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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 N o t t i n g h a m , E n g l a n d , 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  Science)  We a c c e p t t h i s t h e s i s as c o n f o r m i n g to the r e q u i r e d s t a n d a r d  THE UNIVERSITY OF BRITISH COLUMBIA March c~")  David L e s l i e  1981 Spittlehouse,  1981  In  presenting  requirements  this thesis f o r an  of  British  it  freely available  agree t h a t for  understood for  I agree  Library  shall  for reference  and  study.  I  for extensive  that  h i s or  her  copying or  f i n a n c i a l gain  be  shall  publication  not  be  Date  DE-6  (2/79)  the  of  Columbia  make  further this  thesis  head o f  this  It  my  is  thesis  a l l o w e d w i t h o u t my  of  The U n i v e r s i t y o f B r i t i s h 2075 Wesbrook P l a c e V a n c o u v e r , Canada V6T 1W5  by  representatives.  permission.  Department  copying of  granted  the  University  the  p u r p o s e s may by  the  that  permission  department or  f u l f i l m e n t of  advanced degree at  Columbia,  scholarly  in partial  written  /ii  ABSTRACT  Methods of measuring f o r e s t evapotranspiration are reviewed and evaluated.  Measurements on Douglas-fir stands indicated that eddy  c o r r e l a t i o n , Bowen ratio/energy balance, stomatal d i f f u s i o n resistance and s o i l water balance methods agreed with each other to w i t h i n t h e i r respective measurement e r r o r s .  A d e t a i l e d e r r o r analysis of a  Bowen ratio/energy balance system indicated that i t could give  estimates  of evapotranspiration to w i t h i n ± 15% and ± 40% when evapotranspiration was high and low, r e s p e c t i v e l y . The accuracy of t h i s system was  due  to the use of a high s e n s i t i v i t y monitoring system, and the p e r i o d i c reversal of well-matched sensors which r e s u l t s i n the c a n c e l l i n g of c e r t a i n systematic e r r o r s .  The e f f e c t s of c e r t a i n non-cancelling  errors are also i l l u s t r a t e d . Approaches to modelling f o r e s t evapotranspiration are reviewed and two approaches chosen f o r f u r t h e r study.  Data obtained using the  Bowen ratio/energy balance, stomatal d i f f u s i o n resistance and  soil  water balance methods are used i n the development and t e s t i n g of two forest evapotranspiration models.  These models are combined with  simple i n t e r c e p t i o n and drainage r e l a t i o n s h i p s to produce two f o r e s t water balance models. In the energy/soil l i m i t e d (E.S.L.) model, which i s used on a d a i l y b a s i s , the d a i l y evapotranspiration rate (E) f o r dry f o l i a g e is assumed to be the l e s s e r of e i t h e r energy (demand) or s o i l water (supply) l i m i t e d r a t e s .  The energy l i m i t e d rate (E  ) i s equal  /iii  to o £ . where a is a constant (0.8) and E is the equilibrium eq ' eq ^ evapotranspiration rate, a function of the net radiation (R )-  The  soil  (8.6)  n  limited, rate (E ) is equal to b6 , where b is a constant s  g  and 9 is the fraction of extractable water in the root zone. e rainy days, E = E  m o v  + g l , where I is the daily rainfall  and g is a constant (0.6). lesser of (E - I) and E .  On  interception  Transpiration occurs when E > I and is the 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.  zone matric potential  An average root  {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. temperature is assumed equal to air temperature.  Leaf  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. ty or high r . m s r  3  Tree water stress is indicated by times of low  /iv  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 r o o t zone i s t r e a t e d as a s i n g l e  l a y e r t h a t i s u s u a l l y budgeted on a d a i l y b a s i s . o c c u r and r a i n r e a c h i n g the f o r e s t f l o o r i n the c o a r s e s o i l s c o n s i d e r e d h e r e . hydraulic conductivity  Runoff d i d  infiltrated  not  immediately  Drainage i s approximated by the  a t the average r o o t zone water c o n t e n t ( 0 ) .  The average r o o t zone s o i l water r e t e n t i o n g i v e the average v a l u e o f  c h a r a c t e r i s t i c i s used to  f o r the r o o t 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 t h i n n e d {pseudotsuga  menzesii  (Mirb.)  Franco) s t a n d , w i t h  Douglas-fir  a salal  {Gaultheria  shaiion,  Pursh) u n d e r s t o r y * 1 o c a t e d on the e a s t c o a s t o f Vancouver  Island.  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  determined f o r the same s i t e  i n 1978.  and d r a i n a g e models were  Retention  characteristics  were determined f o r each s i t e from f i e l d measurements.  The water  balance models were t e s t e d on the t h i n n e d s t a n d d u r i n g the  growing  seasons o f 1978 and 1979 and a nearby unthinned s t a n d i n 1974. The d a i l y , E . S . L . model w e l l 0 and t r e e water s t r e s s .  s i m u l a t e d the seasonal c o u r s e o f  The 1979 s i m u l a t i o n s 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 . t h a t o v e r 20% o f the summer's r a i n f a l l  The model  was l o s t through  indicated  interception.  In g e n e r a l , the h o u r l y , S . D . R . model a d e q u a t e l y s i m u l a t e d the c o u r s e o f 0 through the summer, though t h e r e was a tendency to 0 and o v e r e s t i m a t e s t r e s s as the summer p r o g r e s s e d .  underestimate  Modelled hourly  /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 w e l l w i t h porometer measurements i n 1975 and 1978.  The s i z e o f the u n d e r s t o r y r  important in c o n t r o l l i n g understory t r a n s p i r a t i o n .  was  b  The r ~ c h a r a c t e r i s t i e s 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 c o n s t a n t between 1975 and 1978 and between the t h i n n e d and unthinned stands w h i l e minimum s a l a l may have d e c r e a s e d by 1978. salal  of  the  The model i n d i c a t e d t h a t the  u n d e r s t o r y used almost 40% o f the a v a i l a b l e water d u r i n g the  growing s e a s o n .  R e l i a b l e ten t o twenty day e s t i m a t e s o f E were  o b t a i n e d i n 1974 and 1979 w i t h h o u r l y vpd s i m u l a t e d by f i t t i n g a s i n e wave t o the d a i l y maximum vpd (mid a f t e r n o o n )  and minimum vpd (dawn).  The two models are compared and e v a l u a t e d .  In g e n e r a l , both  agreed w i t h each o t h e r i n s i m u l a t i n g the t r e n d i n the growing season evapotranspiration.  However, t h e _ S . D . R . model tended to  g i v e up to 15% h i g h e r e v a p o t r a n s p i r a t i o n r a t e s .  P o s s i b l e reasons  are p r e s e n t e d f o r the r e l a t i v e c o n s t a n c y o f a and i t s r e l a t i o n s h i p t o 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 v e g e t a t i o n and the weather conditions.  A p p l i c a t i o n s o f the two models a r e c o n s i d e r e d .  Suggestions  f o r f u r t h e r f i e l d s t u d i e s and f o r improvement o f the model a r e presented.  /vi  ACKNOWLEDGEMENTS  Funding f o r t h i s work was p r o v i d e d through g r a n t s from the N a t u r a l S c i e n c e s and E n g i n e e r i n g C o u n c i l o f Canada and the  University  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 p r o v i d e d by a r e s e a r c h 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 t e a c h i n g a s s i s t a n t s h i p s .  Research s i t e s were p r o v i d e d  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 . During my study a t U . B . C . I have been helped i n a v a r i e t y ways by many p e o p l e .  In g e n e r a l , I wish t o thank the f a c u l t y ,  and s t u d e n t s o f the Department o f S o i l S c i e n c e the t h e i r friendship.  of  staff  h e l p and  In p a r t i c u l a r , I w i s h t o acknowledge the h e l p o f my  s u p e r v i s o r , D r . 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 , and f r i e n d s h i p c o n t r i b u t e d  g r e a t l y t o my r e s e a r c h and i t s  Also,many thanks t o Andy f o r d o i n g a l l  the w o r r y i n g .  D r s . 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  for theirelectronics^wizardry; r e s e a r c h l a i d the f o u n d a t i o n s  presentation.  Thanks a l s o t o : h e l p 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 h e l p w i t h the f i e l d 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  support  s t u d i e s and  d a t a ; Pat Wong and Paul Tang  D r s . McNaughton, Tan and Nnyamah who's ( a t times somewhat shakey) f o r  the  r e s e a r c h r e p o r t e d h e r e ; the s t a f f of the O y s t e r R i v e r Farm  (particularly  F r a n ) , f o r h e l p i n g p r e s e r v e my s a n i t y d u r i n g the 1978 f i e l d  season;  and l a s t , but not l e a s t , Joyce H o l l a n d s f o r p e r s e v e r i n g w i t h the t y p i n g o f t h i s t h e s i s and N a d i n i a and J u l i e f o r d r a f t i n g the d i a g r a m s .  \  /vii  TABLE OF CONTENTS Page ABSTRACT  ii  ACKNOWLEDGEMENTS  vi  TABLE OF CONTENTS LIST OF TABLES  vii x  LIST OF FIGURES  xii  NOTATION  xvii  INTRODUCTION CHAPTER 1  1  MEASURING AND MODELLING FOREST EVAPOTRANSPIRATION: A REVIEW  5  1.  Introduction  2.  Measuring Forest Evapotranspiration 1. Eddy Correlation Methods 2. Aerodynamic Method 3. Bowen Ratio/Energy Balance Method 4. Methods using Stomatal Resistance Measurements Modelling Forest Evapotranspiration  6 7 9 11 14 16  1. 2. 3. 4.  18 18 21 22  3.  4.  Thornthwaite Approach Energy/Soil Limited Approach Penman Approach Approaches using Stomatal Resistance Characteristics.  Conclusions  CHAPTER 2  5  24  A SIMPLE FOREST WATER BALANCE MODEL  26  1.  Introduction  26  2.  Basis of the Model  27  1. 2. 3.  28 37 38  The Evapotranspiration Sub-model The Interception Sub-model The Soil Water Balance Sub-model  /viii  Page 3.  4.  Testing the Model  43  1.  Site Description  43  2.  Performance of the Model  44  Discussion  5. Conclusions CHAPTER 3 A PHYSIOLOGICALLY BASED APPROACH TO EVAPOTRANSPIRATION ESTIMATION IN A FOREST WATER BALANCE MODEL  49 56 58  1.  Introduction  59  2.  Theory  60  1. 2. 3.  60 69 70  Evapotranspiration Interception Soil Water Balance  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  2.  Further Considerations of the Theoretical Bases of the Two Models  93  97  3.  Use of the Models in Water Balance Calculation  101  4.  Suggestions for Further Studies  104  BIBLIOGRAPHY APPENDIX I  106 DETERMINATION OF FOREST EVAPOTRANSPIRATION USING BOWEN RATIO AND EDDY CORRELATION MEASUREMENTS  122  /ix  Page APPENDIX II  APPENDIX III  EVALUATION OF THE BOWEN RATIO/ENERGY BALANCE METHOD FOR DETERMINING FOREST EVAPOTRANSPIRATION I*  ..129  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  1.  Site Description  2.  Micrometeorological  APPENDIX V 1. 2. 3.  4.  206 206  Instrumentation and Data Storage  CALCULATIONS AND DATA USED IN CHAPTER 2  Determination of the Formula for the Effective Emissivity of the Sky (e ) a Normalizing the E versus 6 Relationship.. Field Soil Water Retention Characteristics for the Courtenay Unthinned and Thinned Sites in 1974 and 1975, respectively g  Seasonal Change in Water Stored in the Trees in the Thinned Site  238 263 263 268 273 276  /x  LIST OF TABLES Table 1.1  Page Comparison of micrometeorological methods of measuring the evapotranspiration rate (E).  (a) Ratio  of eddy correlation and aerodynamic measurements of (H + LE) to the available energy (R - G - M). n  (b) Ratio of the measurement of E, using various methods, to the Bowen ratio/energy balance measurement of E 1.2  10  Typical relative probable errors in the evapotranspiration 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 de /dz, respectively.  Relative error in  the available energy was ± 7%.  (From Spittlehouse  Q  and Black, 1980, see Appendix II.) 2.1  13  Coefficients and site parameters used in the calculation of the forest water balance of two Douglas-fir stands.  See text for explanation of  symbols......... 3.1  42  Coefficients used to determine the stomatal resistance (r ) g  of the Douglas-fir and salal.  (a) r -  characteristics for vapour pressure deficit (vpd in kPa), r  p  = exp(a + b vpd ), for four matric  potential 1978).  ) ranges (modified from Tan et al., .  (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  /xii  LIST OF FIGURES Figure  Page  2.1  Components o f the f o r e s t water balance model  2.2  Daily evapotranspiration v e r s u s the f r a c t i o n  (E) f o r dry  ranges o f the  evapotranspiration  (E  content  (9  e c  rate  eq  ).  the  equilibrium  Critical  water  ) is indicated  35  Comparison o f measured and modelled 5-day average daily evapotranspiration water c o n t e n t  (6)  s t a n d i n 1975.  (E) and mean r o o t zone  f o r the t h i n n e d  (I)  (E^) and  components o f modelled d a i l y  E and d a i l y r a i n f a l l E = E  in  A l s o shown a r e modelled  d a i l y drainage (D), t r a n s p i r a t i o n interception  Douglas-fir  Bars i n d i c a t e the p r o b a b l e e r r o r  the measured d a t a .  2.4  foliage  o f e x t r a c t a b l e water i n  r o o t zone (6 ) f o r f i v e r  2.3  rate  29  (P).  On days w i t h o u t  rain 45  T  Comparison o f measured and m o d e l l e d mean r o o t zone water c o n t e n t  (8) f o r the unthinned  s t a n d i n 1974.  Douglas-fir  The bar i n d i c a t e s the  e r r o r i n the measured d a t a .  probable  A l s o shown are  modelled d a i l y drainage (D), 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  (I)  components o f the modelled  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 daily rainfall E = E  x  (P).  (E^)  On days w i t h o u t  (E) and rain 47  /xiii  Figure  Page  2.5  As f o r F i g u r e 2 . 4 but f o r the t h i n n e d stand i n 1978  2.6  Measured r o o t zone m a t r i c p o t e n t i a l  ) at  d e p t h s , w i t h bars ( o n l y one arm shown) range o f d a t a , and m o d e l l e d average ^  m  three  indicating of  the  r o o t zone  50  2.7  As f o r F i g u r e 2.4 but f o r the t h i n n e d s t a n d i n 1 9 7 9 . . .  2.8  E f f e c t on the m o d e l l e d average r o o t zone water content  (8) o f changing a by 25% f o r the  D o u g l a s - f i r s t a n d i n 1978.  51  thinned  Measured 6 a l s o shown  w i t h the bar i n d i c a t i n g the p r o b a b l e e r r o r 2.9  48  Measured and m o d e l l e d r o o t zone water c o n t e n t  53 (9) f o r  a m i c r o s i t e w i t h a 1.05 m r o o t z o n e , l o c a t e d 50 m from the main s i t e i n the t h i n n e d s t a n d , 1979.  Douglas-fir  Bar i n d i c a t e s p r o b a b l e e r r o r  in  measured d a t a 3.1  55  Comparison o f modelled and measured 5-day average daily evapotranspiration water c o n t e n t  (0)  (E) and mean r o o t zone  f o r the t h i n n e d s t a n d i n 1975.  Bars i n d i c a t e p r o b a b l e e r r o r i n the measured d a t a . A l s o shown a r e r a i n f a l l  ( P ) , the modelled  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 t i o n (Ej)  components o f d a i l y  and i n t e r c e p -  evapotranspiration  and the modelled d a i l y d r a i n a g e (D)  77  /xiv  Figure 3.2  Page The upper diagram shows h o u r l y , daytime transpiration  ( E ) , modelled ( s o l i d l i n e )  measured w i t h the Bowen r a t i o / e n e r g y method (x)  stand and  balance  and the porometer ( o ) , f o r the  s t a n d , 30 J u n e , 1975.  The l o w e r 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 ) , modelled T  ( s o l i d and dashed l i n e s , r e s p e c t i v e l y ) measured w i t h the porometer respectively).  thinned  ((A)  and  and ( « ) ,  Measured d a t a m o d i f i e d from Tan  e t al. (1978) w i t h 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 ( S p i t t l e h o u s e and B l a c k , 1980). the e r r o r bar i s shown.  data  Only one arm o f  Soil matric  potential,  i n M P a , p r e d i c t e d by the model i s g i v e n 3.3  78  As f o r F i g u r e 3.2 but f o r 29 J u l y , 1975, w i t h ±30% e r r o r f o r the porometer data  3.4  79  Comparison o f m o d e l l e d and measured mean r o o t zone water c o n t e n t  (6) f o r the t h i n n e d s t a n d i n 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 on J u l y 18.  The bar i n d i c a t e s p r o b a b l e e r r o r  the measured d a t a . rainfall  starting  A l s o shown a r e the  in  daily  ( P ) , the modelled D o u g l a s - f i r and s a l a l  transpiration  and i n t e r c e p t i o n  ( E j ) components  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 the modelled d a i l y d r a i n a g e (D)  of  (E) and 80  /xv  Figure 3.5  Page M o d e l l e d and measured (porometer) transpiration  hourly,  daytime  (Ey) from the D o u g l a s - f i r  (solid  line  and (A), r e s p e c t i v e l y )  and the s a l a l  and ( ® ) , r e s p e c t i v e l y )  f o r f o u r days i n 1978 f o r  the t h i n n e d s t a n d .  (dashed l i n e  The bars ( o n l y one arm shown)  i n d i c a t e the range o f the measured d a t a .  Also  shown i n the upper h a l f o f each quadrant are the h o u r l y above-canopy vapour p r e s s u r e d e f i c i t and s o l a r r a d i a t i o n respectively.  (vpd)  ( K i ) as s o l i d and dashed l i n e s ,  Soil matric p o t e n t i a l s ,  i n MPa,  p r e d i c t e d by the model are g i v e n 3.6  82  As f o r F i g u r e 3.4 but f o r the unthinned s t a n d i n 1974 and no s a l a l t r a n s p i r a t i o n  3.7  Ten t o twenty day average d a i l y rates  85 evapotranspiration  (E) f o r the unthinned s t a n d i n 1979.  Measured  data are from the s o i l water balance ( S . W . B . ) method, w i t h bars ( o n l y one arm shown)  indicating  a ±5 mm o r ±10 mm (when d r a i n a g e was l a r g e ) i n the change i n s t o r a g e measurement.  Modelled E  i s s e p a r a t e d i n t o t h a t from the D o u g l a s - f i r , salal  and i n t e r c e p t e d water ( E j ) .  (P) i s a l s o shown  error  Daily  the  rainfall 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. rainfall  Daily  (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  \  /xvi i  NOTATION  B A  a r e a . o f the s t e m , a t b r e a s t h e i g h t  C  heat c a p a c i t y o f the a i r a t c o n s t a n t p r e s s u r e (= pCp) (J n f  3  0  (m ) 2  C" ) ]  C.  i n t e g r a t o r output  D  d r a i n a g e r a t e (mm d ^)  DBH  t r e e d i a m e t e r a t b r e a s t h e i g h t (mm)  DT  change i n mean p r o f i l e temperature between two time periods  (counts)  (°C)  -2 -1 E  e v a p o t r a n s p i r a t i o n r a t e per u n i t ground a r e a (kg m mm h~^, mm d"^)  s  ,  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 b a l a n c e method, r e s p e c t i v e l y , i n Appendices I and II  -2 -1  E a  e m p i r i c a l v e n t i l a t i o n term i n Penman e q u a t i o n (kg m  E E.p  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 r a t e (kg m d , mm d d a i l y e v a p o r a t i o n r a t e from t h e f o r e s t f l o o r (mm d ^)  -2  -1  -2 Ej  )  -1  -1  e v a p o r a t i o n r a t e of i n t e r c e p t e d water (kg m mm d  d  s  )  -1 , mm h  ,  b -2 -1  E^  t r a n s p i r a t i o n r a t e per u n i t l e a f a r e a (kg m  E max  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 r a t e (mm d ^)  E  Penman e s t i m a t e o f E „ „ (kg m max  p  E  g  -2 -1  m  d  s  )  )  s o i l water s u p p l y 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 r a t e (mm d ^)  -2 -1 Ey  t r a n s p i r a t i o n r a t e per u n i t ground a r e a (kg m mm h ^)  s  ,  /xviii  -2 -1 EQ  e v a p o r a t i o n r a t e w i t h l e a v e s c o m p l e t e l y wet (kg m  G  s o i l heat f l u x d e n s i t y (W n f , MJ rn"  H  s e n s i b l e heat f l u x d e n s i t y (W m  2  s  )  d" )  2  1  -2 ) 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  intercepted r a i n f a l l  (mm)  K+  shortwave r a d i a t i o n f l u x d e n s i t y (W m  -2  -1  -2  , MJ m  d  )  -2 -1 K4-  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  2 -1 s  )  (MJ  m  d  )  eddy d i f f u s i v i t y  f o r heat (m  Ky  eddy d i f f u s i v i t y  f o r w a t e r vapour (m  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 ^)  L*  d a i l y net longwave r a d i a t i o n  LA  l e a f area (m )  LAI  l e a f area index (m  LE  l a t e n t heat f l u x d e n s i t y (W m  M  r a t e of s t o r a g e of energy i n the canopy on a ground area  2 -1 s  )  -2 -1  2 2  M^  multiplier  P  rainfall  R  ground)  rate  d" )  2  to adjust r  )  1  $  for light  maximum v a l u e of P f o r which d a i l y I = P (mm d~^) r u n o f f r a t e (mm d~^)  n  S S  (dimensionless)  (mm d~^)  ~2 R  )  _o  2  c  d  2 leaf/m  b a s i s (W m " , M J m "  P  (MJ m  net r a d i a t i o n f l u x d e n s i t y (W m  -l  _2 , J m  d  )  i n t e r c e p t i o n s t o r a g e c a p a c i t y o f the v e g e t a t i o n (mm) r  integrator  sensitivity  (counts (mV 10 min  /xix  diode s e n s i t i v i t y (mV °C ^) S-j-(n)  spectral energy i n T  S (n) w  spectral energy i n w  S -p(n)  w'T  T  a i r temperature (°C) subscripts D and W i n d i c a t e dry  w  (°C s)  !  2  2 -1 (m s )  1  1  cospectral energy (m °C)  and wet bulb, r e s p e c t i v e l y T T  d a i l y average a i r temperature (°C) i n Chapter 2 turbulent f l u c t u a t i o n i n a i r temperature (°C)  1  leaf temperature (°C) T  T T  d a i l y maximum a i r temperature (°C)  m a x  n  d a i l y minimum a i r temperature.(°C) intercept of diode c a l i b r a t i o n equation (°C)  Q  V  diode junction voltage  (mV) subscripts c and m i n d i c a t e  c a l i b r a t i o n and measurement, r e s p e c t i v e l y integrator input voltage  (mV)  Vp  diode power supply voltage (V)  W  water storage capacity of the root zone (mm)  W c  c r i t i c a l water content (mm)  W max  W a t f i e l d capacity  W .-  W 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 (mm)  Z  sensing head separation  n  K  (mm)  i n the reversing  psychrometer  system (m) a  s o l a r r a d i a t i o n 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 i n d a i l y cloudiness f a c t o r (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 i n d a i l y cloudiness f a c t o r (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 r e s p e c t i v e l y , and W indicates wet bulb  temperatures, temperature  vapour pressure i n l e a f stomatal c a v i t i e s  (kPa)  height-corrected vapour pressure of the a i r (kPa) c o e f f i c i e n t i n the interception of r a i n f a l l  equation  (dimensionless) e r r o r term i n Appendix I I I . l  (counts)  error term i n Appendix I I I . l  (°C)  c o e f f i c i e n t i n the equation f o r the d a i l y evaporation of intercepted water (d~^) c o e f f i c i e n t i n 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 i n k(e) c h a r a c t e r i s t i c  (mm d ^)  c o e f f i c i e n t i n the interception of r a i n f a l l  equation  (dimensionless) exponent i n the s o i l water retention (dimension!ess)  characteristic  /xxi f r e q u e n c y i n Appendix I ( s ~ ^ ) , e l s e w h e r e , number of data p o i n t s  (dimensionless)  turbulent fluctuation (kg w a t e r / k g  i n the s p e c i f i c h u m i d i t y of the  air  air)  correlation coefficient  (dimensionless)  l e a f boundary l a y e r r e s i s t a n c e (s  nf^)  canopy o r s u r f a c e r e s i s t a n c e (s m~^) aerodynamic r e s i s t a n c e t o heat t r a n s f e r d a i l y isothermal  l e a f stomatal  or c l i m a t o l o g i c a l  diffusion  (s nf ^)  r e s i s t a n c e (kPa(MJ m  r e s i s t a n c e (s nf"')  aerodynamic r e s i s t a n c e t o vapour t r a n s f e r  (s m ^)  s l o p e o f t h e s a t u r a t i o n vapour p r e s s u r e c u r v e (kPa °C ^) s a t wet b u l b temperature  (kPa °C  s t a n d a r d d e v i a t i o n of the mean  )  (variable)  s t a n d a r d d e v i a t i o n o f the d i f f e r e n c e between means time  (variable)  (d)  wind speed (m s ^) friction velocity  (m s~^)  vapour p r e s s u r e d e f i c i t wetness parameter  i n the v e r t i c a l  h e i g h t above the ground  wind speed (m s ^)  (m)  (m)  dry a d i a b a t i c l a p s e r a t e (°C difference  (kPa)  (dimensionless)  turbulent fluctuation  roughness l e n g t h  o f the a i r  nf^)  i n a s s o c i a t e d parameter  (dimensionless)  \  /xxii p o t e n t i a l temperature ( C) r a t i o of E  m a x  to E  (dimensionless)  g q  Bowen r a t i o (dimensionless) psychrometric constant (kPa °C ^) e r r o r i n associated parameter (dimensionless) e r r o r term i n Appendices II and I I I (°C) with s u b s c r i p t s i n d i c a t i n g diode and l o c a t i o n e f f e c t i v e longwave e m i s s i v i t y of the sky (dimensionless) longwave e m i s s i v i t y of the vegetation (dimensionless) depth of the root zone (mm,  m)  net r a d i a t i o n e x t i n c t i o n c o e f f i c i e n t (dimensionless) 3 volumetric water content (m  3 water/m s o i l )  average volumetric water content of the root zone (m  3  3 water/m s o i l )  f r a c t i o n of e x t r a c t a b l e water i n the root zone (dimensionless) value of 6" at f i e l d capacity (m  3  3  soil) 3 3 value of 6 at which t r a n s p i r a t i o n ceases (m water/m s o i l ) c r i t i c a l value of e  g  water/m  (dimensionless)  reference value of e i n k(e) and ^ ( s ) c h a r a c t e r i s t i c s (m  3  water/m  3  soil)  r e l a t i v e e r r o r term i n Appendix I I I (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 p o t e n t i a l  (MPa)  /xxiii  ^  s  s o i l water p o t e n t i a l  (MPa)  ^  t  t w i g water p o t e n t i a l  (MPa)  an o v e r b a r i n d i c a t e s an average v a l u e  /I INTRODUCTION R e l i a b l e methods o f measuring and c a l c u l a t i n g  forest  e v a p o t r a n s p i r a t i o n a r e e s s e n t i a l f o r the management o f our water resources.  They a r e a l s o r e q u i r e d t o determine t r e e water  requirements  a n d , 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 resource.  Many o f the t e c h n i q u e s f o r measuring and m o d e l l i n g  e v a p o t r a n s p i r a t i o n have been developed f o r a g r i c u l t u r a l much i s known about the h y d r o l o g y o f these s u r f a c e 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 .  s u r f a c e s , and  However, f o r e s t s  For example, they a r e  a e r o d y n a m i c a l l y r o u g h e r , r e s u l t i n g i n lower wind speeds and s m a l l e r temperature and h u m i d i t y g r a d i e n t s above the c a n o p y , they have a lower reflectivity  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  resistance  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 e t a i . , 1976; Rauner, 1976; S i l v e r s i d e s , 1978).  It  i s o f t e n d i f f i c u l t to o b t a i n adequate f e t c h  i n f o r e s t e d t e r r a i n to a p p l y many o f the t e c h n i q u e s f o r measuring evapotranspiration.  M o d e l l i n g must f r e q u e n t l y  be done w i t h a l i m i t e d  amount o f data f o r l a r g e heterogeneous a r e a s . R e l i a b l e measurements o f e v a p o t r a n s p i r a t i o n must be o b t a i n e d f o r the development o f r e a l i s t i c e v a p o t r a n s p i r a t i o n models.  Measurement  t e c h n i q u e s 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 b a l a n c e method and methods u s i n g stomatal measurements are b r i e f l y  reviewed and e v a l u a t e d i n Chapter 1.  resistance The  Bowen r a t i o / e n e r g y b a l a n c e method i s f u r t h e r reviewed and e v a l u a t e d in detail  i n Appendices TI and I I I  s i n c e t h i s method p r o v i d e d  /2  e v a p o t r a n s p i r a t i o n data used i n d e v e l o p i n g the models d e s c r i b e d i n this thesis.  The stomatal r e s i s t a n c e measurement method and the s o i l  water b a l a n c e method a r e f u r t h e r e v a l u a t e d i n Appendix II  s i n c e data  o b t a i n e d u s i n g these methods were a l s o used i n the model development. A b r i e f r e v i e w o f e v a p o t r a n s p i r a t i o n models i s p r e s e n t e d i n second p a r t o f Chapter 1.  There a r e s t i l l  many c o n c e p t u a l problems  i n the p l a n t water r e l a t i o n s r e q u i r e d i n t h e s e models.  Gardner  et al. (1974) comment t h a t t h e r e i s , as y e t , no u n i v e r s a l and t h a t u s e f u l models w i l l s o i l s and v e g e t a t i o n .  the  relationship  require calibration for different  However, M o n t e i t h (1978) warns t h a t  climates,  there  i s an i m p o r t a n t 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 i m p l i s m .  With  t h e s e comments i n m i n d , two 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 a r e f u r t h e r developed and d e s c r i b e d i n d e t a i l  i n Chapters 2 and 3.  The  c r i t e r i a f o r t h e s e models were t h a t they s h o u l d be based on the p h y s i c a l processes i n v o l v e d and the p l a n t responses to the  environment,  but be a b l e to o p e r a t e w i t h a l i m i t e d amount o f weather and s i t e information. Chapter 2 p r e s e n t s a model r e l a t i n g d a i l y f o r e s t  evapotranspiration.  t o the r o o t zone water c o n t e n t and the d a i l y net r a d i a t i o n f l u x .  This  model i s combined w i t h s i m p l e r o o t zone water b a l a n c e and r a i n f a l l i n t e r c e p t i o n models to p r o v i d e a growing season f o r e s t water b a l a n c e model t h a t i s a p p l i c a b l e t o many f o r e s t e d a r e a s . Such models may be adequate f o r r o u t i n e water b a l a n c e c a l c u l a t i o n s ; however, t h e i r e m p i r i c i s m s may do l i t t l e to e l u c i d a t e  /3  the ways t h a t the p l a n t s r e s p o n d . t o t h e i r p h y s i c a l ( M o n t e i t h , 1978).  For example, the model i n Chapter 2 t r e a t s  v e g e t a t i o n as a s i n g l e e v a p o t r a n s p i r i n g u n i t , but i t 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 the u n d e r s t o r y .  environment the  i s important  to  between the t r e e s and  F u r t h e r , m o d e l l i n g o f water use and s t r e s s d u r i n g  the daytime s h o u l d a i d i n u n d e r s t a n d i n g CC^ uptake and t r e e  growth.  Chapter 3 c o n s i d e r s the a p p l i c a t i o n o f a s i m p l e d i f f u s i o n model (Tan et al., 1978) t h a t determines h o u r l y e v a p o t r a n s p i r a t i o n from the t r e e s and u n d e r s t o r y , s e p a r a t e l y , over the growing s e a s o n . piration  Evapotrans-  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 a r e a index o f the v e g e t a t i o n and the vapour p r e s s u r e of the a i r .  deficit  The model i s combined w i t h the above-mentioned r o o t zone  s o i l water b a l a n c e and r a i n f a l l  i n t e r c e p t i o n models t o produce a  second growing season f o r e s t water b a l a n c e model. O b v i o u s l y computer models s h o u l d not be c o n s i d e r e d an end i n themselves.  They encourage the s y n t h e s i s o f o b s e r v a t i o n , h y p o t h e s i s  and t h e o r y ( M o n t e i t h , 1978). should not be f o r g o t t e n critical  However, t h e i r assumptions and  (Waggoner, 1 9 7 7 ) , so t h a t they s h o u l d  p o i n t s and a r e a s o f i g n o r a n c e .  limitations highlight  M o n t e i t h notes t h a t p r o g r e s s  i n b i o m e t e o r o l o g y r e q u i r e s a b a l a n c e between measurement and modelling.  Areas f o r model improvement, and thus f o r f i e l d measurement,  are c o n s i d e r e d i n D i s c u s s i o n . The two e v a p o t r a n s p i r a t i o n models are::oompared and t h e i r  i m p l i c a t i o n s f o r u n d e r s t a n d i n g the p r o c e s s e s  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 o f measuring and modelling f o r e s t  evapotranspiration are reviewed and evaluated.  Measurement, methods  include eddy c o r r e l a t i o n , aerodynamic, Bowen ratio/energy balance and stomatal d i f f u s i o n resistance techniques.  Modelling approaches  include a model r e l a t i n g the d a i l y evapotranspiration rate to the root zone water content and the d a i l y net r a d i a t i o n .flux, the Penman equation, and vapour d i f f u s i o n models r e q u i r i n g stomatal resistance c h a r a c t e r i s t i c s o f the stand to c a l c u l a t e hourly evapotranspiration.  1.  INTRODUCTION  Evapotranspiration i s an important part o f the water balance of forested areas.  The water balance equation can be w r i t t e n as  P = E + D + R + AW/At  (1)  where P i s the p r e c i p i t a t i o n r a t e , E i s the evapotranspiration rate of the f o r e s t , D i s the drainage rate out o f the root zone, R i s the rate of runoff and AW i s the change i n water content i n the root zone over time At.  The rate at which energy i s used i n evapotranspiration,  /6  the l a t e n t  heat f l u x  L, m u l t i p l i e d  ( L E , i . e . the l a t e n t  by E ) , i s an important  heat o f v a p o u r i z a t i o n ,  term i n t h e f o r e s t  energy  balance,  R  where R  n  n  = LE + H + G + M  i s t h e net r a d i a t i o n f l u x ,  (2)  H i s the s e n s i b l e heat f l u x , G  i s t h e s o i l heat f l u x and M i s the r a t e o f s t o r a g e o f energy ( s e n s i b l e , l a t e n t and p h o t o s y n t h e t i c )  i n t h e canopy.  Changes t o the f o r e s t ,  e . g . t h i n n i n g o r c l e a r c u t t i n g , not o n l y a l t e r t h e m i c r o c l i m a t e through changes t o (2) but may s i g n i f i c a n t l y a l t e r t h e water b a l a n c e . Thus, t h e a b i l i t y  t o c o r r e c t l y measure o r iriodel E a i d s i n d e t e r m i n i n g  these changes as p a r t o f w a t e r s h e d - and f o r e s t management programmes.  2.  MEASURING FOREST EVAPOTRANSPIRATION  In 1970 Federer reviewed the t h e o r y and problems o f measuring E.  S i n c e then t h e r e have been many s i g n i f i c a n t advances i n measurement  t e c h n i q u e s and a l a r g e q u a n t i t y o f i n f o r m a t i o n 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 a c c u m u l a t e d , e . g . J a r v i s et al. ( 1 9 7 6 ) , Rauner ( 1 9 7 6 ) , u s i n g m i c r o m e t e o r o l o g i c a l and n o n - m i c r o m e t e o r o l o g i c a l techniques. method  Some examples o f t h e l a t t e r  i n c l u d e t h e s o i l water balance  where E i s o b t a i n e d as t h e 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 , 1 9 7 7 ) .  T h i s method i s sometimes used  to e v a l u a t e m i c r o m e t e o r o l o g i c a l procedures ( B l a c k , 1 9 7 9 ; 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, a c c u r a t e measurements o f  AW/At, D and R a r e o f t e n 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. the s i z e o f the i n s t r u m e n t a t i o n size.  (1977), i s l i m i t e d  by  and the need f o r an adequate sample  Measurement o f the f l o w o f water through t r e e t r u n k s w i t h heat  p u l s e v e l o c i t y meters ( L a s s o i e et a i . , 1977; R u n n i n g , 1 9 8 0 a ) , o r radioactive  tracers  (Waring and R o b e r t s , 1 9 7 9 ) , may  c a l i b r a t i o n w i t h E determined by o t h e r methods.  require  Severing tree  trunks  and p l a c i n g the c u t t r e e s i n water ( R o b e r t s , 1977; R u n n i n g , 1980a) may g i v e anomalously h i g h v a l u e s o f E due to the r e d u c t i o n r e s i s t a n c e t o water f l o w .  in  However, the method may be u s e f u l  for  c a l i b r a t i n g heat p u l s e 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  diffusion  techniques described l a t e r .  remainder o f t h i s s e c t i o n d e a l s w i t h m i c r o m e t e o r o l o g i c a l  1.  The  techniques.  Eddy C o r r e l a t i o n Methods D i r e c t measurement off E r e q u i r e s f a s t response s e n s o r s to measure  the t u r b u l e n t f l u c t u a t i o n s s p e c i f i c humidity  (q ) 1  o f the v e r t i c a l  wind speed (w )  above the f o r e s t canopy.  1  and  The mean v a l u e  o f E o v e r the s a m p l i n g p e r i o d i s g i v e n by  E = p w'q'  (3)  where p i s the d e n s i t y o f a i r and the o v e r b a r r e p r e s e n t s the time average.  The method i s s u i t a b l e f o r d e t e r m i n i n g 30 to 60 minute average  /8  v a l u e s o f E.  S i m i l a r l y , H i s g i v e n by  H = C w'T  where T'  (4)  1  i s the t u r b u l e n t f l u c t u a t i o n  the heat c a p a c i t y o f the a i r .  i n a i r temperature and C i s  The sum o f LE and H o b t a i n e d u s i n g  (3) and (4) s h o u l d equal the net a v a i l a b l e energy (R  - G - M).  Such  agreement has been o b t a i n e d above f o r e s t s f o r mean wind speeds, (u) above 2 m s " Thompson, 1979)  ( H i c k s et al., 1975; Moore, 1976; G a r r a t t ,  1  1.978a;  (Table l . ' l ) . Webb e t 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 t o (3) t h a t depend on how h u m i d i t y Because i t . i s d i f f i c u l t t o - d i r e c t l y proposed an eddy c o r r e l a t i o n / e n e r g y  i s measured.  measure q ' , F r i t s c h e n (.1970)  b a l a n c e 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 o b t a i n e d from (4) and R , G and M being measured o r c a l c u l a t e d (see Stewart and Thorn, n  1973).  The method has been used w i t h v a r y i n g degrees o f  (McNeil and S h u t t l e w o r t h , 1979, see Appendix I)  success  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 ,  (Table  1,1).  A lack of s u i t a b l e instrumentation  f o r the l o n g - t e r m measurement  o f E has been a major l i m i t a t i o n o f eddy c o r r e l a t i o n methods. bead t h e r m i s t o r s  a d e q u a t e l y measure T ' ;  however, h u m i d i t y  Micro-  sensor,  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  w' and are l i m i t e d Shuttleworth,  underestimate  by low wind speeds (Moore, 1976; McNeil and  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 i n 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 s o n i c anemometry (Campbell and Unsworth, 1.979) may . s o l y e 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  d e s c r i b e d by F i c k s Law,  E = -(CK / L)(de/dz) v  (5)  Y  where y i s the p s y c h r o m e t r i c c o n s t a n t and ( d e / d z )  i s the vapour  p r e s s u r e g r a d i e n t a t h e i g h t z o b t a i n e d 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) a t 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 a t m o s p h e r i c s t a b i l i t y  parameter (4> ), i . e . v  where k i s von Karman's c o n s t a n t and u* i s the f r i c t i o n  Ky = k u* z/<j>^, velocity.  S t a b i l i t y c o r r e c t e d wind p r o f i l e measurements o r d i r e c t measurements o f the s h e a r i n g s t r e s s are r e q u i r e d to c a l c u l a t e u * . c o r r e c t form o f t h e s e s t a b i l i t y stabilities  However, the  parameters under a wide range o f  is uncertain for forests  ( P i e r s o n and J a c k s o n , 1975;  Thorn et ai., 1975; G a r r a t t , 1 9 7 8 a , b ; Raupach, 1979). Large d i s c r e p a n c i e s have been r e p o r t e d between aerodynamic and energy b a l a n c e measurements o f E from f o r e s t s  ( S t e w a r t and Thorn, 1973;  Thorn et al., 1975; B l a c k and McNaughton, 1972; McFarlane and B l a c k , 1976, u n p u b l i s h e d d a t a ; Raupach, 1979) (Table Tl.)l). Thorn et al. (1975)  TABLE 1.1: Comparison o f m i c r o m e t e o r o l o g i c a l methods o f measuring the e v a p o t r a n s p i r a t i o n r a t e (E). (a) R a 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 - G - M). (b) R a t i o o f the measurement o f E, u s i n g v a r i o u s methods, to the Bowen r a t i o / e n e r g y balance measurement o f E. n  (a) Method Eddy  correlation  Aerodynamic (b) Method  Source*  Time p e r i o d (min)  (H + L E ) / ( R  n  - G - M)  1 2 3  30 20 30  0.8 0.7 0.8 -  4 5  60 30  0 . 3 - 0.5 0.4 - 1.0  1.1 1.4 1.0  Source*  Time p e r i o d (min)  Eddy c o r r e l a t i o n / energy b a l a n c e  6 7  60 54  1 0.5 -  Aerodynamic  8 9  30 30  0 . 3 - 0.5 1.1 - 1.5  Stomatal r e s i s t a n c e measurements  10  60  0.8 -  S o i l water b a l a n c e  1 1  weekly monthly  E (Method)/E  (Bowen) 1.4 1.0  1,3  0.9 - 1.2 0.9 - .1.0  * ! . . H i c k s et al. ( 1 9 7 5 ) , Moore ( 1 9 7 6 ) ; 2 . Thompson ( 1 9 7 9 ) ; 3 . G a r r a t t (1978a); 4 . Stewart and Thorn (1973); 5. McFarlane and B l a c k ( u n p u b l i s h e d data 1976); 6. McNeil and S h u t t l e w o r t h ( 1 9 7 5 ) ; 7. S p i t t l e h o u s e and B l a c k ( 1 9 7 9 ; ; 8. Thorn e t al. (1975); 9. B l a c k and McNaughton ( 1 9 7 3 ) , w i t h one anemometer; 10. Tan e t al. ( 1 9 7 8 ) ; 1 1 . B l a c k (1979).  /II p o s t u l a t e d t h a t wake d i f f u s i o n additional  transfer  "...aerodynamic flux  estimates  (1978a,b)  seeding e f f e c t s  mechanisms o v e r f o r e s t s .  equations close  and thermal  Garratt  shows t h a t the aerodynamic method can be used f o r  l e n g t h o f the v e g e t a t i o n .  In G a r r a t t ' s  about 44 iii i n u n s t a b l e c o n d i t i o n s  this  independent  rough surfaces".  a t Z / Z Q > 50 t o 9 0 , depending on s t a b i l i t y ,  forest.  They c o n c l u d e d t h a t  ought not to be used to give  to aerodynamically  a c t as  where z  Q  i s the  measurements roughness  s t u d i e s the minimum z was  f o r an 8 fri t a l l ,  open c a n o p y ,  He suggests t h a t the t u r b u l e n t wakes do not p e n e t r a t e  height.  Grant (1975)  concluded t h a t the Bowen  above  ratio/energy  b a l a n c e method d e s c r i b e d n e x t , would u s u a l l y g i v e more  reliable  measurements o f E than the aerodynamic method.  3.  Bowen R a t i o / E n e r g y Balance Method The Bowen r a t i o / e n e r g y  b a l a n c e method has been s u c c e s s f u l l y  used t o measure E i n many f o r e s t  studies  ( B l a c k and McNaughton, 1 9 7 1 ;  McNaughton and B l a c k , 1973; Droppo and H a m i l t o n , 1973; Gash and Stewart,  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 e t a l . , 1978; Munro, B l a c k , 1979; Tajchman.et al., 1979). s e n s i b l e to l a t e n t heat t r a n s f e r 3 = H/LE.  Substitution  of t h i s  1979; S p i t t l e h o u s e and  The Bowen r a t i o  from the f o r e s t  (3) i s the r a t i o  canopy,  e x p r e s s i o n i n t o (2) t o  i.e. eliminate  H gives  E =  (R  n  -  G -  M)/:t(l  + 3)L ]  (6)  of  /12  E x p r e s s i n g H and LE i n the form o f ( 5 ) , t a k i n g the r a t i o and assuming the eddy d i f f u s i v i t i e s  for  heat (K^) and water vapour (Ky) t o be  equal g i v e s 3 = y ( d O / d z ) / ( d e p / d z ) . measured v e r t i c a l  g r a d i e n t s above the canopy o f p o t e n t i a l  and h e i g h t - c o r r e c t e d  appears to b e . a c c e p t a b l e f o r n e u t r a l  moderately unstable c o n d i t i o n s  ( D y e r , 1967) a l t h o u g h t h e r e  > Ky i n s t a b l e c o n d i t i o n s  Assuming t h a t t h e r e i s no h o r i z o n t a l height,  i.e.  reliability  temperature  vapour p r e s s u r e , r e s p e c t i v e l y (Thorn, 1 9 7 5 ) .  The assumption o f s i m i l a r i t y  evidence t h a t  Here dQ/dz andde^/dz are the  is  (Verma et al., 1978).  a d v e c t i o n below the top measurement  adequate f e t c h , nor net v e r t i c a l o f the Bowen r a t i o / e n e r g y  mass f l o w o f a i r ,  - G - M) measurements.  Sensors w i t h high a c c u r a c y and r e s o l u t i o n are r e q u i r e d measure the small temperature and h u m i d i t y (Table 1 . 2 ; J a r v i s e t a i . , 1976, T a b l e 9 ) . 0  the  balance method depends on the  a c c u r a c y and r e s o l u t i o n o f d 0 / d z , de^/dz and (R  andde /dz d i f f e r e n t i a l l y  to  g r a d i e n t s above  to  forest  Measurement o f d 0 / d z  with a p a i r of psychrometers, that reverse  p e r i o d i c a l l y to remove s y s t e m a t i c e r r o r s ,  i s more a c c u r a t e than  determining  the g r a d i e n t s from p r o f i l e s measured u s i n g f i x e d s e n s o r 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 , 1 9 8 0 ) .  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 a r e shown i n T a b l e 1 . 2 , e x t r a c t e d 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 o f h o u r l y , weekly and monthly t o t a l s methods are shown i n T a b l e 1.1  and I I I .  Good agreement  between t h i s method and o t h e r  and Appendix I I .  from  Webb et al.  d e s c r i b e p o s s i b l e c o r r e c t i o n s t o (6) t h a t depend on howdeq'dz  (1980) is  /13  TABLE 1 . 2 : T y p i c a l r e l a t i v e p r o b a b l e 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 r a t e (o'E/E) o b t a i n e d w i t h a r e v e r s i n g p s y c h r o m e t r i c system (psychrometer v e r t i c a l s e p a r a t i o n 3 m), f o r two Bowen r a t i o (3) ranges and l a r g e and small 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 g r a d i e n t s 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.)  d9/dz  3  °C m"  6E/E {%  |de /dz p  1  Pa m"  1  3 > 0  3 < 0 12  0.10  10  0.02  2  10  38  0.12  2  15  24  0.03  0.5  54  90  0.66  3.96  /14  measured.  The c o r r e c t i o n i s n e g l i g i b l e f o r the case of a vapour  pressure difference from two psychrometers  (equation (34) i n Webb  et  al.).  4.  Methods Using Stomatal Resistance Measurements The t r a n s p i r a t i o n rate of a l e a f per unit l e a f area (E|) i s  E  where e^ i s . leaf, e r  = C(e  £  A  - e )/ L(r Y  s  + r )  (7)  fa  the vapour pressure i n the stomatal c a v i t i e s of the  i s the vapour pressure of the a i r surrounding the l e a f ,  i s the l e a f stomatal d i f f u s i o n r e s i s t a n c e and r ^ i s the boundary  s  layer r e s i s t a n c e of the l e a f .  In p r i n c i p l e s the t o t a l canopy  t r a n s p i r a t i o n rate can be obtained from the summation of E f o r each canopy l a y e r .  Equation (7) has been s i m p l i f i e d f o r needle l e a f t r e e s ,  where l e a f temperature r  b  <  r  s ^  a n  e t  a 1  ''  (T ) i s close to a i r temperature ^978).  (T) and  The t r a n s p i r a t i o n r a t e per unit  ground area (Ey) can be obtained with an error of about ± 20% (Spittlehouse and Black, 1980)  E  T  =  f  (C vpd  from  LAI./lyL 7  .-] )  (8)  where r .' i s the mean stomatal r e s i s t a n c e of the i t h layer of the si J  canopy with l e a f 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 f o r e s t f l o o r evaporation  i s d i f f i c u l t , but i t  could be estimated f o l l o w i n g PTamondon (1972) and Tanner and Jury (1976). However, when the f o r e s t f l o o r i s .dry or with a complete understory cover,, f o r e s t f l o o r ••-'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% f o r moist s o i l conditions and to within ±30% f o r dry s o i l conditions (Table 1)1). The method i s useful f o r i n d i c a t i n g where the major t r a n s p i r i n g 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 d i f f e r e n t from T, and measurement of T^ i s not f e a s i b l e , the Penman-Monteith equation (Monteith, 1965; Thorn, 1972; and Stewart and Thorn, 1973; Shuttleworth, 1978)  E  =  can be used to c a l c u l a t e E, i . e .  [ s  (R  n  - G - M) + (C v p d / r ^ ) j / ( L [ s  + y ( l + r / r ) j ) ) (9) c  v  where :• r  H  -  r  v  -  (u/ui)  and  l / r  c  =_I  (LA I . / r  g  .).  In (9) r ^ and r ^ are the aerodynamic resistances to sensible heat and water vapour t r a n s f e r between the canopy and the above-canopy measurement height z, r  £  i s the canopy or surface r e s i s t a n c e , s i s the slope of  the saturation vapour pressure curve at T and vpd i s evaluated In t h i s approach the canopy i s considered  at z.  as a s i n g l e isothermal  leaf.  /16  Shuttleworth f o r r^,  r^,  (1976b, 1978, 1979) has d e r i v e d more r i g o r o u s and r  c >  In dry needle l e a f canopies r^  compared to the s i z e o f r o f (9)  to i t s v a r i o u s  .  Beven (1979) d i s c u s s e s the  to (9) can be used t o c a l c u l a t e  from f u l l y wet l e a v e s by l e t t i n g r  partially  c  = 0 in (9).  g  sensitivity  evaporation  = 0 i n ( 7 ) , F . = F^  in  These e q u a t i o n s cannot be d i r e c t l y  wet c a n o p i e s ( S h u t t l e w o r t h ,  modifications  i s small  parameters.  E q u a t i o n s (7)  (8) and r  formulations  proposed by S h u t t l e w o r t h  1 9 7 6 a , b , 1978, 1979). for partially  used i n The  wet c a n o p i e s  are p r o b a b l y more s u i t a b l e f o r m o d e l l i n g r a t h e r than measuring evapotranspiration.  It  s h o u l d be emphasized t h a t use o f the e q u a t i o n s  i n t h i s s e c t i o n f o r measuring E from wet o r p a r t i a l l y  wet c a n o p i e s  s h o u l d be avoided where p o s s i b l e . E q u a t i o n s (7) t o (9) a r e time consuming t o use as they many manual measurements w i t h a porometer 1977, 1978) to o b t a i n r  require  (Kanemasu, 1976; Tan e t a l . ,  . , and e x t e n s i v e sampling to o b t a i n L A I . .  However, they may be s u i t a b l e f o r small stands where f e t c h  limitations  p r e c l u d e the use o f p r e v i o u s l y d i s c u s s e d methods.  3.  MODELLING  FOREST  EVAPOTRANSPIRATION  There a r e two major r e q u i r e m e n t s t h a t s h o u l d be met i n 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.  the  F i r s t , the models  s h o u l d be based on the p h y s i c a l p r o c e s s e s i n v o l v e d , and the  plant  /17  responses t o , the environment  (Monteith, 1978).  Second, f o r  practical  u s e , the models s h o u l d r e q u i r e o n l y a l i m i t e d amount o f b a s i c and s i t e i n f o r m a t i o n . another.  climate  Often t h e s e requirements c o n f l i c t w i t h one  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 f o r m a t i o n on w e a t h e r , v e g e t a t i o n and s o i l c o n d i t i o n s , e . g . Waggoner and R e i f s n y d e r ( 1 9 6 8 ) , Cowan ( 1 9 6 8 ) , Murphy and Knoerr Thorn (1972), S h u t t l e w o r t h  (1976b, 1 9 7 9 ) , Federer ( 1 9 7 9 ) .  (1972),  These models  are u s e f u l f o r r e s e a r c h but a r e not o f immediate use to the  forest  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 b a l a n c e c a l c u l a t i o n s . However, some models t h a t r e q u i r e a minimal amount o f  information  ( T h o r n t h w a i t e e t ai., 1957; C u l l e r e t ai., 1976) o f t e n c o n t a i n e x c e s s i v e e m p i r i c i s m and a r e u s u a l l y a p p l i c a b l e o n l y to the r e g i o n 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 e v a p o t r a n s p i r a t i o n are briefly  reviewed.  Models f o r e s t i m a t i n g E f o r l a r g e r e g i o n s from  upper atmosphere d a t a , e . g . Mawdsley and B r u t s a e r t ( 1 9 7 7 ) , are not considered.  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  precipitation,  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 a r e beyond the scope o f t h i s r e v i e w (though they are b r i e f l y d e a l t w i t h i n Chapters 2 and 3 ) .  The use o f o p t i m i z a t i o n t e c h n i q u e s to f i t  model parameters  i s d i s c u s s e d i n Chapman and Dunin (1975) and Johnson and P i l g r i m  (1976).  D i s c u s s i o n s on m o d e l l i n g 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 e t al., 1957; Culler e t a l . , 1976; Linacre, 1977). assumed because T is related to R , and E n  This relationship is  m a x  is usually well correlated  with R (Priestley and Taylor, 1972; Tanner and Ritchie, 1974). n  The  actual evapotranspiration (E) is usually obtained in one of three ways,  (a) E = E  until all P and the available water in the root  m a x  zone are evaporated; decreases;  (b) E / E  m a x  decreases as available soil water  (c) a consumptive use coefficient that is a function of  vegetation cover is defined empirically. The advantage of the Thornthwaite approach is that i t 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 R (and therefore E ) is not well defined and this approach often shows max n  v  poor agreement with more accurate measurements (van Wijk and de Vries, 1954; McNaughton e t 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 (McNaughton 1976a,b; McNaughton e t al., 1979).  E  e q  = (s/(s  + y))(R  n  - G -  extent  It is expressed as  M)/L  (10)  /19  where '('.R  - G ---M) i s determined on a 24 hour b a s i s .  have found t h a t d a i l y E and T a y l o r (1972)  i s w e l l c o r r e l a t e d w i t h (10) and P r i e s t l e y  m g x  proposed t h a t  E  where a i s an e m p i r i c a l  max  = aE  eq  coefficient.  v  For a wide range o f  w i t h small roughness and n o n - l i m i t i n g a = 1.26 ± 0.2  Many r e s e a r c h e r s  s o i l water  (11) '  surfaces  conditions  ( 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 t h a t a > 1 r e p r e s e n t s mesoscale a d v e c t i v e  enhancement o f E.  Values of a < 1 represent advective suppression or  strong surface control  through r  .  Strong surface control  appears to be  the case f o r f o r e s t s where, f o r d r y 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 i v e n 0.6 < a < 1.1  (McNaughton and B l a c k , 1973; J a r v i s et al.,  Moore, 1976; B l a c k , 1979; Munro, 1979; S h u t t l e w o r t h  1976;  and C a l d e r , 1979;  Tajachman e t a l . , 1979) a l t h o u g h l a r g e r v a l u e s have been r e p o r t e d (McCa.ughey,  1978).  Below some c r i t i c a l  v a l u e o f the r o o t zone water s t o r a g e  E becomes s o i l water s u p p l y l i m i t e d . of estimating evapotranspiration  There a r e two e m p i r i c a l  under t h e s e c o n d i t i o n s .  i s to c o n s i d e 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  rate  g  m a x  )  virtually  a function  = (W - W •  (W , - W . ) , where W , i s the maximum s t o r a g e (W a t f i e l d max min max • and W . ^ ' . i i s . t h e r . s t o r a g e a t which t r a n s p i r a t i o n  methods  The f i r s t  (E/E  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 r o o t z o n e , 9  (W),  )/  capacity) r  ceases.  J  In  /20  this method both l i n e a r and nonlinear relationships have been used. the former, E / E 9  e  ^ ec^ ^ 9  s  reac  m a x  ^  (Zahner, 1976).  iec  In  is assumed equal to one until the c r i t i c a l value of ' > below which E/E  declines l i n e a r l y to zero  max  However, i t appears that 8 is dependent on E ec max r  (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 maximum rate of supply of water (E ) A l i n e a r decrease in E  E  s  with 8  g  = be  there is a  to the plant that the s o i l can  g  maintain.  g  is usual Ty assumed,  g  i.e.  (12)  e  I where b is experimentally determined.  A c r i t i c a l value of 8  g  is the  value of Q at which E = E (Cowan, 1969; McNaughton et a l . , 1979). e s max n  p  m = l v  In this two-phase model only meteorological or s o i l factors (but not both) determine E so that for days without rain  E = .[lesser  of  E  m  a  x  >  E ]  (13)  $  Similar methods have been used with E , „ calculated by the Thornthwaite max approach and b determined by optimization techniques (Boughton, 1967; m  J  Federer and Lash, 1978), or E„,„ from (15) max matric potential  and b a function of s o i l  (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, Shuttleworth and Calder, 1979).  1977;  For rainy days, when s o i l water is not  l i m i t i n g transpiration, McNaughton and Black (1973) and Shuttleworth and Calder (1979) suggested that E can be calculated from  E = E + gl max  where I is the d a i l y intercepted r a i n f a l l determined constant. vegetation. (Chapter 2).  3.  If  (14)  3  m a v  and g is an experimentally  E > I then (E - I)  However, i f E  g  < (E - I)  is transpired by the  then transpiration equals E  g  Gash (1978) has demonstrated the theoretical basis of  (14),  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 e f f e c t i v e ventilation of the surface by the air.  The form of Penman's equation that is currently widely used  to obtain a d a i l y Penman estimate of E  E  p  m g x  = (sR /L + YE )/(s n  a  (Ep) is  + )  (15)  Y  where (G + M) i s assumed zero on a 24 hour basis and E  3  a  is an empirical  function of wind run and mean d a i l y vpd at 2 m above the canopy. empirical constant i s frequently used to reduce E  n  An  to the actual E  722  that occurs as the s o i l dries (Thorn and O l i v e r , 1977; Howard and Lloyd, 1979). The c o e f f i c i e n t s 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 c o n t r o l , through r^ and r , respectively. Monteith equation (9)  i s a more exact form of (15)  variations in r^ and r . show how (15)  The Penman-  that allows for  Thorn and Oliver (1977), by considering  (9),  can be modified to allow for variations in r^ and r  due to seasonal and vegetational  changes.  Evaporation of  c  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), 4.  (11)  and  (15).  Approaches Using Stomatal Resistance Characteristics This approach to determining evapotranspiration is the same as  that discussed in Section 2.4,  except that stomatal resistance  c h a r a c t e r i s t i c s are used rather than actual measurements of r .  The  c h a r a c t e r i s t i c s are experimentally determined relationships between r  g  and environmental variables that influence the degree of opening  of the stomata (Running e t a l . , 1975; J a r v i s , 1976; Gash and Stewart, 1977; Calder, 1977, 1978; Tan e t al., 1977, 1978; Federer, 1979; Hinkley e t a l . , 1979; Singh and S z e i c z , 1979, 1980).  Varying degrees of  complexity of these relationships have been used to generate r calculating hourly or daily E.  s  for  *  /23  If T  vpd i s r e l a t i v e l y  - T , (8)  constant with height in the canopy and  can be reduced for dry leaves (Tan et al., 1978)  to  E = Cvpd/[ Lr ] Y  This also follows from (9)  (16)  c  in well ventilated canopies where r  (McNaughton and Black, 1973; Shuttleworth,  1979), and (16)  y  -* 0  has been used  in such canopies, when dry, by Running et al. (1975) and Tan e t ai. (1978). from r  g  If  and r^.  relatively Stewart,  r^ is s i g n i f i c a n t compared t o T , r Equation (9)  should be calculated  has been used in canopies that are  isothermal but with T^ f T (Swift e t ai., 1975; Gash and  1977; Calder, 1977, 1978; Luxmoore e t al., 1978;  1979; Singh and S z e i c z , 1979, 1980). (9)  c  Shuttleworth  Federer,  (1979) has modified  to allow the separate calculation of evapotranspiration from the  understory. The evapotranspiration rate from a f u l l y 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 S z e i c z , 1979; Gash, 1979) (16)  by replacing r  c  with r^.  intercepted water (Ej)  is E . Q  or from  In this situation the evaporation rate of A good approximation to Ej for a  p a r t i a l l y wet canopy is Ej = E Q ( I / S ) , where S is the saturated storage capacity of the canopy (Rutter e t a l . , 1971; Hancock and Crowther, Gash, 1979).  Shuttleworth  (1976b, 1978, 1979)  parameter that is used to adjust r  1979;  has derived a wetness  for p a r t i a l l y wet-conditions.  Gash  724  and Stewart (1977) used an equation similar to (14) hourly basis and E  m a x  from (9)  with E and gl on an  for dry f o l i a g e .  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 p a r t i a l l y wet case they both  require a good estimate of the canopy wind speed to obtain r^.  Forest  f l o o r evaporation could be estimated as in Plamondon (1972) and Tanner and Jury (1976).  A question requiring_.fyrther study is:-  In what way do  the ^ - c h a r a c t e r i s t i c s ^change as the stand ages?  4. CONCLUSIONS  Measurement of the d a i l y evapotranspiration rate from forests over long periods of time i s d i f f i c u l t . high stands, the small v e r t i c a l  Maintenance of equipment above  temperature and humidity gradients  and low wind speed above the canopy l i m i t the successfully used at the present time.  It  methods that can be  appears l i k e l y that routine,  d i r e c t eddy correlation measurements of evapotranspiration w i l 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 i m i t i n g f e t c h , researchers may have t o . r e s o r t to methods that use stomatal d i f f u s i o n resistance or heat pulse velocity measurements, at least where canopies are dry for  /25  s i g n i f i c a n t periods.  The s o i l water balance procedure can be used only  where flow through the base of the root zone is small or can be reliably  determined. Useful evapotranspiration models appear to be of two kinds.  The energy/soil limited approaches .based on • the p r i n c i p l e that evapotranspiration is well correlated with net radiation and root zone water content. daily  It may be well suited to give  estimates of evapotranspiration where data is l i m i t e d .  approach is tested in Chapter 2.  This  The stomatal d i f f u s i o n resistance or  surface resistance approach uses the p r i n c i p l e 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 between the trees and the understory.  transpiration  The method is tested in Chapter 3.  /26  CHAPTER 2 A SIMPLE FOREST WATER BALANCE MODEL  ABSTRACT  A model that calculates the d a i l y growing season forest water balance is presented.  Input parameters are daily solar r a d i a t i o n ,  maximum and minimum a i r temperature,  p r e c i p i t a t i o n , s o i l water  retention and drainage functions and an estimate of s i t e leaf area index.  Evapotranspiration is calculated as a function of the  equilibrium evapotranspiration rate and the fraction of water in the root zone.  extractable  Water d e f i c i t s and the matric potential  the root zone are used to indicate tree water s t r e s s . tested on thinned and unthinned Douglas-fir stands.  of  The model is The same  c o e f f i c i e n t s 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  1.  is over 20% of the growing season r a i n f a l l .  INTRODUCTION  Practical procedures for estimating changes in s o i l water storage, drainage and evapotranspiration in forests are required for the proper management of forested watersheds.  A knowledge of the s o i 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 s o i 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 t e information.  The model calculates d a i l y evapotranspiration, s o i 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. unthinned Douglas-fir (pseudotsuga  The model is tested on an  menziesii  •in - 1974 and a separate, thinned stand .in  2.  (Mirb.) Franco) stand 1975, 1978 and 1979.  BASIS OF THE MODEL  Detailed climate data and s i t e information are not expected to be regularly available for most forested s i t e s ; however, a certain amount of data is required to produce r e a l i s t i c water balances. The climate data required here are: (b) d a i l y r a i n f a l l  and  (a) daily net or solar r a d i a t i o n ;  (c) d a i l y maximum and minimum a4r  The s i t e information required i s :  (a)  temperature.  slope, aspect and l a t i t u d e ;  (b) s o i l p r o f i l e d e s c r i p t i o n , e . g . root zone depth, s o i l texture; (c) root zone s o i l water retention c h a r a c t e r i s t i c s and hydraulic conductivity c h a r a c t e r i s t i c s , o r a drainage versus water content  /28  function,measured or inferred from the s o i l p r o f i l e d e s c r i p t i o n ; (d)  initial  root zone water content;  area index and  (f)  (e) measured or inferred leaf  the c o e f f i c i e n t s in the evapotranspiration function.  The model is composed of three sub-models: ation;  (2)  interception of r a i n f a l l ;  (3)  (1.) evapotranspir-  s o i l water balance.  The components of the model are i l l u s t r a t e d in Figure 2.1.  The  simulated s o i l water content and a tree s t r e s s / s o i l water relationship are used to determine the periods of tree water s t r e s s .  Currently  the model is not designed to.handle conditions of a snow pack or conditions when low temperatures may influence s o i l water movement or uptake by trees.  1.  The Evapotranspiration Sub-model A variety of evapotranspiration models have been reported in the  l i t e r a t u r e 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) of the root zone.  and the average water content  This approach has been chosen rather than physiolo-  g i c a l l y 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 c h a r a c t e r i s t i c s of the vegetation, information that i s not readily available for f o r e s t s .  Non-limiting Soil Water.  The d a i l y evapotranspiration from a surface  with an adequate s o i l water supply depends mainly on the net radiation  /29  RAINFALL _  EVAPOTRANSPIRATION A  M  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 i s the equilibrium evapotranspiration r a t e , R is the net eq n radiation f l u x , G is the s o i l heat f l u x , M is the rate of storage of energy in the canopy (R , G and M are on a 24 hour b a s i s ) , s is the n  slope of the saturation vapour pressure curve at the d a i l y average a i r temperature  ( T ) and y and L are the psychrometric constant and  the latent heat of vapourization of water, r e s p e c t i v e l y , at T.  Many  researchers have found that the maximum daily evapotranspiration rate (E ) is well correlated with (1) max  and Priestley and Taylor (1972)  m =  proposed that  E m  ax  "  «  E  eq  where a is an empirical c o e f f i c i e n t . smooth surfaces, e . g . agricultural a = 1.26 ± 0.2  <> 2  A wide range of aerodynamically  crops, have been shown to have  (Priestley and T a y l o r , 1972; Tanner and R i t c h i e , 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; J a r v i s 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 S e a t t l e , respectively.  However, at Courtenay, on the east  side of Vancouver Island, a rain shadow area where severe water d e f i c i t s occur regularly every summer, a was approximately 0.8 (Black, 1979). Some authors have reported a on a daytime b a s i s , i . e . R > 0, rather than n  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 d a i l y or weekly mean a i r temperature and evapotranspiration, e . g . Thornthwaite e t ai. (1957), Zahner (1967), Culler e t ai. (1976), Federer and Lash (1978), can be quite inaccurate due to the r e l a t i v e l y poor correlation between temperature and net radiation (van Wijk and de V r i e s , 1954; McNaughton e t 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 i s t e d above are found when the foliage i s 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 r a i n f a l l  is considered below,  in a separate subsection. Equation (1) (G + M) < 0.05 R  can be simplified by neglecting (G + M) since  for forests on a daily basis (Jarvis e t al., 1976).  n  The value of 7 can be obtained with s u f f i c i e n t accuracy from ^ max T  +  T  min^ ' 2  w  h  e  r  max  e  T  a  n  d  T  min  a i r temperatures, respectively. difficult;  r  e  t  h  daily Maximum  e  a  Direct measurement of R  n  n  minimum  d  is  however, i t can be calculated from measurements of the  daily solar radiation radiation  a  (Kl),  canopy r e f l e c t i o n c o e f f i c i e n t  (a) and net longwave radiation  (L*) calculated from the a i r  temperature (Jensen e t a l . , 1971; Jury and Tanner, 1975)  R  where L* = (c +  n  = (1  d KVKi  -  „  a)K+  for solar  as follows:  + L*  - e,,)aT . 4  (3)  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 i s in K e l v i n , 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 e t al., 1976).  (Jarvis  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, r e s p e c t i v e l y , rather  733  than the often used value of 0.2 and 0.8.  This improves the  estimation of low values of R and does not s i g n i f i c a n t l y affect the n  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) e  = 1 -  a  as follows: a exp (-7.77E-4(T-273) ) , where T is in Kelvin,  0.261  is used to calculate e 2  Concurrent measurements of Ki and R were available during the n 3  summer of 1975 and 1978. overestimated R  It was found that (3) consistently  by about 10% for R > 8 MJ m" d 2  n  Idso (1980) notes that formulae for e  determined for clear skies in  =  a  continental environments,overestimate e environments.  Reduction of e  g  n  coefficient, r  2  (with corrected e )  n = 169 (Appendix V . l ) . Equation (3)  by about 7% in coastal -2 -1  n>  d  corrected  A least-squares linear regression  had a correlation -2 -1 and a standard deviation, s = ±0.92 MJ m d , y 'X a  = 0.81  g  by 8% for R '> 8 MJ m  the systematic overestimation of R of modelled R  (Appendix V . l ) .  - 1  n  on measured R  n  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 l u s t r a t e s how an average value of R  n  for a small  watershed can be obtained from a single s i t e 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 ) to the plant that the s o i l can maintain (Cowan, 1965; c  734  McNaughton e t a l . , 1979).  A linear relationship between E  and 0  g  e  i s assumed, i . e .  E  -  s  b  e  (4)  e  where b is experimentally determined and 0  g  = (9 - 9 i ) / ( 6 m  n  ~ ^ in^'  m a x  m  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) o^  is the  volumetric water content of the s o i l as a function of depth z .  The  symbols 0"max and 0 m i n are the values of 9 at f i e l d capacity, i . e . where drainage is small, and at which transpiration v i r t u a l l y respectively (Tanner and R i t c h i e , 1974).  ceases,  In the gravelly sandy loam  in this study the matric potentials corresponding to 0~ „ and 6". UlaX  approximately -0.01 particular 0 , E e  E = E  m a x  .  s  MPa and -2.0 ± 0.5 MPa, respectively.  < E  1  m a x  , then E = E , whereas, i f E g  The c r i t i c a l value of 6 ( 9 ) is where E e  e c  $  g  > E = ^-  were  ill 1 n  If m a x  m x  -  at a ,  then This is  i l l u s t r a t e d 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 s o i l water content by neutron s o i l moisture probe and gravimetric sampling.  In this two-phase approach either  meteorological or s o i l factors (but not both) determine the evapotranspiration rate (McNaughton e t al., 1979). Dividing both axes of Figure 2.2 b y - E  m = v  ITIaX  collapses the data" onto a  single curve with a single c r i t i c a l point (Federer, 1979 ; Appendix V.2).  735  DOUGLAS-FIR.  COURTENAY, B.C.  29/6/75 -  FIGURE 2.2:  11/8/75  Daily evapotranspiration rate (E) for dry foliage versus the fraction of extractable water in the root zone (e ) for five ranges of the equilibrium evapotranspiration rate (E ). Critical water content (6 ) is indicated. p  /36  The value of 0  for a day is obtained from the water balance  g  at the end of the previous day (see Section 2.3).  On days when 0  g  may change s i g n i f i c a n t l y due to heavy rain or s i g n i f i c a n t drainage, E w i l l be limited by R .  Evaporation of Intercepted  Rainfall.  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  where I is the d a i l y  = E + gl max m a v  (5)  3  interception.calculated from an interception  model described in the next s e c t i o n , and g is an experimentally determined c o e f f i c i e n t . and E  g  If  E  > I then the lesser of (E- -  is the transpiration rate.  loss and (I  - E)  If  I > E  I)  there is no transpiration  up to the saturated interception capacity of the  canopy i s l e 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 a = 1.05.  A value of g = 0.6 is indicated by r a i n f a l l  piration data during 1975. basis of  (5).  for  and evapotrans-  Gash (1978) has demonstrated the theoretical  /37  2.  The Interception Sub-model Interception of r a i n f a l l  by the forest canopy is an important  part of the forest water balance.  Over 25% of the r a i n f a l l  may be  intercepted by and evaporated from the canopy surface (Rutter e t a i . , 1971; Rutter, 1975; Shuttleworth and Calder, 1979; Gash, 1979). Most interception models are complex requiring r a i n f a l l  data input  in time steps of as short as 5 minutes, e . g . Calder (1977), Gash (1979).  However, with general climate data c o l l e c t i o n , r a i n f a l 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 e t 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 c o e f f i c i e n t s with I < 1, and I = P for P < P  c  (Zinke, 1967; P e r i e r a , 1973; Rutter, 1975; Ford and Deans,  1978; Shuttleworth and Calder, 1979).  The c o e f f i c i e n t s used here  were obtained for a Douglas-fir stand during 1978 using f i v e belowcanopy and one above-canopy rain gauges (Appendix I V . 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. in 1975 (Tan e t a l . , 1978)  The stand LAI was measured  and 1978 (Appendix IV.1)  (Table .2.1).  Relationships between LAI and e a s i l y measured v a r i a b l e s , e . g . Kinerson and Fritschen (1971), Gholz e t al. (1976), would be adequate considering the accuracy of this simple interception model.  3.  The Soil Water Balance Sub-model  Root Zone Water Balance. (Figure 2.1).  The root zone is treated as a single layer  ;  A multilayered root zone is not used because root  water extraction functions and information on root d i s t r i b u t i o n and variations of s o i l hydrologic properties with depth in the are not expected to be available for most forest s i t e s .  profile  However, a  two layered root zone would probably be required for a forest where the root zone consists of layers with s i g n i f i c a n t l y hydrologic properties, e . g . a thick litter-humus soil.  S i g n i f i c a n t horizontal v a r i a b i l i t y  different  layer over the mineral  in the s o i l p r o f i l e could  be accommodated by considering area fractions of the s i t e to be occupied by s o i l s with d i f f e r i n g hydrologic c h a r a c t e r i s t i c s and obtaining the total water balance by summing each f r a c t i o n .  Peck e t a l .  (1977) and Sharma and Luxmoore (1979) indicate that where the variability  is not s u b s t a n t i a l , average s o i l properties can be used  with minimal error.  The two s i t e s modelled here had surfaces  covered by vegetation, slopes of < 10% and s o i l s with high  infiltration  \  739  rates so that runoff was n e g l i g i b l e . rainfall  Horizontal v a r i a b i l i t y  in the  at the s o i 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.)AtA  (6)  where 6. -j i s 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,  r e s p e c t i v e l y , 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 s o i l at the  beginning of the day and drainage is calculated on a daily basis. An exception to this occurs when water content and r a i n f a l l In this case r a i n f a l l  are high.  is divided into four equal amounts and  drainage is calculated on a six hour basis.  Drainage.  In f r e e l y draining s o i l s of varying textures, the hydraulic  gradient is often approximately equal to the gravitational (Black et al., 1969; Nielson et al., 1973; Harr, 1977).  gradient  In this  s i t u a t i o n , termed the unity gradient, D - k ( 0 ) , where k is the hydraulic conductivity of the s o i l at the volumetric water content ( 9 ) of the soil near the base of the s o i l p r o f i l e , or in this case, the mean  /40 volumetric water content of the root zone, 0.  This approximation  has been used i n 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 d i s t o r t e d through removal of water by the plants and through the lack of v e r t i c a l in the s o i l .  homogeneity  In t h i s case a more s u i t a b l e approach i s to obtain a  r e l a t i o n s h i p between drainage and 0, D(9).  This r e l a t i o n s h i p can be  determined by monitoring s o i l water change with time a f t e r soaking an area, while preventing evapotranspiration (Gardner e t a l . , 1975; C l o t h i e r e t a l . , 1977). The s o i l considered here consists of a root zone of g r a v e l l y sandy loam over sandstone.  I t i s r e l a t i v e l y f r e e l y draining and  gradients of less than unity develop as drainage proceeds (Black and S p i t t l e h o u s e , 1980).  Tensiometer and hygrometer  measurements of the matric potential (ty~ ) and neutron moisture probe m  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 characteri s t i c by f i t t i n g the data, f o l l o w i n g Campbell (1974a) and Clapp and Hornberger (1978), to ty = ty m  (0/0 r r  m  where m i s a constant and the  subscript r r e f e r s to a reference value (Table 2.1 )(Appendices IV.1, V.3).  A D(e)  r e l a t i o n s h i p was determined from the residual term i n  water balances c a l c u l a t e d during September 1978, with an estimate of evapotranspiration from (2) and A0/At c a l c u l a t e d from tensiometer p r o f i l e s  /41  of ty and the average ^ ( Q ) c h a r a c t e r i s t i c . ^ m  m  be approximated by an average k(0) k = k^(9/e )^  It  was found that D ( 6 ) could  c h a r a c t e r i s t i c for the root zone s o i l ,  ^  (Campbell, 1974a, with m from the above retention  c h a r a c t e r i s t i c and  from laboratory measurements on an undisturbed  2 m + 3  r  sample from the 0.3 m depth.  This k(0)  c h a r a c t e r i s t i c was used to calcula  drainage, although i t s l i g h t l y 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 properties (Clothier e t a i . , 1977).  If  soil  this relationship cannot be  measured these authors describe a procedure for determining i t ^ ( e ) and k(8) c h a r a c t e r i s t i c s of the s o i l .  Clapp and Horberger (1978)  m  present typical ^ ( 8 ) and k(6) c h a r a c t e r i s t i c s for different m  texture classes.  from  soil  In the model upward flow is neglected since in coarse  s o i l s 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  inability  of trees to meet the atmospheric evaporative demand for water when available s o i l 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:  (a)  Coefficients and Site Parameters Used in the Calculation of the Forest Water Balance of Two Douglas-fir Stands. See text for explanation of symbols.  Coefficients  a  a  b(mm d - v  c  d  g  h  %  0.8  0.12  8..6  0.1  0.9  0,6  0.08  0.6  ±0.07  ±0.02  Site  P  (mm)  c  0.3  ±1  Parameters m  0.22  0.08  • 5.2  0.3  2.8  50  0.75  0.21  0.11  7.2  0.3  1.5  100  0.75  0.21  0.08  . 5.9  0.3  0.9  100  LAI  1974  1840  7.2±2  0.65  1975  840  6.5±1  1978, 1979  822  8.0+1*  *Measured in 1978.  +  ^mr (kPa)  min ±5%  -1 Stem ha"  Douglas-fir plus s a l a l .  max ±5%  e  Year  (m)±20%  8  9  r  (mm d" ) 1  /43  e.g.  Ballard (1974).  large E E  , and 0  e  For example, for high evaporative demand,  < 0.4,  (Figure 2.2).  i.e.  the evapotranspiration rate is less than  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 s t r e s s .  Stomatal opening can be  s i g n i f i c a n t l y reduced when ty < -0.4 MPa (Tan e t al., 1978; Appendix I V . l ) . m  The average root zone ^ ( 0 ) m  ty  mm  for  the root zone.  3.  1.  c h a r a c t e r i s t i c and 0 are used to give an average  TESTING THE MODEL  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 e t a l . , 1978; Black, 1979; Appendix IV).  The s i t e s  are surrounded by a minimum of 5 km of forest of similar age, planted between 1952 and 1955.  The thinned s i t e had a stand density of 820  to 840 stems ha~^ with a thick salal  [Gauitheria  shallon  (Pursh))  understory.  The unthinned s i t e had 1840 stems ha~^ with a scanty  understory.  The s o i l at both sites is a gravelly sandy loam over  sandstone, with roots through the whole p r o f i l e and root density gradually - decreasing with depth. few ridges of 20 to 30 m r e l i e f .  Topography is generally f l a t with a The sites have a slope of less than  744  10% with a NE apsect. droughty summers.  The region is in a rain shadow and has warm,  Model c o e f f i c i e n t s and s i t e parameters are l i s t e d  in Table 2.1.  2.  Performance of the Model Daily (24 hour) R , G, M, T and P were the input data used to n  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 r e l a t i v e l y dry s o i 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 p a r t i a l l y due to an  underestimation of interception by the model. from 0.4 to 1.1 m (Appendix IV.1) a mean root zone depth.  so that i t  Root zone depth varies is d i f f i c u l t  to define  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 R  n  from  daily K i and T in the model gave v i r t u a l l y the same model results as are shown in Figure 2.3. Daily (24 hour) R , T and P were the input data used to test n  the model for the unthinned stand from 17 June to 14 August 1974.  Only  /45  30 JUNE  FIGURE 2.3:  10  20 JULY  31  10 AUG.  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 f o r comparison with the modelled water balance (Figure 2.4).  There was good agreement between measured  and modelled 9 f o r dry and wet conditions.  Evaporation of intercepted  rain accounted f o r a s i g n i f i c a n t fraction of R during the rainy n  period. The 1974 and 1975 data covered only short periods, a l b e i t important ones f o r tree water s t r e s s ; however, they did not provide a major test of the drainage and interception submodels.  Thus, data f o r  longer periods were obtained in 1978 and 1979 at the thinned s i t e . The value of e". was reduced from that used in 1975 (0.11) to agree mm ' N  with observed values during 1978 (0.08) at this s i t e .  3  The adjustment  from the 1975 value was required probably because, f o r 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 s o i l moisture measurements would give the mean water content of the whole root zone.  By 1978 the roots should have grown into areas o r i g i n a l l y  exploited by the cut trees. The input data for 23 May to 30 September 1978 was d a i l y (24 hour) R , G, M, T and P. n  (Figure 2.5).  Measured 9 was used to validate the model  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 s i g n i f i c a n t .  Using daily values  of K+ and T to calculate R from (3) and omitting G and M produced  /47  20  30  JUNE FIGURE 2.4:  10  20 JULY  31  10  20  AUG.  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 i n t e r ception (I) components of the modelled 5-day average daily evapotranspiration (E) and daily r a i n f a l l (P). On days without rain E=Ej.  /48  MAY FIGURE 2.5;  JUNE  JULY  AUG.  SEPT.  As for Figure 2.4 but for the thinned stand i 1978.  749  virtually  the same results as shown in Figure 2.5.  course of the simulated average ^  m  The seasonal  of the root zone (from 0 and the  average TJJ ( 9 ) . c h a r a c t e r i s t i c ' i s compared in_ Figure 2.6.with that measured using tensiometers and hygrometers. Simulated values of ty are, m  general, within the measured range.  in  This is good agreement considering  the approximation involved in using an average ij>(e) c h a r a c t e r i s t i c 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), a further test of the evapotranspiration submodel.  as well as  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 l o o r was used to obtain T and T . . max min  Rainfall was measured in a small clearing 3  and was partitioned into d a i l y amounts based on the r a i n f a l l at a s i t e 9 km away where d a i l y  was also measured.  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 s o i l water content and evapotranspiration and drainage is responsible for the s t a b i l i t y of the  /50  JUNE  FIGURE 2 . 6 :  JULY  AUG.  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 FIGURE 2.7:  JUNE  JULY  AUG.  SEPT. OCT.  As for Figure 2.4 but for the thinned stand in 1979.  /52  model.  Figure 2.8 i l l u s t r a t e s  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 estimates of stress duration.  The model i s r e l a t i v e l y  reliable insensitive  to similar r e l a t i v e changes in b and to changes in g of up to 40%. Interception of r a i n f a l l water to the s o i l .  s i g n i f i c a n t l y reduced  the input of  In 1974, 1978 and 1979 interception was 19, 24  and 23%, r e s p e c t i v e l y . o f the r a i n f a l l  for the periods modelled here.  These values are within the ranges found for f o r e s t , e . g . Zinke (1967), Pereira (1973), Rutter  (1975).  The Douglas-fir trees are water stressed for a s i g n i f i c a n t period of time during the summer.  For example in 1978 E < E  days resulting in an 84 mm water d e f i c i t for the stand.  m g x  for 41  Root zone ii data m r  (Figure 2.6),  suggest s i g n i f i c a n t stress during this period.  vapour pressure d e f i c i t  If  daily  (vpd) data are also available then relationships  between stomatal resistance and vpd and ^ , e.g Tan et al. (1978), can be used to d i r e c t l y indicate tree water s t r e s s .  The severe water  stress indicated by the model for 1978 was confirmed by stomatal resistance measurements (Appendix IV.1) browning of the needles in August. resulting in a 58 mm d e f i c i t .  and the observed severe  In 1979 E < E  m a x  for 39 days  Closure of stomata, with the consequent  reduced photosynthesis, for s i g n i f i c a n t 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 s i t e variations on the water balance i s illustrated  in Figure 2.9 f o r 1979.  This m i c r o s i t e , 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 s i t e so that e , e• max mm and  were estimated to be 0.24, 0.09 and 0.34, respectively.  There  i s 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 t u a l l y  no water  deficit. McNaughton e t 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 l e a s t , partially  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 f o r the size of trees considered (Appendix V . 4 ) .  The values of e during this  period were such that s o i l water would not have limited and drainage would be small.  evapotranspiration  The value of E calculated using (6)  with measured values of P and e in October indicated a ~ 1.1. McNaughton e t al.  (1979), Jackson e t al.  (1976) and de Bruin and  Keijman (1979) found a to increase from warm to cold seasons f o r pasture,  J  /55  JUNE  FIGURE 2.9:  JULY  AUG.  SEPT.  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 s o i 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 c h a r a c t e r i s t i c s w i l l vary between location and vegetation type, and probably through the year; therefore local determination of a is required.  The forest s i t e s 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 s i t e after a 20% increase in canopy leaf area between 1975 and 1978.  This means that the canopy  resistance c h a r a c t e r i s t i c s of the stand had remained constant which suggests t h a t , either the stomatal resistance c h a r a c t e r i s t i c s of the vegetation must have changed, o r , the d i f f u s i v e resistance within the canopy increased s i g n i f i c a n t l y (Chapter 3).  This has implications  for models that use stomatal resistance c h a r a c t e r i s t i c s 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 s i t e and climate data.  Only d a i l y maximum and minimum a i r  temperature and r a i n f a l l , an estimate of leaf area index, and s o i l water retention and drainage functions needed to be s i t e s p e c i f i c ,  "\  /57 while s i t e d a i l y net radiation could adequately be calculated from regional daily solar radiation and s i t e d a i l y temperature. r e l a t i n g d a i l y evapotranspiration to net radiation and the  The function fraction  of extractable water in the root zone gave good estimates of d a i l y evapotranspiration.  The results indicate that the calibrated  evapotranspiration model may hold for varying stand densities and leaf area i n d i c e s . daily r a i n f a l l  Calculating r a i n f a l l  interception as a function of  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 s o i l s 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 s i g n i f i c a n t  water d e f i c i t s 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 w i l l l i m i t 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  rainfall,  vapour pressure d e f i c i t and temperature of the a i r , l e a f area index and stomatal resistance c h a r a c t e r i s t i c s 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 r e l a t i o n 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 d e f i c i t s experienced by the trees.  However, the model tended to underestimate  root-zone water storage as the season progressed, probably through a s l i g h t overestimation of evapotranspiration. characteristics remained r e l a t i v l e y  The stomatal resistance  constant between 1975 and 1978  while the reduced within canopy wind speeds resulted in a s i g n i f i c a n t 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 r a i n f a l l interception by the vegetation.  was l o s t through  /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 r e hazard, stream discharge and other aspects of watershed management.  Evapotranspiration calculations are.also  required'for  predicting tree response to water s t r e s s , partitioning of s o i l water between trees and the understory and determining the effects of stand management p r a c t i c e s , such as thinning, on the s o i l water balance. A wide variety of evapotranspiration models have been reported in the l i t e r a t u r e and are reviewed in Chapter 1 and in Webb (1975). semi-empirical models that give the daily evapotranspiration  Simple, 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 e t al. (1975), Waring and Running (1976), Luxmoore e t a l .  (1978), Tan e t a l .  (1978), Federer  (1979), can be used to p a r t i t i o n the water loss between tree species and can simulate diurnal changes in evapotranspiration, leaf stomatal resistance and leaf water p o t e n t i a l . There may be many situations where the climate data available for calculating evapotranspiration are l i m i t e d .  This chapter presents  an evapotranspiration model based on the simple physiological transpiration model of Tan e t a l .  (1978).  Their model treated  the  trees and understory separately and required only hourly vapour pressure  \  /60  d e f i c i t and temperature of the a i r , and d a i l y root zone matric as the climate data input.  potential  The stomatal resistance c h a r a c t e r i s t i c s and  leaf area index of the vegetation were the required stand characteristics.  Tan e t ai's.  model was modified to allow calculation of  evaporation from wet and p a r t i a l l y wet foliage and to allow for the l i g h t response of the stomata. combined with simple r a i n f a l l  This evapotranspiration model was interception and drainage relationships  to produce a forest water balance model. Douglas-fir [pseudotsuga understory of salal  (Mirb.) Franco) stands with an  menzesii  {Gauitheria  The model was tested on  shaiion,  Pursh).  The model was used to  determine water use and tree water stress during the growing season.  2.  1.  THEORY  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 e t 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 e a s i l y be treated separately. Furthermore, the equation does not work well in the case of a p a r t i a l l y wet canopy (Shuttleworth, presents  1976a).  Shuttleworth  (1976b, 1978,  1979)  modifications to the Penman-Monteith equation, through  a more accurate d e f i n i t i o n of the surface or canopy resistance, that  /61  allow;, the determination of evapotranspiration from the trees and understory separately for wet and dry f o l i a g e .  The l i m i t a t i o n  of  Shuttleworth s approach is that hourly measurements of net radiation 1  above the canopy and the understory, s o i l heat flux and the rate of storage of energy in the canopy are required as well as the vapour pressure d e f i c i t and temperature of the a i r . presented by Tan e t a l .  The transpiration model  (1978) is the p a r t i c u l a r . c a s e 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 / L ) ( e Y  In (1)  £  -  e)/(r  s  + r )  (1)  fa  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 T, e^ is the vapour pressure in the stomatal cavities  temperature,  which can be  approximated to within 2% by the saturated vapour pressure at leaf temperature (e* ) £  for l e a f water potentials greater than -2.5 MPa, e is the  vapour pressure of the canopy a i r and r  g  and r  b  are the stomatal and laminar  boundary layer resistances of the leaf to water vapour d i f f u s i o n , respectively.  Assuming (1)  to describe the average conditions within  the j t h layer of the canopy, the transpiration from this layer per unit ground area i s E . L A I . , where LAI. is the leaf area index of the 0  /62  layer. (Ej)  The transpiration rate of the canopy per unit ground area  is  E  T  =  j  LAIjCC/yLKe^ -  e)j/Cr  s j  »•„.)  +  (2)  Evaporation from a f u l l y 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* SJ  by e* J6  the saturation vapour  X/W  pressure at the temperature of the wet l e a f .  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  s i g n i f i c a n t interaction between the wet and dry f o l i a g e .  Consequently,  there is a f r a c t i o n , w., of the leaf area in a layer that is wet so that evapotranspiration  E  -  (E) is given by  j  IWjLAIjCC/YDle*^  +  (1  -  -  w )LAI (C/YL)(e* j  j  e)j/r  A  -  b  J  e) /(r j  s j  +  ,r .)] b j  Rutter e t 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)  (I/S)EQ,  can be approximated by Ej =  I < S, where I is the ' • • . i n t e r c e p t e d water on the. canopy and S is the saturated interception capacity of the canopy. (The interception model  /63  to obtain I and S i s 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 f o r e s t s .  Thus, i t is now simplified to a two  layered canopy of trees and understory. out r e l a t i v e l y  Assuming that the canopy dries  uniformly, w. - w = I/S, where the overbar indicates an  average wetness factor f o r 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 j with height for the stands g  considered here i s usually small compared with the v a r i a b i l i t y 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 i s the vapour pressure d e f i c 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 s i i g h t underestimation of (e*^ - e),, which i s partly compensated by setting r^ = 0 f o r 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 p a r t i a l l y wet canopy i t i s 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  i s 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  r e l a t i v e error in E due to this assumption, obtained by d i f f e r e n t i a t i n g (1) with respect to T and dividing by E , is (s/vpd)dT, assuming a l l  the  other terms remain constant, and s is the slope of the saturated vapour pressure curve at l e a f temperature.  Thus, there would be an underestimation  of E by 10% for each degree T^ i s greater than T. The above assumptions simplify (3)  E = (C/ L)tvpd /r Y  1  to  + vpd /r  c ]  2  c 2  ]  (4)  where the subscripts 1 and 2 indicate the tree and understory l a y e r s , respectively.  The general form of the canopy resistance ( r )  is  c  r  c  =  ( F  s  +  b  F  )  /  The r ^ i n the numerator of (5)  (  L  A  I  [  1  +  w  ( s ?  / r  b  }  1  }  (  The formulation of r  1979)  but s i m p l i f i e d s i n c e , unlike the Penman-Monteith equation,  is s i m i l a r to that in Shuttleworth  does not contain radiation or aerodynamic resistance terms. wet canopy (w = 1) (5)  reduced to r  canopy (w = 0) i t reduces to  )  i s omitted in the case of the Douglas-  fir.  Q  5  £  (1978, (4)  In a f u l l y  = r^/LAI, while for a f u l l y dry  = r^/LAI^, and  = (r  g 2  + r^/LA^.  /65  Tan e t ai. (1978) found in an open canopy that vpd-j was approximately equal to  and to the vpd at the top of the canopy.  ypdr,  This l a t t e r  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 l o o r evaporation negligible since there is l i t t l e energy to evaporate water. is l i t t l e or no understory forest f l o o r evaporation (E^)  is  When there  is estimated  on a d a i l y basis as the lesser of an energy (net r a d i a t i o n , R ) or s o i l limited rate.  Plamondon (1972) found that v i r t u a l l y  all  R  n  at a moist  forest f l o o r below a Douglas-fir canopy was used to evaporate water. Forest f l o o r P ( R f ) is estimated from above-canopy R n  R  nf  =  R  e x n  1976).  P(  - f |  n  n  ' - A I ) , where in is an extinction c o e f f i c i e n t  Above-canopy R  n  using (Jarvis e t a i . ,  can be measured, or calculated from daily solar  radiation and average T (Jury and Tanner, 1975; Chapter 2).  As the  surface dries, the s o i l below the surface l i m i t s the evaporation rate (Plamondon, 1972; Tanner and Jury, 1976).  A simple approximation of  this s o i l limited rate is the hydraulic conductivity at the water content of the surface layer of s o i 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 s o i 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  variables are termed the ^ - c h a r a c t e r i s t i c s .  environmental  The vpd of the a i r ,  amount of water in the root zone available to the plants and solar  the radiation  /66  (K4-) generally haye the greatest influence on the daily course of  r  g  in conifers ( J a r y i s , 1976; Hinkley et al., 1978; Tan et al., 1977, 1978; Roberts, 1978; Running, 1980b). increases and as the s o i l d r i e s . r  s  The stomata close as vpd  Table 3.1  gives the relationship of  to vpd for four ranges of ty for the Douglas-fir and s a l a l ,  separately.  These relationships are from Tan e t al. (1978) with a  reanalysis of the data for the lowest ranges. In the stands considered here the stomata were f u l l y open when at a leaf was greater than 250 W m  (Tan e t a l . , 1977).  -2  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 i v e f o l d for the f i r s t and l a s t hours of the daytime, and by  doubling r  g  for the second and penultimate hours.  Daylength is determined  from date and l a t i t u d e . Some researchers, e . g . Federer (1979), have used a relationship between twig (^ ) t  or leaf water potential and r  and Meidner (1978) suggested that r  g  g  in transpiration models . Edwards  is related to the water potential  of the epidermis rather than the bulk water potential of the The dependence of r  g  leaf.  on predawn ty^ (Running e t a l . , 1975; Hinkley e t a l . ,  1978; Running, 1980 b,c) can be considered a dependence of r since nightime recovery of tree water potential  g  on ty  m  depends, to a large  extent, on ty (Thompson and Hinkley, 1977; Appendix I V . l ) .  However,  the use of a relationship involving ty may not be adequate for large trees m  767  TABLE 3.1:  Coefficients used to determine the stomatal resistance i r ) of the Douglas-fir and s a l a l . (a) ^ - c h a r a c t e r i s t i c s for vapour pressure d e f i c i t (vpd in kPa); r = exp(a + b v p d ) , for four matric potential (ty ) ranges (modified from Tan e t a l . , 1978). (b) r c h a r a c t e r i s t i c for above-canopy solar radiation (K+) (modified from Tan e t al., 1977). The equations give a m u l t i p l i e r (M ) to increase r predicted by the c h a r a c t e r i s t i c s in (a). s  2  s  m  §  r  Douglas-fir a b  — Salal a  s  , ^m  b  x  (MPa)  6.06  0.27  6 .05  0.19  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  <  10  < U < 350  K+  >  10  W i n "  K+  350  M = r  2  W; m ~  > -0.35  oo  2  Douglas-fir  M = 64.5 r  Salal  M = 137  Wjim"2  r  M = 1 r  -0.71) -0.84)  768  where water stored in the boles, branches and leaves acts as a s i g n i f i c a n t reservoir for t r a n s p i r a t i o n , e . g . Waring and Running (1978).  Boundary' Layer Resistance.  Various formulae are available  calculating r^ for leaves well exposed to the a i r flow.  for  However, leaves  in a canopy are often sheltered by other leaves, e f f e c t i v e l y r^ and making i t d i f f i c u l t to c a l c u l a t e .  increasing  Thorn (1972) and Jarvis et al.  (1976) present formulae describing r^ in terms of shelter factors and average transfer c o e f f i c i e n t s .  However, detailed measurements of  canopy architecture, leaf geometry and wind flow are required to determine these f a c t o r s . In the case of dry needle leaves, an accurate estimate of r^ is not c r i t i c a l of r  s  since r^ < 0 . 1 r ,  e  v  e  n  a  s  (Jarvis et a l . , 1976).  * l°  w  w i n  d speeds and low values  However, an accurate estimate is  required in the case of a wet canopy (see equation-(5)).  The  Douglas-fir canopies considered here are r e l a t i v e l y open and the needles well exposed so that shelter effects are small. is usually dense and wind speed is low.  However, the understory  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  air.  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 w i l l compensate somewhat for the lack of a correction for shelter e f f e c t s .  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, above-canopy wind speed (u) was usually > 1 m s ~ \ in 1975 u > 0.5 m s~^.  the  At the 0.5 m height  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 s t a l l the anemometer (about 0.1 m s~^).  speed of  This reduction of within-canopy u  was due to the increased momemtum absorption by the increased leaf area of the D o u g l a s - f i r . 15 s n f  1  The values of r^ used in 1978 and 1979 were  (u - 0.5 m s ) _ 1  and 300 s rn" (u ^ 0.05 m s" ) 1  Douglas-fir and s a l a l , respectively.  1  for the  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.  2.  There was no understory in the unthinned stand.  Interception Most interception models require r a i n f a l l  data for short time  i n t e r v a l s , 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 r a i n f a l l  totals were available to test the model; however,  for many forest s i t e s r a i n f a l l  w i l l only,be available on a daily basis.  770  Daily interception (I)  I  is  =  h  calculated, from  for  LAIPA  P  >  P  c (6) and  I  =  for  P  P  <  P  c  where P is the daily r a i n f a l l  and h, £ and P  determined in 1978 to be 0.08, Appendix I V . l ) .  £  were experimentally  0.06 and 3.0 mm, respectively (Chapter 2;  On a d a i l y 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 r a i n f a l 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 s o i l water balance model is described in detail  and w i l l be only b r i e f l y described here. a single layer.  All rainfall  in Chapter 2  The root zone is  treated as  reaching the s o i l surface is  assumed to  i n f i l t r a t e immediately, there being no runoff for the sites considered here.  Horizontal v a r i a b i l i t y in the r a i n f a l l  due to concentration by  /71  the vegetation  i s - 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 c h a r a c t e r i s t i c of the soil  (Table 3.2),  k - k (9/6 )( r  2 m + 3  r  ) , "where m i s a constant and the  subscript r indicates a reference value (Campbell, 1974a;Appendix IV.1). The average ty of the root zone (Table 3.2) m  was calculated from the  f i e l d determined average retention c h a r a c t e r i s t i c of the s o i l , ^m  =  ^  ( / e  m r  0 r  )"  m  (  C a m  P  b e 1 1  > 1974a; Appendix IV.1).  end of any day is- used in determining r The value of 0 at the end of day i (0^)  6.  =6.^  + (P.  -  D.  g  at the  for the following day. is  -  The value of  calculated from  E.)At/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 l e v e l .  The s i t e 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 s i t e the stand density was 820 to 840 stems h a  - 1  with a  substantial salal understory, while at the l a t t e r s i t e stand, density was about 1840 stems ha~^ with negligible understory.  The root zone  s o i l at both s i t e s 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 f o r e s t , planted between 1952 and 1955.  They were  on slopes of < 10% with a northeast apsect and the surrounding topography was generally f l a t with a few ridges of 20-30 m r e l i e f . region is in a rainshadow and has warm, droughty summers. c o l l e c t i o n procedures are described in f u l l Nnyamah and Black (1977), Tan et ai.  The  Data  in Tan and Black (1976),  (1977, 1978), Black (1979),  Spittlehouse and Black (1980) and Appendix IV.  The ^.-.characteristics  and s i t e parameters are l i s t e d 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. and 1978, respectively.  Average tree height was 11 m and 13.5 m in 1975 The hourly stand evapotranspiration rate was  determined continuously in 1975 using the Bowen ratio/energy balance method.  Measurements of r a i n f a l l  and ty (with tensiometers and m r  hygrometers) were made d a i l y and measurements of 0 were made weekly with a neutron moisture probe and gravimetric sampling. d i f f u s i o n porometer was used to occasionally measure r  g  A ventilated through the day  TABLE 3.2:  Year  Stand density (stems ha" )  1974  1840  1975  1978, 1979  *measured in 1978.  Site parameters for the thinned and unthinned stands. Symbols explained in the text.  LAI Douglas-fir  k (mm d )  m  0.3  50  5.2  1.5  0.3  100  7.2  0,9  0.3  100  5.9  salal  c(m) (+10%)  <k_ (kPa)  e  7.2±1.5  -  0.65  2.8  840  3.6±0.5  3.0±0.3  0.75  822*  5.0±0.5*  3.0±0.3*  0.75  1  f  r  _ l  r  774  and E was determined from equation (4) within-canopy vpd.  using these r  g  values and measured  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 f u l l y developed until J u l y . between 10 and 20% of the LAI.  The new foliage was estimated to be The Douglas-fir and salal LAI were  estimated to be 4.5 and 2.5 on May 23 and were increased l i n e a r l y 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.  A l s o , 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 l a r g e , 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 s a t i s f a c t o r i l y with limited/climate and s i t e information.  In 1974 daily R  n  and average  T and maximum vpd were determined about 1 m above the t r e e s , 11 m above the ground, from 17 June to 14 August.  Measurements of r a i n f a l l and  8 were made d a i l y and weekly, respectively.  Hourly vpd was obtained by  f i t t i n g 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 v a l u e o f 15% of the saturated vapour pressure at minimum a i r :  775  temperature,  i f a v a i l a b l e , 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 n e g l i g i b l e  amount of salal in the area so that some evaporation would have been taking  place from the forest f l o o r .  An extinction c o e f f i c i e n t 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 r a d i a t i o n , and agrees well with data in Jarvis e t a l .  (1976).  estimated to be 5% of that above the canopy. available r  $  Thus, R ^ was  Since hourly K4- was not  was adjusted in the early morning and eyening as outlined  in section 2.2. At the thinned s i t e , d a i l y maximum and minimum vpd were obtained from a hygrothermograph record of T and r e l a t i v e humidity at 1.6 m above the forest f l o o r , from 10 May to 14 October, 1979. data were f i t t e d to a sine curve to give hourly vpd. 0 and r a i n f a l l  were made every 10 days and r a i n f a l l  Measurements of was partitioned  daily totals based on those obtained 9 km from the s i t e . of LAI and r^ were used with r closure as in 1974.  g  These vpd  into  The 1978 values  modified for early morning and evening  776  4.  RESULTS  The course of 9 and d a i l y evapotranspiration was well simulated during the 1975 period (Figure 3.1). well simulated.  The root zone average ty was also  This was to be expected since the ^ - c h a r a c t e r i s t i c s  were determined in 1975.  The up to 40% underestimation in the daily  E when the s o i l was dry (24 July to 11 August) is less than 10% of the total evapotranspiration for the period. model described in Chapter 2.)  (This also occurred with the  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 i s small (Spittlehouse and Black, 1980).  A l s o , 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 s i t e (Appendix I V . l ) . Increasing the average depth from 0.75 to 0.85 m would provide s u f f i c i e n t water to account f o r much of the above discrepancy.  The diurnal  variation of simulated E compared w e l 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 3.3.).  g  (Figures 3.2 and  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 ^ - c h a r a c t e r i s t i c s . 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 FIGURE  3.1:  AUGUST  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 r a i n f a l l (P), the modelled Douglasf i r and salal transpiration and interception ( E T ) components of d a i l y evapotranspiration ana the modelled d a i l y drainage (D).  P. ST. FIGURE 3.2:  The upper diagram shows hourly, daytime stand transpiration (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  31 MAY FIGURE  3.4;  10  2 0 J U N E  3 0  10  2 0 JULY  31  10  2 0 A U G U S T  31  10  2 0 SEPT.  Comparison of modelled and measured mean root zone water content (S)_ f o r the thinned stand in 1978. The dashed l i n e indicates the simulation starting on July 18. The bar indicates probable error in the measured data. Also shown are the d a i l y r a i n f a l l (P), the modelled Douglas-fir and salal transpiration and interception ( E T ) components of 5-day average d a i l y evapotranspiration ( E ) and the modelled d a i l y drainage (D).  3 0  781  measured v a l u e s , u n t i l A u g u s t , when r a i n f a l l  occurred.  Starting  the  s i m u l a t i o n on J u l y 1 8 , w i t h the measured 8 r e s u l t e d i n a good e s t i m a t i o n o f 0, ty^ and r in Figure 3.4).  g  to the end o f the dry p e r i o d [dashed l i n e  Porometer measurements of r  g  i n 1978 i n d i c a t e d t h a 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 t h a 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 m o d e l l e d d i u r n a l E j compared w e l l w i t h E-j. c a l c u l a t e d from e q u a t i o n (4) w i t h s a l a l r^ = 300 s nf r  s  (Figure 3.5).  and porometer measurements o f  The v a l u e s o f ty i n F i g u r e 3 . 5 . w e r e s i m u l a t e d by the m  m o d e l ; those i n F i g u r e 3.5b and 3 . 5 c r e s u l t e d from the s t a r t i n g on J u l y 18. large v a r i a b i l i t y errors.  simulation  The bars on the measured v a l u e s o f Ey i n d i c a t e  the  i n measured r , some o f which i s due t o measurement  The s t a n d a r d 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 e t a l . , 1978) i n d i c a t e t h a t the v a l u e s o f r  g  the model c o u l d be i n e r r o r by over 50% a t low v a l u e s o f  c a l c u l a t e d by r.  Figure 3.5a i l l u s t r a t e s a reduction i n t r a n s p i r a t i o n  through  stomatal c l o s u r e i n response t o a h i g h v p d , even though the s o i l was moist  = -0.01 MPa).  In t h i s r e g i o n , h i g h v a l u e s o f v p d , daytime  maximum o f 2 . 5 t o 3.5 k P a , u s u a l l y o c c u r i n August r a t h e r , than e a r l y June.  D u r i n g t h i s p e r i o d porometer measurements i n d i c a t e d t h a t  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  > 4000 s m"^ i n the m i d - a f t e r n o o n .  Values of r  s  - 1  i n the morning  to  between 300 and  1000 s m~^ w i t h vpd r a n g i n g from 0.5 to 2.0 kPa are more t y p i c a l t h i s t i m e o f the y e a r .  the  As the s o i l d r i e d through the summer r  s  of increased  782  FIGURE 3.5:  Modelled and measured (porometer) hourly daytime t r a n s p i r ation (Ej) from the Douglas-fir ( s o l i d l i n e and ( A ) , respectively) and the salal (dashed l i n e 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 d e f i c i t (vpd) and solar radiation (K4-) as s o l i d and dashed l i n e s , respectively. Soil matric p o t e n t i a l s , in MPa, predicted by the model are given.  783  and E  T  decreased (Figures 3 . 5 b , c ) .  Stomatal r e s i s t a n c e d u r i n g  f i r s t two weeks o f August was v e r y h i g h , even on low vpd days 3.5c).  Usually r  g  c l o s e d by m i d - d a y . mid-afternoon.  v a r i e d from 2000 s nf^  i n the morning to  the (Figure  virtually  The vpd u s u a l l y reached 3 to 4 kPa by the  The s a l a l was a b l e t o e x t r a c t more water per u n i t  area than the D o u g l a s - f i r a t t h i s time ( p a r t i t i o n i n g s o i l water i s d i s c u s s e d i n s e c t i o n 5 ) .  o f the  leaf  extracted  Both s p e c i e s were observed to  s u f f e r from the s e v e r e w a t e r s h o r t a g e s i n c e a l a r g e number o f l e a v e s t u r n e d brown.  By September the s o i l had f u l l y wetted and v a l u e s o f E  s i m i l a r t o t h o s e i n e a r l y summer were o b t a i n e d ( F i g u r e 3 . 5 d ) . fall  Since  leaf  o c c u r r e d i n September and LAI was not c o r r e c t e d f o r t h i s , t h e r e  will  be a small o v e r e s t i m a t i o n o f E .  As was the s i t u a t i o n  model u s i n g average r - c h a r a c t e r i s t i e s s  was unable t o  f o r 1975, the completely  s i m u l a t e the measured h o u r 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 evaporating intercepted water. after  The D o u g l a s - f i r needles d r i e d out  r a i n due to t h e i r low v a l u e o f r^,  f o r a much l o n g e r t i m e .  and R u t t e r  observations.  d u r i n g the 1978 summer was l o s t  i n good agreement w i t h d a t a i n Z i n k e  (1975) f o r c o n i f e r o u s  rapidly  w h i l e the s a l a l remained wet  T h i s agreed w e l l w i t h v i s u a l  About 23% o f the t o t a l r a i n f a l l through i n t e r c e p t i o n ,  check the approach to  (1967)  forests.  The measured maximum and minimum vpd and c a l c u l a t e d  daylength  were a l s o used i n m o d e l l i n g the 1978 water b a l a n c e .  The seasonal  agreed w e l l w i t h t h a t u s i n g a c t u a l vpd and k> d a t a .  T h i s suggests  trend  t h a t r e a s o n a b l e t r e n d s i n water use and s o i l water d e p l e t i o n would be  784  o b t a i n e d f o r 1974 and 1979. compared i n F i g u r e 3 . 6 .  Measured and modelled 8 f o r 1974 a r e  F o r e s t f l o o r e v a p o r a t i o n under t h i s dense  :  stand was found t o be n e g l i g i b l e and was not i n c l u d e d i n the  figure.  The r e s u l t s a l s o agreed w e l l w i t h the s i m u l a t i o n by the model d e s c r i b e d i n Chapter 2 .  In 1979 measured v a l u e s o f 9 and r a i n f a l l  and v a l u e s o f  d r a i n a g e e s t i m a t e d 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  rates.  These a r e compared i n f i g u r e 3.7 w i t h those from the model. between the two e s t i m a t e s i s good.  Agreement  The model e s t i m a t e s agreed w e l l  w i t h those from the model p r e s e n t e d i n Chapter 2.  Partitioning  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 c e p t e d water showed a s i m i l a r p a t t e r n t o t h a t f o r 1978.  5.  DISCUSSION  There a r e a number o f p o s s i b l e reasons f o r the over d e p l e t i o n of r o o t zone water c o n t e n t by the model d u r i n g J u l y 1978. also highlight  the c r i t i c a l  p o i n t s o f the m o d e l .  These reasons,  An o v e r e s t i m a t i o n  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  overestimation  o f E-j. t o account f o r much o f the above-mentioned e r r o r .  ( T h i s would  not be e v i d e n t i n the d i u r n a l comparisons s i n c e the measured e s t i m a t e s of E-p use the same v a l u e of LAI as the m o d e l . )  T h i s e r r o r would tend  and TJJ . The s -m and ty may be i n e r r o r i n t h a t the y ranges  t o reduce the e f f e c t o f the n e g a t i v e feedback between r 3  r e l a t i o n s h i p between r  c  m  m  /85  20  FIGURE 3.6:  30 JUNE  10  20 JULY  ' 31  10 20 AUGUST  As for Figure 3.4 but for the unthinned stand in 1974 and no salal transpiration.  10  FIGURE 3.7:  20 MAY  31  10  20 30 JUNE  10  20 JULY  31  10 2 0 31 AUGUST  10  2 0 30 SEPT.  10 OCT.  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 l a r g e , e s p e c i a l l y the wettest range where transpiration rates are the highest.  This i l l u s t r a t e s the need for a more detailed  determination of the relationship between r r  and ii . s m.  A l s o , as the  r  s o i l dries the model becomes increasingly sensitive to the accuracy of the ty{Q) c h a r a c t e r i s t i c 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 p r o f i l e can be much d r i e r than the lower part.  However, f i e l d measurements (Figure 2.6  Chapter 2; Nnyamah and Black, 1977) out r e l a t i v e l y uniformly.  in  indicate that the root zone dried  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 t r a n s p i r a t i o n .  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 i r temperature is not 1975 the hourly understory R  n  a major source of error.  During  (Tan and Black, 1975, unpublished data)  was about equal to the salal transpiration when s o i l water was non-limiting.  Furthermore, vpd affects both the numerator and  denominator in (4). and T  0  In dry s o i l conditions, when E is less than R  > T, the underestimation of (e*  0  n  - 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 b a s i s , with maximum  vpd's > 1.5 kPa, the usual situation during dry periods, these l a t t e r 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 ' c a n indicate water stress (leaf water potential < -1.8 MPa) s  but i t also means that there is a high resistance to carbon dioxide uptake, with a consequent reduced rate of photosynthesis. of r r  s  s  A value  equal to 1500 s nf ^ is 5 times greater than the minimum observed  of the Douglas-fir. 3  for vpd > 0.1  Values of r > 1500 s nf^ occur when ty < -0.95 MPa s m -  m  kPa, when -0.95 MPa < ty < -0.35 MPa for vpd > 1.5 kPa m  and when ty > -0.35 MPa for vpd > 2.5 kPa. m -  The model indicated, for  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 t h i s .  The discrepancy in the model is due to the  overestimation in water use noted e a r l i e r . of s i g n i f i c a n t water stress in 1979.  The model estimated 24 days  Closure of stomata for s i g n i f i c a n t  periods during the summer was noted by Emmingham and Waring (1977) for Douglas-fir in Oregon. A transpiration d e f i c 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 . water d e f i c i t .  (It  no s o i l  is assumed that the vpd is not affected by the  /89  increased transpiration.) and 47 mm in 1979.  The transpiration d e f i c i t was 78 mm in 1978  This d e f i c i t was probably due to the fact that  the salal understory used a s i g n i f i c a n t fraction of the available water. The ^ - c h a r a c t e r i s t i c s are such that the salal has lower values of r  than the Douglas-fir for any value of vpd and ty , and this tends  s  m  to compensate for the lower LAI of the s a l a 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. • m m J  r  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 t s 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 i n g of the salal In 1975 about 25% of the daily above-canopy R (Tan and Black, 1975, unpublished data).  n  understory.  reached the understory  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 d e f i c i t and the period of continuous stress was reduced to f i f t e e n 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 w i l l increase.  A l s o , there may be further reductions in the within canopy  790  wind speed and increases in understory r^.  The reduced l i g h t may  further lower understory transpiration through the"light the stomata.  response of  The accompanying reduced heating of the a i r around the  understory would mean that leaf temperature and, therefore, between the vapour pressure in the stomatal would be decreased. further reduced.  the  difference  c a v i t i e s and in the a i r  Consequently, understory transpiration would be  Black and Spittlehouse (1980) and Black et al.  (1980) have also noted the s i g n i f i c a n t 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 d e f i c i t s 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 s o i l that has a low water holding capacity and to the low summer r a i n f a l l . o f  which, the model indicated,  over 20% is l o s t through interception by the f o l i a g e .  A l s o , 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 s o i l was moist to  about 65% when the s o i l was dry.  There was no salal in the unthinned  stand and, for the short period studied, evaporation from the forest f l o o r was found to be negligible due to low s o i l water content and the low level of net radiation at the forest f l o o r . In general, seasonal and diurnal values of the transpiration rate compared well with measured values.  However, when s o i l matric  potential was between -0.15 and -0.35 MPa the evapotranspiration model s l i g h t l y overestimated transpiration so that s o i 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 c h a r a c t e r i s t i c s for the above matric potential  range.  These errors  would tend to counteract the negative feedback between s o i l 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  c h a r a c t e r i s t i c of the s o i l , especially for dry  s o i l where the water potential  changes rapidly for small changes in  s o i l water content. The evapotranspiration model indicated the importance of a good estimation of the boundary layer resistance of the leaves. parameter i s c r i t i c a l  This  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 d e f i c i t was a good approximation of that within the canopy.  This vapour pressure  d e f i c i t was adequately simulated from daily maximunrand minimum values.  Light limitation  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. figures show ten to twenty day mean d a i l y evapotranspiration  The rates.  Since the water balance models use the same interception and drainage r e l a t i o n s h i p s , the figures are a comparison of the evapotranspiration models during the growing season.  The c o e f f i c i e n t s 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 a v a i l a b l e .  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 c h a r a c t e r i s t i c s in the S.D.R. model.  The figures also show the average daily evapotranspiration rate  calculated with the s o i l 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  falls  within the error of the measured data (only one arm of the error bar is shown).  This good agreement is due to the r e l a t i v e accuracy of  the c o e f f i c i e n t s of the models and to the fact that i f too much water  794  n  1  1  r  1  1—  1974 UNTHINNED DOUGLAS-FIR STAND I  E (mmd" ) 1  " Z L  -Hi I  J  I  J  E.S.L. M O D E L S.D.R. M O D E L SW.B. M E T H O D  40i  P , (mm d ')  20 Ol  FIGURE 4.1:  ±  20  i  J U  30 JUNE  10  •  20 JULY  31  10 AUG.  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.S.L. MODEL S.D.R. MODEL S.W.B. METHOD  E (mm  d' ) 1  1978 THINNED DOUGLAS-FIR STAND  -h40  ko  (mm d" ) 1  UL  31  MAY  FIGURE 4.2:  As for Figure 4.1  but for the thinned Douglas-fir  stand in  1978.  -i  1  1  1  1  1  1  i  1  r  r  r  .1  T  r  1  1979 THINNED DOUGLAS-FIR STAND  1~  ~T  r  — i  — ,  E  (mmd ) -1  X  J —  —  L~::  E.S.L. MODEL  T  S.D.R. MODEL S.W.B. METHOD r-60  P  -40 -20  (mmd"')  •• i  10  20 MAY  I i  31  10  20 30 JUNE  FIGURE 4.3:  10  20 31 JULY  As for Figure 4.1 in 1979.  10 20 31 AUGUST  10  20 30 SEPT  but for the thinned Douglas-fir  stand  10 OCT  /97  is l o s t 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  i s that the evaporation rates are high and most of the daily  interception  is l o s t 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 s t r e s s .  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 w e l l .  The S.D.R. model i s  expected to work well i f the LAI, ^ - c h a r a c t e r i s t i c s 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 d a i l y (24 hour)  evapotranspiration rate from the S.D.R. model i s , to a good  798  19 a p p r o x i m a t i o n , £ [ ( C / Y L ) v p d . / r • ] , where i i s hours o f the day and r i=6 i s the canopy r e s i s t a n c e o f the s t a n d . (Outside these l i m i t s to i , 1  E=0.)  c  c  E q u a t i n g t h i s w i t h the d a i l y , ( 2 4 hour)  f o r dry f o l i a g e  i n the energy 1 i m i t i n g  E from the E . S . L . model  case, i!e~  :  a ( s / [ s + y ] ) R / L , a n d rearranging gives n  a  *  (C(s  +  Y)/YS)(  19 I i=6  vpd./r 1  .)/R C  1  (1) n  T h u s , the r e l a t i v e c o n s t a n c y o f a depends on a complex between the a i r t e m p e r a t u r e , daytime v p d , r When s o i l water i s not l i m i t i n g maximum vpd i s l e s s than 1.5 k P a , r c o n s t a n t through the d a y t i m e . t o (£vpd,)/R '. n  climatological  (through r )  £  g  transpiration  , and t h e r e f o r e ,  and R « n  and the r  , is  C o n s e q u e n t l y , from (1) a i s  The r a t i Q 'C(.Eypd)/YR resistance (rj).  relationship  n  i s a d a i l y isothermal  U s u a l l y , r^  daily relatively  proportional or  i s c a l c u l a t e d on an  h o u r l y b a s i s , e . g . S t e w a r t and Thorn (1973) and J a r v i s e t ai, r a t h e r than the d a i l y v a l u e p r e s e n t e d h e r e .  (1976),  In g e n e r a l , low vpd days  a r e u s u a l l y a s s o c i a t e d w i t h low r a d i a t i o n days w h i l e h i g h vpd days (> 1.5 kPa) a r e accompanied by c l e a r s k i e s and h i g h R d a i l y r^ may be r e l a t i v e l y  n  so t h a t  the  c o n s t a n t between c l o u d y and c l e a r d a y s .  s h o u l d be remembered t h a t the vpd i s s t r o n g l y  i n f l u e n c e d by R  n  It  since  t h e a i r temperature a n d , t h e r e f o r e , t h e s a t u r a t e d vapour p r e s s u r e o f 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 v a r y from 1.5 t o 3.0 k P a , so t h a t r^ may not be c o n s t a n t f o r such d a y s .  However,  i n c r e a s e s i n vpd above about  /99  1.5 kPa are compensated by increases in r , in response to the high v p d ' s , such that the hourly evapotranspiration does not increase. Consequently, the term ( £ v p d / r ) / R may remain relativey constant for c  these high vpd, clear sky days. could be r e l a t i v e l y  n  The above arguments suggest that a  constant over a wide range of energy  limiting  weather conditions, assuming there was no mesoscale advection to d r a s t i c a l l y influence the vpd.  Upwind conditions are incorporated into  the S.D.R. model through t h e i r  influence on the vpd of the a i r (assuming  vpd is measured on s i t e ) .  Thus,a may vary s i g n i f i c a n t l y close to a  change in surface cover due to advection (McNaughton 1976b). downwind  a w i l l be r e l a t i v e l y  Further  independent of these conditions.  The s i t e s considered here were surrounded by more than 5 km of s i m i l a r l y 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 e t a l .  (1979), Jackson t al. e  (1976) and de Bruin and  Keijman (1979) for pasture, bare s o i l and a lake, r e s p e c t i v e l y . increase in a indicated here in October 1979 (Figure 2.7) 35%, suggesting other factors may also be involved. weather patterns may vary between the summer and f a l l  The  was about  For example, regional (Maunder, 1968)  the result that the relationship between daily vpd and R  n  with  may change.  The ^ - c h a r a c t e r i s t i c s are not expected to have changed since they have remained r e l a t i v e l y  constant since 1975.  Priestley and Taylor (1972) argue that L E / R decreases  in response to a  that a i s , therefore,  n  It  should be noted that  should decrease as s / ( s + y)  decrease in mean surface temperature,  relatively  temperature  independent.  and  /100  The two models are d i f f e r e n t with respect to the s o i l water supply l i m i t a t i o n of t r a n s p i r a t i o n .  In the case of the S.D.R. model  s o i l water status affects E  values of \b < - 0 . 3 5 MPa. m  T  for a l l  T  However, in the E . S . L . model, when the radiant energy supply i s low, E may be energy limited even through the s o i l is relativey dry.  A  second d i f f e r e n c e , described next, is probably due to i n s u f f i c i e n t data to f u l l y define the ^ - c h a r a c t e r i s t i c s at high matric p o t e n t i a l s .  Under  many conditions the s o i l control of- transpiration is i n i t i a t e d at wetter conditions in the E . S . L . model than in the S.D.R. model. on a sunny day, E  For example,  r 4 . 5 mm d~^, the s o i l w i l l l i m i t 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  (ty ) of m  - 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 ^ - c h a r a c t e r i s t i c may require dividing into narrower  ranges, and that unless t h i s is done, the S.D.R. model may overestimate transpiration when - 0 . 3 5 < ty < - 0 . 1 2 MPa.  This i s probably the  major reason for the underestimation of e in early July 1978 by the S.D.R. model since ^  was about - 0 . 1 2 MPa at the end of June, in good  m  agreement with the E . S . L . model. Since a remained r e l a t i v e l y  constant between stands in 1975 and  1 9 7 8 , the relationship between d a i l y vpd and R  n  and that between  r  £  and vpd must have either remained constant, o r , compensated each other's changes.  From equations.(4) and (5) in Chapter 3 , f o r a dry canopy,  r „ = [LAI-,/^.,  + LAI /(r 9  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 r  c  and vpd appears to have remained constant, the stomatal  between and/or  boundary layer resistance characteristics must have changed to compensate for the LAI change.  The porometer measurements indicated that  the ^ - c h a r a c t e r i s t i c s remained r e l a t i v e l y  constant between 1975 and  1978, which means that the boundary layer resistance (r^) changed.  must have  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 \ i  Thus, salal r, b  increase in salal r^ (from 90 to 300 snf^).  was of a size similar to i t s minimum value of r  s  with the  result that salal transpiration was reduced s u f f i c i e n t l y to compensate f o r the increased transpiration of the D o u g l a s - f i r . in salal t r a n s p i r a t i o n ,  Further reductions  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  c a v i t i e s of the leaves and the a i r .  There may also be greater  l i g h t r e s t r i c t i o n of stomatal opening.  3.  Use of the Models in Water Balance Calculation An important question i s :  models applicable?  Where are each of the  evapotranspiration  This depends on the amount of water balance  information required and the time and e f f o r t available for the measurement programme to determine the s i t e c h a r a c t e r i s t i c s  initial  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 r a i n f a l 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 d a i l y solar radiation and mean a i r temperature. a n  max  The values of  d 9 . (required in the calculation of e ) can be obtained as min ^ e m  the values of 6 at matric potentials of -0.01 -2.5 MPa, respectively.  The E versus 9  g  MPa (in coarse s o i l s ) and  relationship (Figure 2.2)  be reduced to two straight l i n e s by dividing E and e (Figure V . 3 , Appendix V.2).  g  can  by E  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.  F i e l d interception and drainage functions should be  determined where p o s s i b l e , 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 partitioning of the available water between the trees and the understory or the forest f l o o r .  As noted in Chapter 3, Plamondon (1972) indicated  that evaporation from a moist forest f l o o r was approximately equal to the R at the forest f l o o r minus the s o i l heat f l u x . n  The l a t t e r  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 l o o r is moist,forest f l o o r evaporation could be approximated by forest f l o o r R .  However, as the  /103  soil dries the s o i l heat flux may have to be considered. floor R  n  Forest  can be estimated using an extinction c o e f f i c i e n t and LAI'.as  noted in Chapter 3.  Where there i s an understory the forest  evaporation can probably be" neglected.  floor  Measurements in 1975 at the  thinned s i t e (Tan and Black,' unpublished data) indicate that transpiration of the salal understory, when s o i l water was not and the foliage was dry, was approximately equal to the R the s a l a l . E  g q  limiting  just above  n  This is equivalent to an a for the salal of about 1.6 with  calculated from the salal R > n  See also Thorn (1975, p. 103, case  ii).  Tanner and Jury (1976) partitioned water loss between a crop and the s o i l surface by using separate values of a for each surface.  In  the case of the forest  a[s/(s  +  Y  )]R  n  = « [s/(s  + Y)](R  n  + a [s/(s  + y)]R  n 2  1  2  -  R  n 2  )  (2)  where the subscripts 1 and 2 indicate Douglas-fir and s a l a l , respectively. gives  Since, for 1975, a = 0.8,  ~ 0.53.  The partitioning  ~ 1.6 and R  is d i f f i c u l t  n 2  /  R n  to determine  - 0-25, during  the s o i l l i m i t i n g 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 Black et ai.  transpiration.  (1980) note that i f the r a t i o of L A ^ / r ^  is known [also r  K 1  and r , ] , 9  to L A I / > 2  s 2  then the s o i l water balance values of E  (2)  \  /104  can be partitioned even during the s o i l l i m i t i n g phase.  Occasional  f i e l d measurements with a porometer may be used to indicate typical values of r  g  for the above c a l c u l a t i o n .  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 s o i l water was n o n - l i m i t i n g , salal transpiration was about 33% of the stand transpiration.  This indicates R 2 /  obtained using a R data and LAI-j = 5.  n  n  R n  = 0.15,  s i m i l a r to the value  extinction c o e f f i c i e n t of 0.4 from Tan and Black's Consequently, a-j ~ 0.66.  The S.D.R. model i s a more direct method for partitioning  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 - c h a r a c t e r i s t i c s s i s a long and arduous process.  The S.D.R. model should be useful as  a research tool to highlight c r i t i c a l The model is also applicable  to  parts of the transpiration  process.  investigating the effects of stand  management p r a c t i c e s , 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 l d work.  Obviously,  measurements at more forest s i t e s and with d i f f e r e n t species are required to test the generality of these models and determine the  /105  variability  of the s i t e c h a r a c t e r i s t i c s (a,  b and the ^ - c h a r a c t e r i s t i c s ) .  Better resolution of the ^ - c h a r a c t e r i s t i c s is required.  Long term  monitoring of s i t e s is required to determine the s i t e c h a r a c t e r i s t i c s for the f a l l  to spring period, especially in l i g h t of suggestions by  Emmingham and Waring (1977) and Waring and Franklin (1979) that the fall  and spring are the time of maximum growth of west-coast c o n i f e r s .  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 c o e f f i c i e n t s , vapour pressure d e f i c i t and leaf \  temperature. 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Turbulence measurements above a pine f o r e s t . Boundary-Layer Meteorol. 16: 293-310. Thornthwaite, C.W., J . R . Mather and D.B. Carter, 1957. Instruction and tables for computing potential evapotranspiration and the water balance. Publ. Climatol. Vol. 10, No. 3, Drexel Inst. T e c h n o l . , Lab. C l i m a t o l . , Centerton, New Jersey.  /120  van Wijk, W.R. and D.A. de V r i e s , 1954. A g r i c . S c i . 2:105-119.  Evapotranspiration.  Neth. J .  Verma, S . B . , N.J. Rosenberg and B.L. Blad. 1978. Turbulent exchange c o e f f i c i e n t s for sensible heat and water vapour under advective conditions. J . Appl. Meteorol. 17: 330-338. Waggoner, P . E . , 1977. Agriculture  Overview of modeling.  and Forest  Meteorology,  University, West Lafayette,. Indiana,  In:  Am. Met.  13th conference Soc,  on  Purdue  pp. 99-100.  Waggoner, P.E. and W.E. Reifsnyder, 1968. Simulation of the temperature, humidity and evaporation p r o f i l e s in a leaf canopy. J . Appl. Meteorol. 7: 400-409. Waring, R.H. and F . J . F r a n k l i n , 1979. Evergreen coniferous forests of the P a c i f i c Northwest. Science 204: 1380-1386. Waring, R.H. and M.J. Roberts, 1979. Estimating water flux through stems of Scots pine with t r i t i a t e d water and phosphorus-32. J . Exp. Bot. 30: 459-471. Waring, R.H. and S.W. Running, 1976. Water uptake, storage and transpiration by c o n i f e r s : a physiological model. In: Ecological  Studies,  Analysis  and Synthesis,  Vol. 19, Water and  plant Life, O.L. Lange, L. Kappen and E . - D . Schulze, E d s . , Springer-Verlag, B e r l i n , pp. 189-202. Waring, R.H. and S.W. Running, 1978. Sapwood water storage: its contribution to transpiration and effect upon water conductance through the stems of old-growth Douglas-fir. Plant, Cell and Environment 1: 131-140. Webb, E . K . , 1975. Evaporation from catchments., In: Prediction in Catchment Hydrology, T . G . Chapman and F.X. Dunin, E d s . , Australian Acad. S c i . , The G r i f f i n Press, Netley, A u s t r a l i a , pp. 203-236. Webb, E . K . , G.I. Pearman and R. Leuning, 1980. Correction of flux measurements for density effects due to heat and water vapour transfer. Quart. J . R. Met. Soc. 106: 85-100. Wigley, G. and J . A . Clark, 1974. Heat transport c o e f f i c i e n t s for constant energy flux models of broad leaves. Boundary-Layer Meteorol. 7: 139-150.  7121  Yoshitake, M. and I. Shimizu, 1965. psychrometric constant. In: and Content  in Science  Experimental results of the  Humidity and Moisture Measurement and Industry, Vol. 1, A. Wexler, Ed.,  Reinholt, New York, pp. 70-75.  Zahner, R., 1967. Refinement in empirical functions for realistic soil-moisture regimes under forest cover. In: international Symposium on Forest Hydrology, W.E. Soper and H.W. L u l l , Eds., Pergamon Press, Oxford, U.K.,. pp. 261-274. Zinke, P . J . , 1967. Forest interception studies in the United States. In: International Symposium on Forest Hydrology, W.E. Soper and H.W. L u l l , Eds., Pergamon Press, Oxford, pp. 137-161.  /122 Reprinted from JOURNAL OF APPLIED METEOROLOGY, Vol. 18, No. 5, May 1979 American Meteorological Society Printed in U. S. A.  APPENDIX I  Determination of Forest Evapotranspiration Using Bowen Ratio and Eddy Correlation Measurements D . L . SPITTLEHOUSE AND T . A . BLACK Department  of Soil  Science,  University  of British  Columbia,  Vancouver,  B.C.  Canada  V6T 1W5  (Manuscript received 18 August 1978, in final form 26 December 1978) ABSTRACT Rates of evapotranspiration from a 14 m high Douglasfirforest 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 balance/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  measurements of evapotranspiration from a Douglas fir stand by the two methods.  Direct measurement of evaportanspiration is an important part of hydrologic studies of forested water2. Basic considerations sheds. Various micrometeorological techniques available The Bowen ratio (/3) is the ratio of the vertical flux for the determination of forest evapotranspiration have of sensible heat to that of latent heat above the canopy. been reviewed by Fritschen (1970) and Federer (1970), In the energy balance/Bowen ratio method used here and the results of a number of studies are presented in Jarvis et al. (1976). A major problem in such studies evapotranspiration ( £ 3 ) is determined using the equation (see Fuchs and Tanner, 1970) has been the measurement of the very small vertical temperature and humidity gradients above the forest E, = lRn-G-Myi(l+p)L], (1) canopy which result from the high degree of turbulent mixing generated by the large roughness of forests. where R is the net radiation to the canopy, G the soil heat flux, M the canopy energy storage rate and L the However, several groups have had considerable success latent heat of vaporization of water. Assuming that in determining forest evapotranspiration over extended the eddy diffusivities of heat (K~H) and water vapor periods using the energy balance/Bowen ratio method (Kv) above the canopy are equal, the Bowen ratio with reversing sensors (McNaughton and Black, 1973; reduces to /3 = CA0/£Ap„, where A0 and Ap are the McNeil and Shuttleworth, 1975; Black, 1979). Revertical gradients of potential temperature and abcently, eddy correlation methods, which avoid the solute humidity, respectively, above the canopy and C measurement of the above-mentioned gradients, have is the heat capacity of the air. Dyer (1967) and Denbeen used with reasonable success to determine the mead and Mcllroy (1970) have shown this assumption energy fluxes from a forest (McNeil and Shuttleworth, 1975; Hicks et al., 1975; Moore, 1976). This paper con-to be acceptable for neutral to moderately unstable conditions over smooth terrain. Campbell (1973) and siders the merits of the energy balance/Bowen ratio Verma et al. (1978) present data suggesting Kn>Kv method and a method combining energy balance and for stable conditions. The Bowen ratio approach also eddy correlation measurements in making relatively assumes that there is neither horizontal heat or vapor long-term forest evapotranspiration measurements, and advection beneath the upper measurement height nor presents the results of a short experiment comparing n  v  O021-8952/79/05O647-O7S05.75 © 1979 American Meteorological Society  /123 648  JOURNAL  OF A P P L I E D  METEOROLOGY.  VOLUME 18  net vertical mass flow of air transporting heat and eddy correlation method which is used in this study. vapor from the canopy. Here the eddy correlation measurement of sensible heat The vertical gradients of temperature and humidity flux (H ) is combined with the measurement of the net above forests are generally less than 0.1 °C m and energy available for sensible and latent heat exchange 0.1 g m ~ ' m , respectively (see Table I X of Jarvis (R —G—M) to give evapotranspiration ( £ „ ) , i.e., el al., 1976) and require high-resolution sensors for their accurate measurement. Small errors in the measurement E,= {R -G-M-H )/L, (2) of these gradients can result in large errors in deterwhere the measurement of H requires, in addition to mining evapotranspiration, particularly for dry surfaces a fast-response vertical wind sensor, a fast-response (Fuchs and Tanner, 1970). Current energy balance/ temperature sensor. Sensible heat flux is computed from Bowen ratio systems (e.g., Black and McNaughton, H = Cw'T', where w' and T' are the fluctuations of th 1971; M c N e i l ' a n d Shuttleworth, 1975; Tang, 1976) achieve the required accuracy by periodic reversal of vertical wind speed and temperature, respectively, and the sensors to eliminate systematic errors. They obtain the overbar indicates the average for the duration of an average flux by measuring mean temperature and each data run. humidity gradients over periods generally not less than Few measurements of eddy correlation turbulence 30 min in length. These systems are robust and rela- spectra and cospectra have been made in or above tively easy to maintain but the pumps that aspirate the forests. McBean (1968) using a propeller anemometer sensors and the reversing motor have a large power in a pine forest and Holbo et al. (1975) using a sonic requirement. anemometer and a "fluxatron" 8 m above a 30 m high e  - 1  - 1  n  n  c  e  e  Tan et al. (1978) determined 30 min rates of evapo- Douglas fir forest found a significant portion of the transpiration from a Douglas fir forest during the dayfluxes at lower frequencies than is usually found for time using the energy balance/Bowen ratio method and smooth terrain. The predominance of low-frequency a water vapor diffusion model requiring measurements eddies over forests compared to smooth surfaces is of vapor density deficit, stomatal diffusion resistance probably due to the increased scale of mixing that is of the leaves and forest leaf area. When soil water induced by rough, tall vegetation (McNeil and Shuttlecontent was high and, consequently, the evapotranspiraworth, 1975). Using a split-film anemometer at 3 m tion rate was high, the methods agreed to within ± 10%. above an 11 m high pine forest Shaw et al. (1975) found When soil water content was low and evapotranspiration that the sensible heat flux cospectra were more sharply rate was low, agreement was to within ± 3 0 % . At the peaked than those for smooth terrain and had a rapid same site Nnyamah and Black (1977) found on a falloff on both sides of the peak. J. Simpson and L . weekly basis, that under a wide range of soil water Fritschen (personal communication, 1978) of the Unicontents, the energy balance/Bowen ratio and soil versity of Washington have obtained less-peaked heat water balance measurements of evapotranspiration flux cospectra at 8 m above a 31 m high Douglas fir agreed to within ± 8 % . These results suggest that forest. These results suggest that anemometer response K = Kv is a reasonable assumption for forests. requirements may be relaxed for work above forests The eddy correlation method involves summing the and mechanical anemometers that usually have a falloff in response above ~0.5 Hz (McBean, 1972) may instantaneous vertical fluxes from the canopy to obtain be used. a time-averaged value. The instantaneous fluxes of H  heat and vapor are determined by measuring the instantaneous fluctuations of vertical wind speed together with those of temperature and humidity, respectively, 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 characteristics and may underestimate the fluxes (Hicks, 1972; McBean, 1972). Fritschen (1970) has suggested an energy balance/  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 fastresponse 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 MAY  1979  D .  L .  S P I T T L E H O U S E  A N D  T .  A .  649  B L A C K  3. Methods  eters and were vane mounted. One of the anemometers was mounted horizontally and the other pointed downThe study site was a 17-year-old Douglas fir stand at ward at 3 0 ° from the vertical so that the horizontal the University of British Columbia Research Forest at component (u) of the wind vector always kept this Haney, British Columbia. At the time of the experiment propeller turning in the same direction even though the in July 1976, the trees averaged 14 m in height with the vertical component (w) changed directions (see also base of the canopy at a height of ~ 5 m. McNaughton McBean, 1975). Each data run lasted 54 mins with and Black (1973) have given a detailed micrometeorothe output voltages from the sensors recorded by an logical description of the site. Briefly, the site was F M tape recorder. Data analysis involved filtering the located on a 5% slope with a fetch of between 200 and recorded outputs through Kronhite 3340 low-pass filters 400 m, beyond which an older regrowth Douglas fir set at 6 H z and sampling at 20 H z with analogue to forest extended for more than 2 km. McNaughton and digital converters. The digitized data were then analyzed Black (1973) have presented previous energy balance/ following the theory for the tilted w propeller (Pond Bowen ratio measurements of evapotranspiration for and Large, 1978) to obtain w' and V. In these calculathe site. tions the axes were rotated so that tD = 0. The w' and V Mean sensor height was 4.5 m above the top of the power spectra and the w'T' cospectra were calculated canopy. The Bowen ratio system (Black and McNaughby computer using a fast-Fourier transform. No correcton, 1971) used matched pairs of germanium diodes as tions for possible reduced frequency response of the temperature sensors in the psychrometer heads. The two anemometer were made to the cospectra. E q . (2) was sensing heads had a 3 m vertical separation and were then used to calculate the evapotranspiration for each reversed every 15 min. The differential voltage outputs data run. The effect of tilt of the u anemometer away from the sensors were integrated (Tang et al., 1976) tofrom the mean horizontal flow, the noncosine response obtain 10 min average wet- and dry-bulb temperature of the anemometers and calibration and offset errors gradients, after which the heads were reversed and (Pond and Large, 1978) would cause an error of up to allowed to equilibrate for 5 min before integration was ± 2 0 % in the measured sensible heat flux for wind resumed. Two 15 min periods were combined to obtain speeds of ~ 2 m s . 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- 4. Results eter. The soil heat flux and canopy heat storage terms Throughout the measurement period, the average were determined following McNaughton and Black hourly horizontal wind speed (tl) at 4.5 m above the (1973). Evaporation was then calculated from (1). canopy was always less than 3.0 m s and frequently In this experiment, measurement errors, calculated less than 1.0 m s . During the daytime the instanusing an error formula for psychrometric Bowen ratio taneous vertical wind speed was occasionally of the measurement systems (Fuchs and Tanner, 1970), same magnitude as the instantaneous horizontal wind caused less than a 15% error in both the sensible and speed. This was the result of the high degree of turbulent latent heat fluxes. mixing that occurs above rough, tall vegetation. The low -1  _1  _I  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-  horizontal wind speed resulted in the frequent stalling of the propeller anemometers. Adequate wind speeds were only encountered between 2100 P S T 13 Julv and 1000 P S T 15 July 1976 (Table 1). Even during this  TABLE 1. M e a n 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 ( # and E , respectively), for 13-15 J u l y , 1976 at 4.5 m above a 14 m high Douglas fir forest. Starting time of each data run is given. e  T  A0/A2  Time (PST)  ii (m s-')  Wind direction  (°C)  (°C rn"')  2129 0024 0248 0457 1007 1126 1448 1713 0624 0849  2.79 2.76 2.73 2.07 1.60 1.93 1.46 1.40 0.92 0.99  NW N N N SE SE SE E N S  10.7 9.3 8.7 8.7 19.8 20.2 22.4 22.1 11.1 19.9  +0.08 +0.03 +0.06 +0.03 -0.08 -0.10 -0.06 +0.02 -0.02 -0.06  Ap„/Az  (g m "  3  m->)  -0.01 -0.01 =0 ~0  -0.06 -0.06 -0.08 -0.06 -0.03 -0.04  t  11.  (W m"») -29 -33 -20 -27 229 282 204 51 -6 148  lh -54 -55 -49 -17 229 264 104 -36 17 180  E. -0.03 -0.03 -0.05 0.02 0.49 0.52 0.39 0.12 0.18 0.51  (mm h~') . 0.01 0.01 =0 = 0 0.49 0.54 0.53 0.25 0.15 0.46  /125 650  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  VOLUME 18  ""•I TYPICAL POWER SPECTRA 1126-1220 (PS T) JULY 14,1976 4.9 m ABOVE 14-m DOUGLAS-FIR FOREST  • A  V  o.i  SPECTRAL ENERGY  n S.T(n) w'T'  1.0  A° A  NORMALIZED DAYTIME SENSIBLE HEAT FLUX COSPECTRA • JULY 14-15, 1976.  S (n) T  CC •) 1  S»(n)  (mV)  A  * • o # A A  0.1  0.001  •  TIME 1PS.T) Vimt-') — I00T 1.60 — 1126 193 — 1448 1.46 — 1713 1.40 0624 0 92 — 0849 0 99 0.1  0  A A  •4 1.0  NORMALIZED FREQUENCY, Fic. 3. Normalized daytime sensible heat flux cospectra for 1 4 - 1 5 July 1 9 7 6 with a scaling height z = 7.5 m. OOP  0.1 FREQUENCY (Hj)  1.0  10  F I G . 1. Typical w' (solid circles) and V (open circles) power'spectra for 1 1 2 6 - 1 2 2 0 PST 1 4 July 1 9 7 6 .  period there was occasional stalling of the anemometers. Hicks (1972) and McBean (1975) note that below ~ 1 m s 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 ( » ) ] _1  0.12  1 1—• I I 11 11 1 1—i—r TYPICAL »'T' COSPECTRA  1 1 1 1 |  1  1  (Fig. 2) show that there was negligible energy at frequencies >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 daytime 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 H z . The normalized daytime and nighttime cospectra [HS„T(/i)/Vr], where w'T' is the area under the cospectral 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  1 1 T TTT  JULY 14, 1976.  o.to  4 5m ABOVE 14-m OOUGLAS-FIR FOREST  • • o I nS.rin) |  • A  -  °  0248 - 0342 , I • 2.73 nit"'  * A  1126-1220, <T • 1.93 m •"' 0 0 0  0 06 (m«Cl-'>  nS.T<n)  o ° o  NORMALIZED NIGHTTIME  o  0.01fc-SENSBLE HEAT FLUX COSPECTRA  0 0  JULY IS-14, 1976. TIME 1P.S.T.I Mm.') — 2129 I.9S — 0024 2.76 — 0248 2.73 — 0437 207  c  *  °  1  o.o2 r  • 0.001  A » • o  0 •  1 — i — i t m n S: i i — i — L . ...1 0.01 01 FREQUENCY (Hi)  0 • 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) 1 4 July 1 9 7 6 .  0.001 0.01  -J  11  „  I  0.1 1.0 NORMALIZED FREQUENCY,  F I G . 4 . As in Fig. 3 except for nighttime sensible heat flux cospectra.  /126 MAY  D. L. S P I T T L E H O U S E A N D  1979  651  T. A. B L A C K  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 experiment shown in Fig. 5. The curves for unstable conditions 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) F I G . 5. Normalized sensible heat flux cospectra. A scaling for the same site although the trees were smaller. The 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 daytime Bowen ratio varied between 0.2 and 0.8. It Kaimal et al. (1972) was obtained under neutral conditions and appeared that soil water was not limiting evapotranstheir upper curve the most unstable conditions they encountered. piration. The evapotranspiration rate tended to peak in the mid-afternoon following the trend in the absolute 3 min being significant. This may be partially a result humidity deficit rather than the net radiation. The daily of the lower daytime wind speed and the effect of pattern of evapotranspiration is consistent with that stability on eddy frequency distribution (see, e.g., found by other workers for Douglas fir (Gay, 1972; Panofsky and Mares, 1968; McBean. 1971; Kaimal et al., 1972). The normalized frequencies (nz/u) haveFritschen and Doraiswamy, 1973; McNaughton and been determined using a scaling height (z) equal to the Black, 1973). However, the evapotranspiration rate true height of the instruments (18.5 m) minus the zero obtained using the eddy correlation measurements did not show this trend because of the high H values at plane displacement (D) taken as 11 m. The value of D 1448 and 1713. was obtained using the relationship Z) = 0.79 h, where The sensible heat fluxes provide an independent comh is the height of the canopy [the coefficient is a mean of the values in Jarvis et al. (1976)3- Silversides (1974) parison of the two methods. A regression of H on H gave ff« = 0 . 9 3 f f „ + 2 7 [W r r r ] , # = 0.89, s„.x = ±-M has also used this method for normalizing cospectral r  f  2  ' •I  6 0 0  | '  2  -  ENERGY BALANCE OF  NET RADIATION  W-m DOUGLAS-FIR FOREST  SOIL HEAT FLUX + CANOPY HEAT STORAGE  U.B.C. RESEARCH FOREST, HANEY, B.C JULY 13—15, 1976 4 0 0  ENERGY FLUX DENSITY  TIME F I G . 6. Energy balance components of a 14 m high Douglasfirforest 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.  B  /127 652  JOURNAL  OF  APPLIED  EVAPOTRANSPIRATION  /  METEOROLOGY  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" (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 conventional 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 correlation measurements of evapotranspiration. 1  F I G . 7. M ean hourly evapotranspiration rate determined with the energy balance/Bowen ratio method ( £ ) 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. s  Although the above-canopy wind speed can be low, the accompanying small temperature gradients mean W m . During the daytime, when the latent heat flux that during most of the day moderately unstable to exceeded the sensible heat flux, i.e., /3<1, the effect of slightly stable conditions exist. Thus, for that part errors in the eddy correlation measurements of the of the day when there is significant forest evaposensible heat flux on the calculation of evapotranspiratranspiration, the eddy diffusivities for sensible heat tion was minimized. This can be seen in the following and water vapor should be approximately the same and regression £ = 0 . 9 6 £ - 0 . 0 2 [mm h" ], /c = 0.93, the energy balance/Bowen ratio method should gi\i_ sy.z = ± 0 . 0 7 mm h (see also Fig. 7). a good estimate of evapotranspiration provided there is an accurate measurement of net radiation. Although current Bowen ratio systems have a high power require5. Discussion ment for the ventilation system and the reversing motor, they have the advantage of durability and simple Eddy correlation systems with propeller anemomanalysis. Consequently, at present, the energy balance/ eters have frequently been found to underestimate the Bowen ratio method, with periodic reversal of the sensible heat flux (e.g., McNeil and Shuttleworth, psychrometric sensors to eliminate systematic errors, 1975). This has usually been ascribed to reduced reappears to be more suitable than the energy balance/ sponse of propeller anemometers at high frequencies eddy correlation method to determine forest evapo(Dyer and Hicks, 1972; McBean, 1972), or low-frequency cutoff (Holbo el al., 1975). It was noted that the transpiration rates in long-term water balance studies. former was probably not a limitation in this study. Since the low-frequency cutoff in this experiment was 6. Conclusions at 0.004 Hz, contributions from frequencies below this point would tend to flatten out the peaks in the normalUnder moderate wind speeds, values of forest evapoized cospectral curves (Figs. 3, 4 and 5). transpiration rate obtained using the energy balance/ The energy balance/Bowen ratio and energy balance/ eddy correlation and energy balance/Bowen ratio eddy correlation determinations of evapotranspiration methods agreed to within ± 0 . 0 7 mm h . The eddy rate agreed to within ± 0 . 0 7 mm h (Fig. 7 and correlation measurements of sensible heat flux, required Table 1). However, the low wind speed above the in the former method, were difficult to obtain because forest canopy made it difficult to use the energy balance/ the generally low wind speed above the forest resulted eddy correlation method. In the runs starting at 1448 in occasional stalling of the Gill anemometers. Spectral and 1713 there is a marked disagreement between the analysis of the eddy correlation data indicated that a two measurement methods. During these runs, the significant fraction of the sensible heat flux was at freaverage wind speeds were low (1.46 and 1.40 m s , quencies <0.01 Hz. The results suggest that at present, respectively) and there was occasional stalling of the the energy balance/Bowen ratio method, with periodic anemometers. Under these low wind conditions errors sensor reversal, is preferable in long-term water balance - 2  e  1  a  2  _ 1  - 1  _ 1  _l  /I 28 MAY  D. L. S P I T T L E H O U S E  1979  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 for much of the time. _1  A N D T. A. B L A C K  653  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 hygrometer for evaporation measurement. J. Appl. Meteor., 1 4 , 301-307.  Jarvis, P. G., G. B. James and J. J. Landsberg, 1976: Coniferous  Acknowledgments. We wish to thank Dr. Steve Pond forests. Vegetation and the Atmosphere, Vol. 2, Case Studies, J. L. Monteith, Ed., Academic Press, 171-240. and Bill Large, Institute of Oceanography, University Kaimal, J. C , J. C Wyngaard, V . Izumi and O. R. Cote\ 1972: of British Columbia, for the loan of the eddy correlaSpectral characteristics of the surface layer. Quart. J. Roy. tion system and Bill Buckingham and Colin Walker Meteor. Soc. 9 8 , 563-589. for their aid in data collection and analysis. Funding McBean, G . A . , 1968: An investigation of turbulence within a forest. J. Appl. Meteor., 7, 410-416. for this research was provided by the National Research , 1971: The variation of the statistics of wind, temperature Council of Canada. REFERENCES Bergen. J. D . , 1971: Vertical profiles of wind speed in a pine stand. For. Sci., 1 7 . 314-321. Black, T . A., 1979: Evaporation from Douglas-fir stands exposed to soil water deficits. Water Resour. Res., 1 5 , 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 evapotranspiration rates measured bv the energy balance method. Agric. Meteor.. 1 1 . 261-267. Denmead, O. T . , and I. C. Mcllroy, 1970: Measurement of nonpotential 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 atmospheric turbulence. Bound.-Layer Meteor., 3, 214-228. Hicks, B. B., P. Hyson and C. J. Moore, 1975: A study of eddyfluxes 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  and humidity fluctuations with stability. Bound.-Layer Meteor., 1, 438-457. , 1972: Instrument requirements for eddy correlation measurements. J. Appl. Meteor., 1 1 , 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 evapotranspiration 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, 1 0 3 . 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., 41, 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, 9 4 , 581-585. Pond, S., and W. G . Large, 1978: A system for remote measurements of air-sea fluxes of momentum, heat and moisture 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.. 1 3 , 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 Douglasfir 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. QAvailable from Library, University of British Columbia, Vancouver, 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  APPENDIX 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 ofBritish 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 vapourpressure 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 ( P L 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 tofivelimes 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 dufluxturbulent 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 directly 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, application of these methods to forests is generally more difficult than for agricultural 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 evapotranspiration 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 measurement for determining forest evapotranspiration. We also compare this method with evapotranspiration measurements made using an eddy correlation/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 heatfluxto 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 evapotranspiration rate. Assuming that the eddy diffusivities for heat (K ) and water vapour (K ) are equal, the Bowen ratio reduces to H  v  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 assumption K = K \s acceptable for neutral to moderately unstable conditions over smooth terrain. Campbell (1973) and Verma et al. (1978) present data suggesting K > K 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. H  v  H  v  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 accurate 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 micrometeorological 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" (0.07 g m - n r ) (See Table IX in Jarvis et al., 1976). Sinclair et al. (1975) suggest errors of ± 0 . 0 1 ° 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 difference was a function of the arrangement of the sensors in the profile. Droppo and Hamilton (1973) made their profile measurements with a single psychrometer 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 atmospheric conditions changed relatively slowly. 1  3  1  The second method of obtaining the Bowen ratio was first reported by Tanner (1960). The psychrometers are interchanged between two measurement 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, = (T + e«,i)-(7 + e ) al  o2  (4)  M  and the difference after reversal (AT,,) is AT/i=(7'„2 + e„ )-(r + e ) 2  el  (5)  el  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,, = (T + T ) - (T + T ) + (e„, + e ) - (e + e ) al  bl  a2  b2  a2  BI  62  (6)  is twice the mean temperature difference (AT), since (e + e |) ~ ( £ + e ), 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 dependence is avoided if the psychrometers are constructed symmetrically and have the same orientation in each position. al  6  a2  62  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 following 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 measurements 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 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 . The mean sensitivity of a diode pair must be used to convert the differential _1  _ I  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 resulted in a probable error in the differential temperature measurement of ± 0 . 0 0 5 ° 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 temperature differences was + I Pa (+0.007 g m ) and the maximum error was + 3 Pa. The rate of change of the saturation vapour pressure curve with temperature (s ) 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. 1  w  /135  104 / D.L. Spittlehouse and T.A. Black TABLE  1.  Typical probable relative errors in the forest Bowen ratio (83/3), the evapotranspiration rate (SEt/Ep), and sensible heat flux i$H IH ) for positive and negative Bowen ratios. Calculations are for a 3-m separation 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 k g " ) while 3 = 3.96 is typical of dry soil conditions (V, < - 8 0 0 J k g " ) . t  '  9  1  1  Positive Bowen Ratio A6/Az "Cm" 1  A<>/Az Pa m -  1  83/3 ±%  SE /E f  ±%  t  ±%  Negative Bowen Ratio  8E /£±% s  B  ±%  0.10 0.02  10 2  5 19  7 10  8 13  12 38  16 56  0.10 0.02  5 1  8 35  8 21  8 17  34 145  25 110  0.12 0.03  2 0.5  17 67  15 54  8 15  24 90  9 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. nighttime and advection situations, there is a large relative error in the evapotranspiration rate measurement especially when the temperature and vapourpressure gradients are small. The error may be enhanced because, as noted in Section 2a, for stable conditions K is possibly larger than K which would result in an overestimation of E. H  v  The probable relative error in the sensible heat flux (Table 1) is generally  Evaluation of a Method for Determining Forest Evapotranspiration / 105 8OO1  600 ENERGY FLUX DENSITY  400r  (Wm-'l  200  •Ms* -200  0  6  12 HOURS  18  24  (PST)  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 heatflux,LE is the latent heatflux.G is the soil heatfluxand 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 measurements 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 signals were later filtered at 6 Hz, sampled at 20 Hz and then analyzed to obtain the instantaneousfluctuationsin 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 fastFourier-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 (H ) was calculated from e  H  e  = CVT  (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 evapotranspiration rate ( £ ) was obtained from P  (8)  E = (R„ — G — M - H )/L. e  e  The wind speed at 4.5 m above the trees was always less than 3 m s " and frequently less than 2 m s . 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 E 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 E (Fig. 3). In a similar experiment McNeil and Shuttleworth (1975) obtained values for £ p that were 25% lower than those for £ . They attributed this to an under-estimation of H by their eddy correlation system. 1  _l  e  e  e  e  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 ash (mm h-') e  Fig. 3  H o u r l y mean evapotranspiration rate determined with the B o w e n ratio/energy balance method 1976.  and with the eddy correlation/energy balance method ( £ , , ) . for July 13-15.  M e a n soil water potential (il< ) of the top 0.45 m o f the soil was > - 100 J k g ' . E r r o r s  bars are shown o n two data points. (Modified from.Spittlehouse and B l a c k . 1979.)  The stomatal diffusion resistance method requires measurements of leaf stomatal diffusion resistance (r ) 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. Measurements of / 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-m plots of the salal undergrowth. Transpiration from a leaf, on a per unit leaf area basis (£,) is s  s  2  _ 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 r 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 assumption that is correct to within 3%, even for a leaf water potential (v|v) as low as -4000 J kg" . In a well-ventilated canopy r 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 r < 0. Ir,, (9) is well approximated by £/ = (  b  1  b  b  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 ( L A i 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 (E ) per unit ground area. i.e. SR  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 , V P D and L A I contribute equally to the error in E . Tan et al. (1977). in their Table 1, suggest that the porometer measurement error in r is ±5%. The error in sampling to obtain f is more difficult to assess. Field measurements show that r, can vary by 5 0 % 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 r together with the assumption of saturation within the stomatal cavities partially offset the error in using the V P D (Tan et al., 1978). The L A I , was accurate to ± 10%. Thus, E 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 evaporation conditions (moist soil, i.e. mean soil water potential of the root zone, ty > — 200 J kg ) and to within ± 3 0 % 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 E to be greater than £ p when evapotranspiration is low and less than £ p when evapotranspiration is high. However, this discrepancy is within the errors of the two methods. SR  s  s  si  (  b  SR  s  -1  SR  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 (E ) is the residual term in the soil water balance and is given by WB  E  WB  = -AWIM  + P-  D-  R.  (11)  Summary of probable relative errors in determining evapotranspiration, and agreement in measured evapotranspiration 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  Method Bowen Ratio/Energy Balance  Estimation Period hourly and weekly  Probable Relative Error (%) Moist Soil  Dry Soil  < +15  ± 10 to ± 4 5  Eddy Correlation/Energy Balance  hourly  ±20  —  Stomatal Diffusion Resistance  hourly  ± 1 5 to ± 2 0  ± 1 5 to ± 2 0  Soil Water Balance  weekly monthly  ± 15 to ± 2 0  ± 30 to + 50 <±10  Agreement (%) Moist Soil  Dry Soil  ±20 ±8  - 3 0 to  -15 to+7 + 4 to  t  +12  +10  +20  /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 E . 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 evapotranspiration 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 HB  Evaluation of a Method for Determining Forest Evapotranspiration / i n  o.  •  0  .  1  1  0.1  0,2  .  .  .  0 3  .  0.4  1  (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 ( £ ) . 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.) i R  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 < ± 2 0 % when soil water content was high (\J/„ > —200 J kg" ) and < ± 5 0 % when soil water content waslow(v|/ < -800 J kg )- However, the absolute error in E 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 Ew 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 E 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 affecting 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 Re1  -1  g  B  WB  WB  /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 . 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 . (Modified from Black, 1979.) -1  -1  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 ) the Bowen ratio/energy balance method gave 4% more evapotranspiration than the soil water balance method. -1  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 measuring 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 measurement 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 increasing 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. Consequently, for routine measurements of forest evapotranspiration the eddycorrelation 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 measurement 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 ± 6 0 % 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 psychrometers 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 1977. Atmospheric and surface control of evapotranspiration during soybean maturation. Ph.D. Thesis. McMaster Univ., Hamilton. Ont.. 162 pp. B L A C K , T . A . 1979. Evapotranspiration from Douglasfirstands exposed to soil water deficits. Water Resour. Res. 15: 164-170. B A I L E Y , w.G.  and  K.G. M C N A U G H T O N .  1971.  Psy-  chrometric apparatus for Bowen-ratio determination 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. CAMPBELL.  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. o.T. 1969. Comparative micrometeorology of a wheatfieldand a forest of  DEN MEAD,  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. D R O P P O , 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.  1967. The turbulent transport of heat and water vapour in an unstable atmo-  DYER, A.J.  sphere. Quart. J. R. Meteorol. Soc. 93:  501-508. 1968. Spatial variation of net radiation, albedo and surface temperature of forests. J. Appl. Meteorol. 7: 789-795. . 1970. Measuring forest evapotranspiration - theory and problems. U.S.D.A. For. Serv. Res. Pap. NE-165. Northeastern For. Exp. Stn, Upper Darby, PA.. 25 pp.  FEDERER, C A .  F R I T S C H E N . L . J . ; J . H S I A and p.  DORAISWAMY.  1977. Evapotranspiration of a Douglas fir determined with a weighing lysimeter. Water Resour. Res. 13: 145-148. FUCHS,  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 differential 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 derived from Bowen ratio measurements. Boundary-Layer Meteorol. 8: 453-464.  1975. Comparison of evaporation measurements using different methods.  G R A N T , D.R.  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 -  T E R . 1964. Instrumental and soil moisture variance using the neutron-scattering method. Soil Sci. 97: 19-24. H I C K S , B.B. ; p. H Y S O N and c j .  M O O R E . 1975.  A  study of eddyfluxesover 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. R I C H A R D S .  1967. Measurement of soil water. In: Irrigation 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. H I C K S . 1975. A single-beam infrared hygrometer for evaporation measurement. J. Appl. Meteorol. 14: 301-307. J A R V I S . P.G.; G.B. J A M E S and J.J.  LANDSBERG.  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. MCNAUGHTON.  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.  Layer Meteorol. 16: 351-364.  and R.B. J O R D A N . 1976. Precision 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 Mathematical Analysis. (6th edit.) Johns Hopkins Press. Baltimore. 600 pp. S C H O L L , D . G . 1976. Soil moisturefluxand evapotranspiration determined from soil hydraulic properties in a Chaparral stand. Soil Sci. Soc. Am. J. 40: 14-18. R E V F E I M . K.J.A.  S H U T T L E W O R T H , W . J . and  1975.  Boundary-Layer Meteorol. 16: 67-81.  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. MOORE. C J .  s.; W.G. L A R G E , M . M I Y A K E  and  R.W.  I.R. C A L D E R .  1979.  Has the Priestley-Taylor equation any relevance 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.  LEMON.  1975. An analysis of errors in the calculation of energyfluxdensities above vegetation by a Bowen-ratio profile method. BoundaryLayer Meteorol. 8: 129-139.  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.  S P I T T L E H O U S E . D.L.  Appl. Meteorol. 18: 647-653.  and A.S. T H O M . 1973. Energy budgets in pine forest. Quart. J. R. Meteorol. Soc. 99: 154-170. TAN. c s . and T . A . B L A C K . 1976. Factors affecting the canopy resistance of a Douglas-fir forest. Boundary-Layer Meteorol. 10: 475-488. S T E W A R T . J.B.  ; SHUTTLEWORTH.  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 resistance of a young Sitka Spruce plantation.  POND,  B U R L I N G . 1979. A Gill twin propeller-vane anemometer for flux measurements during moderate and strong winds. Boundary-  and  J.u.  NNYAMAH.  1977.  Characteristics of stomatal diffusion resistance in a Douglasfirforest 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. TANG.  P.A.; K.G. M C N A U G H T O N  and  T.A.  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. BLACK.  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-  GASH. 1975. Comparison of aerodynamic and energy budget estimates offluxesover a tion and the Atmosphere, Vol. 1, Principles, pine forest. Quart. J. R. Meteorol. Soc. 101: (J.L. Monteith, Ed.) Acad. Press, London, 93-105. pp. 57-109. THOMPSON, N. 1979: Turbulence measure. 1978. Evaporation from forests in rements above a pine forest. Boundary-Layer lation to climate and hydrology. Paper preMeteorol. 16: 293-310. sented at the First International Symposium VERMA, S.B.; N.J. ROSENBERG and B.L. BLAD. of Forest Meteorology, Aug. 21-25, 1978, 1978. Turbulent exchange coefficients for Univ. of Ottawa, Ottawa, Ont. Sponsored sensible heat and water vapor under adby the World Meteorological Organization. vective conditions. J. Appl. Meteorol. 17: ; J.B. STEWART, H.R. OLIVER and J.H.C. 330-338.  /148 APPENDIX III - ERROR ANALYSIS FOR THE REVERSING PSYCHROMETER 1.  1.  CALIBRATION AND MEASUREMENT ERRORS FOR THE REVERSING PSYCHROMETER  THEORY The method of assessing the errors in the Bowen ratio  described here i s similar to that in Fuchs and Tanner (1970), S i n c l a 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  relatively  small ( S i n c l a i r et al., 1975). A value y is a function of a set of measurements x^, x , with associated errors 6x^, ... 6 x . n  Thus,  n  y = f (x  :  +  SXj, . . .  x  p  + 6x )  (1)  n  The maximum total error in y is given by d i f f e r e n t i a t i n g respect to x^, . . .  6 y  max  =  ...  (1) with  x , n  \TT  X  6 x  ll  +  + \~<5Xn 3x  (2)  n  The probable error in y is given by taking the root-niean-square of (2),  (3)  sy  The respective maximum and root-mean-square relative errors are (6y  /y)  and (6y/y),and 6y w i l 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  In (4)  (R  -  n  G -  M ) / [ L ( 1 + 3)]  (4)  - G - M) i s the energy available for evapotranspiration and the  sensible heat flux, where R i s the net radiation f l u x , G i s the s o i l n  \  flux,  heat  M i s the rate of canopy heat storage, L i s the latent heat of  vapourization of water  and 3 i s the Bowen r a t i o .  Similarly the  sensible heat flux (H) i s given by  H = [(R  -  n  G -  M)B]/(1  + B)  (5)  The probable error in E is  6E = [ { [ 1 / ( L ( 1  + 3))]  6(R  + U(R  n  -  G -  M)/(L (1  + H(R  n  -  G -  M)/(L(1  2  n  -  G -  M)}  2  + 3))]  5L}  2  + 3) )] 2  ^} ~\ Z  h  (6)  S i m i l a r l y the probable error in H i s  6H = [{ [ 3 / ( 1  + U(R  + 3)] 6(R  n  -  G -  - G - M)/(l + 3 ) ] 2  n  M)}  2  6$} ]] 2  h  ( 7 )  /I 50  L can be calculated from the mean a i r temperature T,  2500 - . 2 . 3 6 1  T  (8)  The probable error in L is  6L = 2.361  ST  (9)  The probable error in T is a function of c a l i b r a t i o n and measurement accuracy and i s dealt with later  2.  (Equation  31).  Available Energy The available energy is (R  radiometer is to within ±2%,  n  - G - M).- Calibration of the net  and measurement accuracy varies from  ± 2% to ± 0.2% depending on the net radiation f l u x . measurement error is about ± 4%.  Thus the maximum  This value is in agreement with  Federer (1968) and Fuchs and Tanner (1970).  McNeil and Shuttleworth  (1975) suggest that uncertainties in the representativeness of R may n  be ± 5%. It  A value of (<5R /R ) n  is d i f f i c u l t  n  =  ±5%  w i l l be used in this a n a l y s i s .  to make accurate measurements of the s o i l  flux and canopy heat storage.  heat  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 s u n s e t , (G + M) i s radiation.  -  < 10% o f the net  T h u s , a 50% e r r o r i n (G + M) causes an e r r o r  of  < 5 % i n the a v a i l a b l e energy. From the a b o v e , 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 o f u n c e r t a i n t i e s t h a t cannot be q u a n t i f i e d , t h i s v a l u e w i l l  i n the measurements,  be used f o r both the maximum  and r o o t - m e a n - s q u a r e c a l c u l a t i o n s .  v  3C.  Bowen R a t i o The Bowen r a t i o ( 3 ) i s g i v e n by  6  = yAB/Ae~  (io);  0  where y i s the p s y c h r o m e t r i c c o n s t a n t and A0- and A e potential  Q  are t h e . a v e r a g e  a i r 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 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 n e g a t i v e when temperature and vapour :  pressure decrease with 63 =  height.  [{(Y/Ae )6AQ}  + {(YAe/Ae  2  o  2 0  )6Ae" } 0  + {(A07Ae" )6Y> j ' 2  o  The p o t e n t i a l  }  2  2  ... • OD  temperature d i f f e r e n c e i s g i v e n by  AG = A T  n  •+  T Z  (12)  /152  where AT  is the average dry bulb temperature difference, r is the dry adia-  Q  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  (13)  + {YSl} ] 2  h  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 f o r e s t s , 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. (Ae ) Q  It  can be shown that the corrected vapour pressure difference'  is given by  Ae  o  = Ae +  7.6  x 10"' Ze  where e" is the mean vapour pressure of the p r o f i l e .  (14)  The probable error  in A~e^, where A~e^ is a difference in kPa over Z metres,  6Ai  Q  =  HoAe"}  2  + {0.00008  Ae is obtained by d i f f e r e n t i a t i o n *  where  and f  w  - «W-  e 5Z}  is  + (0.00008 Z 5 e } ] ^  2  (15)  2  of the psychrometric equation *<TD  - W> T  (  are the mean dry and wet bulb temperatures  is the saturation vapour pressure at the mean wet bulb  and e^  temperature.  1  6  )  / l 53  Thus: Ai  where s  w  = (s  M  + Y)ATW  - YAT  (17)  d  i s the rate o f change o f 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 d i f f e r e n c e .  SAe  = [{AT 6 S } W  +f(s  2  W  +  By  The probable e r r o r i n Ae" i s  + Y)6AT }  w  + {ySATp}  2  W  {(AT  - AT )6 } I 2  W  D  %  2  (  1  8  )  Y  definition s  and  w  6s  w  =  8 e  w  / 3 T  w  _ = (3s /3T ) w  w  (19)"  6T.  f  W  W  From (16) the probable e r r o r i n e i s  Se = [ { S e * j }  2  + ar  D  - T )6 } W  + {yST^,} ]^ 2  Y  2  +  (Y-sTp}  2  (20)  7154 From the definition of s,, i t can be seen that W  6e  w  =  s  w w  ( )  6T  2]  Substituting (21) in (20) gives  66 =  [{(T  D  -  T )6 } W  Y  2  +  {Y<5T } d  2  +  [(s  2  +  2 Y  )<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 psychrometric 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 )/(S S 2) 2  c  d  (23)  /T55  where C and C are the count totals f o r the two consecutive measurement n  2  periods, S  c  i s the s e n s i t i v i t y of the integrating system and S^ is  the mean s e n s i t i v i t y of the diodes (Table I I I . l ) . 6 A f = [{ [ l / ( S S ) ] 6 C } c  +  + { [(C  1  The probable error in AT i s  2  a  -  C )/(S  -  C )/(S  2  C  S 2)]  6S >  S 2)j  6S } J  d  2  2  2  d  2  d  %  C  + SAT-d  (24)  b  The term 5 A T i s the absolute error in AT due to the use of a mean diode s e n s i t i v i t y difficult  and i s included as a separate term since i t i s  to include i t e x p l i c i t l y in the second term on the right  hand side of (24). 5.  This term and  are defined below.  Diode S e n s i t i v i t y  Calibration-sensi t i vi ty: from  S  where V and g  In c a l i b r a t i o n , diode s e n s i t i v i t y i s calculated  d • <a " V / ' a " V v  and T  fl  .  T  <> 2 5  and T^ are corresponding diode junction voltages  and c a l i b r a t i n g thermometer temperature.  During c a l i b r a t i o n the error  (6V )in V i s due to the measuring accuracy, since the supply voltage m  is kept constant.  6S  The probable error in S^ i s  d  = [2{[l/(T  + 2{[(V  a  - T )]  a  b  -  SV }  V )/(T b  2  m  a  -  T ) ]6T} ] ' 2  b  2  1  2  (26)  /156  Self-heating of a diode i s <, 0.005 °C in s t i l l even smaller when the diode i s v e n t i l a t e d .  a i r * and w i l l be  Also i t i s a constant o f f s e t  and would not a f f e c t the s e n s i t i v i t y of the diodes.  Mean s e n s i t i v i t y :  The error i n AT due to the use of a mean diode s e n s i t i v i t y  (S~) can be shown to be (see Appendix III.2)  6AT  as . D T / S  =  T  (27)  H  where DT i s the change i n the mean p r o f i l e temperature between the two measurement periods, and SS. from the mean  (Table  the deviation of the  diode s e n s i t i v i t y  III.l).  Calibration,absolute temperature:  Diode temperature  (T) i s given  by  T = T  where T i s the offset temperature. Q  -  0  V/S  (28)  d  As before, during c a l i b r a t i o n the  error in V i s SV so that m 6T = [ { 6 T } Q  2  + {(1/S )  6V }  +  6S } ]  d  {(V/Sjj)  2  m  2  h  d  S e l f heating effects are n e g l i g i b l e compared to the other e r r o r s . Furthermore, ventilation o f the diodes during c a l i b r a t i o n and use would quickly disperse most of this heat.  (29)  /157  6.  Measurement Errors  Diodes:  Measurement errors f o r the diodes are related to change in the *  diode power supply  and a voltage drop down the lead wires.  The l a t t e r  i s not considered as there i s no current flowing down the measurement leads.  Changes in the former ( i f they are < ± 10 mV) should not be  enough to affect the s e n s i t i v i t y of the diodes.  However, they may  be large enough to affect the absolute temperature reading. Since each diode pair i s driven by the same power supply both diodes should be affected equally so that  the d i f f e r e n t i a l  voltage is independent of  power supply changes of < ± 10 mV. The uncertainty in the diode junction voltage (<5V ) due to a change p  (SVp)in the power supply voltage (V,p)is given by Tang et al. (1974) as 5V  where  p  = 456 V / V p  (30)  p  6V is in m i l l i v o l t s . p  For f i e l d measurements  6V must be included in (29). p  In this  case i t is added to 6V to give the total uncertainty (SV) in the diode m  junction voltage.  Furthermore, the sampling to obtain T i s infrequent;  thus, an error term f  T  must be included in (29) to account for the  error in T caused by infrequent sampling. absolute error.  f  T  is taken as an  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 =  [{6T }  2  0  + {(1/S ) d  +  Integrators:  6V}  2  {(V/S )6S } ] 2  2  d  3 §  + f  ( )  T  31  The s e n s i t i v i t y of an integrator (S ) i s c  S  = C//V  c  (32)  c  whereC. i s the number of counts per u n i t time due to the applied voltage  V^.  The probable e r r o r i n  6S  C  =  [ { ( 1 / V ) 6C.} C  is  2  .+ { ( C . / V . ) 6 V } ] ' 2  2  i  (33)  2  c  The integrators are stable over a wide range of temperature conditions and within the voltage range encountered.  Any v a r i a t i o n s i n  due to these  factors could be accounted f o r by increasing 6C.,.or by adding a c o r r e c t i o n f a c t o r f ^ to SS^.  /159  2.  CALCULATIONS FOR GERMANIUM DIODES • The appropriate values for calculating the probable and maximum errors i n the estimation o f evapotranspiration are given in Table I I I . l . Calculated error terms are l i s t e d 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 s e n s i t i v i t y i s  h SS  = [2.0 x 1 0 " + 2.6 x 1 0 " ] 6  d  6  o -  1  = ± 0.002 mV C  and  6S /S d  d  = ± 0.1%.  The maximum r e l a t i v e error i s ± 0.2%.  (340 From (27) the absolute  error in AT due to using a mean s e n s i t i v i t y , f o r diode pairs matched to 0.4% and 0.1%, i s , respectively  5ATV = 0 . 0 0 0 4 ° C , 0.0001 ° C f o r DT = 0.1 ° C d S  and = 0 . 0 0 4  ° C , 0.001  ° C f o r DT = 1..C ° C  From (30) and Table I I I . l , <SV = 0.02 mV and 6V p  0.04 mV.  m  = 0.02 mV so that, 6V =  From (31) the probable error i n an absolute temperature  measurement i s  (35)  /160 Table III.l.  (a)  Typical calibration and resolution data for germanium diodes. Symbols are defined in th'e text.  Diodes (T a - T.b') = 20 C (V - V ) = 46 m V  6T = ± 0.01 °C  U  v  6V = ± 0.02 mV (calibration) m  fa  V = 125 mV S  = 2.3 mV C  d  6V  o-l  = ± 0.02 mV (measurement)  1  V ,= 6.750 V  6V = ± 0.003 V  p  p  6V DT = 0.1 °C to 1.0 °C (b)  = ± 0.02 mV = ±  fj  0.3 °C  Integrators S« = 166.7 counts (mV 10 min) -1 C.' = 833.5 counts  6C = ± 1 count  ;  V = 5 mV  6V = ± 0.005 mV  c  f  (c)  c  C  = 0.1%  Temperature and Vapour Pressure Y = 0.066 kPa V  6y = ± 0.002 kPa  1  s.. = 0.12 kPa °C~ at 15 °C  1  W  V  3S../3T = ± 0.006 kPa ° C " at 15 °C  2  W  6Z = 0.005 m Z = 3 m  r = 0.01  ST = 0.0003 °C m"  1  °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 " at 15 °C 1  W = 1.2 kPa  1  /161  fiT =  [10"  + 3 x 10"  4  = ± 0.35  4  + 22 x I O " ] * 4  1  + 0.3  °C.  (36)  The maximum error i s ± 0.4 °C.  Integrators From (33) the probable c a l i b r a t i o n error of an integrator i s 6S  C  =  [0.04  + 0.028]  ± 0.26 and  6  S  / C  counts(mV  10  C  The maximum r e l a t i v e error i s 0.22%.  (37)  During use, f  integrator s e n s i t i v i t y and is of the order of ± 0.1%.  C  = ± 0.26  ± 0.43  and  6S /S C  1  = 0.16%  S  6S  min)"  C  = ± 0.26%  The maximum error i s 0.32%.  +  f  equals the d r i f t in Thus,  c  counts(mV  10  min)"  1  (38)  /162  Temperature Errors w i l l be calculated for typical AT, 0.30 and 0.03 °C,over 3 m. AT = 0.30  high and low values of  From (24) and Tables III.l and III.2 for  °C/3 m  6AT =  x 10"  [7  6  + 6: x T O  - 8  + 5 x lO  - 7  ]^  + 6ATV d b  In the above equation, of the terms in parentheses, only the f i r s t i s significant.  This i s also the situation for-AT = 0.03 ° C / 3 m and for  the maximum as well as probable e r r o r .  Thus, the above equation  reduces to  <SAT = 0.00 3 + 6ATV b  6 l T  max  Taking values of 6A7s"  = 0-00 4  from (35)  d  SAT^  +  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  6M  =  [2.5  x >10" :  5  +' -  10^  6  + 3 x  lO" ]^ 9  the l a s t two terms in the above equation are n e g l i g i b l e ,  SAO  thus  5AT = ± 0.005  A typical maximum error i s ± 0.006 ° C .  °C  (  4  0  )  /163 Table 111.2.  Calculated probable and maximum absolute and r e l a t i v e errors f o r germanium diodes. Symbols defined i n text.  Probable E r r o r  Maximum Error  absolute  relative  absolute  relative  0.002  0.1%  0.004  0.2%  ST (°C)  0.35  -  0.4  SV (mV)  0.04  -  0.04  -  0.26  0.2%  0.37  0.2%  0.43  0.3%  0.53  0.3%  6S^  d  6S  V ) 1  (mV  (counts (mV 10 min)" ) 1  C  (ss  c  +  SAiy  c  (°c) d  SAT  f )  {0.0001 to 0.004}  (°C)  {0.003 to 0.007}  6AB  (°C)  0.005  «SL  (J g" )  Ss  (kPa  0.8  1  w  V ) 1  -  {0.004 to 0.008} 0.006  0.03%  0.002  {0.0001 to 0.004}  2%  0.9  0.04%  0.002  2%  Se"  (kPa)  0.05  -  0.12  -  SAe  (kPa)  0.001  -  0.0021  -  (kPa)  0.001  -  0.0021  -  6Ae  Q  /164  Vapour pressure From (22) using a value f o r a Targe (10 °C) wet bulb depression and data from Tables I I I . l and III.2 Se  = [4 x 1 0 " + 5 x 10" 4  + 23 x 10" ]  4  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 i n the"'wet  bulb temperature measurement so that 6e _ 6  and  ^  •'•  :  = . 0 . 0 5 kPa  N  (41)  w °-  1 2 kPa  From (18) the probable e r r o r i n Ae i s dependent on the dry and wet bulb temperature d i f f e r e n c e s .  For large dry and wet bulb d i f f e r e n c e  over 3 m, 0.3 °C and 0.25 °C r e s p e c t i v e l y , I,  6Ae  = [3 x 1 0 "  7  + 9 x 1 0 " + 1 0 ~ + 0.1 x 1 0 " ] 7  7  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 n e g l i g i b l e a f f e c t on Ae. For small dry and wet bulb gradients the f i r s t and fourth terms i n parentheses i n (42) are reduced.  Thus <SAe  w i l l be taken to be equal to (42) f o r a l l dry and wet bulb gradients. From (15) the error i n the corrected vapour pressure difference i s I,  6Ae  = [10" + 4 6  0  x  10"  1 3  +  1 x IO" }' 1 0  2  /165  The last two terms in the above equation are negligible even for large vapour pressures.  Thus  SAe  o  -  6Ae  = +' 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),  (0.03  for large temperature  (0.3 °C) and vapour pressure  kPa) differences, with 3 = 0.66,  63 =  [0.6  x 10"  and  4  + 4.8 x 1 0 " = ± 0.031  6 3 / 3 '=  4  +  4  ± 5%'  x  10"-j  (44)  The maximum r e l a t i v e error is ±T2% From (11),  for small temperature  (0.03 °C) and vapour pressure (0.003 kPa)  differences, with 3 = 0.66; -4 63 =  [0.012 + 0 . 0 4 8 M x 10 = ± 0.25 and  6 3 / 3 = ± 37%  The maximum r e l a t i v e error is ± '93%.'..  h  1  (45)  /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]* = and  2  ± 2.2  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. presented below for 6 = .0,,66, (R m" s " (301 W n f ) . 2  1  2  An example calculation is  - G - M) = 500 W m" and E = 0.122 g 2  From (6) and (9)  6E = [73 x 1 0 " + 2 x 1 0 " + 6 x 1 0 * ] * 6  = ± 0.009 g m~ and  9  2  s~  6  2  2  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, (R - G -M) = 500 W n f and H = 199 W m . From (7), 2  n  /167  Table 111.3.  Probable and maximum r e l a t i v e errors in the Bowen r a t i o (6) calculated_for various potential temperature (A0) and vapour pressure (Ae ) differences over 3 m. Errors are independent of the sign of 8. 0  A0  3_  (°C)  o (kPa)  Probable error  Maximum 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%  A e  75%.  /168  Table III.4.  Probable and maximum r e l a t i v e e r r o r s i n 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 SeS°r1?lSt10Rilit-r0,n . ' ' P o s i t i v e and negative Bowen r a t i o s . 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% T  a  b  l  e  I  n  3  f  o  r  6 > 0 Probable  3 < 0  Maximum  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 9 4 +  32]  = ± 15 W m~ 6H/H  =  ± 8%  The maximum relative error is ± 14%.  h  2  (48)  /170  Table III.5.  Probable and maximum r e l a t i v e errors in the sensible heat f l u x . Calculated from equation (7) using errors in the Bowen ratio (B) from Table 111,3, for positive and negative Bowen r a t i o s . Relative error in the available energy was 7%.  B < 0  B >0 B  Probable  0.66  Maximum  Probable  14%  Maximum  42%  0.66  13%  36%  56%  148%  0.97  8%  16%  233%  607%  1.32  8%  25%  66%  1.32  17%  43%  110%  266%  2.06  8%  17%  14%  37%  3.96  8%  15%  3.96  15%  5.0  11%  26%  6.6  8%  17%  21% 58% 35% 9%  20%  /171 3.  CALCULATIONS FOR SILICON DIODES The appropriate values f o r calculating the probable and maximum  errors i n the estimation of evapotranspiration are given in Table III.6. Calculated error terms are l i s t e d in Table 111.7.  1.  Temperature and Vapour Pressure Diodes From (26) the probable error in the diode s e n s i t i v i t y i s 6S  = [5.5 x 1 0 " + 0.9 x I O ' ] * 6  d  = ± 0.0025  6  mV ° C ~  5  1  (49) and  SS /S d  d  = ± 0.1%  The maximum r e l a t i v e error i s ± 0.2%. From (27) the absolute error in AT due to using a mean s e n s i t i v i t y for a diode pair matched to ± 0.1% i s JT^  = 0.0005  ° C f o r DT = 0 . 5 ° C  From (30) and Table III.6 6V - 0.02 mV and 6V  m  (50)  = 0.25 mV, thus 6V =  0.27 mV, and from (31) the probable error in an absolute temperature measurement i s •4 ST = [10 " + 0 . 0 2 = ± 0 . 7 3 °C  The maximum error i s 0.86  C.  + 0.165]  l.  2  + 0.3 (51)  /172  Table 111.6.  (a)  Typical calibration and resolution data for s i l i c o n diodes, Symbols are defined in the text.  Diodes (T  a  - T )  (V  a  - V ) = 60 m V  b  = 30 °C  6T = ± 0.01  <5V = ± 0.05 mV (calibration)  b  m  V = 650 mV S  d  o-l = 2.0 mV C  V  p  = 6.750 V  6V 6  V  (b)  °C  f  = ± 0.003 V  p  = ± 0.02 mV  p  = ± 0.3 °C  T  Integrators S  r L  C  f  = 166.7 counts (mV 10 m i n ) "  1  = 833.5 counts  i  = 5  v  (c)  °C to 1.0  = ± 0.5 mV (measurement)  m  6V DT = 0.1  °C  6C = ± 1 count 6V  m V  C  = ± 0.005 mV  = 0.1%  c  Temperature  and Vapour Pressure  Y = 0.066 kPa V s., = 0.12 w  6Y = ± 0.002 kPa  1  kPa ° C " at 15 °C 1  dsJdJ  V  = ± 0.006 kPa ° C " at 15 °C  2  w  6Z = 0.005 m Z = 3 m r = 0.01  6T = 0.0003 °C m" °C m"  1  (C, - C ) = 200 counts (large AT) = 20 counts (small AT) 9  1  L  AT = 0.03 ° C / 3 m to 0.3 ° C / 3 m L = 2465 J g " e = 1.2 kPa  1  at 15 °C  1  1  /173  Integrators From (33)  the probable c a l i b r a t i o n error of an integrator 6S  =  C  [0.04  + 0.028]  = ± 0.26 and  «S /S C  counts. (mV 10  min)"  (  During use, f  <5S = ± 0.26 C  ± 0.43  / S C  c  °-  = 1  +.  f  5  2  equals the d r i f t in  Q  integrator s e n s i t i v i t y and is of the order .of ± 0.1%.  6 S  1  •= 0; 1 6%  C  The maximum r e l a t i v e error i s 0.22%.  and  is  Thus  c  counts (mV 10  min)  -1  ^^  26%  53  The maximum error is 0.32%.  Temperature . ~ -  The absolute probable error in AT is r e l a t i v e l y the size of AT. from (24)  <5A0  independent of  The error in AG is mainly that in AT.  Therefore,  for AT = 0.3 °C  6AT  =  [9  x 10"  6  +. 1 x. 1 0 "  = ± 0 . 0 0 4 °C  The maximum error is ± 0.005  7  + 6 x 10" ].' 7  s  + 0.0005  ;  (54)  C.  )  Table I I I . ? .  Calculated probable and maximum absolute.and r e l a t i v e errors, f o n s i l i c o n , diodes.". Symbols defined' in text.  Probable Error  6S  V  (mV  d  )  1  Maximum Error  absolute  relative  absolute  relative  0.0025  0.1%  0.0047  0.2%  6T ( ° C )  0.78  6V (mV)  0, 3  0.05%  0.3  0.05%  0.26  0.2%  0.37  0.2%  0.43  0.3%  0.53  0.3%  0.0001 to. 0.001  0.0001 to  0.001  6AT (°C)  0.004  0.005  &~® ( ° C )  0.004  0.005  6S  (counts (mV 10 m i n ) ) -1  C  (6S  C  +  6AT<r  f ) c  (°C)  6L (J g ' )  1.8  1  6s  (kPa °  w  Se  C  (kPa)  _  1  )  0.004  1.32  0.1% 4%:  3.1 0.005  0.1.1  0.24  <5Ae ( k P a )  0.001  0.002  6Ae (kPa)  0.001  0.002 ,  0  0.1% 5%  /175 Vapour pressure From (22), for a large wet bulb depression (10 °C)  6e = [0.4  x 10"  + 2.3  3  x 10"  3  + 10 x  lO  - 3  ]^  = 0 . 1 ? kPa and  (55)  6 e = 0 . 2 4 kPa max m  The dominant second two terms are independent of the size of the wet bulb depression, and &e i s 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 TO"  7  + T O " + 0.1 7  x 10~ ] ^ 7  = ± 0.0013 kPa  (56)  The maximum error i s ± 0.00^6 kPa.  These errors do not change  s i g n i f i c a n t l y for smaller gradients. From (15) the error in the corrected vapour pressure difference is = .[-T.7-.-x 1 0 "  6  + .4 x T O "  1 3  + 8 x TO"  1 0  ]^  (57)  The last two terms in the above equation are negligible even for large vapour pressures.  Thus  <5Ae  o  ~. (SAe = ± 0.0013 kPa  (58)  /176  2.  The Bowen Ratio Probable errors in the Bowen ratio f o r the s i l i c o n diodes are  s i m i l a r to those f o r the germanium diodes.  Maximum r e l a t i v e errors are  l a r g e r , because there i s a larger maximum error in the vapour pressure difference measurement.  The reader i s referred to Table  III.3 f o r  the probable r e l a t i v e errors in the Bowen r a t i o . 3.  Evapotranspiration and the Sensible Heat Flux Probable r e l a t i v e errors in evapotranspiration and the sensible heat  flux f o r the s i l i c o n diodes are similar to those f o r the germanium diodes, Tables III.4 and III.5, respectively.  Maximum errors are larger f o r the  s i l i c o n diodes.  The improved c a l i b r a t i o n accuracy of the s i l i c o n  diodes (equation  (54)) i s 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 i s the major error i n Ae (equations (56) to (58)). Q  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%. 3 < 2.  If we consider a maximum error <20%,  Small gradients  (AG/AZ < 0.02  r e s u l t in s i g n i f i c a n t l y larger e r r o r s .  °C m" and 1  t h i s - a p p l i e s to 0 <<*< 0 . 0 0 3 kPa m" ) 1  A? /AZ Q  The sensible heat flux is estimated  to within ± 10% (probable error) and to within ± 2 0 % (maximum error) f o r 0 < 3 < 5.  Again, small gradients r e s u l t in a doubling of the error.  The  increasing sensible heat flux with increasing Bowen ratio offsets the e f f e c t of the increasing error in the Bowen ratio on the sensible heat f l u x . The  error in evapotranspiration is large for 3 < 0.  This w i l l be  especially true at night when vapour pressure gradients are small.  The error  the sensible heat flux is also increased f o r 3 < 0. Errors in the available energy are s i g n i f i c a n t f o r most values of 3 and large gradients.  It would be d i f f i c u l t to s i g n i f i c a n t l y reduce this  error due to the d i f f i c u l t y of determining (G + M) and in taking account of the s p a t i a l v a r i a t i o n -in net r a d i a t i o n . ;  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. for equation ( 1 1 ) and (44) that decreasing AG and ~Ke  Q  psychrometer separation would increase 63.  It can be seen by^decreasing  For small 3,uncertainties in  Y are as important as the accuracy of A9 and A e  Q  (see equation (44),).  3 increases or the gradients decrease then error in A e predominates Q  (see equations (45) and (46)). Contrary to the findings of Revfeim and Jordan ( 1 9 7 6 ) 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 i s through diode and integrator c a l i b r a t i o n and s t a b i l i t y errors (equation (39)). The l a t t e r is  mainly due to errors in T^, the major one being the r e s u l t o f  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) i s the ± 1 count resolution of the measurement system, (see equation ( 3 9 ) and the equation above i t ) . can  only be reduced by increasing the integrator  This error  sensitivity  As  /178 (see equation (24)).  These equations also show that diode s e n s i t i v i t y  matching and c a l i b r a t i o n , and integrator c a l i b r a t i o n should be to better than ± 0.5%.  This gives a combined error of < i 0.003 °C.  of the count rate with the 0.5% l i m i t a t i o n a probable error in SAT of ± 0.004 °C. counting period, i . e .  l i s t e d above would result in  Increasing the length of a  increasing (C-j - Z^) in equation (24)  four count periods, i . e .  A doubling  or combining  {[(C-| - Z^) + (Cg - C^)]/2}, w i l l increase the  error in AT, because the f i n a l  term <5A?V w i l l be increased since DT (see d would be increased.  equation (24))  5.  THE PROFILE BOWEN RATIO METHOD For the p r o f i l e Bowen r a t i o method, S i n c l a i r e t al. (1975) claim  errors in measuring AG and Ae" of ± 0.01 o  for d i f f e r e n t i a l  °C and ± 0.004 kPa, respectively  measurements with thermopiles.  McNeil and Shuttleworth  (1975) were less optimistic about their measurements with platinum resistance thermometers. temperature of ± 0.01  They suggest a measurement accuracy for absolute  °C and vapour pressure of up to ± 0.007 kPa for  SAG .= ± 0.014 °C and SAe = ± 0.01 o  kPa.  Table III.8, showing the errors  in 3 and E, was determined using the accuracy given by S i n c l a i r e t al. and AG and A e  o  in Table  111.3.  Comparing Tables  111.8,  111.3  and  111.4  shows the  profile  equipment gave errors in the Bowen r a t i o and evapotranspiration rate measurements of two to four times those of the reversing equipment. Furthermore, the p r o f i l e method may s t i l l  6.  be subject to systematic e r r o r s .  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. statements are v a l i d only i f the psychrometers are v e r t i c a l l y  The above separated  /T79  Table III.8".  Probable relative errors in the Bowen ratio (63/3): and evapotranspiration (6E/E) for the p r o f i l e Bowen ratio equipment of S i n c l a 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  (63/3)  (6E/E)  3 <0 (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 case).  The d i f f e r e n t i a l  measured.  at 1000 counts (m V h )  - 1  in this  output of the dry or wet bulb pairs should be  A f i n a l requirement i s that the sensors must be reversed  between each integrating period so that the effects of systematic errors in the sensors are minimized. also required.  An accurate measurement o f -(.R  - G - M) i s  /181  ANALYSIS  2.  OF THE.EFFECT  OF MISMATCHED  ON THE MEASUREMENT DIFFERENCE  OF A  DIODE  SENSITIVITY  TEMPERATURE  WITH.THE.  .REVERSING  PSYCHROMETER  The c a l i b r a t i o n equation f o r the germanium and s i l i c o n diodes i s  V  where V  = V  Q  -  ST  (1)  d  i s the diode junction voltage (mV), VQ i s the voltage at  0°C (mV).Syis the s e n s i t i v i t y (mV ° C ~ ) and T is the temperature  (0°C).  1  Two diodes, "a" and " b " , at temperatures T-j and 1^, in positions 1 and 2, r e s p e c t i v e l y , have diode junction voltages V -j = V and V| 2 = Vg^ - S^T-,. 3  - S^T-j,  Q a  The measurement system integrates the difference  in output between the two diodes continuously over 10 minutes.  This  can be expressed as JO  10 < al- " b 2 > V  V  d t  =  < 0a " V V  d  t  10. " da S  T  "0  10 T  d t  +  S  T- dt (2)  d*  0"  2  Q-  from which a 10 minute mean voltage difference i s obtained as follows  < al V  "  V  b 2 . ' " < 0a " 0b> * V  V  < d, l  where the overbars indicate mean values.  S  T  "  s  T d b  2>  <> 3  When the psychrometer heads  reverse, diode "a" goes to position 2 and diode "b" goes to position 1.  7182  The mean temperatures a t l e v e l s 1 and 2 change to T^ and T^, r e s p e c t i v e l y , f o r the second 10 minute period so that  <V" bl> " V  " da 4 (S  < 0a- " 0 b » V  V  T  S  '  dbV  >  (4  Subtracting (4) from (3) gives  • < da 4 " %S 3>  2 f l  S  T  "  T  ( S  da l  where 2A = (V-,1 " b2^ " ( 2 " Vx) • V  " db 2>  T  I  v  S  f  6  B  a  V  T  S  t h e  ( 5 )  deviation of each  diode from the mean s e n s i t i v i t y , S ,so that S^^=  SS^and S^=  d  S^- 6S  then (5) becomes  2A = S ( 2 A T ) +5S^(T  3  d  + T ) - {T 4  }  + T )J• 2  (6)  where AT i s the average temperature d i f f e r e n c e over the two 10 minute periods, i . e .  AT =  i ( T - T ) + (T . - T y ) j ; / 2 4  3  2  (7)  The second term on the right-hand side of (6) can be w r i t t e n as  25S (T d  n  - Tjj  = 26S DT d  (8)  /183  where DT i s the d i f f e r e n c e between the mean a i r temperature of the two 10 minute periods, Tj and T J J , r e s p e c t i v e l y .  S u b s t i t u t i n g (8) into  (.6) and s o l v i n g f o r AT gives  AT = (A - 6 S D T ) / S d  I f Tj = T j j , o r 8S^= 0 ( i . e . S^=  d  (9)  , then (8) equals zero and AT i s  given by  AT = A / S  d  (10)  I f Tj f T J J and S S ^ 0 then-the absolute error i n 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 e r r o r in AT (£) i s  5 = 5S DT/(S AT) d  with AT from (9).  d  (11)  Thus, the accuracy of the measurement of the tempera-  ture d i f f e r e n c e depends on how well the diode s e n s i t i v i t i e s are matched and the change i n mean a i r temperature between the two sampling periods. The sign of 6S DT/S depends on the d i r e c t i o n of t h i s change, with (TO) d  overestimating  d  AT when mean a i r temperature i s increasing with time,  i . e . DT > 0. Values of S / S 5  d  d  matching, r e s p e c t i v e l y .  °f 1% and 0.1% represent poor and good sensor The r a t i 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) reasonable accuracy.  can be used to give AT i f DT can be obtained with However, there w i l l be an error in obtaining  DT due to sensor and measurement l i m i t a t i o n s .  Integration of the  diode voltage, even with the voltage offset to allow an increase in integrator s e n s i t i v i t y , 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 r e l a t i v e error in measuring DT varies from 100 to 3%.  If  DT i s large and the sensors are not well matched then AT should  be corrected.  However, matching of the diode s e n s i t i v i t i e s 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 r e l a t i v e l y 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 c a l i b r a t i o n equation as a result of an incorrect c a l i b r a t i o n , e l e c t r i c a l effects in the monitoring system, e . g . extra resistance in the c u r c u i t , or modifications of the energy balance of the diode, e . g . heat conduction along the diode mounting stem.  Thus, the diode  temperature w i l 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 i s  AT  I  < al  =  T  +  £  al>  " < b2 T  +  £  b2>  () ]  and f o r the period after r e v e r s a l ,  ^11  < a2  =  T  +  e  a2>  " < bl T  +  £  bl >  (2  >  In (1) and (2) T and e indicate the true mean a i r temperature and the e r r o r , r e s p e c t i v e l y , and the subscripts indicate diodes "a" and "b" and levels 1 and 2.  AT  I  "  A T  II  Subtracting (2) from (1) and rearranging gives  ^ al  =  T  +  ( e  al  +  T  +  bl> e  b l  " }  ( T  "  = 2AT + ( e r r o r  a2 u  a2  +  T  +  terms)  b2> £  b 2  }  (3)  / 1 8 6  so that the true ayerage temperature d i f f e r e n c e (AT) i s given by  AT =  (AT  T  - AT  t t  ;/2  -  ( e r r o r terms)/2  ,4)  The true temperature d i f f e r e n c e i s obtained only i f  { £  al  +  £  b l  } =  ( e  a2  +  e  b2>  There are two ways i n which t h i s i s expected to occur f o r systematic errors:  Case 1  e  a l  =  and e  f a l  Case 2  e  a l  =  and e  a 2  = e  b 2  =  (6)  (7)  Symmetric Errors Case 1 and Case 2 are examples of the c a n c e l l i n g of systematic errors.  In Case 1 the e r r o r i s unique to a sensor and i s independent  of the p o s i t i o n of the sensing head, e.g. a c a l i b r a t i o n i n t e r c e p t e r r o r . In Case 2 the same e r r o r occurs on both sensors o f a sensor p a i r at the same time.  For example, the sensing heads are constructed symmetrical  so that each has the same geometrical arrangement i n space at the same time, i . e . sensing head "a" i n p o s i t i o n 1 has the same o r i e n t a t i o n with respect to the sun as sensing head "b" i n p o s i t i o n 2.  Since any e r r o r  /187  should be the same f o r both sensors of a p a i r of sensors, these symmetric errors cancel and the true temperature d i f f e r e n c e obtains.  Non-symmetric Errors P o s i t i o n dependent errors are non-symmetric e r r o r s .  The  non-symmetric geometrical arrangement of the sensors i n space shown i n Figure I I I . l would cause such an e r r o r . heating Of the  For example, the r a d i a t i o n a l  lead'wires *• on a head only occurs i n the lower p o s i t i o n  .position l ) , so that Case I i s obviously v i o l a t e d .  Furthermore, the  e q u a l i t y i n Case 2 cannot be f u i l f i l l e d since the e r r o r f o r sensor "a" in p o s i t i o n 1 must be d i f f e r e n t from that f o r sensor "b" i n p o s i t i o n 2. Various combinations of values f o r the e r r o r terms could f u l l f i l l (5). However, t h i s i s u n l i k e l y to occur since tne general symmetry of sensing head construction usually r e s u l t s i n the e r r o r being s i m i l a r f o r both heads i n the same p o s i t i o n , i . e . e , - e . , and al bl r  as i s shown i n Figure I l i . l .  a2  - e. with e , f e , , b2 al a2 0  Thus, when.non-symmetric errors;  occur, the true temperature d i f f e r e n c e i s not measured.  0  /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 e a r l i e r in this Appendix (III.3).  Identifying these errors and determining  their effect on the measured temperature difference is since i t  difficult  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 i n f e r r e d .  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 with reversing psychrometers.  system  Agreement between the methods i s good,  suggesting that i f non-cancelling errors are present they are not a major source of error. ratio systems.  Another approach is to compare various Bowen  'Identical'  systems would be expected to have similar  e r r o r s , and which system is in e r r o r , i f any., cannot be i d e n t i f i e d . 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 e r r o r s .  This Appendix  presents laboratory and f i e l d 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 i c o n diode sensors  (Kalanda et al., 1980). further different  The s i l i c o n diode system (Figure III.2) is  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 i c o n diode systems (BRM4 and BRM5) is also b r i e f l y  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. systems were exchanged  The locations of the reversing  occasionally to allow for spatial  variation  in v e r t i c a l temperature gradients in the room. The f i e l d 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 l e a r , 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 l e v e l s . 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 c a l i b r a t i o n 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 i c o n sensors. Thus, only data where the measurement and c a l i b r a t i o n errors were less than 10% of AT, i . e .  large temperature gradients, are considered, so  that any s i g n i f i c a n t non-cancelling errors should be apparent.  Jhe results  are presented as ratios of temperature d i f f e r e n c e s , with a value of 1 indicating complete agreement.  In general, dry bulb differences  (AT ) are from 0.15 to 0.6°C and wet bulb differences (AT^) are from D  0.1 to 0.3°C for measurement r e l a t i v e 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 e r r o r s . The results are presented as averages of a number of data points (n) and t h e i r standard deviation.  Comparisons between systems  are generally in the form of the ratios of measured dry bulb differences (RAT ) and the wet bulb, differences (RAT ) and the r a t i o of these two n  U  /193  ratios (RRAT). for each system.  This l a s t r a t i o i s the r a t i o of the values of ATg/AT,^ 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  to A T , since 3~ (C(s + Y ^ ^ Y Z n p J - l } " . 1  D  lated for each measurement period. number of periods may'be different the mean RAT^ and RAT^ values.  i s small compared  The r a t i o RRAT i s calcu-  Thus the mean value of RRAT f o r a from the value of RRAT calculated from  The f i e l d data used in this analysis  are stored on f i l e s HY77C0MMENTS RA0925.  m~^)  and HY77DATA  of tape  '  Results and Discussion The wet and dry bulb pairs within a single system are compared in Table III.9.  Agreement i s generally to within 7%, about the l i m i t  of thejrieasurement error.  However, there i s a trend for the wicked  sensor to s l i g h t l y 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 i s generally within the l i m i t s of the measurement accuracy (Table Disagreement i s by only 0.01 to- 0 . 0 2 ° C . due to horizontal  variability,  systems changed the r a t i o s .  III.ll).  This appears to be p a r t i a l l y  since reversing locations of the  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 1 .06 + 0..02  5 3  BRM2  1..06 + 0..02  5  BRM3  1 .06 + 0.,01  3  BRM4  1,.01 1 . .02 .98 >' $0..97 +  + + + +  0.,04 0.,01 0.,01 0.,03  8 4 10 4  dry bulbs also wicked *no wicks on either sensor Sboth sensors with wet wicks  TABLE III.10:  Comparison  Laboratory comparison of Bowen r a t i o systems with both dry and wet bulbs d,ry. See text for explanation of symbols.  RAT  W  RAT  D  RRAT  BRM2/BRM1  0.98 ± 0.02  0.99 ± 0.03  0.99 ± 0.03  5  BRM3/BRM1  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  RAT  BRM2/BRM1  1 .07 + 0,.02 1 .00 + 0.,03  1 .05 + 0,,02 0 .93 + 0.,04  1 .02 + 0,.03 1 .08 + 0,.03  6 6  BRM3/BRM1  0 .87 + 0.,04 1 .04 + 0.,03  0 .88 + 0.,05 1,.02 + 0.,03  0 .98 + 0..04 1 .02 + 0..03  11 11  BRM3/BRM1*  1,.10 + 0. 04 1..06 + 0. 02  1,.06 + 0. 03 1,.05 + 0. 02  1..04 + 0.,01 1,.01 + 0.,01  6 4  BKM4/BRM5  0.,97 0. 02 1, 03 + 0. 02  1.,00 + 0. 07 1. 02 + 0. 02  0.,98 + 0. 05 1.,01 + 0. 02  24 24  +  +  n  RAT,,  RRAT  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 A T / A T D  W  ratios are s i m i l a r , i . e . * R R A T - 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 l d data are shown in Table 111.12.  There are systematic differences between  systems in AT of up to 50%.  However, there i s 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 l d 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 i n e for agreement between systems, allowing for spatial and system v a r i a b i l i t y and net longwave l o s s .  The agree-  ment i s 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 l d data. The daytime data indicate the presence of non-cancelling e r r o r s .  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 t s 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 f o r BRMl and BRM2.-;* Ratios;o.f ATrj, AT and RRAT are BRM2/BRM1, 5.August 1977. See text f o r explanation of symbols. W  BRMl AT0  BRM2  ATW  AT D  Time  (°C)  (°c)  AT /AT  0900  0.214  0.169  0930  0.165  1000  ATu  (°c)  (°c)  ATD/ATW  RAT  D  RATW  RRAT  1 .27  0.197  0.134  1.47  0.92  0.79  1.16  0.132  1.25  0.121  0.089  1.36  0.73  0.67  1.09  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  D  W  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 Comparison  RAT  BRM2/BRM1  0,.90 ±0, .04  BRM3/BRM1  D  0..91  1230 - 1600  RRAT  n.  R T  0 .89  1,.02  33  0,.76  0..74  1 .03  14  0,.9.3  ±0 .05  ±0. .04  11  ±0, .13  ±0. .13  ±0 .13  14  19  1..00  0..81  1,.25  0  ±0. .09  ±0. ,12  RAT  W  No data  ±0. .06 BRM3/BRM2  0900 - 1200 A  0  RAT  W  n  RRAT  ri,  0,.92  1 .01  10  ±0. .09  ±0. .09  ±0 .03  10  6  0.,85  0.,84  1,.03  8  ±0, .10  6  ±0. ,10  ±0. 16  ±0, .18  8  RRAT  R T A  D  RAT  W  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 i s . h i g h e r 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 r e l a t i v e l y 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 i m i t s imposed by measurement and c a l i b r a t i o n e r r o r s , i . e . of <±10%.  an error  Even in the f i e l d where there may be s i g n i f i c a n t horizontal  v a r i a t i o n , 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 I I I . 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 s e l f cancelling in the calculation of the Bowen r a t i o , since  B^AT^/AT^  Therefore, the error in B is generally within ±10% for AT>0.05°C, and results in a small enhancement of the measurement and c a l i b r a t i o n errors.  /201  5.  LABORATORY EXPERIMENT  EXTERNAL  RADIATION REVERSING  TO DETERMINE THE INFLUENCE  OF  ON THE TEMPERATURE OF THE 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 i n 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 c u l t y  in obtaining equal heating of both  heads and warming o f the a i r being sampled by the unheated c o n t r o l . Consequently, the problem was investigated by constructing a model head from material  s i m i l a r 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 and ventilated externally with a fan at about 3 m s~^.  at the head The temperature  difference between various points on the head and the sampled a i r was measured with thermocouples. as shown i n Figure H I . 3 ,  The presence of the external s h i e l d ,  i s equivalent to the exposure of the lead  wire to radiation i l l u s t r a t e d by the upper head in Figure I I I . l . The absence of the shield i s equivalent to the exposure to radiation i l l u s t r a t e d by the lower head in Figure I I I . l . The data in Tables 111.14 and 111.15 i l l u s t r a t e that, with illumination and external  v e n t i l a t i o n , 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 s h e i l d i n g ,  FAN  LAMP  E X T E R N A L SHIELD  L  L E A D WIRE  M Y L A R TAPE -INSULATION -METAL TUBE  ®  AIR T E M P E R A T U R E ASPIRATION  =  FIGURE III.3:  2 0  mm  (x)= T H E R M O C O U P L E JUNCTION  Experimental arrangement to determine the influence of external radiation and ventilation on sensing head temperature.  ro o ro  /203  TABLE III.14:  Effect of r a d i a t i o n , 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 - T r ; ) , where the subscript X indicates the location (Figure III.3) of the measurement and Trr is the temperature of the a i r entering the sensing head.  Treatment Rad.  Ext. Vent.  (T Shield  Wire (A)  X  - T )°C E  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 ( l e t t e r s 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 . 0 1 ° C and are (Tx - T E ) , where the subscript X indicates the location of the measurement and T E is the temperature of the a i r entering the head. -  Treatment Rad.  Shield  (Tx - T E ) ° C 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 i g h t on the opposite side of the head to the lead wire  -0.5  +0.1  +0.1  -0.2  off  -0.8  -0.2  -0.1  -0.7  on  /205  respectively.  S i m i l a r l y , the insulation and metal tube were warmer  than the a i r .  There were s i g n i f i c a n t 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 l u m i n a t i o n , the diode was below a i r temperature, while with illumination the diode temperature increased to a i r temperature or j u s t above a i r 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 l d measurements of AT by BRM1 and BRM2.  Figure I I I . l i l l u s t r a t e s 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 s i g n i f i c a n t 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 s i t e is on a NE slope (< 10%), about 150 m above sea l e v e l , 49° 51' N, 125° 14'  1.  W.  Soil Soil  Profile  The s o i l p r o f i l e is quite variable.  About 1% of the area  consists of rock outcrops, 5% with s o i l depth < 0.4 m and > 50% coarse fragments, 50% with s o i l depth 0.4 to 0.6 m and 20 to 50% coarse fragments and 44% with s o i l depth 0.6 to 1.1 m and < 20% coarse fragments.  The s o i l is an Orthic Humo-Ferric Podzol and the b r i e f  description in Table IV.1 Goldstein, 1980).  is for a typical deep p r o f i l e (modified from  The shallower p r o f i l e s have smaller Bf and C  horizons.  Bulk Density and Coarse Fragment Content Bulk density data for the s o i l were obtained for 0.25 x 0.25 x 0.1 m deep sections of the p r o f i l e .  Volume of s o i l was obtained  by l i n i n g the holes with a p l a s t i c bag and f i l l i n g with water.  The  s o i l samples were dried and seived to separate out the < 2 mm f r a c t i o n . 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 p r o f i l e description for the thinned Courtenay, B.C.  Horizon  Depth (mm)  LFH  site,  Description  20 - 0  Ah  0-40  Very dark grayish brown (10YR 3/2 m). Sandy loam. Weak subangular blocky structure. Clear boundary. Abundant roots, f i n e 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  C  '  150 - 680  680 - 930  Dark grayish brown (7.5YR 4/4 m). Sandy loam. Fine s i n g l e - g r a i n structure. Gradual boundary. Few roots, fine to medium. Dark brownish yellow (10YR 4/4 m). Loam. Fine single-grain structure. Sandstone bedrock with a fine root mat forms boundary. Few r o o t s , fine.  /208  TABLE IV.2:  Location Depth (m)  Bulk density (kg  1  2  _3 m  ), thinned  3  +  s i t e , Courtenay, B.C.  4  5  6  0-0.1  770  1230  890  810  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  1160  1260  Values s i m i l a r to those a t l o c a t i o n 3, a deep sandy s i t e , were obtained by Goldstein (1980) i n an area 50 m NE of the main s i t e .  /209  TABLE IV-3:  Location Depth (m)  Volume f r a c t i o n (%) occupied by > 2 mm f r a c t i o n , thinned s i t e , Courtenay, B.C.  1  2  3  4  5  6  30  44  0-0.1  4  42  6  18  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 t o bedrock (Table I V . 2 ) .  Coarse fragment  (> 2 mm) c o n t e n t  i s l i s t e d i n T a b l e I V . 3 . The d e n s i t y o f t h e s e sandstone fragments was o b t a i n e d by c o a t i n g them i n wax and w e i g h i n g i n water -3 50 kg m , n = 8) and by vacuum s a t u r a t i o n  (2170 ±  -3 (2190 ± 70 kg m , n = 7 ) .  _3 The average i s 2180 ± 60 kg m which i m p l i e s a p o r o s i t y o f 18% s i n c e the p a r t i c a l  Soil  d e n s i t y o f t h e sandy.by vacuum s a t u r a t i o n , was 2660 ± 20 kg m~  Water R e t e n t i o n C h a r a c t e r i s t i c s  The d a t a were o b t a i n e d w i t h f i v e t e n s i o m e t e r s and a s i n g l e neutron a c c e s s tube l o c a t e d next t o t h e t e n s i o m e t e r s . were n o t used i n d e t e r m i n i n g t h e f i e l d r e t e n t i o n they were l o c a t e d some d i s t a n c e from t h i s variability.  characteristics since  tube and t h e data had a l a r g e  The data were f i t t e d t o ty = ^ ( 9 / 0 ) " m  1974a;Clapp and H o r n b e r g e r , 1978).  Hygrometers  mr  m  r  (Campbell,  The c o e f f i c i e n t s a r e l i s t e d i n  3 - 3 Table I V . 4 f o r 0  r  = 0.3 m m  and a c o a r s e fragment c o n t e n t o f about  The average i> {9)  15% by volume.  m  o b t a i n e d by a v e r a g i n g m and ty this function  f o r each d e p t h .  F i g u r e I V . 2 compares  from t e n s i o m e t e r d a t a w i t h t h e hygrometer  ty < - 0 . 0 1 MPa. m  laboratory  mr  c h a r a c t e r i s t i c shown i n F i g u r e IV,1 was  data,  F i g u r e I V . 3 compares t h e average ^ (8) c h a r a c t e r i s t i c w i t h m  r e t e n t i o n d a t a f o r u n d i s t u r b e d c o r e s ( G o l d s t e i n , 1980). The  s l o p e o f t h e l a b o r a t o r y d a t a i s s i m i l a r t o t h a t from t h e f i e l d b u t , d u e t o l o w e r c o a r s e fragment c o n t e n t f o r t h e same ty .  data,  (< 5% by v o l u m e ) , 8^ i s h i g h e r  /211  TABLE IV.4:  Coefficientsm for the f i e l d retention function, ty = for four depths from tensiometer and mr r neutron moisture probe measurements, thinned s i t e , Courtenay, B . C . , 1978. Correlation c o e f f i c i e n t (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 is 0.3 m 3.  ty {Q/Q )~  m  _  r  Depth (m)  m  (kPa)  r  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  5.9  -0.9  Average  2  n  /212 1  FIGURE IV.1:  1  1  1  Thinned site, field retention charact e r i s t i c , 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 ty > -0.1 MPa, hygrometer data for ty < -0.1 MPa. Line from Figure. IV. 1. m  m  /214  -1.0  1978 \ FIELD DATA  o  CL  -0.  1979 LAB. DATA  \  Depth (m) \ V o  -0.05  -0.01  \  0.07 0.30 0.60 0.90  1 0.1 0 (m  FIGURE IV.3:  0.2 3  0.3  m" ) 3  Thinned S i t e , laboratory determined retention data, 1979 (from Goldstein, 1980). Dashed l i n e is from Figure IV.1.  /215  Hydraulic Conductivity Characteristics Data for k  s a t  and for u> < -10 kPa are from Nnyamah and Black m  (1977) and Nnyamah (1977), ( s o l i d c i r c l e s 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). 99 mm d~^ at -1.5 kPa and 140 mm d s o l i d triangles in Figure IV.4. data.  - 1  The values were  at -1.4 kPa and are shown as  The dashed l i n e is an eye f i t  The s o l i d l i n e was obtained from the exponent of the average  ty (Q) m  c h a r a c t e r i s t i c following Campbell (1974a), and has a slope equal to  2 + (3/m).  A k(6j c h a r a c t e r i s t i c s , k = k - ( G / 0 ) ^ r  3 + 2 m  r  ^ (Campbell, :1974a), with 3  k  r  to the  from the above laboratory experiment and 6  to a 15% stone content),  is shown in Figure  r  -3  = 0.3 m m  (equivalent  IV.5.  Drainage Versus Root Zone Average Water Content Relationship This relationship was obtained from f i e l d measurements in August and September 1978. ^  m  Daily tensiometer measurements (set no. 1) of  were converted to 8 using the average ^ ( 8 ) c h a r a c t e r i s t i c .  These values  of 0 were converted to storage, summed over the p r o f i l e to give W and then divided by p r o f i l e depth to give 8.  Daily evapotranspiration  was obtained from the relationship ( E ' = a E ^ + g l ) , limit E.  since 8 did not  Daily drainage was obtained as the residual term in  D = AW + P - E .  Due to the v a r i a b i l i t y  of the data and the errors  /216  10* COURTENAY GRAVELLY SANDY LOAM (0-0.4m DEPTH) 10'  ^ k - 100 ( - l . 5 / Y )  J  m  10  k  ( mm d" ) 1  10"  10"  -I0"  1  -10°  -10 V  FIGURE IV.4:  M  -10  2  -IO  3  (kPa)  Hydraulic conductivity (k) characteristic for the thinned and unthinned sites, 0-0.4 m.  -IO  4  0.24  0.22  FIGURE IV.5:  0  (m m~ ) 3  3  0.26  Drainage versus storage relationship, thinned site, 1978. Curve represents the average k(9) characteristic.  0.28  /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). shown in Figure IV.5  is the k(6)  The curve  c h a r a c t e r i s t i c described previously.  there is unity gradient drainage D(0) can be approximated by the characteristic. the k(0)  2.  If  k(0)  Since-gradients, become less than unity as drainage proceeds  c h a r a c t e r i s t i c s l i g h t l y overestimates drainage as. ©-.decreases.  Vegetation The trees are Douglas-fir {pseudotsuga  The understory is mainly salal  {oauitheria  species such as v a n i l l a l e a f [Achiys grape [Mahonia  menziesii  shaiion  triphyiia  sp.) and bracken [Pteridium  (Mirb.) Franco).  Pursh).  Other  (Smith) DC), Oregon  aquilinum  (L.) Kuhn)  account for less than 6%, projected l e a f area b a s i s , of the understory leaf area.  Tree Diameter at Breast Height (D.B.H.) The D.B.H. d i s t r i b u t i o n was determined in early August, 1978 for a 25 x 35 m p l o t , containing 72 l i v e trees (Table IV.5) dead tree.  and one  Trunk water storage was probably at a minimum since this was  the d r i e s t 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, f o r a 25 x 35 m p l o t .  Size c l a s s ^ (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  O r i g i n a l l y 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: (Table IV.7).  The LAI was determined f o r four trees in August 1978 An average branch from each whorl was removed and the  needles s t r i p p e d , dried and weighed.  On every f i f t h or sixth whorl  the current years foliage was separated out before drying.  Leaf area  to weight r a t i o s , o n 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 t r e e , 5.4 ± 0.2 m kg half.  f o r the lower  The leaf areas are on a projected area basis since the r -  c h a r a c t e r i s t i c s 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 t h i s , the leaf area to weight  ratios presented above are about 20% lower than those presented by 2 -1 Gholz et al. f o r 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:  Tree  D.B.H. and dendrometer band readings (Dendr.) i n 1978, 1979and 1980. D.B.H. (AD.B.H.) i s from 5 May, 1978 to 6 May, 1980.  5 May 1978 Dendr. D.B.H (mm)  12 May 1979 Dendr.  6 May 1980 Dendr. D.B.H. (mm)  The change i n  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  FIGURE IV.6:  0  M A M 1980  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 l e a f area (LA), thinned stand, August, 1978. Height i s where whorls joined the trunk. Tree 30 D.B.H.(mm) 138 Height m 1 .0 1 .32 1 .76 2 .31 2 .89 3..58 4,.14 4..72 5..26 5..84 6..50 7.,34 8.,13 8.84 9. 54 10. 18 10. 82 11. 42  Total LA  37-2 97  LA m 2  Height m  0.02 1.11 1.14 3.79(old) 0.74(new) 5.08 7.72 7.39 4.81 5.34(old) 1.35(new) 4.14 3.85 3.99 2.26(old) 1.10(new) 2.00 0.92 0.58 0.30 0.09  63.20  0 .18 0 .38 0 .62 0 .80 1 .02 1 .22 1 .70 2,.38 2,.80 3,.18 3..48 3.,66 3.,94 4.,32 4. 83 5.44 6. 35 6. 53 6. 96 7. 54 8. 18  80 166 LA m 2  Height m  0.28 1.20 1.06 1.57 1.00 2.00 1.12 2.74 0.93 1.22(old) 3.25 0.08(new) 4.04 4.45 4.88 3.84 5.61 4.63 6.35 1 .87 2.39(old) 7.06 0.43(new) 7.87 1.97 8.53 1.24 9.35 2.36 9.98 1.72 1.37 10.71 0.39(old)11.45 0.32(new)12.07 0.84 12.44 0.72 13.43 0.12 0.04 48.52  37-1 118 LA m 2  Height m  0.32 0 .40 3.15 0 .68 2.51 1 .03 5.25(old) 1,.44 0.37(new) 1..87 4.80 2,.50 8.96 16.37 2,.97 6.33 3.,53 9.07(old) 4..03 1.73(new) 4.,39 8.23 4.81 4..90 6.32 5..50 4.37 6. 42 3.14(old) 7. 26 1.24(new) 8. 14 1.78 1.72 8. 98 0.92 9. 70 0.55 10. 38 0.12 11. 28  91.48  LA m2 0.03 0.03 0.19 0.44 1.30 0.80(old) 0.11(new) 2.11 2.05 3.04 1.56(old) 0.32(new) 2.14 2.71 2.77 2.42 0.98(old) 0.68(new) 1.47 1.18 0.27 0.07  26.69  7224  D.B.H.  FIGURE IV.7:  (mm)  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  r = 0.986, s . • = ± 11.m y. x  ?  ? , with LA in m and D.B.H. in mm.  (D.B.H.) " 1  5 2  This  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 average tree leaf area in each D.B.H. c l a s s .  the  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 ) .  Douglas-  - 1  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 1975 (Tan et a l . , 1978).  in 1978 compared to  3.0  However, the s o i 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 t h e s i s .  TABLE IV.8:  Understory leaf area index, thinned stand, August 1978. 2"  Sample area 1 m location Salal (m ) Other sp. (m ) 2  d  1  2  3  2.73 0.05  3.93 0.24  3.59 0.01  2.78  4.1 7  3.60  /226  Stomatal Resistance C h a r a c t e r i s t i c s Measurements were made between June and September, 1978 with the v e n t i l a t e d d i f f u s i o n porometer used by Tan and Black (1976, 1978) and Tan e t al. (1977, 1978).  C a l i b r a t i o n checks during the summer and  in the f a l l were l i m i t e d and there i s , therefore, some uncertainty in the c a l i b r a t i o n .  The c a l i b r a t i o n data, and data i n 1980 ( K e l l i h e r ,  pers. comm.), i n d i c a t e that the t h e o r e t i c a l curves (Table IV.9), calculated from data i n Tan and Black (1978), are adequate. Douglas-fir:  Tree number 55 was sampled r e g u l a r l y 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 i n each measurement,within 5  minutes o f the sampling. Needle plan area was determined to w i t h i n ± 20% from measurements of length and breadth of each needle.  Measurements  of r were made on young and o l d needles, separately and i n s  combination.  Canopy vpd measurements were also made at the time o f  needle sampling. The r data are shown i n Figure IV.8 p l o t t e d against vpd $  f o r two \  ranges.  The measurement error f o r each, point, could; e a s i l y be +20%.  The curves are the regression l i n e s from Tan e t a i . (1978) f o r the s i t e i n 1975.  The data f o r ^  > - 0.35 MPa f i t the curve quite w e l l .  There i s i n s u f f i c i e n t data t o judge the other range. e t ai.  As noted by Tan  (1977) there i s a trend f o r the resistance to increase s l i g h t l y  with the depth i n the canopy.  In e a r l y June, new needles tended to  TABLE IV.9:  Theoretical t r a n s i t times (3-6 uA) f o r the ventilated d i f f u s i o n porometer, c a l culated from data i n Tan and Black (1978).  10°C  0  20°C  H  30°C  3.7  3.2  0.97  31.8  26.8  0.91  19.4  17.9  1.62  50.6  42.7  1.52  30.9  2.80  84.7  71.5  2.63  2.90  87.6  73.9  5.71  168.8  142.5  *r  s  i n ks m  1  0  2.4  2.2  0  1.4  1.3  0.85  10.2  9.8  28.4  1.43  16.2  15.6  51.6  47.5  2.47  27.0  26.0  2.72  53.3  49.0  2.56  30.0  26.9  5.35  102.5  94.3  5.04  53.8  51.7  corresponds to c a l i b r a t i o n plates with correction made f o r one end e f f e c t .  'Scales H, and H , t r a n s i t times i n seconds. 9  7228  vpd FIGURE IV.8:  (kPa)  Douglas-fir, tree 55, stomatal resistance (r ) versus vpd for three heights and two ty ranges, thinned stand, June to September, 1978. Curves are from Tan et al. (1978). s  m  /229  have higher values of r variation  in r  variability  g  g  than old ones.  However, the  between d i f f e r e n t age classes was similar to the  within an age c l a s s .  The data do not include early  morning or early evening readings when l i g h t levels may have influenced r . s In J u l y , August and September six other trees were sampled regularly to investigate between-tree v a r i a b i l i t y  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. 1 hour since twig water potential the sampled twigs.  Sampling a l l  six trees took about  measurements were also made on  The ^ - c h a r a c t e r i s t i c s  (Figure IV.9)  show good  agreement with the regression lines for 1975 (Tan et a i . , 1978) with tree 55.  and  No s i g n i f i c a n t systematic differences between trees were  apparent. Salal:  The ^ - c h a r a c t e r i s t i c s for the salal  determined at three s i t e s .  (Figure V.10) were  At least four leaves were sampled each  period and an accompanying measurement of the vpd was made at 0.5 m above the ground. had r  g  In June and July shaded leaves often  values of up to f i v e times those of s u n l i t leaves.  plotted separately in Figure IV.10.  The regression curves for  salal for three ty ranges (Tan et a i . , 1978) Figure.  Values of r  g  They are  are also shown in this  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 - c h a r a c t e r i s t i e s , thinned stand June-September, 1978. s  Tree ho.  15  22  30  38  49  54  55  D.B.H.  91  74  135  86  137  145  170  33.2  24.2  LA  (nf)  (mm)  60.5  30.4  61.8  67.4  85.9  /231  i  CLOSED h  •  XK  AAM  r AA  DOUGLAS-FIR, JULY-SEPT. 1978  . A A  A  o /  >*<X  DOO  A -BAA  0 FIGURE IV.9:  O  oAA oo „  xA A  OD  AA  A OA  . . =*'.  air  Attl  O  1  o  / O <ftn»-0.35 MPa  A AA A  A -0.95s Vm<-0.35 MPa x - 1.25* Vm<-0.95 MPa  o  A Vm<-l.25MPa  2 vpd (kPa)  s  I  ,  Douglas-fir, six trees at the 4.5 m height, stomatal resistance (r ) versus vpd for four ty ranges, thinned stand, July to September, 1978. Curves are from Tan et a l . (1978). s  m  7232  FIGURE IV.10;  Salal stomatal resistance (r ) versus vpd for thre 4> ranges, thinned stand, June to September, 1978 Curves are from Tan et ai, (1978). s  m  7233  corresponding 1975 data.  This may be at least p a r t i a l l y  due to  errors in the porometry technique that could result in an underestimation of salal r Occasional gave ' i n f i n i t e '  s  by over 20%.  measurements of the upper surface of the salal leaves  resistance.  leaf showed that i t  Infrequent measurements on the v a n i l l a  had similar resistances to the salal for  lower surface, while i t s upper surface had ' i n f i n i t e '  its  resistance.  Twig Water Potential Twig water, potential  (ij;^)  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 r a i n .  S i m i l a r l y , maximum predawn \p for salal was t  between -0.07 and -0.23 MPa, with about -0.07 ± 0 0 3 M P a for the above r  damp conditions.  Maximum predawn ty^ for the Douglas-fir is generally  0.4 to 0.6 MPa lower than the average ty , and for salal 0.1 m  0.2 MPa lower than ty . m  to  ^  Minimum daytime ty^ f o r Douglas-fir and salal were  relatively  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 s o i l water a v a i l a b i l i t y .  The lowest salal  7234  TABLE IV.11:  Maximum predawn twig water potential (ty ). Average and range of ty data and number of samples (n) indicated. The range of the measured root zone ty and estimated average ty are also shown. t  t  m  ^ (MPax-l)  ^(MPax-1)  t  Douglas-fir  Salal  Average  0 . 1 6 ± 0 . 0 9 , n=ll  0.02  0.01-0.1  0 . 8 5 ± 0 . 3 6 , n=22  0.36±0.20,  0.1  0.05-0.3  1 . 2 4 ± 0 . 2 4 , n=6  *  0.6  0.2-0.8  1.45±0.28,  *  1.1  0.8-1.3  1.9  1.4-2.6  0.58±0.22,  n=18  n=12  2 . 0 4 ± 0 . 2 3 , n=6  +  2.25  n=10  , n=3  Range  At end of rainstorm and on a foggy morning with dew on the leaves (1000 PST) 0 . 3 5 ± 0 . 1 3 , n=ll  0 . 0 7 ± 0 . 0 3 , n=4  0.005  -  *Salal ty higher than ty . Salal s i t e was an area without trees. It appears that the s o i l water was not depleted as rapidly in this area as in other areas. t  Sample s i t e by a tree.  m  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 y and estimated average ^ are also shown. m  m  ^ (MPax-l)  ^(MPax-l)  t  Douglas- f i r  Salal  Average  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,  *  0.6  0.2-0.8  1.1  0.8-1.3  1.9  1.4-2.6  n=13  2 . 2 ± 0 . 9 , n=9 2 . 4 ± 0 . 5 , n=8  *2. 2 ± 0 . 4 , n=7 2. H O . 6 , n=17  *See footnote to Table IV.11.  Range  /236  values (-2.2  ± 0.5 MPa) occurred at the time of minimum s o i l water  availability  (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.  of these gauges were at different  positions d i r e c t l y under the trees.  The other two were located in the 'open'. above  the s a l a l .  determined.  Three  Gauge o r i f i c e was  Thus, only interception by the Douglas-fir was  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 t h r o u g h f a l l . . was calculated from the r a i n f a l l  Average interception  above the canopy minus average  t h r o u g h f a l l , and plotted against r a i n f a l l relationship I = 0.4 P '  (I)  (Figure I \ M 1 ) ,  The  was f i t t e d 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  for P > 0.3 mm.  P  0 - 6  ,  A l 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.  1.  MICROMETEOROLOGICAL INSTRUMENTATION AND DATA STORAGE  Instrumentation In T978 most of the above-ground equipment was located on a  10 inch triangular tower.  Net r a d i a t i o n , solar r a d i a t i o n , 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 t r e e , and an anemometer at 0.6 m above the ground (just above the s a l a l ) .  Two s o i l heat flux plates were at 0.05 m below  the s o i l surface and two s o i l temperature probes were used to give the 0 - 0.05 m average temperature.  A l l of this  instrumentation,  except the rain gauge, was integrated by a data logger (see later) and analysed to give half-hourly averages. daily.  The rain.gauge was read  A hygrothermograph was located in a screen 2 m above the ground..  Soil moisture was monitored with a neutron moisture probe (5 l o c a t i o n s ) , tensiometers (2 locations) and s o i l hygrometers (4 l o c a t i o n s ) . In 1979 d a i l y solar radiation was measured 9 km east of the thinned s i t e at the U.B.C. Research Farm at Oyster River.  Temperature  and r e l a t i v e humidity were monitored on a hygrothermograph in a screen 1.6 m above the ground.  A rain gauge, located in a nearby c l e a r i n g ,  was read every 7 to 10 days and partitioned into d a i l y r a i n f a l l on the r a i n f a l l  at Oyster River.  based  Soil moisture was measured with a  neutron moisture probe (5 l o c a t i o n s ) .  7239  Above Canopy Psychrometer The temperature sensors in the psychrometer were F a i r c h i l d FD300 s i l i c o n 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 c e l l foam rubber and covered with aluminized tape ^  (3M C o . , No. 850, s i l v e r , polyester f i l m 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  radial fan (Pamotor, RL90-18/24).  - 1  by a 24 V D.C.  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  psychrometric constant of 0.7 was required.  A  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 linear and second order polynomial regressions of 8  i  FIGURE IV.12:  1  1  RATIO  '  /240  r  Neutron moisture probe calibration, thinned stand, 1978, 1979.  on the r a t i o of actual to s h e i l d counts (RATIO) are: s o l i d 9 = (0.400 RATIO) - 0.051 (m m" ), r 3  3  2  = 0.904, s  line,  = 0.015 m nf 3  w  dashed l i n e , e = 0.040 + (0.054 RATIO) + (0.304 (RATIO) ) (m n f 2 3-3 2  r  = 0.908, Sy  x  = 0.014 m  m  determine-6 i n 1 9 7 8 and 1 9 7 9 .  3  . The l i n e a r equation.was used to  3  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 b u i l t measure micrometeorological data at remote s i t e s .  to  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. i n i t i a t e d by an external takes 12.5 s .  clock.  Scanning and resetting the counters  The current drawn by the logger i s about 0.8 A, the  printer accounting for 70% of this value. CAN $1050.  Scanning is  Component cost was about  The data logger worked continuously in the f i e l d from May  to October 1978 with an overall s t a b i l i t y of better than ± 0.5%. Proposed improvements w i l l s i g n i f i c a n t l y reduce power consumption and cost.  1.  INTRODUCTION  Studies of forest and agricultural  environments often  the longterm, continuous monitoring and recording of sensors.  require There  *By D. L. Spittlehouse, P. W. Y. Wong and T. A. Black. Presented at the Northwest S c i e n t i f i c Association Annual Meeting, Western Washington University, Bellingham, Washington, March 28-30, 1979.  v  7243  may frequently be a need to do t h i s in remote locations where the equipment i s not under constant supervision, power is l i m i t e d , 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, A result of the current rapid development  in electronics is the  a v a i l a b i l i t y of low power consuming, compact data loggers. vary in cost and complexity.  These  Commercially available loggers o f f e r a  wide variety of options but are expensive, often more sophisticated than required and are not e a s i l y user modified and maintained. Harrington (1978) has reported on a data-logging system that telemeters information to a central recording s t a t i o n .  Strangeways (1972) and  Ross (1978) have described on-site recording,automatic weather stations for use in remote environments.  The l a t t e r two data-logging systems  appear to be very u s e f u l , but are s t i l l expensive, and make spotreadings of analogue voltages.  However, for certain a p p l i c a t i o n s , 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 t s 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 s i g n a l s .  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 l a t t e r 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 l o s t i f the sensor output i s not lagged to match t h i s 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 r e l i a b l e average.  Fortunately most  sensors used in micrometeorology have a l i n e a r i z e d output. time averaged reading is a l l  that is required.  Often, a  To obtain a r e l i a b l e  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  f a c i l i t a t e an increased scanning rate and to do on-line averaging of and reduction in data output. and d i f f i c u l t  to use.  However, microprocessors are expensive,  /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 i z e , power requirement and cost of the data logger w i l 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 r c u 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 i v e major subsystems (Figure IV.13).  are the voltage integrators, the counters and counter input  These  interface,  the printer and counter/printer i n t e r f a c e , the scan control logic and the power supply.  In describing these subsystems schematics are  presented rather than c i r c u i t diagrams since the l a t t e r may change depending on the a v a i l a b i l i t y of electronic components and the type of data.recording device used.  C i r c u i t diagrams for the data logger we  constructed are available from the authors.  7246  DATA  LOGGER  SCHEMATIC  DATA LINE POWER SUPPLY CONTROL SIGNAL VOLTAGE COUNTER / PRINTER INTERFACE  1~  12V  — «  N  —  <,  POWER  0  SUPPLY  + 3V -SV • 12V  SCAN CONTROL LOGIC • 5V  •H2vf'Y  SCAN INITIATE  FIGURE IV.13:  Data l o g g e r schematic.  PRINTER^  7247  The  Integrators P r e c i s i o n , dual ramping, electronic integrators, as described  by Tang e t 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 w i l l only accept positive voltages.  Thus,  '  a l l negative voltages must be o f f s e t so that the integrator always monitors a positive s i g n a l .  The output of the integrators is a t r a i n  of 5 V pulses with the pulse rate and the integration rate.  a function of the input voltage  The l a t t e r is set by adjusting the gain on  the preamplifier and on the integrating a m p l i f i e r .  The integration rate  chosen depends on the expected size of the input s i g n a l , the length of time for integration and the number of d i g i t s that can be handled by the counters and printer.  Typical c a l i b r a t i o n graphs of counts  against input voltage are presented in Figure IV.14.  There is an  upper and lower l i m i t to the voltage range for any count rate.  The lower  l i m i t is set by the s e n s i t i v i t y of the preamplifier while the upper l i m i t 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 i g n a l , or pulses, to the integrators, or d i r e c t l y to the counters, respectively.  /248  INPUT VOLTAGE  FIGURE IV.14:  (mV)  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 r c u i t (R.C.A. CD4069, CD4011) to the counters.  The interface c i r c u i t isolates the counters from the sensors  and the integrators,and controls count i n h i b i t i o n during p r i n t i n g . The interface c i r c u i t also conditions the input pulses. out low level noise and blocks any negative pulses. regulates a l l  pulses to no greater than 5 V.  It  filters  A zenner diode  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. (Motorola MC14534CP, 1975).  chips  There is one counter per sensor.  The  counters w i l 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 l o g i c consume about 10 mA.  The output from the counters is a  binary coded decimal (B.C.D.) s i g n a l , with multiplexing of the d i g i t s , and an accompanying signal indicating which d i g i t is being released.  The Printer and Counter/Printer  Interface  The printer is a mechanical, d i g i t a l tape p r i n t e r ) .  It  initially  printer  (MFE C o r p . , RPGE  had a current consumption of about 0.8 A  when i d l i n g and a momentary 2 A during p r i n t i n g .  Replacing many of  the printer I . C . s with their low power equivalents, reduced the 1  i d l i n g current to 560 mA.  The printer can be switched o f f 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 d i g i t s of a number to be presented  at i t s input terminals at the same time.  Thus, the  counter/printer  interface c i r c u i t must demultiplex the counter s i g n a l .  This is done  by dropping each d i g i t from a counter into a separate latch (R.C.A. CD4042).  A l l nine counters feed into the same f i v e latches.  The  latches are triggered by the d i g i t select signals from the counter being scanned. printed.  When a l l  f i v e latches are s e t , then the number can be  The interface c i r c u i t requires a +5 V supply and draws less  than 5 mA.  The Scan Control Logic Scanning n's i n i t i a t e d  by an externally supplied s i g n a l , a  momentary short to ground, which triggers the internal IV.15).  timer  (Figure  This timer is a synchronous clock generator (National  74C76) which produces 300 ms, 5 V pulses at 1 s i n t e r v a l s .  NE556 and  The clock  also enables the printer and triggers the counter i n h i b i t c u r c u i t r y .  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 full  description of the operation of the scan control logic is presented in the section on the operation of the data logger.  7251  PRINT COMMAND  SCAN CONTROL  4  LOGIC  COUNTER INHIBIT  COUNTER  SCAN CONTROL  SCANNER CLOCK  COUNTER _TT_SCANNER  SCANNER CLOCK CONTROL  500 Hi CLOCK  RESET  SYNCHRONOUS SCANNER CLOCK  SCAN INITIATE  COUNTER ENABLE PULSES  ENABLIN6 CONTROL  PRINTER ENABLE  3  1s CLOCK  RESET COUNTER  SYNCHRONOUS SCAN CLOCK GENERATOR  RESET  PAPER ADVANCE  FIGURE IV.15:  Scan control logic  schematic.  POWER SUPPLY 20 V P P AC  • K)V D.C.  • 5V 0 . C BATTERY 12V DC  - o  • 5 V D.C. • PRINTER  12  TORROIDAL OSCILLATOR  BRIDGE RECTIFIER  \ .  (  o  v  c  5V REGULATORS  V DC  FIGURE IV.16:  o  Power supply  schematic.  7252  The Power Supply Twelve v o l t b a t t e r i e s i n 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 p r i n t e r , while the r e s t 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 r e s t o f the l o g i c requires only +5 V. The DC-DC converter i s shown i n Figure IV.16.  A ferrite  t o r r o i d 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  e f f i c i e n c y of about 75%, and the ±5 V supplies are s t a b l e t o b e t t e r than 0.1%v  2.  Logic Operation The data logger has two operational phases, the count phase and  the p r i n t phase.  During the count phase,pulses  from the integrators  or pulse-output sensors are c o n t i n u a l l y fed into the counters. p r i n t phase i s entered when the data logger  receives a scan  The  initiate  signal that t r i g g e r s the one-second synchronous scan clock generator. The timing diagram f o r the operation of the scan control l o g i c i s presented i n Figure IV.17. The synchronous scan clock acts as an i n t e r n a l timer c o n t r o l l i n g the p r i n t i n g o f the data stored i n the counters.  The scan clock  enables the p r i n t e r and the counter i n h i b i t c i r c u i t f o r the whole o f  SCAN  C O N T R O L LOGIC  "lTLPJinr  FIGURE IV.17:  TIMING  DIAGRAM  uumnr  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 r c u i t to enable the counter, and resets the scanner in the counter.  first  After a 10 ms delay  the 500 Hz scanner clock generator is triggered to produce a t r a i n 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 d i g i t  appears at the output terminals of the enabled counter, a d i g i 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 The release of a l l  f i v e d i g i t s takes about 50 ms.  s i g n a l , which triggers the p r i n t e r , edge of the 1-s timing pulse.  interface.  A print command  is generated on the  trailing  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 channels have been scanned.  nine  As the counter enable c i r c u i t r y i s .  triggered by the tenth timing pulse, the enable c i r c u i t triggers the reset c i r c u i t .  The reset pulse resets the counter enabling c i r c u 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 i n h i b i t l o g i c . phase.  The logger then enters the count  The print phase is 12.5 s long.  /255  COUNTER SCANNER RESET  TIMING  DIAGRAM  U~1  COUNTER ENABLE SCANNING CLOCK  1  I  T  L  1  I  TENS  L  I  L  TEN THOUSANDS L  J THOUSANDS L DIGIT SELECT  J HUNDREDS ]_ J  J  B. C. D. OUTPUT!  r—L  FIGURE IV.18:  Counter timing diagram.  UNITS  L  /256  A l l of the counters are inhibited for the whole of the phase.  However,this  print  is a negligible loss of data for scan cycles  occurring with periods greater than 10 min.  If  integrator  calibration  i s done using the same scan frequencies as are used to c o l l e c t data, then corrections need not be made for the time l o s t during the phase.  The procedure of i n h i b i t i n g a l l  print  the counters for a set period  of time s i m p l i f i e s 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 b u i l t during the Spring of 1978.  The total cost of components  in Canadian dollars was about $1050.  Of t h i s , the printer accounted  for $450, the integrators $,400, the counters and accompanying interface c i r c u i t r y $150, the scan control logic $70, the power supply c i r c u i t $30 and the cabinet and miscellaneous supplies $50.  The logger weighs  10 kg and i t s size is 0.44 x 0.38 x 0.21 m.  1.  Field Testing The logger was f i e l d tested from May 22 to October 1, 1978.  was used to c o l l e c t micrometeorological data in a Douglas-fir near Courtenay on the east coast of Vancouver Island. located in a well ventilated  forest  The logger was  shack in the f o r e s t , and the logger  cabinet was not moisture proof.  It  Printing was i n i t i a t e d 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 p a r a l l e l .  voltage-output sensors monitored by the logger were a net  Analogue radiometer,  a solarimeter, s o i l heat flux plates and s i l i c o n diode temperature sensors.  The pulse-output sensors monitored were anemometers.  The  control c i r c u 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 v o 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 s i g n i f i c a n t portion  of the output of a sensor, e . g . a s o i l heat flux plate, was close to the lower l i m i t of integrator  sensitivity, i.e.  the 100 counts/(mV h) rate (see Figure IV.14).  between 0 and 1 mV for 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 r e s i s t o r s were used  to provide a 5 mV offset signal that had a s t a b i l i t y of ±20 uV over two months.  The power supply for the s i l i c o n diode temperature sensors  (Tang e t a i . , 1974) was used to provide a 610 mV o f f s e t to the diode signal.  This was done so as to improve resolution for  temperature measurement.  differential  For example, a 100 counts/(mV h)  integrator  s e n s i t i v i t y 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 c a l i b r a t i o n checks on the integrators in the field. 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 i n s t a l l a dividing c i r c u i t ahead of the counters. Calibration and s t a b i l i t y checks on the counters were performed in the laboratory using a pulse generator and in the f i e l d 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 r c u i t r y a r e l a t i v e l y quick and easy task.  During  the f i e l d test the logger was exposed to ambient a i r temperature of 5 to 35°C and ambient r e l a t i v e humidity of 10 to 100%.  Only lh days  of data were l o s t 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 l d  season and occasional checks were performed in the f i e l d .  These data  show a s t a b i l i t y of the data logger to within ± 0 . 5 % over the 4% month field trial.  Analysis of the data collected by the logger also shows  no indication of i n s t a b i l i t y ... The logger was easy to operate and could be l e f t to run unattended between power supply changes.  7259  The i n 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 e a r l i e r .  The power supply was changed every f i v e  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 i n s t a l l a t i o n of a better p r i n t e r .  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 a i r 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 initiate, the data.  scan-  signal is not required, and time of day can be printed with This should increase the logger cost to about CAN$900  without s i g n i f i c a n t l y increasing power consumption.  4 . SUMMARY  An inexpensive, low-power 12 V D.C. voltage integrating and pulse counting data logger has been b u i l t , that is suitable for c o l l e c t i n g micrometeorological data in remote areas. and operation of the logger is r e l a t i v e l y easy.  Construction  Sensors with analogue  voltage ouptuts of up to 3 V as well as pulse-output devices can be  /260  readily monitored.  The logger uses p r e c i s i o n , dual rampings voltage  integrators and 5-decade counting I . C . s in i t s measurement c i r c u i t r y . 1  The data is output on a mechanical, d i g i t a l  printer upon  initiation  by an externally supplied pulse. The logger worked well during a 4% month summer f i e l d t r i a l at a forest micrometeorological research s i t e . logger had an overall  During this period the data  s t a b i l i t y to better than ± 0.5% for an ambient  a i r temperature range of 5 to 35°C and r e l a t i v e humidity of 10 to 100%.  Current consumption was about 0.8 A during i d l i n g with a  momentary 2 A during p r i n t i n g . improvements  The logger cost CAN$1050.  Proposed  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 B r i t i s h Columbia Ministry of Forests.  We wish to thank the Courtenay  d i v i s i o n of Crown Zellerbach L t d . , for providing the research s i t e and the Faculty of Agricultural Sciences, University of B r i t i s h Columbia, for the use of their Oyster River Farm as a base camp.  /261  6.  REFERENCES  Brach, E . J . , P.W. Voisey and P. P o i r i e r , 1974. Electronic integrator to measure environmental c h a r a c t e r i s t i c s . A g r i c . Meteorol. 13: 169-179. Byrne, G . F . , 1970. Data-logging and scanning rate considerations in micrometeorological experiments. A g r i c . Meteorol. 7: 415-418. Campbell, G . S . , 1974b. A micropower electronic integrator for micrometeorological applications. A g r i c . Meteorol. 13: 399-404. Fritschen, L . J . , 1977. A m i l l i v o l t - t o - v o l t and p u l s e - t o - v o l t integrator for meteorological purposes. A g r i c . Meteorol. 18: 321-325. Harrington, J . B . , 1978.  A remote weather station for use in forest  f i r e management. In:- Fourth Symposium on Meteorological Observations and*Instrumentation. Am. Meteorological S O C ,  April 10-14, 1978, Denver, C o l . , pp. 33-34. Motorola, 1975. The Semiconductor Data Library. Ser. A . , V o l . V, McMOS Integrated C i r c u i t s . Tech. Info. Centre, Motorola I n c . , pp. 7.253-7.258. Ross, P . J . , 1978. Two d i g i t a 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 , operation.  1972. Automatic weather stations for network Weather 27: 403-408.  Tang, P.W., 1976. Electronic Data Aguisition System for'the Energy Balance/Bowen Ratio-Measurement of-Evaporation. M.Sc. T h e s i s ,  Univ. B r i t i s h Columbia, Vancouver, B . C . , 96 pp. Tang, P.W., K.G. McNaughton and T.A. Black, 1974. Inexpensive diode thermometry using integrated c i r c u 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. A g r i c . 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 b r i e f description  of the f i l e and the format of the data. ST0RE1, DENSITY -  The tape ID = ANDY, VOL =•  1600 BPI, RACK NO. = RA0925, has the following  fixed block f i l e s with format FB(4000,200) or  F i l e Name  FB(4000,80):  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  1.  CALCULATIONS AND DATA USED IN CHAPTER 2  DETERMINATION OF THE FORMULA FOR THE EFFECTIVE  EMISSIVITY  OF THE SKY (Za)  Equations Tested (1)  Idso and Jackson (Aase and Idso, 1979). e  (2)  a  = 1 - (0.261 x expI-7.77E-4 x (273 -  Modified Idso and Jackson (I a.  e, = e-(I a  e b.  (3)  & J) x 0.92  for a l l R  2  n  a  = 0.937E-06 x T  2  1961)  = 0.53 + (0.206 x e ° - ) 5  a  a  = 1.72(e /T)  Idso (1980) e  (7)  ejl  2  Brutsaert (1975) e  (6)  =  & J)  R > 8.0 MJ rn" d " n R < 8.0 MJ m" d "  Brunt (Monteith, e  (5)  a  a  = 0.70 + (5.95E-0.4 x e. x exp[1500/TJ)  Satterlund (1979) c  a  2  & J)  Swinbank (1963) e  (4)  e  a  a = e (I  & J) x 0.92  T) ])  = 1.08(1 - e x p [ - ( e  x 10)  ( T / 2 0 1 6 )  J)  1  1  /264  Discussion: temperature  In the above equations T and i~  are the mean daily  in Kelvin and vapour pressure in k i l o - P a s c a l s , r e s p e c t i v e l y ,  at the top of the canopy. net radiation (R )  Data was available for 1975 and 1978.  The  was calculated from (Chapter 2)  n  R  n  L*  = (1  -  0.12)K+ + L*  = (0.1  +  £0.9  K+/K+  m a Y  J )(£„  III a A  -  0.96)aT  4  a  Table V.l compares measured and calculated clear sky R  n  '(K4-/.K+  ^ > 0.95).  Table V.2 l i s t s the least-squares l i n e a r regressions of calculated on measured R . for a l l n  the R 'data. n  Figures V . l and V.2 i l l u s t r a t e  the  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 R  n  using unmodified formulae.  This may be because the c o e f f i c i e n t s were obtained in a maritime environment and at a similar latitude  (Monteith,  1961).  temperature based formulae can be used in the model.  However, only  Thus, the modified  Idso and Jackson formula, modification a , has been used. If  an average daily temperature i s not available i t  calculated from ( T  m g x  a hygrothermograph.  + T • )/2, where T  and T  m a x  m i n  is  are obtained from  A least-squares l i n e a r 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  FIGURE V . l :  R  (MJ m" d- ) 2  p  1  Calculated versus measured net radiation, 1975 and 1978, with e from the unmodified Idso and Jackson formula. a  7266  \  FIGURE V . 2 :  As f o r F i g u r e V . l but w i t h e from m o d i f i c a t i o n " a " t o the Idso and Jackson f o r m u l a . a  7267  Using calculated temperatures did not s i g n i f i c a n t l y a l t e r the values of simulated R  TABLE V . l :  from those using the true mean a i r  temperature.  Mean, standard deviation of mean (s ) and standard deviation between the calculated and measured ( s y . ) clear sky net radiation for 1975 and 1978, n = 41." y  x  Equation  Mean  — (MJ m~  Idso and Jackson unmodified modified a,b  19.20 17.00  2.36 2.29  2.92 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  d  d ) - 1  —  /268  TABLE V.2: Least-squares l i n e a r regression o f c a l c u l a t e d on measured net Radiation f o r a l l net r a d i a t i o n data f o r 1975 and 1978. C o r r e l a t i o n c o e f f i c i e n t ( r ) and the standard d e v i a t i o n o f the estimate ( s . ) given, n = 169. 2  y  x  Intercept (MJ rn" d" )  Equation  2  1  Slope  r  2  (MJ m ^ V l )  Idso and Jackson unmodified modified a modified b  -0.37 0.26 -0.83  1.158 0.990 1.058  0.808 0.824 0.794  1.00 0.87 0.90  Swinbank  -0.41  1.154  0.807  0.98  Brunt  0.10  1.023  0.820  0.68  Brutsaert  0.40  1.065  0.827  0.70  Idso  0.94  1.107  0.838  0.74  Satterlund  0.49  1.141  0.828  0.82  2.  (i)  NORMALIZING THE E VERSUS 0 RELATIONSHIP e  The family o f curves i n Figure 2.2 i s given by  E = aE „ eq E  =  0 > 0 e - ec  (la) v  K e<- - ec Q  D0 Q  e  ;  ( l b )' v  ar  where a and b are constants.  The c r i t i c a l value of 0 f o r a given e E„„ occurs when b0„ = a E _ so that eq e eq 3  /269  =  ec  6  ~e  (a/b)E eq  =  (2)  v  1  or 9  and all values of 0  g  ec  / E  eq  =  a  /  (3)  b  can be replaced by a single number equal to a / b .  c  Dividing all of (la) and (lb) by E  and substituting (3) into the  result and rearranging gives  E / E  eq  E/0  e  =  a  9  = b  e  / E  e q >-  9 /E e  e q  a  /  b  ( 4 a )  < 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  E divided by E  m g x  or its equivalent.  g  relationship with only  This is valid for non-limiting  soil water conditions; however when E is limited by Q  &  E may be incorrect.  the calculated  The two forms of this relationship that are  commonly used are illustrated in Figure V.4 and are given by  E/E  max  =1  E/E = JW max m a v  6 0  e e  > 9  ec  < 0 „ ec  v  (Sa) - '  x  (5b) '  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 d a i l y evapotranspiration rate ( E / E ) versus normalized fraction of extractable water in the root zone ( 6 / E ) for the data in Figure 2.2. C r i t i c a l value (a/b) indicated. e q  e  e q  /271  FIGURE V.4:  Two examples of the r e l a t i v e evapotranspiration rate ( E / E ) versus the fraction of extractable water in the root zone ( 6 ) . C r i t i c a l value of 6 ( 0 ) indicated. m a x  e  e  e c  /272  root zone and z, i s root zone depth (mm).  Only equation (5b) may be  incorrect. When drainage is negligible E = -(dW/dt). E in (5b),  rearranging and integrating  ^(l/W)dW  =  Substituting for  from t-j to t  E  - M j  m a y  gives  2  dt  (6)  Assuming that J is a constant the solution to (6) is t 2' 1 H  *2 Since \ E = W^ - W  2>  =  e  x  P ^  J  /  \  E  L a x ) m t 1  (*>  eliminating W^ from (!7) gives  *1 t  t  2  IE  = II  - exp(- lE J  1  l  When 6  = 9  e  critical  ec<>  2  r  m a x  )JW  (8)  1  l  ( 5 a ) equals (Sb), therefore J = 1/W , C  water storage, W at 9  .  However, part (i)  shows that 9 „ is not constant, rather i t ec  where W is the c  of this section  is a function of E , and 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 R i t c h i e , 1974), probably because J is r e l a t i v e l y of 9  ec  conservative.  Using a constant value  obtained under high E conditions could result in an underestimation max  of E as the s o i l d r i e s .  m 3 v  /273  3.  FIELD SOIL WATER RETENTION CHARACTERISTICS FOR THE COURTENAY UNTHINNED AND THINNED SITES IN 1974 AND 1975, RESPECTIVELY  Date are from the Appendices i n Nnyamah (1977).  S o i l water content  i s the average of f i v e (1974) or s i x (1975) neutron probe moisture measurements.  Matric p o t e n t i a l i s from tensiometers and hygrometers.  Data are f i t t e d f o l l o w i n g Campbell (1974a)to ty = ^ ( 0 / 0 ) ~ mr  9  r  with  m  r  3 -3 = 0.30 m m . There are s i x data points f o r each depth.  The average  curves (Figures V.5 and V.6) are the mean of the m and ty values i n mr Table V.3. r  TABLE V.3:  C o e f f i c i e n t s f o r the f i e l d retention r e l a t i o n s h i p , ^m * m r ( / J " with 0 = 0.30 m m-3 f o r the unthinned (1974) and thinned (1975) s i t e s , Courtenay, B.C. C o r r e l a t i o n c o e f f i c i e n t ( r ) i s shown. =  9  e  m  3  r  2  Depth (m)  m  1974  0.15 0.30 0.45  3.8 4.5 5.8  - 7.2 - 4.8 - 1.8  0.949 0.952 0.963  1975  0.15 0.30 0.45 0.60 0.70  ,5.4 5.7 .7.3 7.9 6.9  -10.6 - 4.8 - 1.5 - 1.1 - 2.0  0.928 0.958 0.965 0.959 0.975  1974  (0.3,0.45)  5.2  - 2.8  1975  (0.3-0.7)  7.0  - 1.5  ,^mr. (kPa)  r  Average Curve  -  2  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 l a t t e r 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, r e s p e c t i v e l y , for an average tree volume 3 of 0.0757 m .  1 At 822 trees ha  3 " -1 there is approximately 62 m of wood ha .  Sapwood density for Douglas-fir is about 450 kg m Running, 1978)  .(Waring and  and the density of c e l l u l o s e and l i g n i n is 1530 kg m  (Running 1980c) so that porosity is approximately 0.7. the pores are i n i t i a l l y  Assuming that  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 i m i t of the loss over the summer is 3 3.5 mm or < 0.5 m of water per tree. than two days transpiration  This is the equivalent of less  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., S e a t t l e , (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 evapotranspiration. Atmosphere-Ocean 18: 98-116. Spittlehouse, D. L. and T. A. Black, 1979. Determination of forest evapotranspiration using Bowen r a t i o and eddy correlation measurements. J . Appl. Meteorol. 18: 647-653. Sondheim, M. W. and D. L. Spittlehouse, 1979. Comments on, 'Hydrologic behavior of a forested mountain s o i l in coastal B r i t i s h 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. F i r e studies in the upper MacKenzie Valley and adjacent Precambrian Uplands. Dept. Indian and Northern A f f a i r s , Ottawa, INA Publ. No. QS-8045-000-EE-A1, A r c t i c Land Use Research Programme 74-75-61. Spittlehouse, D. L. and E. A. Ripley, 1974. Micrometeorology:X. Relationships between plant microclimate and structure. Rep. 55, C . C . I . B . P . Matador Project, U. Saskatchewan, Saskatoon, S a s k . , Canada, 99 pp.  Tech.  

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