Wednesday, 25 January 2012: 11:45 AM

Nonlinear Model Parameter Estimation: Comparison of Results From a Markov Chain Monte Carlo Algorithm and An Ensemble Transform Kalman Filter

Room 340 and 341 (New Orleans Convention Center )

**Derek J. Posselt**, University of Michigan, Ann Arbor, MI

The characteristics of numerically simulated clouds, precipitation, and radiation depend to a significant extent on the details of the model's physical parameterizations. The behavior of model physics schemes is, in turn, governed by a set of tunable empirical parameters. It follows that estimates of model uncertainty and/or ensemble based representations of variability in the system should logically incorporate variability in these parameters. However, in cases for which parameters are nonlinearly related to the output of the model, it is unclear how to properly estimate parameter values or vary them in a realistic manner. In this presentation, a Markov chain Monte Carlo (MCMC) algorithm is used to explore the effect of nonlinearity on ensemble Kalman filter-based estimates of model physics parameters. A simplified model with fully realistic cloud microphysics and radiation driven with prescribed temperature, water vapor, and winds is used to realistically simulate the environment inside a convective squall line. The evolution of the model error associated with poorly known physics parameters over the length of the simulation is examined using MCMC. An ensemble transform Kalman filter algorithm is then used to evolve the model parameter joint PDF, and the robustness of the parameter estimates and ensemble parameter distributions derived from ETKF is assessed via comparison with MCMC.

As expected, nonlinearity in the relationship between parameters and model output gives rise to a non-Gaussian posterior probability distribution for the parameters. However, ETKF-based estimates of the posterior mean and covariance are shown to be robust, as long as the posterior PDF has a single mode. Once multimodality manifests in the solution, the posterior mean estimates differ from the sample mean. The same is true of the analysis error variance. Results suggest the need for conditional mode estimation that preserves the nonlinear propagation of information in the ensemble. The shape of posterior PDFs also indicates a formulation that allows skewness in the posterior PDF (e.g., Gamma distribution) may have promise for more accurate mode estimation, especially in the case of nonlinear model parameters and observations of clouds and water vapor.

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