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

Hydrometeorological flood generating processes (excess rain, short rain, long rain, snowmelt, and rain-on-snow) underpin our understanding of flood behavior. Knowledge about flood generating processes improves hydrological models, flood frequency analysis, estimation of climate change impact on floods, etc. Yet, not much is known about how climate and catchment attributes influence the spatial distribution of flood generating processes. This study aims to offer a comprehensive and structured approach to close this knowledge gap. We employ a large sample approach (671 catchments across the contiguous United States) and evaluate how catchment attributes and climate attributes influence the distribution of flood processes. We use two complementary approaches: A statistics-based approach which compares attribute frequency distributions of different flood processes; and a random forest model in combination with an interpretable machine learning approach (accumulated local effects [ALE]). The ALE method has not been used often in hydrology, and it overcomes a significant obstacle in many statistical methods, the confounding effect of correlated catchment attributes. As expected, we find climate attributes (fraction of snow, aridity, precipitation seasonality, and mean precipitation) to be most influential on flood process distribution. However, the influence of catchment attributes varies both with flood generating process and climate type. We also find flood processes can be predicted for ungauged catchments with relatively high accuracy (R2 between 0.45 and 0.9). The implication of these findings is flood processes should be considered for future climate change impact studies, as the effect of changes in climate on flood characteristics varies between flood processes.

Hydrometeorological flood generating processes (excess rain, short rain, long rain, snowmelt, and rain-on-snow) underpin our understanding of flood behavior. Knowledge about flood generating processes improves hydrological models, flood frequency analysis, estimation of climate change impact on floods, etc. Yet, not much is known about how climate and catchment attributes influence the spatial distribution of flood generating processes. This study aims to offer a comprehensive and structured approach to close this knowledge gap. We employ a large sample approach (671 catchments across the contiguous United States) and evaluate how catchment attributes and climate attributes influence the distribution of flood processes. We use two complementary approaches: A statistics-based approach which compares attribute frequency distributions of different flood processes; and a random forest model in combination with an interpretable machine learning approach (accumulated local effects [ALE]). The ALE method has not been used often in hydrology, and it overcomes a significant obstacle in many statistical methods, the confounding effect of correlated catchment attributes. As expected, we find climate attributes (fraction of snow, aridity, precipitation seasonality, and mean precipitation) to be most influential on flood process distribution. However, the influence of catchment attributes varies both with flood generating process and climate type. We also find flood processes can be predicted for ungauged catchments with relatively high accuracy (R2 between 0.45 and 0.9). The implication of these findings is flood processes should be considered for future climate change impact studies, as the effect of changes in climate on flood characteristics varies between flood processes.

• 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.

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.

This paper is the outcome of a community initiative to identify major unsolved scientific problems in hydrology motivated by a need for stronger harmonisation of research efforts. The procedure involved a public consultation through online media, followed by two workshops through which a large number of potential science questions were collated, prioritised, and synthesised. In spite of the diversity of the participants (230 scientists in total), the process revealed much about community priorities and the state of our science: a preference for continuity in research questions rather than radical departures or redirections from past and current work. Questions remain focused on the process-based understanding of hydrological variability and causality at all space and time scales. Increased attention to environmental change drives a new emphasis on understanding how change propagates across interfaces within the hydrological system and across disciplinary boundaries. In particular, the expansion of the human footprint raises a new set of questions related to human interactions with nature and water cycle feedbacks in the context of complex water management problems. We hope that this reflection and synthesis of the 23 unsolved problems in hydrology will help guide research efforts for some years to come.