Long-term water resource management involving multipurpose coordination requires robust decision-making in water infrastructure cases to cope with various types of uncertainties. Traditional robust optimization methods generally do not explicitly propagate input or parametric uncertainties into estimates of the robustness of solutions, which limits their ability to address uncertainty comprehensively across solution spaces. In this study, we introduce an explicit robust decision-making framework that blends multiobjective search, probabilistic analysis of robustness, and diagnostic verification tools to identify robust optimal solutions to external uncertainty. The proposed framework is illustrated on four diverse robustness formulations, which capture a wide variety of stakeholder attitudes from highly risk-averse to risk-neutral, for the primary operating objectives (hydropower production, water diversion, and hydrological alteration degree) in China's Hanjiang cascade reservoir system. By analyzing the Pareto front propagated from inflow uncertainty, it is found that optimal robust policies with a significantly higher degree of hydrological alteration are preferred in most formulations to achieve relatively lower joint uncertainty of hydropower and water diversion. These policies also yield sufficiently stable model performance in the case of an out-of-sample streamflow set during diagnostic verification. Furthermore, a comparative analysis of four different formulations suggests that a composite normalized robustness indicator (NRI) developed in this study to integrate various robustness metrics can achieve an effective balance for all considered objectives. These findings highlight the benefits of explicit robust optimization for managing hydrological uncertainties in multipurpose cascade reservoirs.