1. Remote Sensing ET Algorithm— Remote Evapotranspiration Calculation (RET)
Junming Wang,

2. Build the Model ASTER Satellite from NASA
15 by 15 m visible and near-infrared radiance. Bands 1-3
30 by 30 m shortwave infrared radiance. Bands 4-9
90 by 90 m infrared radiance. Bands 10-14
Reflectance(Bands1-9) and temperature data can be requested as secondary processed data
Availability: potentially 16 days upon request

3. Reflectance (resolution 15 by 15 m)
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Band 3

4. Temperature (resolution 90 by 90 m)
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5. Build the model Theory ETins = Rn - G - H R H ETins G n
Graph from Allen, et. al., (2002)

6. General flowchart Build the Model Start
Satellite inputs: surface temperature and reflectance.
Local weather inputs: solar radiation, humidity and wind speed
Rn=f(Rs, reflectance)
General flowchart
NDVI=f(reflectance)
G=f(NDVI, solar radiation, reflectance)
H=f(NDVI, temperature, reflectance, solar radiation, wind speed)
ETins=Rn-H-G
Output daily ET
End

7. Rn Rn=Rns-Rnl = net radiation
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Rn=Rns-Rnl = net radiation
Rns=(1-)Rs = net solar radiation  is surface albedo,
=0.484      
i is the reflectance for ASTER data band I, averaged to 90m2 resolution.
Rnl=f(RH,Ts) =net long wave radiation

8. Empirical function G=Rn
Empirical function G=Rn*C NDVI from ASTER reflectance data of bands 3 and 2,
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9. Sensible Heat Flux (H) H rah dT H = (r × cp × dT) / rah
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H = (r × cp × dT) / rah
dT = the near surface temperature difference (K).
rah = the aerodynamic resistance to heat transport (s/m). H
rah z2
rah=ln(z2/z1)/(u*×k)
u*= friction velocity dT
Cp specific heat of air 75.4 J mol-1 C-1 z1
Graph from Allen, et. al., (2002)

10. Selection of “Anchor Pixels” for dT calculation
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Selection of “Anchor Pixels” for dT calculation
“wet” pixel: Ts  Tair
“dry” pixel: ET  0
Ts=303 K
Ts=323 K

11. Should be an alfalfa field, not cut and not stressed for water
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At the “wet” pixel:
dTwet = Ts-Tair=0
Should be an alfalfa field, not cut and not stressed for water
At the “dry” pixel: Hdry = Rn – G - ETdry
where ETdry = 0
dTdry = Hdry× rah / ( × cp)
Should be a bare soil field where evaporation is zero.

12. dT regression
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13. Sensible Heat Flux (H)
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dT for each pixel is computed using the regression.
H is calculated for each pixel after calculating rah for each pixel
H = (  × cp × dT) / rah

14. Calculate stability parameter for each pixel
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Start
Calculate friction velocity (u*) at weather station and use to get wind speed at 200m
Calculate H for each pixel
Calculate stability parameter for each pixel
Calculate roughness length( zom) for each pixel from NDVI
Update H for each pixel based on stability parameter and iterate till change in H less than 10%
Calculate friction velocity ( u*) for each pixel
Calculate rah for each pixel
Calculate Et from energy balance
Calculate dT for each pixel from Ts
End

15. Et Calculation Obtain instant latent heat for each pixel
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Obtain instant latent heat for each pixel
ETins = Rn - G - H
Obtain instant reference latent heat for irrigated alfalfa field (ETrins)
Obtain Daily reference ET calculated by FAO Penman-Monteith from weather station for alfalfa field (ETrdaily)
Calculated ET daily for each pixel
ETdaily=ETins/ ETrins×ETrdaily

16. Validate the model Measurement sites
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Validate the model Measurement sites
Pecan orchard
Alfalfa field

17. Validate the Model
ET measurement
Li Cor
system

18. ET map
Validate the Model
mm/day

19. The pecan ET of simulation vs. observation.
Validate the Model
The pecan ET of simulation vs. observation.

20. Sensitivity analysis ET=Rn-G-H Sensitivity Analysis areas
Full vegetation area (6 points, NDVI=0.57)
Half vegetation area (6 points, NDVI=0.31)
Little vegetation area (6 points, NDVI=0.19)

21. Sensitivity analysis
Sensitivity Analysis
Variables related to Rn
Rs ( w/m2),  ( ),
Variables related to G
C (G/Rn, ),
Variables related to H
rah (0-100 s/m )
Variables were changed over a typical rang for the selected six pixels

22. dT regression
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23. ET vs. dT dT is linearly related to Ts, H=f(dT, rah, u*, L, Zom)
Sensitivity analysis
dT is linearly related to Ts, H=f(dT, rah, u*, L, Zom)
The u* at the full vegetation is bigger than at he half and little vegetation areas, so the ET at the full vegetation area decrease faster than at the other areas.

24. ET vs. dT ET is sensitive to dT which is calculated from Ts.
Sensitivity analysis
ET vs. dT
ET is sensitive to dT which is calculated from Ts.
An error in your hot or cold spot dT calculation results in error in H and ET for intermediate points.
Ts from satellite is not sensitive as an absolute number only as a relative number which may represent a 2% error in dT and ET
If the algorithms in the model are to be changed, the dT calculation equation will be the key equation. It may not be linear

25. ET vs. Rs Rns=(1-)Rs, Rn=Rns-Rnl
Sensitivity analysis

26. ET vs. Rs ET is sensitive to Rs which determines Rn.
Sensitivity analysis
ET vs. Rs
ET is sensitive to Rs which determines Rn.
Rs is from local weather stations and errors in this value can be as high as 5 to 10 % depending on the quality control for the climate network.
An error of 10 % in Rs results in an ET error of 0.2 mm/day or a 3% error in ET

27. ET vs. Albedo Rns=(1-)Rs, Rn=Rns-Rnl

28. ET vs. Albedo ET is sensitive to albedo because it affects Rn value.
Sensitivity analysis
ET vs. Albedo
ET is sensitive to albedo because it affects Rn value.
The albedo function is an empirical function that may not be applicable over conditions different from the experimental sites where the function was derived.
The function is critical when vegetation cover exits and ET is occurring. For bare soil the function is not critical because this condition represents the dry point.

29. ET vs. C (G/Rn) C is a polynomial function of NDVI
Sensitivity analysis

30. Sensitivity analysis
ET vs. C (G/Rn)
ET is highly sensitive to C when there is full or half vegetation covered.
But ET is not sensitive to C when there is little vegetation covered.
If algorithm improvement is needed, the equation for C calculation is a key function.

31. ET vs. rah rah=f(u*, z2, z1), H=f(dT, rah, u*, L, Zom)
Sensitivity analysis
Z2: above canopy reference height, z1: close to canopy height

32. When rah<40s/m, ET is sensitive to it.
Sensitivity analysis
ET vs. rah
When rah<40s/m, ET is sensitive to it.
The rah calculation equation is a key equation for the algorithm and is a function of u* (friction velocity) which is a function of wind speed, roughness length and atmospheric stability which is also related to dT.

33. Conclusion Most sensitive variables and equations
Input variables
Rs, u from weather station
Ts from satellite is not sensitive as an absolute number only as a relative number
Intermediate variables (and their calculation equations)
dT, albedo, C(G/Rn), and rah

34. Thank You!