Abstract In this study, we examine the spatial pattern of the surface amplification factor (SAF). SAF corresponds to the surface element of the energy gain kernel derived in Part I of this three-part series papers, representing the amplification rate of input energy perturbations at the surface. At a given location, SAF amplifies surface energy perturbations at an equal rate regardless of their origins. Therefore, the spatial variation of SAF can provide insight into the spatial variability of climate sensitivity. The global mean of SAF is about 2.6, and its spatial pattern closely resembles the climate mean cloud field. SAF values range from 4 over the western equatorial Pacific, 2.8-3.2 over mid-latitude storm track regions, and 2.0-2.8 over the Arctic, to 1.4-1.7 over the Antarctic. The more longwave (LW) absorbers in the atmosphere, the greater SAF is. Therefore, SAF is greater in regions where atmospheric water vapor is abundant such as the tropics, and where clouds are prevalent such as mid-latitude storm tracks and the Arctic, but have smaller values close to unity in cold, high-elevation regions. Moreover, SAF tends to negatively correlate with surface temperature when LW absorbers are abundant and positively when they are scarce. With limited LW absorbers, SAF exhibits a negative (positive) correlation in cold (warm) conditions. While the spatial pattern of surface temperature plays a secondary role in shaping SAF, it may help explain why the climate sensitivity in models can either increase or decrease with surface temperature depending on the LW absorbers in the atmosphere.
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