[18-1] March 2, 13:20-13:50

[Invited]

Model Parameter Estimation Using Nonlinear Ensemble Algorithms

D. J. Posselt (JPL) and C. H. Bishop (Naval Research Laboratory, Monterey, CA)

While data assimilation (DA) has most often been used to estimate initial conditions for numerical prediction models, it is increasingly used to interrogate aspects of the model internal physics. In particular, DA techniques can be used to examine how changes in empirical model parameters affect the evolution of the model state. It is now generally acknowledged that introducing variability in parameters in an ensemble data assimilation and prediction context can increase the realism of the prediction system. There are, however, several challenges that must be addressed. Specifically, many parameters are nonlinearly related to the model output, and the transfer functions that map from state to observation space may introduce further nonlinearity. In addition, the prior parameter distributions may be poorly known, and are often bounded at zero.

Our approach to parameter estimation uses a Markov chain Monte Carlo (MCMC) algorithm to sample the Bayesian posterior distribution of model parameters. We are then able to test approximate data assimilation methodologies that are less computationally expensive. In this presentation, we show results of parameter estimation using a MCMC algorithm. We demonstrate the various types of nonlinearity present in cloud microphysical parameterizations, in particular. We then show results from various ensemble filter algorithms, including the Ensemble Transform Kalman Filter (ETKF), and a newly developed filter based on Gamma and Inverse Gamma distributions (the Gamma - Inverse Gamma (GIG) filter). The ETKF exhibits well known problems associated with nonlinearity in the parameter - model state relationship. In contrast, the GIG produces a posterior estimate that is more accurate in both state and observation space, and closely approximates the Bayesian solution generated by MCMC.