The goal of this commentary is to critically evaluate the use of popular performance metrics in hydrologic modeling. We focus on the Nash-Sutcliffe Efficiency (NSE) and the Kling-Gupta Efficiency (KGE) metrics, which are both widely used in hydrologic research and practice around the world. Our specific objectives are: (1) to provide tools that quantify the sampling uncertainty in popular performance metrics; (2) to quantify sampling uncertainty in popular performance metrics across a large sample of catchments; and (3) to prescribe the further research that is needed to improve the estimation, interpretation, and use of popular performance metrics in hydrologic modeling. Our large-sample analysis demonstrates that there is substantial sampling uncertainty in the NSE and KGE estimators. This occurs because the probability distribution of squared errors between model simulations and observations has heavy tails, meaning that performance metrics can be heavily influenced by just a few data points. Our results highlight obvious (yet ignored) abuses of performance metrics that contaminate the conclusions of many hydrologic modeling studies: It is essential to quantify the sampling uncertainty in performance metrics when justifying the use of a model for a specific purpose and when comparing the performance of competing models.

We live in a world where biophysical and social processes are tightly coupled. Hydrologic systems change in response to a variety of natural and human forces such as climate variability and change, water use and water infrastructure, and land cover change. In turn, changes in hydrologic systems impact socioeconomic, ecological, and climate systems at a number of scales, leading to a coevolution of these interlinked systems. The Harvard Water Program, Hydrosociology, Integrated Water Resources Management, Ecohydrology, Hydromorphology, and Sociohydrology were all introduced to provide distinct, interdisciplinary perspectives on water problems to address the contemporary dynamics of human interaction with the hydrosphere and the evolution of the Earth's hydrologic systems. Each of them addresses scientific, social, and engineering challenges related to how humans influence water systems and vice versa. There are now numerous examples in the literature of how holistic approaches can provide a structure and vision of the future of hydrology. We review selected examples, which taken together, describe the type of theoretical and applied integrated hydrologic analyses and associated curricular content required to address the societal issue of water resources sustainability. We describe a modern interdisciplinary science of hydrology needed to develop an in‐depth understanding of the dynamics of the connectedness between human and natural systems and to determine effective solutions to resolve the complex water problems that the world faces today. Nearly, every theoretical hydrologic model introduced previously is in need of revision to accommodate how climate, land, vegetation, and socioeconomic factors interact, change, and evolve over time.

The Nash‐Sutcliffe efficiency (NSE) and the Kling‐Gupta efficiency (KGE) are now the most widely used indices in hydrology for evaluation of the goodness of fit between model simulations S and observations O. We introduce two theoretical (probabilistic) definitions of efficiency, E and E′, based on the estimators NSE and KGE, respectively, which enable controlled Monte Carlo experiments at 447 watersheds to evaluate their performance. Although NSE is generally unbiased, it exhibits enormous variability from one sample to another, due to the remarkable skewness and periodicity of daily streamflow data. However, use of NSE with logarithms of daily streamflow leads to estimates of E with almost no variability from one sample to the next, though with high upward bias. We introduce improved estimators of E and E′ based on a bivariate lognormal monthly mixture model that are shown to yield considerable improvements over NSE and slight improvements over KGE in controlled Monte Carlo experiments. Our new estimators of E should avoid most previous criticisms of NSE implied by the literature. Improved estimators of E that account for skewness and periodicity are needed for daily and subdaily streamflow series because NSE is not suited to such applications.

A distributed hydrologic model of an urban watershed in the northeast United States was developed and combined with a genetic algorithm to determine the optimal location of infiltration-based best management practices (BMPs) for storm water management. The distributed, event-based hydrologic model integrates the curve number method with a distributed hydrologic network model of the catchment using a system of 4,533 hydrologic response units (HRUs). The infiltration-based BMP was conceptualized as an element that alters the infiltration/runoff partitioning of the HRUs in which it was applied. The results indicate that the optimal location and number of BMPs is a complex function of watershed network connectivity, flow travel time, land use, distance to channel, and contributing area, requiring an optimization approach of the type introduced here. A Pareto frontier describing the trade-off between the number of BMPs, representing project cost, and watershed flooding was developed.