Urban water resources planning is complicated by unprecedented uncertainty in supply and demand. Scenario analysis is commonly used to test a water system under several uncertain futures to assess the system response to different uncertain drivers. Real-world planning often simplifies the full range of uncertainty faced by a system into a limited set of deterministic scenarios to enhance accessibility for decision-makers and the public. However, overlooking uncertainty can expose the system to failures. In contrast, applying scenario analysis to the full set of uncertain drivers can identify vulnerabilities, but current approaches to visualizing this information are difficult to communicate and therefore have limited practical applications. In this work, we present a case study of the city of Santa Barbara, CA, facing multiple uncertainties in their water supply portfolio and demand, from pending state and federal regulations, to changing hydrology and water demand. The city seeks to increase their water portfolio robustness by expanding its seawater desalination plant, but must determine the expansion capacity. We introduced computational tools that enable a comprehensive assessment of uncertainty across nine uncertain drivers, identified with the help of water planners in Santa Barbara. To allow public participation in the desalination expansion decision, we develop interactive visual analytics to aid decision-makers and stakeholders in navigating complex scenario analysis outcomes. Our results quantify the tradeoffs between increased capacity and system robustness. We also categorize uncertain drivers according to their criticality and the level of control that the municipality can exert over them, for instance the city's water demand can be partially controlled through water efficiency campaigns. This work aims to enhance participation and uncertainty characterization of urban water planning efforts.