A regression-based method to estimate vessel mass for use in whale-ship strike risk models

Vessel-whale collisions are one of the major threats that large whales face worldwide. The probability of lethal injury is an important factor to consider when conducting vessel strike risk assessment, which helps identify areas most at risk. To calculate the probability of lethality, these assessments have commonly used published models, which only account for the vessel speed. A biophysical model has been developed to simulate a vessel strike and estimate a probability of lethality, better accounting for the multiple parameters involved in the interaction, such as whale morphology, vessel dimensions, as well as speed. While the biophysical model is likely to provide more accurate estimates of lethality, some of the parameters required in the model input are not readily accessible, particularly a vessel's displacement (i.e., its total mass). To facilitate the use of the biophysical model for all users, our objective was to compute vessel-type-specific equations to convert a vessel's length overall to an estimated displacement. We collected the characteristics from n = 873 vessels, including vessel length overall, maximum deadweight tonnage, and total displacement when available. Vessel data was collected from Automatic Information System static data and other sources, and represented twelve vessel types. We computed a linear regression to test the correlation between the log of vessel length and the log of displacement, by vessel type. The model was significant (p < 0.001, R2 = 0.978) and each vessel type was significantly different from at least one other vessel type. We demonstrated that these equations can then be used to compute the probability of lethality of a vessel strike with the biophysical model and obtain an estimate factored by vessel size. This can be an important tool for risk assessments and can better inform management and conservation measures for large whales.