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