Abstract. Salinity modelling in river systems is complicated by a number of processes, including in-stream salt transport and various mechanisms of saline accession that vary dynamically as a function of water level and flow, often at different temporal scales. Traditionally, salinity models in rivers have either been process- or data-driven. The primary problem with process-based models is that in many instances, not all of the underlying processes are fully understood or able to be represented mathematically. There are also often insufficient historical data to support model development. The major limitation of data-driven models, such as artificial neural networks (ANNs) in comparison, is that they provide limited system understanding and are generally not able to be used to inform management decisions targeting specific processes, as different processes are generally modelled implicitly. In order to overcome these limitations, a generic framework for developing hybrid process and data-driven models of salinity in river systems is introduced and applied in this paper. As part of the approach, the most suitable sub-models are developed for each sub-process affecting salinity at the location of interest based on consideration of model purpose, the degree of process understanding and data availability, which are then combined to form the hybrid model. The approach is applied to a 46 km reach of the Murray River in South Australia, which is affected by high levels of salinity. In this reach, the major processes affecting salinity include in-stream salt transport, accession of saline groundwater along the length of the reach and the flushing of three waterbodies in the floodplain during overbank flows of various magnitudes. Based on trade-offs between the degree of process understanding and data availability, a process-driven model is developed for in-stream salt transport, an ANN model is used to model saline groundwater accession and three linear regression models are used to account for the flushing of the different floodplain storages. The resulting hybrid model performs very well on approximately 3 years of daily validation data, with a Nash–Sutcliffe efficiency (NSE) of 0.89 and a root mean squared error (RMSE) of 12.62 mg L−1 (over a range from approximately 50 to 250 mg L−1). Each component of the hybrid model results in noticeable improvements in model performance corresponding to the range of flows for which they are developed. The predictive performance of the hybrid model is significantly better than that of a benchmark process-driven model (NSE  =  −0.14, RMSE  =  41.10 mg L−1, Gbench index  =  0.90) and slightly better than that of a benchmark data-driven (ANN) model (NSE  =  0.83, RMSE  =  15.93 mg L−1, Gbench index  =  0.36). Apart from improved predictive performance, the hybrid model also has advantages over the ANN benchmark model in terms of increased capacity for improving system understanding and greater ability to support management decisions.

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Abstract. Salinity modelling in river systems is complicated by a number of processes, including in-stream salt transport and various mechanisms of saline accession that vary dynamically as a function of water level and flow, often at different temporal scales. Traditionally, salinity models in rivers have either been process-or data-driven. The primary problem with process-10 based models is that in many instances, not all of the underlying processes are fully understood or able to be represented mathematically, and that there are often insufficient historical data to support model development. The major limitation of data-driven models, such as artificial neural networks (ANNs), is that they provide limited system understanding and are generally not able to be used to inform management decisions targeting specific processes, as different processes are generally modelled implicitly. In order to overcome these limitations, a hybrid modelling approach is introduced and applied in this 15paper. As part of the approach, the most suitable sub-models are developed for each sub-process affecting salinity at the location of interest based on consideration of model purpose, degree of process understanding and data availability, which are then combined to form the hybrid model. The approach is applied to a 46 km reach of the River Murray in South Australia, which is affected by high levels of salinity. In this reach, the major processes affecting salinity include in-stream salt transport, Hydrol. Earth Syst. Sci. Discuss., https://doi

<p>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:</p><p>1. Evaluate the impact of objective function inconsistency on the quality of probabilistic predictions;</p><p>2. 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.</p><p>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.</p>

<p>Probabilistic predictions provide crucial information regarding the uncertainty of hydrological predictions, which are a key input for risk-based decision-making. However, they are often excluded from hydrological modelling applications because suitable probabilistic error models can be both challenging to construct and interpret, and the quality of results are often reliant on the objective function used to calibrate the hydrological model.</p><p>We present an open-source R-package and an online web application that achieves the following two aims. Firstly, these resources are easy-to-use and accessible, so that users need not have specialised knowledge in probabilistic modelling to apply them. Secondly, the probabilistic error model that we describe provides high-quality probabilistic predictions for a wide range of commonly-used hydrological objective functions, which it is only able to do by including a new innovation that resolves a long-standing issue relating to model assumptions that previously prevented this broad application.  </p><p>We demonstrate our methods by comparing our new probabilistic error model with an existing reference error model in an empirical case study that uses 54 perennial Australian catchments, the hydrological model GR4J, 8 common objective functions and 4 performance metrics (reliability, precision, volumetric bias and errors in the flow duration curve). The existing reference error model introduces additional flow dependencies into the residual error structure when it is used with most of the study objective functions, which in turn leads to poor-quality probabilistic predictions. In contrast, the new probabilistic error model achieves high-quality probabilistic predictions for all objective functions used in this case study.</p><p>The new probabilistic error model and the open-source software and web application aims to facilitate the adoption of probabilistic predictions in the hydrological modelling community, and to improve the quality of predictions and decisions that are made using those predictions. In particular, our methods can be used to achieve high-quality probabilistic predictions from hydrological models that are calibrated with a wide range of common objective functions.</p>