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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

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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. 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.

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Procedure Build the model Build the model Validate it Validate it Sensitivity analysis Sensitivity analysis

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

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Reflectance (resolution 15 by 15 m) Build the Model

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Temperature (resolution 90 by 90 m) Build the Model

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

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

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Rn Rn=Rns-Rnl = net radiation Rn=Rns-Rnl = net radiation Rns=(1- )Rs = net solar radiation is surface albedo, 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 is the reflectance for ASTER data band I, averaged to 90m 2 resolution. i is the reflectance for ASTER data band I, averaged to 90m 2 resolution. Rnl=f(RH,Ts) =net long wave radiation Rnl=f(RH,Ts) =net long wave radiation Build the Model

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Empirical function G=Rn*C NDVI from ASTER reflectance data of bands 3 and 2, Build the Model

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Sensible Heat Flux (H) H = ( × c p × dT) / r ah H r ah dT r ah = the aerodynamic resistance to heat transport (s/m). z1z1 z2z2 dT = the near surface temperature difference (K). Graph from Allen, et. al., (2002) Build the Model r ah =ln(z2/z1)/(u*×k) u*= friction velocity

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

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At the “wet” pixel: 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 At the “dry” pixel: Hdry = Rn – G - ETdry where ETdry = 0 where ETdry = 0 dTdry = Hdry× rah / ( × cp) dTdry = Hdry× rah / ( × cp) Should be a bare soil field where evaporation is zero. Build the Model

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dT regression Build the Model

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

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

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Et Calculation Obtain instant latent heat for each pixel ETins = Rn - G - H ETins = Rn - G - H Obtain instant reference latent heat for irrigated alfalfa field ( 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 ( 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 Build the Model

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Validate the model Measurement sites Pecan orchard Alfalfa field Build the Model

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ET measurement Li Cor system Validate the Model

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ET map mm/day Validate the Model

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

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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. Average error Validate the Model

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

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Sensitivity Analysis Variables related to Rn Variables related to Rn Rs (500-1100 w/m 2 ), (0.1-0.4), Rs (500-1100 w/m 2 ), (0.1-0.4), Variables related to G Variables related to G C (G/Rn, 0.1-0.5), C (G/Rn, 0.1-0.5), Variables related to H Variables related to H rah (0-100 s/m ) Variables were changed over a typical rang for the selected six pixels

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dT regression Build the Model

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

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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 Sensitivity analysis

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

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ET vs. Rs ET is sensitive to Rs which determines Rn. 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. 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 An error of 10 % in Rs results in an ET error of 0.2 mm/day or a 3% error in ET Sensitivity analysis

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

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ET vs. Albedo ET is sensitive to albedo because it affects Rn value. 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 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. 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. Sensitivity analysis

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

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ET vs. C (G/Rn) ET is highly sensitive to C when there is full or half vegetation covered. 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. 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. If algorithm improvement is needed, the equation for C calculation is a key function. Sensitivity analysis

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

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ET vs. rah When r<40s/m, ET is sensitive to it. When r ah <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. 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. Sensitivity analysis

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Conclusion Most sensitive variables and equations Input variables 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) Intermediate variables (and their calculation equations) dT, albedo, C(G/Rn), and r ah

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