Uncertainty quantification (UQ) in weather and climate models is required to assess the sensitivity of their outputs to various parameterization schemes and thereby improve their consistency with observations. Herein, we present an efficient UQ and Bayesian inference for the cloud parameters of the NCAR Single Column Atmosphere Model (SCAM6) using surrogate models based on a polynomial chaos expansion. The use of a surrogate model enables to efficiently propagate uncertainties in parameters into uncertainties in model outputs. We investigated eight uncertain parameters: the auto-conversion size threshold for ice to snow (dcs), the fall speed parameter for stratiform cloud ice (ai), the fall speed parameter for stratiform snow (as), the fall speed parameter for cloud water (ac), the collection efficiency of aggregation ice (eii), the efficiency factor of the Bergeron effect (berg_eff), the threshold maximum relative humidity for ice clouds (rhmaxi), and the threshold minimum relative humidity for ice clouds (rhmini). We built two surrogate models using two non-intrusive methods: spectral projection (SP) and basis pursuit denoising (BPDN). Our results suggest that BPDN performs better than SP as it enables to filter out internal noise during the process of fitting the surrogate model. Five out of the eight parameters (namely dcs, ai, rhmaxi, rhmini, and eii) account for most of the variance in predicted climate variables (e.g., total precipitation, cloud distribution, shortwave and longwave cloud forcing, ice and liquid water path). A first-order sensitivity analysis reveals that dcs contributes approximately 40–80% of the total variance of the climate variables, ai around 15–30%, and rhmaxi, rhmini, and eii around 5–15%. The second- and higher-order effects contribute approximately 20% and 11%, respectively. The sensitivity of the model to these parameters was further explored using response curves. A Markov chain Monte Carlo (MCMC) sampling algorithm was also implemented for the Bayesian inference of dcs, ai, as, rhmini, and berg_eff using cloud distribution data collected at the Southern Great Plains (USA). Our study has implications for enhancing our understanding of the physical mechanisms associated with cloud processes leading to uncertainty in model simulations and further helps to improve the models used for their assessment.