Earth's Surface Energy Balance

Introduction. The Sun is the most important energy source for the Earth’s climate system. The Earth’s climate is to a great extent determined by the solar radiation absorbed by the Earth and the emission of the terrestrial (longwave) radiation by the Earth into space. Any change in these components will result in climate change. The basic energy flow in the present climate system is the main contribution of this article, and its main structure is briefly summarized in the following paragraph, and in detail starting in Section 2.

Of the total absorbed solar radiation by the Earth, the atmosphere absorbs about 40%, while the Earth’s surface absorbs the remaining 60%. When the Earth’s surface is heated, it expels the energy by blackbody emission, evaporation, turbulent heat conduction (enthalpy), subsurface conduction, and melting ice, in the order of numerical importance. It is important to note that about 80% of the Earth’s surface net radiation is removed from the surface through evaporation and only 20% through turbulent heat conduction.

Therefore, the Earth’s energy balance is closely connected to the hydrological balance. The 80% of net radiation evaporated into the atmosphere will be converted to heat (enthalpy) within 10 days to weeks upon condensation in the cloud formation. This release of latent heat occurs in limited space (clouds) and limited time. This is how the changes in radiation, whether solar or terrestrial, are related to extreme events in precipitation and temperature. These processes will be dealt with quantitatively in the following sections. The energy balance equation for the Earth’s surface is formulated as follows:

where S is the solar global radiation; a is the albedo; L↓ is the longwave incoming radiation; H is the sensible heat flux; L_vE is the latent heat flux of vaporization, where L_v is the specific latent heat of vaporization and E the evaporation rate; C is the subsurface heat flux; σT⁴ is the longwave outgoing radiation, where a is the Stefan-Boltzmann constant and T the surface absolute temperature; and M is the heat of melt.

This way of formulation for the surface energy balance is preferred, as all self-active components are grouped on the left-hand side and the passive terms on the right-hand side. The two terms on the right-hand side, longwave outgoing radiation and the heat of melt, cannot change spontaneously, but are entirely determined by the terms on the left-hand side. Further, these two terms are self-determinant, as when one term is a variable, the other is always a constant. For example, during the melt, the amount of melt, M, changes depending on the energy sources on the left-hand side, but the temperature T remains constant at 0 °C (273.15 K).

Before and after the melt, M is obviously zero and constant, while T varies in accordance with the energy sources and sinks on the left-hand side. The longwave outgoing radiation is expressed as the blackbody emission avoiding the use of emissivity. The use of emissivity is usually unnecessary, as the outgoing radiation includes longwave reflected radiation. The sum of the emission and reflection comes very close to the blackbody emission.