A Sensitivity Analysis on Remote Sensing ET Algorithm— Remote Evapotranspiration Calculation (RET)

1. A Sensitivity Analysis on Remote Sensing ET Algorithm—Remote Evapotranspiration Calculation (RET) Junming Wang, Ted. Sammis, Luke Simmons, David Miller, and Craig Meier Agronomy and Horticulture Dept. New Mexico State University

2. Objective • Find the key variables and equations in the ET estimate that are most sensitive to change in input or change in functions within the calculations.

3. Procedure • Build the model • Validate it • Sensitivity analysis

4. Build the ModelASTER 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

5. Reflectance (resolution 15 by 15 m) Build the Model

6. Temperature (resolution 90 by 90 m) Build the Model

7. Build the modelTheory Build the Model ETins = Rn - G - H R H n ETins G Graph from Allen, et. al., (2002)

8. Start Build the Model 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

9. Rn Build the Model • Rn=Rns-Rnl = net radiation Rns=(1-)Rs = net solar radiation  is surface albedo, =0.484 1+ 0.3353 -0.3245 +0.5516 +0.3058 -0.3769-0.0015 i is the reflectance for ASTER data band I, averaged to 90m2 resolution. • Rnl=f(RH,Ts) =net long wave radiation

10. Empirical function G=Rn*CNDVI from ASTERreflectance data of bands 3 and 2, Build the Model

11. Build the Model H rah Sensible Heat Flux (H) H = (r ×cp× dT) / rah dT= the near surface temperature difference (K). rah = the aerodynamic resistance to heat transport (s/m). z2 rah=ln(z2/z1)/(u*×k) u*= friction velocity dT z1 Graph from Allen, et. al., (2002)

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

13. Build the Model • 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.

14. dT regression Build the Model

15. Build the Model Sensible Heat Flux (H) • 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

16. Build the Model 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

17. Build the Model Et Calculation 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

18. Build the Model Validate the modelMeasurement sites Pecan orchard Alfalfa field

19. Validate the Model ET measurement Li Cor system

20. Validate the Model ET map mm/day

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

22. Validate the Model Average error • The data represent no cover, partial leaf cover and closed canopy. • Average of relative error all days 11% with the greatest % error when Et was small in the winter and early spring.

23. Sensitivity analysis Sensitivity analysisET=Rn-G-HSensitivity 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)

24. Sensitivity analysis Sensitivity Analysis • Variables related to Rn Rs (500-1100 w/m2),  (0.1-0.4), • Variables related to G C (G/Rn, 0.1-0.5), • Variables related to H rah (0-100 s/m) Variables were changed over a typical rang for the selected six pixels

25. dT regression Build the Model

26. Sensitivity analysis ET vs. dT dT is linearly related to Ts, H=f(dT, rah, u*, L, Zom)

27. 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

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

29. 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

30. ET vs. AlbedoRns=(1-)Rs, Rn=Rns-Rnl

31. 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.

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

33. 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.

34. Sensitivity analysis ET vs. rahrah=f(u*, z2, z1), H=f(dT, rah, u*, L, Zom)

35. 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.

36. ConclusionMost 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

37. Thank You!