Accurately representing the microphysical state of precipitation using bulk microphysics schemes, including the hydrometeor particle size distributions (PSDs), is vital to improving convective-scale forecasts. In this dissertation, results will be presented from three related projects that combine the use of dual-polarimetric (dual-pol) radar observations and ensemble forecast methods to evaluate and improve the forecast model microphysical state. The dual-pol variables provide additional information on hydrometeor types and their PSDs compared to reflectivity (Z) alone. In the first project, simulated dual-pol variables from several members of the 2013 CAPS Storm Scale Ensemble Forecasts (SSEF) that use different microphysics schemes are compared to dual-pol observations. The microphysics schemes vary significantly and include single-moment (SM) WSM6, partially double-moment (DM) Thompson and WDM6, and fully DM Milbrandt and Yau and Morrison. Both a mesoscale convective system (MCS) and supercell case are considered due to the different patterns in the dual-pol variable fields unique to each case. Results show that the forecasts using the Morrison scheme and the Milbrandt and Yau scheme have patterns of high differential reflectivity (ZDR) indicative of size sorting that match similar patterns in the observations. The dual-pol variables also help highlight biases in the forecasts including the under-prediction of liquid water content and the over-prediction of particular hydrometeor types such as graupel. In the second project, probabilistic forecasts of simulated dual-pol variables are performed. Ensemble forecasts of a mesoscale convective system (MCS) from 9 May 2007 are initialized from ensemble Kalman filter (EnKF) analyses using both SM and DM microphysics schemes. Qualitative analysis of simulated ZDR shows that the DM experiment better represents the PSDs of the convective and stratiform precipitation regions, while the KDP fields show that the SM experiment over-forecasts liquid water content in the convective areas. Quantitative ensemble forecast verification methods using dual-pol variables are considered for the first time and reveal the challenges associated with evaluating dual-pol fields that have very fine-scale details. Finally, in the third project, dual-pol variables are assimilated using the EnKF and a DM microphysics scheme for two supercell cases: 10 May 2010 and 20 May 2013. For each case, both ZDR and KDP are assimilated in separate experiments in addition to Z and radial velocity (Vr) and compared to a control experiment that assimilates only Z and Vr. The results show that the simulated dual-pol fields in the analyses of the dual-pol experiments better represent documented polarimetric signatures, such as the ZDR arc, compared to the control experiment. Additionally, comparisons of model microphysical variables and mean mass diameter between the dual-pol and control experiments show that the dual-pol experiments have an improved microphysical state. For example, the mean mass diameter of raindrops in the ZDR experiment is increased along the ZDR arc. This work, as far as we know, represents the first to directly assimilate dual-pol radar observations into the convective-scale model for real cases.