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Empirical Analysis and Statistical Modeling of Errors in Satellite Precipitation Sensors

Empirical Analysis and Statistical Modeling of Errors in Satellite Precipitation Sensors Yudong Tian, Ling Tang, Robert Adler, and Xin Lin University of Maryland & NASA/GSFC http://sigma.umd.edu Sponsored by NASA ESDR-ERR Program. Motivation. Two error sources in merged satellite data:

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Empirical Analysis and Statistical Modeling of Errors in Satellite Precipitation Sensors

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  1. Empirical Analysis and Statistical Modeling of Errors in Satellite Precipitation Sensors Yudong Tian, Ling Tang, Robert Adler, and Xin Lin University of Maryland & NASA/GSFC http://sigma.umd.edu Sponsored by NASA ESDR-ERR Program

  2. Motivation Two error sources in merged satellite data: -- the merging algorithm -- the upstream sensors Studying errors in the sensors is necessary in understanding errors in merged products 2

  3. Outline • To understand: empirical analysis of systematic errors: characterizing errors in passive microwave (PMW) sensors • To quantify and to predict: statistical modeling of errors: with a measurement error model, to quantify both systematic and random errors • Summary and Conclusions

  4. Data and Study Period • Time period: 3 years, 2009 ~ 2011 • Ground reference: Q2 (NOAA NSSL Next Generation QPE), bias-corrected with NOAA NCEP Stage IV (hourly, 4-km) • Resolution: 5 minutes, 1 km, remapped to 5 mins,0.25o • Satellite sensor instantaneous rainfall measurements aggregated to 5 minutes time interval • Sensors: TMI, AMSR-E, and SSMIS – Imagers only for now • Resolution: 5 minutes, 0.25o • Satellite data matched with Q2 over CONUS

  5. Sensors covered by the study period

  6. Q2 has biases and was corrected with Stage IV data Before After CPC Gauge Stage IV Radar

  7. Sample sizes matched between sensors and Q2 AMSR-E TMI SSMIS F16 SSMIS F17

  8. Mean Precipitation(Summer 2009~2011, units: mm/hr) AMSR-E matched Q2 TMI matched Q2 SSMIS F16 matched Q2 SSMIS F17 matched Q2

  9. Precipitation – Density Scatter Plots(Summer 2009~2011) AMSR-E TMI SSMIS F16 SSMIS F17

  10. More overestimates in SSMIS for summer AMSR-E TMI SSMIS F16 SSMIS F17

  11. More underestimates in AMSR-E & TMI for winter AMSR-E TMI SSMIS F16 SSMIS F17

  12. PDF Comparisons confirm season-dependent error characteristics AMSR-E TMI AMSR-E TMI Summer Winter SSMIS F16 SSMIS F17 SSMIS F16 SSMIS F17 12

  13. Modeling the Measurement Errors: A-B-σ model • A nonlinear multiplicative measurement error model: • Xi: truth, error free. Yi: measurements • With a logarithm transformation, • the model is now a linear, additive error model, with three parameters: • A=log(α), B=β, and σ • which can be easily estimated with ordinary least squares (OLS) method.

  14. Justification for the nonlinear multiplicative error model • 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.

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

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

  17. Summary and Conclusions1. what we did 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 17

  18. Summary and Conclusions2. what we found Sensor biases have seasonal and rain-rate dependency: summer – overestimates; winter: underestimates AMSR-E and TMI did better in summer; SSMI F16 and F17 in winter The multiplicative error model works consistently well Both systematic and random errors are quantified Model indicated AMSR-E had the lowest uncertainty Results useful for data assimilation, algorithm cal/val, etc. 18

  19. Extra slides

  20. Summary and Conclusions • What we did: • A nonlinear multiplicative error model • Constant variance in random errors • More appropriate for variables with several orders of variability • A parametric model is useful for data assimilation, cal/val • What we found: • The model works well • Constant variance in random errors • More appropriate for variables with several orders of variability • A parametric model is useful for data assimilation, cal/val

  21. Summary and Conclusionswhat we did: • AMSR-E and TMI underestimate rainfall in winter in Southeast US. • AMSR-E , SSMIS F16 and F17 overestimate rainfall in Summer in Central and Southeast US. • SSMIS F16 and F17 have high positive BIAS in Summer, over Central US; AMSR-E and TMI have high negative BIAS in Winter, over Southeast US. • TMI performs the best compared with the other three sensors.

  22. Biases become less pronounced with all-year data(2009~2011) AMSR-E TMI SSMIS F16 SSMIS F17

  23. Satellite Sensor Data Availability

  24. Precipitation – Density Scatter Plots(2009~2011) AMSR-E TMI SSMIS F16 SSMIS F17

  25. Precipitation – Density Scatter Plots(Winter 2009~2011) AMSR-E TMI SSMIS F16 SSMIS F17

  26. Sensors show mostly overestimates for summer Summer AMSR-E TMI AMSR-E TMI SSMIS F16 SSMIS F17 SSMIS F16 SSMIS F17 26

  27. Spatial distribution of the model parameters (for winter) A B σ TMI AMSR-E F16 F17

  28. Spatial distribution of the model parameters for summer A B σ TMI AMSR-E F16 F17

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