Achieving a detailed understanding of aerosol-cloud-precipitation interactions is one of the many challenges of developing global climate models and Numerical Weather Prediction (NWP) models. This thesis explores the aerosol effect on clouds and precipitation based on two case studies of the COnvective Precipitation Experiment (COPE), which was a joint US-UK field campaign that took place during July and August of 2013 over the southwest peninsula of UK. COPE was a new measurement campaign, encompassing both in-situ observations and ground-based measurements of aerosol properties and microphysical properties obtained in convective clouds over the southwestern peninsula of England. The vast variety of aerosol properties and cloud microphysical processes observed during COPE is significant to assess the accuracies of NWP model for forecasts of the timing and location of heavy precipitation. Among the case studies of COPE, two cases with distinct aerosol backgrounds are picked out to make a detailed investigation of impacts of small aerosol particles and giant cloud condensation nuclei (GCCN) on the rain process. Detailed description of aerosols, clouds, and precipitations measured during two cases were given. Comparisons between two case studies, such as in-situ measurements at the same heights above the cloud base and the UK operational radar observation, indicate a strong suppression of large cloud drops, drizzle and warm precipitation by high small aerosol concentrations. The effect of high number concentrations of small aerosols on mixed phase clouds is also indicated by the analysis for the polluted case. Aerosol data in the boundary layer and sounding from these two case studies were applied to initiate the Aerosol-Cloud-Precipitation Interactions Model (ACPIM) from the University of Manchester and the kinematic driver model (KiD) with all parameters set to control values. Then simulation results were compared to the in-situ observations and precipitation properties from radar. Sensitivity runs were presented and discussed, and it was revealed that the model was most sensitive to the number concentration of small aerosol particles and GCCN used in the simulation for these two cases. This thesis presents a summary of COPE and detailed observations obtained from two cases, along with simulation results and a discussion on possible future work.