Overview:Single Source Remote Sensing based Energy Balance for EvapotranspirationRick Allen -- University of Idaho, Kimberly, Idaho

Two Questions posed:

Single-source vs. Two-source for aerodynamic transport

Of most concern for tall, sparse vegetation (not in most agriculture)

Approach to ‘Calibration’ of the Surface Energy Balance Process:

Use of ‘absolutes’ for Tsurface, Tair

Use of Calibration using Inverse Modeling of Extreme Conditions (CIMEC)

ET is calculated as a “residual” of the energy balance

ET = R - G - Hn

Rn

G (heat to ground)

H (heat to air) ET

The energy balance includes all major sources (Rn) and consumers (ET, G, H) of energy

Basic Truth: Evaporation consumes Energy

Why Energy balance?

(radiation from sun and sky)

We can ‘see’ impacts on ET caused by:

water shortagediseasecrop varietyplanting densitycropping datessalinitymanagement

(these effects can be converted directly into a crop coefficient)

Energy balance gives us “actual” ET

Sensible Heat Flux (H) –“Classical”

H = ρ cp (Taero - Tair) / rah

rah = the aerodynamic resistance

HrahdT

z1

z2

Taero = aerodynamic temperature

u* = friction velocityk = von karmon

constant (0.41)

kuz

dz

rzhzh

ohah

*

)()(2

12ln Ψ+Ψ−⎟⎟

⎠

⎞⎜⎜⎝

⎛ −

=

Challenge (BIAS):Unknown Spatial Distribution of Tair (feedback between EB, Trad, Tair)

Challenge (BIAS):Up to 2 K different from Trad(satellite)

Satellite Energy Balance is ‘Plagued’ by Uncertainty, Bias, and Error in EB components

Surface temperatureAerodynamic vs. Radiative TemperatureBias in Satellite Sensor CalibrationAtmospheric Correction

Air temperature Albedo calculationNet radiation calculation (incoming long-wave)Soil heat flux Aerodynamic resistance calculationWind speed fieldExtrapolation of instantaneous ET to 24-hour periods

Calibration using Inverse Modeling of Extreme Conditions – CIMEC

-- used by SEBAL, METRIC, SEBIQuestion: Are there ‘conditions’ in the image where we ‘know’ at least three components of the EB? (Rn, G, H, LE)Answer: Yes.

at a ‘dry’ condition:LE ~ 0 so that H = Rn – G

At a ‘wet’ (vegetated condition):H ~ 0 so that LE = Rn – G (SEBAL--classical)

For full cover, ET ETref so that H = Rn – G – c ETref(METRIC – at a specific location; SEBI – for each pixel, theoretical condition)

Why use Inverse Modeling?

Net Radiation (SEBAL vs. Ground)

Natural (Desert)Vegetation

Soil Heat Flux (SEBAL vs. Ground)Natural (Desert)Vegetation

Aerodynamic roughess

How, from space, pixel by pixel?

Sensible Heat Flux (H) – CIMEC models

H = (ρ × cp × dT) / rah

rah = the aerodynamic resistancefrom z1 to z2

HrahdT

z1

z2

dT = “floating” near surface temperature difference (K)

u* = friction velocityk = von karmon

constant (0.41)

kuzz

rzhzh

ah ×

Ψ+Ψ−⎟⎟⎠

⎞⎜⎜⎝

⎛

=*

)()(1

212

ln

Advantage:dT is inverse calibrated (simulated) (free of Trad vs. Taerovs. Tair)

Advantage:rah ‘floats’ above the surface and is ‘free’ of zohand some limitations of a single source approach

dT definition

From Sung-ho Hong, NMT

Calibration of SEBAL and METRIC CIMEC models:

pcoldair

coldahcoldcold c

rHdT

ρ=

photair

hotahhothot c

rHdT

ρ=

HrahdT

z1

z2

HrahHrahdT

z1

z2

Rn - GRn – G - 1.05 ETref alfalfa (METRIC)or 0 (SEBAL – classical)

Near Surface Temperature Difference (dT)

To compute the sensible heat flux (H), define near surface temperature difference (dT) for each pixel

Classical: dT = Tsurface – TairSEBAL/METRIC: dT = Tz1 – Tz2

Tair is unknown and unneeded

SEBAL and METRICtm assume a linear relationship between Ts and dT:

dT = b + aTs

HrahdT

z1

z2

Hrah HrahdT

z1

z2

Ts is used only as an index and can have large bias (it’s OK, Dorothy) and does not need to represent aerodynamic surface temperature

BastiaanssenBastiaanssen ‘‘breakthroughbreakthrough’’

Calibration of SEBALand METRIC CIMEC’s:

Derivation of linear dT vs. Ts function

coldshots

coldhotTTdTdT

a−−

=

hotshot TadTb −=

sTbadT +=and at all pixels

Regardless of ‘1-source’or ‘2-source’ model:‘the dry condition’(bare, dry field) is a ‘1-source’ condition.

Regardless of ‘1-source’or ‘2-source’ model:‘the wet condition’ (fully veg. field) is a ‘1-source’ condition.

‘2-sour

ce reg

ion’

(partia

l cover

)

40

60

50

30

20

Temperature(oC)

Surface Temperature – southcentral Idaho – August 14, 2000

basaltbasaltrecent burnrecent burn

Lake WalcottLake Walcott

NorthNorth

Wood River ValleyWood River Valley

Craters of the MoonCraters of the Moon

Thousand SpringsThousand Springs

Twin FallsTwin Falls

BurleyBurley

400

800+

600

200

0

Net Radiation (W/m2)

Net Radiation – southcentral Idaho – August 14, 2000

basaltbasaltrecent burnrecent burn

Lake WalcottLake Walcott

NorthNorth

Wood River ValleyWood River Valley

Craters of the MoonCraters of the Moon

Thousand SpringsThousand Springs

Twin FallsTwin Falls

BurleyBurley

Rn

G

H ET

Calibration of METRIC:

HrahdT

z1

z2

HrahHrahdT

z1

z2

The Sensible Heat (H) Function calibrates around Biases in many of theEnergy balance components:

(Biases exist in: net radiation, soil heat flux, aerodynamic stability, aerodynamic roughness, absolute surface temperature, atmospheric correction)

H = Rn – G – LE (for calibration)

LE = Rn – G – H (during application)

Biases cancel out

biases

biasRn-G biasH-cal biasdT biasH-pixel LE

200

400+

300

100

0

Sensible Heat(W/m2)

Heat Flux to Air – southcentral Idaho – August 14, 2000

basaltbasaltrecent burnrecent burn

Lake WalcottLake Walcott

NorthNorth

Wood River ValleyWood River Valley

Craters of the MoonCraters of the Moon

Thousand SpringsThousand Springs

Twin FallsTwin Falls

BurleyBurley

Rn

G

H ET

200

400+

300

100

0

Latent Heat (W/m2)

Instantaneous ET – southcentral Idaho – August 14, 2000

basaltbasaltrecent burnrecent burn

Lake WalcottLake Walcott

NorthNorth

Wood River ValleyWood River Valley

Craters of the MoonCraters of the Moon

Thousand SpringsThousand Springs

Twin FallsTwin Falls

BurleyBurley

Rn

G

H ET

8/14/00

Hypothesis: Two source problems do not generally appear in agricultural applications

Crops are generally uniformCrops are not very tallSun angle is usually > 50o (less side

loading of radiation)

Exceptions:tall, sparse trees

12/17/01

Comparison with Lysimeter Measurements:

Lysimeter at Kimberly (Wright)

1968-1991

Kimberly, Idaho – Periods between Satellites

Lysimeter data by Dr. J.L. Wright, USDA-ARS

Sugar Beets, 1989

Kimberly, Idaho

0

50

100

150

200

250

300E

T du

ring

perio

d, m

m

18-Apr

04-May20-May

05-Jun

21-Jun07-Jul

23-Jul

25-Sep

Lys. Kc on Sat. date x sum ETr Sum. all lysimeter meas. (Truth)

SEBAL ET for period

Impact of using Kc from a single dayto represent a period: Kimberly 1989

METRIC ET for period

Perio

d of P

artial

Cove

r

Sugar Beets

60 100 140 180 220 260 3000.0

0.2

0.4

0.6

0.8

1.0

1.2

S.BeetK

c

100 140 180 220 260 300 0.0

0.2

0.4

0.6

0.8

1.0

1.2

60 Day of Year

516 fields

Kc near 1.0 indicating high production agriculture

60 100 140 180 220 260 3000.0

0.2

0.4

0.6

0.8

1.0

1.2

W.GrainK

c

100 140 180 220 260 300 0.0

0.2

0.4

0.6

0.8

1.0

1.2

60 Day of Year

564 fields

Question: Is the ‘floating one-source’ method of SEBAL and METRIC sufficiently elevated above the canopy for sparse vegetation to function well with a single-source gradient? (or is a ‘two source’ model needed?)

Hrah dT

z1

z2

Tsoil

Tveg

Observation:

For tall vegetation and dT vs. Tsfunction:

As h zom Turb. dT and Ts

As soilmoisture ET Ts and dT

Therefore, these are all in the right direction and….….does a single source compensate well enough??

Dry Beans Twin Falls, Idaho 2000

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1/1/2000 3/2/2000 5/2/2000 7/2/2000 9/1/2000 11/1/2000 1/1/2001

Month

Mea

n K

c

Agrim et for 2000 Allen-Robison - 14 yr ave. METRIC for 2000

Comparing METRIC vs. traditional Kc ETref methods

Sugar BeetsTwin Falls, Idaho 2000

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1/1/2000 3/2/2000 5/2/2000 7/2/2000 9/1/2000 11/1/2000 1/1/2001

Month

Mea

n K

c

Agrim et for 2000 Allen-Robison - 14 yr ave. METRIC for 2000

Comparing METRIC vs. traditional Kc ETref methods

Field CornTwin Falls, Idaho 2000

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1/1/2000 3/2/2000 5/2/2000 7/2/2000 9/1/2000 11/1/2000 1/1/2001

Month

Mea

n K

c

Agrim et for 2000 Allen-Robison - 14 yr ave. METRIC for 2000

Comparing METRIC vs. traditional Kc ETref methods

PotatoesTwin Falls, Idaho 2000

0.00.10.20.30.40.50.60.70.80.91.0

1/1/2000 3/2/2000 5/2/2000 7/2/2000 9/1/2000 11/1/2000 1/1/2001

Month

Mea

n K

c

Agrim et for 2000 Allen-Robison - 14 yr ave. METRIC for 2000

Comparing METRIC vs. traditional Kc ETref methods

Comparison with Satellite-based Energy Balance (METRIC)

Seasonal ET in the Magic Valley - 2000

0

200

400

600

800

1000

1200

1400

Alfalfa Dry Beans SugarBeets

Corn Potato-early

Potato-late

Sp. Grain WinterGrain*

~Gro

win

g Se

ason

ET,

mm

METRIC Magic Valley 2000Allen-Robison (2006) - Twin FallsAllen-Robison (2006) - JeromeAgrimet - Twin Falls - 2000**Allen-Robison (2006) -Twin Falls - Mar-July 2000Allen-Robison (2006) - Twin Falls Agrimet 2000

Surface AlbedoSugar Beets at Kimberly, Idaho

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

100 120 140 160 180 200 220 240 260 280

Day of Year, 1989

Alb

edo

METRIC_2000 METRIC_2005

bare soil developing full cover

wet soil

New band-by-bandatmospheric correctionand integration to albedo

Instantaneous Net Radiation Fux (Rn)Sugar Beets at Kimberly, Idaho

0

100

200

300

400

500

600

700

100 120 140 160 180 200 220 240 260 280

Day of Year, 1989

Rn,

W/m

2

METRIC_2000 METRIC_2005

bare soil developing full cover

Instantaneous Soil Heat FluxSugar Beets at Kimberly, Idaho

0

20

40

60

80

100

120

140

100 120 140 160 180 200 220 240 260 280

Day of Year, 1989

G, W

/m2

METRIC_2000 METRIC_2005

bare soil developing full cover

Instantaneous Sensible Heat Flux (H)Sugar Beets at Kimberly, Idaho

-200

-100

0

100

200

300

400

100 120 140 160 180 200 220 240 260 280

Day of Year, 1989

H, W

/m2

METRIC_2000 METRIC_2005

(Because ET = Rn – G – H)

bare soil developing full cover

(internal calibration of dTusing reference ETr)

Daily EvapotranspirationSugar Beets at Kimberly, Idaho

0

1

2

3

4

5

6

7

8

100 120 140 160 180 200 220 240 260 280

Day of Year, 1989

ET24

(mm

/d)

METRIC_2000 METRIC_2005

bare soil developing full cover

Weather DataIn METRIC, Weather Data are used for:

• Wind speed for sensible heat fluxsensible heat flux calculation

•Reference ET for Calibrating the Cold PixelCalibrating the Cold Pixel

•Reference ET to Extrapolate ETExtrapolate ET over:• 2424--hour periodhour period• Days between ImagesDays between Images

Cold Pixel of METRIC:

Why use ETr ????

We must have high quality hourly weather data

Standardized Reference ET

Penman-Monteith equation applied to alfalfa for hourly application

λγ

ρ

⎟⎟⎠

⎞⎜⎜⎝

⎛++∆

−+−∆=

a

s

aaspnref

rr

reecGRET

1

/)()(

30 s m-1

(daylight)= f(0.5 m ht)

(ASCE-EWRI, 2005)

-0.10

0.10

0.30

0.50

0.70

0.90

1.10

ET,

mm

/hou

r

0100 0300 0500 0700 0900 1100 1300 1500 1700 1900 2100 2300Time of Day

Etr Lys. 2 alfalfa

Kimberly Lysimeters - September 4,1990Data from Dr. J.L Wright

ASCE StandardizedPenman-Monteith(alfalfa reference)at Kimberly, Idaho

- hourly time step

-0.10

0.10

0.30

0.50

0.70

0.90

1.10

ET,

mm

/hou

r

0100 0300 0500 0700 0900 1100 1300 1500 1700 1900 2100 2300Time of Day

Etr Lys. 2 alfalfa

Kimberly Lysimeters -September 7, 1990

0

2

4

6

8

10

12

Eva

potra

nspi

ratio

n, m

m/d

ay

100 125 150 175 200 225 250 275 300Day of Year

Lysimeter ASCE P-M 24-hr Rn

Kimberly, Idaho 1969

Full cover alfalfa - Data from Dr. J.L. Wright

0.0

0.5

1.0

1.5

2.0

2.5

3.0E

T / R

n

50 100 150 200 250 300Day of Year

Full cover alfalfa - measured by Lysimeter-- Data from Dr. J.L. Wright, USDA-ARS

Ratio of ET to Rn -- 24-hour periods (G ~ 0)Full Cover Alfalfa – 1969 - 1971

Effects of Advection on ‘Cold Pixel’

CIMEC models when Extremes do not exist:

“DRY” condition – (does ET = 0???)Always run a daily soil water – evaporation balance for a dry soil condition. Use to set LE for bare soil if there has been antecedent precipitation.For METRIC, we use a simple FAO-56 based evaporation model (Ke)

ET at the Hot pixel: (is it really zero?): The operator must direct METRIC concerning any residual ET at the hot pixel. ET can be estimated using the FAO-56 surface evaporation estimation procedure

Bare soil water balance, MRG, 2002

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1/1/

2002

2/1/

2002

3/1/

2002

4/1/

2002

5/1/

2002

6/1/

2002

7/1/

2002

8/1/

2002

9/1/

2002

10/1

/200

2

11/1

/200

2

12/1

/200

2

Kc

base

d on

ETr

0

6

12

18

24

30

36

42

Prec

ipita

tion

(mm

)

Satellite date

CIMEC models when Extremes do not exist:

“Wet” condition – (is ETcold = 1.05 ETr?)In a RAINFED region with no irrigation, a well-watered, fully vegetated condition may not exist.Again, run a daily soil water model for a known, fully vegetated crop.

Apply a stress function. Use to set LE for the ‘wet’ condition:Hcold = Rn – G – LEsoil water balance

For METRIC, we use a simple FAO-56 based evaporation model (Ks Kcb + Ke)

Iowa – SMEX 2002 – rainfed, dry, advective

Corn, Rainfed

0.00

0.20

0.40

0.60

0.80

1.00

1.20

110

123

136

149

162

175

188

201

214

227

240

253

266

279

Day of Year, 2002

Kcb, Kc

0

10

20

30

40

50

60

70

80

Prec

ip, m

m

Basal Kcb Ks Kcb + Ke Irrig Precip

Satellite dateIowa, July 1, 2002 – 18 days since significant rain.

stress

CIMEC models when Extremes do not exist:

“Wet” condition –Early in spring, a ‘full cover’ condition may not exist where ET ~ ETref

Estimate ETwet using Kc from NDVIKcb pixel x = a + b NDVIpixel x

ETcold = Kcb pixel x ETref

Hcold = Rn – G - ETcold

Estimating ‘basal’ Kcb from Vegetation Indices

rednir

rednirNDVIρρρρ

+−

=rednir

rednir

LL

SAVIρρρρ

++−+

=))(1(

Potato (DOY 155-259)

y = 1.43x - 0.1

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1

SAVI at surface

ETrF

Potato (DOY 155-259)

y = 1.1299x - 0.0808

y = 1.1892x - 0.1892

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1

NDVI at surface

ETr

F

General Kcb Kcb custom

6000 potato fields

‘basal’ Kcb represents mostly transpiration ~ a + b (VI)

ETrF = fraction of reference ET = Kc

Bare soil(all crops)

(potatoes)

Other CIMEC models:

CalibrationSEBI/SEBS:

Trained using extreme theoretical conditions at each pixelWet ConditionDry Condition

assumptions on spatial structure of vapor pressure over image Assume little heat storge between surface and blending height (may cause problems due to flux divergence)

Estimated 24 hour ET (mm/day), 7/21/2000, path 40/30, Agr. Area Only

y = 1.0042xR2 = 0.9996

0

2

4

6

8

10

12

0 2 4 6 8 10 12Estimated ET using corrected Ts

Estim

ated

ET

usin

g un

corre

cted

Ts

Sensitivity of METRIC To Correction of Surface Temperaturefor Atmosphere

(Predictions are not sensitive due to calibration at hot and cold pixels)

Impact of Irrigation System Type on ET-- south-central Idaho -- 2003

METRIC Analyses by Lorite, Allen and Robison

Impact of Irrigation System Type on ET-- south-central Idaho -- 2003

METRIC Analyses by Lorite, Allen and Robison

Impact of Irrigation System Type on ET-- south-central Idaho -- 2003

METRIC Analyses by Lorite, Allen and Robison

“Performance” of Irrigation Projects

Mar Apr May Jun Jul Aug Sep Oct0.0

0.1

0.20.3

0.4

0.5

0.6

0.7

Project wide Crop Coefficient -- METRICTwin Falls Tract -- 220,000 acres -- Alfalfa Reference Basis

20002003K

c

March, Sept., and Oct. unavailable for 2003

Irrigation Project Performance -- Idaho

Apr May Jun Jul Aug Apr-Aug0.0

0.2

0.4

0.6

0.8

1.0

Evapotranspiration as a Ratio of Diversion plus Precipitation

20002003

Rat

io

Twin Falls Canal Company, Idaho

Irrigation Project Performance -- Idaho

Landsat 5 -- Albacete, Spain, 07/15/2003

ET ratio before sharpening ET ratio after sharpening

Sharpening of Thermal Band of Landsat 5 from 120 m to 30 m using NDVI

Conclusions

Inverse Modeling for Extreme Condition Calibration compensates for: • Biases in Rn, G, roughness, atm. correction• Increases accuracy of ET ‘map’• Does require a ‘thinking human’• Does require modification if no ‘dry’ condition or no ‘wet’ condition

Sugar Beet

0

0.2

0.4

0.6

0.8

1

1.2

3/1/

00

3/31

/00

4/30

/00

5/30

/00

6/29

/00

7/29

/00

8/28

/00

9/27

/00

10/2

7/00

Kc

SEBAL

Allen&Brockway (1983)

Requirements for SEBAL or METRICtm

Satellite images with Thermal BandHigher resolution (Landsat) is needed for field scale maps

Good quality weather data if local calibration is desirable

Experienced, thinking human at the controls(determination of ET conditions at calibration pixels)

Limitations of METRICtm

Can not be used with clouds(8 or more images per season are needed for Seasonal ET)Difficult to find images and apply METRIC in winterRainfall impacts the image (ET snapshots show influences of recent rainfall events)

Only provides ET snapshotsNeed GIS and perhaps water balance model to produce volumetric information for management

Experienced, thinking human at the controls

More information at:www.kimberly.uidaho.edu/water/ (METRICtm)

www.waterwatch.nlwww.sebal.us (SEBALtm)

http://maps.idwr.idaho.gov/et/