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1 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 2 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 3 Inventory of existing products Need for a homogeneous level 4 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 5 Statistical background • Cumulative Density Function (CDF) Cumulative density Density or histogram 1 15% of the dataset is under the value 3.5 0.15 0 3.5 1) Statistics theory General CDF matching Copulas 6 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 7 1) Statistics theory General CDF matching Copulas Copulas - Theory • Function linking U and V through the joint probability function : 8 1) Statistics theory General CDF matching Copulas – Family examples • Clayton • Gumbel • Frank Copulas 9 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 10 2) Results for 2010 Presentation Walnut Gulch Little Washita 11 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 12 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 13 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 14 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 15 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 16 17 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) 18 Thank you (again) for your attention Any questions ?