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Review of 2-Source Surface Energy Balance Models and Comparison of
1-source vs. 2 source Approaches
Christopher M. U. NealeChristopher M. U. Neale
Professor, Department of Biological and Irrigation Engineering Utah State University, Logan, Utah
Contributions from Martha Anderson, MPat Gonzalez-Dugo, Bill Kustas
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Introduction and OutlineReview the two source and one source energy Review the two source and one source energy balance approach (not comprehensive)balance approach (not comprehensive)Give examples of both modelsGive examples of both modelsDiscuss the advantages and disadvantages of each Discuss the advantages and disadvantages of each approachapproachShow examples of comparisons and applicationsShow examples of comparisons and applications
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Methods of Estimating Evapotranspirationfrom Remote Sensing:
Crop coefficient and reference ET:Crop coefficient and reference ET:ReflectanceReflectance--based crop coefficient modelsbased crop coefficient models
Energy balance models:Energy balance models:One layer models examples: empirical models One layer models examples: empirical models (OLEM), SEBAL, METRIC(OLEM), SEBAL, METRICTwoTwo--source models source models Detailed Process modelsDetailed Process models
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The main difference between energy balance models is in how the sensible heat H is estimated:Bulk aerodynamic resistance heat equation:Bulk aerodynamic resistance heat equation:
where ρa is air density (kg/m3), Cpa is specific heat of air, (J/kg/ K), Ta is average air temperature (K), Taero is average surface aerodynamic temperature (K), which is defined for a uniform surface as the temperature at the height of the zero-plane displacement plus the roughness length for sensible heat transfer Zoh (m) (d + Zoh)rah is surface aerodynamic resistance (s/m) to heat transfer from Zohto Zm [height of wind speed measurement (m)].
⇒ For full, well watered canopies Taero has been approximated in the past using canopy temperature Tc. However this cannot be done under sparse, water-limited conditions
⇒ Ta is not available over all terrain or fields over large areas
H = ρa Cpa (Taero – Ta) / rah
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Two-Source vs. Single-Source ModelsTwo-Source vs. Single-Source Models
H = ρcp
TRAD - TA
RA + REX
HH
REX
RA
TATA
TRADTRAD
SINGLE SOURCE
HC = ρcpTC - TAC
RX
HSHS
HCHC
H = HC + HSH = HC + HS
RS
RA
RX
TATA
TCTC
TSTS
TACTAC
HS = ρcpTS - TAC
RS
H = ρcpTAC - TA
RA= HC + HS
TRAD(θ) ~ fc(θ)Tc + [1-fc(θ)]Ts
TWO SOURCE
Function of:• vegetation cover• surface roughness • sensor view angle
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One Layer Energy Balance Model
( ) 441 ssaasn TTRR σεσεα −+−= NIR0.418 + RED0.512=α
( ) ( )[ ]( ) ( )( ){ }7/1/*6/*2sin*06.022.1*1 aaa Temoclfclf πε ++−+=
Gcorn, soy = {[(0.3324 + (-0.024 LAI)) (0.8155 + (- 0.3032 ln (LAI)))] Rn}
LE = Rn - G - H
)()1)((
LREDNIRLREDNIROSAVI
+++−
=
H = ρa Cpa (Taero – Ta) / rahGround Measured Data [Ta, U, Rs]
L = 0.16
LAI_air = (4 * OSAVI – 0.8)* (1 + 4.73E-6 * EXP [15.64 * OSAVI])1
LAI_sat = (2.88 * NDWI + 1.14)* (1 + 0.104 * EXP [4.1 * NDWI])1
hc_CORN air = (1.86 * OSAVI – 0.2)* (1 + 4.82E-7 * EXP [17.69 * OSAVI])1
hc_SOY air = (0.55 * OSAVI – 0.02)* (1 + 9.98E-5 * EXP [9.52 * OSAVI])1
Taero = [(0.534 Ts_RS) + (0.39 Ta) +
(0.224 LAI_RS) – (0.192 U) + 1.67]
G alfalfa = (038 * EXP [-1.65 * NDVI]) * Rn
1Anderson, M.C., C.M.U. Neale, F. Li, J.M. Norman, W. P. Kustas, H. Jayanthi, and J. Chavez, (RSE Vol. 92, pp. 447-464 2004)
Brest and Goward (1987)
Brutsaert (1975); Crawford and Duchon, 1999
hc_CORN sat = (1.20 NDWI + 0.6) (1 + 4.00E-2 EXP [5.3 NDWI])1
hc_SOY sat = (0.5 NDWI + 0.26) (1 + 5.0E-3 EXP [4.5 NDWI]) 1
)()(
SWIRNIRSWIRNIRNDWI
+−
=
Chavez et al, (2005)Neale et al, (2005)
Chavez et al, (2005)
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Surface Aerodynamic Resistance (rah) Iterative Procedure based on the Monin-Obukhov Method
⎟⎟⎠
⎞⎜⎜⎝
⎛ −=
om
m
ZdZ
Ln
Uu κ*
H = ρa Cpa (Taero – Ta) / rahkU
Zd-Z
Zd-Z
=r 2oh
m
om
m
ah
⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡ lnln
Taero_RS
HkgCTu
L apaaOM
ρ3*
_
−=
41
_
*161 ⎟⎟⎠
⎞⎜⎜⎝
⎛ −−=
OM
m
LdZ
x
⎟⎟⎠
⎞⎜⎜⎝
⎛ +=
21*2
2xLnhψ( )2
tan*22
12
1*22 πψ +−⎟⎟⎠
⎞⎜⎜⎝
⎛ ++⎟⎠⎞
⎜⎝⎛ +
= xaxLnxLnm
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟
⎟⎠
⎞⎜⎜⎝
⎛ −−⎟⎟⎠
⎞⎜⎜⎝
⎛ −=
OM
omm
OM
mm
om
m
LZ
LdZ
ZdZ
Ln
Uu
__
*
ψψ
κ
κ
ψψ
*
__
uLZ
LdZ
ZdZLn
r OM
ohh
OM
mh
oh
m
ah
⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟⎠
⎞⎜⎜⎝
⎛ −−⎟⎟⎠
⎞⎜⎜⎝
⎛ −
=
If rah_i-1 = rah_i
Zom = 0.123 hc
Zoh = 0.1 Zom
d = 0.67 hc
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Instantaneous R.S. LE to daily ETETd = [EF (Rn – G)d] x [cf / λv ρw]
EF = LEi / (Rn – G)i
Latent Heat FluxLE = Rn – G – H
ETd = Daily or 24 hours evapotranspiration rate, mm d-1(Rn – G)d = Measured mean 24 hr available energy, W m-2 cf = Time (unit) conversion factor equal to 86400 s d-1,λv = Latent heat of vaporization, W s kg-1ρw = Density of Water, kg m-3
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One Source Empirical ModelsChavez et al (2005)
SC HHH += SC HHH += SC HHH += S
S buar
+=
1 S
S buar
+=
1 S
S buar
+=
1
Advantages: Simpler to program and useProvide actual evapotranspiration of the crops
Disadvantages:Requires careful atmospheric correction and absolute calibration of the satellite imagery in the visible, near-IR and thermal infrared
Many previously developed empirical relationships are needed
Because of the empirical nature of the relationships within the model, it will only work for the crops and agro-meteorological regions that it was developed and calibrated for
Needs a land use / crop type layer obtained a priori to running the model to direct the use of the empirical models within
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TRAD(θ) ~ fc(θ)Tc + [1-fc(θ)]Ts
θθ
HSHS
HCHC
H = HC + HSH = HC + HS
RS
RA
RX
TATA
TCTC
TSTS
ABL closure
θθ
HSHS
HCHC
H = HC + HSH = HC + HS
RS
RA
RX
TATA
TCTC
TSTS
ABL closure
(two-source approximation)Norman, Kustas et al. (1995)
Provides information onsoil/plant fluxes and stress
TRAD(θ) ~ fc(θ)Tc + [1-fc(θ)]Ts
Accommodates off-nadirthermal sensor view angles
Treats soil/plant-atmosphere coupling differences explicitly
Two-Source Energy Balance Model (TSEB)Two-Source Energy Balance Model (TSEB)
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The
rmal
Vis
ible
Nadir Off-nadir
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λE = λEC + λESλE = λEC + λES
λESλES
λECλEC
CGPTC Rnγ∆
∆fαλE+
=
)(0~
)(3.1~
stressedfullyα
unstressedα
PT
PT
)(residualHGRnλE SSS −−=
unstressedstre
ssed
3.1~~0 PTα
Two-Source Energy Balance Model (TSEB)Two-Source Energy Balance Model (TSEB)
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RNRN
System and Component Energy BalanceSystem and Component Energy Balance
== HH ++ λEλE ++ GG
RNCRNC == HCHC ++ λECλEC
RNSRNS == HSHS ++ λESλES ++ GG
== == ==
++ ++ ++
TSTS
TCTCTAEROTAERO
SY
STE
MC
AN
OP
YS
OIL
Derived fluxes
Derived states
TRADTRAD
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100
0
100
200
300
400
-100 0 100 200 300 400-100
0
100
200
300
400
-100 0 100 200 300 400-100
0
100
200
300
400
-100 0 100 200 300 400
-100
0
100
200
300
400
-100 0 100 200 300 400-100
0
100
200
300
400
-100 0 100 200 300 400-100
0
100
200
300
400
-100 0 100 200 300 400
-100
0
100
200
300
400
500
-100 0 100 200 300 400 500-100
0
100
200
300
400
500
-100 0 100 200 300 400 500-100
0
100
200
300
400
-100 0 100 200 300 400
Tower Flux (Wm-2)
Mod
eled
Flu
x (W
m-2
)
Tallgrass
Prairie
(FIFE)
Grass
(Monsoon 90)
Shrub
(Monsoon 90)
H LE G
1: 482: 421: 482: 42
RMSE1: 462: 421: 462: 42
1: 232: 141: 232: 14
1: 512: 431: 512: 43
1: 672: 611: 672: 61
1: 262: 351: 262: 35
1: 942: 631: 942: 63
1: 1032: 541: 1032: 54
1: 532: 641: 532: 64
Yellow: one source, Green two source
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Two-Source ModelNormal et al (1995)Kustas et al (1999)Li et al (2005)
SC HHH += SC HHH += SC HHH += S
S buar
+=
1 S
S buar
+=
1
Advantages:
Well suited for modeling sparse canopies either in the agricultural or natural vegetation context where water could be limited
Has a more diverse ecosystem area of application
Provides actual evapotranspiration of the vegetation
Disadvantages:
Requires carefully calibrated and atmospherically corrected satellite imagery
More complex to program and run
Works better with higher spatial resolution thermal infrared imagery
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SEBAL/METRIC ModelsBastiaansen et al (1995)Allen et al. (2007)
SC HHH += SC HHH += SC HHH += S
S buar
+=
1 S
S buar
+=
1 S
S buar
+=
1
One-layer models
Uniquely solve for H using the dT method, a linearrelationship between air temperature and surface temperature obtained through a transformation generated from surface temperatures observed over selected “hot” and “cold” pixels in the satellite image.
Advantages: Does not require absolute calibration of the thermal imageryWell suited for irrigated areas under well watered conditionsProvides actual evapotranspiration of the crops or surfaces
Disadvantages:Requires experienced operator to identify the “hot and cold” pixels in the imageMay not work as well in water limited, semi-arid natural vegetation unless calibrated or adjusted?
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Modeling Environment (SETMI) Application code written in Visual Basic within ArcGIS 9.1
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Study Area: Corn and Soybean Fields (Ames, Iowa)2002 NASA SMACEX – SMEX02
LANDSAT Thematic Mapper Image of study area: 30 meter resolution July 1st (182). Images also available for June 23rd, July 8th, July 16,17
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Analysis upwind rectangles for averaging the estimated energy balance fluxes
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LANDSAT Thermal Infrared Imagery
Calibrated using MODTRAN Atmospheric Transmission Model and adjusted for surface emmissivity to obtain at-surface temperatures Berk et al (1989)
Brunsel and Gillies (2002)
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Energy balance fluxes measured with 11 eddy covariance systems (full energy balance) placed in the corn and soybean fields
4 sets of soil heat flux plates distributed in rows and furrows
Corn Soybean
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Land use/crop cover for region obtained from classification of and early satellite image
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Energy Balance Model Input Data and Output Settings
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Kcrf Model Input Settings and Data
From FAO56:
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Kcrf Model Output Settings
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Output Temporal Run
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Results Spatial Output: Regional Daily ET on July 1, 2002
(Spatial Model Output using the OLEM)
Actual ET (mm/day)
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-150
-50
50
150
250
350
-150 -50 50 150 250 350
Observed H (W m-2)
OLE
M p
redi
cted
H (W
m-2
)
174 soy182 soy189 soy174 corn182 corn189 corn
-150
-50
50
150
250
350
-150 -50 50 150 250 350
Observed H (W m-2)
TSM
pre
dict
ed H
(W m
-2)
174 soy182 soy189 soy174 corn182 corn189 corn
Results: Energy Balance Models(closure forced with the residual method)
Sensible Heat Flux (H)
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200
300
400
500
600
700
800
200 300 400 500 600 700 800
Observed LE (W m-2)
OLE
Mpr
edic
tedL
E(W
-2)d
d
174 soy182 soy189 soy174 corn182 corn189 corn
200
300
400
500
600
700
800
200 300 400 500 600 700 800Observed LE (W m-2)
TSM
pre
dict
ed L
E (W
m-2
)
174 soy182 soy189 soy174 corn182 corn189 corn
Latent Heat Fluxes
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50
150
250
50 150 250
Observed daily LE (W m-2)
OLE
M p
redi
cted
dai
ly L
E (W
m-2
174 soy182 soy189 soy174 corn182 corn189 corn
50
150
250
50 150 250
Observed daily LE (W m-2)
TSM
pre
dict
ed d
aily
LE
(W m
-2
174 soy182 soy189 soy174 corn182 corn189 corn
Daily Evapotranspiration Integrated Using the Evaporative Fraction
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TRAD(θ) ~ fc(θ)Tc + [1-fc(θ)]Ts
θθ
HSHS
HCHC
H = HC + HSH = HC + HS
RS
RA
RX
TATA
TCTC
TSTS
ABL closure
θθ
HSHS
HCHC
H = HC + HSH = HC + HS
RS
RA
RX
TATA
TCTC
TSTS
ABL closure
(two-source approximation)Norman, Kustas et al. (1995)
Provides information onsoil/plant fluxes and stress
Accommodates off-nadirthermal sensor view angles
Treats soil/plant-atmosphere coupling differences explicitly
PROBLEM: Air temperature boundary conditionPROBLEM: Air temperature boundary condition
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TRAD(θ) ~ fc(θ)Tc + [1-fc(θ)]Ts
θθ
HSHS
HCHC
H = HC + HSH = HC + HS
RS
RA
RX
TATA
TCTC
TSTS
ABL closure
θθ
HSHS
HCHC
H = HC + HSH = HC + HS
RS
RA
RX
TATA
TCTC
TSTS
ABL closure
(two-source approximation)Norman, Kustas et al. (1995)
Provides information onsoil/plant fluxes and stress
Accommodates off-nadirthermal sensor view angles
Treats soil/plant-atmosphere coupling differences explicitly
Atmosphere-Land Exchange Inverse Model (ALEXI)Atmosphere-Land Exchange Inverse Model (ALEXI)
Anderson et al. (1997)
Time-differential ABL closure
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ALEXI Disaggregation (DisALEXI)ALEXI Disaggregation (DisALEXI)
Regional scale∆TRAD - GOESfc - MODIS
Landscape scaleTRAD - TM, ASTER, MODISfc - TM, ASTER, MODIS
Rsoil
TcTac
Hs
Ts
RaH = Hc + Hs
Rx
Hc
Ta
ABL
Ta
ALEXI DisALEXI5 km
30 m
Tw
o-S
ou
rce M
od
el
TRAD (φ), fc
TRAD,i(φi), fc,i
i
Ra,i
Blending height
Rsoil
TcTac
Hs
Ts
RaH = Hc + Hs
Rx
Hc
TaTa
ABL
Ta Ta
ALEXI DisALEXI5 km
30 m
Tw
o-S
ou
rce M
od
el
TRAD (φ), fc
TRAD,i(φi), fc,i
i
Ra,i
Blending height
Surface temp:Cover fraction:
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SURFACE TEMPERATURESURFACE TEMPERATURE EVAPOTRANSPIRATIONEVAPOTRANSPIRATION
30
35
40
45
0
100
200
300
400
500
600
ALE
XI(G
OE
S Im
ager
)A
LEXI
(GO
ES
Imag
er)
Dis
ALE
XI(L
ands
at)
Dis
ALE
XI(L
ands
at)
Dis
ALE
XI(U
SU
airc
raft)
Dis
ALE
XI(U
SU
airc
raft)
Regional
Regional
Watershed
Watershed
Field scaleField scale
CORN
SOY
ALE
XI(G
OE
S S
ound
er)
ALE
XI(G
OE
S S
ound
er) C
ontinentalC
ontinental
Tem
pera
ture
(C)
Latent Heat (W
m-2)
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… evapotranspiration… evapotranspirationAPPLICATIONSAPPLICATIONS
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AP
RA
PR
MA
YM
AY
JUN
JUN
JUL
JUL
AU
GA
UG
SE
PS
EP
20022002 20032003 20042004
(Wm
-2)
EV
AP
OT
RA
NS
PIR
AT
ION
LowH
igh
(Anderson et al, 2007)
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ALEXI validation sitesALEXI validation sites
SMEX02/05SMEX02/05
SGP97SGP97
BondvilleBondville
Fort PeckFort Peck
Walker BranchWalker Branch
AudubonAudubon Goodwin CreekGoodwin CreekGainesvilleGainesville
EvergladesEverglades
SevilletaSevilletaSMEX04SMEX04BushlandBushland
Black HillsBlack Hills
BARCBARC
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GOES-DERIVED FLUXES (5-10 km)
1000 2000 3000 4000 5000
meters
1000
2000
3000
4000
5000
meters
1000 2000 3000 4000 5000
meters
1000
2000
3000
4000
5000
met
ers
LANDSAT-DISAGGREGATED FLUXES
5000
4000
3000
2000
1000
Validation through disaggregationValidation through disaggregation
tower
sourcefootprint
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Clear-sky fluxes using Landsat thermal (60m)Clear-sky fluxes using Landsat thermal (60m)
• rangeland• pasture• corn• soybean…
0
200
400
600
800
0 200 400 600 800
Tower flux (Wm-2)
Mod
eled
flux
(Wm
-2)
RNETHG
RMSD: 33 Wm-2 (10%)
(Anderson et al, 2007)
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… drought & stress monitoring… drought & stress monitoring
ESI = 1 –ESI = 1 –AETAETPETPET
APPLICATIONSAPPLICATIONS
Evaporative Stress IndexEvaporative Stress Index
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0
10
20
30
40
50
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
Date
Cum
ulat
ive
area
l per
cent
age
Climatological Study: 2002-2005Climatological Study: 2002-2005
Extreme dryExtreme dryExtreme wetExtreme wet
2002 2003 2004Palmer Drought Index - NCDC
• 2002: extreme-severe drought conditions covering 40% of the US in July• 2003: some improvement (10-25% extreme-severe drought coverage) • 2004: extreme drought coverage falls < 5% due to increased late rainfall• 2005: wetter than average in western US, drought in east
2005
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20022002 20032003 20042004 20052005A
PRAPR
MA
YM
AY
JUN
JUN
JUL
JUL
AU
GA
UG
SEP
SEP
DRY WETMONTHLY ESI ANOMALIESMONTHLY ESI ANOMALIES
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APRAPR
MA
YM
AY
JUN
JUN
JUL
JUL
AU
GA
UG
SEP
SEP
∆∆ESIESI ∆∆ZZ20022002
2002WetDry
EvaporativeStress IndexEvaporativeStress Index
2002
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APRAPR
MA
YM
AY
JUN
JUN
JUL
JUL
AU
GA
UG
SEP
SEP
∆∆ESIESI ∆∆ZZ20032003
2003WetDry
EvaporativeStress IndexEvaporativeStress Index
2003
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APRAPR
MA
YM
AY
JUN
JUN
JUL
JUL
AU
GA
UG
SEP
SEP
∆∆ESIESI ∆∆ZZ20042004
2004WetDry
EvaporativeStress IndexEvaporativeStress Index
2004
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APRAPR
MA
YM
AY
JUN
JUN
JUL
JUL
AU
GA
UG
SEP
SEP
∆∆ESIESI ∆∆ZZ20052005
2005WetDry
EvaporativeStress IndexEvaporativeStress Index
2005
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20022002
20032003
20042004
ALEXIALEXI PrecipitationPrecipitation
ESI anomaly Precipitation anomaly (mm)Dry Wet
20052005
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METEOSAT ApplicationMETEOSAT Application
0.6
0.7
0.8
0.9
1
0
100
200
300
400
500
600
EvapotranspirationEvapotranspiration
ESIESI (low)
(high)
LEBRIJA, SPAINLEBRIJA, SPAIN
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EURO ALEXI (coming soon)EURO ALEXI (coming soon)
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Final ObservationsBoth oneBoth one--layer and twolayer and two--layer energy balance models have their merits for layer energy balance models have their merits for providing spatial ETproviding spatial ET
Thermal infrared band very important for estimating plantThermal infrared band very important for estimating plant--soil water soil water conditioncondition
Models need to be further tested in irrigated areas using a combModels need to be further tested in irrigated areas using a combination of flux ination of flux towers for actual ET measurements and water delivery and runoff towers for actual ET measurements and water delivery and runoff measurements for closing the water balancemeasurements for closing the water balance
Further testing and comparison of these models is needed for natFurther testing and comparison of these models is needed for natural, semiural, semi--arid vegetation under water limited conditionsarid vegetation under water limited conditions
Future use of energy balance models in the irrigated agriculturaFuture use of energy balance models in the irrigated agricultural context will l context will depend on the continuity of existing satellites, availability ofdepend on the continuity of existing satellites, availability of thermal imagery thermal imagery from future sensors at appropriate pixel resolutions and scalesfrom future sensors at appropriate pixel resolutions and scales
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THANK YOU!