Transcript Little Washita

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Constructing a long time series of
soil moisture using SMOS data with
statistics
Leroux Delphine, CESBIO, France
Yann Kerr, CESBIO, France
Eric Wood, Princeton University, USA
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Inventory of existing products
SMAP
C
X
K
Ka
C
X
Ku
Ka
Ku
Ka
W
C
(active)
21h30-9h30
L
6h-18h
Aquarius
SMOS
13h30-1h30
ASCAT
AMSR-E
6h-18h
F15
F14
12h-24h
F13
F11
F8
SMMR
78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11
time
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Inventory of existing products
 Need for a homogeneous level
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Structure
1) Statistics theory
-> 2 methods : CDF matching and copulas
2) Results over 2009 & 2010 and comparison
with in situ measurements
-> comparison between the two sets of simulations
3) Time series from 2002 to 2010
1) Statistics theory
General
CDF matching
Copulas
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Statistical background
• Cumulative Density Function (CDF)
Cumulative density
Density or histogram
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15% of the
dataset is under
the value 3.5
0.15
0
3.5
1) Statistics theory
General
CDF matching
Copulas
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CDF matching - Principle
• CDF matching between 2 variables X and Y
▫ Computation of the 2 CDF : U and V
▫ Set u=v
v
t
Pr
x,y
u
Pr
Pr
y,x
v
u
y
x,y
x
x,y
y
x,y
x
t
1) Statistics theory
General
CDF matching
Copulas
CDF matching – Starting assumption
• CDF matching : u = v
u
Pr
v
v
y
x,y
x
• Need to model this order
• Copulas : u = f(v)
u
copulas
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1) Statistics theory
General
CDF matching
Copulas
Copulas - Theory
• Function linking U and V through the joint
probability function :
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1) Statistics theory
General
CDF matching
Copulas – Family examples
• Clayton
• Gumbel
• Frank
Copulas
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1) Statistics theory
General
CDF matching
Copulas
Simulation from copulas
x, u
t
vN
x, u
x,y
x,y
t
Pr
Pr
x,y
v1
y1 yN
x,y
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2) Results for 2010
Presentation
Walnut Gulch
Little Washita
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Examples of Walnut Gulch, Arizona,
and Little Washita, Oklahoma, USA
Jackson et al., 2010
Walnut Gulch :
• South West US
• Semiarid climate (rainfall: 320mm)
• Shrubland
Little Washita :
• Great Plains US
• Sub humid climate (rainfall: 750mm)
• Cropland
2) Results for 2010
Presentation
Walnut Gulch
Little Washita
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R
RMSE
SMOS
0.82
0.040
VUA
0.75
0.138
Simu
by CDF
0.80
0.054
Simu
by Cop
0.77
0.043
2) Results for 2010
Presentation
Walnut Gulch
Little Washita
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R
RMSE
SMOS
0.78
0.049
VUA
0.59
0.148
Simu
by CDF
0.71
0.059
Simu
by Cop
0.71
0.043
3) Time series
Results for 2009
Walnut Gulch
Little Washita
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R
RMSE
VUA
0.64
0.128
Simu
by CDF
0.79
0.076
Simu
by Cop
0.75
0.060
R
RMSE
VUA
0.52
0.149
Simu
by CDF
0.53
0.069
Simu
by Cop
0.58
0.051
3) Time series
Results for 2009
Walnut Gulch
Little Washita
o Simulations lower than the original data
o CDF matching lower and greater than copulas simulations
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3) Time series
Results for 2009
Walnut Gulch
Little Washita
o Simulations lower than the original data
o CDF matching lower and greater than copulas simulations
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Conclusion
• Many soil moisture products with gaps and different dynamics
• Need to have homogeneous time series for climate purpose
• 2 statistical methods have been presented to rescale VUA soil
moisture at “SMOS level”
▫ Both methods improve the original performances
▫ Copulas method gives better results (RMSE) but is much more
time-consuming than CDF matching
▫ The biggest difference can be seen for low/high SM
• The main goal is to provide a time series from 1978 until now
(further work would be to apply these methods to older satellites)
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Thank you (again) for your
attention
Any questions ?