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Abstract The hydrostatic equilibrium addresses the approximate balance between the positive force of the vertical pressure gradient and the negative gravity force and has been widely assumed for atmospheric applications. The hydrostatic imbalance of the mean atmospheric state for the acceleration of vertical motions in the vertical momentum balance is investigated using tower, the global positioning system radiosonde, and Doppler lidar and radar observations throughout the diurnally varying atmospheric boundary layer (ABL) under clear-sky conditions. Because of the negligibly small mean vertical velocity, the acceleration of vertical motions is dominated by vertical variations of vertical turbulent velocity variances. The imbalance is found to be mainly due to the vertical turbulent transport of changing air density as a result of thermal expansion/contraction in response to air temperature changes following surface temperature changes. In contrast, any pressure change associated with air temperature changes is small, and the positive vertical pressure-gradient force is strongly influenced by its background value. The vertical variation of the turbulent velocity variance from its vertical increase in the lower convective boundary layer (CBL) to its vertical decrease in the upper CBL is observed to be associated with the sign change of the imbalance from positive to negative due to the vertical decrease of the positive vertical pressure-gradient force and the relative increase of the negative gravity force as a result of the decreasing upward transport of the low-density air. The imbalance is reduced significantly at night but does not steadily approach zero. Understanding the development of hydrostatic imbalance has important implications for understanding large-scale atmosphere, especially for cloud development. Significance StatementIt is well known that the hydrostatic imbalance between the positive pressure-gradient force due to the vertical decrease of atmospheric pressure and the negative gravity forces in the vertical momentum balance equation has important impacts on the vertical acceleration of atmospheric vertical motions. Vertical motions for mass, momentum, and energy transfers contribute significantly to changing atmospheric dynamics and thermodynamics. This study investigates the often-assumed hydrostatic equilibrium and investigate how the hydrostatic imbalance is developed using field observations in the atmospheric boundary layer under clear-sky conditions. The results reveal that hydrostatic imbalance can develop from the large-eddy turbulent transfer of changing air density in response to the surface diabatic heating/cooling. The overwhelming turbulence in response to large-scale thermal forcing and mechanical work of the vast Earth surface contributes to the hydrostatic imbalance on large spatial and temporal scales in numerical weather forecast and climate models.
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This content will become publicly available on March 27, 2026
Total energy conservation for explaining discrepancies between field observations and the traditional thermal energy balance
Abstract To address the inability of the traditional thermal energy balance to explain field observations in the atmospheric boundary layer (ABL), this study investigates total energy conservation for atmospheric applications. Total energy conservation serves as a unique constraint on variations among different energy forms, especially when these variations are interconnected, as observed in the non‐isothermal atmosphere. In contrast, the first law of thermodynamics for the derivation of the traditional thermal energy balance is a special case of total energy conservation for a closed system at rest with thermal energy variations only. By keeping both total and kinetic energy conservation, a generalized thermal energy balance is found to contain two additional terms related to airflows compared with the traditional balance. They represent the thermal energy contribution to non‐hydrostatic energy transfer via heat transfer by vertical airflows and dissipation heating via air viscosity due to airflow deformation. Because of the effective vertical heat transfer by airflows, the non‐hydrostatic energy transfer contributes to major stability‐dependent differences between the traditional and generalized thermal energy balances. The stability‐dependent bias of the traditional balance is consistent with disagreement between field observations and traditional theoretical expectations such as the well‐known observed surface thermal energy imbalance, among others.
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- PAR ID:
- 10646713
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Quarterly Journal of the Royal Meteorological Society
- Volume:
- 151
- Issue:
- 771
- ISSN:
- 0035-9009
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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