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 1

2. 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 C X Ku Ka 12h-24h Ku Ka W 6h-18h C X K Ka 13h30-1h30 C (active) 21h30-9h30 L 6h-18h 2 time Aquarius SMAP

3. Inventory of existing products 3  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 4

5. Statistical background Cumulative Density Function (CDF) 5 1) Statistics theoryGeneralCDF matchingCopulas Density or histogram Cumulative density 3.5 0.15 15% of the dataset is under the value 3.5 0 1

6. 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 Pr x,y u xy v Pr x,y u xy v 6 1) Statistics theoryGeneralCDF matchingCopulas

7. CDF matching – Starting assumption CDF matching : u = v Need to model this order copulas Copulas : u = f(v) u v 7 1) Statistics theoryGeneralCDF matchingCopulas Pr x,y u xy v

8. Copulas - Theory Function linking U and V through the joint probability function : 8 1) Statistics theoryGeneralCDF matchingCopulas

9. Copulas – Family examples Clayton Gumbel Frank 9 1) Statistics theoryGeneralCDF matchingCopulas

10. Simulation from copulas t x,y x, u Pr x,y t Pr x,y 10 x, u v1v1 vNvN y1y1 yNyN 1) Statistics theoryGeneralCDF matchingCopulas

11. Examples of Walnut Gulch, Arizona, and Little Washita, Oklahoma, USA 11 Walnut Gulch : South West US Semiarid climate (rainfall: 320mm) Shrubland Little Washita : Great Plains US Sub humid climate (rainfall: 750mm) Cropland 2) Results for 2010PresentationWalnut GulchLittle Washita Jackson et al., 2010

12. 12 RRMSE SMOS0.820.040 VUA0.750.138 Simu by CDF 0.800.054 Simu by Cop 0.770.043 2) Results for 2010PresentationWalnut GulchLittle Washita

13. 13 RRMSE SMOS0.780.049 VUA0.590.148 Simu by CDF 0.710.059 Simu by Cop 0.710.043 2) Results for 2010PresentationWalnut GulchLittle Washita

14. 14 3) Time seriesResults for 2009Little WashitaWalnut Gulch RRMSE VUA0.520.149 Simu by CDF 0.530.069 Simu by Cop 0.580.051 RRMSE VUA0.640.128 Simu by CDF 0.790.076 Simu by Cop 0.750.060

15. 15 3) Time seriesResults for 2009Little WashitaWalnut Gulch o Simulations lower than the original data o CDF matching lower and greater than copulas simulations

16. 16 3) Time seriesResults for 2009Little WashitaWalnut Gulch o Simulations lower than the original data o CDF matching lower and greater than copulas simulations

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) 17

18. Thank you (again) for your attention Any questions ? 18

19. Simulation from copulas Clayton Derivative :Pr ~ U (0,1) Thus : y simulatedmean (y) 19

20. 20 Results for Walnut Gulch, Arizona, USA Mar-Apr-May Jun-Jul-Aug Sep-Oct-Nov Original data Simulation with CDF matching Simulation with copulas R=0.50 RMSE=0.073 R=0.71 RMSE=0.058 R=0.44 RMSE=0.070 R=0.51 RMSE=0.063 R=0.68 RMSE=0.056 R=0.48 RMSE=0.058

21. Results for Little Washita, Oklahoma, USA 21 Mar-Apr-May Jun-Jul-Aug Sep-Oct-Nov Original data Simulation with CDF matching Simulation with copulas R=0.87 RMSE=0.028 R=0.71 RMSE=0.071 R=0.36 RMSE=0.048 R=0.84 RMSE=0.030 R=0.70 RMSE=0.069 R=0.38 RMSE=0.040