Empirical Analysis and Statistical Modeling of Errors in Satellite Precipitation Sensors Yudong Tian, Ling Tang, Robert Adler, and Xin Lin University of.
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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: -- the merging algorithm -- the upstream sensors
• Studying errors in the sensors is necessary in understanding errors in merged products
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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
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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
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Mean Precipitation(Summer 2009~2011, units: mm/hr)
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AMSR-E matched Q2 TMI matched Q2
SSMIS F16 matched Q2 SSMIS F17 matched Q2
PDF Comparisons confirm season-dependent error characteristics
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AMSR-E TMI AMSR-E TMI
SSMIS F16 SSMIS F17 SSMIS F16 SSMIS F17
Summer Winter
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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.
Modeling the Measurement Errors: A-B-σ model
eXY ii ),0(~ 2 N
)1()log()log()log( ii XY
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• 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
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TMI
AMSR-E
F16
F17
)()log()log( stdevXBAY ii A B σ(random error)
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
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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.
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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:
5. The model works well
6. Constant variance in random errors
7. More appropriate for variables with several orders of variability
8. A parametric model is useful for data assimilation, cal/val
Summary and Conclusions
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.
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Satellite Sensor Data Availability
1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011SSMIF13
0101-0502
0707-1231
1120-1231
No data
No data
SSMIF14
No data
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0101-0506
0824-1231
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SSMIF15
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0101-0222, 1201
0814-1231
No data
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SSMISF16
No data
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No data No data
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0101-1031
SSMISF17
No data
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No data No data
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0101-1212
SSMISF18
No data
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No data No data
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0101-0307
TMI No data
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0101-1207
AMSR-E No data
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0101-0618,0730-0807,0913-0919
1004-1231
No data Missing files Complete
Sensors show mostly overestimates for summer
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AMSR-E TMI AMSR-E TMI
SSMIS F16 SSMIS F17 SSMIS F16 SSMIS F17
Summer
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