Reply to comment by K. Beven et al. on "Pursuing the method of multiple working hypotheses for hydrological modelling"

Martyn P. Clark, Dmitri Kavetski, and Fabrizio Fenici

Evaluating post-processing approaches for monthly and seasonal streamflow forecasts

Streamflow forecasting is prone to substantial uncertainty due to errors in meteorological forecasts, hydrological model structure, and parameterization, as well as in the observed rainfall and streamflow data used to calibrate the models. Statistical streamflow post-processing is an important technique available to improve the probabilistic properties of the forecasts. This study evaluates post-processing approaches based on three transformations – logarithmic (Log), log-sinh (Log-Sinh), and Box–Cox with λ=0.2 (BC0.2) – and identifies the best-performing scheme for post-processing monthly and seasonal (3-months-ahead) streamflow forecasts, such as those produced by the Australian Bureau of Meteorology. Using the Bureau's operational dynamic streamflow forecasting system, we carry out comprehensive analysis of the three post-processing schemes across 300 Australian catchments with a wide range of hydro-climatic conditions. Forecast verification is assessed using reliability and sharpness metrics, as well as the Continuous Ranked Probability Skill Score (CRPSS). Results show that the uncorrected forecasts (i.e. without post-processing) are unreliable at half of the catchments. Post-processing of forecasts substantially improves reliability, with more than 90 % of forecasts classified as reliable. In terms of sharpness, the BC0.2 scheme substantially outperforms the Log and Log-Sinh schemes. Overall, the BC0.2 scheme achieves reliable and sharper-than-climatology forecasts at a larger number of catchments than the Log and Log-Sinh schemes. The improvements in forecast reliability and sharpness achieved using the BC0.2 post-processing scheme will help water managers and users of the forecasting service make better-informed decisions in planning and management of water resources.Fitsum Woldemeskel, David McInerney, Julien Lerat, Mark Thyer, Dmitri Kavetski, Daehyok Shin, Narendra Tuteja and George Kuczer

High-quality probabilistic predictions for existing hydrological models with common objective functions

Conference theme 'Digital Water.'Probabilistic predictions describe the uncertainty in modelled streamflow, which is a critical input for many environmental modelling applications. A residual error model typically produces the probabilistic predictions in tandem with a hydrological model that predicts the deterministic streamflow. However, many objective functions that are commonly used to calibrate the parameters of the hydrological model make (implicit) assumptions about the errors that do not match the properties (e.g. of heteroscedasticity and skewness) of those errors. The consequence of these assumptions is often low-quality probabilistic predictions of errors, which reduces the practical utility of probabilistic modelling. Our study has two aims: Firstly, to evaluate the impact of objective function inconsistency on the quality of probabilistic predictions; Secondly, to demonstrate how a simple enhancement to a residual error model can rectify the issues identified with inconsistent objective functions in Aim 1, and thereby improve probabilistic predictions in a wide range of scenarios. Our findings show that the enhanced error model enables high-quality probabilistic predictions to be obtained for a range of catchments and objective functions, without requiring any changes to the hydrological modelling or calibration process. This advance has practical benefits that are aimed at increasing the uptake of probabilistic predictions in real-world applications, in that the methods are applicable to existing hydrological models that are already calibrated, simple to implement, easy to use and fast. Finally, these methods are available as an open-source R-shiny application and an R-package function.Jason Hunter, Mark Thyer, David McInerney, Dmitri Kavetsk

A strategy for diagnosing and interpreting hydrological model nonstationarity

Article first published online: 24 JUN 2014This paper presents a strategy for diagnosing and interpreting hydrological nonstationarity, aiming to improve hydrological models and their predictive ability under changing hydroclimatic conditions. The strategy consists of four elements: (i) detecting potential systematic errors in the calibration data; (ii) hypothesizing a set of “nonstationary” parameterizations of existing hydrological model structures, where one or more parameters vary in time as functions of selected covariates; (iii) trialing alternative stationary model structures to assess whether parameter nonstationarity can be reduced by modifying the model structure; and (iv) selecting one or more models for prediction. The Scott Creek catchment in South Australia and the lumped hydrological model GR4J are used to illustrate the strategy. Streamflow predictions improve significantly when the GR4J parameter describing the maximum capacity of the production store is allowed to vary in time as a combined function of: (i) an annual sinusoid; (ii) the previous 365 day rainfall and potential evapotranspiration; and (iii) a linear trend. This improvement provides strong evidence of model nonstationarity. Based on a range of hydrologically oriented diagnostics such as flow-duration curves, the GR4J model structure was modified by introducing an additional calibration parameter that controls recession behavior and by making actual evapotranspiration dependent only on catchment storage. Model comparison using an information-theoretic measure (the Akaike Information Criterion) and several hydrologically oriented diagnostics shows that the GR4J modifications clearly improve predictive performance in Scott Creek catchment. Based on a comparison of 22 versions of GR4J with different representations of nonstationarity and other modifications, the model selection approach applied in the exploratory period (used for parameter estimation) correctly identifies models that perform well in a much drier independent confirmatory period.Seth Westra, Mark Thyer, Michael Leonard, Dmitri Kavetski, and Martin Lamber

State updating and calibration period selection to improve dynamic monthly streamflow forecasts for an environmental flow management application

Monthly to seasonal streamflow forecasts provide useful information for a range of water resource management and planning applications. This work focuses on improving such forecasts by considering the following two aspects: (1) state updating to force the models to match observations from the start of the forecast period, and (2) selection of a shorter calibration period that is more representative of the forecast period, compared to a longer calibration period traditionally used. The analysis is undertaken in the context of using streamflow forecasts for environmental flow water management of an open channel drainage network in southern Australia. Forecasts of monthly streamflow are obtained using a conceptual rainfall–runoff model combined with a post-processor error model for uncertainty analysis. This model set-up is applied to two catchments, one with stronger evidence of non-stationarity than the other. A range of metrics are used to assess different aspects of predictive performance, including reliability, sharpness, bias and accuracy. The results indicate that, for most scenarios and metrics, state updating improves predictive performance for both observed rainfall and forecast rainfall sources. Using the shorter calibration period also improves predictive performance, particularly for the catchment with stronger evidence of non-stationarity. The results highlight that a traditional approach of using a long calibration period can degrade predictive performance when there is evidence of non-stationarity. The techniques presented can form the basis for operational monthly streamflow forecasting systems and provide support for environmental decision-making.Matthew S. Gibbs, David McInerney, Greer Humphrey, Mark A. Thyer, Holger R. Maier, Graeme C. Dandy and Dmitri Kavetsk

The importance of spatiotemporal variability in irrigation inputs for hydrological modelling of irrigated catchments

Irrigation contributes substantially to the water balance and environmental condition of many agriculturally productive catchments. This study focuses on the representation of spatio‐temporal variability of irrigation depths in irrigation schedule models. Irrigation variability arises due to differences in farmers' irrigation practices, yet its effects on distributed hydrological predictions used to inform management decisions are currently poorly understood. Using a case study of the Barr Creek catchment in the Murray Darling Basin, Australia, we systematically compare four irrigation schedule models, including uniform vs variable in space, and continuous‐time vs event‐based representations. We evaluate simulated irrigation at hydrological response unit and catchment scales, and demonstrate the impact of irrigation schedules on the simulations of streamflow, evapotranspiration and potential recharge obtained using the Soil and Water Assessment Tool (SWAT). A new spatially‐variable event‐based irrigation schedule model is developed. When used to provide irrigation inputs to SWAT, this new model: (i) reduces the over‐estimation of actual evapotranspiration that occurs with spatially‐uniform continuous‐time irrigation assumptions (biases reduced from ∼40% to ∼2%) and (ii) better reproduces the fast streamflow response to rainfall events compared to spatially‐uniform event‐based irrigation assumptions (seasonally‐adjusted Nash‐Sutcliffe Efficiency improves from 0.15 to 0.56). The stochastic nature of the new model allows representing irrigation schedule uncertainty, which improves the characterization of uncertainty in simulated catchment streamflow and can be used for uncertainty decomposition. More generally, this study highlights the importance of spatio‐temporal variability of inputs to distributed hydrological models and the importance of using multi‐variate response data to test and refine environmental models.David McInerney, Mark Thyer, Dmitri Kavetski, Faith Githui, Thabo Thayalakumaran, Min Liu, George Kuczer

A robust Gauss-Newton algorithm for the optimization of hydrological models: benchmarking against industry-standard algorithms

Optimization of model parameters is a ubiquitous task in hydrological and environmental modeling. Currently, the environmental modeling community tends to favor evolutionary techniques over classical Newton‐type methods, in the light of the geometrically problematic features of objective functions, such as multiple optima and general nonsmoothness. The companion paper (Qin et al., 2018, https://doi.org/10.1029/2017WR022488) introduced the robust Gauss‐Newton (RGN) algorithm, an enhanced version of the standard Gauss‐Newton algorithm that employs several heuristics to enhance its explorative abilities and perform robustly even for problematic objective functions. This paper focuses on benchmarking the RGN algorithm against three optimization algorithms generally accepted as “best practice” in the hydrological community, namely, the Levenberg‐Marquardt algorithm, the shuffled complex evolution (SCE) search (with 2 and 10 complexes), and the dynamically dimensioned search (DDS). The empirical case studies include four conceptual hydrological models and three catchments. Empirical results indicate that, on average, RGN is 2–3 times more efficient than SCE (2 complexes) by achieving comparable robustness at a lower cost, 7–9 times more efficient than SCE (10 complexes) by trading off some speed to more than compensate for a somewhat lower robustness, 5–7 times more efficient than Levenberg‐Marquardt by achieving higher robustness at a moderate additional cost, and 12–26 times more efficient than DDS in terms of robustness‐per‐fixed‐cost. A detailed analysis of performance in terms of reliability and cost is provided. Overall, the RGN algorithm is an attractive option for the calibration of hydrological models, and we recommend further investigation of its benefits for broader types of optimization problems.Youwei Qin, Dmitri Kavetski, George Kuczer