How best to add structural complexity to cloud microphysics parameterization schemes?

Bulk cloud microphysics parameterization schemes represent highly complex cloud and precipitation particle distributions via moments of these distributions (e.g. liquid water content, number concentration) that are evolved in time via simple relationships. These schemes are thus gross approximations of an arbitrarily complex natural system, and these approximations result in forecast error in numerical weather models. A flexible rain microphysics parameterization, the Bayesian Observationally-constrained Statistical-physical Scheme (BOSS) has been developed that is capable of evolving any choice of drop-size distribution moments using a series of power laws to represent cloud microphysical processes such as evaporation, droplet collision-coalescence and breakup. The complexity of BOSS can therefore be altered either by changing the number and choice of prognostic drop size distribution moments, or by changing the number of power law terms that represent microphysical processes. In either case, increased complexity results in an increase in the numbers of free parameters to fit to observations, e.g. via Markov Chain Monte Carlo (MCMC) sampling. However, we find that increasing scheme complexity by adding prognostic moments is of more value than by adding power law terms, owing to natural co-variability of drop-size distribution moments. Furthermore, when a single power law is used, MCMC-based estimation of the model parameters is greatly simplified because the underlying parameter probability distribution more closely resembles a Gaussian distribution.