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

SMMR

F8

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 products

3

Need for a homogeneous level

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

4

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

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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

t

y,x

t

x,y

x,y

Pr

Pr

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

10

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 0.040

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

2) Results for 2010

Presentation Walnut Gulch Little Washita

143) Time series Results for 2009 Little WashitaWalnut Gulch

R RMSE

VUA 0.52 0.149

Simu by CDF

0.53 0.069

Simu by Cop

0.58 0.051

R RMSE

VUA 0.64 0.128

Simu 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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