13 Marzo 2008 Univ. Nac. Agraria La Molina 1 Issues in SEB modeling with multi-spectral image data: vertical vs. horizontal scales reference land surface states (« wet », « dry ») Massimo Menenti 1,2 , Jerome Colin 1 and Li Jia 3 1 Laboratoire des Sciences de l’Image, de l’Informatique et de la Télédétection - LSIIT Illkirch, France 2 Istituto per I Sistemi Agricoli e Forestali del Mediterraneo – ISAFOM Ercolano (NA), Italy 3 ALTERRA Wageningen University and Research Centre, Wageningen, The Netherlands
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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
13 Marzo 2008 Univ. Nac. Agraria La Molina 3
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
13 Marzo 2008 Univ. Nac. Agraria La Molina 4
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)
13 Marzo 2008 Univ. Nac. Agraria La Molina 5
Vertical vs. Horizontal Scales
13 Marzo 2008 Univ. Nac. Agraria La Molina 6
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).
13 Marzo 2008 Univ. Nac. Agraria La Molina 7
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
13 Marzo 2008 Univ. Nac. Agraria La Molina 9
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
13 Marzo 2008 Univ. Nac. Agraria La Molina 11
Land Surface Temperature : Definitions
13 Marzo 2008 Univ. Nac. Agraria La Molina 12
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
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
13 Marzo 2008 Univ. Nac. Agraria La Molina 14
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
13 Marzo 2008 Univ. Nac. Agraria La Molina 15
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
13 Marzo 2008 Univ. Nac. Agraria La Molina 16
LST of 3D - Structured Heterogeneous Targets
13 Marzo 2008 Univ. Nac. Agraria La Molina 17
3D Land Targets
13 Marzo 2008 Univ. Nac. Agraria La Molina 18
LST of 3D Structured Heterogeneous Targets : Simple model
A 2-components mixture model can describe directional emittance
Ph : hemispheric gap frequency (canopy trasmittance)
)()()1()1(*gvgvhgg TBTBP εεεε −−+=
)()()1()1(*vgsvvvvv TBTBεεβεεαεε −+−+=
13 Marzo 2008 Univ. Nac. Agraria La Molina 19
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)
13 Marzo 2008 Univ. Nac. Agraria La Molina 20
Constraints Based on Correlation of LST and Albedo
13 Marzo 2008 Univ. Nac. Agraria La Molina 21
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?
13 Marzo 2008 Univ. Nac. Agraria La Molina 22
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
13 Marzo 2008 Univ. Nac. Agraria La Molina 23
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
13 Marzo 2008 Univ. Nac. Agraria La Molina 24
Dominant pattern in land surface response to absorbed irradiance
13 Marzo 2008 Univ. Nac. Agraria La Molina 25
Does it always work?
Alpilles6/6/1997
Alpilles12/3/1997
EFEDA, SpainSummer 1991
13 Marzo 2008 Univ. Nac. Agraria La Molina 26
Empirical dry – wet references
13 Marzo 2008 Univ. Nac. Agraria La Molina 27
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
13 Marzo 2008 Univ. Nac. Agraria La Molina 28
Barrax: (Tmax-Tmin) vs. sample size
Barrax TM multi-temporal analysis
(Tmax-Tmin) reaches a steady value for a sample >400 km2