An approach for addressing Non-Gaussian error in microphysical parameterization

Recent studies have shown the importance of quantifying and representing model physics uncertainty within probabilistic forecasts (e.g. Stensrud 2000). The characteristics of microphysical parameterization uncertainty, however, have been found to be strongly nonlinear (Posselt & Vukicevic 2010, van Lier-Walqui et al 2012), calling into question the possibility of estimating and propagating this error using Gaussian statistical techniques such as ensemble Kalman methods (Vukicevic & Posselt 2008, Posselt & Bishop 2012). One possible option for addressing these issues is choosing new variables over which to represent and estimate uncertainty. In particular, recent results have suggested that while probability density functions (PDFs) of microphysical parmameters are strongly non-Gaussian, PDFs of individual microphysical process tendency output is more `well-behaved' (van Lier-Walqui et al 2012). Here, results are presented of a Monte Carlo estimation of microphysical parameterization uncertainty using a delayed rejection, adaptive Metropolis sampler (Haario 2006), where the uncertain parameters are perturbations on individual microphysical process tendencies. Shannon information content and Bayesian evidence are used to assess the ability of the new uncertain parameters to represent forecast uncertainty. Preliminary results with the new parameters show both the promise and the limitations of the new approach.