The Myth of the Surface Energy Imbalance

The traditional surface energy balance (SEB) issue is investigated by applying the first principal of thermodynamics to the soil layer and the atmosphere layer dominated by molecular thermal conduction below and above the surface, respectively. Extra heat energy transfer terms missed in the traditional SEB are identified. As the heat energy balance refers to the energy related to a mass body, the simple argument of the traditional SEB based on the matching condition of the upward and the downward heat energy flux at the air-land interface is only valid for the heat flux transfer across the air-land interface, not for the heat energy associated with a mass body. The energy balance has to be discussed in the two layers separated by the interface. Therefore, all the missing energy terms are associated with the heat transfer within the two layers. The traditional SEB includes the latent heat flux from the water evaporation at the surface, but cannot include the energy associated with the temperature change of the moisture flux through both layers, as well as the soil heat storage, the temperature variation of the incoming water flow from below the soil layer, and the net radiation of the atmosphere layer.

Based on observations from the Cooperative Atmosphere-Surface Exchange Study 1999 (CASES-99) field experiment, the most important missing terms are the moisture flux transfer through the soil layer and the heat storage in the soil layer. Using the CASES-99 data set, the sum of all the missing energy terms approximately balances the residual of the traditional SEB. The heat transfer across the interface depends on only the top-soil temperature and the moisture flux transfer, which are examined through their relationships with soil moisture and temperature, and incoming and outgoing short- and long-wave radiation.