This paper presents a Bayesian inverse modelling approach to simultaneously assess the ability of a pseudo-adiabatic cloud parcel model to match in-situ measurements of the droplet size distribution in a cloud as well as model parameters describing the updraft and different aerosol microphysical properties (herein termed calibration parameters). Our methodology is tested using observations from two clean (average accumulation mode number concentration < 60 cm-3) and two polluted clouds (average accumulation mode number concentration > 100 cm-3) observed during the Marine Stratus/Stratocumulus Experiment (MASE II) campaign. Our framework capitalizes on recent developments in Markov Chain Monte Carlo (MCMC) simulation and retrieves the most likely parameter values and their underlying posterior probability density function. This distribution provides necessary information to efficiently and in a statistically robust manner, assess both the global sensitivity of aerosol physiochemical and meteorological parameters, and the suitability of cloud parcel models to comprehensively describe the evolution of cloud droplet size distributions in stratocumulus clouds.
We demonstrate that the updraft velocity is the most important calibration parameter for describing the observed droplet distribution for each cloud case, corroborating previous findings. The accumulation mode number, shape and size are found to be more important than chemistry except for the most polluted conditions (average accumulation mode number concentration ~455 cm-3). This highlights that conditions exist for marine stratocumulus clouds in which an accurate description of the aerosol chemistry is a pre-requisite for the accurate representation of cloud microphysical properties.
Overall, the MCMC algorithm successfully matches the observed droplet size distribution for each cloud case. In doing so, however, the subsequent agreement between the derived and measured calibration parameters is generally poor. An important result from this analysis is that for certain calibration parameters, consistent patterns of deviation were found in the posterior distributions for all the clouds included in this study. This finding indicates that either there is systematic sampling or averaging artefacts in our observations, or our pseudo-adiabatic cloud parcel model omits or consistently misrepresents processes and/or parameter(s) required to accurately simulate the droplet size distributions of the observed marine stratocumulus. By repeating our inverse methodology with more calibration parameters of which current measurements are uncertain (surface tension, mass accommodation coefficient), we find that it is likely that the process description within the current formulation of the pseudo-adiabatic cloud model used in this study misses a dynamical process rather than parameter(s).