Climate analysts use Coupled Model Intercomparison Project Phase 5 (CMIP5) simulations to make sense of models performance in predicting extreme events such as heavy precipitation. Similarly, weather analysts use numerical weather prediction models (NWP) to simulate weather conditions either by perturbing initial conditions or by changing multiple input parameterization schemes, e.g., cumulus and microphysics schemes. These simulations are used in operational weather forecasting and for studying the role of parameterization schemes in synoptic weather events like storms. This work addresses the need for visualizing the differences in both CMIP5 and NWP model output. This work proposes three glyph designs used for communicating CMIP5 model error. It also describes Ensemble Visual eXplorer tool that provides multiple ways of visualizing NWP model output and the related input parameter space. The proposed interactive dendrogram provides an effective way to relate multiple input parameterization schemes with spatial characteristics of model uncertainty features. The glyphs that were designed to communicate CMIP5 model error are extended to encode both parameterization schemes and graduated uncertainty, to provide related insights at specific locations such as storm center and the areas surrounding it. The work analyzes different ways of using glyphs to represent parametric uncertainty using visual variables such as color and size, in conjunction with Gestalt visual properties. It demonstrates the use of visual analytics in resolving some of the issues such as visual scalability. As part of this dissertation, we evaluated three glyph designs using average precipitation rate predicted by CMIP5 simulations, and Ensemble Visual eXplorer tool using WRF 1999 March 4th, North American storm track dataset.