As a result of backward time integration up to 3 hr, a strong sensitivity with respect to the potential temperature and velocity field is found to amplify in the lower troposphere outside of the SEF region. A weak sensitivity is also found around the primary eyewall and there is almost no sensitivity near an eye. It exhibits that an increase of potential temperature and velocity located outside and around primary eyewall substantially contribute to the SEF in the light of energy budget.
An outward propagation from the primary eyewall region to the SEF region is consistent with the behavior of vortex Rossby wave. As for a strong sensitivity amplifying outside of the SEF region, the vertical gradient of equivalent potential temperature becomes negative and thus the necessary condition of convective instability is satisfied. In other words, the SEF is fueled by an intake of potential energy located outside. It is consistent with the previous studies that regard the environmetal humidity as an important component of the SEF.
Acknowledgment: This work is funded by MEXT KAKENHI Grant 26800250.