Large uncertainties persist in modeling shallow, low clouds because there are many interacting nonlinear processes and multiple cloud-controlling environmental factors. In addition, sharp changes in behavior can occur when environmental thresholds are met. Model studies that follow a traditional approach of exploring the effects of factors "one-at-a-time" are unable to capture interactions between factors. We simulate a stratocumulus cloud based on the Second Dynamics and Chemistry of Marine Stratocumulus field study using a large-eddy simulation model coupled with a two-moment cloud microphysics scheme. The simulations are used to train a Gaussian process emulator, which we then use to visualize the relationships between two cloud-controlling factors and domain-averaged cloud properties. Only 29 model simulations were required to train the emulators, which then predicted cloud properties at thousands of new combinations of the two factors. Emulator response surfaces of cloud liquid water path and cloud fraction show two behavioral regimes, one of thin and patchy yet steady stratocumulus and one of thick, growing stratocumulus with cloud fraction near 1. Natural variability (initial-condition uncertainty) creates unrealistic "bumpy" response surfaces. However, we show that the variability causing the bumpiness can be characterized in an emulator "nugget term" that is adjusted to match the distribution of a small number of initial-condition ensemble simulations at various points on the surface, thereby allowing a smoother, deterministic response surface to be constructed. Accounting for variability leads to the firm conclusion that there is a smooth but steep change in cloud behavior between regimes, but not a sharp transition.