On the temporal decay of tropical cyclones over the ocean

It is important to understand how tropical cyclones (TCs) decay over the ocean as this is a critical pre-landfall stage. A modified exponential decay model ($\beta$ model) with two parameters $\alpha$ and $\beta$ is proposed. The scale parameter $\alpha$ defines the decay scale, while the shape parameter $\beta$ determines whether the decay rate decelerates or accelerates over time. Global fittings indicate that around 40\% of TCs exhibit decelerating decay ($\beta \leq 1$), while the majority (about 60\%) show accelerating decay ($\beta > 1$). Correlation analysis reveals a strong negative correlation between the scale parameter $\alpha$ and the initial Coriolis parameter ($r=-0.96$) and a positive correlation between the shape parameter $\beta$ and the meridional component of the initial translation velocity ($r=0.75$). The $\beta$ model provides a comprehensive understanding of how TCs decay with time and how environmental conditions affect the decay scale and evolution.