Abstract Risk management has reduced vulnerability to floods and droughts globally 1,2 , yet their impacts are still increasing 3 . An improved understanding of the causes of changing impacts is therefore needed, but has been hampered by a lack of empirical data 4,5 . On the basis of a global dataset of 45 pairs of events that occurred within the same area, we show that risk management generally reduces the impacts of floods and droughts but faces difficulties in reducing the impacts of unprecedented events of a magnitude not previously experienced. If the second event was much more hazardous than the first, its impact was almost always higher. This is because management was not designed to deal with such extreme events: for example, they exceeded the design levels of levees and reservoirs. In two success stories, the impact of the second, more hazardous, event was lower, as a result of improved risk management governance and high investment in integrated management. The observed difficulty of managing unprecedented events is alarming, given that more extreme hydrological events are projected owing to climate change 3 .

Global Institute for Water Security, University of Saskatchewan, Saskatoon, Saskatchewan, Canada School of Geosciences, University of Birmingham, Birmingham, UK Dept of Earth, Ocean & Atmospheric Sciences, University of British Columbia, Vancouver, British Columbia, Canada Landcare Research, Lincoln, New Zealand Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland Centre for Hydrology, University of Saskatchewan, Canmore, Alberta, Canada School of Geographical Sciences, University of Bristol, Bristol, UK Cabot Institute, University of Bristol, Bristol, UK Hetch Hetchy Power, San Francisco, California, USA Division of Earth and Ocean Sciences, Nicolas School of the Environment, Duke University, Durham, North Carolina, USA GNS Science, Lower Hutt, New Zealand Department of Civil Engineering, Univeristy of Calgary, Calgary, Alberta, Canada Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan Department of Geography, University of Zurich, Zurich, Switzerland Dept of Biological and Ecological Engineering, Oregon State University, Corvallis, Oregon, USA Faculty of Environment & Natural Resources, University of Freiburg, Freiburg, Germany Faculty of Engineering, University of Bristol, Bristol, UK

Global Institute for Water Security, University of Saskatchewan, Saskatoon, Saskatchewan, Canada School of Geosciences, University of Birmingham, Birmingham, UK Dept of Earth, Ocean & Atmospheric Sciences, University of British Columbia, Vancouver, British Columbia, Canada Landcare Research, Lincoln, New Zealand Swiss Federal Institute of Aquatic Science and Technology, Dübendorf, Switzerland Centre for Hydrology, University of Saskatchewan, Canmore, Alberta, Canada School of Geographical Sciences, University of Bristol, Bristol, UK Cabot Institute, University of Bristol, Bristol, UK Hetch Hetchy Power, San Francisco, California, USA Division of Earth and Ocean Sciences, Nicolas School of the Environment, Duke University, Durham, North Carolina, USA GNS Science, Lower Hutt, New Zealand Department of Civil Engineering, Univeristy of Calgary, Calgary, Alberta, Canada Disaster Prevention Research Institute, Kyoto University, Kyoto, Japan Department of Geography, University of Zurich, Zurich, Switzerland Dept of Biological and Ecological Engineering, Oregon State University, Corvallis, Oregon, USA Faculty of Environment & Natural Resources, University of Freiburg, Freiburg, Germany Faculty of Engineering, University of Bristol, Bristol, UK

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: (a) to provide tools that quantify the sampling uncertainty in popular performance metrics; (b) to quantify sampling uncertainty in popular performance metrics across a large sample of catchments; and (c) 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.

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: (a) to provide tools that quantify the sampling uncertainty in popular performance metrics; (b) to quantify sampling uncertainty in popular performance metrics across a large sample of catchments; and (c) 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.

• Most conceptual bucket models have an upper limit on simulated soil moisture deficit. • Problems arise when the bucket “empties” because ET drops to unrealistic (low) levels. • Alternatives include bottomless buckets or deficit-based soil moisture accounting. • Here, we switch to a deficit-based scheme while keeping everything else constant. • Tested over historic drought, model performance and realism are enhanced. Rainfall-runoff models based on conceptual “buckets” are frequently used in climate change impact studies to provide runoff projections. When these buckets approach empty, the simulated evapotranspiration approaches zero, which places an implicit limit on the soil moisture deficit that can accrue within the model. Such models may cease to properly track the moisture deficit accumulating in reality as dry conditions continue, leading to overestimation of subsequent runoff and possible long-term bias under drying climate. Here, we suggest that model realism may be improved through alternatives which remove the upper limit on simulated soil moisture deficit, such as “bottomless” buckets or deficit-based soil moisture accounting. While some existing models incorporate such measures, no study until now has systematically assessed their impact on model realism under drying climate. Here, we alter a common bucket model by changing the soil moisture storage to a deficit accounting system in such a way as to remove the upper limit on simulated soil moisture deficit. Tested on 38 Australian catchments, the altered model is better able to track the decline in soil moisture at the end of seasonal dry periods, which leads to superior performance over varied historic climate, including the 13-year “Millennium” drought. However, groundwater and GRACE data reveal long-term trends that are not matched in simulations, indicating that further changes may be required. Nonetheless, the results suggest that a broader adoption of bottomless buckets and/or deficit accounting within conceptual rainfall runoff models may improve the realism of runoff projections under drying climate.

• Most conceptual bucket models have an upper limit on simulated soil moisture deficit. • Problems arise when the bucket “empties” because ET drops to unrealistic (low) levels. • Alternatives include bottomless buckets or deficit-based soil moisture accounting. • Here, we switch to a deficit-based scheme while keeping everything else constant. • Tested over historic drought, model performance and realism are enhanced. Rainfall-runoff models based on conceptual “buckets” are frequently used in climate change impact studies to provide runoff projections. When these buckets approach empty, the simulated evapotranspiration approaches zero, which places an implicit limit on the soil moisture deficit that can accrue within the model. Such models may cease to properly track the moisture deficit accumulating in reality as dry conditions continue, leading to overestimation of subsequent runoff and possible long-term bias under drying climate. Here, we suggest that model realism may be improved through alternatives which remove the upper limit on simulated soil moisture deficit, such as “bottomless” buckets or deficit-based soil moisture accounting. While some existing models incorporate such measures, no study until now has systematically assessed their impact on model realism under drying climate. Here, we alter a common bucket model by changing the soil moisture storage to a deficit accounting system in such a way as to remove the upper limit on simulated soil moisture deficit. Tested on 38 Australian catchments, the altered model is better able to track the decline in soil moisture at the end of seasonal dry periods, which leads to superior performance over varied historic climate, including the 13-year “Millennium” drought. However, groundwater and GRACE data reveal long-term trends that are not matched in simulations, indicating that further changes may be required. Nonetheless, the results suggest that a broader adoption of bottomless buckets and/or deficit accounting within conceptual rainfall runoff models may improve the realism of runoff projections under drying climate.

Landscape evolution models (LEMs) have the capability to characterize key aspects of geomorphological and hydrological processes. However, their usefulness is hindered by model equifinality and paucity of available calibration data. Estimating uncertainty in the parameter space and resultant model predictions is rarely achieved as this is computationally intensive and the uncertainties inherent in the observed data are large. Therefore, a limits-of-acceptability (LoA) uncertainty analysis approach was adopted in this study to assess the value of uncertain hydrological and geomorphic data. These were used to constrain simulations of catchment responses and to explore the parameter uncertainty in model predictions. We applied this approach to the River Derwent and Cocker catchments in the UK using a LEM CAESAR-Lisflood. Results show that the model was generally able to produce behavioural simulations within the uncertainty limits of the streamflow. Reliability metrics ranged from 24.4% to 41.2% and captured the high-magnitude low-frequency sediment events. Since different sets of behavioural simulations were found across different parts of the catchment, evaluating LEM performance, in quantifying and assessing both at-a-point behaviour and spatial catchment response, remains a challenge. Our results show that evaluating LEMs within uncertainty analyses framework while taking into account the varying quality of different observations constrains behavioural simulations and parameter distributions and is a step towards a full-ensemble uncertainty evaluation of such models. We believe that this approach will have benefits for reflecting uncertainties in flooding events where channel morphological changes are occurring and various diverse (and yet often sparse) data have been collected over such events.

Landscape evolution models (LEMs) have the capability to characterize key aspects of geomorphological and hydrological processes. However, their usefulness is hindered by model equifinality and paucity of available calibration data. Estimating uncertainty in the parameter space and resultant model predictions is rarely achieved as this is computationally intensive and the uncertainties inherent in the observed data are large. Therefore, a limits-of-acceptability (LoA) uncertainty analysis approach was adopted in this study to assess the value of uncertain hydrological and geomorphic data. These were used to constrain simulations of catchment responses and to explore the parameter uncertainty in model predictions. We applied this approach to the River Derwent and Cocker catchments in the UK using a LEM CAESAR-Lisflood. Results show that the model was generally able to produce behavioural simulations within the uncertainty limits of the streamflow. Reliability metrics ranged from 24.4% to 41.2% and captured the high-magnitude low-frequency sediment events. Since different sets of behavioural simulations were found across different parts of the catchment, evaluating LEM performance, in quantifying and assessing both at-a-point behaviour and spatial catchment response, remains a challenge. Our results show that evaluating LEMs within uncertainty analyses framework while taking into account the varying quality of different observations constrains behavioural simulations and parameter distributions and is a step towards a full-ensemble uncertainty evaluation of such models. We believe that this approach will have benefits for reflecting uncertainties in flooding events where channel morphological changes are occurring and various diverse (and yet often sparse) data have been collected over such events.

The Panola Mountain Research Watershed (PMRW) is a 41-hectare forested catchment within the Piedmont Province of the Southeastern United States. Observations, experimentation, and numerical modelling have been conducted at Panola over the past 35 years. But to date, these studies have not been fully incorporated into a more comprehensive synthesis. Here we describe the evolving perceptual understanding of streamflow generation mechanisms at the PMRW. We show how the long-term study has enabled insights that were initially unforeseen but are also unachievable in short-term studies. In particular, we discuss how the accumulation of field evidence, detailed site characterization, and modelling enabled a priori hypotheses to be formed, later rejected, and then further refined through repeated field campaigns. The extensive characterization of the soil and bedrock provided robust process insights not otherwise achievable from hydrometric measurements and numerical modelling alone. We focus on two major aspects of streamflow generation: the role of hillslopes (and their connection to the riparian zone) and the role of catchment storage in controlling fluxes and transit times of water in the catchment. Finally, we present location-independent hypotheses based on our findings at PMRW and suggest ways to assess the representativeness of PMRW in the broader context of headwater watersheds.

The Panola Mountain Research Watershed (PMRW) is a 41-hectare forested catchment within the Piedmont Province of the Southeastern United States. Observations, experimentation, and numerical modelling have been conducted at Panola over the past 35 years. But to date, these studies have not been fully incorporated into a more comprehensive synthesis. Here we describe the evolving perceptual understanding of streamflow generation mechanisms at the PMRW. We show how the long-term study has enabled insights that were initially unforeseen but are also unachievable in short-term studies. In particular, we discuss how the accumulation of field evidence, detailed site characterization, and modelling enabled a priori hypotheses to be formed, later rejected, and then further refined through repeated field campaigns. The extensive characterization of the soil and bedrock provided robust process insights not otherwise achievable from hydrometric measurements and numerical modelling alone. We focus on two major aspects of streamflow generation: the role of hillslopes (and their connection to the riparian zone) and the role of catchment storage in controlling fluxes and transit times of water in the catchment. Finally, we present location-independent hypotheses based on our findings at PMRW and suggest ways to assess the representativeness of PMRW in the broader context of headwater watersheds.

Abstract. The theory that forms the basis of TOPMODEL (a topography-based hydrological model) was first outlined by Mike Kirkby some 45 years ago. This paper recalls some of the early developments, the rejection of the first journal paper, the early days of digital terrain analysis, model calibration and validation, the various criticisms of the simplifying assumptions, and the relaxation of those assumptions in the dynamic forms of TOPMODEL. A final section addresses the question of what might be done now in seeking a simple, parametrically parsimonious model of hillslope and small catchment processes if we were starting again.

Water resources in semi‐arid regions like the Mediterranean Basin are highly vulnerable because of the high variability of weather systems. Additionally, climate change is altering the timing and pattern of water availability in a region where growing populations are placing extra demands on water supplies. Importantly, how reservoirs and dams have an influence on the amount of water resources available is poorly quantified. Therefore, we examine the impact of reservoirs on water resources together with the impact of climate change in a semi‐arid Mediterranean catchment. We simulated the Susurluk basin (23.779‐km2) using the Soil and Water Assessment Tool (SWAT) model. We generate results for with (RSV) and without reservoirs (WRSV) scenarios. We run simulations for current and future conditions using dynamically downscaled outputs of the MPI‐ESM‐MR general circulation model under two greenhouse gas relative concentration pathways (RCPs) in order to reveal the coupled effect of reservoir and climate impacts. Water resources were then converted to their usages – blue water (water in aquifers and rivers), green water storage (water in the soil) and green water flow (water losses by evaporation and transpiration). The results demonstrate that all water resources except green water flow are projected to decrease under all RCPs compared to the reference period, both long‐term and at seasonal scales. However, while water scarcity is expected in the future, reservoir storage is shown to be adequate to overcome this problem. Nevertheless, reservoirs reduce the availability of water, particularly in soil moisture stores, which increases the potential for drought by reducing streamflow. Furthermore, reservoirs cause water losses through evaporation from their open surfaces. We conclude that pressures to protect society from economic damage by building reservoirs have a strong impact on the fluxes of watersheds. This is additional to the effect of climate change on water resources.

The choice of hydrological model structure, that is, a model's selection of states and fluxes and the equations used to describe them, strongly controls model performance and realism. This work investigates differences in performance of 36 lumped conceptual model structures calibrated to and evaluated on daily streamflow data in 559 catchments across the United States. Model performance is compared against a benchmark that accounts for the seasonality of flows in each catchment. We find that our model ensemble struggles to beat the benchmark in snow-dominated catchments. In most other catchments model structure equifinality (i.e., cases where different models achieve similar high efficiency scores) can be very high. We find no relation between the number of model parameters and performance during either calibration or evaluation periods nor evidence of increased risk of overfitting for models with more parameters. Instead, the choice of model parametrization (i.e., which equations are used and how parameters are used within them) dictates the model's strengths and weaknesses. Results suggest that certain model structures are inherently better suited for certain objective functions and thus for certain study purposes. We find no clear relationships between the catchments where any model performs well and descriptors of those catchments' geology, topography, soil, and vegetation characteristics. Instead, model suitability seems to relate strongest to the streamflow regime each catchment generates, and we have formulated several tentative hypotheses that relate commonalities in model structure to similarities in model performance. Modeling results are made publicly available for further investigation.

Hydrology is still, and for good reasons, an inexact science, even if evolving hydrological understanding has provided a basis for improved water management for at least the last three millennia. The limitations of that understanding have, however, become much more apparent and important in the last century as the pressures of increasing populations, and the anthropogenic impacts on catchment forcing and responses, have intensified. At the same time, the sophistication of hydrological analyses and models has been developing rapidly, often driven more by the availability of computational power and geographical data sets than any real increases in understanding of hydrological processes. This sophistication has created an illusion of real progress but a case can be made that we are still rather muddling along, limited by the significant uncertainties in hydrological observations, knowledge of catchment characteristics and related gaps in conceptual understanding, particularly of the sub-surface. These knowledge gaps are illustrated by the fact that for many catchments we cannot close the water balance without significant uncertainty, uncertainty that is often neglected in evaluating models for practical applications.