A suite of semi-idealized numerical experiments are conducted to investigate the sensitivity of tropical cyclone (TC) intensity to changes of sea surface temperature (SST) over different radial extents.It is found that the increase of inner SST within the range 1.5-2.0 times the radius of maximum wind (RMW), defined as the effective radius (ER), contributes greatly to the increase of TC intensity and the reduction of TC inner-core size, whereas the increase of outer SST (defined as SST outside the ER)reduces TC intensity and increases TC inner-core size.Further analysis suggests that, the effects of SST inside and outside the ER on TC intensity rely on the factors that influence the TC development.AS the SST increases inside the ER, more surface enthalpy flux enters TC eyewall and less enters the outer spiral rainbands.This will decrease the RMW, leading to a smaller eyewall radius where strong latent heating is released.As a result, the central pressure of the TC deepens with stronger radial pressure gradient.Meanwhile, difference between SST and upper-tropospheric temperature increases.All above factors contribute to TC intensification as the inner SST increases.The opposite happen as the SST increases outside the ER.How TC intensity responds to the change of entire SST depends on the competitive and opposite effects of inner and outer SST.Moreover, understanding the mechanisms is vital to the forecast of variations in TC intensity and inner-core size when a TC comes across an ocean cold or warm pool.