Lei Zhao. F&ES Yale University

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Katherine Anderson
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1 Lei Zhao F&ES Yale University

2 Outline Basic Idea Algorithm Results: modeling vs. observation Discussion

3 Basic Idea Surface Energy Balance Equation Diagnostic form: Heat capacity of ground zero ; ground heat flux zero; the terms in SEB are either computed separately or parameterized in terms of Ts, so that the equation is solved iteratively Non-rate equation for Ts

4 Basic Idea Through parameterization, SEB contains Ts as an only unknown variable Known variables: incoming Solar radiation, albedo, incoming longwave radiation, wind speed

5 Algorithm Net radiation defined as: All the terms in the SEB are either specified from the dataset or parameterized in terms of Ts: S d (1 a) L d T 4 s (1 ) L d c p ( T s T a ) / r a ( q * q) /( r s r a )

6 Algorithm Given specified L d, a, S d, the resistance needs to be parameterized in terms of Ts so as to close the whole system Theoretically, one can solve the SEB for surface temperature Ts, since Ts is the only unknown variable in the system Nonlinear system, thus Newton s method applied

7 Algorithm Monin-Obukhov Parameterization The resistance parameterization scheme should involve the surface temperature Ts as the only unknown variable Big-leaf model: Aerodynamic resistance Stoma resistance At this stage, only incorporate the subroutine of aerodynamic resistance by leaving the stoma resistance as a constant

8 Algorithm Monin-Obukhov Parameterization Based on Monin-Obukhov similarity theory, different models proposed According to Liu et al(2006), Choudhury (1986), Thom(1975), Xie Xianqun(1988) model showed better agreement Thom and Xie model applied in this study

9 Algorithm Monin-Obukhov Parameterization Thom model In neutral condition, In unstable condition, In stable condition, where, ) ( ) ln( ) ( ) ln( * L d z z d z L d z z d z U k r h T m z a 0 h m 2 / ) 2arctan( ) 2 1 ln( ) 2 1 2ln( 2 x x x m 5 h m L d z 4 1/ ) 16 (1 x

10 Algorithm Thom model How to evaluate L : L is a funtion of u* and Ts u* can be calculated from C D Therefore, all the quantities are looped tegother:

11 Algorithm Thom model Loop: C D C D, C H u* ψ(ξ) L ξ

12 Algorithm Thom model Convergence problem: A good initial guess is required for convergence How to get a close guess for C D C DN (neutral condition) is introduced to trigger the loop C DN is only dependent on z-d and z 0

13 Algorithm Thom model Convergence problem: still encounter unconvergence Examine the shape of drag coefficient

14 Algorithm Thom model Figure 1 Relation of Drag coefficient C D vs. Stability correction function ψ

15 Algorithm Thom model Therefore, some thresholds for are needed As widely used in the literatures, is cut in the interval between -5 and 1

16 Algorithm Monin-Obukhov Parameterization Xie model r a r aa 1 z ln( d ) r aa is the aerodynamic resistance in neutral condition, h z 0 z d ln( ) z 0 raa 2 k U z ln( z z T d ) In neutral condition, =0 In unstable condition, In stable condition, h h (1 where, n is empirical coefficient, when,n=5.2; when, n= ) 1/ h 1 n

17 Algorithm Model structure Newton s method is the main iteration for solving Ts In each iteration, new computed Ts goes to the resistance loop for resistance calculation The resistance return to the main iteration for calculating a newer Ts

18 Input data Driven by: the measurements of incoming solar radiation, surface albedo, incoming longwave radiation, and wind velocity at a certain height Data used: Old aspen site 2000 Jan.

19 Results Comparison between the modeling results and the observations: Surface Temperature Ts Sensible Heat Flux H Latent Heat Flux λe

20 Results - Surface temperature Thom model

21 Results - Surface temperature Thom model

22 Results - Surface temperature Xie model

23 Results - Surface temperature Xie model

24 Results sensible heat flux Thom model

25 Results sensible heat flux Xie model

26 Results latent heat flux Thom model

27 Results latent heat flux Xie model

28 Discussion Why the heat flux modeling results are bad: r s is set as a constant Soil heat flux G is not taken into account Real temperature vs. Potential temperature Reliability of the turbulent flux measurement Need your ideas

29 Discussion Tuning value of r s by examining the error of Ts

30 Discussion Diagnostic form heat capacity of the canopy is assumed as zero Not take into account the canopy heat flux G

31 Discussion Temperature using real temperature, rather than potential temperature, since only have the pressure measurement at one level

32 Discussion Reliability of the turbulent flux measurement

33 Discussion NARR prediction

34 Discussion NARR prediction

35 Discussion NARR prediction

36 Discussion NARR prediction

37 Discussion NARR prediction

39 Lei Zhao F&ES Yale University

40 Results - Surface temperature

41 Results - Surface temperature

42 Results sensible heat flux Thom model

43 Results sensible heat flux Thom model

44 Results latent heat flux Thom model

45 Results latent heat flux Thom model

46 Observation Check with NARR

47 Observation Check with NARR

48 Observation Check with NARR

49 Lei Zhao F&ES Yale University

50 Canopy Resistance

51 Canopy Resistance Canopy resistance shows a strong response to PAR, LAI, saturation deficit, air temperature and soil water content. The paper discussed the diurnal dynamic response to PAR and saturation deficit Also seasonal dynamics of canopy resistance, mainly dependent on forest LAI

52 Canopy Resistance

53 Canopy Resistance Simple method in the subroutine: Parameterize it as a function of PAR and saturation deficit Different PAR corresponds to different g_max Exponentially decay on increasing saturation deficit

54 Canopy Resistance

55 Canopy Resistance

56 Canopy Resistance

57 Canopy Resistance

Contents. 1. Evaporation

Contents. 1. Evaporation Contents 1 Evaporation 1 1a Evaporation from Wet Surfaces................... 1 1b Evaporation from Wet Surfaces in the absence of Advection... 4 1c Bowen Ratio Method........................ 4 1d Potential