Markov-chain Monte Carlo assimilation of radar reflectivity to improve microphysical parameterization

The bulk parameterization of microphysical processes within numerical weather prediction models requires continuous improvement. To address this issue, a data assimilation system comprising an idealized, semi-Lagrangian cloud resolving model coupled with a Markov Chain Monte Carlo (MCMC) sampler has been used to perform an simulated inversion on ten bulk microphysical parameters, using vertically resolved synthetic radar reflectivity. Following Posselt and Vukicevic (2010), it is found that many microphysical parameters remain unconstrained by column-integral measurements such as precipitation, ice water path and radiative fluxes. Radar reflectivity has the potential to provide greater information relevant to microphysical processes, partly because of the vertical resolution inherent in radar measurement as well as the sensitivity of radar reflectivity to varying hydrometeor type and concentration. On the other hand, radar reflectivity is a measurement which is related to hydrometeors in a strongly nonlinear fashion, and thus, care must be taken to treat it accordingly. In particular, reflectivity measurements may be correlated in the vertical. Using a best estimate for uncertainty in the atmospheric state, the vertical correlation of reflectivity is computed. The associated covariance is then used to calculate a cost function within a MCMC inversion of ten microphysical parameters using radar reflectivity. The result of this experiment is a ten-dimensional probability density function for radar reflectivity measurements. From this the linearity, monotonicity and sensitivity of the chosen microphysical parameters to radar reflectivity measurements can be assessed, from which follows the ability of radar reflectivity to give insight into the performance of microphysical parameterization schemes.