A Dynamics of Surface Temperature Forced by Solar Radiation

Due to lack of a unified description of the Earth surface temperature, a generic dynamic equation is postulated as an inference from the special case of snow. Solar radiation is explicitly included in the formulation for transparent media such as snow, ice and water while implicitly through (conductive) surface heat flux for non‐transparent media such as soil. The physical parameters of the equation are medium thermal inertia, thermal and radiative diffusivity. The equation for transparent media reduces to the familiar force‐restore model of soil surface temperature when the penetration depth of solar radiation tends to zero. Proof‐of‐concept validation for snow surface temperature as a paradigm of transparent media at three sites in the Arctic and Antarctica confirms the postulated equation as a generic description of the dynamics of surface temperature. Plain Language Summary Surface temperature of the Earth is a primary indicator of Earth climate system. Change of surface temperature depends on conductive and turbulent heat transport processes at either side of Earth surface and the media (soil, air, water, snow, etc.) specific absorption of solar radiation. Understanding and simulating surface temperature is a long‐standing challenge in the study of energy and mass exchange at the Earth‐atmosphere interface. This study postulates a unified governing equation of the dynamics of surface temperature for all surface types (soil, water, snow/ice, etc.). The new dynamic equation is independent of the parameterization of heat transfer processes within the atmosphere and surface media. The classical force‐restore equation of surface soil temperature is shown to be a special case of the general equation. The new dynamic equation can be used for simulating surface temperature without using the coupled earth‐atmosphere models or for the specification of surface boundary conditions of temperature and/or heat fluxes required by coupled earth‐atmosphere models. Key Points A unified dynamic equation of surface temperature for all surface types is postulated Explicit characterization of solar radiation absorption in the surface forcing for transparent media Heat flux in the dynamic equation is parameterized using non‐gradient formula