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. ARTICLE HISTORY

Hydrologic models have potential to be useful tools in planning for future climate variability. However, recent literature suggests that the current generation of conceptual rainfall runoff models tend to underestimate the sensitivity of runoff to a given change in rainfall, leading to poor performance when evaluated over multiyear droughts. This research revisited this conclusion, investigating whether the observed poor performance could be due to insufficient model calibration and evaluation techniques. We applied an approach based on Pareto optimality to explore trade‐offs between model performance in different climatic conditions. Five conceptual rainfall runoff model structures were tested in 86 catchments in Australia, for a total of 430 Pareto analyses. The Pareto results were then compared with results from a commonly used model calibration and evaluation method, the Differential Split Sample Test. We found that the latter often missed potentially promising parameter sets within a given model structure, giving a false negative impression of the capabilities of the model. This suggests that models may be more capable under changing climatic conditions than previously thought. Of the 282[347] cases of apparent model failure under the split sample test using the lower [higher] of two model performance criteria trialed, 155[120] were false negatives. We discuss potential causes of remaining model failures, including the role of data errors. Although the Pareto approach proved useful, our aim was not to suggest an alternative calibration strategy, but to critically assess existing methods of model calibration and evaluation. We recommend caution when interpreting split sample results.

Abstract. This paper presents the Modular Assessment of Rainfall–Runoff Models Toolbox (MARRMoT): a modular open-source toolbox containing documentation and model code based on 46 existing conceptual hydrologic models. The toolbox is developed in MATLAB and works with Octave. MARRMoT models are based solely on traceable published material and model documentation, not on already-existing computer code. Models are implemented following several good practices of model development: the definition of model equations (the mathematical model) is kept separate from the numerical methods used to solve these equations (the numerical model) to generate clean code that is easy to adjust and debug; the implicit Euler time-stepping scheme is provided as the default option to numerically approximate each model's ordinary differential equations in a more robust way than (common) explicit schemes would; threshold equations are smoothed to avoid discontinuities in the model's objective function space; and the model equations are solved simultaneously, avoiding the physically unrealistic sequential solving of fluxes. Generalized parameter ranges are provided to assist with model inter-comparison studies. In addition to this paper and its Supplement, a user manual is provided together with several workflow scripts that show basic example applications of the toolbox. The toolbox and user manual are available from https://github.com/wknoben/MARRMoT (last access: 30 May 2019; https://doi.org/10.5281/zenodo.3235664). Our main scientific objective in developing this toolbox is to facilitate the inter-comparison of conceptual hydrological model structures which are in widespread use in order to ultimately reduce the uncertainty in model structure selection.

Evidence suggests that catchment state variables such as groundwater can exhibit multiyear trends. This means that their state may reflect not only recent climatic conditions but also climatic conditions in past years or even decades. Here we demonstrate that five commonly used conceptual "bucket" rainfall-runoff models are unable to replicate multiyear trends exhibited by natural systems during the "Millennium Drought" in south-east Australia. This causes an inability to extrapolate to different climatic conditions, leading to poor performance in split sample tests. Simulations are examined from five models applied in 38 catchments, then compared with groundwater data from 19 bores and Gravity Recovery and Climate Experiment data for two geographic regions. Whereas the groundwater and Gravity Recovery and Climate Experiment data decrease from high to low values gradually over the duration of the 13-year drought, the model storages go from high to low values in a typical seasonal cycle. This is particularly the case in the drier, flatter catchments. Once the drought begins, there is little room for decline in the simulated storage, because the model "buckets" are already "emptying" on a seasonal basis. Since the effects of sustained dry conditions cannot accumulate within these models, we argue that they should not be used for runoff projections in a drying climate. Further research is required to (a) improve conceptual rainfall-runoff models, (b) better understand circumstances in which multiyear trends in state variables occur, and (c) investigate links between these multiyear trends and changes in rainfall-runoff relationships in the context of a changing climate.Plain Language Summary It is common in science to use a mental picture or metaphor that simplifies a complex phenomenon. A common metaphor used for a water supply catchment is that of a leaky bucket. When it rains, the bucket fills up; when it does not rain for a while, the bucket empties due to evaporation and water used by trees; and leaking water is like river flow. Computer models based on variants of this metaphor are common and can provide predictions of how much streamflow might occur under future scenarios. This paper explores limitations of the bucket metaphor and associated models. Recently, during a 13-year drought in Australia, river catchments gradually started to dry up. With each passing year, the depth to groundwater increased gradually as the water used by trees was not replenished by rainfall. We compare this long, slow behavior to that of five commonly used "bucket" models. The models do not show the long, slow drying up-they only show the seasonal ups and downs, and their predictions of streamflow over the drought are poor. This is surprising, and it means we should choose our models carefully and seek out models that can simulate this behavior and its impact on streamflow.

It has been widely shown that rainfall-runoff models often provide poor and biased simulations after a change in climate, but evidence suggests existing models may be capable of better simulations if calibration strategies are improved. Common practice is to use ''least squares''-type objective functions, which focus on hydrological behavior during high flows. However, simulation of a drying climate may require a more balanced consideration of other parts of the flow regime, including mid-low flows and drier years in the calibration period, as a closer analogue of future conditions. Here we systematically test eight objective functions over 86 catchments and five conceptual model structures in southern and eastern Australia. We focus on performance when evaluated over multiyear droughts. The results show significant improvements are possible compared to least squares calibration. In particular, the Refined Index of Agreement (based on sum of absolute error, not sum of squared error) and a new objective function called the Split KGE (which gives equal weight to each year in the calibration series) give significantly better split-sample results than least squares approaches. This improvement held for all five model structures, regardless of basin characteristics such as slope, vegetation, and across a range of climatic conditions (e.g., mean precipitation between 500 and 1,500 mm/yr). We recommend future studies to avoid least squares approaches (e.g., optimizing NSE or KGE with no prior transformation on streamflow) and adopt these alternative methods, wherever simulations in a drying climate are required.Plain Language Summary Rainfall-runoff models are useful tools in water resource planning under climate change. They are commonly used to quantify the impact of changes in climatic variables, such as rainfall, on water availability for human consumption or environmental needs. Many parts of the world are projected to be substantially drier, possibly with threatened water resources. Given the importance of water, reliable tools for understanding future water availability are vital for society. However, literature would suggest that the current generation of rainfall-runoff models is not reliable when applied in changing climatic conditions, underestimating the sensitivity of runoff to a given change in precipitation. Many hydrologists have assumed deficiencies in the underlying model equations are to blame. However, this paper demonstrates significant improvement without changing model equations, by using a different ''objective function.'' The objective function defines how the model is ''tuned'' to observations of river discharge, and this article identifies objective functions that tend to make model simulations more robust when applied in a drying climate. Using these objective functions can improve the accuracy and plausibility of future water availability estimates made for climate change impact studies.

Large-sample hydrology (LSH) relies on data from large sets (tens to thousands) of catchments to go beyond individual case studies and derive robust conclusions on hydrological processes and models. Numerous LSH datasets have recently been released, covering a wide range of regions and relying on increasingly diverse data sources to characterize catchment behaviour. These datasets offer novel opportunities, yet they are also limited by their lack of comparability, uncertainty estimates and characterization of human impacts. This article (i) underscores the key role of LSH datasets in hydrological studies, (ii) provides a review of currently available LSH datasets, (iii) highlights current limitations of LSH datasets and (iv) proposes guidelines and coordinated actions to overcome these limitations. These guidelines and actions aim to standardize and automatize the creation of LSH datasets worldwide, and to enhance the reproducibility and comparability of hydrological studies.

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.

Rainfall-runoff models are often deficient under changing climatic conditions, yet almost no recent studies propose new or improved model structures, instead focusing on model intercomparison, input sensitivity, and/or quantification of uncertainty. This paucity of progress in model development is (in part) due to the difficulty of distinguishing which cases of model failure are truly caused by structural inadequacy. Here we propose a new framework to diagnose the salient cause of poor model performance in changing climate conditions, be it structural inadequacy, poor parameterization, or data errors. The framework can be applied to a single catchment, although larger samples of catchments are helpful to generalize and/or cross-check results. To generate a diagnosis, multiple historic periods with contrasting climate are defined, and the limits of model robustness and flexibility are explored over each period separately and for all periods together. Numerous data-based checks also supplement the results. Using a case study catchment from Australia, improved inference of structural failure and clearer evaluation of model structural improvements are demonstrated. This framework enables future studies to (i) identify cases where poor simulations are due to poor calibration methods or data errors, remediating these cases without recourse to structural changes; and (ii) use the remaining cases to gain greater clarity into what structural changes are needed to improve model performance in changing climate.Plain Language Summary Rainfall runoff models are tools used by hydrologists in climate change assessments to estimate how future streamflow might change in response to a given (often hypothetical) climate scenario. For example, suppose we can assume that rainfall in a particular location is going to reduce by 20% in the future. Does this mean that streamflow will also reduce by 20%? Or will it be 10% less or 40% less? Although rainfall runoff models are among the best tools available, they are often not very good at answering this question. When tested on historical multiyear droughts, they often perform poorly, and we are unsure why. One problem is that when a model fails in this task, it is difficult to know what went wrong. Perhaps there was a problem with the data, since environmental monitoring is often subject to large errors. Perhaps the problem lay not with the model itself but with the way it was trained, or calibrated, to the data. Lastly, perhaps the model itself-its mathematical equations-need to be changed. To improve our estimates, we need a method to test which cause is behind the model failure; otherwise, we might make changes where none are warranted. This paper proposes such a method, in the form of a multistep framework that can isolate the causes of model failures. By ensuring that our attention is focused in the correct direction, this framework will help us to understand and make better estimates of how river flow will be altered by a changing climate.