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

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.

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

Build the Model ASTER Satellite from NASA 15 by 15 m visible and near-infrared radiance. Bands by 15 m visible and near-infrared radiance. Bands by 30 m shortwave infrared radiance. Bands by 30 m shortwave infrared radiance. Bands by 90 m infrared radiance. Bands by 90 m infrared radiance. Bands 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

Reflectance (resolution 15 by 15 m) Build the Model

Temperature (resolution 90 by 90 m) Build the Model

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

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

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       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

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

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

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

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

dT regression Build the Model

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

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

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

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

ET measurement Li Cor system Validate the Model

ET map mm/day Validate the Model

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

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

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

Sensitivity Analysis Variables related to Rn Variables related to Rn Rs ( w/m 2 ),  ( ), Rs ( w/m 2 ),  ( ), Variables related to G Variables related to G C (G/Rn, ), C (G/Rn, ), 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

dT regression Build the Model

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

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

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

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

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

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

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

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

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

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