Using bootstrap ELM and LSSVM models to estimate river ice thickness in the Mackenzie River Basin in the Northwest Territories, Canada

River ice plays an important role in biophysical and socio-economic systems in northern regions and is related to climate variability at both regional and global scales. The objective of this study was to estimate river ice thickness using several new machine learning methods: extreme learning machine (ELM), least squares support vector machine (LSSVM), and their bootstrap versions (BELM and BLSSVM, respectively). To explore the usefulness of these methods, we chose two stations, Mackenzie River and Yellowknife River in the Mackenzie River Basin in the Northwest Territories, Canada. The variables used to develop the river ice thickness (cm) estimation models included: water flow (m(3)/s), snow depth (cm) and mean air temperature (degrees C) (with a time period of 1981-2016). Two techniques, namely the Kendall-Theil Robust Line (KTRL) and the regularized expectation maximization (RegEm) methods, were utilized to fill in the missing values in the time series records. The performance of the developed models was measured using several statistical indicators (correlation coefficient (r), root mean square error (RMSE), mean absolute error (MAE), their normalized equivalents expressed as a percentage (root mean square percentage error (RMSPE) and mean absolute percentage error (RMPE)), bias error (BIAS) and Willmott's Index (WI)). Results indicated that the bootstrap ELM model outperformed the ELM, LSSVM and BLSSVM models in the testing phases based on a number of statistical measures. For the BELM using RegEM at the Mackenzie River station, the results were: r = 0.826, RMSE = 19.756 cm, RMSPE = 33.011%, MAE = 15.364 cm, MAPE = 35.988%, BIAS = 1.199 cm and WI = 0.818. For the BELM using KTRL at the Yellowknife River station, the results were: r = 0.856, RMSE = 15.444 cm, RMSPE = 19.468%, MAE = 12.006 cm, MAPE = 19.045%, BIAS = 0.966 cm and WI = 0.868. The findings of this study indicate that the BELM machine learning approach using meteorological variables is a promising new tool for river ice thickness estimation.