Technical note: How many models do we need to simulate hydrologic processes across large geographical domains?

Abstract. Robust large-domain predictions of water availability and threats require models that work well across different basins in the model domain. It is currently common to express a model's accuracy through aggregated efficiency scores such as the Nash-Sutcliffe Efficiency and Kling-Gupta Efficiency, and these scores often form the basis to select among competing models. However, recent work has shown that such scores are subject to considerable sampling uncertainty: the exact selection of time steps used to calculate the scores can have large impacts on the scores obtained. Here we explicitly account for this sampling uncertainty to determine the number of models that are needed to simulate hydrologic processes across large spatial domains. Using a selection of 36 conceptual models and 559 basins, our results show that model equifinality, the fact that very different models can produce simulations with very similar accuracy, makes it very difficult to unambiguously select one model over another. If models were selected based on their validation KGE scores alone, almost every model would be selected as the best model in at least some basins. When sampling uncertainty is accounted for, this number drops to 4 models being needed to cover 95% of investigated basins, and 10 models being needed to cover all basins. We obtain similar conclusions for an objective function focused on low flows. These results suggests that, under the conditions typical of many current modeling studies, there is limited evidence that using a wide variety of different models leads to appreciable differences in simulation accuracy compared to using a smaller number of carefully chosen models.