Modeling Errors in Satellite Data Yudong Tian University of Maryland & NASA/GSFC
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Modeling Errors in Satellite Data Yudong Tian University of Maryland & NASA/GSFC http://sigma.umd.edu Sponsored by NASA ESDR-ERR Program
description
Modeling Errors in Satellite Data Yudong Tian University of Maryland & NASA/GSFC http://sigma.umd.edu Sponsored by NASA ESDR-ERR Program. Optimal combination of independent o bservations (or how human knowledge grows). Information content. “Conservation of Information Content”. - PowerPoint PPT Presentation
Transcript of Modeling Errors in Satellite Data Yudong Tian University of Maryland & NASA/GSFC
Modeling Errors in Satellite Data
Yudong Tian
University of Maryland & NASA/GSFC
http://sigma.umd.edu
Sponsored by NASA ESDR-ERR Program
Optimal combination of independent observations(or how human knowledge grows)
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Information content
“Conservation of Information Content”
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Why uncertainty quantification is always needed
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Information content
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1. Most commonly, subconsciously used error model:
Ti: truth, error free. Xi: measurements, b: systematic error (bias)
2. A more general additive error model:
The additive error model
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A nonlinear multiplicative measurement error model:
Ti: truth, error free. Xi: measurements
With a logarithm transformation,
the model is now a linear, additive error model, with three parameters:
A=log(α), B=β, xi=log(Xi), ti=log(Ti)
The multiplicative error model
),0(~ 2 N
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Correct error model is critical in quantifying uncertainty
Ti
Xi
Ti
Xi
Ti
Xi
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Additive model does not have a constant variance
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Additive error model: why variance is not constant?-- systematic errors leaking into random errors
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The multiplicative error model predicts better
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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.
The multiplicative error model has clear advantages
Spatial distribution of the model parameters
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TMI
AMSR-E
F16
F17
)()log()log( stdevXBAY ii A B σ(random error)
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Probability distribution of the model parameters
A B σ
TMI
AMSR-E
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F17
)()log()log( stdevXBAY ii
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• 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
Extra slides
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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
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