Abstract
This dissertation document details work completed in the field of cloud microphysical model error and uncertainty quantification. The general motivation is a need to account for error and uncertainty in microphysical parameterization schemes, which remain a large source numerical weather prediction error. The techniques used have been drawn from the fields of nonlinear parameter estimation, data assimilation and uncertainty quantification. First, microphysical parameter uncertainty has been quantified in a manner identical to that of Posselt and Vukicevic (2010), except that a vertically resolved simulated radar reflectivity observation was used as observation constraint on parameter uncertainty, rather than column-integral observations (such as IWP, LWP, etc.). This necessitated work on estimation of the error characteristic of the vertically resolved radar reflectivity observations, in particular, the estimation of a vertically correlated radar error model. Additionally, work has been conducted on estimating uncertainty in microphysics schemes by using perturbations on the hydrometeor time tendency equations as control parameters within a probabilistic Monte Carlo inversion. In order to further facilitate probabilistic inverse modeling studies, and to provide an educational tool for future students, a simplified, Matlab-based framework has been developed for testing advanced Monte Carlo techniques on simple models (e.g. damped harmonic oscillator, Lorenz 1963 model, etc). Finally, an ensemble Kalman transform smoother (EnTKS or ETKS, Posselt and Bishop (2012)) is used to confim that new choices of uncertain model control variables may aid in the use of ensemble Kalman techniques for non-Gaussain model uncertainty analysis.