A Quasi-Linear Relationship between Planetary Outgoing Longwave Radiation and Surface Temperature in a Radiative-Convective-Transportive Climate Model of a Gray Atmosphere

Abstract

In this study, we put forward a radiative-convective-transportive energy balance model of a gray atmosphere to examine individual roles of the greenhouse effect of water vapor, vertical convection, and atmospheric poleward energy transport as well as their combined effects for a quasi-linear relationship between the outgoing longwave radiation (OLR) and surface temperature (T_S). The greenhouse effect of water vapor enhances the meridional gradient of surface temperature, thereby directly contributing to a quasi-linear OLR-T_S relationship. The atmospheric poleward energy transport decreases the meridional gradient of surface temperature. As a result of the poleward energy transport, tropical (high-latitude) atmosphere-surface columns emit less (more) OLR than the solar energy input at their respective locations, causing a substantial reduction of the meridional gradient of the OLR. The combined effect of reducing the meridional gradients of both OLR and surface temperature by the poleward energy transport also contributes to the quasi-linear OLR-T_S relationship. Vertical convective energy transport reduces the meridional gradient of surface temperature without affecting the meridional gradient of OLR, thereby suppressing part of the reduction to the increasing rate of OLR with surface temperature by the greenhouse effect of water vapor and poleward energy transport. Because of the nature of the energy balance in the climate system, such a quasi-linear relationship is also a good approximation for the relationship between the annual-mean net downward solar energy flux at the top of the atmosphere and surface temperature.

摘 要

本研究建立了一个灰色大气辐射-对流-传输能量**衡气候模式, 并且利用它研究在向外长波辐射(OLR)随地表温度(TS)准线性增加的关系中, 水汽温室效应、 垂直对流和大气极向能量传输过程对该关系的单独作用及其综合效应. 水汽的温室效应增**地表温度的经向梯度, 直接导致了OLR随TS准线性增加. 大气极向能量传输虽然降低地表温度的经向梯度, 但由于极向能量传输, 热带(高纬)大气-地表气柱辐射的OLR会少于(多于)其局地接受的太阳能量, 导致OLR径向梯度以更大的幅度降低. 因此, 极向能量传输导致OLR与TS的经向梯度同时降低, 进一步减小OLR随TS 的增加率, 有助于形成OLR-TS的准线性关系. 垂直能量传输减小了地表温度的经向梯度, 但不改变OLR的经向梯度, 从而抵消了部分水汽温室效应和极向能量输送对OLR随TS增加率的减小作用. 由于气候系统能量收支**衡, 类似于OLR与TS的准线性关系, 大气层顶年均向下净太阳能量通量与TS之间数学上也会有很好的准线性关系.