An analytical model for tropical cyclone outer-size expansion on the f-plane

Tropical cyclones are known to expand to an equilibrium size on the $f$-plane, but the expansion process is not understood. In this study, an analytical model for tropical cyclone size expansion on the $f$-plane is proposed. Conceptually, the storm expands because the imbalance between latent heating and radiative cooling drives a lateral inflow that imports absolute vorticity. Volume-integrated latent heating increases more slowly with size than radiative cooling, and hence the storm expands towards an equilibrium size. The predicted expansion rate is given by the ratio of the difference in size from its equilibrium value ($r_{t,eq}$) to an environmentally-determined time scale $\tau_{rt}$ of $10\sim15$ days. The model is fully predictive if given a constant $r_{t,eq}$, which can also be estimated environmentally. The model successfully captures the first-order size evolution across a range of numerical simulation experiments in which the potential intensity and $f$ are varied. The model predictions of the dependencies of lateral inflow velocity and expansion rate on latent heating rate also compare well with numerical simulations. This model provides a useful foundation for understanding storm size dynamics in nature.