Quantification of Cloud Microphysical Parameterization Uncertainty Using Radar Reflectivity

Uncertainty in cloud microphysical parameterization-a leading order contribution to numerical weather prediction error-is estimated using a Markov chain Monte Carlo (MCMC) algorithm. An inversion is performed on 10 microphysical parameters using radar reflectivity observations with vertically covarying error as the likelihood constraint. An idealized 1D atmospheric column model with prescribed forcing is used to simulate the microphysical behavior of a midlatitude squall line. Novel diagnostics are employed for the probabilistic investigation of individual microphysical process behavior vis-a-vis parameter uncertainty. Uncertainty in the microphysical parameterization is presented via posterior probability density functions (PDFs) of parameters, observations, and microphysical processes. The results of this study show that radar reflectivity observations, as expected, provide a much stronger constraint on microphysical parameters than column-integral observations, in most cases reducing both the variance and bias in the maximum likelihood estimate of parameter values. This highlights the enhanced potential of radar reflectivity observations to provide information about microphysical processes within convective storm systems despite the presence of strongly nonlinear relationships within the microphysics model. The probabilistic analysis of parameterization uncertainty in terms of both parameter and process activity PDFs suggest the prospect of a stochastic representation of microphysical parameterization uncertainty-specifically the results indicate that error may be more easily represented and estimated by microphysical process uncertainty rather than microphysical parameter uncertainty. In addition, these new methods of analysis allow for a detailed investigation of the full nonlinear and multivariate relationships between microphysical parameters, microphysical processes, and radar observations.