1. Modeling Errors in Satellite Data Yudong Tian University of Maryland & NASA/GSFC http://sigma.umd.edu Sponsored by NASA ESDR-ERR Program

2. Optimal combination of independent observations (or how human knowledge grows) 2 Information content

3. “Conservation of Information Content” 3

4. Why uncertainty quantification is always needed 4 Information content

5. 5 1. Most commonly, subconsciously used error model: T i : truth, error free. X i : measurements, b: systematic error (bias) 2. A more general additive error model: The additive error model

6. 6 A nonlinear multiplicative measurement error model: T i : truth, error free. X i : measurements With a logarithm transformation, the model is now a linear, additive error model, with three parameters: A=log(α), B=β, x i =log(X i ), t i =log(T i ) The multiplicative error model

7. 7 Correct error model is critical in quantifying uncertainty TiTi XiXi TiTi XiXi TiTi XiXi

8. 8 Additive model does not have a constant variance

9. 9 Additive error model: why variance is not constant? -- systematic errors leaking into random errors

10. 10 The multiplicative error model predicts better

11. 11 Clean separation of systematic and random errors More appropriate for measurements with several orders of magnitude variability Good predictive skills Tian et al., 2012: Error modeling for daily precipitation measurements: additive or multiplicative? to be submitted to Geophys. Rev. Lett. The multiplicative error model has clear advantages

12. Spatial distribution of the model parameters 12 TMI AMSR-E F16 F17 A B σ(random error)

13. 13 Probability distribution of the model parameters A B σ TMI AMSR-E F16 F17

14. 14 A measurement without uncertainly is meaningless Wrong error models produce wrong uncertainties Multiplicative model is recommended for fine resolution precipitation measurements Tian et al., 2012: Error modeling for daily precipitation measurements: additive or multiplicative? to be submitted to Geophys. Rev. Lett. Summary

15. Extra slides 15

16. Summary and Conclusions Created bias-corrected radar data for validation Evaluated biases in PMW imagers: AMSR-E, TMI and SSMIS Constructed an error model to quantify both systematic and random errors 16