Large uncertainties remain in simulating clouds in global climate models, and part of these uncertainties result from multiple tunable parameters in cloud parameterizations. A multi-institutional team led by U.S. Department of Energy scientists at Pacific Northwest National Laboratory investigated the sensitivity of simulated shallow cumulus and stratocumulus clouds. The investigation selected tunable parameters in a newly-implemented cloud scheme in the single-column version of the Community Atmosphere Model version 5 (SCAM5), called Cloud Layers Unified by Binormals (CLUBB). The team found that most of the variance in simulated cloud fields can be explained by a small number of tunable parameters. They used a quasi-Monte Carlo sampling approach to explore the high-dimensional parameter space in CLUBB and adopted a generalized linear model to study the responses of simulated cloud fields to tunable parameters. They found that among 40 to 50 tunable parameters in CLUBB, only a handful of parameters are influential. The identified influential parameters are different for different types of clouds. This study improves the understanding of the parameter-dependence of this newly implemented scheme. This study helps to reduce the number of tunable parameters for ongoing sensitivity and calibration study of global simulations.