Review of 2-Source Surface Energy Balance Models and … · 2008. 3. 27. · Review of 2-Source Surface Energy Balance Models and Comparison of 1-source vs. 2 source Approaches Christopher

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

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

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

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

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

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)

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

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

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


θθ

HSHS

HCHC


RS

RA

RX

TATA

TCTC

TSTS

ABL closure

θθ

HSHS

HCHC


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

Two-Source Energy Balance Model (TSEB)Two-Source Energy Balance Model (TSEB)

The

rmal

Vis

ible

Nadir Off-nadir

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)

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

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

Two-Source ModelNormal et al (1995)Kustas et al (1999)Li et al (2005)


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

SEBAL/METRIC ModelsBastiaansen et al (1995)Allen et al. (2007)


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?

Modeling Environment (SETMI) Application code written in Visual Basic within ArcGIS 9.1

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

Analysis upwind rectangles for averaging the estimated energy balance fluxes

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)

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

Land use/crop cover for region obtained from classification of and early satellite image

Energy Balance Model Input Data and Output Settings

Kcrf Model Input Settings and Data

From FAO56:

Kcrf Model Output Settings

Output Temporal Run

Results Spatial Output: Regional Daily ET on July 1, 2002

(Spatial Model Output using the OLEM)

Actual ET (mm/day)

-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)


Results: Energy Balance Models(closure forced with the residual method)

Sensible Heat Flux (H)

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


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

)


Latent Heat Fluxes

50

150

250

50 150 250

Observed daily LE (W m-2)

OLE

M p

redi

cted

dai

ly L

E (W

m-2


50

150

250

50 150 250

Observed daily LE (W m-2)

TSM

pre

dict

ed d

aily

LE

(W m

-2


Daily Evapotranspiration Integrated Using the Evaporative Fraction


θθ

HSHS

HCHC


RS

RA

RX

TATA

TCTC

TSTS

ABL closure

θθ

HSHS

HCHC


RS

RA

RX

TATA

TCTC

TSTS

ABL closure





PROBLEM: Air temperature boundary conditionPROBLEM: Air temperature boundary condition


θθ

HSHS

HCHC


RS

RA

RX

TATA

TCTC

TSTS

ABL closure

θθ

HSHS

HCHC


RS

RA

RX

TATA

TCTC

TSTS

ABL closure





Atmosphere-Land Exchange Inverse Model (ALEXI)Atmosphere-Land Exchange Inverse Model (ALEXI)

Anderson et al. (1997)

Time-differential ABL closure

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:

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)

… evapotranspiration… evapotranspirationAPPLICATIONSAPPLICATIONS

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)

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

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

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)

… drought & stress monitoring… drought & stress monitoring

ESI = 1 –ESI = 1 –AETAETPETPET

APPLICATIONSAPPLICATIONS

Evaporative Stress IndexEvaporative Stress Index

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

20022002 20032003 20042004 20052005A

PRAPR

MA

YM

AY

JUN

JUN

JUL

JUL

AU

GA

UG

SEP

SEP

DRY WETMONTHLY ESI ANOMALIESMONTHLY ESI ANOMALIES

APRAPR

MA

YM

AY

JUN

JUN

JUL

JUL

AU

GA

UG

SEP

SEP

∆∆ESIESI ∆∆ZZ20022002

2002WetDry

EvaporativeStress IndexEvaporativeStress Index

2002

APRAPR

MA

YM

AY

JUN

JUN

JUL

JUL

AU

GA

UG

SEP

SEP

∆∆ESIESI ∆∆ZZ20032003

2003WetDry


2003

APRAPR

MA

YM

AY

JUN

JUN

JUL

JUL

AU

GA

UG

SEP

SEP

∆∆ESIESI ∆∆ZZ20042004

2004WetDry


2004

APRAPR

MA

YM

AY

JUN

JUN

JUL

JUL

AU

GA

UG

SEP

SEP

∆∆ESIESI ∆∆ZZ20052005

2005WetDry


2005

20022002

20032003

20042004

ALEXIALEXI PrecipitationPrecipitation

ESI anomaly Precipitation anomaly (mm)Dry Wet

20052005

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

EURO ALEXI (coming soon)EURO ALEXI (coming soon)

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

THANK YOU!

Documents

Review of 2-Source Surface Energy Balance Models and … · 2008. 3. 27. · Review of 2-Source Surface Energy Balance Models and Comparison of 1-source vs. 2 source Approaches Christopher