constructing a long time series of soil moisture using smos data with statistics leroux delphine,...
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Inventory of existing products 3 Need for a homogeneous levelTRANSCRIPT
Constructing a long time series of soil moisture using SMOS
data with statistics
Leroux Delphine, CESBIO, FranceYann Kerr, CESBIO, FranceEric Wood, Princeton University, USA
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Inventory of existing products
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
SMMRF8
F11
F13
F14
F15
AMSR-E
ASCAT
SMOS
CX
KuKa
12h-24h
KuKaW
6h-18h
CXKKa
13h30-1h30
C (active)
21h30-9h30
L6h-18h
2
time
Aquarius
SMAP
Inventory of existing products3
Need for a homogeneous level
Structure1) 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
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Statistical background• Cumulative Density Function (CDF)
51) Statistics theory General CDF matching Copulas
Density or histogram Cumulative density
3.5
0.15
15% of the dataset is under the value 3.5
0
1
CDF matching - Principle• CDF matching between 2 variables X and Y
▫ Computation of the 2 CDF : U and V▫ Set u=v
t
y,x
t
x,y
x,y
PrPr
x,y
u
xy
v
Pr
x,y
u
xy
v
61) Statistics theory General CDF matching Copulas
CDF matching – Starting assumption • CDF matching : u = v
• Need to model this order copulas• Copulas : u = f(v)
u
v
71) Statistics theory General CDF matching Copulas
Pr
x,y
u
xy
v
Copulas - Theory
•Function linking U and V through the joint probability function :
81) Statistics theory General CDF matching Copulas
Copulas – Family examples•Clayton
•Gumbel
•Frank
91) Statistics theory General CDF matching Copulas
Simulation from copulas
t
x,y
x, u
Pr
x,y
t
x,y
Pr
x,y
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x, u
v1
vN
y1yN
1) Statistics theory General CDF matching Copulas
Examples of Walnut Gulch, Arizona, and Little Washita, Oklahoma, USA
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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
Jackson et al., 2010
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R RMSE
SMOS 0.82 0.040VUA 0.75 0.138Simu 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 0.049VUA 0.59 0.148Simu by CDF
0.71 0.059
Simu by Cop
0.71 0.043
2) Results for 2010
Presentation Walnut Gulch Little Washita
143) Time series Results for 2009 Little WashitaWalnut Gulch
R RMSE
VUA 0.52 0.149Simu by CDF
0.53 0.069
Simu by Cop
0.58 0.051
R RMSE
VUA 0.64 0.128Simu by CDF
0.79 0.076
Simu by Cop
0.75 0.060
153) Time series Results for 2009 Little WashitaWalnut Gulch
o Simulations lower than the original data
o CDF matching lower and greater than copulas simulations
163) Time series Results for 2009 Little WashitaWalnut Gulch
o Simulations lower than the original data
o CDF matching lower and greater than copulas simulations
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 ?
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