Abstract. Water temperature in rivers is a crucial environmental factor with the ability to alter hydro-ecological as well as socio-economic conditions within a catchment. The development of modelling concepts for predicting river water temperature is and will be essential for effective integrated water management and the development of adaptation strategies to future global changes (e.g. climate change). This study tests the performance of six different machine-learning models: step-wise linear regression, random forest, eXtreme Gradient Boosting (XGBoost), feed-forward neural networks (FNNs), and two types of recurrent neural networks (RNNs). All models are applied using different data inputs for daily water temperature prediction in 10 Austrian catchments ranging from 200 to 96 000 km2 and exhibiting a wide range of physiographic characteristics. The evaluated input data sets include combinations of daily means of air temperature, runoff, precipitation and global radiation. Bayesian optimization is applied to optimize the hyperparameters of all applied machine-learning models. To make the results comparable to previous studies, two widely used benchmark models are applied additionally: linear regression and air2stream. With a mean root mean squared error (RMSE) of 0.55 ∘C, the tested models could significantly improve water temperature prediction compared to linear regression (1.55 ∘C) and air2stream (0.98 ∘C). In general, the results show a very similar performance of the tested machine-learning models, with a median RMSE difference of 0.08 ∘C between the models. From the six tested machine-learning models both FNNs and XGBoost performed best in 4 of the 10 catchments. RNNs are the best-performing models in the largest catchment, indicating that RNNs mainly perform well when processes with long-term dependencies are important. Furthermore, a wide range of performance was observed for different hyperparameter sets for the tested models, showing the importance of hyperparameter optimization. Especially the FNN model results showed an extremely large RMSE standard deviation of 1.60 ∘C due to the chosen hyperparameters. This study evaluates different sets of input variables, machine-learning models and training characteristics for daily stream water temperature prediction, acting as a basis for future development of regional multi-catchment water temperature prediction models. All preprocessing steps and models are implemented in the open-source R package wateRtemp to provide easy access to these modelling approaches and facilitate further research.

Estimating parameters for distributed hydrological models is a challenging and long studied task. Parameter transfer functions, which define model parameters as functions of geophysical properties of a catchment, might improve the calibration procedure, increase process realism, and can enable prediction in ungauged areas. We present the function space optimization (FSO), a symbolic regression method for estimating parameter transfer functions for distributed hydrological models. FSO is based on the idea of transferring the search for mathematical expressions into a continuous vector space that can be used for optimization. This is accomplished by using a text generating neural network with a variational autoencoder architecture that can learn to compress the information of mathematical functions. To evaluate the performance of FSO, we conducted a case study using a parsimonious hydrological model and synthetic discharge data. The case study consisted of two FSO applications: single-criteria FSO, where only discharge was used for optimization, and multicriteria FSO, where additional spatiotemporal observations of model states were used for transfer function estimation. The results show that FSO is able to estimate transfer functions correctly or approximate them sufficiently. We observed a reduced fit of the parameter density functions resulting from the inferred transfer functions for less sensitive model parameters. For those it was sufficient to estimate functions resulting in parameter distributions with approximately the same mean parameter values as the real transfer functions. The results of the multicriteria FSO showed that using multiple spatiotemporal observations for optimization increased the quality of estimation considerably. Plain Language Summary Hydrological models are widely used tools for predicting river runoff or other components of the hydrological cycle that are important for the management of water resources. Typically, processes in those models use parameters to characterize the unique aspect of the studied area. Usually, these parameters are optimized to produce a well-performing prediction model. This potentially leads to a loss of their physical meaning. Preserving the physical meaning of model parameters can be achieved by defining them with a relationship to properties of the modeled area (soil properties, topography, etc). These relationships are given as mathematical equations that compute parameters from a set of geophysical properties. We here present a method to automatically estimate such equations, called function space optimization (FSO). FSO transfers the search for mathematical equations into an optimization problem by using a neural network to encode the information of potential equations. We show FSO's ability in a case study using a hydrological model and synthetic runoff data. The results show that FSO is able to approximate the true relationship sufficiently. Furthermore, we show that additional spatial observation data can increase FSO performance.

Objective To determine if three different commercially available seizure‐detection software packages (Besa 2.0, Encevis 1.7, and Persyst 13) accurately detect seizures with high sensitivity, high specificity, and short detection delay in epilepsy patients undergoing long‐term video–electroencephalography (EEG) monitoring (VEM). Methods Comparison of sensitivity (detection rate), specificity (false alarm rate), and detection delay of three commercially available seizure‐detection software packages in 81 randomly selected patients with epilepsy undergoing long‐term VEM. Results Detection rates on a per‐patient basis were not significantly different between Besa (mean 67.6%, range 0–100%), Encevis (77.8%, 0–100%) and Persyst (81%, 0–100%; P = .059). False alarm rate (per hour) was significantly different between Besa (mean 0.7/h, range 0.01–6.2/h), Encevis (0.2/h, 0.01–0.5/h), and Persyst (0.9/h, 0.04–6.5/h; P < .001). Detection delay was significantly different between Besa (mean 30 s, range 0–431 s), Encevis (25 s, 2–163 s), and Persyst (20 s, 0–167 s; P = .007). Kappa statistics showed moderate to substantial agreement between the reference standard and each seizure‐detection software (Besa: 0.47, 95% confidence interval [CI] 0.36–0.59; Encevis: 0.59, 95% CI 0.47–0.7; Persyst: 0.63, 95% CI 0.51–0.74). Significance Three commercially available seizure‐detection software packages showed similar, reasonable sensitivities on the same data set, but differed in false alarm rates and detection delay. Persyst 13 showed the highest detection rate and false alarm rate with the shortest detection delay, whereas Encevis 1.7 had a slightly lower sensitivity, the lowest false alarm rate, and longer detection delay.

Abstract. Water temperature in rivers is a crucial environmental factor with the ability to alter hydro-ecological as well as socio-economic conditions within a catchment. The development of modelling concepts for predicting river water temperature is and will be essential for an effective integrated water management and the development of adaptation strategies to future global changes (e.g. climate change). This study tests the performance of 6 different machine learning models: step-wise linear regression, Random forest, eXtreme Gradient Boosting (XGBoost), Feedforward neural networks (FNN), and two types of Recurrent neural networks (RNN). All models are applied using different data inputs for daily water temperature prediction in 10 Austrian catchments ranging from 200 km2 to 96000 km2 and exhibiting a wide range of physiographic characteristics. The evaluated input data sets include combinations of daily means of air temperature, runoff, precipitation and global radiation. Bayesian optimization is applied to optimize the hyperparameters of all applied machine learning models. To make the results comparable to previous studies, two widely used benchmark models are applied additionally: linear regression and air2stream. With a mean root mean squared error (RMSE) of 0.55 °C the tested models could significantly improve water temperature prediction compared to linear regression (1.55 °C) and air2stream (0.98 °C). In general, the results show a very similar performance of the tested machine learning models, with a median RMSE difference of 0.08 °C between the models. From the 6 tested machine learning models both FNNs and XGBoost performed best in 4 of the 10 catchments. RNNs are the best performing models in the largest catchment, indicating that RNNs are mainly performing well when processes with long-term dependencies are important. Furthermore, a wide range of performance was observed for different hyperparameter sets for the tested models, showing the importance of hyperprameter optimization. Especially the FNN model results showed an extremely large RMSE standard deviation of 1.60 °C due to the chosen hyperparamerters. This study evaluates different sets of input variables, machine learning models and training characteristics for daily stream water temperature prediction, acting as a basis for future development of regional multi-catchment water temperature prediction models. All preprocessing steps and models are implemented into the open source R package wateRtemp, to provide easy access to these modelling approaches and facilitate further research.