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

F16

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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