a sensitivity analysis on remote sensing et algorithm— remote evapotranspiration calculation (ret)...

A Sensitivity Analysis on A Sensitivity Analysis on Remote Sensing ET Remote Sensing ET

Algorithm—Algorithm—Remote Remote

Evapotranspiration Evapotranspiration Calculation (RET)Calculation (RET)Junming Wang, Ted. Sammis, Luke SimJunming Wang, Ted. Sammis, Luke Sim

mons, David Miller, and Craig Meiermons, David Miller, and Craig Meier

Agronomy and Horticulture Dept.Agronomy and Horticulture Dept.New Mexico State UniversityNew Mexico State University

ObjectiveObjective

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

ProcedureProcedure

Build the modelBuild the model Validate itValidate it Sensitivity analysisSensitivity analysis

Build the ModelBuild the ModelASTER Satellite from NASAASTER Satellite from NASA

15 by 15 m visible and near-infrared 15 by 15 m visible and near-infrared radiance. Bands 1-3radiance. Bands 1-3

30 by 30 m shortwave infrared radiance. 30 by 30 m shortwave infrared radiance. Bands 4-9Bands 4-9

90 by 90 m infrared radiance. Bands 10-1490 by 90 m infrared radiance. Bands 10-14 Reflectance(Bands1-9) and temperature Reflectance(Bands1-9) and temperature

data can be requested as secondary data can be requested as secondary processed dataprocessed data

Availability: potentially 16 days upon Availability: potentially 16 days upon requestrequest

Reflectance Reflectance (resolution 15 by 15 m)(resolution 15 by 15 m)

Build the Model

Temperature Temperature (resolution 90 by 90 m)(resolution 90 by 90 m)

Build the Model

Build the modelBuild the modelTheoryTheory

ETins = Rn - G - H

Rn

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 ModelSatellite inputs: surface

temperature and reflectance. Local weather inputs: solar

radiation, humidity and wind speed

RnRn

Rn=Rns-Rnl = net radiation Rn=Rns-Rnl = net radiation

Rns=(1-Rns=(1-)Rs = net solar radiation )Rs = net solar radiation is surface albedo, is surface albedo,

=0.484 1+ 0.3353 -0.3245 +0.551 6 +0.3058 -0.376 9-0.0015i is the reflectance for ASTER data band I, is the reflectance for ASTER data band I, averaged to 90maveraged to 90m2 2 resolution. resolution.

Rnl=f(RH,Ts) =net long wave radiationRnl=f(RH,Ts) =net long wave radiation

Build the Model

y = -2. 6955x4 + 3. 9817x3 - 1. 6401x2 -0. 1102x + 0. 4079

R2 = 0. 6633

0

0. 1

0. 2

0. 3

0. 4

0. 5

0. 6

0 0. 2 0. 4 0. 6 0. 8 1NDVI

C

Empirical function G=Rn*CEmpirical function G=Rn*CNDVI from NDVI from ASTERASTER reflectance data of bands 3 and reflectance data of bands 3 and

2, 2,

Build the Model

Sensible Heat Flux (H)Sensible Heat Flux (H)

H = (×cp × dT) / rah

HrahdT

rah = the aerodynamic resistance to heat transport (s/m).

z1

z2

dT = the near surface temperature difference (K).

Graph from Allen, et. al., (2002)

Build the Model

rah=ln(z2/z1)/(u*×k)u*= friction velocity

Selection of “Anchor Pixels” Selection of “Anchor Pixels” for dT calculationfor dT calculation

““wet” pixel:wet” pixel: Ts Ts Tair Tair

““dry” pixel: dry” pixel: ET ET 0 0

Ts=303 K

Ts=323 K

Build the Model

At the “wet” pixel: At the “wet” pixel: dTwet = Ts-Tair=0dTwet = Ts-Tair=0

Should be an alfalfa field, not cut and not strShould be an alfalfa field, not cut and not stressed for wateressed for water

At the “dry” pixel: Hdry = Rn – G - At the “dry” pixel: Hdry = Rn – G - ETdETdryry where where ETdry = 0ETdry = 0 dTdry = Hdry× rah / (dTdry = Hdry× rah / ( × cp) × cp)Should be a bare soil field where evaporaShould be a bare soil field where evapora

tion is zerotion is zero. .

Build the Model

dT regression

y = 0. 2813x - 84. 993

0

12

3

45

6

300 305 310 315 320 325

Surface temperature (k)

Dt (

k)

Build the Model

Sensible Heat Flux (H)Sensible Heat Flux (H)

dT for each pixel is computed dT for each pixel is computed using the regression.using the regression.

H is calculated for each pixel H is calculated for each pixel after calculating rah for each after calculating rah for each pixel pixel

H = ( H = ( × cp × dT) / rah × 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( zom) for each pixel fr

om NDVI

Calculate dT for each pixel from Ts

Calculate friction velocity ( u*) for each pixel

Calculate rah 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 CalculationEt CalculationObtain instant latent heat for each pixel Obtain instant latent heat for each pixel ETins = Rn - G - HETins = Rn - G - HObtain instant reference latent heat for iObtain instant reference latent heat for i

rrigated alfalfa field (rrigated alfalfa field (ETrins)Obtain Daily reference ET calculated by Obtain Daily reference ET calculated by

FAO Penman-Monteith from weather FAO Penman-Monteith from weather station for alfalfa field (station for alfalfa field (ETrdaily)

Calculated ET daily for each pixelCalculated ET daily for each pixelETdaily=ETins/ ETrins×ETrdaily

Build the Model

Validate the modelValidate the modelMeasurement sitesMeasurement sites

Pecan orchard

Alfalfa field

Build the Model

ET measurementET measurement

Li Cor system

Validate the Model

ET mapET map

mm/day

Validate the Model

The pecan ET of simulation The pecan ET of simulation vs. observation.vs. observation.

0123456789

02/1

3/02

05/2

4/02

09/0

1/02

12/1

0/02

03/2

0/03

06/2

8/03

10/0

6/03

01/1

4/04

04/2

3/04

Time (day)

ET

(m

m/d

ay)

ObservationModel

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 errorValidate the Model

Sensitivity analysisSensitivity analysisET=Rn-G-H ET=Rn-G-H

Sensitivity Analysis areasSensitivity Analysis areas

Full vegetation area (6 points, Full vegetation area (6 points, NDVI=0.57)NDVI=0.57)

Half vegetation area (6 points, Half vegetation area (6 points, NDVI=0.31)NDVI=0.31)

Little vegetation area (6 points, Little vegetation area (6 points, NDVI=0.19)NDVI=0.19)

Sensitivity analysis

Sensitivity analysisSensitivity analysisSensitivity AnalysisSensitivity Analysis

Variables related to RnVariables related to Rn

Rs (500-1100 w/mRs (500-1100 w/m22), ), (0.1-0.4), (0.1-0.4), Variables related to GVariables related to G

C (G/Rn, 0.1-0.5), C (G/Rn, 0.1-0.5), Variables related to HVariables related to H

rah (0-100 s/mrah (0-100 s/m ) )

Variables were changed over a typical Variables were changed over a typical rang for the selected six pixelsrang for the selected six pixels

dT regression

y = 0. 2813x - 84. 993

0

12

3

45

6

300 305 310 315 320 325

Surface temperature (k)

Dt (

k)

Build the Model

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


0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

dT (K)

ET (

mm/d

ay)

Ful l vegetat i onLi t t l e vegetat i onHal f vegetat i on

ET vs. dTET vs. dT

ET is sensitive to dT which is calculated from ET is sensitive to dT which is calculated from Ts.Ts.

An error in your hot or cold spot dT An error in your hot or cold spot dT calculation results in error in H and ET for calculation results in error in H and ET for intermediate points. intermediate points.

Ts from satellite is not sensitive as an absolute numTs from satellite is not sensitive as an absolute number only as a relative number which may represenber only as a relative number which may represent a 2% error in dT and ETt a 2% error in dT and ET

If the algorithms in the model are to be If the algorithms in the model are to be changed, the dT calculation equation will changed, the dT calculation equation will be the key equation. It may not be linearbe the key equation. It may not be linear


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


0

1

2

3

4

5

6

7

8

500 600 700 800 900 1000 1100 1200

Rs (w/ m2)

ET (

mm/d

ay)


ET vs. RsET vs. Rs

ET is sensitive to Rs which ET is sensitive to Rs which determines Rn.determines Rn.

Rs is from local weather stations and Rs is from local weather stations and errors in this value can be as high as errors in this value can be as high as 5 to 10 % depending on the quality 5 to 10 % depending on the quality control for the climate network.control for the climate network.

An error of 10 % in Rs results in an An error of 10 % in Rs results in an ET error of 0.2 mm/day or a 3% ET error of 0.2 mm/day or a 3% error in ETerror in ET


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

0015.0367.0305.0

551.0324.0335.0484.0

98

6531

0

1

2

3

4

5

6

0. 1 0. 15 0. 2 0. 25 0. 3 0. 35 0. 4

Al bedo

ET (

mm/d

ay)


ET vs. AlbedoET vs. Albedo

ET is sensitive to albedo because it affects ET is sensitive to albedo because it affects Rn value.Rn value.

The albedo function is an empirical The albedo function is an empirical function that may not be applicable over function that may not be applicable over conditions different from the experimental conditions different from the experimental sites where the function was derived. sites where the function was derived.

The function is critical when vegetation The function is critical when vegetation cover exits and ET is occurring. For bare cover exits and ET is occurring. For bare soil the function is not critical because soil the function is not critical because this condition represents the dry point. this condition represents the dry point.


ET vs. C (G/Rn)ET vs. C (G/Rn) C is a polynomial function C is a polynomial function

of NDVIof NDVI


0

1

2

3

4

5

6

7

8

0 0. 1 0. 2 0. 3 0. 4 0. 5 0. 6 0. 7 0. 8

C (Rn/ G)

ET (

mm/d

ay)

Ful l vegetat i onHal f vegetat i onLi t t l e vegetat i on

ET vs. C (G/Rn)ET vs. C (G/Rn)

ET is highly sensitive to C when ET is highly sensitive to C when there is full or half vegetation there is full or half vegetation covered.covered.

But ET is not sensitive to C when But ET is not sensitive to C when there is little vegetation covered.there is little vegetation covered.

If algorithm improvement is needed, If algorithm improvement is needed, the equation for C calculation is a the equation for C calculation is a key function.key function.


ET vs. rahET vs. rahrrah=f(u*, z2, z1), H=f(dT, rah, u*, L, =f(u*, z2, z1), H=f(dT, rah, u*, L,

Zom)Zom)


0

1

2

3

4

5

6

7

0 20 40 60 80 100

rah ( s/ m)

ET (

mm/d

ay)


ET vs. rahET vs. rah

When rWhen rah<40s/m, ET is sensitive <40s/m, ET is sensitive to it.to it.

The rah calculation equation is a The rah calculation equation is a key equation for the algorithm key equation for the algorithm and is a function of u* (friction and is a function of u* (friction velocity) which is a function of velocity) which is a function of wind speed, roughness length wind speed, roughness length and atmospheric stability which and atmospheric stability which is also related to dT.is also related to dT.


ConclusionConclusion Most sensitive variables and equationsMost sensitive variables and equations

Input variables Input variables Rs, u from weather station Rs, u from weather station Ts from satellite is not sensitive as an Ts from satellite is not sensitive as an

absolute number only as a relative nabsolute number only as a relative number umber

Intermediate variables (and their calIntermediate variables (and their calculation equations)culation equations)

dT, albedo, C(G/Rn), and rdT, albedo, C(G/Rn), and rahah

a sensitivity analysis on remote sensing et algorithm— remote evapotranspiration calculation (ret)...

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