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Uncertainty analysis is an integral part of any scientific modeling, particularly within the domain of hydrological sciences given the various types and sources of uncertainty. At the center of uncertainty rests the concept of equifinality, that is, reaching a given endpoint (finality) through different pathways. The operational definition of equifinality in hydrological modeling is that various model structures and/or parameter sets (i.e., equal pathways) are equally capable of reproducing a similar (not necessarily identical) hydrological outcome (i.e., finality). Here we argue that there is more to model equifinality than model structures/parameters, that is, other model components can give rise to model equifinality and/or could be used to explore equifinality within model space. We identified six facets of model equifinality, namely, model structure, parameters, performance metrics, initial and boundary conditions, inputs, and internal fluxes. Focusing on model internal fluxes, we developed a methodology called flux mapping that has fundamental implications in understanding and evaluating model process representation within the paradigm of multiple working hypotheses. To illustrate this, we examine the equifinality of runoff fluxes of a conceptual rainfall-runoff model for a number of different Australian catchments. We demonstrate how flux maps can give new insights into the model behavior that cannot be captured by conventional model evaluation methods. We discuss the advantages of flux space, as a subspace of the model space not usually examined, over parameter space. We further discuss the utility of flux mapping in hypothesis generation and testing, extendable to any field of scientific modeling of open complex systems under uncertainty.

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.

Analysis of flood and streamflow timing has recently gained prominence as a tool for attribution of climatic changes to flooding. Such studies generally apply circular statistics to the day of maximum flow in a calendar year and use nonparametric linear trend tests to investigate changes in flooding on a local or regional scale. Here we investigate both the center timing of streamflow and the day of maximum flow using a local water year. For each station, the start of the water year is defined as the month of lowest average monthly streamflow. This definition of water year prevents ambiguity in the direction of computed trends and enables flood and streamflow timing to be described by a normal distribution. Using the assumption of normality, we calculate the historical trend in both flood and streamflow timing using linear regression. While shifts in flood and streamflow timing are consistent with climate change and are shifting in a similar direction, shifts in the timing of the annual maxima flood are approximately three times that of streamflow timing. The results here have implications for water resources and environmental management where streamflow and flood timing are critical to planning. The applicability of the normal approximation to flood and streamflow timing will enable future analyses to use parametric statistics.

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.

Due to difficulties in identifying a climate change signal in flood magnitude, it has been suggested that shifts in flood timing, that is, the day of annual streamflow maxima, may be detectable. Here, we use high‐quality streamflow, largely free of snowmelt, from 221 catchments across Australia to investigate the influence of shifts in soil moisture and rainfall timing on annual streamflow maxima timing. In tropical areas we find that flood timing is strongly linked to the timing of both rainfall and soil moisture annual maxima. However, in southern Australia flood timing is more correlated with soil moisture maxima than rainfall maxima. The link between flood, soil moisture, and rainfall timing is confounded by event severity: For less extreme events flood timing is more likely to correspond to soil moisture timing, whereas rainfall timing becomes increasingly important as flood severity increases. Using circular regression to investigate nonstationarity, we find that flood timing is shifting to earlier in the year in the tropics and later in the year in the southwest of the continent, consistent with changes in mean and extreme rainfall and shifts in soil moisture timing due to tropical expansion. In southeast Australia, there is evidence that the mechanisms controlling flood seasonality are changing with a reversal of trends post Millennium Drought. Overall, changes in soil moisture timing, compared to changes in rainfall timing, are found to have a greater influence on changes in annual maxima streamflow flood timing.

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.

While the majority of hydrological prediction methods assume that observed interannual variability explores the full range of catchment response dynamics, recent cases of prolonged climate drying suggest otherwise. During the ∼decade-long Millennium drought in south-eastern Australia significant shifts in hydrologic behavior were reported. Catchment rainfall-runoff partitioning changed from what was previously encountered during shorter droughts, with significantly less runoff than expected occurring in many catchments. In this article, we investigate the variability in the magnitude of shift in rainfall-runoff partitioning observed during the Millennium drought. We re-evaluate a large range of factors suggested to be responsible for the additional runoff reductions. Our results suggest that the shifts were mostly influenced by catchment characteristics related to predrought climate (aridity index and rainfall seasonality) and soil and groundwater storage dynamics (predrought interannual variability of groundwater storage and mean solum thickness). The shifts were amplified by seasonal rainfall changes during the drought (spring rainfall deficits). We discuss the physical mechanisms that are likely to be associated with these factors. Our results confirm that shifts in the annual rainfall-runoff relationship represent changes in internal catchment functioning, and emphasize the importance of cumulative multiyear changes in the catchment storage for runoff generation. Prolonged drying in some regions can be expected in the future, and our results provide an indication of which catchments characteristics are associated with catchments more susceptible to a shift in their runoff response behavior.

Most current long-term (decadal and longer) hydrological predictions implicitly assume that hydrological processes are stationary even under changing climate. However, in practice, we suspect that changing climatic conditions may affect runoff generation processes and cause changes in the rainfall-runoff relationship. In this article, we investigate whether temporary but prolonged (i.e., of the order of a decade) shifts in rainfall result in changes in rainfall-runoff relationships at the catchment scale. Annual rainfall and runoff records from south-eastern Australia are used to examine whether interdecadal climate variability induces changes in hydrological behavior. We test statistically whether annual rainfall-runoff relationships are significantly different during extended dry periods, compared with the historical norm. The results demonstrate that protracted drought led to a significant shift in the rainfall-runoff relationship in ∼44% of the catchment-dry periods studied. The shift led to less annual runoff for a given annual rainfall, compared with the historical relationship. We explore linkages between cases where statistically significant changes occurred and potential explanatory factors, including catchment properties and characteristics of the dry period (e.g., length, precipitation anomalies). We find that long-term drought is more likely to affect transformation of rainfall to runoff in drier, flatter, and less forested catchments. Understanding changes in the rainfall-runoff relationship is important for accurate streamflow projections and to help develop adaptation strategies to deal with multiyear droughts.

[1] Research into the role of catchment vegetation within the hydrologic cycle has a long history in the hydrologic literature. Relationships between vegetation type and catchment evapotranspiration and runoff were primarily assessed through paired catchment studies during the 20th century. Results from over 200 paired catchment studies from around the world have been reported in the literature. Two constraints on utilizing the results from paired catchment studies in the wider domain have been that the catchment areas studied are generally (1) small (

[1] This study introduces a method based on LH moments to use the generalized extreme value (GEV) distribution for low-flow frequency analysis and investigates the capability of the GEV distribution fitted by LH moments to effectively model the lower tail of the low-flow frequency curve, without explicitly censoring the data sample. The performance of the GEV/L moment (the GEV distribution fitted by L moments) and GEV/LH moment (the GEV distribution fitted by LH moments) methods are assessed by evaluating the bias, mean square error, and relative accuracy of quantile estimates through Monte Carlo simulations. It is shown that when both frequent low flows and extreme low flows can be adequately described by an assumed parent distribution, both GEV/L2 moment and GEV/L moment methods make equally accurate quantile estimates. However, when frequent low flows and extreme low flows do not follow a single trend, the bias of the GEV/L2 moment estimator is negligible, while the bias of the GEV/L moment estimator is significant at large annual recurrence intervals. On average, the GEV/L2 moment quantile estimator displays less bias than the GEV/L moment quantile estimator. Furthermore, as the annual recurrence interval increases, the relative accuracy of the GEV/L2 moment method consistently improves over the GEV/L moment method. The GEV/LH moment method is thus considered to be the more suitable method to model low flows.