Constructing a long time series of soil moisture using SMOS data with statistics Leroux Delphine, CESBIO, France Yann Kerr...
Inventory of existing products time Aquarius SMAP 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 ...
Inventory of existing products <ul><li>Need for a homogeneous level </li></ul>
Structure <ul><li>Statistics theory </li></ul><ul><ul><li>-> 2 methods : CDF matching and copulas </li></ul></ul><ul><li>R...
Statistical background <ul><li>Cumulative Density Function (CDF) </li></ul>1) Statistics theory General CDF matching Copul...
CDF matching - Principle <ul><li>CDF matching between 2 variables X and Y </li></ul><ul><ul><li>Computation of the 2 CDF :...
CDF matching – Starting assumption  <ul><li>CDF matching : u = v  </li></ul><ul><li>Need to model this order  copulas </li...
Copulas - Theory <ul><li>Function linking U and V through the joint probability function : </li></ul>1) Statistics theory ...
Copulas – Family examples <ul><li>Clayton </li></ul><ul><li>Gumbel </li></ul><ul><li>Frank </li></ul>1) Statistics theory ...
Simulation from copulas x, u v 1 v N y 1 y N 1) Statistics theory General CDF matching Copulas t x,y x, u Pr x,y t x,y Pr ...
Examples of Walnut Gulch, Arizona, and Little Washita, Oklahoma, USA <ul><li>Walnut Gulch : </li></ul><ul><li>South West U...
2) Results for 2010 Presentation Walnut Gulch Little Washita R RMSE SMOS 0.82 0.040 VUA 0.75 0.138 Simu by CDF 0.80 0.054 ...
2) Results for 2010 Presentation Walnut Gulch Little Washita R RMSE SMOS 0.78 0.049 VUA 0.59 0.148 Simu by CDF 0.71 0.059 ...
3) Time series Results for 2009 Little Washita Walnut Gulch R RMSE VUA 0.52 0.149 Simu by CDF 0.53 0.069 Simu by Cop 0.58 ...
3) Time series Results for 2009 Little Washita Walnut Gulch <ul><li>Simulations lower than the original data </li></ul><ul...
3) Time series Results for 2009 Little Washita Walnut Gulch <ul><li>Simulations lower than the original data </li></ul><ul...
Conclusion <ul><li>Many soil moisture products with gaps and different dynamics </li></ul><ul><li>Need to have homogeneous...
Thank you (again) for your attention Any questions ?
Simulation from copulas <ul><li>Clayton </li></ul>Derivative : Pr ~ U (0,1) Thus : y simulated mean  (y)
Results for Walnut Gulch, Arizona, USA Mar-Apr-May Jun-Jul-Aug Sep-Oct-Nov Original data Simulation with CDF matching Simu...
Results for Little Washita, Oklahoma, USA Mar-Apr-May Jun-Jul-Aug Sep-Oct-Nov Original data Simulation with CDF matching S...
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Constructing a long time series of soil moisture using SMOS data with statistics.ppt

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  • From 1978, many satellites have been launched and soil moisture has been derived from some of them: SMMR, SSM/I, AMSR-E, ASCAT, SMOS, and others like SMAP will be launched in the near future. However, these satellites have different technical differences as the frequency, crossing time, swath that can lead to very different SM retrievals.
  • An example of the gaps that can be observed when we plot the time series of soil moisture : Namib in South Africa. There is a crucial need to build a homogeneous time series As SMOS is the best, SMOS will be used as the reference.
  • Rouge N(3,0.5) Bleu N(8,2)
  • Puisque c’est une fonction de répartition, sa propre distribution suit une loi uniforme sur [0,1] Probabilité conditionnelle
  • Toutes les familles que je présente n’ont qu’un seul paramètre qui permet de gérer à quel point u et v sont liés
  • There will be 2 application examples for 2 sites in the US : Walnut Gulch in Arizona (dry site) and Little Washita in Oklahoma (with more dynamic). We will use 2010 to compute SMOS cdf and choose the copula family in order to simulate an homogeneous time series from 2003 until 2010. The goal is to put VUA at “SMOS level” so that we will be able to simulate VUA at “SMOS level” even when there will not be any SMOS data. We have divided the year into seasons as we except to have different behaviors for each season. Winter will not be treated here because there is not enough points.
  • The three other seasons have been treated separately. At the bottom, scatter plots with the original data VUA vs. SMOS, in green the simulation from the CDF matching and in red from the copulas. No difference during Spring period. Summer and Autumn are only giving different results for high values of SM. Some statistics have been computed for each site. And from the original stats of VUA, we can see a big improvement in the R value but mostly in the RMSE. Here the simulations with copulas are giving very good results in terms of RMSE (almost the same as SMOS).
  • In this example there is a difference in the simulations for the low and high values, especially during Spring and Autumn. Simulations from copulas and from CDF matching give the same R value but the RMSE is much better for the copulas.
  • We have ground measurements for 2009 as well so it has been possible to compute some statistics with the simulations. Once again here, the R value is almost the same for both methods but the RMSE is much lower with the simulations from copulas method.
  • Homogeneous time series from 2003 to 2010 Green higher for high values and lower for low values A long time series would be interesting to validate.
  • Homogeneous time series from 2003 to 2010
  • Possible question : how do you choose the best copula family that fits your data ? By a Bayesian approach where we compute the probability that “this” family has been able to simulate our original dataset.
  • Constructing a long time series of soil moisture using SMOS data with statistics.ppt

    1. 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. 2. Inventory of existing products time Aquarius SMAP 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
    3. 3. Inventory of existing products <ul><li>Need for a homogeneous level </li></ul>
    4. 4. Structure <ul><li>Statistics theory </li></ul><ul><ul><li>-> 2 methods : CDF matching and copulas </li></ul></ul><ul><li>Results over 2009 & 2010 and comparison with in situ measurements </li></ul><ul><ul><li>-> comparison between the two sets of simulations </li></ul></ul><ul><li>Time series from 2002 to 2010 </li></ul>
    5. 5. Statistical background <ul><li>Cumulative Density Function (CDF) </li></ul>1) Statistics theory General CDF matching Copulas 0 1 Density or histogram Cumulative density 3.5 0.15 15% of the dataset is under the value 3.5
    6. 6. CDF matching - Principle <ul><li>CDF matching between 2 variables X and Y </li></ul><ul><ul><li>Computation of the 2 CDF : U and V </li></ul></ul><ul><ul><li>Set u=v </li></ul></ul>u x y v 1) Statistics theory General CDF matching Copulas t y, x t x,y x,y Pr Pr x,y Pr x,y u x y v
    7. 7. CDF matching – Starting assumption <ul><li>CDF matching : u = v </li></ul><ul><li>Need to model this order copulas </li></ul><ul><li>Copulas : u = f(v) </li></ul>1) Statistics theory General CDF matching Copulas u v Pr x,y u x y v
    8. 8. Copulas - Theory <ul><li>Function linking U and V through the joint probability function : </li></ul>1) Statistics theory General CDF matching Copulas
    9. 9. Copulas – Family examples <ul><li>Clayton </li></ul><ul><li>Gumbel </li></ul><ul><li>Frank </li></ul>1) Statistics theory General CDF matching Copulas
    10. 10. Simulation from copulas x, u v 1 v N y 1 y N 1) Statistics theory General CDF matching Copulas t x,y x, u Pr x,y t x,y Pr x,y
    11. 11. Examples of Walnut Gulch, Arizona, and Little Washita, Oklahoma, USA <ul><li>Walnut Gulch : </li></ul><ul><li>South West US </li></ul><ul><li>Semiarid climate (rainfall: 320mm) </li></ul><ul><li>Shrubland </li></ul><ul><li>Little Washita : </li></ul><ul><li>Great Plains US </li></ul><ul><li>Sub humid climate (rainfall: 750mm) </li></ul><ul><li>Cropland </li></ul>2) Results for 2010 Presentation Walnut Gulch Little Washita Jackson et al., 2010
    12. 12. 2) Results for 2010 Presentation Walnut Gulch Little Washita 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
    13. 13. 2) Results for 2010 Presentation Walnut Gulch Little Washita 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
    14. 14. 3) Time series Results for 2009 Little Washita Walnut 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
    15. 15. 3) Time series Results for 2009 Little Washita Walnut Gulch <ul><li>Simulations lower than the original data </li></ul><ul><li>CDF matching lower and greater than copulas simulations </li></ul>
    16. 16. 3) Time series Results for 2009 Little Washita Walnut Gulch <ul><li>Simulations lower than the original data </li></ul><ul><li>CDF matching lower and greater than copulas simulations </li></ul>
    17. 17. Conclusion <ul><li>Many soil moisture products with gaps and different dynamics </li></ul><ul><li>Need to have homogeneous time series for climate purpose </li></ul><ul><li>2 statistical methods have been presented to rescale VUA soil moisture at “SMOS level” </li></ul><ul><ul><li>Both methods improve the original performances </li></ul></ul><ul><ul><li>Copulas method gives better results (RMSE) but is much more time-consuming than CDF matching </li></ul></ul><ul><ul><li>The biggest difference can be seen for low/high SM </li></ul></ul><ul><li>The main goal is to provide a time series from 1978 until now (further work would be to apply these methods to older satellites) </li></ul>
    18. 18. Thank you (again) for your attention Any questions ?
    19. 19. Simulation from copulas <ul><li>Clayton </li></ul>Derivative : Pr ~ U (0,1) Thus : y simulated mean (y)
    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. 21. Results for Little Washita, Oklahoma, USA 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

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