How does tropical cyclone genesis frequency respond to a changing climate?

Global tropical cyclone (TC) genesis frequency (TCGF) has been documented to decrease or increase linearly in a changing climate. However, our numerical experiments show that the global TCGF exhibits a parabolic relation withspatio-uniform climate changes in sea surface temperature (SST) from -15K to 5K relative to the present climate, with the peak in the 5K-cooler climate. The parabolic relation is found in all TC basins except the eastern North Pacific where TCGF keeps increasing with the changing climate. TCGF can be expressed as the product of the frequency of TC seeds and the TC survival rate. Further analysis shows that this parabolic structure in the global TCGF depends on TC seeds rather than the TC survival rate. The TC survival rate exhibits an increasing trend with the SST increase, while TC seeds show a consistent change with TCGF, which might be linked to the changes in low-level relative humidity.