Warming of SST in the cool wake of a moving hurricane

Satellite imagery and in situ ocean data show that the cool anomaly of sea surface temperature in the wake of a moving hurricane will disappear over an e-folding time of 5 to 20 days. We have constructed a very simple, local model of the warming process by evaluating the heat budget of the surface layer. This requires ( 1) an estimate of the heat flux anomaly, delta Q, that we presume is associated with the cool anomaly of sea surface temperature (SST), delta Q = lambda delta T, where delta T is the SST anomaly and for nominal trade wind conditions, lambda = -65 W m(-2) C-1, and (2) the thickness, D, of the surface layer that absorbs this heat flux anomaly. Evidence from numerical simulations is that D is the trapping depth of the diurnal cycle, and from existing models we estimate D = c(1)tau/Q(n)(1/2), where tau is the wind stress magnitude, Q(n) is the diurnal maximum (noon) heat flux and c(1) is a product of known physical constants. The cool anomaly is then a decaying exponential, delta T alpha delta T(0)exp(-t/Gamma), where delta T-0 is the spatially dependent cooling amplitude, and the e-folding time is G = c(2)t/lambda Q(n)(1/2), with c(2) also known. This solution agrees reasonably well with the observed e-folding time of cooling in the wake of Hurricane Fabian (2003), approximately 5 days, and in the wake of Hurricane Frances (2004), very roughly 20 days. The latter e-folding time was greater (i.e., the normalized warming rate was slower) primarily because winds were fresher and secondarily because cloud cover was greater. It is notable that the e-folding time in this solution depends upon two properties of the surface heat flux, the slowly varying heat flux anomaly and the diurnal variation of the heat flux, here represented by the noon maximum, Q(n).