Evapotranspiration: Theory and Applications

Transcription

1 Evapotranspiration: Theory and Applications Lu Zhang ( 张橹 ) CSIRO Land and Water

2 Evaporation: part of our everyday life

3 Evapotranspiration Global Land: P = 800 mm Q = 315 mm E = 485 mm Evapotranspiration = transpiration + soil Evaporation + Canopy Interception E = E t + E s + E i 100% = 65% + 25% + 10%

4 Evaporation Mechanisms Evaporation requires: Energy supply to provide water molecules the necessary kinetic energy to escape from the liquid surface Aerodynamic turbulence to transfer the water vapour from the vicinity of the liquid surface to the atmosphere However, Energy supply and aerodynamic mass transfer can not be considered in isolation from each other.

5 Turbulent transport of water vapour Turbulent transport: Fvz r w q where F Vz is the vertical flux of water vapor, r is the density of the air, w' is the fluctuation of vertical wind velocity; and q' is the fluctuations of the specific humidity.

6 Turbulent transport of water vapour Turbulent transport: wind profile u ( )( / ) * z d0 du dz k In general, this logarithmic profile can be written as u u ln z d * u1 k z1 d0 u u ln z d * 0 k z0

7 Turbulent transport of water vapour Turbulent transport: specific humidity E / r u ( z d )( dq / dz) * 0 k Integration yields a logarithmic profile as follows, q E ln z d 2 0 1q2 ku* r z1 d0 when one of the specific humidity values is taken at the surface, z = 0, is q s E ln z d 0 q ku* r z0v

8 Monin-Obukhov Similarity Theory (MOST) Monin and Obukhov (1954) z d 0 L where L is known as the Obukhov stability length, defined by u L k ( g / T )( w 0.61 T w q 3 * ) a 0 a 0 The dimensionless gradients of the mean wind, of the temperature and of the humidity, can be written as: k( z d0) du u dz * 0 ( ) m ku* ( z d0) d h ( ) w dz ku* ( z d0) dq wq dz 0 ( ) v

9 Monin-Obukhov Similarity Theory (MOST) The above forms can be expressed as, u u u [ln( / ) ( ) ( )] k * m 2 m 1 w [ln( / ) ( ) ( )] q h 2 h 1 ku* wq q [ln( / ) ( ) ( )] v 2 v 1 ku* in which each of the -functions, with its respective subscript, is defined by ( ) [1 ( x)] dx/ x 0

10 Monin-Obukhov Similarity Theory (MOST) In the present case, u u ln z d z d z * m m k z0 L L H 0 0 0h s ln z d z d z h h ku* rcp z0h L L q E ln z q d z d z 0 0 ov s v v ku* r z0v L L

11 Evaporation: mass transfer formulations Turbulent transport: E rq ' w ' where r is the density of the air, w' is the fluctuation of vertical wind velocity; and q' is the fluctuations of the specific humidity. In a neutrally stratified atmosphere, evaporation can be calculated as: z w'dt q

12 Mass transfer formulations Bulk transfer method E Ce r u ( q q ) Mass transfer coefficient 1 s 2 Ce 2 k ln[( z d ) / z ]ln[( z d ) / z ] 2 0 0v Given q = e/p Therefore, E f ( u )( e e ) e 1 s 2

13 Surface radiation budget Surface radiation budget: R R (1 ) R R n s s s ld lu where R s is the (global) short-wave radiation, α s is the albedo of the surface, R ld is the downward long-wave or atmospheric radiation, ε s is the emissivity of the surface and R lu is the upward long-wave radiation.

14 Surface radiation budget Short-wave radiation Q s = Q se [a + b (n/n)] where a and b are constants which depend on the location, the season and the state of the atmosphere; their values have been determined for many locations and on average they appear to be around a = 0.25 and b = The extraterrestrial radiation Q se can readily be calculated for a given latitude, time of day and day of the year from the solar constant (R so ): Q (2 R / )(cos sin h cosd h sin sin d) se so s s

15 Surface radiation budget Long-wave or terrestrial radiation R R T 4 lu s s in terms of the (absolute) surface temperature T s ; σ (= W m 2 K 4 = cal cm 2 s 1 K 4 ) is the Stefan Boltzmann constant. The downward long-wave radiation R ld can be calculated accurately on the basis of vertical profile data of humidity and temperature. T 4 ldc ac a where T a is the air temperature near the ground, usually taken at shelter level, and ε ac is the atmospheric emissivity under clear skies. The resulting atmospheric emissivity can be written as ac a( ea / Ta ) b

16 Mass Transfer formulations Bowen ratio method Bo = H/L e E Based on profile Bo c ( ) p 1 2 L ( q q ) e 1 2

17 Evaporation: energy balance formulations Surface energy balance: L e E + H = Q n Qn Rn G Lp Fp Ah W / t In many applications, the last three terms can be neglected: E + H e = Q ne E Qne 1+ Bo

18 Evaporation: combination formulations Bo Ts e A crucial step in Penman s derivation is the assumption of e T * a a Bo 1 ( es ea ) and s cp p L * * s a s ( e e ) e T a T e e a a E Qne 1+ Bo e e * a a Qne 1 E E es ea

19 Evaporation: combination formulations Penman equation: E Qne E A E f ( u )( e e ) * A e r a a

20 Evaporation: combination formulations Penman wind function (Penman 1948): f ( u ) 0.26 ( u ) e 2 2 A more fundamental approach to determine the wind function is based on turbulent similarity f u p u 1 e( 1) 0.622r Ce 1 Under neutral conditions, the wind function can be determined: f ( u ) e ku1 R T ln [( z d ) / z ] ln [( z d ) / z ] d a 2 0 0v 1 0 0

21 Concept of canopy resistance stomata

22 Penman-Monteith Equation ET ( R n G) r C p (1 r ( e c s / r e a ) a ) / r a

23 Evapotranspiration: measurements Bowen ratio system Eddy covariance system Heat pulse technique Lysimeters

24 Evaporation: concept of potential evaporation The term potential evaporation was introduced by Thornthwaite (1949) to classify climate. Potential evaporation is generally understood to represent the maximal rate of evaporation from a large area covered by vegetation with adequate soil moisture at all times. Why do we need potential evaporation? Actual evaporation = f() (potential evaporation)

25 Theory vs applications: scale issues: Brutsaert (2005)

26 Estimation of land surface evaporation using a generalized nonlinear complementary relationship Lu Zhang 1, Lei Cheng 1, Wilfried Brutsaert 2 1 CSIRO Land and Water, Canberra, Australia 2 School of Civil and Environmental Engineering, Cornell University, New York, USA

27 Global water balance & ET Baldocchi (2014) Raupach et al (2001) Jung et al (2010) Brutsaert (2005) Page 27

28 Generalized Complementary Principle Actual evaporation (E): Evaporation from spatially uniform, sufficiently large and homogeneous surface. No edge effects due to local advection. Potential evaporation (E po ): Evaporation from the same surface when water is not a limiting factor, but with the same solar radiative input and the same meso-alpha scale pressure gradient pattern. Apparent potential evaporation (E pa ): Evaporation from a small saturated surface insider the larger surface, defined in connection with E above, subject to the same non-potential atmospheric conditions. Brutsaert (2015)

29 Generalized Complementary Principle When the surface is wet and the available energy is the only limiting factor: E E po E pa When the surface is no longer wet: E E po E pa Following equation was obtained based on the complementary principle: E po E 2E E pa 2 pa E po Bouchet (1963): E 2E po E pa Brutsaert and Parlange (1998): E [( 1 b) / b] E (1/ b) po E pa Brutsaert (2015)

30 Generalized Complementary Principle E po E 2E E pa 2 pa E po Where the potential evaporation E po can be determined from the Priestley-Taylor equation (1972): Epo e Rn G The apparent potential evaporation E pa can be determined from Penman s equation (1948): E pa * R G f u )( e ) n e( 1 2 e2 Where the wind function f e (u 1 ) can be expressed as: f e ( u 1 ) R d T a ln z d / z ln z d k 0 ov 2 u / z 0 Brutsaert (2015)

31 Generalized Complementary Principle Following Penman (1948), the wind function can also be expressed as: f e ( u 1 ) 0.26(1 0.54u1 ) The apparent potential evaporation E pa can also be taken as Class A evaporation pan Brutsaert (2015)

32 Implementation of Brutsaert (2015) Method 1: E po E 2E E pa E po 2 e pa R n E G po e E pa = Class A evaporation pan Method 2: E E po pa e * R G f u )( e ) n R n G e( 1 2 e2 e z 0, d 0, z 0v f e ( u 1 ) R T d a ln z d / z ln z d k 0 ov 2 u / z 0 Brutsaert (2015)

33 Implementation of Brutsaert (2015) E po E 2E E pa 2 pa E po Method 3: E E po pa f e e * R G f u )( e ) n R n G ( u 1 ) 0.26(1 0.54u1 ) e( 1 2 e2 e Brutsaert (2015)

34 OzFlux stations Zhang et al. (2016)

35 Testing the CR principle and Brutsaert (2015): Results from OzFlux stations Method 1 Zhang et al. (2016)

36 Testing the CR principle and Brutsaert (2015): Results from OzFlux stations Method 2 Zhang et al. (2016)

37 Testing the CR principle and Brutsaert (2015): Results from OzFlux stations Method 3 Zhang et al. (2016)

38 Testing the CR principle and Brutsaert (2015): Results from OzFlux stations Scaled by Class A pan evaporation Zhang et al. (2016)

39 Testing the CR principle and Brutsaert (2015): Results from OzFlux stations Scaled by the Penman equation Zhang et al. (2016)

40 Testing the CR principle and Brutsaert (2015): Results from OzFlux stations Zhang et al. (2016)

41 Testing the CR principle and Brutsaert (2015): Results from OzFlux stations Zhang et al. (2016)

42 Testing the CR principle and Brutsaert (2015): Results from OzFlux stations Site Name RMSE r Bias Fogg Dam Method 1 Howard Springs Tumbarumba Wallaby Creek Method 2 Site Name RMSE r Bias z 0 d 0 z 0v Fogg Dam Howard Springs Tumbarumba Wallaby Creek Site Name RMSE r Bias Method 3 Fogg Dam Howard Springs Tumbarumba Wallaby Creek Zhang et al. (2016)

43 Estimation of global mean annual evaporation

44 Pan evaporation: decreasing Actual evaporation: increasing

45 Summary The generalized complementary relationship equation of Brutsaert (2015) was shown to be accurate in predicting daily land surface evaporation; The flux station data from Australia showed strong asymmetrical complementary relationship, which is well represented by Brutsaert s equation; Brutsaert s equation is a reliable tool to estimate land surface evaporation and its trends from routing meteorological data; The optimized model parameter values are fairly conservative and well within the range of reported values in the literature and this provides further supporting evidence for the method; The results from this study are promising as they indicate the potential of this method for estimating historical trends in landscape evaporation from long-term records of meteorological data.

46 Thank you The data used in this study were obtained from OZFlux and we would like to thank Jason Beringer, Lindasy Hutley, Steve Zegelin, Dale Hughes, and others involved in the experiments. We would like to thank Longhui Li for helping with data quality checks. LAND AND WATER