The proper quantification and visualization of uncertainty requires a high level of domain knowledge. Despite this, few studies have collected and compared the roles, experiences and opinions of scientists in different types of uncertainty analysis. I address this gap by conducting two types of studies: 1) a domain characterization study with general questions for experts from various fields based on a recent literature review in ensemble analysis and visualization, and; 2) a long-term interview with domain experts focusing on specific problems and challenges in uncertainty analysis. From the domain characterization, I identified the most common metrics applied for uncertainty quantification and discussed the current visualization applications of these methods. Based on the interviews with domain experts, I characterized the background and intents of the experts when performing uncertainty analysis. This enables me to characterize domain needs that are currently underrepresented or unsupported in the literature. Finally, I developed a new framework for visualizing uncertainty in climate ensembles.