Modeling Errors in Satellite Data Yudong Tian University
- Slides: 16
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) Information content 2
“Conservation of Information Content” 3
Why uncertainty quantification is always needed Information content 4
The additive error model 1. Most commonly, subconsciously used error model: Ti: truth, error free. Xi: measurements, b: systematic error (bias) 2. A more general additive error model: 5
The multiplicative error model 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) 6
Correct error model is critical in quantifying uncertainty Xi Xi Ti Ti 7
Additive model does not have a constant variance 8
Additive error model: why variance is not constant? -- systematic errors leaking into random errors 9
The multiplicative error model predicts better 10
The multiplicative error model has clear advantages • 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. 11
Spatial distribution of the model parameters A B σ(random error) TMI AMSR-E F 16 F 17 12
Probability distribution of the model parameters A B σ TMI AMSR-E F 16 F 17 13
Summary • 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. 14
Extra slides 15
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 16
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