. , E. and D. are the r a i n f a l l , evapotranspiration (including evaporated interception) and drainage from the root zone, respectively, for day i and.At is one day.. Note that - • the product of 9 and 5 is the equivalent depth of water stored in the root zone (W). Rainfall minus interception is input to the soil at the beginning of the day and drainage is calculated on a daily basis. An exception to this occurs when water content and ra infa l l are high. In this case ra infa l l is divided into four equal amounts and drainage is calculated on a six hour basis. Drainage. In freely draining soi ls of varying textures, the hydraulic gradient is often approximately equal to the gravitational gradient (Black et al., 1969; Nielson et al., 1973; Harr, 1977). In this si tuat ion, termed the unity gradient, D - k ( 0 ) , where k is the hydraulic conductivity of the soil at the volumetric water content ( 9 ) of the soil near the base of the soil p ro f i l e , or in this case, the mean /40 volumetric water content of the root zone, 0. This approximation has been used in various drainage models, e.g. Hi 11 el and van Bavel (1976), Federer and Lash (1978), Federer (1979). Although there may be an approximate unity gradient through the root zone while the s o i l is very wet, the potential gradients w i l l be distorted through removal of water by the plants and through the lack of v e r t i c a l homogeneity in the s o i l . In this case a more suitable approach i s to obtain a relationship between drainage and 0, D(9). This relationship can be determined by monitoring s o i l water change with time after soaking an area, while preventing evapotranspiration (Gardner et a l . , 1975; Clothier et a l . , 1977). The s o i l considered here consists of a root zone of gravelly sandy loam over sandstone. I t i s r e l a t i v e l y freely draining and gradients of less than unity develop as drainage proceeds (Black and Spittlehouse, 1980). Tensiometer and hygrometer measurements of the matric potential (ty~m) and neutron moisture probe and gravimetric measurements of 0 (Nnyamah and Black, 1977; Appendix IV.1) were used to obtain an average root zone s o i l water retention character-i s t i c by f i t t i n g the data, following Campbell (1974a) and Clapp and Hornberger (1978), to tym = ty (0/0 rrm where m i s a constant and the subscript r refers to a reference value (Table 2.1 )(Appendices IV.1, V.3). A D(e) relationship was determined from the residual term in water balances calculated during September 1978, with an estimate of evapotranspiration from (2) and A0/At calculated from tensiometer p r o f i l e s /41 of tym and the average ^ m (Q ) characteristic.^ It was found that D (6 ) could be approximated by an average k(0) characteristic for the root zone s o i l , k = k ^ ( 9 / e r ) ^ 2 m + 3 ^ (Campbell, 1974a, with m from the above retention characteristic and from laboratory measurements on an undisturbed sample from the 0.3 m depth. This k(0) characteristic was used to calcula drainage, although i t s l ight ly overestimated drainage as 0 decreased (Appendix IV.1). A D(8) relationship is appropriate where a root zone does not drain 'freely due to an underlying subzone with different soil properties (Clothier et a i . , 1977). If this relationship cannot be measured these authors describe a procedure for determining i t from ^ m ( e ) and k(8) characteristics of the s o i l . Clapp and Horberger (1978) present typical ^ m ( 8 ) and k(6) characteristics for different soi l texture classes. In the model upward flow is neglected since in coarse soi ls with bedrock, or a deep water table,upward flow is small because k is usually very small by the time the gradients reverse. 4. Determining Periods of Tree Water Stress An indication of periods of tree water stress is important since water stress can severely influence forest growth, e .g. Emmingham and Waring (1977). Tree water stress is a consequence of the inabi l i ty of trees to meet the atmospheric evaporative demand for water when available soil water is low. Thus, an estimate of the length of the stress period can be the time for which 8 is below a c r i t i c a l value, TABLE 2.1: Coefficients and Site Parameters Used in the Calculation of the Forest Water Balance of Two Douglas-fir Stands. See text for explanation of symbols. (a) Coefficients a a b(mm d - v c d g h % P c (mm) 0.8 0.12 8. .6 0.1 0.9 0,6 0.08 0.6 0.3 ±0.07 ±0.02 ±1 Site Parameters Year Stem ha" -1 LAI + (m)±20% emax ±5% 8min ±5% m 9 r ^mr (kPa) (mm d"1) 1974 1840 7.2±2 0.65 0.22 0.08 • 5.2 0.3 2.8 50 1975 840 6.5±1 0.75 0.21 0.11 7.2 0.3 1.5 100 1978, 1979 822 8.0+1* 0.75 0.21 0.08 . 5.9 0.3 0.9 100 Douglas-fir plus sa la l . *Measured in 1978. /43 e.g. Ballard (1974). For example, for high evaporative demand, i .e . large E , and 0 e < 0.4, the evapotranspiration rate is less than E (Figure 2.2). This situation can be interpreted in terms of II Id A a water d e f i c i t , i .e . the difference between the sum of E and the max sum of E for a given period of time. The average ty of the root zone has limited meaning (Black, 1979; Federer, 1979); however, i t can be used as an indicator of water stress. Stomatal opening can be s igni f icant ly reduced when tym < -0.4 MPa (Tan et al., 1978; Appendix IV. l ) . The average root zone ^ m ( 0 ) characteristic and 0 are used to give an average tym for the root zone. m 3. TESTING THE MODEL 1. Site Description The model was evaluated on thinned and unthinned Douglas-fir stands 26 km northwest of Courtenay on Vancouver Island (Nnyamah and Black, 1977; Tan et a l . , 1978; Black, 1979; Appendix IV). The sites are surrounded by a minimum of 5 km of forest of similar age, planted between 1952 and 1955. The thinned si te had a stand density of 820 to 840 stems ha~^ with a thick salal [Gauitheria shallon (Pursh)) understory. The unthinned si te had 1840 stems ha~^ with a scanty understory. The soi l at both sites is a gravelly sandy loam over sandstone, with roots through the whole prof i le and root density gradually - decreasing with depth. Topography is generally f la t with a few ridges of 20 to 30 m re l i e f . The sites have a slope of less than 744 10% with a NE apsect. The region is in a rain shadow and has warm, droughty summers. Model coeff icients and site parameters are l is ted in Table 2.1. 2. Performance of the Model Daily (24 hour) R n , G, M, T and P were the input data used to test the model for the thinned stand from 29 June to 11 August 1975. There was good agreement between Bowen ratio/energy balance measurements of E and modelled E when E was large (Figure 2.3), but for low values of E and relat ively dry soi l the model underestimated the measured flux by up to 40%. This may be partly due to possible large errors in Bowen ratio/energy balance measurements of E when evaporation rates are low (Spittlehouse and Black, 1980). The underestimation (12 mm over 30 days) is about 13% of the total evapotranspiration for the experimental period. The discrepancy could be part ia l ly due to an underestimation of interception by the model. Root zone depth varies from 0.4 to 1.1 m (Appendix IV.1) so that i t is d i f f i c u l t to define a mean root zone depth. Increasing the mean root zone depth from 0.75 to 0.85 m would provide enough water to account for most of the above underestimation. Measured and' modelled 9 over the period were in good agreement. Omitting G and M and simulating Rn from daily K i and T in the model gave v ir tual ly the same model results as are shown in Figure 2.3. Daily (24 hour) R n , T and P were the input data used to test the model for the unthinned stand from 17 June to 14 August 1974. Only /45 30 10 20 31 10 JUNE JULY AUG. FIGURE 2.3: Comparison of measured and modelled 5-day average daily evapotranspiration (E) and mean root zone water content (9) for the thinned Douglas-fir stand in 1975. Bars indicate the probable error in the measured data. Also shown are modelled daily drainage (D), transpiration (Ej) and interception (I) components of modelled daily E and daily rainfall (P). On days without rain E=Ej. /46 measured 9 was available for comparison with the modelled water balance (Figure 2.4). There was good agreement between measured and modelled 9 for dry and wet conditions. Evaporation of intercepted rain accounted for a signif icant fraction of Rn during the rainy period. The 1974 and 1975 data covered only short periods, albeit important ones for tree water stress; however, they did not provide a major test of the drainage and interception submodels. Thus, data for longer periods were obtained in 1978 and 1979 at the thinned s i te . The value of e". was reduced from that used in 1975 (0.11) to agree mm N ' 3 with observed values during 1978 (0.08) at this s i te . The adjustment from the 1975 value was required probably because, for the period after thinning during the spring of 1975, the remaining trees and the understory did not exploit a l l of the root zone, whereas the soil moisture measurements would give the mean water content of the whole root zone. By 1978 the roots should have grown into areas or ig inal ly exploited by the cut trees. The input data for 23 May to 30 September 1978 was daily (24 hour) R n , G, M, T and P. Measured 9 was used to validate the model (Figure 2.5). There was good agreement for June, July and August when transpiration was the major term in the water balance, and good agreement in May, August and September when transpiration was small and interception and drainage were signi f icant . Using daily values of K+ and T to calculate R from (3) and omitting G and M produced /47 20 30 10 20 31 10 20 JUNE JULY A U G . FIGURE 2.4: Comparison of measured and modelled mean root zone water content (8) for the unthinned Douglas-fir stand in 1974. The bar indicates the probable error in the measured data. Also shown are modelled daily drainage (D), transpiration (Ej) and inter-ception (I) components of the modelled 5-day average daily evapotranspiration (E) and daily ra infal l (P). On days without rain E=Ej. /48 MAY JUNE JULY AUG. SEPT. FIGURE 2.5; As for Figure 2.4 but for the thinned stand i 1978. 749 vir tual ly the same results as shown in Figure 2.5. The seasonal course of the simulated average ^ m of the root zone (from 0 and the average TJJ ( 9 ) .character ist ic ' is compared in_ Figure 2.6.with that measured using tensiometers and hygrometers. Simulated values of tym are, in general, within the measured range. This is good agreement considering the approximation involved in using an average ij>(e) characteristic for the 0.75 m deep root zone. The 1979 data allow an independent test of the interception and drainage submodels and the net radiation equation (3), as well as a further test of the evapotranspiration submodel. The climate data were obtained from 12 May to 14 October as in a routine climate network. A hygrothermograph in a screen 1.6 m above the forest f loor was used to obtain T and T . . Rainfall was measured in a small clearing max min 3 and was partitioned into daily amounts based on the ra infa l l measured at a site 9 km away where daily was also measured. There was generally good agreement between measured and modelled water content (Figure 2.7). However, by October, the model overestimated 9 by up to 20%. 4. DISCUSSION The preceeding section shows that the model well simulates the growing season forest water balance from limited input data. The feedback within the model between soil water content and evapotranspiration and drainage is responsible for the s tab i l i ty of the /50 JUNE JULY AUG. FIGURE 2 . 6 : Measured root zone matric potential Ol^ ) at three depths, with bars (only one arm shown) indicating range of data, and modelled average ty of the root zone. /51 20 31 10 20 30 10 20 31 10 20 31 10 20 30 10 MAY JUNE JULY AUG. SEPT. OCT. FIGURE 2.7: As for Figure 2.4 but for the thinned stand in 1979. /52 model. Figure 2.8 i l lustrates for 1978 that although a 25% change in a results in a small change in total water use for the growing season, the estimated stress duration is seriously in error. Further analysis suggests that an accuracy of ± 10%''- in a is required for rel iable estimates of stress duration. The model is relat ively insensitive to similar relative changes in b and to changes in g of up to 40%. Interception of ra infa l l s igni f icant ly reduced the input of water to the s o i l . In 1974, 1978 and 1979 interception was 19, 24 and 23%, respectively.of the ra infa l l for the periods modelled here. These values are within the ranges found for forest , e .g. Zinke (1967), Pereira (1973), Rutter (1975). The Douglas-fir trees are water stressed for a signif icant period of time during the summer. For example in 1978 E < E m g x for 41 days resulting in an 84 mm water def ic i t for the stand. Root zone ii data rm (Figure 2.6), suggest signif icant stress during this period. If daily vapour pressure de f ic i t (vpd) data are also available then relationships between stomatal resistance and vpd and ^ , e.g Tan et al. (1978), can be used to direct ly indicate tree water stress. The severe water stress indicated by the model for 1978 was confirmed by stomatal resistance measurements (Appendix IV.1) and the observed severe browning of the needles in August. In 1979 E < E m a x for 39 days resulting in a 58 mm d e f i c i t . Closure of stomata, with the consequent reduced photosynthesis, for signif icant periods during the summer was noted by Emmingham and Waring (1977) for Douglas-fir in Oregon. /53 FIGURE 2.8: Effect on the modelled average root zone water content (6) of changing a by 25% for the thinned Douglas-fir stand in 1978. Measured 8 also shown with the bar indicating the probable error. 754 The effect of local site variations on the water balance is i l lustrated in Figure 2.9 for 1979. This microsite, located 50 m downslope from the main s i t e , had a 1.05 m^deep root zone (Goldstein, 1980). The root zone had a volume fraction of coarse fragments of about 0.05 compared to about 0.15 at the main site so that e , e • max mm and were estimated to be 0.24, 0.09 and 0.34, respectively. There is good agreement between the measured (Goldstein, 1980) and modelled values of 9 . The model indicated that due to water stored in the extra 0.3 m of root zone, the microsite had v i r tual ly no water d e f i c i t . McNaughton et a l . (1979) and Shuttleworth and Calder (1979) warn against the indiscriminate use of equation (2) in evapotranspiration calculations. The discrepancy shown in Figure 2.7 between measured and modelled e in late September and early October 1979, i s , at least , part ia l ly due to an underestimation of evapotranspiration by (2). Rainfall and interception were not major components of the water balance at this time, and the amount of water required to recharge trunk storage was a negligible term in the water balance for the size of trees considered (Appendix V.4). The values of e during this period were such that soil water would not have limited evapotranspiration and drainage would be small. The value of E calculated using (6) with measured values of P and e in October indicated a ~ 1.1. McNaughton et al. (1979), Jackson et al. (1976) and de Bruin and Keijman (1979) found a to increase from warm to cold seasons for pasture, J /55 JUNE JULY AUG. SEPT. FIGURE 2.9: Measured and modelled root zone water content (8) for a microsite with a 1.05 m root zone, located 50 m from the main site in the thinned Douglas-fir stand, 1979. Bar indicates probable error in measured data. 756 bare soi l and a lake, respectively. The physiological response of the vegetation to the environment and mesoscale advective effects are incorporated in a (see Discussion). Advection effects and vegetation response characteristics wil l vary between location and vegetation type, and probably through the year; therefore local determination of a is required. The forest sites were located in extensive forested areas and in this case a appears to be a reasonably conservative parameter for a major portion- of the growing season. Thinned and unthinned stands were well modelled with the same value of a . This same value was also suitable for the thinned site after a 20% increase in canopy leaf area between 1975 and 1978. This means that the canopy resistance characteristics of the stand had remained constant which suggests that, either the stomatal resistance characteristics of the vegetation must have changed, or , the diffusive resistance within the canopy increased signi f icant ly (Chapter 3). This has implications for models that use stomatal resistance characteristics in simulating evapotranspiration. 5. CONCLUSIONS The simple forest water balance model well simulated the growing season water balance of thinned and unthinned Douglas-fir stands from limited site and climate data. Only daily maximum and minimum ai r temperature and r a i n f a l l , an estimate of leaf area index, and soil water retention and drainage functions needed to be si te spec i f i c , /57 while site daily net radiation could adequately be calculated from regional daily solar radiation and si te daily temperature. The function relating daily evapotranspiration to net radiation and the fraction of extractable water in the root zone gave good estimates of daily evapotranspiration. The results indicate that the calibrated evapotranspiration model may hold for varying stand densities and leaf area indices. Calculating ra infal l interception as a function of daily ra infa l l was found to be adequate. Treating the root zone as a single layer with drainage approximated by the hydraulic conductivity at the mean water content of the root zone worked well in "\ the freely draining soi ls considered here. However, i t would be advisable to determine a field,drainage versus average water content relationship where possible. The model well predicted the signif icant water def ic i ts and periods of tree water stress that occur during the growing season. The model could be a useful tool in forest management for indicating when water stress wil l l imit tree growth, and in determining evapotranspiration in hydrologic models of forested watersheds. 758 CHAPTER 3 A PHYSIOLOGICALLY BASED APPROACH TO EVAPOTRANSPIRATION ESTIMATION IN A FOREST WATER BALANCE MODEL ABSTRACT A forest evapotranspiration model that uses intercepted r a i n f a l l , vapour pressure def ic i t and temperature of the a i r , leaf area index and stomatal resistance characteristics of the vegetation, and estimated laminar boundary layer resistances of the leaves to calculate hourly evapotranspiration from wet and dry foliage is presented. The model was combined with simple interception and drainage relat ion-ships to produce a forest water balance model which was tested on a thinned Douglas-fir stand during the growing seasons of 1975, 1978 and 1979, and an unthinned stand in 1974. The model generally well simulated the diurnal and seasonal course of transpiration of the Douglas-fir and salal understory and the severe water def ic i ts experienced by the trees. However, the model tended to underestimate root-zone water storage as the season progressed, probably through a sl ight overestimation of evapotranspiration. The stomatal resistance characteristics remained relat iv ley constant between 1975 and 1978 while the reduced within canopy wind speeds resulted in a signif icant increase inthe boundary layer resistance of the understory. The model indicated that the understory used about 40% of the available water during the summer and that over 20% of the ra infal l was lost through interception by the vegetation. /59 1. INTRODUCTION Evapotranspiration is a major component of the forest water balance. Methods for accurately calculating evapotranspiration are required in making water balance calculations used in the estimation of forest f i re hazard, stream discharge and other aspects of watershed management. Evapotranspiration calculations are.also required'for predicting tree response to water stress, partit ioning of soi l water between trees and the understory and determining the effects of stand management practices, such as thinning, on the soi l water balance. A wide variety of evapotranspiration models have been reported in the l i terature and are reviewed in Chapter 1 and in Webb (1975). Simple, semi-empirical models that give the daily evapotranspiration rate, e.g. Federer and Lash (1979) and the model presented in Chapter 2, are suitable for general water balance calculations. However, physiologically based models, e .g. Running et al. (1975), Waring and Running (1976), Luxmoore et a l . (1978), Tan et a l . (1978), Federer (1979), can be used to partit ion the water loss between tree species and can simulate diurnal changes in evapotranspiration, leaf stomatal resistance and leaf water potential . There may be many situations where the climate data available for calculating evapotranspiration are l imited. This chapter presents an evapotranspiration model based on the simple physiological transpiration model of Tan et a l . (1978). Their model treated the trees and understory separately and required only hourly vapour pressure /60 def ic i t and temperature of the a i r , and daily root zone matric potential as the climate data input. The stomatal resistance characteristics and leaf area index of the vegetation were the required stand character-i s t i c s . Tan et ai's. model was modified to allow calculation of evaporation from wet and part ia l ly wet foliage and to allow for the l ight response of the stomata. This evapotranspiration model was combined with simple ra infa l l interception and drainage relationships to produce a forest water balance model. The model was tested on Douglas-fir [pseudotsuga menzesii (Mirb.) Franco) stands with an understory of salal {Gauitheria shaiion, Pursh). The model was used to \ determine water use and tree water stress during the growing season. 2. THEORY 1. Evapotranspiration One of the equations most frequently used to calculate evapotranspiration in water balance models is the Penman-Monteith equation (Monteith, 1965), e .g. Swift et al. (1975), Gash and Stewart (1977), Calder (1977, 1978), Luxmoore et al. (1978), Federer (1979), Singh and Szeicz (1980). However,the Penman-Monteith equation considers the canopy as a single layer, and the understory, or individual canopy layers, cannot easily be treated separately. Furthermore, the equation does not work well in the case of a part ia l ly wet canopy (Shuttleworth, 1976a). Shuttleworth (1976b, 1978, 1979) presents modifications to the Penman-Monteith equation, through a more accurate def init ion of the surface or canopy resistance, that /61 allow;, the determination of evapotranspiration from the trees and understory separately for wet and dry fol iage. The l imitation of Shuttleworth 1s approach is that hourly measurements of net radiation above the canopy and the understory, soi l heat flux and the rate of storage of energy in the canopy are required as well as the vapour pressure de f ic i t and temperature of the a i r . The transpiration model presented by Tan et a l . (1978) is the particular.case of the Penman-Monteith equation for canopies with very low aerodynamic resistances, e.g. conifers (McNaughton and Black, 1973; Stewart and Thorn, 1973; Tan and Black, 1976; Shuttleworth, 1978). \ Model. Transpiration from a unit area of dry leaf (E^) is given by E^ = ( C / Y L ) ( e £ - e ) / ( r s + r f a ) (1) In (1) C, y and L are the heat capacity of the a i r , the psychrometn'c constant and the latent heat of vapourization of water at a i r temperature, T, e^ is the vapour pressure in the stomatal cavities which can be approximated to within 2% by the saturated vapour pressure at leaf temperature (e* £) for leaf water potentials greater than -2.5 MPa, e is the vapour pressure of the canopy air and r g and r b are the stomatal and laminar boundary layer resistances of the leaf to water vapour d i f fus ion, respectively. Assuming (1) to describe the average conditions within the jth layer of the canopy, the transpiration from this layer per unit ground area is E 0 . LAI . , where LAI. is the leaf area index of the /62 layer. The transpiration rate of the canopy per unit ground area (Ej) is E T = j L A I j C C / y L K e ^ - e ) j / C r s j + »•„.) (2) Evaporation from a fu l ly wet canopy (EQ) is obtained from (2) by considering evaporation to take place from the leaf surface, so that r . does not apply, and by replacing e* by e* the saturation vapour S J J6 X/W pressure at the temperature of the wet leaf. Following Shuttleworth (1976b, 1978, 1979), the individual leaves are considered to be either completely wet or completely dry and i t is assumed that there is no signif icant interaction between the wet and dry fol iage. Consequently, there is a f ract ion, w., of the leaf area in a layer that is wet so that evapotranspiration (E) is given by E - j I W j L A I j C C / Y D l e * ^ - e ) j / r b J + (1 - w j ) L A I j ( C / Y L ) ( e * A - e ) j / ( r s j + , r b j . ) ] Rutter et al. (1971) and Hancock and Crowther (1979) have shown that as the canopy or individual branches dry from saturation, the evaporation of the free water (Ej) can be approximated by Ej = ( I / S ) E Q , I < S, where I is the ' • • . intercepted water on the. canopy and S is the saturated interception capacity of the canopy. (The interception model /63 to obtain I and S is described in section 2.2.) The f i r s t term in (3) can be equated to E , . , giving w. = ( I - /S . ) . Equation (3) requires more within-canopy information than is usually available for forests. Thus, i t is now simplified to a two layered canopy of trees and understory. Assuming that the canopy dries out relat ively uniformly, w. - w = I/S, where the overbar indicates an average wetness factor for the trees or the understory. Within either of these two layers wind speed does not show a large change with height so that r^ can be approximated by an average laminar boundary resistance, r^, for each layer. The variation of r g j with height for the stands considered here is usually small compared with the var iab i l i ty of r g within a layer (Tan et ai., 1977; Appendix IV.1), so that an average stomatal resistance, r , can be assumed. Tan et ai. (1978) noted that for the case of dry needle leaves in an open canopy T^ - T so that e*^ - e* and (e*^ - e) - vpd, where vpd is the vapour pressure def ic i t of the a i r (e* - e). This approximation can be made as a consequence of the small value of r^  in the case of needle leaves and i t results in a si ight underestimation of (e*^ - e),, which is partly compensated by setting r^ = 0 for the dry needle leaves. In the case of wet leaves, r^ must be retained; however, since the leaf is being cooled strongly by rapid evaporation from a free water surface, the leaf could be below a i r temperature. In a part ia l ly wet canopy i t is assumed that the wet and dry leaves are at the same temperature so that e* 0 - e*. In the case of 3oW the understory, with broad leaves and low wind speeds, r h is not small. /64 However, i f the understory is shaded so that the absorbed energy is small, or i f much of this absorbed energy is dissipated as latent heat, the assumption that e*^ - e* should not cause too large an error. The relative error in E due to this assumption, obtained by dif ferentiat ing (1) with respect to T and dividing by E, is (s/vpd)dT, assuming al l the other terms remain constant, and s is the slope of the saturated vapour pressure curve at leaf temperature. Thus, there would be an underestimation of E by 10% for each degree T^ is greater than T. The above assumptions simplify (3) to E = ( C / Y L ) t v p d 1 / r c ] + v p d 2 / r c 2 ] (4) where the subscripts 1 and 2 indicate the tree and understory layers, respectively. The general form of the canopy resistance (r c ) is r c = ( F s + F b ) / ( L A I [ 1 + w ( ? s / r b } 1 } ( 5 ) The r^in the numerator of (5) is omitted in the case of the Douglas-f i r . The formulation of rQ is similar to that in Shuttleworth (1978, 1979) but simplif ied since, unlike the Penman-Monteith equation, (4) does not contain radiation or aerodynamic resistance terms. In a fu l ly wet canopy (w = 1) (5) reduced to r £ = r^/LAI, while for a fu l ly dry canopy (w = 0) i t reduces to = r^/LAI^, and = ( r g 2 + r ^ / L A ^ . /65 Tan et ai. (1978) found in an open canopy that vpd-j was approximately equal to ypdr, and to the vpd at the top of the canopy. This latter approximation can be made due to the very low aerodynamic resistance of rough surfaces such as forests (Stewart and Thorn, 1973). In a stand with a dense understory forest f loor evaporation is negligible since there is l i t t l e energy to evaporate water. When there is l i t t l e or no understory forest f loor evaporation (E^) is estimated on a daily basis as the lesser of an energy (net radiation, R ) or soi l limited rate. Plamondon (1972) found that v i r tual ly a l l Rn at a moist forest f loor below a Douglas-fir canopy was used to evaporate water. Forest f loor P n (R n f ) is estimated from above-canopy Rn using R nf = R n e x P ( - f | ' - A I ) , where in is an extinction coeff icient (Jarvis et a i . , 1976). Above-canopy Rn can be measured, or calculated from daily solar radiation and average T (Jury and Tanner, 1975; Chapter 2). As the surface dries, the soi l below the surface l imits the evaporation rate (Plamondon, 1972; Tanner and Jury, 1976). A simple approximation of this soi l limited rate is the hydraulic conductivity at the water content of the surface layer of soi l (Black et al., 1970). However, since the root zone is treated as a single layer in the water balance model presented here (see section 2.3), the soi l limited rate is the hydraulic conductivity at the average water content of the root zone. Stomatal Resistance. The responses of the stomata to various environmental variables are termed the ^ - c h a r a c t e r i s t i c s . The vpd of the a i r , the amount of water in the root zone available to the plants and solar radiation /66 (K4-) generally haye the greatest influence on the daily course of r g in conifers (Jaryis, 1976; Hinkley et al., 1978; Tan et al., 1977, 1978; Roberts, 1978; Running, 1980b). The stomata close as vpd increases and as the soi l dr ies. Table 3.1 gives the relationship of r s to vpd for four ranges of ty for the Douglas-fir and s a l a l , separately. These relationships are from Tan et al. (1978) with a reanalysis of the data for the lowest ranges. In the stands considered here the stomata were fu l ly open when at a leaf was greater than 250 Wm - 2 (Tan et a l . , 1977). Since K+ was measured above the canopy, this relationship was adjusted on the basis of early morning and evening measurements of r g during 1975, and 1978 to allow for the extinction of K4- by the canopy (Table 3.1). If K+ is unavailable, early morning and evening closure is simulated by increasing r s f ive fold for the f i r s t and last hours of the daytime, and by doubling r g for the second and penultimate hours. Daylength is determined from date and lat i tude. Some researchers, e .g. Federer (1979), have used a relationship between twig (^t) or leaf water potential and r g in transpiration models . Edwards and Meidner (1978) suggested that r g is related to the water potential of the epidermis rather than the bulk water potential of the leaf. The dependence of r g on predawn ty^ (Running et a l . , 1975; Hinkley et a l . , 1978; Running, 1980 b,c) can be considered a dependence of r g on tym since nightime recovery of tree water potential depends, to a large extent, on ty (Thompson and Hinkley, 1977; Appendix IV . l ) . However, the use of a relationship involving tym may not be adequate for large trees 767 TABLE 3.1: Coefficients used to determine the stomatal resistance i r s ) of the Douglas-fir and sa la l . (a) ^ -charac te r is t ics for vapour pressure def ic i t (vpd in kPa); r s = exp(a + b vpd 2 ) , for four matric potential (tym) ranges (modified from Tan et a l . , 1978). (b) r § -characteristic for above-canopy solar radiation (K+) (modified from Tan et al., 1977). The equations give a mult ipl ier (Mr) to increase r s predicted by the characteristics in (a). Douglas-fir a b — Salal a b , ^ m x (MPa) 6.06 0.27 6 .05 0.19 > -0.35 6.60 0.34 6 .35 0.31 > -0.95 to < -0. 35 7.30 0.57 6 .40 0.53 > -1.25 to < -0. 94 7.30 1.10 6 .80 0.53 > -2.5 to < -1 . 25 K+ < 10 W i n " 2 M = r oo 10 < U < 350 W; m ~ 2 Douglas-fir M = r 64.5 -0.71) Salal M r = 137 -0.84) K+ > 350 W j i m " 2 M = r 1 768 where water stored in the boles, branches and leaves acts as a signif icant reservoir for transpiration, e.g. Waring and Running (1978). Boundary' Layer Resistance. Various formulae are available for calculating r^ for leaves well exposed to the a ir flow. However, leaves in a canopy are often sheltered by other leaves, effectively increasing r^  and making i t d i f f i c u l t to calculate. Thorn (1972) and Jarvis et al. (1976) present formulae describing r^ in terms of shelter factors and average transfer coeff ic ients. However, detailed measurements of canopy architecture, leaf geometry and wind flow are required to determine these factors. In the case of dry needle leaves, an accurate estimate of r^ is not c r i t i ca l since r^  < 0 .1r s , e v e n a * l ° w w i n d speeds and low values of r s (Jarvis et a l . , 1976). However, an accurate estimate is required in the case of a wet canopy (see equation-(5)). The Douglas-fir canopies considered here are relat ively open and the needles well exposed so that shelter effects are small. However, the understory is usually dense and wind speed is low. Thus, the lower leaves may be well sheltered, and the rate of water vapour diffusion from such leaves may approach the molecular rate of diffusion in s t i l l a i r . The r^ values used were estimated from formulae for laminar flow (Campbell, 1977), using average canopy wind speeds. Values of r^ for turbulent flow are lower than for laminar flow (Wigley and Clark, 1974). Howeyer, ignoring this effect wil l compensate somewhat for the lack of a correction for shelter effects. Douglas-fir needles were treated as cylinders of 1.5 mm /69 diameter in cross flow, while the salal leaves were considered discs of 70 mm diameter. During the measurement periods in 1974, 1975 and 1978, the above-canopy wind speed (u) was usually > 1 m s ~ \ At the 0.5 m height in 1975 u > 0.5 m s~^. Consequently, in 1975 r^ values of 12 s m~^  (u _ 0.8 m s"^) and 90 s m~^  (u ~ 0.5 m s~^) were used for the Douglas-fir and s a l a l , respectively. In 1978, u at the 0.5 m height rarely exceeded 0.3 m s~^ and was frequently below the sta l l speed of the anemometer (about 0.1 m s~^). This reduction of within-canopy u was due to the increased momemtum absorption by the increased leaf area of the Douglas-fir . The values of r^ used in 1978 and 1979 were 15 s nf 1 (u - 0.5 m s _ 1 ) and 300 s rn"1 (u ^ 0.05 m s" 1) for the Douglas-fir and s a l a l , respectively. Within-canopy wind speed was not measured in the unthinned stand in 1974. However, since the Douglas-fir LAI was greater than that in 1978 (Table 3.2), i t was expected that the within-canopy values of u would be lower than in 1978. Consequently a value of 20 s m"^  (u - 0.3 m s~^) was used for r^  of the Douglas-fir. There was no understory in the unthinned stand. 2. Interception Most interception models require ra infa l l data for short time intervals, e.g. Rutter et al. (1971), Calder (1977, 1978), and Gash (1979). The wetness parameter incorporated into (5) allows the evapotranspiration model to be combined with such interception models. Only daily ra infa l l totals were available to test the model; however, for many forest sites ra infa l l wil l only,be available on a daily basis. 770 Daily interception (I) is calculated, from I = h L A I P A f o r P > P c (6) and I = P f o r P < P c where P is the daily ra infal l and h, £ and P £ were experimentally determined in 1978 to be 0.08, 0.06 and 3.0 mm, respectively (Chapter 2; Appendix IV. l ) . On a daily basis (I) can be greater than the interception capacity of the foliage (S) due to the evaporation of intercepted rain during the rainstorm (Rutter et al., 1971; Gash, 1979). It is assumed that at saturation a layer of water 0.2 mm thick existed over the upper surface of the leaves (Rutter, 1975) so that S = 0.2 LAI mm. The time at which the ra infal l started during a day was unknown. Thus, evaporation of I i s . started at dawn, and the hourly rate i s , -not allowed to exceed S. Water is allowed to remain on the foliage overnight. 3. Soil Water Balance The soil water balance model is described in detail in Chapter 2 and wil l be only br ief ly described here. The root zone is treated as a single layer. Al l ra infa l l reaching the soil surface is assumed to in f i l t ra te immediately, there being no runoff for the sites considered here. Horizontal var iab i l i ty in the rainfal l due to concentration by /71 the vegetation is- not considered. Drainage (D) from the root zone is approximated by the hydraulic conductivity (k) at the average volumetric water content of the root zone (6), where k(6) was obtained from the laboratory determined hydraulic conductivity characteristic of the soi l (Table 3.2), k - k r ( 9 / 6 r ) ( 2 m + 3 ) , "where m is a constant and the subscript r indicates a reference value (Campbell, 1974a;Appendix IV.1). The average tym of the root zone (Table 3.2) was calculated from the f ie ld determined average retention characteristic of the s o i l , m^ = ^ m r ( e / 0 r ) " m ( C a m P b e 1 1 > 1974a; Appendix IV.1). The value of at the end of any day is- used in determining r g for the following day. The value of 0 at the end of day i (0^) is calculated from 6. = 6 . ^ + (P . - D. - E . ) A t / c (7) where 0.j_-| is 6 at the end of the previous day, P. , D.. arid".E. are r a i n f a l l , drainage and evapotranspiration (including interception) on day i , At is one day and £ is root zone depth. 3. SITE DESCRIPTION AND PROCEDURE The model was tested on two Douglas-fir stands, one thinned and the other unthinned, on the east coast of Vancouver Island, about 150 m above sea leve l . The site of the thinned stand was 28 km northwest of Courtenay and that of the unthinned stand a further 1.5 km northwest. At 772 the.!> former site the stand density was 820 to 840 stems h a - 1 with a substantial salal understory, while at the lat ter site stand, density was about 1840 stems ha~^ with negligible understory. The root zone soil at both sites was a gravelly sandy loam over a sandstone bedrock, and varied in depth from 0.4 to 1.1 m. The sites were surrounded by a minimum of 5 km of forest , planted between 1952 and 1955. They were on slopes of < 10% with a northeast apsect and the surrounding topography was generally f la t with a few ridges of 20-30 m re l ie f . The region is in a rainshadow and has warm, droughty summers. Data collection procedures are described in fu l l in Tan and Black (1976), Nnyamah and Black (1977), Tan et ai. (1977, 1978), Black (1979), Spittlehouse and Black (1980) and Appendix IV. The ^.-.characteristics and site parameters are l is ted in Tables 3.1 and 3.2, respectively. Weather data were obtained at 1 m above the thinned stand from 29 June to 11 August 1975 and from 23 May to 30 September 1978. Hourly average values of K-f, T and vpd were obtained using a pyranometer and psychrometer monitored at 15 minute intervals in 1975 and integrated over 30 minutes in 1978. Average tree height was 11 m and 13.5 m in 1975 and 1978, respectively. The hourly stand evapotranspiration rate was determined continuously in 1975 using the Bowen ratio/energy balance method. Measurements of ra infa l l and ty (with tensiometers and rm hygrometers) were made daily and measurements of 0 were made weekly with a neutron moisture probe and gravimetric sampling. A ventilated diffusion porometer was used to occasionally measure r g through the day TABLE 3.2: Site parameters for the thinned and unthinned stands. Symbols explained in the text. Stand density LAI c(m) <k_r k f Year (stems ha" 1) Douglas-fir salal (+10%) (kPa) e r (mm d _ l ) m 1974 1840 7.2±1.5 - 0.65 2.8 0.3 50 5.2 1975 840 3.6±0.5 3.0±0.3 0.75 1.5 0.3 100 7.2 1978, 1979 822* 5 .0±0.5* 3 .0±0.3* 0.75 0,9 0.3 100 5.9 *measured in 1978. 774 and E was determined from equation (4) using these r g values and measured within-canopy vpd. The LAI was measured in August of each year and represents a maximum for the year. During late May and June, 1978, the. new leaves of the Douglas-fir and the salal were growing and were not fu l ly developed until July. The new foliage was estimated to be between 10 and 20% of the LAI. The Douglas-fir and salal LAI were estimated to be 4.5 and 2.5 on May 23 and were increased l inear ly in the model to 5.0 and 3.0, respectively by July 1. During 1975 above and within-canopy vpd were in good agreement (Tan et al., 1978). During 1978, above-canopy vpd occasionally lagged within canopy vpd by up to an hour. Also, salal vpd tended to drop more rapidly.than the above-canopy vpd after the mid-afternoon maximum. Since these differences from above-canopy vpd were variable and not large, the above-canopy vpd was used for both the salal and Douglas-fir layers. Data obtained in 1974 in the unthinned stand and 1979 in the thinned stand were used to test i f the model would perform sat is factor i ly with limited/climate and site information. In 1974 daily Rn and average T and maximum vpd were determined about 1 m above the trees, 11 m above the ground, from 17 June to 14 August. Measurements of ra infal l and 8 were made daily and weekly, respectively. Hourly vpd was obtained by f i t t ing maximum and minimum vpd to a sine curve with the maximum in the mid-afternoon and the minimum at sunrise. The minimum vpd was set at a value : of 15% of the saturated vapour pressure at minimum air 775 temperature, i f available, or at 0.1 kPa. This procedure was tested on the 1978 data and found to give a reasonable estimation of the diurnal course of the vpd. Douglas-fir LAI was not measured but was estimated from data in Tan and Black (1976) and Black (1979). There was a negligible amount of salal in the area so that some evaporation would have been taking place from the forest f loor . An extinction coeff icient for solar radiation of 0.42 ± 0.04 determined for this canopy (Hardy and Black, 1975, unpublished data) would be similar to that for net radiation, and agrees well with data in Jarvis et a l . (1976). Thus, R ^ was estimated to be 5% of that above the canopy. Since hourly K4- was not available r $ was adjusted in the early morning and eyening as outlined in section 2.2. At the thinned s i t e , dai ly maximum and minimum vpd were obtained from a hygrothermograph record of T and relative humidity at 1.6 m above the forest f loor , from 10 May to 14 October, 1979. These vpd data were f i t ted to a sine curve to give hourly vpd. Measurements of 0 and ra infa l l were made every 10 days and ra infal l was partitioned into daily totals based on those obtained 9 km from the s i te . The 1978 values of LAI and r^ were used with r g modified for early morning and evening closure as in 1974. 776 4. RESULTS The course of 9 and daily evapotranspiration was well simulated during the 1975 period (Figure 3.1). The root zone average ty was also well simulated. This was to be expected since the ^ -charac ter is t ics were determined in 1975. The up to 40% underestimation in the daily E when the soil was dry (24 July to 11 August) is less than 10% of the total evapotranspiration for the period. (This also occurred with the model described in Chapter 2.) Since 9 was well simulated, the error may be in the Bowen ratio/energy balance measurements of E. This method can have large errors when E is small (Spittlehouse and Black, 1980). Also, i t was d i f f i c u l t to define an average root zone depth since the depth varied from 0.4 to 1.1 m within the site (Appendix IV. l ) . Increasing the average depth from 0.75 to 0.85 m would provide suff ic ient water to account for much of the above discrepancy. The diurnal variation of simulated E compared wel l , in general, with that from the Bowen ratio/energy baliance measurements and from equation (4), with salal r^  = 90 s nf ^, and porometer measurements of r g (Figures 3.2 and 3.3.). Discrepancies were probably due to the effects of other variables such as the release of water stored in the boles, branches and leaves arid leaf water potential that were not taken into account by the model using average ^ -charac te r is t i cs . For 1978, the model well simulated the course of 9 up to the end of June (Figure 3.4). However, i t then overestimated the depletion of water stored in the root zone and underestimated ty , compared to 777 JULY AUGUST FIGURE 3.1: Comparison of modelled and measured 5-day average daily evapotranspiration ( E ) and mean root zone water content (8) for the thinned stand in 1975. Bars indicate probable error in the measured data. Also shown are ra infal l (P), the modelled Douglas-f i r and salal transpiration and interception ( E T ) components of daily evapotranspiration ana the modelled daily drainage (D). P. ST. FIGURE 3.2: The upper diagram shows hourly, daytime stand transpir-ation (E), modelled (solid line) and measured with the Bowen ratio/energy balance method (x) and the porometer (o), for the thinned stand, 30 June, 1975. The lower diagram shows Douglas-fir and salal transpiration (Ej), modelled (solid and dashed lines, respectively) and measured with the porometer ((&) and (,•), respectively. Measured data modified from Tan et al. (1978) with error bars indicating ±10% for the Bowen ratio and ±20% for the porometer data (Spittlehouse and Black, 1980). Only one arm of the error bar is shown. Soil matric potential, in MPa, predicted by the model is given. 779 P. ST. FIGURE 3.3: As for Figure 3.2 but for 29 July 1975, with ±30% error for the porometer data. 780 3 1 1 0 2 0 3 0 1 0 2 0 3 1 1 0 2 0 31 10 2 0 3 0 M A Y J U N E J U L Y A U G U S T S E P T . FIGURE 3.4; Comparison of modelled and measured mean root zone water content (S)_ for the thinned stand in 1978. The dashed l ine indicates the simulation starting on July 18. The bar indicates probable error in the measured data. Also shown are the daily ra infal l (P), the modelled Douglas-fir and salal transpiration and interception (ET ) components of 5-day average daily evapotranspiration ( E ) and the modelled daily drainage (D). 781 measured v a l u e s , u n t i l August , when r a i n f a l l occu r red . S t a r t i n g the s i m u l a t i o n on J u l y 18, w i th the measured 8 r e s u l t e d in a good es t ima t i on o f 0, ty^ and r g to the end o f the dry pe r iod [dashed l i n e in F igure 3 . 4 ) . Porometer measurements of r g i n 1978 i n d i c a t e d tha t the D o u g l a s - f i r c h a r a c t e r i s t i c s were s i m i l a r to those i n 1975 and tha t minimum r e s i s t a n c e s f o r the s a l a l were s l i g h t l y lower than i n 1975. However, the model led d i u r n a l E j compared we l l w i th E-j. c a l c u l a t e d from equat ion (4) w i th s a l a l r^ = 300 s nf and porometer measurements o f r s (F igure 3 . 5 ) . The va lues o f tym i n F igure 3.5.were s imula ted by the model ; those in F igure 3.5b and 3.5c r e s u l t e d from the s i m u l a t i o n s t a r t i n g on J u l y 18. The bars on the measured va lues o f Ey i n d i c a t e the l a rge v a r i a b i l i t y i n measured r , some o f which i s due to measurement e r r o r s . The s tandard d e v i a t i o n o f the average ^ - c h a r a c t e r i s t i c curves (Tan et a l . , 1978) i n d i c a t e t ha t the va lues o f r g c a l c u l a t e d by the model cou ld be i n e r r o r by over 50% at low va lues of r . F igu re 3.5a i l l u s t r a t e s a reduc t i on i n t r a n s p i r a t i o n through stomatal c l o s u r e in response to a h igh vpd , even though the s o i l was moist = -0.01 MPa). In t h i s r e g i o n , h igh va lues of vpd , daytime maximum of 2.5 to 3.5 kPa , u s u a l l y occur i n August ra ther , than e a r l y June. Dur ing t h i s pe r iod porometer measurements i n d i c a t e d tha t the D o u g l a s - f i r and s a l a l r $ v a r i e d from 400 ± 100 s m - 1 i n the morning to > 4000 s m"^ i n the m id -a f te rnoon . Values o f r s between 300 and 1000 s m~^  w i th vpd rang ing from 0.5 to 2.0 kPa are more t y p i c a l o f t h i s t ime o f the y e a r . As the s o i l d r i e d through the summer r s i nc reased 782 FIGURE 3.5: Modelled and measured (porometer) hourly daytime transpir-ation (Ej) from the Douglas-fir (solid l ine and ( A ) , respectively) and the salal (dashed l ine and (a), respectively) for four days in 1978 for the thinned stand. The bars (only one arm shown) indicate the range of the measured data. Also shown in the upper half of each quadrant are the hourly above-canopy vapour pressure de f ic i t (vpd) and solar radiation (K4-) as sol id and dashed l ines , respectively. Soil matric potentials, in MPa, predicted by the model are given. 783 and E T decreased (F igu res 3 . 5 b , c ) . Stomatal r e s i s t a n c e du r ing the f i r s t two weeks of August was v e r y h i g h , even on low vpd days (F igure 3 . 5 c ) . U s u a l l y r g v a r i e d from 2000 s nf^ i n the morning to v i r t u a l l y c l osed by mid-day. The vpd u s u a l l y reached 3 to 4 kPa by the m id -a f te rnoon . The s a l a l was ab le to e x t r a c t more water per u n i t l e a f area than the D o u g l a s - f i r a t t h i s t ime ( p a r t i t i o n i n g o f the e x t r a c t e d s o i l water i s d i scussed in s e c t i o n 5 ) . Both spec ies were observed to s u f f e r from the severe water shortage s i nce a l a r g e number o f leaves turned brown. By September the s o i l had f u l l y wetted and va lues o f E s i m i l a r to those i n e a r l y summer were obta ined (F igu re 3 .5d ) . S ince l e a f f a l l occur red i n September and LAI was not co r rec ted f o r t h i s , there w i l l be a smal l ove res t ima t i on of E. As was the s i t u a t i o n f o r 1975, the model us ing average r s - c h a r a c t e r i s t i e s was unable to comple te ly s imu la te the measured hour l y E-p. Data were not a v a i l a b l e to d i r e c t l y check the approach to evapora t ing i n t e r c e p t e d water . The D o u g l a s - f i r needles d r i e d out r a p i d l y a f t e r r a i n due to t h e i r low va lue o f r^, w h i l e the s a l a l remained wet f o r a much longer t ime. Th is agreed we l l w i th v i s u a l o b s e r v a t i o n s . About 23% of the t o t a l r a i n f a l l dur ing the 1978 summer was l o s t through i n t e r c e p t i o n , i n good agreement w i th data i n Z inke (1967) and Ru t te r (1975) f o r con i f e rous f o r e s t s . The measured maximum and minimum vpd and c a l c u l a t e d day length were a l s o used in mode l l i ng the 1978 water ba lance . The seasonal t rend agreed we l l w i th tha t us ing ac tua l vpd and k> d a t a . Th is suggests t ha t reasonable t rends i n water use and s o i l water d e p l e t i o n would be 784 obta ined f o r 1974 and 1979. Measured and model led 8 f o r 1974 are compared i n : F igu re 3 .6 . Fores t f l o o r evapora t ion under t h i s dense stand was found to be n e g l i g i b l e and was not i nc luded i n the f i g u r e . The r e s u l t s a l s o agreed we l l w i th the s i m u l a t i o n by the model desc r i bed i n Chapter 2 . In 1979 measured va lues o f 9 and r a i n f a l l and va lues o f dra inage est imated from the k(0) c h a r a c t e r i s t i c were used i n (8) to determine the ten to twenty day average d a i l y e v a p o t r a n s p i r a t i o n r a t e s . These are compared i n f i g u r e 3.7 w i th those from the model. Agreement between the two es t imates i s good. The model es t imates agreed we l l w i th those from the model presented i n Chapter 2. P a r t i t i o n i n g of e v a p o t r a n s p i r a t i o n . between the D o u g l a s - f i r , s a l a l and i n t e r cep ted water showed a s i m i l a r pa t te rn to tha t f o r 1978. 5. DISCUSSION There are a number o f p o s s i b l e reasons f o r the over dep le t i on of root zone water content by the model dur ing J u l y 1978. These reasons, a l s o h i g h l i g h t the c r i t i c a l po in t s o f the model . An ove res t ima t i on of the canopy LAI by 10% would r e s u l t i n a s u f f i c i e n t ove res t ima t ion o f E-j. to account f o r much o f the above-mentioned e r r o r . (This would not be ev iden t i n the d i u r n a l comparisons s i nce the measured es t imates of E-p use the same va lue of LAI as the model . ) Th is e r r o r would tend to reduce the e f f e c t o f the negat ive feedback between r and TJJ . The 3 s -m r e l a t i o n s h i p between rc and tym may be i n e r r o r i n tha t the ym ranges /85 20 30 10 20 ' 31 10 20 JUNE JULY AUGUST FIGURE 3.6: As for Figure 3.4 but for the unthinned stand in 1974 and no salal transpiration. 10 2 0 31 10 2 0 3 0 10 2 0 31 10 2 0 31 10 2 0 30 10 MAY J U N E JULY AUGUST SEPT. OCT. FIGURE 3.7: Ten to twenty day average daily evapotranspiration rates (E) for the unthinned stand in 1979. Measured data are from the soil water balance (S.W.B.) method, with bars (only one arm shown) indicating a ± 5 mm or ± 10 mm (when drainage was large) error in the change in storage measurement. Modelled E is separated into that from the Douglas-fir, the salal and intercepted water (Ej). Daily rainfall (P) is also shown. 787 may be too large, especially the wettest range where transpiration rates are the highest. This i l lustrates the need for a more detailed determination of the relationship between r and ii . Also, as the r s rm. soil dries the model becomes increasingly sensitive to the accuracy of the ty{Q) characteristic since for small values of 9 , ^ decreases rapidly with decreasing 9 . The use of an average root zone y may not be appropriate where 70% of the roots are located in the upper 0.4 m of the root zone (Nnyamah and Black, 1977) and where the upper part of the prof i le can be much drier than the lower part. However, f i e ld measurements (Figure 2.6 in Chapter 2; Nnyamah and Black, 1977) indicate that the root zone dried out relat ively uniformly. An underestimation in root zone depth, as suggested in the simulation for 1975, would partly account for the error in 9 since there would be an underestimation of the volume of water available for transpiration. Rainfall was low in July so that errors in the evaporation and interception relationships would have l i t t l e influence on the modelling of evapotranspiration. The assumption that the temperature of the large salal leaves was close to a ir temperature is not a major source of error. During 1975 the hourly understory Rn (Tan and Black, 1975, unpublished data) was about equal to the salal transpiration when soil water was non-limiting. Furthermore, vpd affects both the numerator and denominator in (4). In dry soi l conditions, when E is less than Rn and T 0 > T, the underestimation of (e* 0 - e) causes an underestimation /88 of E for vpd < 1.5 kPa and an overestimation of E for vpd > 1.5 kPa (Tan et ai., 1978). Consequently, on a daily basis, with maximum vpd's > 1.5 kPa, the usual situation during dry periods, these latter errors tend to cancel. A practical application of the model is the routine estimation of the degree and duration of tree water stress during the growing season. A high r s ' can indicate water stress (leaf water potential < -1.8 MPa) but i t also means that there is a high resistance to carbon dioxide uptake, with a consequent reduced rate of photosynthesis. A value of r s equal to 1500 s nf ^ is 5 times greater than the minimum observed r of the Douglas-fir. Values of r > 1500 s nf^ occur when tym < -0.95 MPa s 3 s - m for vpd > 0.1 kPa, when -0.95 MPa < tym < -0.35 MPa for vpd > 1.5 kPa and when ty > -0.35 MPa for vpd > 2.5 kPa. The model indicated, for m -the 1978 period, that these conditions occurred, continuously for -twenty-nine days with a further twelve days prior to this period, for a total of 41 days. The measurements of ty and vpd indicate about six days less than th is . The discrepancy in the model is due to the overestimation in water use noted ear l ier . The model estimated 24 days of signif icant water stress in 1979. Closure of stomata for signif icant periods during the summer was noted by Emmingham and Waring (1977) for Douglas-fir in Oregon. A transpiration de f ic i t for the Douglas-fir in the thinned stand can be calculated by comparing actual transpiration with that calculated assuming ty > -0.35 MPa for the whole period, i .e . no soi l water de f ic i t . (It is assumed that the vpd is not affected by the /89 increased transpiration.) The transpiration def ic i t was 78 mm in 1978 and 47 mm in 1979. This def ic i t was probably due to the fact that the salal understory used a signif icant fraction of the available water. The ^ -charac te r is t ics are such that the salal has lower values of r s than the Douglas-fir for any value of vpd and tym, and this tends to compensate for the lower LAI of the sa la l . Thus, after thinning in 1975, the salal accounted for about 50% of the water transpired from dry foliage when ty > -0.95 MPa and for 60 to 70% when ty < -0.95 MPa. J • rm m By 1978 the respective values were 33% and 60 to 70%. The reduction in the former value was due to an increase in Douglas-fir LAI and the increased r^ of the s a l a l , which had i ts greatest effect when r g was smal1. The model can be used to estimate the reduction in tree water stress in-the thinned stand following the k i l l ing of the salal understory. In 1975 about 25% of the daily above-canopy Rn reached the understory (Tan and Black, 1975, unpublished data). Since LAI had increased in 1978 i t was assumed that about 20% reached the forest floor.and E^ was estimated as the lesser of this and k(0). Assuming that the 1978 climate conditions would not be changed as a result of the removal of a transpiring source, the model calculated a 12 mm water def ic i t and the period of continuous stress was reduced to f i f teen days. As the overstory continues to f i l l in the Douglas-fir trees may be expected to use more of the available water since their LAI wil l increase. Also, there may be further reductions in the within canopy 790 wind speed and increases in understory r^. The reduced l ight may further lower understory transpiration through the"light response of the stomata. The accompanying reduced heating of the a ir around the understory would mean that leaf temperature and, therefore, the difference between the vapour pressure in the stomatal cavities and in the a ir would be decreased. Consequently, understory transpiration would be further reduced. Black and Spittlehouse (1980) and Black et al. (1980) have also noted the signif icant influence of the understory on the water balance of the trees and the consequent effect on tree growth. They note that in regions with a low amount of available water during the summer i t may be best to keep the stocking density high so as to maximize the amount of water used by the trees. 6. CONCLUSIONS The forest water balance model well simulated the root zone water content in a thinned and an unthinned Douglas-fir stand during the growing season. The model indicated that, during the summer on the east coast of Vancouver Island, transpiration water def ic i ts of 40 to 80 mm can occur and that the trees can be severely water stressed for periods of up to a month long. This is due to the stands having a shallow root zone in a coarse soi l that has a low water holding capacity and to the low summer ra in fa l l .o f which, the model indicated, over 20% is lost through interception by the fol iage. Also, in the case /91 of the thinned stand, the model indicated that about 40% of the available water was used by the salal understory during the 1973 and 1979 growing seasons. This use varied from about 33% when the soil was moist to about 65% when the soi l was dry. There was no salal in the unthinned stand and, for the short period studied, evaporation from the forest f loor was found to be negligible due to low soil water content and the low level of net radiation at the forest f loor . In general, seasonal and diurnal values of the transpiration rate compared well with measured values. However, when soil matric potential was between -0.15 and -0.35 MPa the evapotranspiration model s l ight ly overestimated transpiration so that soi l water content was underestimated during the subsequent drying period. This was probably due to either an overestimation of canopy leaf area index or an underestimate of stomatal resistance from the stomatal resistance characteristics for the above matric potential range. These errors would tend to counteract the negative feedback between soil water content and transpiration through the effect of matric potential on stomatal resistance. This also indicates the need for a good estimate of the matric potential characteristic of the s o i l , especially for dry soil where the water potential changes rapidly for small changes in soi l water content. The evapotranspiration model indicated the importance of a good estimation of the boundary layer resistance of the leaves. This parameter is c r i t i ca l in determining the transpiration from the broad /92 leaves of the understory and the evaporation rate of water from wet leaves of the overstory and understory. In open canopies the above-canopy vapour pressure def ic i t was a good approximation of that within the canopy. This vapour pressure def ic i t was adequately simulated from daily maximunrand minimum values. Light l imitation on stomatal resistance in the early morning and evening was adequately simulated empirically without the need for solar radiation measurements. /93 DISCUSSION AND CONCLUSIONS: THE TWO EVAPOTRANSPIRATION MODELS COMPARED 1. Performance of the Models The energy/soil limited (E.S.L. ) model (Chapter 2) and the stomatal'diffusion resistance (S.D.R.) model (Chapter 3) are compared in Figures 4.1 to 4.3, for 1974, 1978 and 1979, respectively. The figures show ten to twenty day mean daily evapotranspiration rates. Since the water balance models use the same interception and drainage relat ionships, the figures are a comparison of the evapotranspiration models during the growing season. The coefficients in the evapotranspir-ation models were obtained during 1975 so that this year is not included in the comparison. The two simulations generally agree with each other though there is a tendency for the S.D.R. model to evaporate up to 15% more water than the E.S.L . model in 1978 and 1979 when water is readily available. This could be due to an overestimation of the leaf area index, an underestimation in boundary layer resistance of the salal or incorrect stomatal resistance characteristics in the S.D.R. model. The figures also show the average daily evapotranspiration rate calculated with the soil water balance (S.W.B.) method. Agreement between the modelled and measured data is good, even when drainage is a major term in the measured water balance. Modelled E generally f a l l s within the error of the measured data (only one arm of the error bar is shown). This good agreement is due to the relative accuracy of the coefficients of the models and to the fact that i f too much water 794 E (mmd" 1) Ol n 1 1 1 r 1 — 1974 UNTHINNED DOUGLAS-FIR STAND I " Z L I J J - H i E.S.L. MODEL S.D.R. MODEL SW.B. METHOD ± J U I 4 0 i 2 0 i • P , (mm d ') 2 0 3 0 JUNE 10 2 0 JULY 31 10 AUG. FIGURE 4.1: Ten to twenty day average daily evapotranspiration rate (E) for the unthinned Douglas-fir stand in 1974, simulated by the energy/soil limited (E.S.L.) model and the stomatal diffusion resistance (S.D.R.) model and calculated with the soil water balance (S.W.B.) method. Error bars (only one arm shown) are for the S.W.B. method. Daily rainfall (P) is also shown. E (mm d' 1) 1978 THINNED DOUGLAS-FIR STAND -h40 k o (mm d"1) UL E.S.L. MODEL S.D.R. MODEL S.W.B. METHOD 31 MAY FIGURE 4.2: As for Figure 4.1 but for the thinned Douglas-fir stand in 1978. E (mmd -1) -i 1 1 1 1 1 1 i r 1979 THINNED DOUGLAS-FIR STAND X J 1~  r r — i .1 — , E.S.L. MODEL S.D.R. MODEL S.W.B. METHOD r-60 -40 -20 • • i P (mmd"') I i r 10 20 31 MAY 10 20 30 10 20 31 JUNE JULY 1 ~ T 1 T r — T — L~:: 10 20 31 10 20 30 10 AUGUST SEPT OCT FIGURE 4.3: As for Figure 4.1 but for the thinned Douglas-fir stand in 1979. /97 is lost at any time, the negative feed-back of root zone water content tends to reduce evapotranspiration, thereby correcting the models. Both models agree to within ±20% for daily evapotranspiration on rainy days. This is good considering hoty different the evapotranspiration models are in concept and that the S.D.R. model requires hourly interception data to function best. The main reason for this agreement is that the evaporation rates are high and most of the daily interception is lost in one day. In conclusion, both models appeared to well simulate forest evapotranspiration. When they were combined with simple interception and drainage relationships they adequately simulated the root zone water balance and the duration and magnitude of tree water stress. This indicates that by using either of the two models and these simple relationships a complete growing season forest water balance can be obtained.-2. Further Considerations of the Theoretical Bases of the Two Models It is interesting that the two evapotranspiration models, based on very different concepts, do agree so well . The S.D.R. model is expected to work well i f the LAI, ^ -charac ter is t ics and r^  and are accurately determined since the model uses an equation, based on Ficks Law, for water vapour diffusion through stomata, a process that is well understood. How does this physical equation relate to the semi-empirical equations of the E .S .L . model? The daily (24 hour) evapotranspiration rate from the S.D.R. model i s , to a good 798 19 app rox ima t ion , £ [ (C/YL ) v p d . / r • ] , where i i s hours of the day and r i=6 1 c c i s the canopy r e s i s t a n c e of the s tand . (Outs ide these l i m i t s to i , E=0.) Equat ing t h i s w i th the d a i l y , ( 2 4 hour) E from the E . S.L. model f o r dry f o l i a g e in the energy 1 i m i t i n g c a s e , i !e~ : a ( s / [ s + y ] ) R n / L , a n d rea r rang ing g ives 19 a * ( C ( s + Y ) / Y S ) ( I v p d . / r . ) / R (1) i=6 1 C 1 n Thus, the r e l a t i v e constancy of a depends on a complex r e l a t i o n s h i p between the a i r temperature , daytime vpd , r £ ( through r g ) and Rn« When s o i l water i s not l i m i t i n g t r a n s p i r a t i o n and the d a i l y maximum vpd i s l e s s than 1.5 kPa , r , and t h e r e f o r e , r , i s r e l a t i v e l y constant through the dayt ime. Consequent ly , from (1) a i s p ropo r t i ona l to (£vpd,)/Rn'. The r a t i Q 'C(.Eypd ) /YR n i s a d a i l y iso thermal or c l i m a t o l o g i c a l r e s i s t a n c e ( r j ) . Usua l ly , r^ i s c a l c u l a t e d on an hour ly b a s i s , e . g . Stewart and Thorn (1973) and J a r v i s e t ai, (1976) , r a the r than the d a i l y va lue presented here . In g e n e r a l , low vpd days are u s u a l l y a s s o c i a t e d w i th low r a d i a t i o n days wh i l e high vpd days (> 1.5 kPa) are accompanied by c l e a r s k i e s and high R n so tha t the d a i l y r^ may be r e l a t i v e l y cons tant between c loudy and c l e a r days . I t should be remembered tha t the vpd i s s t r o n g l y i n f l uenced by R n s i n c e the a i r temperature and , t h e r e f o r e , the sa tu ra ted vapour p ressure of the a i r , depends on the energy a v a i l a b l e to heat the a i r . The vpd f o r c l e a r sky days may vary from 1.5 to 3.0 kPa , so tha t r^ may not be constant f o r such days . However, i nc reases i n vpd above about /99 1.5 kPa are compensated by increases in r , in response to the high vpd's, such that the hourly evapotranspiration does not increase. Consequently, the term ( £ v p d / r c ) / R n may remain relativey constant for these high vpd, clear sky days. The above arguments suggest that a could be relat ively constant over a wide range of energy l imiting weather conditions, assuming there was no mesoscale advection to drast ical ly influence the vpd. Upwind conditions are incorporated into the S.D.R. model through their influence on the vpd of the a i r (assuming vpd is measured on s i te ) . Thus,a may vary s igni f icant ly close to a change in surface cover due to advection (McNaughton 1976b). Further downwind a wil l be relat ively independent of these conditions. The sites considered here were surrounded by more than 5 km of similarly aged forest and further distances were also forested. The term (s + y)/s in ( l ) i s temperature dependent, increasing by 24% as the temperature decreases from 20 to 10°C. Thus, a might be expected to increase from warm to cool seasons, as was found by McNaughton et a l . (1979), Jackson et al. (1976) and de Bruin and Keijman (1979) for pasture, bare soi l and a lake, respectively. The increase in a indicated here in October 1979 (Figure 2.7) was about 35%, suggesting other factors may also be involved. For example, regional weather patterns may vary between the summer and f a l l (Maunder, 1968) with the result that the relationship between daily vpd and Rn may change. The ^ -charac ter is t ics are not expected to have changed since they have remained relat ively constant since 1975. It should be noted that Priestley and Taylor (1972) argue that LE/R n should decrease as s/ (s + y) decreases in response to a decrease in mean surface temperature, and that a i s , therefore, re lat ively temperature independent. / 1 0 0 The two models are different with respect to the soi l water supply l imitation of transpiration. In the case of the S.D.R. model soi l water status affects E T for a l l values of \b < - 0 . 3 5 MPa. T m However, in the E.S.L . model, when the radiant energy supply is low, E may be energy limited even through the soil is relativey dry. A second difference, described next, is probably due to insuff ic ient data to fu l ly define the ^ -charac ter is t ics at high matric potentials. Under many conditions the soi l control of- transpiration is ini t iated at wetter conditions in the E .S .L . model than in the S.D.R. model. For example, on a sunny day, E r 4 . 5 mm d~^, the soi l wil l l imit transpiration in the E.S.L . model when the average volumetric water content of the root zone (e) f a l l s below 0 . 1 3 , equivalent to a matric potential (tym) of - 0 . 1 2 MPa. However, as indicated above, in the S.D.R. model i|> has no effect on r until i> < - 0 . 3 5 MPa. This indicates that the highest s m ^ m range of the ^ -charac te r is t i c may require dividing into narrower ranges, and that unless this is done, the S.D.R. model may overestimate transpiration when - 0 . 3 5 < ty < - 0 . 1 2 MPa. This is probably the major reason for the underestimation of e in early July 1978 by the S.D.R. model since ^ m was about - 0 . 1 2 MPa at the end of June, in good agreement with the E .S .L . model. Since a remained relat ively constant between stands in 1975 and 1978 , the relationship between daily vpd and Rn and that between r £ and vpd must have either remained constant, or , compensated each other's changes. From equations.(4) and (5) in Chapter 3 , for a dry canopy, r„ = [LAI-,/^., + L A I 9 / ( r c 9 + r K 9 ) ] \ where the subscripts 1 and 2 /101 indicate Douglas-fir and s a l a l , respectively. Since the canopy LAI increased by 20% between 1975 and 1978 and the relationship between r c and vpd appears to have remained constant, the stomatal and/or boundary layer resistance characteristics must have changed to compensate for the LAI change. The porometer measurements indicated that the ^ -charac ter is t ics remained relat ively constant between 1975 and 1978, which means that the boundary layer resistance (r^) must have changed. This was indicated by the reduced canopy wind speed in 1978. Calculations indicated a negligible increase in Douglas-fir r^  between 1975 and 1978, but a three-fold increase in salal r^  (from 90 to 300 snf^). \ Thus, salal r, was of a size similar to i ts minimum value of r with the i b s result that salal transpiration was reduced suf f ic ient ly to compensate for the increased transpiration of the Douglas-fir . Further reductions in salal transpiration, required to compensate further increases in Douglas-fir LAI, may occur through reduced energy levels at the understory. This would cause a reduction in leaf temperature and consequently a reduction in the vapour pressure difference between the stomatal cavit ies of the leaves and the a i r . There may also be greater l ight restr ict ion of stomatal opening. 3. Use of the Models in Water Balance Calculation An important question i s : Where are each of the evapotranspiration models applicable? This depends on the amount of water balance information required and the time and effort available for the i n i t i a l measurement programme to determine the site characteristics required /102 by each model. The a and b parameters of the E.S.L . model could be determined from a simple soil water content measurement programme. Weekly measurements of the average root zone water content (e) and r a i n f a l l , when drainage is small and ra infal l preferably zero, would be used to obtain weekly average values of E from the water balance equation. The average value of E can be calculated from measurements of daily solar radiation and mean a i r temperature. The values of a n d 9 m . (required in the calculation of e ) can be obtained as max min ^ e the values of 6 at matric potentials of -0.01 MPa (in coarse soi ls) and -2.5 MPa, respectively. The E versus 9 g relationship (Figure 2.2) can be reduced to two straight l ines by dividing E and e g by E (Figure V.3, Appendix V.2). The values of a and b can probably be determined more easily using the approach of Figure V.3 rather than than Figure 2.2. Field interception and drainage functions should be determined where possible, and subsequent measurements of e should occasionally be made to check the model. The E.S.L . model can be adapted to allow the estimation of partit ioning of the available water between the trees and the understory or the forest f loor . As noted in Chapter 3, Plamondon (1972) indicated that evaporation from a moist forest f loor was approximately equal to the Rn at the forest f loor minus the soil heat f lux. The lat ter term is d i f f i c u l t to measure; however, on a daily basis i t is usually very small so that when the forest f loor is moist,forest f loor evaporation could be approximated by forest f loor R . However, as the /103 soil dries the soi l heat flux may have to be considered. Forest f loor Rn can be estimated using an extinction coeff icient and LAI'.as noted in Chapter 3. Where there is an understory the forest f loor evaporation can probably be" neglected. Measurements in 1975 at the thinned site (Tan and Black,' unpublished data) indicate that transpiration of the salal understory, when soi l water was not l imit ing and the foliage was dry, was approximately equal to the Rn just above the s a l a l . This is equivalent to an a for the salal of about 1.6 with E g q calculated from the salal Rn> See also Thorn (1975, p. 103, case i i ) . Tanner and Jury (1976) partitioned water loss between a crop and the soil surface by using separate values of a for each surface. In the case of the forest a [ s / ( s + Y ) ] R n = « 1 [ s / ( s + Y ) ] ( R n - R n 2 ) (2) + a 2 [ s / ( s + y ) ] R n 2 where the subscripts 1 and 2 indicate Douglas-fir and s a l a l , respectively. Since, for 1975, a = 0.8, ~ 1.6 and R n 2 / R n - 0-25, (2) gives ~ 0.53. The partit ioning is d i f f i c u l t to determine during the soi l l imiting phase since a separate value of b must also be determined. The output from the S.D.R. model may be of use here to provide separate estimates of Douglas-fir and salal transpiration. Black et ai. (1980) note that i f the ratio of L A ^ / r ^ to L A I 2 / > s 2 is known [also r K 1 and r , 9 ] , then the soil water balance values of E /104 can be partitioned even during the soi l l imiting phase. Occasional f i e ld measurements with a porometer may be used to indicate typical values of r g for the above calculat ion. A similar approach was used by Nnyamah and Black (1978). If the stand value of a is to remain constant over time then the value of a for the trees must change. For example, the f i e l d porometer measurements and the S.D.R. model indicate that, in 1978 when soil water was non-l imiting, salal transpiration was about 33% of the stand transpiration. This indicates R n 2 / R n = 0.15, similar to the value obtained using a Rn extinction coeff icient of 0.4 from Tan and Black's \ data and LAI-j = 5. Consequently, a-j ~ 0.66. The S.D.R. model is a more direct method for partit ioning the available water between the trees and understory and for taking account of forest growth through changes in LAI. However, accurate measurement of the LAI is d i f f i c u l t and the determination of the r -characterist ics s is a long and arduous process. The S.D.R. model should be useful as a research tool to highlight c r i t i ca l parts of the transpiration process. The model is also applicable to investigating the effects of stand management practices, e .g . thinning or removal of the understory (Black and Spittlehouse, 1980). 4. Suggestion for Further Studies The two models indicate areas for further f i e ld work. Obviously, measurements at more forest sites and with different species are required to test the generality of these models and determine the /105 var iab i l i ty of the site characteristics (a, b and the ^ - c h a r a c t e r i s t i c s ) . Better resolution of the ^ -charac ter is t ics is required. Long term monitoring of sites is required to determine the site characteristics for the f a l l to spring period, especially in l ight of suggestions by Emmingham and Waring (1977) and Waring and Franklin (1979) that the fa l l and spring are the time of maximum growth of west-coast conifers. The S.D.R. model would benefit from improved knowledge of the climate within the canopy, e .g . boundary layer and aerodynamic resistances, solar radiation extinction coef f ic ients , vapour pressure def ic i t and leaf temperature. \ Other sections of the water balance model could be s igni f icant ly improved. Measurements are required to better determine the coefficients of the daily ra infa l l interception model especially in relation to stand LAI. A lso, r a i n f a l l , interception and evaporation data on a time base of an hour or less are required to properly test the wetness parameter calculations in the S.D.R. model. F ina l ly , drainage models are required for sites that do not drain f ree ly , have signif icant upward movement of water from a water-table, or act as receiving areas for drainage water. /106 BIBLIOGRAPHY Aase, J.K. and S.B. Idso, 1978. A comparison of two formula types for calculating long-wave radiation from the atmosphere. Water Resour. 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Canada V6T 1W5 (Manuscript received 18 August 1978, in final form 26 December 1978) A B S T R A C T Rates of evapotranspiration from a 14 m high Douglas fir forest on the southwest coast of British Columbia were obtained using the energy balance/Bowen ratio method and an energy balance/eddy correlation method. In the former method, the Bowen ratio was measured using reversing diode psychrometers. In the latter, the sensible heat flux was obtained by eddy correlation analysis of data obtained from a fast response thermistor and Gill anemometers mounted horizontally and at 30° from the vertical. The generally low wind speed above the forest resulted in occasional stalling of the anemometers and made obtaining adequate eddy correlation data difficult. Spectral analysis of the eddy correlation data indicates that a significant fraction of the sensible heat flux was at low frequencies. The regression relationship between evapotranspiration rate obtained using the energy balance/eddy correlation method (£ , ) and that obtained using the energy bal-ance/Bowen ratio method (£$) was found to be £ , = 0 . 9 6 £ „ - 0 . 0 2 [ m m h"'], # = 0.93, ^, . , = 0.07 mm h~>. The experiment suggests that an eddy correlation system using mechanical anemometers is not suitable for extended water balance studies of forests where low wind speeds predominate. 1. Introduction Direct measurement of evaportanspiration is an im-portant part of hydrologic studies of forested water-sheds. Various micrometeorological techniques available for the determination of forest evapotranspiration have been reviewed by Fritschen (1970) and Federer (1970), and the results of a number of studies are presented in Jarvis et al. (1976). A major problem in such studies has been the measurement of the very small vertical temperature and humidity gradients above the forest canopy which result from the high degree of turbulent mixing generated by the large roughness of forests. However, several groups have had considerable success in determining forest evapotranspiration over extended periods using the energy balance/Bowen ratio method with reversing sensors (McNaughton and Black, 1973; McNeil and Shuttleworth, 1975; Black, 1979). Re-cently, eddy correlation methods, which avoid the measurement of the above-mentioned gradients, have been used with reasonable success to determine the energy fluxes from a forest (McNeil and Shuttleworth, 1975; Hicks et al., 1975; Moore, 1976). This paper con-siders the merits of the energy balance/Bowen ratio method and a method combining energy balance and eddy correlation measurements in making relatively long-term forest evapotranspiration measurements, and presents the results of a short experiment comparing measurements of evapotranspiration from a Douglas fir stand by the two methods. 2. Basic considerations The Bowen ratio (/3) is the ratio of the vertical flux of sensible heat to that of latent heat above the canopy. In the energy balance/Bowen ratio method used here evapotranspiration ( £ 3 ) is determined using the equa-tion (see Fuchs and Tanner, 1970) E, = lRn-G-Myi(l+p)L], (1) where Rn is the net radiation to the canopy, G the soil heat flux, M the canopy energy storage rate and L the latent heat of vaporization of water. Assuming that the eddy diffusivities of heat (K~H) and water vapor (Kv) above the canopy are equal, the Bowen ratio reduces to /3 = CA0/£Ap„, where A0 and Apv are the vertical gradients of potential temperature and ab-solute humidity, respectively, above the canopy and C is the heat capacity of the air. Dyer (1967) and Den-mead and Mcllroy (1970) have shown this assumption to be acceptable for neutral to moderately unstable conditions over smooth terrain. Campbell (1973) and Verma et al. (1978) present data suggesting Kn>Kv for stable conditions. The Bowen ratio approach also assumes that there is neither horizontal heat or vapor advection beneath the upper measurement height nor O021-8952/79/05O647-O7S05.75 © 1979 American Meteorological Society /123 648 J O U R N A L OF A P P L I E D METEOROLOGY. net vertical mass flow of air transporting heat and vapor from the canopy. The vertical gradients of temperature and humidity above forests are generally less than 0.1 °C m - 1 and 0.1 g m~' m - 1 , respectively (see Table IX of Jarvis el al., 1976) and require high-resolution sensors for their accurate measurement. Small errors in the measurement of these gradients can result in large errors in deter-mining evapotranspiration, particularly for dry surfaces (Fuchs and Tanner, 1970). Current energy balance/ Bowen ratio systems (e.g., Black and McNaughton, 1971; McNeil 'and Shuttleworth, 1975; Tang, 1976) achieve the required accuracy by periodic reversal of the sensors to eliminate systematic errors. They obtain an average flux by measuring mean temperature and humidity gradients over periods generally not less than 30 min in length. These systems are robust and rela-tively easy to maintain but the pumps that aspirate the sensors and the reversing motor have a large power requirement. Tan et al. (1978) determined 30 min rates of evapo-transpiration from a Douglas fir forest during the day-time using the energy balance/Bowen ratio method and a water vapor diffusion model requiring measurements of vapor density deficit, stomatal diffusion resistance of the leaves and forest leaf area. When soil water content was high and, consequently, the evapotranspira-tion rate was high, the methods agreed to within ± 10%. When soil water content was low and evapotranspiration rate was low, agreement was to within ± 3 0 % . At the same site Nnyamah and Black (1977) found on a weekly basis, that under a wide range of soil water contents, the energy balance/Bowen ratio and soil water balance measurements of evapotranspiration agreed to within ± 8 % . These results suggest that KH = Kv is a reasonable assumption for forests. The eddy correlation method involves summing the instantaneous vertical fluxes from the canopy to obtain a time-averaged value. The instantaneous fluxes of heat and vapor are determined by measuring the in-stantaneous fluctuations of vertical wind speed to-gether with those of temperature and humidity, re-spectively, using fast response sensors (e.g., Hicks, 1972; McBean, 1971, 1972). Like the energy balance/ Bowen ratio method, the eddy correlation method assumes that there is no net transport of heat and vapor by horizontal advection beneath the measurement height or by mass flow. Relatively fast response, robust, wind speed and temperature sensors are available; however, humidity sensors are usually delicate and difficult to maintain (Hyson and Hicks, 1975) making long-term measurements difficult. Furthermore, if a significant fraction of the fluxes is carried in small eddies, certain eddy correlation sensors, e.g., propeller anemometers, may not have adequate response charac-teristics and may underestimate the fluxes (Hicks, 1972; McBean, 1972). Fritschen (1970) has suggested an energy balance/ V O L U M E 1 8 eddy correlation method which is used in this study. Here the eddy correlation measurement of sensible heat flux (He) is combined with the measurement of the net energy available for sensible and latent heat exchange (Rn—G—M) to give evapotranspiration (£„) , i.e., E,= {Rn-G-M-Hc)/L, (2) where the measurement of He requires, in addition to a fast-response vertical wind sensor, a fast-response temperature sensor. Sensible heat flux is computed from He = Cw'T', where w' and T' are the fluctuations of the vertical wind speed and temperature, respectively, and the overbar indicates the average for the duration of each data run. Few measurements of eddy correlation turbulence spectra and cospectra have been made in or above forests. McBean (1968) using a propeller anemometer in a pine forest and Holbo et al. (1975) using a sonic anemometer and a "fluxatron" 8 m above a 30 m high Douglas fir forest found a significant portion of the fluxes at lower frequencies than is usually found for smooth terrain. The predominance of low-frequency eddies over forests compared to smooth surfaces is probably due to the increased scale of mixing that is induced by rough, tall vegetation (McNeil and Shuttle-worth, 1975). Using a split-film anemometer at 3 m above an 11 m high pine forest Shaw et al. (1975) found that the sensible heat flux cospectra were more sharply peaked than those for smooth terrain and had a rapid falloff on both sides of the peak. J. Simpson and L. Fritschen (personal communication, 1978) of the Uni-versity of Washington have obtained less-peaked heat flux cospectra at 8 m above a 31 m high Douglas fir forest. These results suggest that anemometer response requirements may be relaxed for work above forests and mechanical anemometers that usually have a falloff in response above ~0.5 Hz (McBean, 1972) may be used. There have been few comparisons of forest sensible or latent heat fluxes obtained from the eddy correlation method with other methods. McNeil and Shuttleworth (1975) compared eddy correlation sensible heat fluxes determined with a fluxatron above a 16 m high pine forest with sensible heat fluxes obtained using the energy balance/Bowen ratio method. They found that the fluxatron underestimated the heat flux by up to 25%. Shuttleworth (personal communication, 1977) attributed this to an electronic filter in the circuitry filtering out much of the low-frequency energy. This problem was also noted by Holbo et al. (1975). Hicks et al. (1975) and Moore (1976) used a fluxatron and fast-response humidity sensor at 4 m above a 13 m high pine forest. They found that the sum of the sensible and latent heat fluxes was within 20% of the net available energy (R„—G—M) under conditions of adequate fetch and winds > 2 m s - 1 . /124 M A Y 1979 D . L . S P I T T L E H O U S E A N D T . A . B L A C K 3. Methods The study site was a 17-year-old Douglas fir stand at the University of British Columbia Research Forest at Haney, British Columbia. At the time of the experiment in July 1976, the trees averaged 14 m in height with the base of the canopy at a height of ~ 5 m. McNaughton and Black (1973) have given a detailed micrometeoro-logical description of the site. Briefly, the site was located on a 5% slope with a fetch of between 200 and 400 m, beyond which an older regrowth Douglas fir forest extended for more than 2 km. McNaughton and Black (1973) have presented previous energy balance/ Bowen ratio measurements of evapotranspiration for the site. Mean sensor height was 4.5 m above the top of the canopy. The Bowen ratio system (Black and McNaugh-ton, 1971) used matched pairs of germanium diodes as temperature sensors in the psychrometer heads. The two sensing heads had a 3 m vertical separation and were reversed every 15 min. The differential voltage outputs from the sensors were integrated (Tang et al., 1976) to obtain 10 min average wet- and dry-bulb temperature gradients, after which the heads were reversed and allowed to equilibrate for 5 min before integration was resumed. Two 15 min periods were combined to obtain an average 30 min Bowen ratio. Net radiation was measured at 4.5 m above the canopy by integrating the output of a Funk-type (Swissteco S-l) net radiom-eter. The soil heat flux and canopy heat storage terms were determined following McNaughton and Black (1973). Evaporation was then calculated from (1). In this experiment, measurement errors, calculated using an error formula for psychrometric Bowen ratio measurement systems (Fuchs and Tanner, 1970), caused less than a 15% error in both the sensible and latent heat fluxes. The eddy correlation system is fully described in Pond and Large (1978) and only a brief description is given here. The temperature sensor was a fast-response thermistor while the wind sensors were Gill anemom-649 eters and were vane mounted. One of the anemometers was mounted horizontally and the other pointed down-ward at 30° from the vertical so that the horizontal component (u) of the wind vector always kept this propeller turning in the same direction even though the vertical component (w) changed directions (see also McBean, 1975). Each data run lasted 54 mins with the output voltages from the sensors recorded by an F M tape recorder. Data analysis involved filtering the recorded outputs through Kronhite 3340 low-pass filters set at 6 Hz and sampling at 20 Hz with analogue to digital converters. The digitized data were then analyzed following the theory for the tilted w propeller (Pond and Large, 1978) to obtain w' and V. In these calcula-tions the axes were rotated so that tD = 0. The w' and V power spectra and the w'T' cospectra were calculated by computer using a fast-Fourier transform. No correc-tions for possible reduced frequency response of the anemometer were made to the cospectra. Eq. (2) was then used to calculate the evapotranspiration for each data run. The effect of tilt of the u anemometer away from the mean horizontal flow, the noncosine response of the anemometers and calibration and offset errors (Pond and Large, 1978) would cause an error of up to ± 2 0 % in the measured sensible heat flux for wind speeds of ~ 2 m s - 1 . 4. Results ' Throughout the measurement period, the average hourly horizontal wind speed (tl) at 4.5 m above the canopy was always less than 3.0 m s _ 1 and frequently less than 1.0 m s _ I . During the daytime the instan-taneous vertical wind speed was occasionally of the same magnitude as the instantaneous horizontal wind speed. This was the result of the high degree of turbulent mixing that occurs above rough, tall vegetation. The low horizontal wind speed resulted in the frequent stalling of the propeller anemometers. Adequate wind speeds were only encountered between 2100 PST 13 Julv and 1000 PST 15 July 1976 (Table 1). Even during this TABLE 1. Mean horizontal wind speed (u), wind direction, mean temperature (T), potential temperature gradient (Afl/As), absolute humidity gradient (Ap,/Az), sensible heat flux and evapotranspiration determined by the energy balance/eddy correlation method (H, and E„ respectively) and by the energy balance/Bowen ratio method (# e and Et, respectively), for 13-15 July , 1976 at 4.5 m above a 14 m high Douglas fir forest. Starting time of each data run is given. Time (PST) ii (m s-') W i n d direction T (°C) A0/A2 (°C rn"') Ap„/Az (g m " 3 m->) 11. (W lh m"») E. (mm h~') . 2129 2.79 N W 10.7 +0.08 -0 .01 - 2 9 - 5 4 - 0 . 0 3 0.01 0024 2.76 N 9.3 +0.03 -0 .01 - 3 3 - 5 5 - 0 . 0 3 0.01 0248 2.73 N 8.7 +0.06 =0 - 2 0 - 4 9 - 0 . 0 5 =0 0457 2.07 N 8.7 +0.03 ~0 - 2 7 - 1 7 0.02 = 0 1007 1.60 S E 19.8 - 0 . 0 8 - 0 . 0 6 229 229 0.49 0.49 1126 1.93 S E 20.2 - 0 . 1 0 - 0 . 0 6 282 264 0.52 0.54 1448 1.46 S E 22.4 - 0 . 0 6 - 0 . 0 8 204 104 0.39 0.53 1713 1.40 E 22.1 +0.02 - 0 . 0 6 51 - 3 6 0.12 0.25 0624 0.92 N 11.1 - 0 . 0 2 - 0 . 0 3 - 6 17 0.18 0.15 0849 0.99 S 19.9 - 0 . 0 6 - 0 . 0 4 148 180 0.51 0.46 /125 650 J O U R N A L O F A P P L I E D M E T E O R O L O G Y V O L U M E 18 SPECTRAL ENERGY 1.0 S T(n) CC 1 •) S»(n) ( m V ) 0.1 TYPICAL POWER SPECTRA 1126-1220 (PS T) JULY 14,1976 4.9 m ABOVE 14-m DOUGLAS-FIR FOREST OOP 0.1 1.0 10 FREQUENCY (Hj) F I G . 1. Typical w' (solid circles) and V (open circles) power'spectra for 1 1 2 6 - 1 2 2 0 PST 14 July 1976 . period there was occasional stalling of the anemometers. Hicks (1972) and McBean (1975) note that below ~1 m s _ 1 the sensitivity (devolutions per meter of air) of Gill anemometers rapidly decreases due to friction and inertial effects. Typical daytime w' and T power spectra [£„•(«) and Sr(n), respectively] (Fig. 1) show the region of —5/3 slope of the inertial subrange. The vertical-wind power spectra show the expected falloff in response of the Gill anemometer at frequencies («) >0.5 Hz. However, typical daytime and nighttime w' T cospectra [ ; : 5 „ r ( » ) ] o.i n S.T(n) w'T' 0.001 ""•I • A A V A° A NORMALIZED DAYTIME SENSIBLE HEAT FLUX COSPECTRA • JULY 14-15, 1976. TIME 1PS.T) Vimt-') * — I00T 1.60 • — 1126 193 o — 1448 1.46 # — 1713 1.40 A 0624 0 92 A — 0849 0 99 • 0 A A •4 0.1 1.0 NORMALIZED FREQUENCY, Fic. 3. Normalized daytime sensible heat flux cospectra for 1 4 - 1 5 July 1976 with a scaling height z = 7.5 m. (Fig. 2) show that there was negligible energy at fre-quencies >0.3 Hz. Therefore, the falloff in response of the anemometer should not have had a significant effect on the resulting flux measurements. As has been found by Holbo et al. (1975), a large fraction of the day-time sensible heat flux energy in transported by lower frequency eddies than is found for smooth terrain. The cospectra peak between 0.01 and 0.08 Hz. The normalized daytime and nighttime cospectra [HS„T(/i)/Vr], where w'T' is the area under the co-spectral curve, shown in Figs. 3 and 4, respectively, peak between the normalized frequencies of 0.08 and 0.3. However, the daytime fluxes had a higher fraction of their energy at lower normalized frequencies than the nighttime fluxes, with eddies of periods of up to 0.12 o.to I nS.rin) | 0 06 (m«Cl-'> o.o2 r 1 1—• I I 11 11 1 1—i—r TYPICAL »'T' COSPECTRA 1 1 1 1 | 1 1 1 1 T T T T JULY 14, 1976. 4 5m ABOVE ° -14-m OOUGLAS-FIR FOREST • 0248 - 0342 , I • 2.73 nit"' • o 1126-1220, <T • 1.93 m •"' 0 0 0 o ° o o 0 0 • 1 — i — i t m n S: i i — i — L 0 • 0 . ...1 • 0.001 0.01 01 FREQUENCY (Hi) 10 Fic. 2. Typical w'T' cospectra for 0 2 4 8 - 0 3 4 2 PST (solid circles) and 1 1 2 6 - 1 1 2 0 PST (open circles) 14 July 1976. nS.T<n) 0.001 • A * A NORMALIZED NIGHTTIME c 0.01 fc- SENSBLE HEAT FLUX COSPECTRA * JULY IS-14, 1976. ° TIME 1P.S.T.I Mm.'1) A — 2129 I.9S » — 0024 2.76 „ • — 0248 2.73 o — 0437 207 -J 1 1 I 0.01 0.1 1.0 NORMALIZED FREQUENCY, F I G . 4. As in Fig. 3 except for nighttime sensible heat flux cospectra. /126 M A Y 1 9 7 9 D. L. S P I T T L E H O U S E AND T. A. B L A C K 651 F I G . 5. Normalized sensible heat flux cospectra. A scaling height i = 4 m was chosen so that the peak of the curves in Figs. 3 and 4 matches that of Shaw et ol. (1974). The lower curve of Kaimal et al. (1972) was obtained under neutral conditions and their upper curve the most unstable conditions they encountered. 3 min being significant. This may be partially a result of the lower daytime wind speed and the effect of stability on eddy frequency distribution (see, e.g., Panofsky and Mares, 1968; McBean. 1971; Kaimal et al., 1972). The normalized frequencies (nz/u) have been determined using a scaling height (z) equal to the true height of the instruments (18.5 m) minus the zero plane displacement (D) taken as 11 m. The value of D was obtained using the relationship Z) = 0.79 h, where h is the height of the canopy [the coefficient is a mean of the values in Jarvis et al. (1976)3- Silversides (1974) has also used this method for normalizing cospectral data. The resulting curves peak at a higher value than is found for smooth terrain. The data were also normalized so that the peak of the cospectral curves matched that of Shaw et al. (1974). [Shaw el al. had normalized their cospectral curve so that its peak matched the peak of the curve for the generalized unstable case for smooth terrain in Panofsky and Mares (1968).] Curves were fitted by eye to the data in Figs. 3 and 4 and a scaling height of 4 m was required to generate the cospectral curves for this ex-periment shown in Fig. 5. The curves for unstable condi-tions for smooth terrain from Kaimal et al. (1972) are also included in Fig. 5. As noted by Shaw et al. there is a sharper peak for forests than for smooth terrain. The Bowen ratio data (Fig. 6 and Table 1) is similar to that presented by McNaughton and Black (1973) for the same site although the trees were smaller. The daytime Bowen ratio varied between 0.2 and 0.8. It appeared that soil water was not limiting evapotrans-piration. The evapotranspiration rate tended to peak in the mid-afternoon following the trend in the absolute humidity deficit rather than the net radiation. The daily pattern of evapotranspiration is consistent with that found by other workers for Douglas fir (Gay, 1972; Fritschen and Doraiswamy, 1973; McNaughton and Black, 1973). However, the evapotranspiration rate obtained using the eddy correlation measurements did not show this trend because of the high Hr values at 1448 and 1713. The sensible heat fluxes provide an independent com-parison of the two methods. A regression of Hf on HB gave ff« = 0 . 9 3 f f „ + 2 7 [W r rr 2 ] , #2 = 0.89, s„.x = ±-M 6 0 0 4 0 0 ENERGY FLUX DENSITY ' • I | ' -ENERGY BALANCE OF  W-m DOUGLAS-FIR FOREST U.B.C. RESEARCH FOREST, HANEY, B.C JULY 13—15, 1976 NET RADIATION SOIL HEAT FLUX + CANOPY HEAT STORAGE TIME F I G . 6. Energy balance components of a 14 m high Douglas fir forest for the period 2000 PST 13 July to 1000 PST IS July 1976 obtained using the energy balance/Bowen ratio method. Also shown are eddy correlation measurements of the sensible heat flux. /127 652 J O U R N A L OF A P P L I E D M E T E O R O L O G Y EVAPOTRANSPIRATION / F I G . 7. M ean hourly evapotranspiration rate determined with the energy balance/Bowen ratio method ( £ s ) and with the energy balance/eddy correlation method ( £ , ) , for 1 3 - 1 5 July 1976. Numbers by the data points refer to the start time (PST) of the data run. W m - 2 . During the daytime, when the latent heat flux exceeded the sensible heat flux, i.e., /3<1, the effect of errors in the eddy correlation measurements of the sensible heat flux on the calculation of evapotranspira-tion was minimized. This can be seen in the following regression £ e = 0 . 9 6 £ a - 0 . 0 2 [mm h" 1 ] , /c2 = 0.93, sy.z = ± 0 . 0 7 mm h _ 1 (see also Fig. 7). 5. Discussion Eddy correlation systems with propeller anemom-eters have frequently been found to underestimate the sensible heat flux (e.g., McNeil and Shuttleworth, 1975). This has usually been ascribed to reduced re-sponse of propeller anemometers at high frequencies (Dyer and Hicks, 1972; McBean, 1972), or low-fre-quency cutoff (Holbo el al., 1975). It was noted that the former was probably not a limitation in this study. Since the low-frequency cutoff in this experiment was at 0.004 Hz, contributions from frequencies below this point would tend to flatten out the peaks in the normal-ized cospectral curves (Figs. 3, 4 and 5). The energy balance/Bowen ratio and energy balance/ eddy correlation determinations of evapotranspiration rate agreed to within ± 0 . 0 7 mm h _ 1 (Fig. 7 and Table 1). However, the low wind speed above the forest canopy made it difficult to use the energy balance/ eddy correlation method. In the runs starting at 1448 and 1713 there is a marked disagreement between the two measurement methods. During these runs, the average wind speeds were low (1.46 and 1.40 m s _ l , respectively) and there was occasional stalling of the anemometers. Under these low wind conditions errors V O L U M E 18 due to tilt of the anemometers from the mean horizontal flow and noncosine response of the anemometers are likely to be large. For many forests the average, hourly horizontal wind speed during the daytime frequently may be less than 2 m s"1 (e.g., McBean, 1968; Bergen, 1971; Oliver, 1975; Moore, 1976). In forested terrain such as that on the west coast of North America, wind flow may be deflected and reduced by the irregular topography. Silversides (1978) has shown that due to the large roughness of forested terrain, the wind speed 10 m above the forest canopy can be expected to be about half that at 10 m above smooth terrain. Thus the con-ventional use of mechanical anemometers in an eddy correlation system for the long-term measurement of forest evapotranspiration appears to be impractical for many locations. Other, more sensitive, eddy correlation wind sensors, e.g., sonic anemometers and strain gage anemometers, have disadvantages such as high cost and inability to operate under a wide range of weather conditions. Similarly, suitable humidity sensors are not yet readily available for extended direct eddy correla-tion measurements of evapotranspiration. Although the above-canopy wind speed can be low, the accompanying small temperature gradients mean that during most of the day moderately unstable to slightly stable conditions exist. Thus, for that part of the day when there is significant forest evapo-transpiration, the eddy diffusivities for sensible heat and water vapor should be approximately the same and the energy balance/Bowen ratio method should gi\i_ a good estimate of evapotranspiration provided there is an accurate measurement of net radiation. Although current Bowen ratio systems have a high power require-ment for the ventilation system and the reversing motor, they have the advantage of durability and simple analysis. Consequently, at present, the energy balance/ Bowen ratio method, with periodic reversal of the psychrometric sensors to eliminate systematic errors, appears to be more suitable than the energy balance/ eddy correlation method to determine forest evapo-transpiration rates in long-term water balance studies. 6. Conclusions Under moderate wind speeds, values of forest evapo-transpiration rate obtained using the energy balance/ eddy correlation and energy balance/Bowen ratio methods agreed to within ± 0 . 0 7 mm h - 1 . The eddy correlation measurements of sensible heat flux, required in the former method, were difficult to obtain because the generally low wind speed above the forest resulted in occasional stalling of the Gill anemometers. Spectral analysis of the eddy correlation data indicated that a significant fraction of the sensible heat flux was at fre-quencies <0.01 Hz. The results suggest that at present, the energy balance/Bowen ratio method, with periodic sensor reversal, is preferable in long-term water balance MAY 1 9 7 9 D. L. S P I T T L E H O U S E AND T. A. B L A C K /I 28 6 5 3 studies of forests. Eddy correlation systems with mechanical anemometers should be avoided in such studies when mean wind speeds are likely to be less than 2 m s _ 1 for much of the time. Acknowledgments. We wish to thank Dr. Steve Pond and Bill Large, Institute of Oceanography, University of British Columbia, for the loan of the eddy correla-tion system and Bill Buckingham and Colin Walker for their aid in data collection and analysis. Funding for this research was provided by the National Research Council of Canada. R E F E R E N C E S Bergen. J. D., 1971: Vertical profiles of wind speed in a pine stand. For. Sci., 17 . 314-321. Black, T. A., 1979: Evaporation from Douglas-fir stands exposed to soil water deficits. Water Resour. Res., 15 , 164-170. Black, T. A., and K. G. McNaughton, 1971: Psychrometric apparatus for Bowen ratio determination over forests. Bound.-Layer Meteor., 2, 246-254. Campbell, A. P., 1973: The effect of stability on evapotranspira-tion rates measured bv the energy balance method. Agric. Meteor.. 1 1 . 261-267. Denmead, O. T., and I. C. Mcllroy, 1970: Measurement of non-potential evaporation from wheat. Agric. Meteor., 7, 285-302. Dyer, A. J., 1967: The turbulent transport of heat and water vapor in an unstable atmosphere. Quart. J. Row Meteor. Soc, 93,501-508. Dyer, A. J., and B. B. Hicks, 1972: The spatial variability of eddv fluxes in the constant flux layer. Quart. J. Row Meteor. Soc., 9 8 , 206-212. Federer, A. C , 1970: Measuring forest evapotranspiration— theory and problems. USD A Forest Serv. Res. Pap. N'E-165, Northeast Forest Expt. Stn., Upper Darby, PA, 25 pp. Fritschen, L. J., 1970: Evapotranspiration and meteorological estimation as applied to forests. Proc. Third Forest Micro-climate Symp. J. M . Powell and C. F. Nolasco, Eds. Calgary, Alberta. Can. For. Serv., Dept. Fish. For.,pp 8-27. [Available from Northern Forest Research Centre, Can. For. Serv., Edmonton, Alberta]. Fritschen, L. J., and P. Doraiswamy, 1973: Dew: An addition to the hydrologic balance of Douglas-fir. Water Resour. Res., 9, 891-894. Fuchs, M . , and C. B. Tanner, 1970: Error analysis of Bowen ratios measured in differential psychrometry. Agric. Meteor., 7, 285-302. Gay, L. W., 1972: Energy flux studies in a coniferous forest ecosystem. Proc. Research on Coniferous Forest Ecosystems— A Symp. J. F. Franklin, L. J. Dempster and R. H. Waring, Eds. Pacific N. W. Forest Range Expt. Stn., Portland, OR, 243-253. QU. S. Government Printing Office, Washington, D C 20402.] Hicks, B. B., 1972: Propeller anemometers as sensors of atmo-spheric turbulence. Bound.-Layer Meteor., 3, 214-228. Hicks, B. B., P. Hyson and C. J. Moore, 1975: A study of eddy-fluxes over a forest. J. Appl. Meteor., 14, 58-66. Holbo, H . R., L. J. Fritschen and M . O. Smith, 1975: Eddy correlation and fluxatron estimates of sensible heat flux of a Douglas-fir canopy. Preprints 12th Conf. Agriculture and Forest Meteorology, Tucson, Amer. Meteor. Soc, 1 7 - 1 8 . Hyson, P., and B. B. Hicks, 1975: A single-beam infrared hygrom-eter for evaporation measurement. J. Appl. Meteor., 14, 3 0 1 - 3 0 7 . Jarvis, P. G., G. B. James and J. J. Landsberg, 1976: Coniferous forests. Vegetation and the Atmosphere, Vol. 2, Case Studies, J. L. Monteith, Ed., Academic Press, 171-240. Kaimal, J. C , J. C Wyngaard, V. Izumi and O. R. Cote\ 1972: Spectral characteristics of the surface layer. Quart. J. Roy. Meteor. Soc. 9 8 , 563-589. McBean, G. A., 1968: An investigation of turbulence within a forest. J. Appl. Meteor., 7, 410-416. , 1971: The variation of the statistics of wind, temperature and humidity fluctuations with stability. Bound.-Layer Meteor., 1, 438-457. , 1972: Instrument requirements for eddy correlation mea-surements. J. Appl. Meteor., 11 , 1078-1084. , 1975: Comments on "Limitations of the eddy correlation technique for the determination of turbulent fluxes near the surface." Bound.-Layer Meteor., 9, 361-362. McNaughton, K. G., and T. A. Black, 1973: A study of evapo-transpiration from a Douglas-fir forest using the energy balance approach. Water Resour. Res., 9, 1579-1590. McNeil, D. D., and W. J. Shuttleworth, 1975: Comparative measurements of the energy fluxes over a pine forest. Bound.-Layer Meteor., 9, 297-313. Moore, C. J., 1976: Eddy flux measurements above a pine forest. Quart. J. Roy. Meteor. Soc, 103 . 913-918. Nnyamah, J. U. , and T. A. Black, 1977: Rates and patterns of water uptake in a Douglas-fir forest. Soil Sci. Soc. Amer. J., 4 1 , 972-979. Oliver, H . R., 1975: Ventilation in a forest. Agric. Meteor., 14, 347-355. Panofsky, H . A., and E. Mares, 1968: Recent measurements of cospectra for heat-flux and stress. Quart. J. Roy. Meteor. Soc, 94, 581-585. Pond, S., and W. G. Large, 1978: A system for remote mea-surements of air-sea fluxes of momentum, heat and mois-ture during moderate to strong winds. Ms. Rep. 32, Inst. Oceanogr., University of British Columbia, 55 pp. Shaw, R. H. , R. H . Silversides and G. W. Thurtell, 1974: Some observations of turbulence and turbulent transport within and above plant canopies. Bound.-Layer Meteor.. 5, 429-449. Silversides, R. H . , 1974: On scaling parameters for turbulence spectra within plant canopies. Agric. Meteor.. 13, 203-211. , 1978: Forest and airport wind speeds. Atmosphere-Ocean. 16. 293-299. Tan, C. S.. T. A. Black and J. U. Nnyamah. 1978: A simple diffusion model of transpiration applied to a thinned Douglas-fir stand. Ecology,*?), 1221-1229. Tang, P. A., 1976: Electronic data acquisition system for the energy balance/Bowen ratio measurement of evaporation. M.Sc. thesis, University of British Columbia, 96 pp. QAvail-able from Library, University of British Columbia, Van-couver, B. C ] , K. G. McNaughton and T. A. Black, 1976: Precision elec tronic integrator for environmental measurement. Trans. Amer. Soc. Agric. Engr., 19, 550-552. Verma, S. S., N. J. Rosenberg and B. L. Bladd, 1978: Turbulent exchange coefficients for sensible heat and water vapor under advective conditions. J. Appl. Meteor., 17, 330-338. /129 A P P E N D I X I I Evaluation of the Bowen Ratio/Energy Balance Method for Determining Forest Evapotranspiration D.L. Spittlehouse and T . A . Black Department of Soil Science, University of British Columbia, Vancouver, B.C. [Original manuscript received 4 September 1979; in revised form 11 December 1979] A B S T R A C T The Bowen ratio/energy balance method using periodic reversal of the psychrometers to remove systematic errors is evaluated. Temperature and vapour-pressure differences can be measured with accuracies of +0.005 °C and ±1 Pa, respectively. For a 3-m vertical separation of the psychrometers and the Bowen ratio (PL 0 < P < 4, the probable relative error in the forest evapotranspiration (E) is < ±15% if the temperature and vapour-pressure gradients are large, and ranges from ± 10 to ±60% if the gradients are small. The error in E is from two to five limes these values for (3 < 0. Measurements of E made with the Bowen ratio/energy balance method are compared with those made concurrently with an eddy correlation/energy balance method, a stomatal diffusion resistance method and a soil water balance method. Agreement is generally within ±20% and frequently within ±10%, well within the errors associated with the methods. RESUME La methode du rapport Bowenlbilan energetique, utilisant 1'inversion periodique des psychrometres pour eliminer les erreurs systematiques, est evaluee. Les differences de temperature et de pression de vapeur peuvent etre mesurees avec une precision de ±0.005 "C et ±1 Pa, respectivemenl. Avec une separation verticale des psychrometres de 3 m et le rapport Bowen ($), 0 < P< 4, Yerreur relative probable de I'evapotranspiration forestiere f Ej est < ± 15% si les gradients de temperature et de pression de vapeur sont grands, et varie entre ±10 a ±60% si les gradients sont petits. L'erreur de E est de deux a cinq fois ces valeurs pour P < 0. Les resultats obtenus en mesurant E avec la methode du rapport Bowenlbilan energetique sont compares avec ceux obtenus avec une methode de la correlation du flux turbulent Ibilan energetique, une methode de resistance de diffusion stomatique et une methode du bilan d'eau du sol. L'accord est generale me nt a ±20% et frequemment a ±10% ce qui est bien au-dessous des erreurs associees avec ces methodes. 1 Introduction Studies of the forest water balance frequently require measurements of evapotranspiration over extended periods of time. Various methods of di-rectly and indirectly measuring evapotranspiration from vegetation have been ATMOSPHERE-OCEAN 18 (2) 1980,98-116 07O5-590O/80/00O0-0098$01.25/0 ©Canadian Meteorological and Oceanographic Society /130 Evaluation of a Method for Determining Forest Evapotranspiration / 99 reported in the literature. Many of these methods have been shown to give accurate results in a wide variety of agricultural situations. However, appli-cation of these methods to forests is generally more difficult than for agricul-tural crops, and the suitability of many of these methods for forest water balance studies is uncertain. Direct measurements of forest evapotranspiration have been made with a tree in a lysimeter (Fritschen et al., 1977) and with an eddy correlation method (Hicks et al., 1975; Moore, 1976; Thompson, 1979). Indirect methods include the Bowen ratio/energy balance method (Denmead, 1969; Black and McNaughton, 1971; McNaughton and Black, 1973; Droppo and Hamilton. 1973; Gash and Stewart, 1975; McNeil and Shuttleworth, 1975; Jarvis et al., 1976; McCaughey. 1978; Tan et al., 1978), the aerodynamic method (Stewart and Thorn, 1973; Thorn et al., 1975), an eddy correlation/energy balance method (McNeil and Shuttleworth, 1975; Milne, 1979; Spittlehouse and Black, 1979), a stomatal diffusion resistance method (Tan and Black, 1976; Tan et al., 1978), and a soil water balance method (Calder, 1976; Nnyamah and Black. 1977; Scholl, 1976). All of the above methods have disadvantages for routine measurements of the forest evapotranspiration. The size of trees and the need to sample a representative area of the forest means that lysimeters are not practical. Eddy correlation methods are limited by complexity of analysis, high cost and the limitations imposed on certain systems by the generally low wind speed above forests (Moore. 1976; Spittlehouse and Black. 1979). Grant (1975) concluded from an error analysis of a variety of methods of measuring evapotranspira-tion that there would be few occasions when the aerodynamic method would be more accurate than the Bowen ratio/energy balance method. Thorn et al. (1975) have shown that current wind profile theory is not adequate to allow accurate routine determination of forest evapotranspiration with the aerodynamic method. The high degree of turbulent mixing over forests results in small temperature and humidity gradients that demand high measurement resolution and accuracy from the Bowen ratio/energy balance method. The stomatal diffusion resistance method is very time consuming and does not measure soil evaporation. Drainage from and upward movement of water into the root zone are difficult to measure in the soil water balance method (Federer, 1970). In this paper we consider the accuracy of a Bowen ratio/energy balance method using reversing psychrometers and differential temperature mea-surement for determining forest evapotranspiration. We also compare this method with evapotranspiration measurements made using an eddy correla-tion/energy balance method, a stomatal diffusion resistance method and a soil water balance method. 2 The Bowen ratio/energy balance method a Theory The energy balance of the forest, neglecting photosynthetic energy storage, is /I 31 ioo / D.L. Spittlehouse and T.A. Black R„= H + LE + M + G. (1) In (1) R „ is the net radiation flux, H is the sensible heat flux, L is the latent heat of vapourization of water, E is the evapotranspiration rate, G is the soil heat flux and M is the rate of canopy storage of heat. The Bowen ratio (P) is the ratio of the sensible heat flux to the latent heat flux. Thus (1) can be rearranged to give £ p = [ 7 ? „ - G - M ] / [ ( l + p)L] (2) where £ p is the Bowen ratio/energy balance estimate of the evapotranspira-tion rate. Assuming that the eddy diffusivities for heat (KH) and water vapour (Kv) are equal, the Bowen ratio reduces to p = Y(A8/AZ)/(A«J/AZ) (3) where y is the psychrometric constant and AG/Az and A§/Az are the vertical gradients of potential temperature and vapour pressure, respectively. Thorn (1976) notes that for forests the vapour-pressure gradient should be corrected for the decrease in atmospheric pressure with height. (His correction factor is about twice as large as it should be because he used the gas constant for air rather than that for water vapour.) Dyer (1967) and Denmead and Mcllroy (1970) have shown that the assump-tion KH = Kv\s acceptable for neutral to moderately unstable conditions over smooth terrain. Campbell (1973) and Verma et al. (1978) present data sug-gesting KH > Kv for stable conditions. The Bowen ratio approach also assumes that there is neither horizontal heat or vapour advection beneath the top measurement height, nor net vertical mass flow of air transporting heat and vapour to or from the canopy. Assuming the above to apply, the reliability of the Bowen ratio/energy balance method depends on the accuracy and resolution of the measurements of the temperature and humidity gradients and of (R„ — G — M) the energy available for sensible and latent heat exchange. The available energy is usually obtained as follows. Net radiation flux is measured with a net radiometer above the forest canopy. A net radiation measurement at a single location has an error of about ± 6 % (Federer, 1968; Droppo and Hamilton, 1973; McNeil and Shuttleworth, 1975). Soil heat flux (G) is usually obtained from heat flux transducers at 0.05 m below the soil surface, plus a correction for heat stored in the 0 to 0.05 m layer calculated from measurements of the change in temperature of the layer with time and the heat capacity of the layer. The rate of canopy heat storage (M) is obtained from measurements of the change in canopy temperature and humidity with time and the canopy heat capacity (see, for example, Stewart and Thorn, 1973; McNeil and Shuttleworth, 1975). It is difficult to measure G and M accurately for a forest; however, except for periods around sunrise and sunset, (G + M) is < 5% of the net radiation flux. Thus, even a 50% error in (G + M) results in a minor error in the available energy measurement. The rate of photosynthetic /132 Evaluation of a Method for Determining Forest Evapotranspiration /101 energy storage in a forest is usually less than 3% of the net radiation flux (Jarvis et al., 1976). Thus the available energy measurement should be accu-rate to better than ± 10%. The Bowen ratio is obtained from measurements of vertical temperature and humidity gradients above the canopy. This is usually done at one location that must be sufficiently downwind of any significant changes in the surface characteristics to allow development of the boundary layer to a depth greater than the top measurement height, and to smooth out the effect of local surface inhomogeneity. Droppo and Hamilton (1973) found that under good fetch conditions for a 18-m high mixed hardwood stand, three profiles 15 m apart gave turbulent fluxes to within 10% of each other for the same net radiation flux. Gash and Stewart (1975) comment on possible measurement errors that are due to the influence of a large instrument tower on the local micro-meteorological conditions. Temperature and humidity gradients are usually obtained by the profile method or by the reversing psychrometer method. The profile method uses temperature and humidity measurements at three or more heights (Denmead, 1969; Stewart and Thorn, 1973; Droppo and Hamilton, 1973; Gash and Stewart, 1975; McCaughey, 1978). The rationale of this method assumes that although each measurement may be subject to systematic errors, over the whole profile these errors can be treated as pseudo-random deviations, and, if sufficient sensors are used, a line fitted through the data should have an error less than that between any pair (McNeil and Shuttleworth, 1975). However, this error must be small in relation to the size of the gradients. This latter condition is difficult to fulfill for forests where the temperature gradients are generally less than 0.1°C m"' and the humidity gradients less than 10 Pa m" 1 (0.07 g m- 3 nr 1 ) (See Table IX in Jarvis et al., 1976). Sinclair et al. (1975) suggest errors of ±0.01°C and ± 4 Pa for the differential temperature and vapour-pressure measurements, respectively, obtained with their profile Bowen ratio system. McNeil and Shuttleworth (1975) measured temperature to ±0.01°C and vapour pressure to ± 7 Pa with their profile system. They found that the profile Bowen ratio measurements of the evapotranspiration rate differed systematically from the second Bowen ratio method (described below) and an eddy correlation/energy balance method and that this differ-ence was a function of the arrangement of the sensors in the profile. Droppo and Hamilton (1973) made their profile measurements with a single psy-chrometer attached to a vertical pulley system. Consequently, systematic errors in the temperature sensors would tend to subtract out in the calculation of a temperature difference. This system would work well as long as atmo-spheric conditions changed relatively slowly. The second method of obtaining the Bowen ratio was first reported by Tanner (1960). The psychrometers are interchanged between two measure-ment heights on a regular, short time interval, with the temperature difference between the heights being measured directly. If the systematic errors are /133 102 / D . L . Spittlehouse and T . A . Black independent of sensor position and slowly changing with time then the mean temperature difference should have a much reduced error. The temperature difference before reversal (AT,) is AT, = (Tal + e«,i)-(7o2 + e M) (4) and the difference after reversal (AT,,) is AT/i=(7'„2 + e„2)-(rel + e e l) (5) where the subscripts a and b refer to the two sensors and the subscripts 1 and 2 refer to the measurement heights, T is the true dry- or wet-bulb temperature being measured, and E is the systematic measurement error of each sensor. The temperature differences before and after reversal of the psychrometers are of opposite sign. Thus AT; - AT,, = (Tal + Tbl) - (Ta2 + Tb2) + (e„, + eB I) - (ea2 + e62) (6) is twice the mean temperature difference (AT), since (eal + e6|) ~ ( £ a 2 + e62), i.e. the systematic errors cancel. There may be situations when the error terms do not cancel. This occurs when an error is position dependent. For example, if the psychrometers have different orientations in upper and lower positions, the sensors could be subject to different radiational heating errors in each position. Position de-pendence is avoided if the psychrometers are constructed symmetrically and have the same orientation in each position. b Error Analysis The error analysis is similar to that in Fuchs and Tanner (1970). Sinclair et al. (1975) and Bailey (1977). Maximum and probable errors are calculated fol-lowing Scarborough (1966). The complete error analysis for our Bowen ratio/energy balance system is in Spittlehouse (1980). Only the results are referred to in this paper. The error in the available energy was discussed earlier. For our measure-ments it was taken to be ± 7 % . The Bowen ratio system analyzed here is described in Black and McNaughton (1971). The measurement periods were 10 min long with 5 min allowed for equilibration after reversal before measurement was restarted. The vertical separation of the psychrometers was either 1 or 3 m. The psychrometers and reversing system were mounted about 2 m away from the 0.25-m wide, open, triangular instrumentation tower (Fig. 1) facing into the major wind direction. Such a small tower should have a negligible effect on the local temperature and humidity profiles. The psychrometers were ventilated at 3.5 m s _ 1 with a vacuum pump. The temperature sensors were germanium diodes and the differential outputs of the wet-bulb pair and the dry-bulb pair were constantly monitored with integrators (Tang et al., 1976). The sensitivity of the germanium diodes is approximately 2.3 mV ° C _ I . The mean sensitivity of a diode pair must be used to convert the differential 7134 Evaluation of a Method for Determining Forest Evapotranspiration /103 thinned Douglas-fir forest at Courtenay, B.C. output of the pair to a temperature difference. Each pair was calibrated and matched to within +0.5%. Integrator sensitivity was 1000 counts (mV h)"' with a combined calibration and stability error of ± 0 . 3 % . These errors re-sulted in a probable error in the differential temperature measurement of ±0 .005°C. The maximum error was +0.008°C. These errors do not include any possible non-cancelling measurement errors. The probable error in a vapour-pressure difference calculated from the wet- and dry-bulb tempera-ture differences was + I Pa (+0.007 g m 1 ) and the maximum error was + 3 Pa. The rate of change of the saturation vapour pressure curve with temperature (sw) should be determined to within 5%. Revfeim and Jordan (1976) suggest that changes in the psychrometric constant (y) due to changes in pressure should be taken into account. Also, y will vary with changes in air temperature, insufficient wetting of the wet-bulb wicks and contamination of the wicks. /135 104 / D.L. Spittlehouse and T.A. Black T A B L E 1. Typical probable relative errors in the forest Bowen ratio (83/3), the evapotranspiration rate (SEt/Ep), and sensible heat flux i$HtIH9) for positive and negative Bowen ratios. Calculations are for a 3-m separa-tion of the psychrometers and large and small potential temperature (A6/Ar) and vapour-pressure (AeJAz) gradients. Relative error in the ' available energy (R„ — G — M) was ± 7 % . Values of 3 = 0.66 and 1.32 are typical of moist soil conditions (soil water potential >—200 J kg" 1 ) while 3 = 3.96 is typical of dry soil conditions (V, < -800 J kg" 1 ) . Positive Negative Bowen Ratio Bowen Ratio A6/Az " C m " 1 A<>/Az Pa m - 1 83/3 ± % SEf/Et ± % ±% 8Es/£-B ± % ±% 0.10 10 5 7 8 12 16 0.02 2 19 10 13 38 56 0.10 5 8 8 8 34 25 0.02 1 35 21 17 145 110 0.12 2 17 15 8 24 9 0.03 0.5 67 54 15 90 24 However, the error analysis shows that variations in y of <5% do not significantly affect the measurement of the vapour pressure difference (Ac). The error in the Bowen ratio is a function of the error in the temperature and vapour-pressure gradients but is independent of the sign of the gradients. The error is also dependent on the vertical separation of the sensors. Decreasing the separation from 3 to 1 m almost quadruples the error in the Bowen ratio. The three terms on the right-hand side of (3) contribute equally to the error for IPI< 0.5. As |p | increases above 0.5, or as the gradients decrease, the error in the vapour-pressure gradient predominates. Table 1 contains examples of probable relative errors in the Bowen ratio; maximum relative errors are about three times the probable relative errors. The errors in the evapotranspiration rate and the sensible heat flux depend on the sign of the Bowen ratio (Table 1). Maximum errors are 2 to 3 times the probable errors; decreasing the psychrometer separation to 1 m almost triples these errors. For a 3-m separation and 0< P < 4 the probable relative error in the evapotranspiration rate is < ±15%, unless the gradients are small, then the error is < ±55%. The error in the available energy is significant for -0.6< P < 4 and large gradients. As shown by Fuchs and Tanner (1970) and others there is a large relative error in the evapotranspiration rate for large positive Bowen ratios. It can also be seen that for negative Bowen ratios, e.g. night-time and advection situations, there is a large relative error in the evapotrans-piration rate measurement especially when the temperature and vapour-pressure gradients are small. The error may be enhanced because, as noted in Section 2a, for stable conditions KH is possibly larger than Kv which would result in an overestimation of E. The probable relative error in the sensible heat flux (Table 1) is generally Evaluation of a Method for Determining Forest Evapotranspiration / 105 8OO1 ( W m - ' l DENSITY 400r ENERGY FLUX 200 600 • M s * -200 0 6 12 HOURS (PST) 18 24 Fig. 2 Typical Bowen ratio/energy balance data for a 9-m high Douglas-fir forest at Courtenay, B .c. R „ is the net radiation flux, H is the sensible heat flux, LE is the latent heat flux. G is the soil heat flux and M is the rate of canopy heat storage. Soil water potential (i|/,) is a mean for the top 0.45 m of the soil. Bars show typical probable errors in the fluxes. (Modified from Black, 1979.) < +15% for B > 0 unless the gradients are very small because, although the error in the Bowen ratio increases with increasing Bowen ratio, the sensible heat flux also increases, so that its relative error changes slightly. As noted earlier, Sinclair et al. (1975) measured AO and L\e to ±0.01°C and ±4 Pa, respectively, with a profile Bowen ratio system. These values were used in the error analysis formulae with the temperature and vapour-pressure data from Table 1 for a 3-m psychrometer separation. The errors in the Bowen ratio and the evapotranspiration rate were from two to four times those of the reversing Bowen ratio method for B > 0.8; (for 0 < P < 0.8 errors in the available energy are of greater significance than those in the Bowen ratio). Furthermore, there may still be systematic errors in the measurements that have not been taken into account, thus increasing the error in the profile method. The profile Bowen ratio systems of McNeil and Shuttleworth (1975) and McCaughey (1978) probably have an accuracy similar to that of Sinclair et al., since temperature at a level was measured to no better than ±0.01°C. 3 Comparison of evapotranspiration estimates Three methods were used to measure forest evapotranspiration concurrently with the Bowen ratio/energy balance method. The eddy correlation/energy balance method and the stomatal resistance method provided comparisons of hourly measurements of the evapotranspiration rate. The soil water balance method, provided comparisons on weekly and monthly bases. Typical data from the Bowen ratio/energy balance method using reversing psychrometers with a 3-m vertical separation are shown in Fig. 2. /137 106 / D.L. Spittlehouse and T.A. Black a The Eddy Correlation/Energy Balance Method In July 1976 we made concurrent Bowen ratio and eddy correlation measure-ments 4.5 m above a 14-m high Douglas-fir forest at the University of British Columbia Research Forest, Haney, B.C. (Spittlehouse and Black, 1979). The vertical separation of the psychrometers was 3 m. The eddy correlation system is described in detail in Pond et al. (1979). Briefly, the system used Gill anemometers as wind sensors, one mounted horizontally and one at 30° from the vertical, and a thermistor as a temperature sensor. The sensor outputs were recorded on an FM tape recorder. These sig-nals were later filtered at 6 Hz, sampled at 20 Hz and then analyzed to obtain the instantaneous fluctuations in the vertical wind speed {w') and temperature (7"'). In these calculations the axes were rotated so that ir « 0. The w' and 7" spectra and w'T' cospectra were calculated by computer with a fast-Fourier-transform. No corrections were made for reduced response of the anemometers at high frequencies or for low frequency cutoff since they were considered to be small. The eddy correlation sensible heat flux (He) was calculated from He = C V T 7 (7) where C is the heat capacity of the air and the overbar represents an average for a 54-min data run. The eddy correlation/energy balance evapotranspira-tion rate ( £ P ) was obtained from Ee = (R„ — G — M - He)/L. (8) The wind speed at 4.5 m above the trees was always less than 3 ms" 1 and frequently less than 2 m s _ l . It was difficult to obtain adequate data due to the occasional stalling of the anemometers and operation in their regions of non-linear response. Other sources of error resulted from the tilt of the horizontal anemometer away from the mean horizontal flow, the non-cosine response of the anemometers and calibration and offset errors (Pond et al., 1979). The error in Ee was estimated to be ± 2 0 % . The spectra and cospectra were internally consistent and similar to those found by other workers for forests. The evapotranspiration rate from the Bowen ratio/energy balance method ( £ p ) was up to 30% greater than Ee (Fig. 3). In a similar experiment McNeil and Shuttleworth (1975) obtained values for £ p that were 25% lower than those for £ e . They attributed this to an under-estimation of He by their eddy correlation system. b The Stomatal Diffusion Resistance Method A comparison, on an hourly basis, of the Bowen ratio/energy balance method and the stomatal diffusion resistance method was made from June to August, 1975 (Tan et al., 1978). The site was a recently thinned Douglas-fir stand, 7 to 10 m tall, with an undergrowth of salal, and was located 27 km northwest of Courtenay on the east coast of Vancouver Island. Psychrometer vertical separation was 3 m, at 11 m above the ground. /I38 Evaluation of a Method for Determining Forest Evapotranspiration /107 EODY CORRELATION E e ash (mm h-') Fig . 3 Hourly mean evapotranspiration rate determined with the Bowen ratio/energy balance method and with the eddy correlation/energy balance method ( £ , , ) . for July 13-15. 1976. Mean soil water potential (il<s) of the top 0.45 m of the soil was > - 100 J k g ' . Error bars are shown on two data points. (Modified from.Spittlehouse and Black. 1979.) The stomatal diffusion resistance method requires measurements of leaf stomatal diffusion resistance (rs) to the loss of water vapour, vapour-pressure deficit of the air ( V P D ) at various levels within the canopy and the leaf area index ( L A I ) of canopy layers corresponding to the V P D measurements. Mea-surements of / s and V P D were made intensively on selected days using, respectively, a porometer (Tan et al., 1977) and silicon diode psychrometers. The L A I measurements were made in August on a sample of four trees and three 1-m2 plots of the salal undergrowth. Transpiration from a leaf, on a per unit leaf area basis (£,) is _ C(e, - e )  £ ' - YKr. + r.) ( 9 ) where e( is the vapour pressure in the stomatal cavities of the leaf, e is the vapour pressure of the air surrounding the leaf, and rb is the boundary-layer resistance of the leaf. The vapour pressure in the stomatal cavities is assumed equal to the saturation vapour pressure at leaf temperature (e*(T{)), an as-sumption that is correct to within 3%, even for a leaf water potential (v|v) as low as -4000 J kg" 1 . In a well-ventilated canopy rb is small. Consequently leaf temperature was usually within two degrees Celsius of air temperature (7") (Tan et al., 1978) so that e*(T() ~ e*(T ) to within 15% for a worst case and usually to within 10%. Also, since rb < 0. Ir,, (9) is well approximated by £/ = C vPD / (yLr s ) . io8 / D.L. Spittlehouse and T.A. Black The transpiration per unit ground area for a layer / of the canopy is obtained by multiplying £/by the leaf area index of the layer (LAi j ) and by using a mean stomatal resistance (/%,) for the layer. Summing over the number of layers (n) in the canopy gives the transpiration rate of the canopy (ESR) per unit ground area. i.e. Es* = I (10) Because of the salal undergrowth and the dry soil surface, evaporation from the soil surface was taken to be zero. Errors in r s, V P D and L A I contribute equally to the error in ESR. Tan et al. (1977). in their Table 1, suggest that the porometer measurement error in rs is ±5%. The error in sampling to obtain fsi is more difficult to assess. Field measurements show that r, can vary by 50% and could have a standard deviation of ±10 to ±25%, with ±15% being the norm. The use of V P D resulted in a 10% underestimation of e( — e . However, the omission of rb together with the assumption of saturation within the stomatal cavities par-tially offset the error in using the V P D (Tan et al., 1978). The L A I , was accurate to ± 10%. Thus, ESR had a probable relative error of ± 15 to ±20% (Table 2), and this error was relatively independent of the evapotranspiration rate. Agreement between the Bowen ratio/energy balance method and the stomatal diffusion resistance method was to within ± 10% for high evapora-tion conditions (moist soil, i.e. mean soil water potential of the root zone, tys > — 200 J kg - 1) and to within ±30% for low evaporation conditions (moist and dry soils). Typical high and low soil moisture conditions are shown in Fig. 4. All the comparison data are shown in Fig. 5. There is a tendency for ESR to be greater than £ p when evapotranspiration is low and less than £ p when evapo-transpiration is high. However, this discrepancy is within the errors of the two methods. c The Soil Water Balance Method Nnyamah and Black (1977) and Black (1979) have presented data comparing the soil water balance method with the Bowen ratio/energy balance method. Their 1975 data (site 2) were obtained at the site of the stomatal diffusion resistance method comparison. Their 1974 data (site 1) were obtained at a site 1.5 km northwest of site 2, with twice the density of Douglas-fir trees as compared with site 2. Psychrometer vertical separation was 1 m, 10.5 m above the ground at site 1 and 3 m, 11 m above the ground at site 2. The soil water balance method requires the measurement of the rate of change of the root zone soil water content (A W/A/), the precipitation rate (P), the drainage rate (D) downward out of the root zone (positive) or upward into the root zone (negative) and the run-off rate (/?). Evapotranspiration rate (EWB) is the residual term in the soil water balance and is given by EWB = -AWIM + P- D- R. (11) Summary of probable relative errors in determining evapotranspiration, and agreement in measured evapotranspira-tion between the Bowen ratio/energy balance method and three other methods. + and - mean that the Bowen ratio/ energy balance method gives evapotranspiration values, respectively, greater than, or less than the other methods Estimation Probable Relative Error (%) Agreement (%) Method Period Moist Soil Dry Soil Moist Soil Dry Soil Bowen Ratio/Energy Balance hourly and weekly < +15 ± 10 to ± 4 5 Eddy Correlation/Energy Balance hourly ± 2 0 — ± 2 0 Stomatal Diffusion Resistance hourly ± 1 5 to ± 2 0 ± 1 5 to ± 2 0 ± 8 -30 to +20 Soil Water Balance weekly monthly ± 15 to ± 2 0 ± 30 to + 50 < ± 1 0 -15 to+7 +10 + 4 to +12 t /141 I io / D.L. Spittlehouse and T . A . Black v. HOUR, P. ST. Fig. 4 Comparison of the daytime course of evapotranspiration rate ( £ ) obtained from the Bowen ratio/energy balance measurements and the stomatal diffusion resistance method for days with (a) high and (b) low soil water potential (v|/,). The values of net radiation (/? „) are for the 24-h period. \|/, is a mean for the top 0.45 m of the soil. Error bars are not shown for every data point. (Modified from Tan et al.. 1978.) In this study run-off was zero. Precipitation was measured with a raingauge mounted on the instrument tower so as to include canopy interception in EHB. Precipitation was probably measured to ±5%. However, during the study periods precipitation was less than 5% of E^g. Soil water content was measured by gravimetric sampling and by a neutron-scattering technique (Holmes et al.. 1967). Hewlett et al. (1964) and Federer (1970) note that instrumentation errors in the neutron-scattering technique are small compared to sampling errors in inhomogeneous soils. Although the error in a single mean water content measurement may be large, the error in the moisture change over time is greatly reduced when the sampling is done at the same locations each time (Hewlett et al., 1964). Nnyamah and Black (1977) used four sampling locations with four depths at site 1 and six sampling locations with six depths at site 2 to obtain changes in a mean soil water content for a site to within ±3 to ±4 mm (the daily evapo-transpiration amount when the soil was moist). Drainage is also difficult to determine accurately. It was calculated from Darcy's Law using measurements of the daily water potential profile obtained with tensiometers and soil hygrometers, and the hydraulic conductivity curve Evaluation of a Method for Determining Forest Evapotranspiration / i n o. • . 1 1 . . . . 1 0 0.1 0,2 0 3 0.4 (mm h") Fig. 5 Hourly mean evapotranspiration rate obtained from the Bowen ratio/energy balance method (£R) plotted against corresponding values obtained from the stomatal diffusion resistance method ( £ i R ) . The data were obtained on 7 selected fine days when stomatal resistance was intensively measured. Soil water potential (v|>,) is a mean for the top 0.45 m of the soil. Error bars have been shown on two data points. (Modified from Tan et al.. 1978.) for the soil determined in the laboratory (Nnyamah and Black. 1977). The amount of drainage (upward and downward) was small and may be in error by ± 1 mm over a week. The soil water balance estimate of evapotranspiration may be in error by up to ±5 mm. On a weekly basis this had a probable relative error of < ±20% when soil water content was high (\J/„ > —200 J kg"1) and < ±50% when soil water content waslow(v|/g < -800 J kg - 1)- However, the absolute error in EWB was relatively independent of the length of time between measurements and relative error was decreased by increasing the measurement time period. On a monthly basis the error in EwB was < ± 10% (Table 2). The Bowen ratio and the soil water balance methods agreed to about ± 10% on a weekly basis at both sites, over a wide range of soil moisture conditions (Fig. 6). There is a tendency for EWB to be consistently lower than £ p . At site 1 this was felt to be partially a result of poor fetch conditions and the 1-m separation of the psychrometers of the Bowen ratio system adversely affect-ing the Bowen ratio measurements (Black, 1979). On a monthly basis total evapotranspiration estimated by the Bowen ratio/energy balance method was greater than that by the soil water balance method by 8 and 2% for sites 1 and 2, respectively. Figure 6 also shows the result of a comparison by McNaughton and Black (1973). Their site was a 7.8-m tall Douglas-fir plantation at the Haney Re-/143 112/ D . L . Spittlehouse and T . A . Black {mm day"') Fig. 6 Comparison of average Bowen ratio/energy balance (£n) and soil water balance (£«•«) values of evapotranspiration rate at Courtenay sites 1 and 2. Also shown are regression equations and lines for the data at both sites. Soil water potential (>(*,), as a mean for the top 0.45 m of the soil, varied from - 10 to - 1200 J kg - 1 . Error bars are shown for two data points. A data point for a 15-day period at the U.B.C. Research Forest at Haney, B.C. is also shown where v|/, > — 100 J kg - 1 . (Modified from Black, 1979.) search Forest. The psychrometer separation was 1 m at 8.8 m above the ground. For a 15-day period, with moist soil conditions (v^ , > - 100 J kg - 1) the Bowen ratio/energy balance method gave 4% more evapotranspiration than the soil water balance method. 4 Discussion The error in determining evapotranspiration with each of the four methods is summarized in Table 2. Also listed is the agreement between the Bowen ratio/energy balance method and the other three methods. The agreement on an hourly, weekly and monthly basis is well within the errors of the methods. None of the methods is significantly more accurate than the Bowen ratio method with reversing psychrometers separated by 3 m. Furthermore, the Bowen ratio method has the advantage of giving hourly, daily, weekly and monthly measurements of evapotranspiration. The success of the Bowen ratio/energy balance method in reliably measur-ing evapotranspiration is related to three factors: first, the periodic reversal of symmetrically constructed psychrometers in order to remove systematic measurement errors; second, the differential measurement of temperature over a vertical distance of at least 3 m; and third, the matching of the sensitivity of the diode temperature sensors, and the calibration of the mea-surement system to better than ±0.5%. Evaluation of a Method for Determining Forest Evapotranspiration /113 It is difficult to increase significantly the accuracy of the Bowen ratio/energy balance method. For -0.6 < B < 2 the error in the available energy is the major contributor to the total error in the evapotranspiration rate. It is probably not feasible to improve the accuracy of the measurement of available energy. For B > 2 the accuracy of the vapour-pressure gradient measurement is important, and this depends on the accuracy of the dry- and wet-bulb temperature differences. Greater accuracy can be achieved by in-creasing the separation of the psychrometers, and therefore reducing the relative error. However, this increases the fetch requirements. A better way to achieve greater accuracy in temperature-difference measurement would be to increase the sensitivity of the measurement system (integrators in this case). The elucidation of the accuracy of the Bowen ratio/energy balance method is important for forest evapotranspiration studies. It validates the findings of McNaughton and Black (1973), Jarvis et al. (1976), Black (1979) and others that, unlike from agricultural crops, maximum evapotranspiration from forests when soil water content is high and the foliage is dry is often less than or equal to the equilibrium evapotranspiration rate. Shuttleworth and Calder (1979) and Thorn (1978) also reached this conclusion from other considerations. Unlike the aerodynamic method (Thorn et al., 1975) it appears that reliable measurements can be made close to the top of the forest canopy. The assumption of equality for the diffusivities of heat and water vapour, implicit in the Bowen ratio/energy balance method, appears to be applicable for a wide range of conditions over forests. Ideally, an eddy-correlation system could be used to measure humidity and wind fluctuations and, therefore, evapotranspiration. However, suitable instrumentation is not available, though instruments reported in Hyson and Hicks (1975) and Campbell and Unsworth (1979) appear promising. Con-sequently, for routine measurements of forest evapotranspiration the eddy-correlation method is limited by its complexity of analysis, high cost and inability to operate under a wide range of weather conditions. The stomatal diffusion resistance method is time-consuming, since it requires continuous manual measurements. Also it does not measure evaporation from the soil. The soil water balance method is less time-consuming; however, it may be difficult to obtain a good estimate of drainage and a good spatial average of the soil water content. A major disadvantage of the Bowen ratio/energy balance method is the need for an extensive study site having sufficient fetch to allow equilibration of the surface boundary layer to a height greater than the mea-surement height. The stomatal diffusion resistance method and the soil water balance method could be used for small areas of forest and for individual trees. 5 Conclusions An error analysis of the Bowen ratio/energy balance method shows that with certain limitations forest evapotranspiration can be measured to ±15% for -0.5 < B < 2, and to within ± 15% and ±60% for large and small temperature /145 114 / D.L. Spittlehouse and T.A. Black and vapour-pressure gradients, respectively, for 2 < (J < 4. The limitations are: (a) there must be periodic reversal of symmetrically constructed psy-chrometers to remove systematic measurement errors; (b) the differential temperature measurements should be made over a distance of at least 3 m; and (c) the temperature sensor sensitivities should be matched to better than ± 0 . 5 % and the calibration and stability of a high resolution measurement system must be within ± 0 . 5 % . Such a system is significantly more accurate than profile Bowen ratio systems especially those using absolute rather than differential temperature measurement. Comparison of the reversing Bowen ratio/energy balance method with an eddy-correlation method, a stomatal diffusion resistance method and a soil water balance method confirmed the suitability of the Bowen ratio/energy balance method for measuring forest evapotranspiration. Agreement between the methods was well within their own errors. The Bowen ratio method can be reliably used for continuous measurements of evapotranspiration over long periods of time. Acknowledgements This work was funded by a grant from the Natural Sciences and Engineering Research Council and by a contract from the British Columbia Ministry of Forests. References B A I L E Y , w.G. 1977. Atmospheric and surface control of evapotranspiration during soy-bean maturation. Ph.D. Thesis. McMaster Univ., Hamilton. Ont.. 162 pp. B L A C K , T.A . 1979. Evapotranspiration from Douglas fir stands exposed to soil water de-ficits. Water Resour. Res. 15: 164-170. and K.G. M C N A U G H T O N . 1971. Psy-chrometric apparatus for Bowen-ratio de-termination over forests. Boundary-Layer Meteorol. 2: 246-254. C A L D E R . I.R. 1976. The measurement of water losses from a forested area usinga "natural" lysimeter. J. Hydrol. 30: 311-325. C A M P B E L L , A.p. 1973. The effect of stability on evaporation rates measured by the energy balance method. Agric. Meteorol. 11: 261-267. C A M P B E L L . G.S. and M.H. U N S W O R T H . 1979. An inexpensive sonic anenometer for eddy correlation. J. Appl. Meteorol. 18: 1072-1077. D E N M E A D , o.T. 1969. Comparative micro-meteorology of a wheat field and a forest of Pinus radiata. Agric. Meteorol. 6: 357-371. and i.e. M C I L R O V . 1970. Measurement of non-potential evaporation from wheat. Agric. Meteorol. 7: 285-302. DROPPO, J.G . and H.L. H A M I L T O N . 1973. Ex-perimental variability in the determination of the energy balance in a deciduous forest. J. Appl. Meteorol. 12: 781-791. DYER, A.J . 1967. The turbulent transport of heat and water vapour in an unstable atmo-sphere. Quart. J. R. Meteorol. Soc. 93: 501-508. F E D E R E R , C A . 1968. Spatial variation of net radiation, albedo and surface temperature of forests. J. Appl. Meteorol. 7: 789-795. . 1970. Measuring forest evapotranspi-ration - theory and problems. U.S.D.A. For. Serv. Res. Pap. NE-165. Northeastern For. Exp. Stn, Upper Darby, PA.. 25 pp. F R I T S C H E N . L.J.;J. HSIA and p. D O R A I S W A M Y . 1977. Evapotranspiration of a Douglas fir determined with a weighing lysimeter. Water Resour. Res. 13: 145-148. F U C H S , M . and C.B. T A N N E R . 1970. Error Evaluation of a Method for Determining Forest Evapotranspiration /115 analysis of Bowen ratios measured by dif-ferential psychrometry. Agric. Meteorol. 7: 329-334. G A S H , J.H.C . and J.B. S T E W A R T . 1975. The av-erage surface resistance of a pine forest de-rived from Bowen ratio measurements. Boundary-Layer Meteorol. 8: 453-464. G R A N T , D.R. 1975. Comparison of evaporation measurements using different methods. Quart. J. R. Meteorol. Soc. 101: 543-550. H E W L E T T . J.D.: J.E. D O U G L A S S and J.L. C L U T -TER. 1964. Instrumental and soil moisture variance using the neutron-scattering method. Soil Sci. 97: 19-24. HICKS, B.B . ; p. H Y S O N and cj . M O O R E . 1975. A study of eddy fluxes over a forest. J. Appl. Meteorol. 14: 58-66. H O L M E S . J.W.; S.A. T A Y L O R and S.J. RICHARDS. 1967. Measurement of soil water. In: Irriga-tion of Agricultural Lands. (R.M. Hagen. H.R. Haise and T.W. Edminster, Eds.) Monogr. 11. Am. Soc. Agron.. Madison. Wis., pp. 275-303. H Y S O N , p. and B.B. HICKS . 1975. A single-beam infrared hygrometer for evaporation mea-surement. J. Appl. Meteorol. 14: 301-307. JARVIS. P.G.; G.B. J A M E S and J.J. L A N D S B E R G . 1976. Coniferous forests. In: Vegetation and the Atmosphere. Vol. 2. Case Studies. (J.L. Monteith. Ed.) Acad. Press, London, pp. 171-240. M C C A U G H E Y . J.H . 1978. Energy balance and evapotranspiration estimates for a mature coniferous forest. Can. J. For. Res. 8: 456-462. M C N A U G H T O N . K.G. and T.A. B L A C K . 1973. A study of evapotranspiration from a Douglas-fir forest using the energy balance approach. Water Resour. Res. 9: 1579-1590. M C N E I L . D U . and w.j. S H U T T L E W O R T H . 1975. Comparative measurements of the energy fluxes over a pine forest. Boundary-Layer Meteorol. 9:297-313. M I L N E . R. 1979. Water loss and canopy resis-tance of a young Sitka Spruce plantation. Boundary-Layer Meteorol. 16: 67-81. MOORE. C J . 1976. Eddy flux measurements above a pine forest. Quart. J. R. Meteorol. Soc. 101: 913-918. N N Y A M A H . J.U. and T.A. B L A C K . 1977. Rates and patterns of water uptake in a Douglas-fir forest. Soil Sci. Soc. Am. J. 41: 972-979. P O N D , s.; W.G. L A R G E , M. M I Y A K E and R.W. B U R L I N G . 1979. A Gill twin propeller-vane anemometer for flux measurements during moderate and strong winds. Boundary-Layer Meteorol. 16: 351-364. R E V F E I M . K.J.A . and R.B. J O R D A N . 1976. Preci-sion of evaporation measurements using the Bowen ratio. Boundary-Layer Meteorol. 10: 97-111. S C A R B O R O U G H , J.B . 1966. Numerical Ma-thematical Analysis. (6th edit.) Johns Hop-kins Press. Baltimore. 600 pp. S C H O L L , D.G . 1976. Soil moisture flux and evapotranspiration determined from soil hydraulic properties in a Chaparral stand. Soil Sci. Soc. Am. J. 40: 14-18. S H U T T L E W O R T H , W.J . and I.R. C A L D E R . 1979. Has the Priestley-Taylor equation any rele-vance to forest evaporation? J. Appl. Meteorol. 18: 639-646. S I N C L A I R . T.R.; L.H. A L L E N and E.R. L E M O N . 1975. An analysis of errors in the calculation of energy flux densities above vegetation by a Bowen-ratio profile method. Boundary-Layer Meteorol. 8: 129-139. S P I T T L E H O U S E . D.L . 1980. Measurement and modelling of forest evapotranspiration. PH.D . Thesis. Univ. of British Columbia, Vancouver. B.C. (in preparation). a n d T . A . B L A C K . 1979. Determination of forest evapotranspiration using Bowen ratio and eddy correlation measurements. J. Appl. Meteorol. 18: 647-653. S T E W A R T . J.B . and A.S. T H O M . 1973. Energy budgets in pine forest. Quart. J. R. Meteorol. Soc. 99: 154-170. T A N . cs. and T.A. B L A C K . 1976. Factors affecting the canopy resistance of a Douglas-fir forest. Boundary-Layer Mete-orol. 10: 475-488. ; and J .u. N N Y A M A H . 1977. Characteristics of stomatal diffusion resis-tance in a Douglas fir forest exposed to soil waterdeficits. Can.J. For. Res. 7: 595-604. ; and . 1978. A simple diffusion model of transpiration applied to a thinned Douglas-fir stand. Ecology. 59: 1221-1229. T A N G . P.A.; K.G. M C N A U G H T O N and T.A. B L A C K . 1976. Precision electronic integrator for environmental measurement. Trans. Am. Soc. Agric. Eng. 19: 550-552. T A N N E R , C.B . 1960. Energy balance approach to evapotranspiration from crops. Soil Sci. Soc. Am. Proc. 24: 1-9. /147 u6 / D.L. Spittlehouse and T . A . Black THOM. A.S. 1976. Momentum, mass and heat exchange of plant communities. In: Vegeta-tion and the Atmosphere, Vol. 1, Principles, (J.L. Monteith, Ed.) Acad. Press, London, pp. 57-109. . 1978. Evaporation from forests in re-lation to climate and hydrology. Paper pre-sented at the First International Symposium of Forest Meteorology, Aug. 21-25, 1978, Univ. of Ottawa, Ottawa, Ont. Sponsored by the World Meteorological Organization. ; J.B. STEWART, H.R. OLIVER and J.H.C. GASH. 1975. Comparison of aerodynamic and energy budget estimates of fluxes over a pine forest. Quart. J. R. Meteorol. Soc. 101: 93-105. THOMPSON, N. 1979: Turbulence measure-ments above a pine forest. Boundary-Layer Meteorol. 16: 293-310. VERMA, S.B.; N.J. ROSENBERG and B.L. BLAD. 1978. Turbulent exchange coefficients for sensible heat and water vapor under ad-vective conditions. J. Appl. Meteorol. 17: 330-338. APPENDIX III - ERROR ANALYSIS FOR THE REVERSING PSYCHROMETER /148 1. CALIBRATION AND MEASUREMENT ERRORS FOR THE  REVERSING PSYCHROMETER 1. THEORY The method of assessing the errors in the Bowen ratio described here is similar to that in Fuchs and Tanner (1970), S inc la i r et al. (1975) and Bailey (1977). Maximum and probable errors are calculated following Scarborough (1966). The method of calculating probable errors assumes that the observed variables are independent. However, a l l the variables are related by the energy balance equation so that i t must be assumed that any error resulting from the interactions of the observations is relat ively small (Sinclair et al., 1975). A value y is a function of a set of measurements x^, . . . x n , with associated errors 6x^, ... 6x n. Thus, y = f ( x : + S X j , . . . x p + 6 x n ) (1) The maximum total error in y is given by differentiat ing (1) with respect to x^, . . . x n , 6 y m a x = \TTX 6 x l l + + \~- <5X 3 x n n (2) The probable error in y is given by taking the root-niean-square of (2), sy (3) The respective maximum and root-mean-square relative errors are (6y /y) and (6y/y),and 6y wil l be smaller than 6y . /149 1. The Bowen Ratio/Energy Balance The Bowen ratio/energy balance calculation of evapotranspiration (E) is given by: E = (R n - G - M)/[L(1 + 3)] (4) In (4) (R - G - M) is the energy available for evapotranspiration and the sensible heat flux, where Rn is the net radiation f lux , G is the soil heat \ f lux, M is the rate of canopy heat storage, L is the latent heat of vapourization of water and 3 is the Bowen rat io . Similarly the sensible heat flux (H) is given by H = [ (R n - G - M)B]/(1 + B) (5) The probable error in E is 6E = [ { [1 / (L(1 + 3) ) ] 6 (R n - G - M)} 2 + U ( R n - G - M ) / ( L 2 ( 1 + 3 ) ) ] 5L} 2 + H ( R n - G - M)/ (L(1 + 3 ) 2 ) ] ^}Z~\h (6) Similarly the probable error in H is 6H = [{ [3 / ( 1 + 3)] 6 (R n - G - M)} 2 + U ( R n - G - M ) / ( l + 3 ) 2 ] 6$}2]]h ( 7 ) /I 50 L can be calculated from the mean a i r temperature T, The probable error in L is 2500 -.2.361 T (8) 6L = 2.361 ST (9) The probable error in T is a function of calibration and measurement accuracy and is dealt with later (Equation 31). 2. Available Energy The available energy is (Rn - G - M).- Calibration of the net radiometer is to within ±2%, and measurement accuracy varies from ± 2% to ± 0.2% depending on the net radiation f lux. Thus the maximum measurement error is about ± 4%. This value is in agreement with Federer (1968) and Fuchs and Tanner (1970). McNeil and Shuttleworth (1975) suggest that uncertainties in the representativeness of Rn may be ± 5%. A value of (<5R n/R n) = ±5% wil l be used in this analysis. It is d i f f i c u l t to make accurate measurements of the soil heat flux and canopy heat storage. Thus, measurement errors are probably much greater than any instrumentation errors. However, except for /I 51 periods around s u n r i s e and sunse t , (G + M) i s - < 10% o f the net r a d i a t i o n . Thus, a 50% e r r o r i n (G + M) causes an e r r o r o f <5% i n the a v a i l a b l e energy. From the above, the e r r o r i n the a v a i l a b l e energy measurement can be taken as 7%, and because of u n c e r t a i n t i e s i n the measurements, tha t cannot be q u a n t i f i e d , t h i s va lue w i l l be used f o r both the maximum and root-mean-square c a l c u l a t i o n s . v 3C. Bowen Ra t io The Bowen r a t i o (3) i s g iven by 6 = y A B / A e ~ 0 (io); where y i s the psychromet r ic cons tant and A0- and Ae Q are the .average p o t e n t i a l a i r temperature and he igh t co r rec ted vapour p ressure d i f f e r e n c e s , r e s p e c t i v e l y , between two h e i g h t s : a n d are negat ive when temperature and vapour pressure decrease w i th he igh t . 63 = [ { ( Y / A e o ) 6 A Q } 2 + { ( Y A e / A e 0 2 ) 6 A e " 0 } 2 ... • + { ( A 0 7 A e " o ) 6 Y > 2 j } ' 2 O D The p o t e n t i a l temperature d i f f e r e n c e i s g iven by AG = A T n •+ T Z (12) /152 where ATQ is the average dry bulb temperature difference, r is the dry adia-batic lapse rate and Z in the separation distance of the sensors,(Table I I I . l ) . From (12) the probable error in A9 is 6A9 - [{6AT^}2 + {1ST}2 + {YSl}2]h (13) The error in r comes from using the dry adiabatic lapse rate instead of that for moist a i r . The measured vapour pressure difference Ae can be obtained from the psychrometric equation. However, Thorn (1976) notes that with the small humidity gradients that exist over forests, Ae .should be corrected to allow for the natural decrease in the water vapour pressure of the a i r with height corresponding to the decrease in atmospheric pressure. It can be shown that the corrected vapour pressure difference' (AeQ) is given by Ae = Ae + 7.6 x 10"' Ze (14) o where e" is the mean vapour pressure of the prof i le . The probable error in A~e^ , where A~e^  is a difference in kPa over Z metres, is 6 A i Q = HoAe"} 2 + {0.00008 e 5Z} 2 + (0.00008 Z 5 e } 2 ] ^ (15) Ae is obtained by differentiat ion of the psychrometric equation * - « W - * < T D - TW> ( 1 6 ) where and f w are the mean dry and wet bulb temperatures and e^ is the saturation vapour pressure at the mean wet bulb temperature. / l 53 Thus: A i = ( s M + Y ) ATW - Y AT d (17) where s w i s the rate of change of the saturation vapour pressure with temperature at the wet bulb mean p r o f i l e temperature, and AT^ i s the average wet bulb v e r t i c a l temperature difference. The probable error in Ae" i s SAe = [{AT W 6 S W } 2 + f ( s w + Y ) 6 A T W } 2 + {ySATp} 2 + { ( A T W - A T D ) 6 Y } 2 I % ( 1 8 ) By d e f i n i t i o n sw = 8 e w / 3 T w and _ 6 s w = ( 3 s w / 3 T w ) f 6T.W (19)" W From (16) the probable error in e is Se = [{Se * j } 2 + arD - T W ) 6 Y } 2 + ( Y -sTp} 2 + {yST^,} 2]^ (20) 7154 From the definition of s,, i t can be seen that W 6 e w = s w 6 T w ( 2 ] ) Substituting (21) in (20) gives 66 = [{(TD - T W ) 6 Y } 2 + {Y<5T d } 2 + [ (s 2 + Y 2 )<ST 2 ] ] % (22) The error in Y should be considered as many psychrometers do not necessarily have the thermodynamic value, e.g. when the wicks are \ contaminated or there is insufficient wetting. Also various researchers have found that their psychrometers to have the psychro-metric constant greater than 0.066 kPa °C"^ at normal temperature and pressure. For example, Lourence and Pruitt (1969) and Yoshitake and Shurigu (1965) used y - 0.07 kPa °C~ 1 . I found values of .0.966 and 0.069 appropriate for psychrometers with silicon diodes as temperature sensors. Furthermore, often y is not corrected for variations with temperature or changes in atmospheric pressure (Revfeim and Jordan, 1976). 4 • Temperature Difference The mean temperature difference between the two measurement levels (AT) of a reversing psychrometric system is given by AT = ( C 1 - C 2 ) / ( S c S d 2 ) (23) /T55 where Cn and C 2 are the count totals for the two consecutive measurement periods, S c is the sensi t iv i ty of the integrating system and S^ is the mean sensi t iv i ty of the diodes (Table I I I . l) . The probable error in AT is 6Af = [{ [ l / ( S c S a ) ] 6 C } 2 + - C 2 ) / ( S C S d 2 ) ] 6 S d > 2 + { [ (C 1 - C 2 ) / ( S 2 S d 2 ) j 6 S C } 2 J % + SAT-- (24) b d The term 5 A T i s the absolute error in AT due to the use of a mean diode sensi t iv i ty and is included as a separate term since i t is d i f f i c u l t to include i t exp l ic i t l y in the second term on the right hand side of (24). This term and are defined below. 5. Diode Sensi t iv i ty Calibration-sensi t i vi ty: In ca l ibrat ion, diode sensi t iv i ty is calculated from S d • <va " V / ' T a " V . <25> where V g and and T f l and T^ are corresponding diode junction voltages and cal ibrating thermometer temperature. During cal ibrat ion the error (6Vm)in V is due to the measuring accuracy, since the supply voltage is kept constant. The probable error in S^ is 6Sd = [2{[ l / (T a - T b)] SVm} 2 + 2{ [ (V a - V b ) / ( T a - T b ) 2 ] 6 T } 2 ] 1 ' 2 (26) /156 Self-heating of a diode is <, 0.005 °C in s t i l l a i r * and will be even smaller when the diode is ventilated. Also i t is a constant offset and would not affect the sensit iv i ty of the diodes. Mean sensi t iv i ty : The error in AT due to the use of a mean diode sensi t iv i ty (S~) can be shown to be (see Appendix III.2) 6 A T T = as . D T / S H (27) where DT is the change in the mean prof i le temperature between the two measurement periods, and SS. the deviation of the diode sensi t iv i ty from the mean (Table I I I . l ) . Calibration,absolute temperature: Diode temperature (T) is given by T = T 0 - V / S d (28) where T Q is the offset temperature. As before, during cal ibration the error in V is SV so that m 6T = [ {6T Q } 2 + { ( 1 / S d ) 6 V m } 2 + { ( V / S j j ) 6 S d } 2 ] h (29) Self heating effects are negligible compared to the other errors. Furthermore, ventilation of the diodes during calibration and use would quickly disperse most of this heat. /157 6. Measurement Errors Diodes: Measurement errors for the diodes are related to change in the * diode power supply and a voltage drop down the lead wires. The lat ter is not considered as there is no current flowing down the measurement leads. Changes in the former ( i f they are < ± 10 mV) should not be enough to affect the sensi t iv i ty of the diodes. However, they may be large enough to affect the absolute temperature reading. Since each diode pair is driven by the same power supply both diodes should be affected equally so that the dif ferent ial voltage is independent of power supply changes of < ± 10 mV. The uncertainty in the diode junction voltage (<5Vp) due to a change (SVp)in the power supply voltage (V,p)is given by Tang et al. (1974) as 5V p = 456 V p / V p (30) where 6Vp is in m i l l i v o l t s . For f i e ld measurements 6Vp must be included in (29). In this case i t is added to 6Vm to give the total uncertainty (SV) in the diode junction voltage. Furthermore, the sampling to obtain T is infrequent; thus, an error term f T must be included in (29) to account for the error in T caused by infrequent sampling. f T is taken as an absolute error. Thus the error in the measurement of an: average temperature from a diode junction voltage, V, is This may be due to actual changes in the power supply voltage or through changes in resistance in the parts of the curcuit carrying current, e .g. due to aging of solder junctions, and temperature changes in the lead wires and the diodes themselves /158 6T = [ { 6 T 0 } 2 + { ( 1 / S d ) 6 V } 2 + { ( V / S 2 ) 6 S d } 2 ] 3 § + f T ( 3 1) Integrators: The s e n s i t i v i t y of an integrator (S c) i s S c = C//Vc (32) whereC. i s the number of counts per unit time due to the applied voltage V^. The probable error in i s 6 S C = [ { ( 1 / V C ) 6C.} 2 .+ {(C./V. 2)6V c} 2] i' 2 (33) The integrators are stable over a wide range of temperature conditions and within the voltage range encountered. Any variations in due to these factors could be accounted for by increasing 6C.,.or by adding a correction factor f^ to SS^. /159 2. CALCULATIONS FOR GERMANIUM DIODES • The appropriate values for calculating the probable and maximum errors in the estimation of evapotranspiration are given in Table I I I . l . Calculated error terms are l is ted in Table III.2. 1. Temperature and Vapour Pressure  Diodes Equations (26) to (31) are used to calculate the error in the temperature measurement due to the diodes. From (26) the probable error in diode sensi t iv i ty is h S S d = [2.0 x 1 0 " 6 + 2.6 x 10" 6 ] o - 1 = ± 0.002 mV C and 6 S d / S d = ± 0.1%. (340 The maximum relative error is ± 0.2%. From (27) the absolute error in AT due to using a mean sens i t iv i ty , for diode pairs matched to 0.4% and 0.1%, i s , respectively 5ATV = 0.0004 ° C , 0.0001 °C f o r DT = 0.1 °C S d (35) and = 0.004 ° C , 0.001 °C f o r DT = 1..C °C From (30) and Table I I I . l , <SVp = 0.02 mV and 6Vm = 0.02 mV so that, 6V = 0.04 mV. From (31) the probable error in an absolute temperature measurement is /160 Table III.l. Typical calibration and resolution data for germanium diodes. Symbols are defined in th'e text. (a) Diodes (T - T. ) = 20 UC 6T = ± 0.01 °C v a b' (V - V f a) = 46 m V 6Vm = ± 0.02 mV (calibration) V = 125 mV 6V = ± 0.02 mV (measurement) o - l S d = 2.3 mV C 1 Vp,= 6.750 V 6Vp = ± 0.003 V 6V = ± 0.02 mV DT = 0.1 °C to 1.0 °C fj = ± 0.3 °C (b) Integrators S« = 166.7 counts (mV 10 min) -1 C.';= 833.5 counts 6C = ± 1 count Vc = 5 mV 6VC = ± 0.005 mV f c = 0.1% (c) Temperature and Vapour Pressure Y = 0.066 kPa V 1 6y = ± 0.002 kPa V 1 s.. = 0.12 kPa °C~ 1 3S../3T = ± 0.006 kPa °C" 2 W at 15 °C W at 15 °C 6Z = 0.005 m Z = 3 m ST = 0.0003 °C m"1 r = 0.01 °C m"1 (C. - C?)• = 200 counts (large_Zf) = 20 counts (small AT) AT = 0.03 °C/3 m to 0.3 °C/3 m L = 2465 J g" 1 at 15 °C W = 1.2 kPa /161 fiT = [10" 4 + 3 x 1 0 " 4 + 22 x IO" 4 ] 1 * + 0.3 = ± 0.35 ° C . (36) The maximum error is ± 0.4 °C. Integrators From (33) the probable calibration error of an integrator is 6 S C = [0.04 + 0.028] ± 0.26 counts(mV 10 m i n ) " 1 and 6 S C / S C = 0.16% (37) The maximum relative error is 0.22%. During use, f equals the dr i f t in integrator sensi t iv i ty and is of the order of ± 0.1%. Thus, 6 S C = ± 0.26 + f c ± 0.43 counts(mV 10 m i n ) " 1 and 6 S C / S C = ± 0.26% (38) The maximum error is 0.32%. /162 Temperature Errors wil l be calculated for typical high and low values of AT, 0.30 and 0.03 °C,over 3 m. From (24) and Tables III.l and III.2 for AT = 0.30 °C/3 m 6AT = [7 x 1 0 " 6 + 6: x T O - 8 + 5 x l O - 7 ] ^ + 6ATV b d In the above equation, of the terms in parentheses, only the f i r s t is s igni f icant . This is also the situation for-AT = 0.03 °C/3 m and for the maximum as well as probable error. Thus, the above equation reduces to <SAT = 0.00 3 + 6ATV b d 6 l T m a x = 0-00 4 + S A T ^ Taking values of 6A7s" from (35) the probable error, <5AL ranges from ± 0.003 °C to ±0.007 °C and the maximum error from ±0.004 °C to ± 0 . 0 0 8 ° C . From (1:3) the probable error in the potential temperature difference over 3 m, for a typical SAT of 0.005 °C, is 6 M = [2.5 x :>10" 5 +' - 10^ 6 + 3 x l O " 9 ] ^ the last two terms in the above equation are negl igible, thus SAO 5AT = ± 0.005 °C ( 4 0 ) A typical maximum error is ± 0.006 °C. /163 Table 111.2. Calculated probable and maximum absolute and r e l a t i v e errors for germanium diodes. Symbols defined in text. Probable Error Maximum Error absolute r e l a t i v e absolute r e l a t i v e 6S^ (mV V 1) d 0.002 0.1% 0.004 0.2% ST (°C) 0.35 - 0.4 -SV (mV) 0.04 - 0.04 -6S C (counts (mV 10 min)" 1) 0.26 0.2% 0.37 0.2% (ssc + f c ) 0.43 0.3% 0.53 0.3% SAiy (°c) d {0.0001 to 0.004} {0.0001 to 0.004} SAT (°C) {0.003 to 0.007} {0.004 to 0.008} 6AB (°C) 0.005 - 0.006 -«SL (J g"1) 0.8 0.03% 0.9 0.04% Ss w (kPa V 1) 0.002 2% 0.002 2% Se" (kPa) 0.05 - 0.12 -SAe (kPa) 0.001 - 0.0021 -6Ae Q (kPa) 0.001 - 0.0021 -/164 Vapour pressure From (22) using a value for a Targe (10 °C) wet bulb depression and data from Tables I I I . l and III.2 Se = [4 x 1 0 " 4 + 5 x 10" 4 + 23 x 10"4] The f i r s t term i s close to i t s maximum value, while the other two terms are r e l a t i v e l y constant. Thus, <5e- i s ' mainly, dependent on the error in the"'wet bulb temperature measurement so that ^ •'• :6e =.0.05 kPa N and _ (41) 6w °-12 kPa From (18) the probable error i n Ae i s dependent on the dry and wet bulb temperature differences. For large dry and wet bulb difference over 3 m, 0.3 °C and 0.25 °C respectively, I , 6Ae = [3 x 1 0 " 7 + 9 x 1 0 " 7 + 1 0 ~ 7 + 0.1 x 10" 7] 2 = ± 0.001 kPa (42) The maximum error i s £ 0.0021 kPa. For large dry bulb (0.3 °C) and small wet bulb (0.13 °C) differences only the f i n a l term changes s i g n i f i c a n t l y , however, i t has a negligible affect on Ae. For small dry and wet bulb gradients the f i r s t and fourth terms in parentheses in (42) are reduced. Thus <SAe w i l l be taken to be equal to (42) for a l l dry and wet bulb gradients. From (15) the error in the corrected vapour pressure difference i s I , 6 A e 0 = [ 1 0 " 6 + 4 x 1 0 " 1 3 + 1 x I O " 1 0 } ' 2 /165 The last two terms in the above equation are negligible even for large vapour pressures. Thus SAe - 6Ae o = +' 0.001 kPa (43) with the maximum error of + 0.0021. kPa 2. The Bowen Ratio. Typical potential temperature and vapour, pressure differences' over 3 m vary from 0.3 °C to 0.03 °C and 0.03 kPa to 0.003 kPa respectively. From (11), for large temperature (0.3 °C) and vapour pressure (0.03 kPa) differences, with 3 = 0.66, 6 3 = [0.6 x 1 0 " 4 + 4.8 x 1 0 " 4 + 4 x 10"- j = ± 0.031 and 63/3 '= ± 5%' (44) The maximum relative error is ±T2% From (11), for small temperature (0.03 °C) and vapour pressure (0.003 kPa) differences, with 3 = 0.66; -4 h 63 = [0.012 + 0.048 M x 10 1 = ± 0.25 and 63/3 = ± 37% (45) The maximum relative error is ± '93%.'.. /166 From (11), for large temperature (0.3 °G) and small vapour pressure (0.003 kPa) differences with 3 = 6.6; 6 3 = [0.012 + 4.8 + 0.04]*2 = ± 2.2 and 63/6 = ± 34% (46) The maximum relative error is ±7.5%. Probable and maximum errors in the Bowen ratio are listed in Table III.3. 3. Evapotranspiration and the Sensible Heat Flux A listing of absolute and relative errors in the calculation of evapotranspiration is presented in Table III.4. An example calculation is presented below for 6 = .0,,66, (R - G - M) = 500 W m"2 and E = 0.122 g m"2 s " 1 (301 W nf 2 ) . From (6) and (9) 6E = [73 x 10" 6 + 2 x 10" 9 + 6 x 10* 6 ]* 2 = ± 0.009 g m~2 s ~ 2 and 6E/E = ± 7% (47) The maximum relative error is ± It can be seen that the error due to L is negligible. The absolute and relative errors in the sensible heat flux are presented in Table III.5. An example calculation is presented below for 3 =0.66, (Rn - G -M) = 500 W nf 2 and H = 199 W m . From (7), /167 Table 111.3. Probable and maximum relative errors in the Bowen ratio (6) calculated_for various potential temperature (A0) and vapour pressure (Ae0) differences over 3 m. Errors are independent of the sign of 8. A0 A e o Probable Maximum 3_ (°C) (kPa) error error 0.66 0.3 0.;03. 5% 12% 0.66 0.06 0.006 19% 48% 0.97 0.25 0.017 7% 18% 1.32 0.3 0.015 8% 19% 1.32 0.06 0.003 35% 83% 2.06 0.25 0.008 13% 32% .• 3.96 0.36 0.006 17% 40%' 3.96 0.09 0.0015 67% 150% 5.0 0.15 0.002 50% 112% 6.6 0.3 0.003 34% 75%. /168 Table III.4. Probable and maximum re l a t i v e errors in the p w a n n t r a n e n < « + -rate. Calculated from Equation (6) using e r r o r ^ ? ™ S p i r a t l 0 n B S e S ° r 1 ? l S t 1 0 R i l i t - r 0 , n T a b l e . I n ' 3 ' f o r Pos i t i ve and negative Bowen r a t i o s . Relative error in the available energy was 7% 6 > 0 Probable Maximum 3 < 0 Probable Maximum 0.66 7% 12% 12% 30% 0.66 10% 26% 38% 100% 0.97 8% 16% 226% 589% 1.32 8% 18% 34% 85% 1.32 21% 54% 145% 349% 2.06 11% 29% 26% 69% 3.96 15% 39% 24% 61% 3.96 54% 126% 90% 208% 5.0 42% 100% 63% 147% 6.6 30% 72% 41% 95% /"i 69 6H = [1 94 + 32]h = ± 15 W m~2 6H/H = ± 8% (48) The maximum relative error is ± 14%. /170 Table III.5. Probable and maximum relative errors in the sensible heat f lux. Calculated from equation (7) using errors in the Bowen ratio (B) from Table 111,3, for positive and negative Bowen rat ios. Relative error in the available energy was 7%. B B > 0 Probable Maximum B < 0 Probable Maximum 0.66 0.66 0.97 1.32 1.32 2.06 3.96 3.96 5.0 6.6 13% 8% 8% 17% 8% 8% 15% 11% 8% 14% 36% 16% 43% 17% 15% 26% 17% 56% 233% 25% 110% 14% 9% 42% 148% 607% 66% 266% 37% 21% 58% 35% 20% /171 3. CALCULATIONS FOR SILICON DIODES The appropriate values for calculating the probable and maximum errors in the estimation of evapotranspiration are given in Table III.6. Calculated error terms are l is ted in Table 111.7. 1. Temperature and Vapour Pressure  Diodes From (26) the probable error in the diode sensi t iv i ty is 6S d = [5.5 x 1 0 " 6 + 0.9 x I O ' 6 ] 5 * = ± 0.0025 mV ° C ~ 1 (49) and S S d / S d = ± 0.1% The maximum relative error is ± 0.2%. From (27) the absolute error in AT due to using a mean sensi t iv i ty for a diode pair matched to ± 0.1% is JT^ = 0.0005 °C f o r DT = 0.5 °C (50) From (30) and Table III.6 6V - 0.02 mV and 6Vm = 0.25 mV, thus 6V = 0.27 mV, and from (31) the probable error in an absolute temperature measurement is •4 l . ST = [10 " + 0.02 + 0.165] 2 + 0.3 = ± 0.73 °C (51) The maximum error is 0.86 C. /172 Table 111.6. Typical calibration and resolution data for s i l icon diodes, Symbols are defined in the text. (a) Diodes (T a - T b ) = 30 °C 6T = ± 0.01 °C (V a - V b) = 60 m V <5Vm = ± 0.05 mV (calibration) V = 650 mV 6V = ± 0.5 mV (measurement) o - l m S d = 2.0 mV C V p = 6.750 V 6 V p = ± 0.003 V 6Vp = ± 0.02 mV DT = 0.1 °C to 1.0 °C f T = ± 0.3 °C (b) Integrators S r = 166.7 counts L (mV 10 min)" 1 C i = 833.5 counts 6C = ± 1 count v = 5 m V 6VC = ± 0.005 mV f c = 0.1% (c) Temperature and Vapour Pressure Y = 0.066 kPa V 1 6Y = ± 0.002 kPa V 1 s., = 0.12 kPa ° C " 1 dsJdJ = ± 0.006 kPa ° C " 2 w at 15 °C w at 15 °C 6Z = 0.005 m Z = 3 m 6T = 0.0003 °C m"1 r = 0.01 °C m"1 (C, - C 9 ) = 200 counts (large AT) 1 L = 20 counts (small AT) AT = 0.03 °C/3 m to 0.3 °C/3 m L = 2465 J g " 1 at 15 °C e = 1.2 kPa /173 Integrators From (33) the probable calibration error of an integrator is 6S C = [0.04 + 0.028] = ± 0.26 counts. (mV 10 m i n ) " 1 and « S C / S C •= 0; 1 6% ( 5 2 ) The maximum relative error is 0.22%. During use, fQ equals the dr i f t in integrator sensi t iv i ty and is of the order .of ± 0.1%. Thus <5SC = ± 0.26 +. f c ± 0.43 counts (mV 10 min) -1 and 6 S C / S c = 1 °-26% ^53^ The maximum error is 0.32%. Temperature-. ~ The absolute probable error in AT is relat ively independent of the size of AT. The error in AG is mainly that in AT. Therefore, from (24) for AT = 0.3 °C <5A0 6AT = [9 x 1 0 " 6 +. 1 x. 1 0 " 7 + 6 x 10" 7 ] . ' s + 0.0005 ; = ± 0.004 °C (54) The maximum error is ± 0.005 C. Table III.?. Calculated probable and maximum absolute.and relative errors, fon s i l icon, diodes.". Symbols defined' in text. 6Sd (mV V 1 ) 6T ( ° C ) 6V (mV) 6SC (counts (mV 10 min) - 1 ) (6SC + f c ) 6AT<r ( ° C ) 6AT (°C) &~® ( ° C ) 6L (J g ' 1 ) 6s w (kPa ° C _ 1 ) Se (kPa) <5Ae (kPa) 6Ae0 (kPa) Probable Error absolute relative 0.0025 0.1% 0.78 0, 3 0.05% 0.26 0.2% 0.43 0.3% 0.0001 to. 0.001 0.004 0.004 1.8 0.1% 0.004 4%: 0.1.1 0.001 0.001 Maximum Error absolute relative 0.0047 0.2% 1.32 0.3 0.05% 0.37 0.2% 0.53 0.3% 0.0001 to 0.001 0.005 0.005 3.1 0.1% 0.005 5% 0.24 0.002 0.002 , /175 Vapour pressure From (22), for a large wet bulb depression (10 °C) 6e = [0.4 x 1 0 " 3 + 2.3 x 1 0 " 3 + 10 x l O - 3 ] ^ = 0 .1? kPa (55) and 6e m = 0.24 kPa max The dominant second two terms are independent of the size of the wet bulb depression, and &e is mainly dependent on the error in the measurement of wet bulb temperature. From (18) for large dry and wet bulb differences over 3 m, 0.3 °C and 0.25 °C respectively. 5AT = [ 1 0 " 6 + 6 x T O " 7 + T O " 7 + 0.1 x 10~ 7] ^ = ± 0.0013 kPa (56) The maximum error is ± 0.00^6 kPa. These errors do not change signi f icant ly for smaller gradients. From (15) the error in the corrected vapour pressure difference is (57) = .[-T.7-.-x 1 0 "6 + .4 x T O " 1 3 + 8 x T O " 1 0 ] ^ The last two terms in the above equation are negligible even for large vapour pressures. Thus <5Aeo ~. (SAe = ± 0.0013 kPa (58) /176 2. The Bowen Ratio Probable errors in the Bowen ratio for the s i l icon diodes are similar to those for the germanium diodes. Maximum relat ive errors are larger, because there is a larger maximum error in the vapour pressure difference measurement. The reader is referred to Table III.3 for the probable relative errors in the Bowen rat io. 3. Evapotranspiration and the Sensible Heat Flux Probable relative errors in evapotranspiration and the sensible heat flux for the s i l icon diodes are similar to those for the germanium diodes, Tables III.4 and III.5, respectively. Maximum errors are larger for the s i l i con diodes. The improved cal ibration accuracy of the s i l icon diodes (equation (54)) is offset by the poor accuracy in measuring the absolute temperature (equation (51)). The large error in T^ results in a large uncertainty in s^ (Table III.7) which in turn is the major error in AeQ (equations (56) to (58)). This error could best be reduced by constantly monitoring the absolute voltage of the diode to reduce f T (equations (31) and (51)). m i 4. , INTERPRETATION-OF THE ERROR ANALYSIS For 0 < 3 < 4 the evapotranspiration can be measured with a probable error of < ± 20%. If we consider a maximum error <20%, this-applies to 0 <<*-3 < 2. Small gradients (AG/AZ < 0.02 °C m"1 and A ? Q / A Z < 0.003 kPa m"1) result in s igni f icant ly larger errors. The sensible heat flux is estimated to within ± 10% (probable error) and to within ± 20% (maximum error) for 0 < 3 < 5. Again, small gradients result in a doubling of the error. The increasing sensible heat flux with increasing Bowen ratio offsets the effect of the increasing error in the Bowen ratio on the sensible heat f lux. The error in evapotranspiration is large for 3 < 0. This wil l be especially true at night when vapour pressure gradients are small. The error the sensible heat flux is also increased for 3 < 0. Errors in the available energy are signi f icant for most values of 3 and large gradients. It would be d i f f i c u l t to s igni f icant ly reduce this error due to the d i f f i cu l ty of determining (G + M) and in taking account of the spat ia l ; var iat ion -in net radiation. The contribution of the various components of 3 to the error in 3 depends on the size of 3 and the size of the gradients. It can be seen for equation ( 1 1 ) and (44) that decreasing AG and ~KeQ by^decreasing psychrometer separation would increase 63. For small 3,uncertainties in Y are as important as the accuracy of A9 and Ae Q (see equation (44),). As 3 increases or the gradients decrease then error in Ae Q predominates (see equations (45) and (46)). Contrary to the findings of Revfeim and Jordan (1976) errors in Y of (Jess than ± 5% are not important in determining Ae. The major sources .of error are in 7IT^  and 6s^. The former is through diode and integrator calibration and stabi l i ty errors (equation (39)). The latter is mainly due to errors in T^, the major one being the result of inadequate sampling to obtain the absolute wet bulb temperature (equation (36)). The major error in the measurement of a wet or dry bulb temper-ature difference (AT) is the ± 1 count resolution of the measurement system, (see equation (39) and the equation above i t ) . This error can only be reduced by increasing the integrator sensi t iv i ty /178 (see equation (24)). These equations also show that diode sensi t iv i ty matching and cal ibrat ion, and integrator calibration should be to better than ± 0.5%. This gives a combined error of < i 0.003 °C. A doubling of the count rate with the 0.5% limitation l is ted above would result in a probable error in SAT of ± 0.004 °C. Increasing the length of a counting period, i .e . increasing (C-j - Z^) in equation (24) or combining four count periods, i .e . {[(C-| - Z^) + (Cg - C^)]/2}, will increase the error in AT, because the f inal term <5A?V will be increased since DT (see d equation (24)) would be increased. 5. THE PROFILE BOWEN RATIO METHOD For the prof i le Bowen ratio method, Sincla ir et al. (1975) claim errors in measuring AG and Ae"o of ± 0.01 °C and ± 0.004 kPa, respectively for dif ferential measurements with thermopiles. McNeil and Shuttleworth (1975) were less optimistic about their measurements with platinum resistance thermometers. They suggest a measurement accuracy for absolute temperature of ± 0.01 °C and vapour pressure of up to ± 0.007 kPa for SAG .= ± 0.014 °C and SAe = ± 0.01 kPa. Table III.8, showing the errors o in 3 and E, was determined using the accuracy given by Sincla ir et al. and AG and Ae o in Table 1 1 1 . 3 . Comparing Tables 1 1 1 . 8 , 111. 3 and 111.4 shows the prof i le equipment gave errors in the Bowen ratio and evapotranspiration rate measurements of two to four times those of the reversing equipment. Furthermore, the prof i le method may s t i l l be subject to systematic errors. 6. CONCLUSIONS In theory, the Bowen ratio/energy balance method can be applied to forests to give measurements of evapotranspiration that have a probable error of < ± 20% for -0.5 < 3 < 4. Sensible heat fluxes can be measured to better than ± 10%, except when gradients are very small. The above statements are valid only i f the psychrometers are ver t ica l ly separated /T79 Table III.8". Probable relative errors in the Bowen ratio (63/3): and evapotranspiration (6E/E) for the prof i le Bowen ratio equipment of S inc la i r et al. (1975). Calculated for 3 > 0 and 3 < 0, and the temperature differences over 3 m in Table 3. Error in the available energy was 7%. 3 -> 0 3 < 0 3 (63/3) (6E/E) (6E/E) 0.66 14% 9% 28% 0.66 69% 28% 134% 0.97 24% 14% 776% 1.32 27% 17% 112% 1.32 134% 77% 553% 2.06 50% 34% 97% 3.96 67% 54% 90% 3.96 267% 213% 357% 5.0 200% 167% 250% 6.6 133% 116% 157% /180 by at least 3 m, the temperature sensors are matched and calibrated to within ± 0.5% and the measurement system (integrators) is calibrated and stable to within ± 0.5%. Furthermore, the measurement system must have a high resolution (integration at 1000 counts (m V h ) - 1 in this case). The dif ferential output of the dry or wet bulb pairs should be measured. A f inal requirement is that the sensors must be reversed between each integrating period so that the effects of systematic errors in the sensors are minimized. An accurate measurement o f -(.R - G - M) is also required. /181 2. ANALYSIS OF THE.EFFECT OF MISMATCHED DIODE SENSITIVITY ON THE MEASUREMENT OF A TEMPERATURE DIFFERENCE WITH.THE. .REVERSING PSYCHROMETER The cal ibrat ion equation for the germanium and s i l i con diodes is V = V Q - SdT (1) where V is the diode junction voltage (mV), VQ is the voltage at 0°C (mV).Syis the sensi t iv i ty (mV °C~ 1 ) and T is the temperature (0°C) . Two diodes, "a" and "b", at temperatures T-j and 1^, in positions 1 and 2, respectively, have diode junction voltages V -j = V Q a - S^T-j , and V|32 = Vg^ - S^T-,. The measurement system integrates the difference in output between the two diodes continuously over 10 minutes. This can be expressed as JO 10 10. 10 <Val- " V b2> d t = <V0a " V d t " Sda "0 0" Q-T T d t + S d * T-2dt (2) from which a 10 minute mean voltage difference is obtained as follows < Val " V b2. ' " <V0a " V0b> * < Sd, Tl " s d b T2> <3> where the overbars indicate mean values. When the psychrometer heads reverse, diode "a" goes to position 2 and diode "b" goes to position 1. 7182 The mean temperatures at levels 1 and 2 change to T^ and T^, respectively, for the second 10 minute period so that <V" Vbl> " <V0a- " V0b» " (SdaT4 ' SdbV (4> Subtracting (4) from (3) gives 2 f l • <SdaT4 " %S T3> " ( S d a T l " SdbT2> ( 5 ) where 2A = (V-,1 " Vb2^ " ( v a2 " VBx) • I f 6 V S t h e deviation of each diode from the mean s e n s i t i v i t y , S d,so that S^^= SS^and S^= S^- 6S then (5) becomes 2A =S d(2AT) +5S^(T3 + T 4 ) - {T} + T 2 ) J • (6) where AT is the average temperature difference over the two 10 minute periods, i.e. AT = i ( T 4 - T 3 ) + (T 2. - Ty)j;/2 (7) The second term on the right-hand side of (6) can be written as 2 5 S d ( T n - Tjj = 26S dDT (8) /183 where DT is the difference between the mean a i r temperature of the two 10 minute periods, Tj and T J J , respectively. Substituting (8) into (.6) and solving f o r AT gives AT = (A - 6S dDT)/S d (9) If Tj = Tj j , o r 8S^= 0 ( i . e . S^= , then (8) equals zero and AT i s given by AT = A/S d (10) If Tj f T J J and S S ^ 0 then-the absolute error in estimating AT from (10) rather than (9) i s fi^DT/Sj, obtained by subtracting (9) from (10). The r e l a t i v e error in AT (£) i s 5 = 5S dDT/(S dAT) (11) with AT from (9). Thus, the accuracy of the measurement of the tempera-ture difference depends on how well the diode s e n s i t i v i t i e s are matched and the change in mean a i r temperature between the two sampling periods. The sign of 6SdDT/Sd depends on the direction of this change, with (TO) overestimating AT when mean a i r temperature i s increasing with time, i.e. DT > 0. Values of 5 S d / S d °f 1% and 0.1% represent poor and good sensor matching, respectively. The rati o |Df/AT| varies from 0.1 to 10 during /184 tHe day- A value of 4 is typical of daytime conditions so that 5 = ± 4% and ± 0.4% for the poorly and well matched pairs of diodes, respectively. Equation (9) can be used to give AT i f DT can be obtained with reasonable accuracy. However, there will be an error in obtaining DT due to sensor and measurement l imitat ions. Integration of the diode voltage, even with the voltage offset to allow an increase in integrator sensi t iv i ty , would result in a measurement uncertainty in Df of 0.05 to 0.1°C. In general, DT varies from 0.1 to 2.0°C over 30 minutes, so that the relative error in measuring DT varies from 100 to 3%. If DT is large and the sensors are not well matched then AT should be corrected. However, matching of the diode sensi t iv i t ies is the best way to keep the error in AT as small as possible. /185 3. SYSTEMATIC MEASUREMENT ERRORS IN THE REVERSING PSYCHROMETER Systematic measurement errors are relat ively constant over time. They may result in an incorrect temperature difference measurement by a diode pair. These errors may be caused by an intercept error in the cal ibration equation as a result of an incorrect ca l ibrat ion, e lectr ical effects in the monitoring system, e.g. extra resistance in the curcuit , or modifications of the energy balance of the diode, e.g. heat conduction along the diode mounting stem. Thus, the diode temperature wil l be the sum of the true a i r temperature and an offset or error. The average a i r temperature difference measured by a sensor pair for the 10 minute period before reversal of the sensing heads is A TI = < Tal + £ a l > " <Tb2 + £b2> ( ] ) and for the period after reversal , ^ 1 1 = <Ta2 + ea2> " < Tbl + £ b l > ( 2> In (1) and (2) T and e indicate the true mean a ir temperature and the error, respectively, and the subscripts indicate diodes "a" and "b" and levels 1 and 2. Subtracting (2) from (1) and rearranging gives A TI " A T I I = ^ T a l + T b l > " ( T a 2 + Tb2> + ( e a l + e b l } " u a 2 + £ b 2 } = 2AT + ( e r r o r terms) (3) / 1 8 6 so that the true ayerage temperature difference (AT) i s given by AT = (AT T - A T t t ; / 2 - ( e r r o r terms)/2 ,4) The true temperature difference i s obtained only i f { £ a l + £ b l } = ( e a 2 + eb2> There are two ways in which this i s expected to occur for systematic errors: Case 1 e a l = and e f a l = e b 2 (6) Case 2 e a l = and e a 2 = (7) Symmetric Errors Case 1 and Case 2 are examples of the cancelling of systematic errors. In Case 1 the error i s unique to a sensor and i s independent of the position of the sensing head, e.g. a ca l i b r a t i o n intercept error. In Case 2 the same error occurs on both sensors of a sensor pair at the same time. For example, the sensing heads are constructed symmetrical so that each has the same geometrical arrangement in space at the same time, i.e. sensing head "a" in position 1 has the same orientation with respect to the sun as sensing head "b" in position 2. Since any error /187 should be the same for both sensors of a pair of sensors, these symmetric errors cancel and the true temperature difference obtains. Non-symmetric Errors Position dependent errors are non-symmetric errors. The non-symmetric geometrical arrangement of the sensors in space shown in Figure I I I . l would cause such an error. For example, the radiational heating Of the lead'wires *• on a head only occurs in the lower position .position l ) , so that Case I i s obviously violated. Furthermore, the equality in Case 2 cannot be f u i l f i l l e d since the error for sensor "a" in position 1 must be different from that for sensor "b" in position 2. Various combinations of values for the error terms could f u l l f i l l (5). However, this i s unlikely to occur since tne general symmetry of sensing head construction usually results in the error being similar for both heads in the same position, i.e. e , - e . , and - e.0 with e , f e , 0 , r al bl a2 b2 al a2 as i s shown in Figure I l i . l . Thus, when.non-symmetric errors; occur, the true temperature difference i s not measured. /188 FIGURE 111,1; Non-symmetrical geometrical arrangement of the sensing heads fn space, The lower head is in position 1 and the upper head is in position 2. /189 4. COMPARISON OF REVERSING PSYCHROMETERS  IN THE LABORATORY AND THE FIELD Introduction The non-cancelling of non-symmetric errors was noted ear l ier in this Appendix (III.3). Identifying these errors and determining their effect on the measured temperature difference is d i f f i c u l t since i t is not feasible to have an exact measure of the true difference. Indirect methods are required from which the accuracy of the measurement can be inferred. For example, in Appendices I and II the sensible heat and latent heat fluxes are determined by other methods and compared with those determined by a Bowen ratio system with reversing psychrometers. Agreement between the methods is good, suggesting that i f non-cancelling errors are present they are not a major source of error. Another approach is to compare various Bowen ratio systems. ' Identical ' systems would be expected to have similar errors, and which system is in error, i f any., cannot be ident i f ied. However, the agreement, or lack of i t , between identical systems can indicate the repeatability of these systems. Comparisons between different systems may help delineate possible errors. This Appendix presents laboratory and f ie ld comparisons of Bowen ratio systems. Two systems (BRM1 and BRM2), with 26 mm I.D. stainless steel sensor housings (heads) and germanium diode sensors (Black and McNaughton, 1971) are compared with each other and with a system (BRM3) that has /190 20.9 mm I.D. polyvinyl chloride (P.V.C.) heads and s i l icon diode sensors (Kalanda et al., 1980). The s i l icon diode system (Figure III.2) is further different from the germanium diode systems in respect to reservoir orientation and construction, placement of the lead wires on the heads and longer, sensor mount, 40 mm as compared to 22 mm. A laboratory comparison of two other s i l icon diode systems (BRM4 and BRM5) is also br ief ly reported. Methods The Bowen ratio method using reversing psychrometers is described in Black and NcNaughton (1971) and Spittlehouse and Black (1980) (Appendix II). In the laboratory tests*.vertical separation of the heads was 1 m and the reversing systems were located with head intakes as close as possible to each other. The locations of the reversing systems were exchanged occasionally to allow for spatial variation in vertical temperature gradients in the room. The f i e ld experiment was performed at the U.B.C. Research Forest, Haney, B .C . , from August 3 to 11, 1977. The reversing systems were placed at 17.7 m above the ground, over a Douglas-fir stand (trees 13-16 m high), with the inlets facing south-east. Vertical separation of the heads was 3 m, and the horizontal separation of each pair of systems compared was 2.5 m. During this experiment the sky was c lear , with the wind from east to south-west during the daytime and from north-west to north-east during the night. Fetch was FIGURE III.2: A silicon diode sensing head. Diodes and wires are thinly coated in electrical resin (3M, Scotcast No. 10) for protection. /192 adequate for these wind directions (Spittlehouse and Black, 1979, see Appendix I). The system output consisted of 10 minute integrated voltages proportional to the difference in temperature between two levels. Two 10 minute values were obtained each half hour and used to give an average temperature difference (AT) for that half hour (see sections 1, 2 and 3 of this Appendix). The analysis was performed on these half hourly averages. The analysis of the calibration and measurement errors (section 1 of this Appendix) shows that these errors combined cause a probable error in AT of + 0.005°C for the germanium and the s i l icon sensors. Thus, only data where the measurement and calibration errors were less than 10% of AT, i .e . large temperature gradients, are considered, so that any signif icant non-cancelling errors should be apparent. Jhe results are presented as ratios of temperature differences, with a value of 1 indicating complete agreement. In general, dry bulb differences (ATD) are from 0.15 to 0.6°C and wet bulb differences (AT^) are from 0.1 to 0.3°C for measurement relative errors of <4% and <6%,. respectively. Thus, the respective difference ratios deviating from 1 by over 8 and 12% indicate the .presence of non-cancelling errors. The results are presented as averages of a number of data points (n) and their standard deviation. Comparisons between systems are generally in the form of the ratios of measured dry bulb differences (RATn) and the wet bulb, differences (RATU) and the ratio of these two /193 ratios (RRAT). This last rat io is the ratio of the values of ATg/AT,^ for each system. The value of AT^/AT^ can be taken as a measure of the agreement between systems in determining the Bowen ratio (3), assuming the adiabatic correction (r=0.01°C m~^ ) is small compared to A T D , since 3~ (C(s + Y ^ ^ Y Z n p J - l } " 1 . The ratio RRAT is calcu-lated for each measurement period. Thus the mean value of RRAT for a number of periods may'be different from the value of RRAT calculated from the mean RAT^ and RAT^ values. The f ie ld data used in this analysis are stored on f i l e s HY77C0MMENTS and HY77DATA of tape RA0925. ' Results and Discussion The wet and dry bulb pairs within a single system are compared in Table III.9. Agreement is generally to within 7%, about the l imit of thejrieasurement error. However, there is a trend for the wicked sensor to s l ight ly underestimate AT when dry for systems 1, 2 and 3. Table II1.10 indicates good agreement between dry bulb sensors in different systems and between dry wet bulb sensors in different systems. Agreement between systems with the wet bulb wetted is generally within the limits of the measurement accuracy (Table I I I . l l ) . Disagreement is by only 0.01 to- 0.02°C. This appears to be part ia l ly due to horizontal var iab i l i ty , since reversing locations of the systems changed the rat ios. Even connecting the intakes of adjacent /194 TABLE 111.9: Laboratory comparison of dry and Wet bulbs either both dry or both wet (BRM4 only) usin2_the_ratio of the dry and wet bulb differences (AT^/AT^). System A T D / A T W BRM1 1 .07 + 0. .03 5 1 .06 + 0. .02 3 BRM2 1. .06 + 0. .02 5 BRM3 1 .06 + 0. ,01 3 BRM4 1, .01 + 0. ,04 8 + 1 . .02 + 0. ,01 4 >' .98 + 0. ,01 10 $0. .97 + 0. ,03 4 dry bulbs also wicked *no wicks on either sensor Sboth sensors with wet wicks TABLE III.10: Laboratory comparison of Bowen ratio systems with both dry and wet bulbs d,ry. See text for explan-ation of symbols. Comparison RAT W RAT D RRAT BRM2/BRM1 BRM3/BRM1 0.98 ± 0.02 0.99 ± 0.03 0.99 ± 0.03 5 1.03+0.07 1.03 ± 0 . 0 7 0.99 ± 0.01 3 /195 TABLE III.11: Laboratory comparison of Bowen ratio;, systems with Wet bulbs wet. See text for explanation of symbols. Comparison RATn RAT,, RRAT BRM2/BRM1+ 1 .07 + 0, .02 1 .05 + 0, ,02 1 .02 + 0, .03 6 1 .00 + 0. ,03 0 .93 + 0. ,04 1 .08 + 0, .03 6 BRM3/BRM1+ 0 .87 + 0. ,04 0 .88 + 0. ,05 0 .98 + 0. .04 11 1 .04 + 0. ,03 1, .02 + 0. ,03 1 .02 + 0. .03 11 BRM3/BRM1* 1, .10 + 0. 04 1, .06 + 0. 03 1. .04 + 0. ,01 6 1. .06 + 0. 02 1, .05 + 0. 02 1, .01 + 0. ,01 4 BKM4/BRM5 0. ,97 0. 02 1. ,00 + 0. 07 0. ,98 + 0. 05 24 1, 03 + 0. 02 1. 02 + 0. 02 1. ,01 + 0. 02 24 locations of systems were interchanged *intakes of both systems at a level were connected by a tee /196 heads with a tee did not produce complete agreement. However, both the dry and the wet bulbs appear to be affected in the same way so that the AT D /AT W ratios are s imi lar , i .e . *RRAT-l . The laboratory data show that agreement between systems is generally within ±10% for AT and within ±5% for 3. Half hourly ratios for a typical sample of the f i e ld data are shown in Table 111.12. There are systematic differences between systems in AT of up to 50%. However, there is a similar proportional difference on the dry and wet bulb so that RRAT is generally within ±10% of 1. The systematic change in AT^ and AT^ with time suggest that the non-cancelling errors may be caused by solar radiation heating of the heads. The f i e ld data were divided into three periods corresponding to the nighttime, morning and afternoon (Table III.13). During the nighttime there was no solar heating of the heads so that this data could be taken as the base l ine for agreement between systems, allowing for spatial and system var iab i l i ty and net longwave loss. The agree-ment is not quite as good as in the laboratory, though, i t is generally within ±10%, with a greater standard deviation in the f i e ld data. The daytime data indicate the presence of non-cancelling errors. In general,BRM1 overestimated AT, with respect to BRM3, in the morning and afternoon while BRM2 underestimated AT, : with respect to BRM3, in the morning only. BRM3 is chosen as-a basis for the comparison since i t has better symmetry in i ts head construction and; orientation and longer sensor mounts than BRM1 and BRM2. TABLE I I I . 12: Half hourly ATrj and ATw f i e l d data for BRMl and BRM2.-;* Ratios;o.f ATrj, ATW and RRAT are BRM2/BRM1, 5.August 1977. See text for explanation of symbols. BRMl BRM2 Time AT0 (°C) ATW (°c) AT D/AT W ATD-(°c) ATu (°c) ATD/ATW RATD RATW RRAT 0900 0.214 0.169 1 .27 0.197 0.134 1.47 0.92 0.79 1.16 0930 0.165 0.132 1.25 0.121 0.089 1.36 0.73 0.67 1.09 1000 0.20/ 0.154 1.34 0.116 " 0.086 1.35 0.56 0.56 1.00 1030 0.^76 0.172 1.60 0.192 0.131 1.47 0.70 0.76 0.91 1100 0.253 0.164 1.54 0.134 0.095 1.41 0.53 0.58 0.91 1130 0.20^ 0.146 1.33 0. 170 0.123 1.38 0.84 0.84 1 .00 1200 0.265 0.213 1 .24 U.266 0.195 1.36 1.00 0.9Z 1 .09 1230 0.207 0.152 1.36 0.T85 0.130 1.42 0.89 0.86 1.04 TABLE I I I . 1 3 : Field comparison of Bowen ratio; Systems, 3 to 11 August 1977. Times are PST. The f i r s t number in n is for RAT§ and.the Second number is n for 'RATu and RRAT. See text for explanation of symbols. Nighttime Daytime  2000 - 0600 0900 - 1200 1230 - 1600 Comparison RAT D RAT W RRAT n. R A T 0 RAT W RRAT n R A T D R A T W RRAT ri, BRM2/BRM1 0, .90 0 .89 1, .02 33 0, .76 0. .74 1 .03 14 0, .9.3 0, .92 1 .01 10 ±0, .04 ±0 .05 ±0. .04 11 ±0, .13 ±0. .13 ±0 .13 14 ±0. .09 ±0. .09 ±0 .03 10 BRM3/BRM1 0. .91 No data 19 1. .00 0. .81 1, .25 6 0. ,85 0. ,84 1, .03 8 ±0. .06 0 ±0. .09 ±0. ,12 ±0, .10 6 ±0. ,10 ±0. 16 ±0, .18 8 BRM3/BRM2 1. .00 0 .97 1. 07 25 1. .39 1. 22 1. .10 8 0. .99 0. 97 1. ,02 7 ±0. 08 ±0, .07 ±0 . 10 10 ±0. .15 ±0. .10 ±0. ,08 5 ±0. 21 ±0. 12 ±0. ,14 7 00 /199 The heads of BRM1 have the asymmetric lead wire arrangement shown previously in Figure I I I . l , while BRM2 has these wires in the reverse position to BRM1. The hypothesis is that solar radiational heating of the lead wires results in heat transfer down the wires to the diodes. 1 In BRM2 this occurs on the upper head where i t could enhance the diode temperature resulting in an underestimation of the daytime temperature lapse. In BRM1 heating would occur on the lower head where an enhanced diode temperature would cause an overestimating of the daytime temperature lapse. The opposite, but much reduced, effect would occur at night due to longwave cooling. The data in Table III. 13 are not completely in agreement with the above hypothesis in that RATQ for the BRM3/BRM1 comparison in,the morning is.higher than might be expected. As with the laboratory data, the dry and wet bulbs of a head appear to be influenced in the same proportion so that ATp/AT^ remains relat ively constant between systems, i .e . RRAT-T to within ±10%. Conclusions Laboratory tests show that good agreement can be obtained in measurements of AT between dry and wet bulbs of the same Bowen ratio system and between systems. The agreement is generally within the l imits imposed by measurement and calibration errors, i .e . an error of <±10%. Even in the f ie ld where there may be signif icant horizontal variat ion, nighttime comparisons between machines were generally within ±10%. However, during the daytime the systems could disagree in the measurement of a temperature difference by up to 50%. It is /200 hypothesized that solar radiational heating of the lead wires on the heads of BRMl and BRM2 caused a position dependant error in the temperature measurement. This was due to a lack of symmetry in the orientation of the heads with respect to one another (Figure III.l) resulting in heat transfer down the lead wires to the diodes. Further, since this is occurring on both the dry and wet bulbs i t tends to be self cancelling in the calculation of the Bowen rat io , since B ^ A T ^ / A T ^ Therefore, the error in B is generally within ±10% for AT>0.05°C, and results in a small enhancement of the measurement and calibration errors. /201 5. LABORATORY EXPERIMENT TO DETERMINE THE INFLUENCE OF  EXTERNAL RADIATION ON THE TEMPERATURE OF THE  REVERSING PSYCHROMETER HEADS It was hypothesized in the previous section that solar radiational heating of the lead wires on a sensing head could cause an error in the measurement of AT. Measurements in the laboratory with the reversing system heads illuminated with 150 W lamps were inconclusive. This was due to the d i f f i cu l ty in obtaining equal heating of both heads and warming of the a i r being sampled by the unheated control. Consequently, the problem was investigated by constructing a model head from material similar to that of BRMl and BRM2 (Figure 111.3). The head was aspirated at 3.5 m s - 1 with a vacuum pump. In order to simulate solar radiation and wind, the head was illuminated with a 150 W lamp to produce a shortwave beam irradiance of 900 W m at the head and ventilated externally with a fan at about 3 m s~^. The temperature difference between various points on the head and the sampled a i r was measured with thermocouples. The presence of the external sh ie ld , as shown in Figure H I . 3 , is equivalent to the exposure of the lead wire to radiation i l lustrated by the upper head in Figure I I I . l . The absence of the shield is equivalent to the exposure to radiation i l lustrated by the lower head in Figure I I I . l . The data in Tables 111.14 and 111.15 i l lust ra te that, with illumination and external vent i lat ion, the lead wires were 0.8 to 0.9°C and 1.3 to 1.4°C above a i r temperature, with or without shei lding, L A M P FAN E X T E R N A L SHIELD L L E A D WIRE ® MYLAR TAPE -INSULATION - M E T A L T U B E AIR TEMPERATURE ASPIRATION = 2 0 mm (x)= T H E R M O C O U P L E JUNCTION FIGURE III.3: Experimental arrangement to determine the influence of external radiation and ventilation on sensing head temperature. r o o r o /203 TABLE III.14: Effect of radiat ion, external ventilation (3 ni s~ ) and radiation shielding on lead wire (position A) and diode (position D) temperature. The head is aspirated at 3.5 m s ~ l . Temperature differences are ±0.1°C and are (Tx - Tr;) , where the subscript X indicates the location (Figure III.3) of the measurement and Trr is the temperature of the a ir entering the sensing head. Treatment (TX - T E ) °C Rad. Ext. Vent. Shield Wire (A) Diode (D) off off off -0.1 -0.3 on off off +5.0 +0.5 on off on +3.9 +0.5 on on off +1.3 +0.1 on on on +0.9 0 off on on -0.2 -0.2 /204 TABLE III.15: Effect of radiation on head temperature (letters indicate the positions shown in Figure III.3) with the head externally ventilated at 3 m s~l and aspirated at 3.5 m s - l . Temperature differences are ±0 .01°C and are (Tx - T E ) , where the subscript X indicates the location of the measurement and TE is the temperature of the a ir entering the head. Treatment (Tx - TE ) ° C  Rad. Shield Wire (A.) Insulation ( B ) Tube ( C ) Diode (D) off on -0.3 0 -0.1 -0.2 on off +1.4 +0.5 +0.5 0 on on +0.8 +0.1 +0.1 0 l ight on the opposite side of the head to the lead wire -0.5 +0.1 +0.1 -0.2 off on -0.8 -0.2 -0.1 -0.7 /205 respectively. Simi lar ly , the insulation and metal tube were warmer than the a i r . There were signif icant temperature gradients (0.02 to 0.03°C per mm of stem distance) between the diode and position A in shielded and unshielded conditions (the distance between A and D was about 40 mm;. Thus, heat would flow towards, the'diode, Without i l lumination, the diode was below air temperature, while with illumination the diode temperature increased to a ir temperature or just above air temperature. The increase in diode temperature was small and was near the measurement accuracy of the experiment. However, an increase in diode temperature of only 0.05°C would have been required to cause the differences noted in the f i e ld measurements of AT by BRM1 and BRM2. Figure III.l i l lustrates the sensor arrangement of BRM1, while the sensor positions should be exchanged for BRM2. Thus, i t would appear that heating of the lead wires on the sensing heads of systems BRMI and BRM2 could have occurred in the f i e l d , and this could have resulted in signif icant heat flow down diode support stems so that BKM1 would give an enhanced AT and BRM2 would give a reduced AT during the daytime (lapse conditions). /206 APPENDIX IV. DATA COLLECTION AND ANALYSIS FOR THE THINNED STAND IN 1978 AND 1979 1. SITE DESCRIPTION The si te is on a NE slope (< 10%), about 150 m above sea l e v e l , 49° 51' N, 125° 14' W. 1. Soil Soil Prof i le The soil prof i le is quite variable. About 1% of the area consists of rock outcrops, 5% with soil depth < 0.4 m and > 50% coarse fragments, 50% with soi l depth 0.4 to 0.6 m and 20 to 50% coarse fragments and 44% with soi l depth 0.6 to 1.1 m and < 20% coarse fragments. The soi l is an Orthic Humo-Ferric Podzol and the brief description in Table IV.1 is for a typical deep prof i le (modified from Goldstein, 1980). The shallower profi les have smaller Bf and C horizons. Bulk Density and Coarse Fragment Content Bulk density data for the soi l were obtained for 0.25 x 0.25 x 0.1 m deep sections of the prof i le . Volume of soi l was obtained by l in ing the holes with a plast ic bag and f i l l i n g with water. The soil samples were dried and seived to separate out the < 2 mm fract ion. Bulk density (total dry weight of a l l solids divided by total volume) _3 was estimated to be accurate to ± 50 kg m . Six locations were /207 TABLE IV.1: Soil prof i le description for the thinned s i t e , Courtenay, B.C. Horizon Depth (mm) Description LFH 20 - 0 Ah 0 - 4 0 Very dark grayish brown (10YR 3/2 m). Sandy loam. Weak subangular blocky structure. Clear boundary. Abundant roots, f ine to coarse. Ae 40 - 70 Light gray (10YR 7/1 m). Sandy loam. weak subangular blocky structure. Gradual boundary. Plentiful roots, fine to coarse. Bfh 70 - 150 Yellowish red (5YR 4/5 m). Sandy loam. Fine single-grain structure. Clear boundary. Few roots. Bf ' 150 - 680 Dark grayish brown (7.5YR 4/4 m). Sandy loam. Fine single-grain structure. Gradual boundary. Few roots, fine to medium. C 680 - 930 Dark brownish yellow (10YR 4/4 m). Loam. Fine single-grain structure. Sandstone bedrock with a fine root mat forms boundary. Few roots, f ine. /208 TABLE IV.2: Bulk density (kg _3 m ), thinned s i t e , Courtenay, B.C. Location Depth (m) 1 2 3 + 4 5 6 0-0.1 770 1230 890 810 1160 1260 0.1-0.2 1010 1760 1170 1090 1420 0.2-0.3 1030 1190 880 1500 0.3-0.4 1360 1130 1120 1200 0.4-0.5 1520 1280 1320 1440 0.5-0.6 T500 1320 0.6-0.7 1420 0.7-0.8 1240 Values si m i l a r to those at location 3, a deep sandy s i t e , were obtained by Goldstein (1980) in an area 50 m NE of the main s i t e . /209 TABLE IV-3: Volume fraction (%) occupied by > 2 mm f r a c t i o n , thinned s i t e , Courtenay, B.C. Location Depth (m) 1 2 3 4 5 6 0-0.1 4 42 6 18 30 44 0.1-0.2 6 62 12 31 47 0.2-0.3 13 14 16 44 0.3-0.4 31 11 17 39 0.4-0.5 39 12 12 51 0.5-0.6 46 8 0.6-0.7 5 0.7-0.8 3 /210 sampled to bedrock (Table I V . 2 ) . Coarse fragment (> 2 mm) content i s l i s t e d i n Tab le I V . 3 . The d e n s i t y o f these sandstone fragments was obta ined by coa t i ng them i n wax and weighing i n water (2170 ± - 3 -3 50 kg m , n = 8) and by vacuum s a t u r a t i o n (2190 ± 70 kg m , n = 7 ) . _3 The average i s 2180 ± 60 kg m which imp l i es a p o r o s i t y o f 18% s i nce the p a r t i c a l d e n s i t y o f the sandy.by vacuum s a t u r a t i o n , was 2660 ± 20 kg m~ S o i l Water Reten t ion C h a r a c t e r i s t i c s The data were ob ta ined w i th f i v e tens iometers and a s i n g l e neutron access tube l oca ted next to the tens iomete rs . Hygrometers were not used i n determin ing the f i e l d r e t e n t i o n c h a r a c t e r i s t i c s s i n c e they were l o c a t e d some d i s t a n c e from t h i s tube and the data had a l a rge variability. The data were f i t t e d to tym = ^ m r (9/0 r )" m (Campbel l , 1974a;Clapp and Hornberger , 1978). The c o e f f i c i e n t s are l i s t e d i n 3 - 3 Table IV.4 f o r 0 r = 0 .3 m m and a coarse fragment content o f about 15% by volume. The average i>m{9) c h a r a c t e r i s t i c shown in F igure IV,1 was obta ined by averag ing m and tymr f o r each depth. F igure IV.2 compares t h i s f u n c t i o n from tens iometer data w i th the hygrometer d a t a , tym < -0.01 MPa. F igure IV .3 compares the average ^m(8) c h a r a c t e r i s t i c w i th l a b o r a t o r y r e t e n t i o n data f o r und is turbed cores ( G o l d s t e i n , 1980). The s lope o f the l a b o r a t o r y data i s s i m i l a r to tha t from the f i e l d d a t a , but ,due to lower coarse fragment content (< 5% by vo lume) , 8^  i s h igher f o r the same ty . /211 TABLE IV.4: Coefficients for the f ie ld retention function, tym = tymr{Q/Qr)~m for four depths from tensiometer and neutron moisture probe measurements, thinned s i t e , Courtenay, B .C . , 1978. Correlation coeff icient (r^) and number of data (n) indicated. Values of 9 are for a coarse fragment content of about 15% by volume The value of 9 r is 0.3 m_3. Depth (m) m (kPa) r 2 n 0.3 5.59 -1.2 0.899 18 0.45 6.20 -0.3 0.909 16 0.6 5.68 -0.9 0.728 17 0.7 6.01 -1.3 0.684 17 Average 5.9 -0.9 /212 1 1 1 1 FIGURE IV.1: Thinned site, field retention charac-terist ic, 1978, > 2 mm fragments about 15% by volume. Data from tensiometer-s and neutron probe. /213 FIGURE IV.2: As for Figure IV.1 for tym > -0.1 MPa, hygrometer data for tym < -0.1 MPa. Line from Figure. IV. 1. -1.0 /214 1978 \ FIELD DATA o CL - 0 . -0 .05 1979 LAB. DATA \ V o Depth (m) 0.07 0.30 0.60 0.90 \ \ -0.01 1 0.1 0.2 0.3 0 (m 3 m"3) FIGURE IV.3: Thinned Si te , laboratory determined retention data, 1979 (from Goldstein, 1980). Dashed l ine is from Figure IV.1. /215 Hydraulic Conductivity Characteristics Data for k s a t and for u>m < -10 kPa are from Nnyamah and Black (1977) and Nnyamah (1977), (sol id c i rc les in Figure IV.4). The data between these points, given in the two references, are unreasonably low, probably due to measurement error. Consequently, k in the wet range was obtained for an undisturbed core from the 0.3 m depth using the steady state measurement technique (Plamondon, 1972). The values were 99 mm d~^ at -1.5 kPa and 140 mm d - 1 at -1.4 kPa and are shown as sol id triangles in Figure IV.4. The dashed l ine is an eye f i t to the data. The sol id l ine was obtained from the exponent of the average tym(Q) characteristic following Campbell (1974a), and has a slope equal to 2 + (3/m). A k(6j character ist ics, k = k - r ( G / 0 r ) ^ 3 + 2 m ^ (Campbell, :1974a), with 3 -3 k r from the above laboratory experiment and 6 r = 0.3 m m (equivalent to a 15% stone content), is shown in Figure IV.5. Drainage Versus Root Zone Average Water Content Relationship This relationship was obtained from f ie ld measurements in August and September 1978. Daily tensiometer measurements (set no. 1) of ^ m were converted to 8 using the average ^ ( 8 ) character ist ic. These values of 0 were converted to storage, summed over the prof i le to give W and then divided by prof i le depth to give 8. Daily evapotranspiration was obtained from the relationship ( E ' = a E ^ + g l ) , since 8 did not l imit E. Daily drainage was obtained as the residual term in D = AW + P - E . Due to the var iab i l i ty of the data and the errors /216 10* 10' 10 k ( mm d"1) 10" COURTENAY GRAVELLY SANDY LOAM (0-0.4m DEPTH) 10" -I0"1 -10° ^ k - 100 ( - l .5 /Y m ) J -10 -10 2 - IO 3 - IO 4 V M (kPa) FIGURE IV.4: Hydraulic conductivity (k) characteristic for the thinned and unthinned sites, 0-0.4 m. 0.22 0.24 0 (m3m~3) 0.26 0.28 FIGURE IV.5: Drainage versus storage relationship, thinned site, 1978. Curve represents the average k(9) characteristic. /218 associated with this approach, the average D for a two day period was usually calculated and 0 taken as the average of these days for purposes of plotting the D(6) relationship (Figure IV.5). The curve shown in Figure IV.5 is the k(6) characteristic described previously. If there is unity gradient drainage D(0) can be approximated by the k(0) characterist ic. Since-gradients, become less than unity as drainage proceeds the k(0) characteristic s l ight ly overestimates drainage as. ©-.decreases. 2. Vegetation The trees are Douglas-fir {pseudotsuga menziesii (Mirb.) Franco). The understory is mainly salal {oauitheria shaiion Pursh). Other species such as vani l la leaf [Achiys triphyiia (Smith) DC), Oregon grape [Mahonia sp.) and bracken [Pteridium aquilinum (L.) Kuhn) account for less than 6%, projected leaf area basis, of the under-story leaf area. Tree Diameter at Breast Height (D.B.H.) The D.B.H. distr ibution was determined in early August, 1978 for a 25 x 35 m plot , containing 72 l ive trees (Table IV.5) and one dead tree. Trunk water storage was probably at a minimum since this was the driest part of the year. The stand density was 822 stems h a ~ \ and the original thinning was to approximately 840 stems ha"^, equivalent to 74 trees in the sample block. TABLE IV.5: D.B.H. class frequencies, thinned s i t e , August 1978, for a 25 x 35 m plot. Size class^ (mm) No. trees Frequency % 64-<80 1 1.4 80-<95 5 6.9 95-<lll 7 9.7 111-<127 21 29.2 127-<143 16 22.2 143-<159 7 9.7 159-<175 10 13.9 175-<191 1 1 .4 191-<207 3 4.2 207-<223 1 1 .4 Total 72 Originally as circumference at breast height. 7220 Penetrometers: Seven trees were monitored with dendrometers through 1978 and 1979. Actual tree D.B.H. and dendrometer reading in May 1978 and 1980 are indicated in Table IV.6. The data are presented as the average change in stem area at breast height (AM) since May 1978, (Figure IV.6). Leaf Area Index Douglas-fir: The LAI was determined for four trees in August 1978 (Table IV.7). An average branch from each whorl was removed and the needles stripped, dried and weighed. On every f i f th or sixth whorl the current years foliage was separated out before drying. Leaf area to weight ratios,on a projected area basis ( C S . Tan, unpublished data), 2 -1 were used to give the leaf area of the sample branch; 4.7 ± 0.3 m kg 2 -1 for the upper half of the tree, 5.4 ± 0.2 m kg for the lower half. The leaf areas are on a projected area basis since the r -characteristics are on this basis. Branch leaf area was multiplied by the number of branches per whorl and the whorl areas summed to give total leaf area for the tree. Gholz et al. (1976) indicate that actual one-sided leaf area for Douglas-fir is about 18% greater than projected leaf area. Allowing for th is , the leaf area to weight ratios presented above are about 20% lower than those presented by 2 -1 Gholz et al. for Douglas-fir in Oregon; values of 7.53 ± 1.05 m kg 2 -1 for a l l foliage and 8.49 ± 0.95 m kg for new foliage. Projected tree leaf area (LA) is plotted against D.B.H. in Figure IV.7. The data agree well with those obtained by Tan et al. TABLE IV.6: D.B.H. D.B.H. and dendrometer band readings (Dendr.) in 1978, 1979 (AD.B.H.) i s from 5 May, 1978 to 6 May, 1980. and 1980. The change in Tree 5 May 1978 Dendr. D.B.H (mm) 12 May 1979 Dendr. 6 May 1980 Dendr. D.B.H. (mm) AD.B.H. (mm) 10 21.0 134 27.6 34.1 160 26 12 22.8 139 27.7 33.3 165 26 28 21.8 132 26.6 33.4 157 25 32 16.0 121 18.8 20.6 142 21 38 20.1 117 26.6 32.8 140 23 39 33.1 180 39.7 48.9 211 31 52 23.4 132 27.8 32.5 155 22 ro ro 7222 J A 1978 0 M A M 1980 FIGURE IV.6: Mean percentage increase per tree in stem area at breast height (ABA) since May 1978 at the thinned site. Bars indicating standard deviation of the mean are not shown on all points. Also shown is the root zone average water content (6). 7223 TABLE IV.7: Douglas-fir tree leaf area (LA), thinned stand, August, 1978. Height i s where whorls joined the trunk. Tree 30 D.B.H.(mm) 138 37-2 97 80 166 37-1 118 Height LA m m2 Height m LA m2 Height m LA m2 Height m LA m2 1 .0 0.02 0 .18 0.28 1.20 1 .32 1.11 0 .38 1.06 1.57 1 .76 1.14 0 .62 1.00 2.00 2 .31 3.79(old) 0 .80 1.12 2.74 0.74(new) 1 .02 0.93 2 .89 5.08 1 .22 1.22(old) 3.25 3. .58 7.72 0.08(new) 4.04 4, .14 7.39 1 .70 4.45 4.88 4. .72 4.81 2, .38 3.84 5.61 5. .26 5.34(old) 2, .80 4.63 6.35 1.35(new) 3, .18 1 .87 5. .84 4.14 3. .48 2.39(old) 7.06 0.43(new) 7.87 6. .50 3.85 3. ,66 1.97 8.53 7. ,34 3.99 3. ,94 1.24 9.35 8. ,13 2.26(old) 4. ,32 2.36 9.98 1.10(new) 4. 83 1.72 8. 84 2.00 5. 44 1.37 10.71 9. 54 0.92 6. 35 0.39(old)11.45 10. 18 0.58 0.32(new)12.07 10. 82 0.30 6. 53 0.84 12.44 11. 42 0.09 6. 96 0.72 13.43 7. 54 0.12 8. 18 0.04 0.32 0 .40 0.03 3.15 0 .68 0.03 2.51 1 .03 0.19 5.25(old) 1, .44 0.44 0.37(new) 1. .87 1.30 4.80 2, .50 0.80(old) 8.96 0.11(new) 16.37 2, .97 2.11 6.33 3. ,53 2.05 9.07(old) 4. .03 3.04 1.73(new) 4. ,39 1.56(old) 8.23 0.32(new) 4.81 4. .90 2.14 6.32 5. .50 2.71 4.37 6. 42 2.77 3.14(old) 7. 26 2.42 1.24(new) 8. 14 0.98(old) 1.78 0.68(new) 1.72 8. 98 1.47 0.92 9. 70 1.18 0.55 10. 38 0.27 0.12 11. 28 0.07 Total LA 63.20 48.52 91.48 26.69 7224 D.B.H. (mm) FIGURE IV.7: Tree leaf area (LA) on a projected area basis versus D.B.H. for the thinned stand. Error bars are ±10% for LA and ±5 mm for D.B.H. > /225 Cl978; in 1975. A least-squares regression gave LA = 0.0346 ( D . B . H . ) 1 " 5 2 ? ? r = 0.986, s . • = ± 11.m , with LA in m and D.B.H. in mm. This y. x is about twice the leaf area per Douglas-fir tree reported by Kinerson and Fritschen (1971) in Washington and Gholz et ai. (1976) in Oregon. The regression equation for Courtenay was used to determine the average tree leaf area in each D.B.H. c lass. Stand tree LAI was obtained from the sum of the frequency weighted leaf area for each D.B.H. class multiplied by the stand density (822 stems h a - 1 ) . Douglas-f i r LAI was 5.0 in 1978 compared to 3.6 in 1975 (Tan et a l . , 1978). It is estimated that 15 to 20% of this was due to the current year's new growth. Understory: The understory LAI (Table IV.8) was determined by clipping p three 1 m plots and then measuring the leaves with an automatic leaf area meter. The average LAI was 3.5 in 1978 compared to 3.0 in 1975 (Tan et a l . , 1978). However, the soi l water content measurements were made in an area with understory leaf area towards the lower end of the range. Thus, an LAI of 3.0 is used for the understory in a l l calculations in this thesis. TABLE IV.8: Understory leaf area index, thinned stand, August 1978. 2" Sample area 1 m location 1 2 3 Salal (m2) 2.73 3.93 3.59 Other sp. (md) 0.05 0.24 0.01 2.78 4.1 7 3.60 /226 Stomatal Resistance Characteristics Measurements were made between June and September, 1978 with the ventilated d i f f u s i o n porometer used by Tan and Black (1976, 1978) and Tan et al. (1977, 1978). Calibration checks during the summer and in the f a l l were limited and there i s , therefore, some uncertainty in the c a l i b r a t i o n . The ca l i b r a t i o n data, and data in 1980 ( K e l l i h e r , pers. comm.), indicate that the theoretical curves (Table IV.9), calculated from data in Tan and Black (1978), are adequate. Douglas-fir: Tree number 55 was sampled regularly during June and July and occasionally during August and September. Needles were randomly chosen from d i f f e r e n t age classes at 2.2, 4.6 and 7.5 m above the ground. Five needles were used in each measurement,within 5 minutes of the sampling. Needle plan area was determined to within ± 20% from measurements of length and breadth of each needle. Measurements of r s were made on young and old needles, separately and in combination. Canopy vpd measurements were also made at the time of needle sampling. The r $ data are shown i n Figure IV.8 plotted against vpd for two \ ranges. The measurement error for each, point, could; easily be +20%. The curves are the regression l i n e s from Tan et a i . (1978) for the s i t e in 1975. The data for ^ > - 0.35 MPa f i t the curve quite well. There i s i n s u f f i c i e n t data to judge the other range. As noted by Tan et ai. (1977) there i s a trend for the resistance to increase s l i g h t l y with the depth in the canopy. In early June, new needles tended to TABLE IV.9: Theoretical t r a n s i t times (3-6 uA) for the ventilated diffusion porometer, c a l -culated from data in Tan and Black (1978). 10°C H 20°C 30°C 0 3.7 3.2 0 2.4 2.2 0 1.4 1.3 0.97 31.8 26.8 0.91 19.4 17.9 0.85 10.2 9.8 1.62 50.6 42.7 1.52 30.9 28.4 1.43 16.2 15.6 2.80 84.7 71.5 2.63 51.6 47.5 2.47 27.0 26.0 2.90 87.6 73.9 2.72 53.3 49.0 2.56 30.0 26.9 5.71 168.8 142.5 5.35 102.5 94.3 5.04 53.8 51.7 * r s in ks m 1 corresponds to c a l i b r a t i o n plates with correction made for one end effect. 'Scales H, and H 9, t r a n s i t times in seconds. 7228 vpd (kPa) FIGURE IV.8: Douglas-fir, tree 55, stomatal resistance (r s) versus vpd for three heights and two tym ranges, thinned stand, June to September, 1978. Curves are from Tan et al. (1978). /229 have higher values of r g than old ones. However, the variation in r g between different age classes was similar to the var iab i l i ty within an age c lass . The data do not include early morning or early evening readings when l ight levels may have influenced r . s In Ju ly , August and September six other trees were sampled regularly to investigate between-tree var iabi l i ty in r g (Table IV.10). A twig was sampled with a tree pruner from about 4.5 m above the ground, at or just above the height of maximum leaf area. Five needles were used, at least one from each age class on the sampled twig. The vpd at 4.5 m was also measured. Sampling a l l six trees took about 1 hour since twig water potential measurements were also made on the sampled twigs. The ^ -charac ter is t ics (Figure IV.9) show good agreement with the regression lines for 1975 (Tan et a i . , 1978) and with tree 55. No signif icant systematic differences between trees were apparent. Sala l : The ^ -charac te r is t ics for the salal (Figure V.10) were determined at three s i tes . At least four leaves were sampled each period and an accompanying measurement of the vpd was made at 0.5 m above the ground. In June and July shaded leaves often had r g values of up to f ive times those of sunli t leaves. They are plotted separately in Figure IV.10. The regression curves for salal for three ty ranges (Tan et a i . , 1978) are also shown in this Figure. Values of r g at low vpd are somewhat lower than the /230 TABLE IV.10: D.B.H. and LA (from Figure IV.7) of the trees sampled for the r s -character is t ies , thinned stand June-September, 1978. Tree ho. 15 22 30 38 49 54 55 D.B.H. (mm) 91 74 135 86 137 145 170 LA ( n f ) 33.2 24.2 60.5 30.4 61.8 67.4 85.9 /231 i • r C L O S E D h AAM X K DOUGLAS-FIR, JULY-SEPT. 1978 A A Attl . A o / A AA A A OA >*<X O . . =*. ' DOO o / A oAA - B A A oo „ x A A A AA A air O o OD O <ftn»-0.35 MPa A -0.95s Vm<-0.35 MPa x - 1.25* Vm<-0.95 MPa A Vm<-l.25MPa I 0 1 2 s , vpd (kPa) FIGURE IV.9: Douglas-fir, six trees at the 4.5 m height, stomatal resistance (rs) versus vpd for four tym ranges, thinned stand, July to September, 1978. Curves are from Tan et a l . (1978). 7232 FIGURE IV.10; Salal stomatal resistance (rs) versus vpd for thre 4>m ranges, thinned stand, June to September, 1978 Curves are from Tan et ai, (1978). 7233 corresponding 1975 data. This may be at least part ia l ly due to errors in the porometry technique that could result in an under-estimation of salal r s by over 20%. Occasional measurements of the upper surface of the salal leaves gave ' i n f in i t e ' resistance. Infrequent measurements on the vanil la leaf showed that i t had similar resistances to the salal for i ts lower surface, while i ts upper surface had ' i n f in i t e ' resistance. Twig Water Potential Twig water, potential ( i j ; ^ ) was measured with a pressure chamber during 1978 in conjunction with the r s measurements. Resolution of the pressure bomb was about ± 0.05 MPa. Maximum predawn ty^. for the Douglas-fir was between -0.4 and -0.8 MPa (Table IV.11). However, the highest values (-0.35 ± 0 . 1 2 MPa) were obtained between 0900 and 1030 PST in September on a foggy day with dew on the leaves, and the next day after rain. Simi lar ly , maximum predawn \p t for salal was between -0.07 and -0.23 MPa, with about -0.07 ±0 r 03MPa for the above damp conditions. Maximum predawn ty^ for the Douglas-fir is generally 0.4 to 0.6 MPa lower than the average tym, and for salal 0.1 to 0.2 MPa lower than ty . m ^ Minimum daytime ty^ for Douglas-fir and salal were relat ively constant through the summer with no apparent dependence on ty or vpd. The lowest values (-2.6 ± 0.3 MPa) for Douglas-fir occurred at times of maximum and minimum soi l water ava i lab i l i ty . The lowest salal 7234 TABLE IV.11: Maximum predawn twig water potential (tyt). Average and range of tyt data and number of samples (n) indicated. The range of the measured root zone tym and estimated average ty are also shown. ^ t(MPax-l) ^(MPax-1) Douglas-fir Salal Average Range 0.58±0.22, n=18 0.16±0.09, n=ll 0.02 0.01-0.1 0.85±0.36, n=22 0.36±0.20, n=10 0.1 0.05-0.3 1.24±0.24, n=6 * 0.6 0.2-0.8 1.45±0.28, n=12 * 1.1 0.8-1.3 2.04±0.23, n=6 + 2.25 , n=3 1.9 1.4-2.6 At end of rainstorm and on a foggy morning with dew on (1000 PST) the leaves 0.35±0.13, n=ll 0 .07±0.03, n=4 0.005 -*Salal tyt higher than tym. Salal si te was an area without trees. It appears that the soi l water was not depleted as rapidly in this area as in other areas. Sample site by a tree. 7235 TABLE IV.12: Minimum daytime twig water potential {tyt). Average and range of tyt data and number of samples (n) indicated. The range of the measured root zone ym and estimated average ^ m are also shown. Douglas-^ t(MPax-l) f i r Salal ^(MPax-l) Average Range 2 .1±0 .8 , n=35 1. 6±0 .6 , n=15 0.01 0.0-0.02 2 .2±0 .5 , n=24 1. 9±0 .3 , n=7 0.1 0.05-0.3 2 .H0 .5 , n=13 * 0.6 0.2-0.8 2 .2±0 .9 , n=9 *2. 2±0.4 , n=7 1.1 0.8-1.3 2 .4±0 .5 , n=8 2. HO.6 , n=17 1.9 1.4-2.6 *See footnote to Table IV.11. /236 values (-2.2 ± 0.5 MPa) occurred at the time of minimum soil water ava i lab i l i ty (Table IV.12). No systematic variations with height for the Douglas-fir were noted. 3. Interception Five rain gauges were located below the canopy in 1978. Three of these gauges were at different positions direct ly under the trees. The other two were located in the 'open'. Gauge or i f ice was above the sa la l . Thus, only interception by the Douglas-fir was determined. Stem flow was observed to be small. The gauges were assumed to represent equal area fractions of canopy cover, and were averaged to give average throughfall . . Average interception (I) was calculated from the ra infa l l above the canopy minus average throughfall , and plotted against ra infal l (Figure I \M1), The relationship I = 0.4 P ' was f i t ted by eye. Leaf area index was incorporated by assuming I was proportional to LAI. Douglas-fir LAI was 5.0 in 1978, so that I = 0.08 LAI P 0 - 6 , for P > 0.3 mm. Al l of P was assumed to be intercepted for P < 0.3 mm. This relationship was used for the Douglas-fir and salal combined in Chapter 2 and for them separately in Chapter 3. FIGURE IV.11: Interception (I) versus rainfall (P) for the thinned Douglas-fir canopy, May to September, 1978. Curve was fitted by eye. /238 2. MICROMETEOROLOGICAL INSTRUMENTATION AND DATA STORAGE 1. Instrumentation In T978 most of the above-ground equipment was located on a 10 inch triangular tower. Net radiat ion, solar radiation, wind speed, a i r temperature and humidity were measured at 13.4 m above the ground. The rain gauge was at 8.0 m, the canopy thermometer at 4.5 m on the north si;de of the tree, and an anemometer at 0.6 m above the ground (just above the sa la l ) . Two soi l heat flux plates were at 0.05 m below the soi l surface and two soil temperature probes were used to give the 0 - 0.05 m average temperature. Al l of this instrumentation, except the rain gauge, was integrated by a data logger (see later) and analysed to give half-hourly averages. The rain.gauge was read dai ly. A hygrothermograph was located in a screen 2 m above the ground.. Soil moisture was monitored with a neutron moisture probe (5 locations), tensiometers (2 locations) and soil hygrometers (4 locations). In 1979 daily solar radiation was measured 9 km east of the thinned site at the U.B.C. Research Farm at Oyster River. Temperature and relative humidity were monitored on a hygrothermograph in a screen 1.6 m above the ground. A rain gauge, located in a nearby clearing, was read every 7 to 10 days and partitioned into daily ra infa l l based on the ra infal l at Oyster River. Soil moisture was measured with a neutron moisture probe (5 locations). 7239 Above Canopy Psychrometer The temperature sensors in the psychrometer were Fairchild FD300 s i l icon diodes. The diodes were mounted on nylon rods inside a 200 mm long x 20 mm I .D. .P.V.C. tube. The tube was insulated with 7 mm thick closed ce l l foam rubber and covered with aluminized tape ^ (3M Co. , No. 850, s i l v e r , polyester f i lm tape). The large reservoir could provide three to four days supply of water even under very dry conditions. The diodes were ventilated at about 5 m s - 1 by a 24 V D.C. radial fan (Pamotor, RL90-18/24). The fan, rated at 100,000 hours continuous operation, drew about 240 mA and provided adequate ventilation even when the supply voltage dropped below 21 V. The flow had to be choked to reduce the ventilation rate to 5 m s " 1 . A psychrometric constant of 0.7 was required. The constant voltage power supply for the diodes (0.5 mA) is described in Tang et al. (1974). Neutron Moisture Probe Calibration Calibration data for the Troxler neutron moisture probe are shown in Figure IV.12. The data by depth are for one sampling area in 1978 and 1979, and three other areas in 1978. The least-squares regression equations were obtained by weighting the individual points by dividing by the number of data in each 0.05 increment of the count ratio so that each of these increments contributed equally to the regression. The l inear and second order polynomial regressions of 8 /240 i 1 1 ' r RATIO FIGURE IV.12: Neutron moisture probe calibration, thinned stand, 1978, 1979. on the rat i o of actual to sheild counts (RATIO) are: s o l i d l i n e , 9 = (0.400 RATIO) - 0.051 (m3 m"3), r 2 = 0.904, s w = 0.015 m3 nf dashed l i n e , e = 0.040 + (0.054 RATIO) + (0.304 (RATIO)2) (m3 n f 3 2 3 - 3 r = 0.908, Sy x = 0.014 m m . The linear equation.was used to determine-6 in 1978 and 1979. 7242 A Simple 9-Channel Data Logger for Micrometeorology* ABSTRACT A simple, inexpensive, voltage integrating and pulse counting, 9-channel data logger that operates on 12 V D.C. has been bui l t to measure micrometeorological data at remote s i tes . Sensor analogue voltages from 1 mV to 3 V are converted to 5 V pulses by precision electronic integrators. These pulses and those from pulse-output devices are counted by 5-decade counting I.C. chips (Motorola, MCI4535). The counters provide a multiplexed binary output that is interfaced to a mechanical printer through a series of latches. Scanning is ini t iated by an external clock. Scanning and resetting the counters takes 12.5 s. The current drawn by the logger is about 0.8 A, the printer accounting for 70% of this value. Component cost was about CAN $1050. The data logger worked continuously in the f i e ld from May to October 1978 with an overall s tab i l i ty of better than ± 0.5%. Proposed improvements wil l s igni f icant ly reduce power consumption and cost. 1. INTRODUCTION Studies of forest and agricultural environments often require the longterm, continuous monitoring and recording of sensors. There *By D. L. Spittlehouse, P. W. Y. Wong and T. A. Black. Presented at the Northwest Scient i f ic Association Annual Meeting, Western Washington University, Bellingham, Washington, March 28-30, 1979. 7243 may frequently be a need to do this in remote locations where the equipment is not under constant supervision, power is l imited, and the ambient temperature and humidity around the data-logging equipment are are not regulated. The data-logging system must be able to monitor analogue voltage-output sensors and pulse-output sensors, v A result of the current rapid development in electronics is the ava i lab i l i ty of low power consuming, compact data loggers. These vary in cost and complexity. Commercially available loggers offer a wide variety of options but are expensive, often more sophisticated than required and are not easily user modified and maintained. Harrington (1978) has reported on a data-logging system that telemeters information to a central recording station. Strangeways (1972) and Ross (1978) have described on-site recording,automatic weather stations for use in remote environments. The lat ter two data-logging systems appear to be very useful , but are s t i l l expensive, and make spot-readings of analogue voltages. However, for certain applications, e .g. radiation measurements, integration is a more appropriate procedure for recording analogue voltages. This paper describes a simple, inexpensive, 9-channel, analogue voltage integrating and pulse counting data logger, that uses 12 V D.C. as i ts power supply, and is suitable for monitoring routine agriculture and forest micrometeorological data. 7244 2. THE DATA LOGGER - DESIGN AND CONSTRUCTION In designing a data logger one of the f i r s t things that must be decided is how to handle the sensor output signals. Pulses from pulse-output sensors are usually accumulated over time. Analogue voltages can be spot read , the readings totalized over time and \ an average value calculated. Alternatively, they can be continuously integrated over time and an average value determined. The data loggers described by Strangeways (1972) and by Ross (1978) use the former method, while those of Brach et al. (1974) and Tang (1976) use the latter method. The advantage of spot reading sensors is that many sensors can be monitored with one voltage measuring c i r c u i t . However, i f the reading frequency is low, information may be lost i f the sensor output is not lagged to match this frequency (Byrne, 1970). If the sensor output is non-linear with respect to the parameter being measured, spot measurements, which are then converted to the required values, are the only way to obtain a rel iable average. Fortunately most sensors used in micrometeorology have a l inearized output. Often, a time averaged reading is a l l that is required. To obtain a rel iable value with a spot reading system necessitates taking a larger number of readings and producing a large volume of output that is inconvenient to handle. A microprocessor can be included in the data logger to fac i l i t a te an increased scanning rate and to do on-line averaging of and reduction in data output. However, microprocessors are expensive, and d i f f i c u l t to use. /245 A data-logging system that integrates voltages and counts pulses only produces data at the end of the averaging period. This reduces the volume of output while providing a more accurate average value than a slow-rate spot reading system. As the integrating system requires one integrator per sensor, the s ize , power requirement and cost of the data logger wil l become large i f more than twenty analogue voltage-output sensors are being monitored. However, many environmental monitoring programmes require that less than twenty sensors be monitored. The data logger described in this paper has been designed to monitor nine sensors with e'ither pulse or analogue voltage outputs. It uses precision analogue integrators and commercially available 5-decade, counting, integrated c i rcu i t (I.C.) chips that have a multiplexed data output. For quick access to the data and to keep costs down, the data is recorded on a printer. 1. Subsystems of the Data Logger The data logger has f ive major subsystems (Figure IV.13). These are the voltage integrators, the counters and counter input interface, the printer and counter/printer interface, the scan control logic and the power supply. In describing these subsystems schematics are presented rather than c i rcu i t diagrams since the latter may change depending on the ava i lab i l i ty of electronic components and the type of data.recording device used. Circuit diagrams for the data logger we constructed are available from the authors. 7246 DATA LOGGER SCHEMATIC VOLTAGE DATA LINE POWER SUPPLY CONTROL SIGNAL 12V + 3V — « N — <, POWER -SV 0 SUPPLY • 12V SCAN CONTROL LOGIC • 5 V COUNTER / PRINTER INTERFACE 1 ~ •H2vf'Y PRINTER^ SCAN INITIATE FIGURE IV.13: Data logger schematic. 7247 The Integrators Precision, dual ramping, electronic integrators, as described by Tang et al. (1976), are used in the data logger. They require +5 V and -5 V power supplies and have a current consumption of 17 mA each. Other integrators such as those of Fritschen (1977) and Campbell (1974b) may also be suitable for use in the data logger. The integrators used wil l only accept positive voltages. Thus, ' a l l negative voltages must be offset so that the integrator always monitors a positive signal . The output of the integrators is a train of 5 V pulses with the pulse rate a function of the input voltage and the integration rate. The latter is set by adjusting the gain on the preamplifier and on the integrating amplifier. The integration rate chosen depends on the expected size of the input s ignal , the length of time for integration and the number of digits that can be handled by the counters and printer. Typical calibration graphs of counts against input voltage are presented in Figure IV.14. There is an upper and lower l imit to the voltage range for any count rate. The lower l imit is set by the sensi t iv i ty of the preamplifier while the upper l imit is due to the saturation of the integrator. This results in a ... maximum pulse rate of about 9 Hz. Bypass switches on the input of each channel are used to route the voltage s ignal , or pulses, to the integrators, or direct ly to the counters, respectively. /248 INPUT VOLTAGE (mV) FIGURE IV.14: Typical integrator calibration curves. 7249 The Counters and Counter Input Interface The pulses from the integrators or pulse-output sensors are fed through an interface c i rcu i t (R.C.A. CD4069, CD4011) to the counters. The interface c i rcu i t isolates the counters from the sensors and the integrators,and controls count inhibit ion during print ing. The interface c i rcu i t also conditions the input pulses. It f i l t e r s out low level noise and blocks any negative pulses. A zenner diode regulates a l l pulses to no greater than 5 V. This allows the logger to monitor sensors that produce pulses of up to 12 V. The counters are 5-decade, real time, counting I.C. chips (Motorola MC14534CP, 1975). There is one counter per sensor. The counters wil l count pulse frequencies of over 1 MHz, which is more than adequate for the integrator output and for most pulse-output sensors. The counters operate from a +5 V supply and the nine counters and auxilary logic consume about 10 mA. The output from the counters is a binary coded decimal (B.C.D.) s ignal , with multiplexing of the d i g i t s , and an accompanying signal indicating which digi t is being released. The Printer and Counter/Printer Interface The printer is a mechanical, digital printer (MFE Corp., RPGE tape printer) . It i n i t i a l l y had a current consumption of about 0.8 A when idl ing and a momentary 2 A during printing. Replacing many of the printer I .C. 1 s with their low power equivalents, reduced the idl ing current to 560 mA. The printer can be switched off to conserve power when not printing only when the a i r temperature is above 10°C. /250 The printer requires a l l the digits of a number to be presented at i ts input terminals at the same time. Thus, the counter/printer interface c i rcu i t must demultiplex the counter signal. This is done by dropping each digi t from a counter into a separate latch (R.C.A. CD4042). Al l nine counters feed into the same five latches. The latches are triggered by the digi t select signals from the counter being scanned. When al l f ive latches are set, then the number can be printed. The interface c i rcu i t requires a +5 V supply and draws less than 5 mA. The Scan Control Logic Scanning n's in i t iated by an externally supplied s ignal , a momentary short to ground, which triggers the internal timer (Figure IV.15). This timer is a synchronous clock generator (National NE556 and 74C76) which produces 300 ms, 5 V pulses at 1 s intervals. The clock also enables the printer and triggers the counter inhibi t curcuitry. The clock pulses are counted by the counter enabling logic (RCA CD4017 and CD4011) which sequentially enables the counters at one second intervals to release the stored numbers. The timing pulses trigger the counter scanner reset logic and the print command logic (National 74C221). The 1-s pulses also trigger a second synchronous clock generator which produces 500 Hz pulses that are the scanner clock pulses that control the output from the counters. The scan control logic operates from a +5 V supply with a current consumption of 35 mA. A fu l l description of the operation of the scan control logic is presented in the section on the operation of the data logger. 7251 SCAN CONTROL LOGIC SCAN INITIATE COUNTER INHIBIT 1 s CLOCK PRINT COMMAND 4 SCANNER CLOCK CONTROL SCAN CONTROL COUNTER _TT_SCANNER RESET 500 H i CLOCK COUNTER SCANNER CLOCK SYNCHRONOUS SCANNER CLOCK PRINTER ENABLE SYNCHRONOUS SCAN CLOCK GENERATOR ENABLIN6 CONTROL 3 R E S E T COUNTER ENABLE PULSES PAPER ADVANCE COUNTER R E S E T FIGURE IV.15: Scan control logic schematic. POWER SUPPLY 20 VPP AC • K)V D.C. BATTERY 12V DC - o • 5V 0.C • 5 V D.C. • - TORROIDAL BRIDGE \ . ( o v o c PRINTER OSCILLATOR RECTIFIER 12 V DC 5 V REGULATORS FIGURE IV.16: Power supply schematic. 7252 The Power Supply Twelve volt batteries in p a r a l l e l , supply the power to the logger. This supply d i r e c t l y drives the pr i n t e r , while the rest of the logger i s driven by a DC to DC converter with +5 V outputs. The integrators require a ±5 V supply, while the rest of the logic requires only +5 V. The DC-DC converter i s shown in Figure IV.16. A f e r r i t e torroid produces a 20 V peak to peak, 25 kHz, A.C. signal which i s f u l l y r e c t i f i e d by a diode (5N.4.934) bridge to produce +10 V and -10 V supplies. Two regulators ( F a i r c h i l d uA7805 and uA7905) are used to control the +5 V and -5 V supplies. The DC-DC converter has an efficiency of about 75%, and the ±5 V supplies are stable to better than 0.1%v 2. Logic Operation The data logger has two operational phases, the count phase and the print phase. During the count phase,pulses from the integrators or pulse-output sensors are continually fed into the counters. The print phase is entered when the data logger receives a scan i n i t i a t e signal that triggers the one-second synchronous scan clock generator. The timing diagram for the operation of the scan control logic i s presented in Figure IV.17. The synchronous scan clock acts as an internal timer controlling the printing of the data stored in the counters. The scan clock enables the printer and the counter i n h i b i t c i r c u i t for the whole of SCAN C O N T R O L LOGIC TIMING DIAGRAM "lTLPJinr uumnr FIGURE IV.17: Scan control logic timing diagram /254 the print phase. The leading edge of the f i r s t timing pulse from the scan clock causes the counter enabling c i rcu i t to enable the f i r s t counter, and resets the scanner in the counter. After a 10 ms delay the 500 Hz scanner clock generator is triggered to produce a train of f i v e , 10 ms pulses that control the release of the data in the enabled counter (Figure IV.18). As the B.C.D. signal for each digi t appears at the output terminals of the enabled counter, a digi t select signal from the counter indicates the decade represented by the B.C.D. signal and sets the appropriate latch of the counter/printer interface. The release of a l l f ive digi ts takes about 50 ms. A print command s ignal , which triggers the printer, is generated on the t ra i l ing edge of the 1-s timing pulse. The scan logic then waits for the second 1-s timing pulse from the scan clock to cause the next counter to be interrogated. An end of scanning and reset signal is generated after a l l nine channels have been scanned. As the counter enable c i rcui t ry i s . triggered by the tenth timing pulse, the enable c i rcu i t triggers the reset c i r c u i t . The reset pulse resets the counter enabling c i rcu i t and the 5-decade counters to zero and advances the printer paper to produce a break in the data record. The reset pulse also disables the 1-s synchronous scan clock which then disables the printer and releases the counter inhibit log ic . The logger then enters the count phase. The print phase is 12.5 s long. /255 COUNTER TIMING DIAGRAM SCANNER RESET COUNTER ENABLE SCANNING CLOCK DIGIT SELECT B. C. D. OUTPUT! U~1 1 I L T I 1 I L TEN THOUSANDS L J THOUSANDS L J HUNDREDS ]_ J TENS L J UNITS L r — L FIGURE IV.18: Counter timing diagram. /256 Al l of the counters are inhibited for the whole of the print phase. However,this is a negligible loss of data for scan cycles occurring with periods greater than 10 min. If integrator calibration is done using the same scan frequencies as are used to col lect data, then corrections need not be made for the time lost during the print phase. The procedure of inhibit ing a l l the counters for a set period of time simplif ies the scan control logic and keeps component costs down. 3. FIELD TESTING AND ASSESSMENT OF- THE DATA. LOGGER A 9-channel integrating and counting data logger was designed and buil t during the Spring of 1978. The total cost of components in Canadian dollars was about $1050. Of th is , the printer accounted for $450, the integrators $,400, the counters and accompanying interface c i rcui t ry $150, the scan control logic $70, the power supply c i rcu i t $30 and the cabinet and miscellaneous supplies $50. The logger weighs 10 kg and i ts size is 0.44 x 0.38 x 0.21 m. 1. Field Testing The logger was f ie ld tested from May 22 to October 1, 1978. It was used to col lect micrometeorological data in a Douglas-fir forest near Courtenay on the east coast of Vancouver Island. The logger was located in a well ventilated shack in the forest , and the logger cabinet was not moisture proof. Printing was ini t iated every half /257 hour by an external clock. Power for the logger and clock was supplied by two 105 amp hour 12 V lead acid batteries in para l le l . Analogue voltage-output sensors monitored by the logger were a net radiometer, a solarimeter, soi l heat flux plates and s i l icon diode temperature sensors. The pulse-output sensors monitored were anemometers. The control c i rcu i t for the anemometers was located inside the data logger. The integration rate is described by the number of pulses, or counts, generated by an integrator, per m i l l i vo l t per hour. It should be chosen on the basis of the size of the signal being monitored and the length of the count phase. For signals in the 0 to 60 mV range, e.g. solarimeters, a count rate of 100 counts/(mV h) was used. This rate would be suitable for count phases of up to 24 hours in length. A count rate of 10 counts/(mV h) was used for signals in the 200 to 600 mV range. Voltage offsets were used where a signif icant portion of the output of a sensor, e .g. a soi l heat flux plate, was close to the lower l imit of integrator sensi t iv i ty , i .e . between 0 and 1 mV for the 100 counts/(mV h) rate (see Figure IV.14). Offsets were also used where the signal was negative for part of the day, e .g. a net radiometer. A 1.35 V battery (Mallory, RM42R) and resistors were used to provide a 5 mV offset signal that had a s tab i l i ty of ±20 uV over two months. The power supply for the s i l icon diode temperature sensors (Tang et a i . , 1974) was used to provide a 610 mV offset to the diode signal . This was done so as to improve resolution for di f ferential temperature measurement. For example, a 100 counts/(mV h) integrator sensi t iv i ty could be used with the resulting 5 to 70 mV signal 7258 rather than the 10 counts/(mV h) count rate that would be required for the 615 to 670 mV diode output voltage. The offsets were also useful for performing calibration checks on the integrators in the f i e l d . The total number of pulses from the anemometers over a half-hour period would not have caused the counters to overflow. Thus, i t was not necessary to insta l l a dividing c i rcu i t ahead of the counters. Calibration and s tab i l i ty checks on the counters were performed in the laboratory using a pulse generator and in the f i e ld by manually turning the anemometer cup assembly. 2. Assessment of the Data Logger The simple design of the data logger made construction and debugging of the c i rcui t ry a relat ively quick and easy task. During the f ie ld test the logger was exposed to ambient a i r temperature of 5 to 35°C and ambient relat ive humidity of 10 to 100%. Only lh days of data were lost due to malfunctioning of the data logger. This was caused by a broken on/off power switch and a jammed paper feed in the printer. The integrators were calibrated before and after the f i e ld season and occasional checks were performed in the f i e l d . These data show a s tab i l i ty of the data logger to within ± 0 . 5 % over the 4% month f ie ld t r i a l . Analysis of the data collected by the logger also shows no indication of instab i l i ty ... The logger was easy to operate and could be le f t to run unattended between power supply changes. 7259 The in i t i a l current drain of the logger was about 1.1 A continuous. This was reduced to 0.8 A by replacing some of the I .C. 's in the printer as noted ear l ier . The power supply was changed every f ive days. Various improvements to the logger are proposed. The current drain can be reduced to around 500 mA and logger costs to about CAN$800 with the instal lat ion of a better printer. Changes to the integrators have reduced current consumption to 10 mA per integrator. An advantage of high current consumption was that the logger was always above air temperature, thus reducing the risk of condensation during wet weather. A further improvement that is underway is the inclusion of a clock inside the data logger so that an external scan-i n i t i a t e , signal is not required, and time of day can be printed with the data. This should increase the logger cost to about CAN$900 without s igni f icant ly increasing power consumption. 4 . SUMMARY An inexpensive, low-power 12 V D.C. voltage integrating and pulse counting data logger has been bu i l t , that is suitable for collecting micrometeorological data in remote areas. Construction and operation of the logger is relat ively easy. Sensors with analogue voltage ouptuts of up to 3 V as well as pulse-output devices can be /260 readily monitored. The logger uses precision, dual rampings voltage integrators and 5-decade counting I .C. 1 s in i ts measurement c i rcu i t ry . The data is output on a mechanical, digital printer upon in i t ia t ion by an externally supplied pulse. The logger worked well during a 4% month summer f i e ld t r ia l at a forest micrometeorological research s i te . During this period the data logger had an overall s tab i l i ty to better than ± 0.5% for an ambient a i r temperature range of 5 to 35°C and relat ive humidity of 10 to 100%. Current consumption was about 0.8 A during idl ing with a momentary 2 A during printing. The logger cost CAN$1050. Proposed improvements could reduce current consumption to about 0.3 A and component cost to CAN$900. 5. ACKNOWLEDGEMENTS Funding for this research was provided by a grant from the National Research Council of Canada and by a contract from the Br i t ish Columbia Ministry of Forests. We wish to thank the Courtenay division of Crown Zellerbach L t d . , for providing the research site and the Faculty of Agricultural Sciences, University of Bri t ish Columbia, for the use of their Oyster River Farm as a base camp. /261 6 . REFERENCES Brach, E . J . , P.W. Voisey and P. Poir ier , 1974. Electronic integrator to measure environmental characterist ics. Agric. Meteorol. 13: 169-179. Byrne, G . F . , 1970. Data-logging and scanning rate considerations in micrometeorological experiments. Agric. Meteorol. 7: 415-418. Campbell, G .S . , 1974b. A micropower electronic integrator for micrometeorological applications. Agric. Meteorol. 13: 399-404. Fritschen, L . J . , 1977. A mi l l i vo l t - to -vo l t and pulse-to-volt integrator for meteorological purposes. Agric. Meteorol. 18: 321-325. Harrington, J . B . , 1978. A remote weather station for use in forest f i re management. In:- Fourth Symposium on Meteorological Observations and*Instrumentation. Am. Meteorological SOC, April 10-14, 1978, Denver, C o l . , pp. 33-34. Motorola, 1975. The Semiconductor Data Library. Ser. A . , Vol. V, McMOS Integrated Ci rcu i ts . Tech. Info. Centre, Motorola Inc. , pp. 7.253-7.258. Ross, P . J . , 1978. Two digi ta l recorders for the f i e l d . C.S.I .R.O. Aust. Div. S o i l s , Tech. Pap. No. 36, Melbourne, 30 pp. Strangeways, I . C , 1972. Automatic weather stations for network operation. Weather 27: 403-408. Tang, P.W., 1976. Electronic Data Aguisition System for'the Energy Balance/Bowen Ratio-Measurement of-Evaporation. M.Sc. Thesis, Univ. Br i t ish Columbia, Vancouver, B .C . , 96 pp. Tang, P.W., K.G. McNaughton and T.A. Black, 1974. Inexpensive diode thermometry using integrated c i rcu i t components. Can. J . For. Res. 4: 250-254. Tang, P.W., K.G. McNaughton and T.A. Black, 1976. Precision electronic integrator for environmental measurement. Trans. Am. Soc. Agric. Eng. 19: 550-552. 7262 2. Data Storage Most of the data collected in 1978 and 1979 are stored on magnetic tape. At the beginning of each f i l e there is a brief description of the f i l e and the format of the data. The tape ID = ANDY, VOL =• ST0RE1, DENSITY - 1600 BPI, RACK NO. = RA0925, has the following fixed block f i l e s with format FB(4000,200) or FB(4000,80): F i le Name Data CY78WEATHER Half-hourly data summary, 1978 CY78SUMMARY Daily summary, 1978 CY79SUMMARY Daily summary, 1979 CY78WATER Neutron moisture probe data, 1978 CY79WATER Neutron moisture probe data, 1979 CY78TENS Tensiometers, 1978 CY78HYGR0M Soil Hygrometers, 1978 CY78RAIN Canopy throughfall data, 1978 ESLMODEL Model from Chapter 2 SDRMODEL Model from Chapter 3 APPENDIX V CALCULATIONS AND DATA USED IN CHAPTER 2 1. DETERMINATION OF THE FORMULA FOR THE  EFFECTIVE EMISSIVITY OF THE SKY (Za) Equations Tested (1) Idso and Jackson (Aase and Idso, 1979). e a = 1 - (0.261 x expI-7.77E-4 x (273 - T) 2 ] ) (2) Modified Idso and Jackson (I & J) a. e, = e-(I & J) x 0.92 R > 8.0 MJ rn"2 d" 1 a a n e a = e a(I & J) Rn < 8.0 MJ m"2 d" 1 b. e = ejl & J) x 0.92 for a l l R (3) Swinbank (1963) e a = 0.937E-06 x T 2 (4) Brunt (Monteith, 1961) e a = 0.53 + (0.206 x e ° - 5 ) (5) Brutsaert (1975) e a = 1.72(e /T) (6) Idso (1980) e a = 0.70 + (5.95E-0.4 x e. x exp[1500/TJ) (7) Satterlund (1979) c a = 1.08(1 - exp [ - (e x 1 0 ) ( T / 2 0 1 6 ) J ) /264 Discussion: In the above equations T and i~ are the mean daily temperature in Kelvin and vapour pressure in k i lo-Pascals, respectively, at the top of the canopy. Data was available for 1975 and 1978. The net radiation (Rn) was calculated from (Chapter 2) Rn = (1 - 0.12)K+ + L* L* = (0.1 + £ 0 . 9 K+ /K+ m a Y J ) ( £ „ - 0 . 9 6 ) a T 4 III a A a Table V.l compares measured and calculated clear sky Rn '(K4-/.K+ ^ > 0.95). Table V.2 l i s t s the least-squares l inear regressions of calculated on measured R . for a l l the R 'data. Figures V. l and V.2 i l lustrate the n n results for the unmodified and modifiea.tion a, Isdo and Jackson .-formula, respectively. Use of e from the Brunt formula results in the best a agreement between measured and calculated Rn using unmodified formulae. This may be because the coefficients were obtained in a maritime environment and at a similar latitude (Monteith, 1961). However, only temperature based formulae can be used in the model. Thus, the modified Idso and Jackson formula, modification a, has been used. If an average daily temperature is not available i t is calculated from ( T m g x + T • )/2, where T m a x and T m i n are obtained from a hygrothermograph. A least-squares l inear regression of calculated T on measured T (integrated through the day) for 1975 and 1978 gave T(cal 0.938 T(measured) + 1.2 °C, r 2 = 0.923, s y , x = ± 1.03 °C, n = 153. /265 MEASURED R p (MJ m"2d-1) FIGURE V . l : Calculated versus measured net radiation, 1975 and 1978, with e a from the unmodified Idso and Jackson formula. 7266 \ FIGURE V . 2 : As f o r F igu re V . l but w i th e a from m o d i f i c a t i o n " a " to the Idso and Jackson fo rmu la . 7267 Using calculated temperatures did not s ignif icant ly alter the values of simulated R from those using the true mean air temperature. TABLE V . l : Mean, standard deviation of mean (s y ) and standard deviation between the calculated and measured (sy. x ) clear sky net radiation for 1975 and 1978, n = 41." Equation Mean — (MJ m~d d - 1 ) — Idso and Jackson unmodified 19.20 2.36 2.92 modified a,b 17.00 2.29 1.04 Swinbank 19.08 2.35 2.80 Brunt 17.13 2.23 0.84 Brutsaert 18.14 2.24 1.75 Idso 19.46 2.23 3.05 Satterlund 19.70 2.20 3.30 Measured 16.53 1.89 /268 TABLE V.2: Least-squares l i n e a r regression of calculated on measured net Radiation for a l l net radiation data for 1975 and 1978. Correlation c o e f f i c i e n t ( r 2 ) and the standard deviation of the estimate ( s y . x ) given, n = 169. Equation Idso and Jackson unmodified modified a modified b Swinbank Brunt Brutsaert Idso Satterlund Intercept (MJ rn"2 d"1) Slope -0.37 0.26 -0.83 1.158 0.990 1.058 -0.41 1.154 0.10 1.023 0.40 1.065 0.94 1.107 0.49 1.141 r 2 (MJ m ^ V l ) 0.808 0.824 0.794 1.00 0.87 0.90 0.807 0.98 0.820 0.68 0.827 0.70 0.838 0.74 0.828 0.82 2. NORMALIZING THE E VERSUS 0 RELATIONSHIP e ( i ) The family of curves in Figure 2.2 is given by E = aE „ 0 > 0 (la) eq e - ec v ; E = D0Q K < Qar- ( lb) e e - ec v ' where a and b are constants. The c r i t i c a l value of 0 for a given e 3 E„„ occurs when b0„ = a E _ so that eq e eq /269 or = 6 ~ = (a/b)E (2) ec e eq v 1 9 e c / E e q = a / b (3) and all values of 0 g c can be replaced by a single number equal to a / b . Dividing all of (la) and (lb) by E and substituting (3) into the result and rearranging gives E / E e q = a 9 e / E e q >- a / b ( 4 a ) E / 0 e = b 9 e / E e q < a / b (4b) Thus, by dividing both e and E,with E , the family of curves in e eq Figure 2.2 can be reduced to two straight lines (Figure V.3). (ii) Many researchers have used aji E versus 8 g relationship with only E divided by E m g x or its equivalent. This is valid for non-limiting soil water conditions; however when E is limited by Q& the calculated E may be incorrect. The two forms of this relationship that are commonly used are illustrated in Figure V.4 and are given by E/E =1 6 > 9 (Sa) max e ec v- ' E / E m a v = JW 0 < 0 „ (5b) max e ec x ' where J is a constant and W is the amount of water stored in the root zone, i.e. W = 8 5 , where 0" is the average volumetric water content of the /270 FIGURE V.3: Normalized daily evapotranspiration rate (E /E e q ) versus normalized fraction of extractable water in the root zone ( 6 e / E e q ) for the data in Figure 2.2. Cr i t ica l value (a/b) indicated. /271 FIGURE V.4: Two examples of the relative evapotranspiration rate (E/E m a x) versus the fraction of extractable water in the root zone (6 e). Critical value of 6 e(0 e c) indicated. /272 root zone and z, is root zone depth (mm). Only equation (5b) may be incorrect. When drainage is negligible E = -(dW/dt). Substituting for E in (5b), rearranging and integrating from t-j to t 2 gives ^(l/W)dW = - M j E m a y dt (6) Assuming that J is a constant the solution to (6) is t \ L t 2 ' H 1 = e x P ^ J / E m a x ) (*> 1 *2 Since \ E = W^  - W2 > eliminating W^  from (!7) gives *1 t 2 t 2 IE = II - e x p ( - J l E m a x ) J W 1 (8) l1 r l When 6 e = 9 e c < > (5a) equals (Sb), therefore J = 1/WC, where Wc is the c r i t i ca l water storage, W at 9 . However, part (i) of this section shows that 9 „ is not constant, rather i t is a function of E , and ec max should be included on the right-hand side of the summation sign in (6). If E m a x is constant or does not vary much ofer time, then ('7) is suitable. Equation (7) has been successfully used by a number of authors (see Priestley and Taylor, 1972; Tanner and Ritchie, 1974), probably because J is relat ively conservative. Using a constant value of 9 obtained under high E m 3 v conditions could result in an underestimation ec max of E as the soil dr ies. /273 3. FIELD SOIL WATER RETENTION CHARACTERISTICS FOR THE COURTENAY UNTHINNED AND THINNED SITES IN 1974 AND 1975, RESPECTIVELY Date are from the Appendices in Nnyamah (1977). Soil water content i s the average of f i v e (1974) or six (1975) neutron probe moisture measurements. Matric potential i s from tensiometers and hygrometers. Data are f i t t e d following Campbell (1974a)to ty = ^m r(0/0 r)~m with 3 -3 9 r = 0.30 m m . There are six data points for each depth. The average curves (Figures V.5 and V.6) are the mean of the m and ty values in rmr Table V.3. TABLE V.3: Coefficients for the f i e l d retention relationship, m^ = * m r ( 9 / e J " m with 0 r = 0.30 m3 m-3 for the unthinned (1974) and thinned (1975) s i t e s , Courtenay, B.C. Correlation c o e f f i c i e n t ( r 2 ) i s shown. Depth (m) m ,^ mr. (kPa) r 2 1974 0.15 3.8 - 7.2 0.949 0.30 4.5 - 4.8 0.952 0.45 5.8 - 1.8 0.963 1975 0.15 ,5.4 -10.6 0.928 0.30 5.7 - 4.8 0.958 0.45 .7.3 - 1.5 0.965 0.60 7.9 - 1.1 0.959 0.70 6.9 - 2.0 0.975 Average Curve 1974 (0.3,0.45) 5.2 - 2.8 -1975 (0.3-0.7) 7.0 - 1.5 -7275 FIGURE V.6: Field soil water retention curve for the thinned site in 1975. 7276 4. SEASONAL CHANGE IN WATER STORED IN THE  TREES IN' THE THINNED STAND It is assumed that the bole of the tree can be approximated by a cone, and a l l of the wood is sapwood. The latter is not the case, but allows for branches and leaves and should give an upper estimate for storage. The average D.B.H. and height of the trees in 1978 were 135 mm and 12.2 m, respectively, for an average tree volume 3 - 1 3 " -1 of 0.0757 m . At 822 trees ha there is approximately 62 m of wood ha . Sapwood density for Douglas-fir is about 450 kg m .(Waring and Running, 1978) and the density of cellulose and l ignin is 1530 kg m (Running 1980c) so that porosity is approximately 0.7. Assuming that the pores are i n i t i a l l y f i l l e d with water and that up to 80% of the stored sapwood water can be depleted (Waring and Running, 1978; Running, 1980c), the upper l imit of the loss over the summer is 3 3.5 mm or < 0.5 m of water per tree. This is the equivalent of less than two days transpiration by the thinned stand. Publications; Black, T. A. and D. L. Spittlehouse, 1981. Modeling the water balance for watershed management. In: Proceedings, Interior West  Watershed Management Symposium, Spokane, Wash., April 8-10, 1980, Am. Soc. Foresters and Univ. Wash., Seattle, (in press). Spittlehouse, D. L. and T. A. Black, 1981. A growing season water balance model applied to Douglas-fir stands. Water Resour. Res. (submitted). Spittlehouse, D. L. and T. A. Black, 1981. Measuring and modelling forest evapotranspiration. Can. J . Chem. Eng. (in press). Kalanda, B. D., T. R. Oke and D. L. Spittlehouse, 1980. Suburban energy balance estimates for Vancouver, B.C. using the Bowen ratio-energy balance approach. J . Appl. Meteorol. 19: 791-802. Spittlehouse, D. L. and T. A. Black, 1980. Evaluation of the Bowen ratio/energy balance method for determining forest evapo-transpiration. Atmosphere-Ocean 18: 98-116. Spittlehouse, D. L. and T. A. Black, 1979. Determination of forest evapotranspiration using Bowen ratio and eddy correlation measurements. J . Appl. Meteorol. 18: 647-653. Sondheim, M. W. and D. L. Spittlehouse, 1979. Comments on, 'Hydro-logic behavior of a forested mountain soi l in coastal Br i t ish Columbia' by J . de Vries and T. L. Chow. Water Resour. Res. 15: 1660. Spittlehouse, D. L. and E. A. Ripley, 1977. Carbon dioxide concentrations over native grassland in Saskatchewan. Tellus 29: 54-56. Rowe, J . S . , D. L. Spittlehouse, E. A. Johnson and M. Jasieniuk, 1975. Fire studies in the upper MacKenzie Valley and adjacent Precambrian Uplands. Dept. Indian and Northern A f fa i rs , Ottawa, INA Publ. No. QS-8045-000-EE-A1, Arct ic Land Use Research Programme 74-75-61. Spittlehouse, D. L. and E. A. Ripley, 1974. Micrometeorology:X. Relationships between plant microclimate and structure. Tech. Rep. 55, C.C. I .B.P. Matador Project, U. Saskatchewan, Saskatoon, Sask., Canada, 99 pp. 

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