Revisiting the Surface Energy Imbalance with Observed Kinetic Energy Dissipation Guided by the Generalized Thermal Energy Balance

The disagreement between observed and theoretically expected thermal energy balances in a soil–air system at the ground surface, known as the surface energy imbalance (SEI), has been observed for over 80 years. This intriguing puzzle is marked by a systematic diurnal variation of the SEI across different surface types, beyond observational uncertainties. Guided by total energy conservation, the generalized thermal energy balance equation indicates that the traditional thermal energy balance equation based on the first law of thermodynamics would result in stability-dependent biases. Specifically, it would overestimate the thermal energy increases under convective conditions, underestimate them under stable conditions, and agree with the generalized thermal energy balance under neutral conditions. Considering the diurnal variation of the atmospheric stability within the atmospheric surface layer, these systematic biases align precisely with what field observations reveal in the SEI conundrum. In other words, the observed SEI suggests that a non-isothermal atmosphere is governed by total energy conservation. Furthermore, the limitation of the traditional thermal energy balance equation may also help explain several actively researched issues in the atmospheric boundary layer community, such as the dissimilarity between vertical temperature and humidity profiles under convective conditions and the difficulty of simulating the stable atmospheric boundary layer, including morning and evening transitions.

Turbulence kinetic energy dissipation is estimated using 4-k Hz hot-film observations at four observation heights ranging from 0.5 to 4 m. Its dependence on the atmospheric stability and wind speed is consistent with the development of turbulence driven by both thermal and mechanical forcing. These observations further demonstrate the important contribution of thermal energy transfer to kinetic energy changes, as revealed by the generalized thermal energy balance equation. Overall, this investigation provides additional evidence for the importance of interactions between kinetic and thermal energy variations in explaining the observed surface energy imbalance.

 

Acknowledgements: The research is supported by the U.S. National Science Foundation, AGS-2231229.