In this study, we investigate the sensitivity of simulated shallow cumulus and stratocumulus to selected tunable parameters of Cloud Layers Unified by Binormals (CLUBB) in the single-column version of Community Atmosphere Model version 5 (SCAM5). A quasi-Monte Carlo (QMC) sampling approach is adopted to effectively explore the high-dimensional parameter space and a generalized linear model is adopted to study the responses of simulated cloud fields to tunable parameters. One stratocumulus and two shallow cumulus cases are configured at both coarse and fine vertical resolutions in this study. Our results show that most of the variance in simulated cloud fields can be explained by a small number of tunable parameters. The parameters related to Newtonian and buoyancy-damping terms of total water flux are found to be the most influential parameters for stratocumulus. For shallow cumulus, the most influential parameters are those related to skewness of vertical velocity, reflecting the strong coupling between cloud properties and dynamics in this regime. The influential parameters in the stratocumulus case are sensitive to the vertical resolution while little sensitivity is found for the shallow cumulus cases, as eddy mixing length (or dissipation time scale) plays a more important role and depends more strongly on the vertical resolution in stratocumulus than in shallow convections. The influential parameters remain almost unchanged when the number of tunable parameters increases from 16 to 35. This study improves understanding of the CLUBB behavior associated with parameter uncertainties and provides valuable insights for other high-order turbulence closure schemes.