Statistical methods to understand and visualise the complex behaviour of clouds in the climate system

Uncertainty surrounding cloud responses to changes in their environments contributes majorly to uncertainty in the radiative effects of aerosol and predictions of future climates. Stratocumulus clouds exert a strong net cooling effect due to their high albedo and large horizontal extent, yet their behaviour in the climate system is particularly uncertain due to their high sensitivity to surroundings. High-resolution modelling is crucial for studying stratocumulus behaviours, which are made up of many complex interacting processes, on many scales from large-scale dynamics to the microphysical responses to aerosol. However, many studies perturb cloud-controlling factors one at a time, which makes it challenging to identify interactions with other factors and how they jointly affect cloud properties. To understand the complex behaviour of marine stratocumulus clouds, this thesis uses two statistical methods: perturbed parameter ensembles and Gaussian process emulation. Perturbed parameter ensembles perturb multiple factors simultaneously so that their joint effects can be analysed. Furthermore, these ensembles can be used as training data for Gaussian process emulation, which is used to create statistical representations of the relationships between multiple cloud-controlling factors and cloud properties of interest. The emulators are used to generate the values of cloud properties for many new combinations of factor values, which allows the joint effects of parameters to be analysed and parameter contributions to the variances in the cloud properties to be quantified. Firstly, two properties of the free troposphere are perturbed from simulations of a homogeneous, nocturnal stratocumulus cloud to analyse cloud behaviour around the break-up threshold for cloud-top entrainment instability. Dense sampling using emulators of liquid water path and cloud fraction showed that there were non-linear interactions between the two perturbed factors and two behavioural regimes. Additionally, a method for approximating the natural variability of the cloud and accounting for it in the emulator build was demonstrated. Secondly, the stratocumulus-to-cumulus transition was simulated to study the roles of aerosol and drizzle in the context of other cloud-controlling factors. From the base simulation, one model parameter and five cloud-controlling factors were perturbed across reasonable ranges. Analysis of the perturbed parameter ensemble showed that the fastest transitions occurred in low-aerosol environments combined with deep boundary layers, high autoconversion rates and dry temperature inversions. When the ensemble was split into high- and low-drizzle environments, the inversion strength was found to have a strong control on transition time, via entrainment, in low-drizzle environments. Thirdly, the ensemble of stratocumulus-to-cumulus transitions was used as training data for Gaussian process emulation, which allowed the joint effects of parameters in transition properties to be fully visualised and quantified. Emulation revealed that there was a low-aerosol regime, where aerosol concentration strongly controlled the transition time, but outside that regime, the transition time was largely dependent on the inversion strength. The transition time was found to be a complex process that was influenced by multiple interacting parameters, whereas the rain water path is controlled by individual parameters.