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 Sponsored by NASA ESDR-ERR Program

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

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 3

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,0.25 o Satellite sensor instantaneous rainfall measurements aggregated to 5 minutes time interval – Sensors: TMI, AMSR-E, and SSMIS – Imagers only for now – Resolution: 5 minutes, 0.25 o – Satellite data matched with Q2 over CONUS 4

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

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

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

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

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

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

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

13 A nonlinear multiplicative measurement error model: X i : truth, error free. Y i : 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. Modeling the Measurement Errors: A-B-σ model

14 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. Justification for the nonlinear multiplicative error model

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

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

Summary and Conclusions 1. 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

Summary and Conclusions 2. 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

Extra slides 19

20 What we did: 1.A nonlinear multiplicative error model 2.Constant variance in random errors 3.More appropriate for variables with several orders of variability 4.A parametric model is useful for data assimilation, cal/val What we found: 1.The model works well 2.Constant variance in random errors 3.More appropriate for variables with several orders of variability 4.A parametric model is useful for data assimilation, cal/val Summary and Conclusions

Summary and Conclusions what 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. 21

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

23 Satellite Sensor Data Availability SSMI F No data SSMI F14 No data No data SSMI F15 No data , No data SSMIS F16 No data SSMIS F17 No data SSMIS F18 No data TMI No data AMSR-ENo data , , No dataMissing filesComplete

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

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

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

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

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