To evaluate models as hypotheses, we developed the method of Flux Mapping to construct a hypothesis space based on dominant runoff generating mechanisms. Acceptable model runs, defined as total simulated flow with similar (and minimal) model error, are mapped to the hypothesis space given their simulated runoff components. In each modeling case, the hypothesis space is the result of an interplay of factors: model structure and parameterization, choice of error metric, and data information content. The aim of this study is to disentangle the role of each factor in model evaluation. We used two model structures (SACRAMENTO and SIMHYD), two parameter sampling approaches (Latin Hypercube Sampling of the parameter space and guided-search of the solution space), three widely used error metrics (Nash-Sutcliffe Efficiency – NSE, Kling-Gupta Efficiency skill score – KGEss, and Willmott’s refined Index of Agreement – WIA), and hydrological data from a large sample of Australian catchments. First, we characterized how the three error metrics behave under different error types and magnitudes independent of any modeling. We then conducted a series of controlled experiments to unpack the role of each factor in runoff generation hypotheses. We show that KGEss is a more reliable metric compared to NSE and WIA for model evaluation. We further demonstrate that only changing the error metric — while other factors remain constant — can change the model solution space and hence vary model performance, parameter sampling sufficiency, and/or the flux map. We show how unreliable error metrics and insufficient parameter sampling impair model-based inferences, particularly runoff generation hypotheses.

Hydrologic models are essential tools to understand and plan for the effect of changing climates; however, they are known to underperform in transitory climate conditions. Research to date identifies the inadequacy of models to perform during prolonged drought, but falls short on pinpointing how and which specific aspects of model performance are affected. Here, we study five conceptual rainfall-runoff models and their performance in 155 Australian catchments which recently experienced a 13-year long dry period, with a focus on a wide range of performance metrics. We show that model performance degrades extensively during the drought across most metrics, with overestimation of flow volumes driving the decline and representation of shape and variability of the hydrograph and the flow-duration curve being more resilient to the prolonged dry climate. This indicates that the overestimation is not linked to specific flow regimes, but is the result of proportional flow decline throughout the hydrograph, suggesting engagement of multiple catchment processes in determining the changes in flow during the drought across high and low flow periods as well as through faster and slower flow routes. Additionally, we show that in most cases model performance does not recover after the end of the drought and that the multi-annual nature of the drought is the likely reason for exacerbated performance decline due to accumulation and aggravation of errors over subsequent dry years. By promoting detailed investigation of models’ shortcomings, we hope to foster the development of more resilient model structures to improve applicability within climate change scenarios.

Recent shifts in the behaviour of natural watersheds suggest acute challenges for water planning under climate change. Shifts towards less annual streamflow for a given annual precipitation have now been reported on multiple continents, usually in response to a multi-year drought. Future drying under climate change may induce similar unexpected hydrological behaviour, and 15 this commentary discusses the implications for water planning and management. Commonly-used hydrological models poorly represent the shifting behaviour and cannot be relied upon to anticipate future shifts. Thus, their use may result in underestimation of hydroclimatic risk and exposure to “surprise” reductions in water supply, relative to projections. The onus is now on hydrologists to determine the underlying causes of shifting behaviour and incorporate more dynamic realism into 20 operational models. Main points 1. Drought-induced hydrological shifts towards less streamflow for a given precipitation have been reported across multiple continents. 2. Future drying under climate change may induce similar unexpected behaviour. 25 3. Such behaviour creates additional uncertainty in runoff projections, and may lead to ‘surprise’ reductions in future streamflow. Main text In a recent article, Peterson et al. (2021) reported shifts in hydrological behaviour induced by the “Millennium” drought (1997-2010) in Australia and persisting years after the drought ended. 30 Reductions in water resources during and after this drought were far more extreme than expected, even given low rainfall (Saft et al., 2015), because many watersheds shifted into a seemingly different state of streamflow behaviour. Concerningly, some watersheds remain in this state despite a return to near-average climate conditions, so that a year of average rainfall now produces less streamflow than it did before the drought (Peterson et al., 2021). With similar hydrological 35 shifts reported elsewhere in the world, including the USA (Avanzi et al., 2020), China (Tian et al.,

Equifinality is understood as one of the fundamental difficulties in the study of open complex systems, including catchment hydrology. A review of the hydrologic literature reveals that the term equifinality has been widely used, but in many cases inconsistently and without coherent recognition of the various facets of equifinality, which can lead to ambiguity but also methodological fallacies. Therefore, in this study we first characterise the term equifinality within the context of hydrological modelling by reviewing the genesis of the concept of equifinality and then presenting a theoretical framework. During past decades, equifinality has mainly been studied as a subset of aleatory (arising due to randomness) uncertainty and for the assessment of model parameter uncertainty. Although the connection between parameter uncertainty and equifinality is undeniable, we argue there is more to equifinality than just aleatory parameter uncertainty. That is, the importance of equifinality and epistemic uncertainty (arising due to lack of knowledge) and their implications is overlooked in our current practice of model evaluation. Equifinality and epistemic uncertainty in studying, modelling, and evaluating hydrologic processes are treated as if they can be simply discussed in (or often reduced to) probabilistic terms (as for aleatory uncertainty). The deficiencies of this approach to conceptual rainfall-runoff modelling are demonstrated for selected Australian catchments by examination of parameter and internal flux distributions and interactions within SIMHYD. On this basis, we present a new approach that expands equifinality concept beyond model parameters to inform epistemic uncertainty. The new approach potentially facilitates the identification and development of more physically plausible models and model evaluation schemes particularly within the multiple working hypotheses framework, and is generalisable to other fields of environmental modelling as well.