Scale-invariant sensitivity for multi-purpose water reservoirs management with temporal scale-dependent modeling

High-resolution temporal data (e.g., daily) is valuable for the decision-making of water resources management because it more accurately captures fine-scale processes and extremes than the coarse temporal data (e.g., weekly or monthly). However, many studies rarely consider this superior suitability for water resource modeling and management; instead, they often use whichever data is more readily available. So far, no comparative investigations have been conducted to determine if access to different time-scale data would change decision-maker perceptions or the rationality of decision making. This study proposes a framework for assessing the impact of different temporal scales on water resource management and the performance objective's sensitivity to uncertainties. We built the multi-objective operation models and operating rules of a water reservoir system based on daily, weekly, and monthly scales, respectively, using an evolution multi-objective direct policy search. The temporal scales of the input variables (i.e., streamflow) affect both the model structures and the output variables. In exploring these effects, we reevaluated the temporal scale-dependent operating rules under uncertain streamflow sets generated from synthetic hydrology. Finally, we obtained the output variable's sensitivities to the uncertain factors at different temporal scales using the distribution-based sensitivity analysis method. Our results show that water management based on too coarse resolution might give decision makers the wrong perception because the effect of actual extreme streamflow process on the performance objectives is ignored. The streamflow uncertainty is more influential than the uncertainty associated with operating rules. However, the sensitivities are characterized by temporal scale invariance, as the differences of the sensitivity between different temporal scales are not obvious over the uncertainties in streamflow and thresholds. These results show that water management should consider the resolution-dependent effect of temporal scales for balancing modeling complexity and computational cost.