Gross Tonnage-Based Statistical Modeling and Calculation of Shipping Emissions for the Bosphorus Strait

Maritime transportation is responsible for most global trade and is generally considered more environmentally efficient compared to other modes of transport, particularly for long-distance trade. With increasingly stringent emission regulations, however, accurately quantifying emissions and identifying their key determinants has become essential for effective environmental management. This study introduced a structured and comparative statistical modeling framework for ship-based emission modeling using gross tonnage (GT) as the primary predictor variable, due to its strong correlation with emission levels. Emissions for hydrocarbon (HC), carbon monoxide (CO), particulate matter with an aerodynamic diameter of less than 10 μm (PM10), carbon dioxide (CO2), sulfur dioxide (SO2), nitrogen oxides (NOx), and volatile organic compounds (VOC) were estimated using a bottom-up approach based on emission factors and formulas defined by the U.S. Environmental Protection Agency (EPA), using data from 38,304 vessel movements through the Bosphorus in 2021. These EPA-estimated values served as dependent variables in the modeling process. The modeling framework followed a three-step strategy: (1) outlier detection using Rosner’s test to reduce the influence of outliers on model accuracy, (2) curve fitting with 12 regression models representing four curve types—polynomial (e.g., linear, quadratic), concave/convex (e.g., exponential, logarithmic), sigmoidal (e.g., logistic, Gompertz, Weibull), and spline-based (e.g., cubic spline, natural spline)—to capture diverse functional relationships between GT and emissions, and (3) model comparison using difference performance metrics to ensure a comprehensive assessment of predictive accuracy, consistency, and bias. The findings revealed that nonlinear models outperformed polynomial models, with spline-based models—particularly natural spline and cubic spline—providing superior accuracy for HC, PM10, SO2, and VOC, and the Weibull model showing strong predictive performance for CO and NOx. These results underscore the necessity of using pollutant-specific and flexible modeling strategies to capture the intricacies of maritime emission dynamics. By demonstrating the advantages of flexible functional forms over standard regression techniques, this study highlights the need for tailored modeling strategies to better capture the complex relationships in maritime emission data and offers a scalable and transferable framework that can be extended to other vessel types, emission datasets, or maritime regions.