Multiple model combination methods for annual maximum water level prediction during river ice breakup

Abstract

The Athabasca River is the largest unregulated river in Alberta, Canada, with ice jams frequently occurring in the vicinity of Fort McMurray. Modelling tools are desired to forecast ice‐related flood events. Multiple model combination methods can often obtain better predictive performances than any member models due to possible variance reduction of forecast errors or correction of biases. However, few applications of this method to river ice forecasting are reported. Thus, a framework of multiple model combination methods for maximum breakup water level (MBWL) Prediction during river ice breakup is proposed. Within the framework, the member models describe the relations between the MBWL (predicted variable) and their corresponding indicators (predictor variables); the combining models link the relations between the predicted MBWL by each member model and the observed MBWL. Especially, adaptive neuro‐fuzzy inference systems, artificial neural networks, and multiple linear regression are not only employed as member models but also as combining models. Simple average methods (SAM) are selected as the basic combining model due to simple calculations. In the SAM, an equal weight (1/n) is assigned to n member models. The historical breakup data of the Athabasca River at Fort McMurray for the past 36 years (1980 to 2015) are collected to facilitate the comparison of models. These models are examined using the leave‐one‐out cross validation and the holdout validation methods. A SAM, which is the average output from three optimal member models, is selected as the best model as it has the optimal validation performance (lowest average squared errors). In terms of lowest average squared errors, the SAM improves upon the optimal artificial neural networks, adaptive neuro‐fuzzy inference systems, and multiple linear regression member models by 21.95%, 30.97%, and 24.03%, respectively. This result sheds light on the effectiveness of combining different forecasting models when a scarce river ice data set is investigated. The indicators included in the SAM may indicate that the MBWL is affected by water flow conditions just after freeze‐up, overall freezing conditions during winter, and snowpack conditions before breakup.

A Stochastic Hydraulic Modelling Approach to Determining the Probable Maximum Staging of Ice-Jam Floods

“…In the Athabasca River along the Fort Mc-Murray, the flood water level is 246.8 m a.s.l. Above this level, the low-lying areas along the left bank of the Clearwater River gets flooded (Sun and Trevor, 2018). Thus, the estimation of PMFice to be approximately 250.43 m a.s.l.…”

Ensemble Learning Enhanced Stepwise Cluster Analysis for River Ice Breakup Date Forecasting

“…As one of popular ensemble learning methods, stacking involves a higher-level (metalevel) learner (combining model) to combine lower-level (base-level) learners (base model) to achieve greater predictive performance (Wolpert, 1992;Ting and Witten, 1999). In this sense, stacking is similar to the multiple model combination method (Sun and Trevor, 2018a). Although stacking is usually employed to combine different-type base learners built by multiple learning algorithms, it can be used to combine same-type base learners with different structures or calibrated parameters as well.…”

“…However, few applications of SCA to river ice forecasting are reported. Meanwhile, it has been reported that stacking ensemble learning can improve the overall performance through effective combinations of different base models (Erdal and Karakurt, 2013;Sun and Trevor, 2017;Sun and Trevor, 2018a). Thus, further improving the accuracy of SCA predictability using the stacking ensemble learning paradigm and its application to river ice forecasting are desired.…”

Neural network modeling of hydrological systems: A review of implementation techniques

“…According to Maier and Dandy (), measures that have been applied to maximize the use of available data sets include the use of a “hold‐out method,” which involves withholding a little portion of the data for validation and training the network on the remaining data sets. Once a significant degree of convergence is observed in the network using the validation set, a different subset of data is withheld and the process is repeated until the network attains significant generalization for the entire data set (Sun & Trevor, ). Another method that is being used to maximize available data is the “cross‐validation” technique.…”