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Non-Gaussian MLEF framework

Log-Normal PDF. Gaussian PDF. Non-Gaussian MLEF framework. Log-likelihood cost-function :. Maximize posterior PDF  minimize cost function. Posterior conditional PDF. Milija Zupanski, CIRA/CSU ZupanskiM@CIRA.colostate.edu. Assume :

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Non-Gaussian MLEF framework

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  1. Log-Normal PDF Gaussian PDF Non-Gaussian MLEF framework Log-likelihood cost-function: Maximize posterior PDF  minimize cost function Posterior conditional PDF Milija Zupanski, CIRA/CSU ZupanskiM@CIRA.colostate.edu

  2. Assume: • Gaussian prior probability distribution (state vector) • Observations: Height (Lognormal), Wind (Gaussian) Non-Gaussian MLEF framework:Lognormal height observation errors Minimize mixed Normal-Lognormal cost function: Higher nonlinearity of the cost function compared to the Gaussian Milija Zupanski, CIRA/CSU ZupanskiM@CIRA.colostate.edu

  3. Stddev(e)=1.e-3 Gaussian framework works only for small observation errors SWM MODEL: Impact of Lognormal obs. errors:Analysis RMS errors Stddev(e)=1.e-2 Lognormal framework works for all error magnitudes Milija Zupanski, CIRA/CSU ZupanskiM@CIRA.colostate.edu

  4. Gaussian framework Lognormal framework Impact of Lognormal height observation errros:Innovation histogram Stddev(e)=1.e-3 Stddev(e)=1.e-2 Height innovations Generalized non-Gaussian framework can handle Gaussian, Lognormal, or mixed PDF errors ! Milija Zupanski, CIRA/CSU ZupanskiM@CIRA.colostate.edu

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