Linearization of Microphysical Parameterization Uncertainty Using Multiplicative Process Perturbation Parameters

Recent studies have shown the importance of accounting for model physics uncertainty within probabilistic forecasts. Attempts have been made at quantifying this uncertainty in terms of microphysical parameters such as fall speed coefficients, moments of hydrometeor particle size distributions, and hydrometeor densities. It has been found that uncertainty in terms of these “traditional” microphysical parameters is highly non-Gaussian, calling into question the possibility of estimating and propagating this error using Gaussian statistical techniques such as ensemble Kalman methods. Here, a new choice of uncertain control variables is proposed that instead considers uncertainty in individual modeled microphysical processes. These “process parameters” are multiplicative perturbations on contributions of individual modeled microphysical processes to hydrometeor time tendency. The new process parameters provide a natural and appealing choice for the quantification of aleatory microphysical parameterization uncertainty. Results of a nonlinear Monte Carlo parameter estimation experiment for these new process parameters are presented and compared with the results using traditional microphysical parameters as uncertain control variables. Both experiments occur within the context of an idealized one-dimensional simulation of moist convection, under the observational constraint of simulated radar reflectivity. Results indicate that the new process parameters have a more Gaussian character compared with traditional microphysical parameters, likely due to a more linear control on observable model evolution. In addition, posterior forecast distributions using the new control variables (process parameters) are shown to have less bias and variance. These results strongly recommend the use of the new process parameters for an ensemble Kalman-based estimation of microphysical parameterization uncertainty.