Improved Model of Deep-Draft Ship Squat in Shallow Waterways Using Stepwise Regression Trees

Abstract

To maintain an optimum balance between security and efficiency of maritime transport in shallow waterways with a lot of deep-draft ship traffic such as in the St. Lawrence Waterway, it is particularly important to accurately estimate the ship squat, which is the reduction of the underkeel clearance between a vessel at rest and in motion. Recently, a squat model based on a regression tree was developed. The skill of this model to predict squat in the St. Lawrence Waterway exceeded the performance of 10 empirical models commonly used by the operational and regularity agencies. Although this approach is promising, two main problems were noticed: (1) the predictions obtained by the regression tree are not smooth and (2) the squat predicted with this model is not always monotonically increasing with ship speed (Froude number). In this paper, a stepwise regression tree algorithm is used to model squat. This approach has the same advantages as the regression tree (allowing the representation of complex and nonlinear relationships) and solves both of the aforementioned problems. Furthermore, the squat predictions of the new stepwise regression model outperform the predictions of the regression tree model and the Eryuzlu model, which is currently used by the Canadian Coast Guard. This new model could provide a handy tool for mariners to get real-time squat predictions in the St. Lawrence River. We also provide an algorithm that can be used to fit a squat model for any other economically important shallow waterway.