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Cold waves are considered one of the important extreme weather events affecting winter crop production in the Indo-Gangetic Plain (IGP). In spite of media coverage of extreme cold events in the Terai area of Nepal (Nepal section of IGP) in recent years, few studies on this topic were found. This study investigates cold waves and their impact on agriculture during winter in the Terai region of Nepal. Historical daily maximum and minimum temperature data from six stations in the Terai (Dhangadhi, Nepalgunj, Bhairahawa, Simara, Janakpur, and Biratnagar) during 1971–2015 were analyzed to study the occurrence of cold days, cold nights, extreme cold days, extreme cold nights, cold wave days, and extreme cold wave days in the Terai. The average number of cold days per annum ranges from 15.6 to 17.9 days and the extreme cold days per annum ranges from 3.2 to 3.6 days in the Terai. Except for Nepalgunj, all the Terai stations show statistically significant increasing trends in the frequency of cold days and extreme cold days over the last four decades. Similarly, the average number of cold wave days varies from 9.2 to 13.8 per annum and the average number of extreme cold wave days varies from 1.4 to 3.8 days in the Terai region of Nepal. By comparing the co-occurrence of foggy days and cold and extreme cold wave days at Biratnagar, Simara, Bhairahawa, and Nepalgunj airport, it is also observed that most of the cold and extreme cold wave days are also foggy days. The perception of farmers regarding the effect of fog and cold wave events was explored through focus group discussions at Dhanusha and Sunsari districts of Nepal and found that the fog and cold events have significantly affected their winter crops, livestock, and their day-to-day life.

The Modular Assessment of Rainfall–Runoff Models Toolbox (MARRMoT) is a flexible modelling framework reproducing the behaviour of 47 established hydrological models. This toolbox can be used to calibrate and run models in a user-friendly and consistent way and is designed to facilitate the sharing of model code for reproducibility and to support intercomparison between hydrological models. Additionally, it allows users to create or modify models using components of existing ones. We present a new MARRMoT release (v2.1) designed for improved speed and ease of use. While improved computational efficiency was the main driver for this redevelopment, MARRMoT v2.1 also succeeds in drastically reducing the verbosity and repetitiveness of the code, which improves readability and facilitates debugging. The process to create new models or modify existing ones within the toolbox is also simplified in this version, making MARRMoT v2.1 accessible for researchers and practitioners at all levels of expertise. These improvements were achieved by implementing an object-oriented structure and aggregating all common model operations into a single class definition from which all models inherit. The new modelling framework maintains and improves on several good practices built into the original MARRMoT and includes a number of new features such as the possibility of retrieving more output in different formats that simplifies troubleshooting, and a new functionality that simplifies the calibration process. We compare outputs of 36 of the models in the framework to an earlier published analysis and demonstrate that MARRMoT v2.1 is highly consistent with the previous version of MARRMoT (v1.4), while achieving a 3.6-fold improvement in runtime on average. The new version of the toolbox and user manual, including several workflow examples for common application, are available from GitHub (https://github.com/wknoben/MARRMoT, last access: 12 May 2022; https://doi.org/10.5281/zenodo.6484372, Trotter and Knoben, 2022b).

Meteorological time‐series data are a fundamental input to hydrological investigations. But sourcing data is often laborious and plagued with difficulties. In an effort to improve efficiency and rigor we present an R‐package, named AWAPer (https://github.com/peterson-tim-j/AWAPer), for the efficient estimation of daily area weighted catchment average and spatial variance of meteorological variables, including evapotranspiration. The package allows creation and updating of a data‐cube of gridded daily data from 1900 onwards. Once created, point and area weighted estimates can be extracted at user‐defined locations and time periods for anywhere within Australia. Examples of point and catchment average extraction are presented.

Justin Francis Costelloe (Fig. 1) was born in 1965. He grew up in the mining city of Bendigo (Victoria, Australia) before studying Earth Sciences at the University of Melbourne. He went on to work as an exploration geologist in the mining industry in the dryland regions of Australia and Chile. He developed a love of Australia’s desert landscapes and returned to undertake Masters and PhD studies on arid zone hydrology at the University of Melbourne, before continuing as a research fellow and senior research fellow leading arid zone research projects. Justin was a leader in research aimed at understanding surface water and groundwater in Australia’s arid zone and also made important interdisciplinary contributions linking the hydrology and ecology of the arid zone, with a focus on Australia’s iconic Channel Country and the Great Artesian Basin (GAB).

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.

Hydrologists are commonly involved in impact, adaption and vulnerability assessments for climate change projections. This paper presents a framework for how such assessments can better differentiate between the impacts of climate change and those of natural variability, an important differentiation as it relates to the vulnerability to water availability under change. The key concept involved is to characterize “hydrologic stress” relative to the range of behaviour encountered under baseline conditions, where the degree to which climate change causes the behaviour of a system to shift outside this baseline range provides a non-dimensional measure of stress. The concept is applicable to any system that is subject to climate forcings, though the approach is applied here to a range of examples illustrative of many environmental and engineering applications. These include hydrologic systems that are dependent on the frequency of flows above or below selected thresholds, those that are dominated by storage and those which are sensitive to the sequencing of selected flow components. The analyses illustrate that systems designed or adapted to accommodate high variability are less stressed by a given magnitude of climate impacts than those operating under more uniform conditions. The metrics characterize hydrologic stress in a manner that can facilitate comparison across different regions, or across different assets within a region. Adoption of the approach requires reliance on the use of climate ensembles that represent aleatory uncertainty under both baseline and impacted conditions, and this has implications for how the outputs of climate models are provided and utilized.

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.

The purpose of this paper is to determine uncertainty in the gauged range of the stage-gauged discharge relationship for 622 rating curves from 171 Australian Bureau of Meteorology Hydrologic Reference stream gauging Stations (HRS). Water agencies use many methods to establish rating curves. Here we adopt a consistent method across all stations and develop rating curves based on Chebyshev polynomials, and estimate uncertainties from standard regression errors in which residuals from the polynomials are adjusted to ensure they are homoscedastic and normally distributed. Uncertainty in input water level is also taken into account. The median uncertainties in mean response of the available gauged discharge relationship at median daily discharges for the HRS dataset range from +4.5% to -4.2% (95% confidence band) and for individual gaugings from +29% to -22% incorporating a water level uncertainty of ±4 mm. The uncertainties estimated are consistent with values estimated in Australia and elsewhere.

Question #20 of the UPH aspires to disentangle and reduce model prediction uncertainty. One feasible approach is to first formulate the relationship between variability (of real-world hydrological processes and catchment characteristics) and uncertainty (of model components and variables), which links the UPH theme of “modelling methods” to “time variability and change” and “space variability and scaling”. Building on this premise, we explored the relationship between runoff generation hypotheses, derived from a large ensemble of catchment model simulations, and catchment characteristics (physiographic, climatic, and streamflow response characteristics) across a large sample of 221 Australian catchments. Using ensembles of 106 runs of SIMHYD model for each catchment, runoff generation hypotheses were formulated based on the interaction of 3 runoff generating fluxes of SIMHYD, namely intensity-based, wetness-based, and slow responses. The hypotheses were derived from model runs with acceptable performance and sufficient parameter sampling. For model performance acceptability, we benchmarked Kling-Gupta Efficiency (KGE) skill score against the calendar day average observed flow, a catchment-specific and more informative benchmark than the conventional observed flow mean. The relative parameter sampling sufficiency was also defined based on the comparative efficacy of two common model parameterisation routines of Latin Hypercube Sampling and Shuffled Complex Evolution for each catchment. Across 186 catchments with acceptable catchment models, we examined the association of uncertain runoff generation hypotheses (i.e. ensemble of modeled runoff fluxes) with 22 catchment attributes. We used the Flux Mapping method (https://doi.org/10.1029/2018WR023750) to characterise the uncertainty of runoff generation hypotheses, and a range of daily and annual summary statistics to characterise catchment attributes. Among the metrics used, Spearman rank correlation coefficient (Rs) was the most informative metric to capture the functional connectivity of catchment attributes with the internal dynamics of model runoff fluxes, compared to linear Pearson correlation and distance correlation coefficients. We found that streamflow characteristics generally have the most important influence on runoff generation hypotheses, followed by climate and then physiographic attributes. Particularly, daily flow coefficient of variability (Qcv) and skewness (Q Skewness), followed by the same summary statistics of precipitation (Pcv and P Skewness), were most important. These four attributes are strongly correlated with one another, and represent the dynamics of the rainfall-runoff signal within a catchment system. A higher Pcv denotes a higher day-to-day variability in rainfall on the catchment, responded by a higher Qcv flow response. A higher variability in rainfall propagates through the catchment model and translates into a higher degree of equifinality in model runoff fluxes, which implies larger uncertainties of runoff generation hypotheses at catchment scale, and hence a greater challenge for reliable/realistic simulation and prediction of streamflow.

Climate change is expected to change the pattern of rainfall resulting in changed flood magnitude. However, in large part due to interannual variability, identifying a climate change signal in flood magnitude remains difficult. As an alternative to investigating trends in flood magnitude, it has been suggested that trends in flood timing, that is, the day of annual streamflow maxima, may be a detectable trend due climate change.Here, using high-quality data from around the world, trends in flood and center timing are investigated. We begin by standardizing the data on a local definition of water year. We find an interesting property, that after standardization, the flood and centre timing of streamflow can be approximated by a normal distribution. Moreover, we find that without the standardization on local water year the calculated trend can reverse. We proceed by analyzing trends in centre and flood timing globally using linear regression.Results are commensurable with large-scale climatic change. But, unlike changes in extreme rainfall, trends are not spatially consistent. Flood timing is shifting to earlier in the year in the tropics, and later in the year in the extra-tropics, consistent with changes in mean rainfall and flood magnitude. There is evidence of a reversal of trends post-drought, suggesting that the mechanisms controlling flooding at a catchment scale are changing as a result of climate change. It is concluded that trends in flood timing are related to flood generating mechanisms, and largely modulated by changing antecedent moisture conditions.

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.

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, chosen 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 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.

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.

Rainfall-runoff models are used across academia and industry, and the number and type have proliferated over time. In this primer we briefly introduce the key features of these models and provide an overview of their historical development and drivers behind those developments. To complete the discussion there is a brief section on model choice including model intercomparison. We also seek to clarify jargon terms for readers new to this area.

Staying dryIs precipitation all that a watershed needs to recover from drought? Conventional wisdom says yes, but this is not necessarily true. Petersonet al.studied streamflow and precipitation in 161 watersheds in southeastern Australia across the Millennium Drought, which stuck the region during the first decade of the 21st century (see the Perspective by Tauro). They found that runoff in approximately one-third of the watersheds had not returned to predrought levels even after 7 years despite the resumption of more normal precipitation. The authors suggest that these longterm changes are due to water loss from increased transpiration. Watersheds may thus have multiple states and a finite resilience to transient disturbances, and hydrological droughts can persist long after meteorological droughts.Science, this issue p.745; see also p.680

Environmental policy is often implemented using market instruments. In some cases, including carbon taxing, the links between financial products and the environmental objectives, are transparent. In other cases, including water markets, the links are less transparent. In Australia’s Murray–Darling Basin (MDB), financial water products are known as ‘entitlements’, and are similar to traditional financial products, such as shares. The Australian water market includes ‘Low Security’ entitlements, which are similar to ‘sub-prime’ mortgage bonds because they are unlikely to yield an amount equal to their financial worth. Nearly half the water purchased under the Murray–Darling Basin Plan for environmental purposes is ‘Low Security’. We suggest that the current portfolio of water held by the Australian Government for environmental purposes reflects the mortgage market in the lead-up to the global financial crisis. Banks assumed that the future value of the mortgage market would reflect past trends. Similarly, it is assumed that the future value of water products will reflect past trends, without considering climate change. Historic records of allocations to ‘Low Security’ entitlements in the MDB suggest that, in the context of climate change, the Basin Plan water portfolio may fall short of the target annual average yield of 2075 GL by 511 GL. We recommend adopting finance sector methods including ‘hedging’ ‘Low Security’ entitlements by purchasing an additional 322–2755 GL of ‘Low Security’, or 160–511 GL of ‘High Security’ entitlements. Securing reliable environmental water is a global problem. Finance economics present opportunities for increasing the reliability of environmental flows.

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.

Hydrological models are conventionally evaluated in terms of their response surface or likelihood surface constructed with the model parameter space. To evaluate models as hypotheses, we developed the method of Flux Mapping to construct a hypothesis space based on model process representation. Here we defined the hypothesis space based on dominant runoff generating mechanisms, and acceptable model runs are defined as total simulated flow with similar (and minimal) model error simulated by distinct combinations of runoff components. We demonstrate that the hypothesis space in each modeling case is the result of interplay between the factors of model structure, parameter sampling, choice of error metric, and data information content. The aim of this study is to disentangle the role of each factor in this interplay. We used two model structures (SACRAMENTO and SIMHYD), two parameter sampling approaches (small samples based on guided-search and large samples based on Latin Hypercube Sampling), three widely used error metrics (NSE, KGE, and WIA — Willmott’s Index of Agreement), and hydrological data from a range of Australian catchments. First, we characterized how the three error metrics behave under different error regimes independent of any modeling. We then conducted a series of controlled experiments, i.e. a type of one-factor-at-a-time sensitivity analysis, to unpack the role of each factor in runoff simulation. We show that KGE is a more reliable error metric compared to NSE and WIA for model evaluation. We also argue that robust error metrics and sufficient parameter sampling are necessary conditions for evaluating models as hypotheses under uncertainty. We particularly argue that sampling sufficiency, regardless of the sampling strategy, should be further evaluated based on its interaction with other modeling factors determining the model response. We conclude that the interplay of these modeling factors is complex and unique to each modeling case, and hence generalizing model-based inferences should be done with caution particularly in characterizing hydrological processes in large-sample hydrology.

Many streams experienced a prominent increase in proportion of cease to flow conditions during and after the multiyear drought in Australia (Millennium drought, circa 1997 – 2009). Change in zero flow occurrence frequency reflects the general transition of stream reaches from gaining to losing conditions, from losing to losing more, and ultimately to the disconnected state. We track and characterise these changes in groundwater-surface water connection using zero flow conditions as a proxy and explore the spatial and temporal patterns in flow regime transformation. The implications for upstream / downstream water availability and management of environmental flows and ecosystems are discussed in view of projected drier future 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.

Winter fog events of the Indo Gangetic plain (IGP) including the Terai area of Nepal are considered to be one of the important public concerns due to their effect on people’s health, transportation, and agriculture. Unlike the IGP area of India, Pakistan and Bangladesh there are only very few fog related studies reported about the Terai region of Nepal. This study is carried out to study the occurrence of fog in the Terai region of Nepal by analysing the historical visibility data from 1980 to 2015 at four airports in the region (Nepalgunj, Bhairahawa, Simara and Biratnagar). It was found that the fog events in the Terai start in the month of November, reach the peak in December/January and end by the end of February. The average number of foggy days ranged from 24 days to 56 days per annum and average number of day-time foggy hours varied from 71 to 169 in the study. Visibility during winter is decreasing at all stations during the study period. The Man Kendall test indicated fog related parameters such as foggy days, foggy hours, dense foggy days, dense foggy hours have increasing trends at least at 0.1 level of statistical significance during the study period. The increasing trend of foggy days and daytime foggy hours may reduce winter crop production and negatively affect the food security of the Terai region of Nepal.

The performance of eight empirical equations for estimating ETo at 80 weather stations in Iran is evaluated. The equations assessed are Hargreaves (HGS), Trajkovic (TKC), Berti (BTI), Ravazzani (RZ...

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.

In central Chile, increasing demand for water and decreasing runoff volumes due to drier conditions have placed catchments in this zone under water stress. However, scarcity of observed data records increases the difficulty of planning future water supply. Instrumental records suggest a reduction in streamflow over the last 56 years. However, this change is not statistically significant and the lack of meteorological stations with long records in this mountainous region hampers a deeper analysis, motivating the use of tree rings to analyse whether these changes are part of a long-term trend. This work represents the first high-elevation runoff reconstruction in Chile using 300 years of tree ring chronologies of Araucaria araucana and Astroceudrus chilensis. The upper part of Biobio river melting season runoff (October–March) and pluvial season runoff (April–September) was reconstructed and analysed to investigate the influence of large-scale climatic drivers on runoff generation, current drought trends and to improve the understanding of climate variability in this region. We obtained positive correlations between the 20-year moving average of reconstructed pluvial season runoff and reconstructed Pacific Decadal Oscillation (PDO), which is indicative of multi-decadal variability. We also found a negative correlation between the 11-year moving average of reconstructed melting season runoff and the PDO and positive correlations with the Southern Annular Mode (SAM). Important differences in the runoff variability of the upper and the lower part of the catchment were identified which are in part led by the influence of the large-scale climatic features that drive runoff generation in both regions. We found that the changes observed in the instrumental records are part of multi-decadal cycles led by the PDO and SAM for pluvial season runoff and melting season runoff, respectively.

Streamflow reductions have been reported in mid-latitude Southern Hemisphere (SH) catchments, in particular in the southwest of Western Australia (SWA) and in central Chile (CC), following decreases in precipitation since the mid-1970s. Although projections from Global Climate Models (GCMs) indicate the observed trends are expected to continue during the rest of the 21st century, they are affected by large uncertainties that challenge informed decision making. Quantification and comparison of uncertainties in runoff projections for the period 2050-2080 relative to 1970-2000, driven by an ensemble of a single GCM with perturbed physics (CPDN) and a multi-model ensemble of different GCMs (CMIP5), were used to account for what we term “within-GCM” and “between-GCM” uncertainty in SWA catchments. Between GCM uncertainty of runoff projections was also quantified in CC catchments. Within and between-GCM uncertainties were found to be very similar (∼55 per cent) in SWA catchments. Between-GCM uncertainty for runoff projections in CC catchments is smaller than in SWA. On average, uncertainty of about 51 per cent, under RCP8.5 scenario, was simulated for the period 2050-2080 compared to 1970-2000. For CC catchments a dichotomy was observed in runoff projections under the RCP4.5 scenario, which according to our preliminary analysis might relate to how ozone is specified within different GCMs. We conclude that the number of models sampled by the CMIP5 ensemble, which includes multiple model runs from some GCMs, provides some insight into within-GCM uncertainties. Furthermore, since CMIP5 model runs report values for all regions and are easily accessible, the CMIP5 ensemble is more convenient for regional hydrological assessments than the perturbed physics experiments.

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.

This paper presents the Modular Assessment of Rainfall-Runoff Models Toolbox (MARRMoT): a modular open-source toolbox containing documentation and model code for 46 existing conceptual hydrologic models. The toolbox is developed in Matlab and works with Octave. Models are implemented following several best practices: 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 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 Supporting Materials, a User Manual is provided together with several workflow scripts that show basic example applications of the toolbox. The toolbox and documentation are available from https://github.com/wknoben/MARRMoT (DOI: https://doi.org/10.5281/zenodo.2482542). 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.

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.

Rainfall‐runoff models are often deficient under changing climatic conditions, yet almost no recent studies propose new or improved model structures, instead focussing 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 parameterisation, or data errors. The framework can be applied to a single catchment, although larger samples of catchments are helpful to generalise 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.

Evaporation plays a key role in the hydrology of a catchment. World-wide actual terrestrial evaporation is approximately two third of terrestrial precipitation. Evaporation is the focus of this study in which we describe the historical developments of models for estimating evaporation from standard meteorological data. Although Aristotle and Descartes made early contributions to understanding evaporation, Perrault is credited with having made the first experimental measurement of evaporation in about 1674 though in fact what he measured was sublimation by recording the loss of weight of a block of ice through time. In 1686, Halley carried out the first direct measurement of the evaporation of liquid water. Following a detailed set of experiments, Dalton in 1802 published an essay describing the relationship between evaporation, vapor pressure deficit, and wind speed which is the forerunner of the mass-transfer equation to estimate open-water evaporation. In 1921, Cummings proposed an approximate energy balance equation which in 1948 Penman combined with a mass-transfer equation based on Dalton's work to develop the Penman equation. A key input was the Bowen ratio published in 1926. Following Penman, the next major development was by Monteith in 1965. He modified Penman's equation for a single leaf to deal with a canopy which led to the Penman–Monteith model and is the basis of the FAO56 Reference Crop model. Priestley and Taylor introduced their model in 1972, which is based on the energy term in Penman's equation, and underpins other models. The application of the Complementary Relationship to estimating regional evaporation is credited separately to Brutsaert and Stricker and to Morton. Budyko offered two important contributions. First, he developed a potential evaporation equation in which the evaporating surface temperature was estimated by iteration, whereas Penman approximated a value from the Clausius–Clapeyron equation. Budyko's second contribution is a simple relationship to estimate runoff and, in turn, mean actual evaporation. WIREs Water 2016, 3:788–818. doi: 10.1002/wat2.1172. This article is categorized under: Science of Water > Hydrological Processes Science of Water > Methods.

Demand for quantitative assessments of likely climate change impact on runoff is increasing and conceptual rainfall-runoff models are essential tools for this task. However, the capacity of these models to extrapolate under changing climatic conditions is questionable. A number of studies have found that model predictive skill decreases with changed climatic conditions, especially when predicting drier climates. We found that model skill only declines under certain circumstances, in particular, when a catchment's rainfall-runoff processes change due to changed climatic drivers. In catchments where the rainfall-runoff relationship changed significantly in response to prolonged dry conditions, runoff was consistently overestimated. In contrast, modeled runoff was unbiased in catchments where the rainfall-runoff relationship remained unchanged during the dry period. These conclusions were not model dependent. Our results suggest that current projections of runoff under climate change may provide overly optimistic assessments of future water availability in some regions expecting rainfall reductions.

Summary Future projections of water supply under climate change scenarios are fundamental for efficient water resource planning. However, runoff projections are affected by uncertainties in the modelling process that limit their utility to decision makers. The main source of uncertainty in runoff projections are the Global Climate Models (GCMs) used to produce future climate projections. The impact on projected runoff of this uncertainty has mainly been assessed through comparison of multi-model runs of future climate with little exploration of uncertainties inside the models due to different parameterisations. Here we investigate the uncertainty response of projected runoff due to perturbed physics parameter variations within a GCM using a novel 2500 member ensemble from the HadCM3L model. Our research evaluates the uncertainties in runoff modelling for southwest Western Australia, a Mediterranean climate region which has experienced reductions in precipitation during the last decades. Results for future projections in southwest Western Australian catchments indicate reductions in modelled precipitation between 0% and 40% and increases in temperature that fluctuate between 0.5 °C and 3 °C by 2050–2080 compared to 1970–2000, which lead to reductions in projected runoff of between 10% and 80%. This range of uncertainty for projected runoff is larger than that calculated for previous estimates of within-model uncertainties of runoff. The perturbed physics approach indicates that current water management assessments underestimate uncertainties in runoff projections.

This study assessed the effect of using observed monthly leaf area index (LAI) on hydrologic model performance and the simulation of streamflow during drought using the variable infiltration capacity (VIC) hydrological model in the Goulburn–Broken catchment of Australia, which has heterogeneous vegetation, soil and climate zones. VIC was calibrated with both observed monthly LAI and long-term mean monthly LAI, which were derived from the Global Land Surface Satellite (GLASS) observed monthly LAI dataset covering the period from 1982 to 2012. The model performance under wet and dry climates for the two different LAI inputs was assessed using three criteria, the classical Nash–Sutcliffe efficiency, the logarithm transformed flow Nash–Sutcliffe efficiency and the percentage bias. Finally, the percentage deviation of the simulated monthly streamflow using the observed monthly LAI from simulated streamflow using long-term mean monthly LAI was computed. The VIC model predicted monthly streamflow in the selected sub-catchments with model efficiencies ranging from 61.5 to 95.9% during calibration (1982–1997) and 59 to 92.4% during validation (1998–2012). Our results suggest systematic improvements from 4 to 25% in the Nash–Sutcliffe efficiency in pasture dominated catchments when the VIC model was calibrated with the observed monthly LAI instead of the long-term mean monthly LAI. There was limited systematic improvement in tree dominated catchments. The results also suggest that the model overestimation or underestimation of streamflow during wet and dry periods can be reduced to some extent by including the year-to-year variability of LAI in the model, thus reflecting the responses of vegetation to fluctuations in climate and other factors. Hence, the year-to-year variability in LAI should not be neglected; rather it should be included in model calibration as well as simulation of monthly water balance.

The objective of this paper is to identify better performing Coupled Model Intercomparison Project phase 3 (CMIP3) global climate models (GCMs) that reproduce grid-scale climatological statistics of observed precipitation and temperature for input to hydrologic simulation over global land regions. Current assessments are aimed mainly at examining the performance of GCMs from a climatology perspective and not from a hydrology standpoint. The performance of each GCM in reproducing the precipitation and temperature statistics was ranked and better performing GCMs identified for later analyses. Observed global land surface precipitation and temperature data were drawn from the Climatic Research Unit (CRU) 3.10 gridded data set and re-sampled to the resolution of each GCM for comparison. Observed and GCM-based estimates of mean and standard deviation of annual precipitation, mean annual temperature, mean monthly precipitation and temperature and Köppen–Geiger climate type were compared. The main metrics for assessing GCM performance were the Nash–Sutcliffe efficiency (NSE) index and root mean square error (RMSE) between modelled and observed long-term statistics. This information combined with a literature review of the performance of the CMIP3 models identified the following better performing GCMs from a hydrologic perspective: HadCM3 (Hadley Centre for Climate Prediction and Research), MIROCm (Model for Interdisciplinary Research on Climate) (Center for Climate System Research (The University of Tokyo), National Institute for Environmental Studies, and Frontier Research Center for Global Change), MIUB (Meteorological Institute of the University of Bonn, Meteorological Research Institute of KMA, and Model and Data group), MPI (Max Planck Institute for Meteorology) and MRI (Japan Meteorological Research Institute). The future response of these GCMs was found to be representative of the 44 GCM ensemble members which confirms that the selected GCMs are reasonably representative of the range of future GCM projections.

Governments often use voluntary agreements to encourage landholders to adopt environmental practices, such as excluding stock from grazing riverbanks. In Victoria, Australia, government agencies subsidize the adoption of these projects, while landholders are required to continue maintaining stock exclusion indefinitely. In the absence of further financial or legal enforcement, landholder compliance depends on the motivation and decision-making of individual landholders. Social beliefs about the responsibility of landholders to improve the condition of degraded riverine ecosystems, known as social norms, influence farmers to adopt new environmental practices. The influence of social norms on behaviour weakens when people perceived themselves to be constrained. From late 1996 to mid-2010 landholders in Victoria endured more than ten years of drought that has reduced productivity, and income. Drought conditions may influence whether landholders continue to exclude stock over the long-term, despite holding positive social norms. However, behaviour is influenced by perceptions of constraint; landholder perceptions may not reflect drought severity. Perceived drought affectedness may also be related to the amount of income obtained from farm activities. This study examined the relationship between social factors, (including injunctive and descriptive social norms, and symbolic and instrumental social beliefs, perceived drought affectedness, actual drought severity), and the percentage of overall income that landholders obtain from farm activities. A social survey, and assessment of river restoration projects, was conducted with 93 landholders in rural Victoria, Australia. We found that landholders who continue to graze riverbanks hold weaker social norms about excluding stock in drought conditions. Grazing behaviour was explained by social norms, and perceived drought affectedness together. Perceived drought affectedness was best explained by actual drought severity, but also by the amount of income obtained from farming activities, rather than either factor alone. Policy makers should consider using drought relief funding to subsidize the purchase of additional stock feed during droughts to encourage farmers to continue environmental stock exclusion, particularly when farmers rely on farm activities for most of their income.

Droughts are a significant stressor for water supply systems and freshwater ecosystems. Studies on drought risks and impacts have focused on the frequency, duration, and severity of drought...

In the discussion of Eq. (1), reference is made to an example calculation of the metric that should have been provided in the right-hand panel of Fig. 1.

Derivation of the hypsometric curve of a catchment, and properties relating to that curve, requires both use of topographical data (commonly in the form of a Digital Elevation Model - DEM), and the estimation of a functional representation of that curve. An early investigation into catchment hypsometry concluded 3rd order polynomials sufficiently describe the hypsometric curve, without the consideration of higher order polynomials, or the sensitivity of hypsometric properties relating to the curve. Another study concluded the hypsometric integral (HI) is robust against changes in DEM resolution, a conclusion drawn from a very limited sample size. Conclusions from these earlier studies have resulted in the adoption of methods deemed to be "sufficient" in subsequent studies, in addition to assumptions that the robustness of the HI extends to other hypsometric properties. This study investigates and demonstrates the sensitivity of hypsometric properties to DEM resolution, DEM type and polynomial order through assessing differences in hypsometric properties derived from 417 catchments and sub-catchments within South Australia. The sensitivity of hypsometric properties across DEM types and polynomial orders is found to be significant, which suggests careful consideration of the methods chosen to derive catchment hypsometric information is required. Refereed/Peer-reviewed

This study assessed the effect of using observed monthly leaf area index (LAI) on hydrological model performance and the simulation of runoff using the Variable Infiltration Capacity (VIC) hydrological model in the Goulburn–Broken catchment of Australia, which has heterogeneous vegetation, soil and climate zones. VIC was calibrated with both observed monthly LAI and long-term mean monthly LAI, which were derived from the Global Land Surface Satellite (GLASS) leaf area index dataset covering the period from 1982 to 2012. The model performance under wet and dry climates for the two different LAI inputs was assessed using three criteria, the classical Nash–Sutcliffe efficiency, the logarithm transformed flow Nash–Sutcliffe efficiency and the percentage bias. Finally, the deviation of the simulated monthly runoff using the observed monthly LAI from simulated runoff using long-term mean monthly LAI was computed. The VIC model predicted monthly runoff in the selected sub-catchments with model efficiencies ranging from 61.5% to 95.9% during calibration (1982–1997) and 59% to 92.4% during validation (1998–2012). Our results suggest systematic improvements, from 4% to 25% in Nash–Sutcliffe efficiency, in sparsely forested sub-catchments when the VIC model was calibrated with observed monthly LAI instead of long-term mean monthly LAI. There was limited systematic improvement in tree dominated sub-catchments. The results also suggest that the model overestimation or underestimation of runoff during wet and dry periods can be reduced to 25 mm and 35 mm respectively by including the year-to-year variability of LAI in the model, thus reflecting the responses of vegetation to fluctuations in climate and other factors. Hence, the year-to-year variability in LAI should not be neglected; rather it should be included in model calibration as well as simulation of monthly water balance.

Anthropogenic climate change is projected to enrich the atmosphere with carbon dioxide, change vegetation dynamics and influence the availability of water at the catchment scale. This study combines a nonlinear model for estimating changes in leaf area index (LAI) due to climatic fluctuations with the variable infiltration capacity (VIC) hydrological model to improve catchment streamflow prediction under a changing climate. The combined model was applied to 13 gauged sub-catchments with different land cover types (crop, pasture and tree) in the Goulburn–Broken catchment, Australia, for the "Millennium Drought" (1997–2009) relative to the period 1983–1995, and for two future periods (2021–2050 and 2071–2100) and two emission scenarios (Representative Concentration Pathway (RCP) 4.5 and RCP8.5) which were compared with the baseline historical period of 1981–2010. This region was projected to be warmer and mostly drier in the future as predicted by 38 Coupled Model Intercomparison Project Phase 5 (CMIP5) runs from 15 global climate models (GCMs) and for two emission scenarios. The results showed that during the Millennium Drought there was about a 29.7–66.3 % reduction in mean annual runoff due to reduced precipitation and increased temperature. When drought-induced changes in LAI were included, smaller reductions in mean annual runoff of between 29.3 and 61.4 % were predicted. The proportional increase in runoff due to modeling LAI was 1.3–10.2 % relative to not including LAI. For projected climate change under the RCP4.5 emission scenario, ignoring the LAI response to changing climate could lead to a further reduction in mean annual runoff of between 2.3 and 27.7 % in the near-term (2021–2050) and 2.3 to 23.1 % later in the century (2071–2100) relative to modeling the dynamic response of LAI to precipitation and temperature changes. Similar results (near-term 2.5–25.9 % and end of century 2.6–24.2 %) were found for climate change under the RCP8.5 emission scenario. Incorporating climate-induced changes in LAI in the VIC model reduced the projected declines in streamflow and confirms the importance of including the effects of changes in LAI in future projections of streamflow.