Reply to "comments on 'revisiting the relationship between eyewall contraction and intensification'"

In their comment, Kieu and Zhang critique the recent study of Stern et al. that examined the contraction of the radius of maximum wind (RMW) and its relationship to tropical cyclone intensification. Stern et al. derived a diagnostic expression for the rate of contraction and used this to show that while RMW contraction begins and accelerates as a result of an increasing negative radial gradient of tangential wind tendency inward of the RMW, contraction slows down and eventually ceases as a result of the increasing sharpness of the wind profile around the RMW during intensification. Kieu and Zhang claim that this kinematic framework does not yield useful understanding, that Stern et al. are mistaken in their favorable comparison of this framework to earlier work by Willoughby et al., and that Stern et al. are mistaken in their conclusion that an equation for the contraction of the RMW derived by Kieu is erroneous. This reply demonstrates that each of these claims by Kieu and Zhang is incorrect.