Radiative kernels have become a useful tool in climate analysis. A set of spectral kernels is calculated using a moderate resolution atmospheric transmission code MODTRAN and implemented in diagnosing spectrally decomposed global outgoing longwave radiation (OLR) changes. It is found that the effect of water vapor on the OLR is in proportion to the logarithm of its concentration. Spectral analysis discloses that this logarithmic dependency mainly results from water vapor absorption bands (0–560 cm~(-1) and 1250–1850 cm~(-1)), while in the window region (800–1250 cm~(-1)), the effect scales more linearly to its concentration. The logarithmic and linear effects in the respective spectral regions are validated by the calculations of a benchmark line-by-line radiative transfer model LBLRTM. The analysis based on LBLRTM-calculated second-order kernels shows that the nonlinear (logarithmic) effect results from the damping of the OLR sensitivity to layer-wise water vapor perturbation by both intra- and inter-layer effects. Given that different scaling approaches suit different spectral regions, it is advisable to apply the kernels in a hybrid manner in diagnosing the water vapor radiative effect. Applying logarithmic scaling in the water vapor absorption bands where absorption is strong and linear scaling in the window region where absorption is weak can generally constrain the error to within 10 of the overall OLR change for up to eightfold water vapor perturbations.
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