issues in seb modeling with multi-spectral image data...

13 Marzo 2008 Univ. Nac. Agraria La Molina 1

Issues in SEB modeling with multi-spectral image data:

vertical vs. horizontal scalesreference land surface states (« wet », « dry »)

Massimo Menenti1,2, Jerome Colin1 and Li Jia3

1Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection - LSIIT Illkirch, France2Istituto per I Sistemi Agricoli e Forestali del Mediterraneo – ISAFOM Ercolano (NA), Italy3ALTERRA Wageningen University and Research Centre, Wageningen, The Netherlands

2

Evaporations

γρ

λ+∆

−+−∆=

−10 )()( espan

p

reecGRE

)1()()(

1

10

maxmin

−

−

++∆−+−∆

=ei

espan

rrreecGR

Eγ

ρλ

1 5

ri= 0

ri �∞

Potential evaporation

Maximum Evaporation

Actual evaporation

Optimal water supply low stomatal resistance

ri≥ rimin

ri= rimin

Available water

Limited water supplyWater stress

+

-

Climatic water requirements

)1()()(

1

10

−

−

++∆

−+−∆=

ei

espana rr

reecGRE

γρ

λ


Limiting cases and additional constraints on SEB

Evaporation controlled vs. radiation controlled T0=T0(r0)

constrT

=∂∂

0

0 0

0

0 =∂∂

rT

Empirical dry – wet references

SEBAL, S-SEBI

δTmax and δTmin from full combination equation

SEBI, SEBS

Reference Ta cannot be local: applies to an area much larger than the length-scale of land heterogeneity

MS-SEBS


Outstanding Issues

• LE scales with Tsurf IF radiative and convective forcing is normalized first

• Additional constraints needed to solve SEB + parameterizations

• Iterative procedures lead to multiple solutions

• Inversion of detailed models abandoned many years ago ⇒ new algorithms + easier access to computing power ⇒ LUT-s may be worth a second life

• Additional equations by segmenting images and assuming some parameters (e.g. ra) constant within the segment

• Add experimental constraints by using limiting cases (reference system states)

• Dry and wet reference states assumed to exist within image (SEBAL)

• Dry and wet reference states evaluated from theory (SEBI ⇒ SEBS ⇒MSSEBS)


Vertical vs. Horizontal Scales


Atmospheric Boundary Layer

Large Eddy Simulation of water vapour concentration in the Convective Boundary Layer over a domain of 10 km x 10 km at a horizontal spatial resolution of 25 m: left) surface; right) 3200 m (courtesy of Siebersma, KNMI).


RS heat flux density -algorithms

• SEBAL (Bastiaanssen, 1995)

• SEBI / SEBS (Menenti & Choudhury, 1993; Su et al, 2000)

• Dual - view angle measurements of surface temperature (Menenti et al, 2001)

temperature

albe

do

LE ≈ 0

H ≈ 0

pbl-temp

obs

8

MSSEBS : a multi-scale approach• MSSEBS : Multi-Scale Surface Energy Balance System

Grid size depends on inherent spatial scales of land surface and CBL: Surface properties: ~30m

Convective Boundary Layer : ~10.hCLA

3 5


Observations of surface temperature of soil and foliage elements

A

10 15 20 25 30 350

5

10

15

20

11 April, 13:00, s50

Freq

uenc

y ( %

)

Brightness temperature ( oC )

10 15 20 25 30 350

5

10

15

2011 April, 10:30, s50

Freq

uenc

y ( %

)

Brightness temperature ( oC )

Photosynthesis depends on leaf temperature

Soil respiration depends on soil temperature

MSSEBS Majadas del Titar

Why horizontal CBL and land surface scales MUST

be different


Land Surface Temperature : Definitions


LST of Flat Homogeneous Targets

• Brightness Temperature: A descriptive measure of radiation in terms of the temperature of a hypothetical blackbody emitting an identical amount of radiation at the same wavelength.

• Brightness Temperature: The Planck temperature associated with the radiance for a given wavelength.

Brightness Temperature

Radiometric Temperature

• Radiometric temperature: The temperature associated with the Planck function divided by spectral emissivity for a given wavelength

• Radiometric temperature: The temperature of a blackbody emitting a radiance equal to measured radiance for a given gray body divided by spectral emissivity for a given wavelength

( )srTBR λλλ ε=

⎥⎦

⎤⎢⎣

⎡= −

λ

λ

εR

BTsr1


Spectral emissivity of land targets

0.4

0.5

0.6

0.7

0.8

0.9

1

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14Wavelength (um-1)

Emis

sivi

ty

Dark grayish brow n silty loamDark brow n f ine sandy loamBrow n sandy loamBrow n silty loamDark yellow ish brow n silty clayReddish brow n fine sandy loam

0.85

0.87

0.89

0.91

0.93

0.95

0.97

0.99

8 9 10 11 12 13 14

Wavelength (um-1)

emis

sivi

ty Dark grayish brow n silty loam

Dark brow n f ine sandy loam

Brow n sandy loam

Brow n silty loam

Dark yellow ish brow n silty clay

Reddish brow n f ine sandy loam

Spectral variability large in 8 – 10 µm range

Spectral variability limited in 10 –12 µm range

Good for radiometric measurements of LST

All terrestrial targets except deep water are grey bodies = ε < 1


Thermal exitance of a soil – foliage system

∑

=

=N

kkk

T SRR1

λλ

RT : total radiance emitted by soil and leaves

Rλk : radiance emitted by element k (soil or leaves)

Sk : k-element of soil – foliage system

Radiative interactions of soil and leaves + target with atmosphere

Rλk : radiance emitted by element k

R’λk : radiance reflected by element k

R ↓at ↑: atmospheric radiance reflected by the elements

R ↓at ↑′: multiple scattering of atmospheric radiance reflected by the elements

[ ] [ ] ′↑+↑+′+= ↓↓

==∑∑ atat

1k

1k RRSRSRR

N

kk

N

kk

Tλλλ

LST of flat heterogeneous targets - I


LST of flat heterogeneous targets - II

↓−+= λλλλλ εε atkkskk RTBR )1()(

↓

==

⎟⎠

⎞⎜⎝

⎛−+= ∑∑ λλλλλ εε at

N

kkk

N

kkskk

T RSSTBR11

1)(

element

Target (N elements)

effective emissivity

effective surface radiometric temperature

⎥⎥⎦

⎤

⎢⎢⎣

⎡= ∑ =−

*11*

)(

λ

λλλ ε

εN

k kkskrs

STBBT

To get

↓−+= λλλλλ εε atrsT RTBR )1()( ***

ελk: spectral emissivity of element k

Tsk: surface temperature of element k

R↓atλ : hemispherical spectral

atmospheric radiance

∑

=

=N

kkkS

1

*λλ εε Equations including leaf-leaf

and soil-leaf interactions too complicated!

Simple model proposed later


LST of 3D - Structured Heterogeneous Targets


3D Land Targets


LST of 3D Structured Heterogeneous Targets : Simple model

A 2-components mixture model can describe directional emittance

εv , εg : foliage, soil spectral emissivities

Tv, Tg : foliage, soil temperatures

f : fractional coverage of foliage

[ ] ( ) [ ] ( )ggvvb TBfTBfTB λλλ εθεθθ )(1()()(0 −+=

taking soil – foliage interactions into account:

[ ] ( ) [ ] ( )ggvvb TBfTBfTB λλλ εθεθθ **0 )(1()()( −+=

ε*g : effective soil emissivity

ε*v : effective foliage emissivity

Ph : hemispheric gap frequency (canopy trasmittance)

)()()1()1(*gvgvhgg TBTBP εεεε −−+=

)()()1()1(*vgsvvvvv TBTBεεβεεαεε −+−+=


Airborne Multi-Angular TIR imaging radiometer

Foliage (left) and soil (right) component temperatures determined from AMTIS multi-angular measurements of exitance at 4200m height; Shunyi experiment, China, April 2001.(after Liu et al., 2002)


Constraints Based on Correlation of LST and Albedo


What do data tell us about SEB?

Two distinct regimes:Excess energy increases with

decreasing evaporation

Excess energy increases less than absorbed irradiance decreases

Land surface response to absorbed irradiance

How does this observation help us?


Evaporation controlled vs. radiation controlled T0=T0(r0)

⎥⎦

⎤⎢⎣

⎡∂∂

−∂∂

−∂∂

−∂∂

=∂∂

↓000

0

0

*0 1

TE

TH

TG

TL

KTr

o

λ

⎥⎦

⎤⎢⎣

⎡∂∂

−∂∂

−∂∂

=∂∂

↓00

0

0

*0 1

TH

TG

TL

KTr

o

dry

ah

pa

rc

TH ρ

=∂∂

0

Radiation controlled δλE/δT0 ≅ 0 does not imply λE ≅ 0

0

00

1 TrT

cr

cTH

dryahBpadry

ah

pa

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂∂

+=∂∂ ρ

ρ

Radiation controlled δλE/δT0 ≅ 0

First implementation of SEBAL


Absorbed irradiance and dissipation of excess energy

Alpilles, FranceMarch – April 1997

Hei He Basin, China 9/7/1991

Quattara, Egypt7/8/1986 13/11/1987


Dominant pattern in land surface response to absorbed irradiance


Does it always work?

Alpilles6/6/1997

Alpilles12/3/1997

EFEDA, SpainSummer 1991


Empirical dry – wet references


The Simplified Surface Energy Balance Index (S - SEBI )

10

20

30

40

50

60

0 0.2 0.4 0.6 0.8 1

Surface reflectance (-)

Sur

face

tem

pera

ture

(o C)

mean temperature

T H

λE max (r 0)

H max (r 0)

T 0

T λE

0

50

100

150

200

250

0 50 100 150 200 250

H [S-SEBI] (W/m2)

H [m

easu

red]

(W/m

2)

eddy correlation

bowen ratio

scintillometer

Menenti and Choudhury, 1993; Roerink et al., 1999


Barrax: (Tmax-Tmin) vs. sample size

Barrax TM multi-temporal analysis

(Tmax-Tmin) reaches a steady value for a sample >400 km2

Seasonality is evident

km2 km2

km2 km2

[A]Tmin=283.7Tmax=321.0

[B]Tmin=288.6Tmax=318.7

[D]Tmin=283.5Tmax=319.9

[C]Tmin=283.5Tmax=319.7

0 10 km

[A] Tmin=283.7;Tmax=321.0 [B] Tmin=288.6;Tmax=318.7

[C] Tmin=283.5;Tmax=319.7 [D] Tmin=283.5;Tmax=319.9

LST, Barrax, 2003-05-20

(K)

0 2 6 km4


δTmax and δTmin from full combination equation

SEBI = Surface Energy Balance Index (Menenti and Choudhury, 1993)

32

Bounds on (T0-Ta)

ei

spaniear rr

eecGRrrTT

//1/)()]/))([(

)( 00 +∆+

−−−+=−

γγρ

)(lim 00 arrTT

i

−→

0GRH n −≈

“Wet” bound “Dry” bound

1 5

0GRE n −≈λ )(lim 0 arrTT

i

−∞→

⎟⎟⎠

⎞⎜⎜⎝

⎛ ∆+⎟

⎟⎠

⎞⎜⎜⎝

⎛ −−

−=−

yee

cGR

rTT s

pa

newwr 1/)( 0

0 γρ

pa

neddr c

GRrTT

ρ0

0 )(−

=−


SEBI definitions

)r()T-T(

-)r(

)T-T()r(

)T-T(-

r)T-T(

SEBI

we

wa0

de

da0

we

wa0

e

a0

=

Menenti and Choudhury (1993)

Reference height = PBL top or blending height

Ta = potential air temperature

SEBI

EE

p

a −= 1λλ


SEBI quasi-linear dry and wet reference states


SEBI from field measurements

-0.4

-0.2

0

0.2

0.4

0.6

0.17 0.18 0.19 0.2 0.21 0.22

albedo

Nor

mor

lized

(T0

- Ta)

(K /

(s m

-1))

Wet conditionActualDry condition

-100

0

100

200

300

400

500

600

09:00 09:20 09:32 09:40 12:00 12:20 12:48 16:14 17:00

Hour(UTC)

Ener

gy fl

ux (

W m

-2)

Rn G H_obsH_sebi LE_obs LE_sebi

SEBI

Flux densities

200

250

300

350

200 250 300 350

LE obsevation ( W m-2 )

LE e

stim

atio

n by

SE

BI (

W m

-2 )

RMSD = 17.4 W m-2

Colmar, sugar beet: SEBI estimates vs. field measurements

RMSD = 17.4 Wm-2

SEBI = Surface Energy Balance Index (Menenti and Choudhury, 1993)


From SEBI to LE - map

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 0.05 0.1 0.15 0.2 0.25

albedo

Nor

mal

ized

(T0-

Ta) (

K/(s

m-1

) )Wet boundaryActualDry boundary

Colmar sugarbeet

Fallow

Sugar beet

Bare soil

maizDistribution of LE at Colmar sub-site; cross indicates location of field measurements

normalized (T0 – Ta) versus surface albedo; airborne HYMAP, DAIS, Colmar, France 1998

Wm-2

LE


SEBS Core Modules

Boundary Layer Similarity Theory

Roughness for Heat Transfer

Surface Energy Balance Index

Meteorological Data

Boundary Layer Variables

Remote Sensing Data

VIS

NIR TIR

Input Output

EvaporativeFraction

Turbulence Heat Fluxes

Actual Evaporation

SEBS - The Surface Energy Balance SystemSu et al., 2000


Regional to continental: SEBS Data Requirements

Surface temperature (K) ATSR

Surface albedo (–) ATSR

NDVI (–) ATSR

Fractional vegetation cover (–) ATSR

PBL depth (m) NWP-RACMO

PBL pressure (Pa) RACMO

PBL potential temperature (K) RACMO

PBL speci.c humidity (%) RACMO

PBL wind speed (m/s) RACMOChannel Central wavelength 50% band wid

(mm) (mm)1 * 12.0 11.60-12.502 * 11.0 10.52-11.333 3.7 3.47-3.904 1.6 1.575-1.6425 * 0.87 0.853-0.8756 * 0.65 0.647-0.6697 0.55 0.543-0.565

Along Track Scanning Radiometer (ATSR)channels


Spain: validation with scintillometers

Location of scintillometer measurements sites

Transmitter Receiver Surface Site Location Height

(m) Location Height

(m)

Distance between transmitter and

receiver (m) Characteristics

Tomelloso 39°07.357′N

2°55.314′W

4.56 39°07.653′N

2°55.951′W

4.15 1070 Dry vineyard

Lleida 41°32.644′N

0°51.644′E

39 41°34.962′N

0°52.444′E

45 4440 Small scale irrigation area with fruit trees, alfalfa

Badajoz 38°55.697′N

6°36.590′W

68 38°56.298′N

6°40.141′W

56 5250 Large scale irrigation area with wheat, corn, alfalfa, lettuce, olives, beans, tomatoes.

Characteristics of scintillometer experimental sites in Spain.

Jia et al., 2003


Sensible heat flux: SEBI vs. scintillometers

100 150 200 250 300 350

100

150

200

250

300

350

H e

stim

ated

by

SE

BS

(W m

-2)

H observed by LAS (W m-2)

Tomelloso Lleida Badajoz

SEBI (SEBS version)

ATSR-2: surface temperature, albedoand NDVI

vertical error bars = standard deviation over pixels along path

horizontal error bars = error LAS measurements


SEBI diagram: Thematic Mapper Barrax


AATSR Spain 1999

Tomelloso

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

N

orm

aliz

ed te

mpe

ratu

re d

iffer

ence

(o C/(s

m-1))

albedo

Tomelloso13-04-1999

Dry limit (T0-Ta)/re Wet limit

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Nor

mal

ized

tem

pera

ture

diff

eren

ce (o C

/(s m

-1))

albedo

Tomelloso06-06-1999


0 .0 5 0 .10 0 .1 5 0 .2 0 0 .25 0 .3 0 0 .3 5 0 .4 0-0 .1

0 .0

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

Nor

mal

ized

tem

pera

ture

diff

eren

ce (o C

/(s m

-1))

a lbe d o

T om e llo so 19 -0 6 -1 99 9

D ry lim it (T 0-T a)/re W e t lim it

0 .0 5 0 .10 0 .15 0 .2 0 0 .2 5 0 .3 0 0 .3 5 0 .40-0 .1

0 .0

0 .1

0 .2

0 .3

0 .4

0 .5

0 .6

Nor

mal

ized

tem

pera

ture

diff

eren

ce (o C

/(s m

-1))

a lb e d o

T om e llo so 2 8 -0 8 -1 99 9

D ry lim it (T 0-T a)/re W e t lim it

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Nor

mal

ized

tem

pera

ture

diff

erre

nce

(o C/(s

m-1))

albedo

Tomelloso 16-09-1999

Dry limit (T

0-t

a)/r

e Wet limit

050

100150200250300350400450500

70 80 90 100

110

120

130

140

150

160

170

180

190

200

210

220

230

240

250

260

270

DOY

prec

ipita

tion

(mm

)

Tomelloso, March - September 1999

DOY 103 DOY 157

DOY 170 DOY 240

DOY 259

Precipitation


AATSR Spain 1999

Lleida

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

N

orm

aliz

ed te

mpe

ratu

re d

iffer

ence

(o C/(s

m-1))

albedo

Lleida 15-07-1999

Dry limit (T

0-T

a)/r

e Wet limit

0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Nor

mal

ized

tem

pera

ture

diff

eren

ce (o C

/(s m

-1))

albedo

Lleida 21-07-1999


0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Nor

mal

ized

tem

pera

ture

diff

eren

ce (o C

/(s m

-1))

albedo

Lleida 29-09-1999

Dry limit (T

0-T

a)/r

e Wet limit

0

10

20

30

40

50

60

181 186 191 196 201 206 211 246 251 256 261 266 271

DOY

Prec

ipita

tion

(mm

)

Lleida, July and September, 1999

Precipitation

DOY 196

DOY 202 DOY 272

44

MSSEBS : a multi-scale approach• MSSEBS : Multi-Scale Surface Energy Balance System

Grid size depends on inherent spatial scales of land surface and CBL: Surface properties: ~30m

Convective Boundary Layer : ~10.hCLA

3 5

Colin, 2006


Barrax: Actual evaporationMSSEBS+TM

46

Estimated RMSE on MSSEBS resultsensemble simulations

5

15 juillet 2003 : évaporation réelle et incertitude par parcelle


The added value of CNR-ISAFOM and ULP/LSIIT-TRIO


SEB + structure: Majadas del Titar

Irrigation 12 hours ahead of flight

Multi spectral imagers + fluxes = SkyArrowISAFOM

Laser altimeter = ULP/LSIIT


Inputs

Satellite dataMulti-angular and multi-spectral

Inputs

Meteorological datainversion of Trad

single-source model H, LE

Z0m

Retrieval of Tv and Ts

Dual-source model

Parameterizationof kB-1

Framework of energy balance study using satellite measurements


What next

Dual source vssingle source

Very high resolution water use indicators

Land surface state and water availabilityΛ

issues in seb modeling with multi-spectral image data...

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