River ice breakup timing prediction through stacking multi-type model trees.

River ice breakup is an annual event with ecological and economic significance in the Northern Hemisphere. Breakup timing forecasting is critical for supporting emergency responses to river-ice related flooding. Little attention has been paid to applications of the classification and regression tree (CART) and M5 models as well as the stacking ensemble of multiple types of model trees to river ice forecasting problem. Thus, a framework of stacking ensemble tree models (SETM) is proposed, which consists of multiple types of model trees in a two-level structure: base and ensemble models. The Athabasca River at Fort McMurray is selected as the study area because the Athabasca River is the largest unregulated river in Alberta, Canada and ice jams frequently occur in the vicinity of Fort McMurray. To facilitate the comparison of models, the historical data in the past 36 years is collected and the leave-one-out cross validation method is employed. The results show that, the indicators influencing or corresponding with the breakup timing can be categorized as temperature and water flow conditions just before breakup (in March), during freeze-up (in last November and last December) and during middle winter (in January). The performance of optimal CART and M5 models are almost the same but the M5 model does simplify the tree structure. Although their performance can be further improved by the SETM framework, the structure of the base models can facilitate explicit explanations of the relations between indicators and the breakup date. In terms of validation performance (RMSE), the optimal ensemble model is the simple average method, which improves upon the two optimal base models (CART and M5) by 13.1% and 13.2%, respectively.