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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. 

Abstract. The science guiding the EUREC4A campaign and its measurements is presented. EUREC4A comprised roughly 5 weeks of measurements in the downstream winter trades of the North Atlantic – eastward and southeastward of Barbados. Through its ability to characterize processes operating across a wide range of scales, EUREC4A marked a turning point in our ability to observationally study factors influencing clouds in the trades, how they will respond to warming, and their link to other components of the earth system, such as upper-ocean processes or the life cycle of particulate matter. This characterization was made possible by thousands (2500) of sondes distributed to measure circulations on meso- (200 km) and larger (500 km) scales, roughly 400 h of flight time by four heavily instrumented research aircraft; four global-class research vessels; an advanced ground-based cloud observatory; scores of autonomous observing platforms operating in the upper ocean (nearly 10 000 profiles), lower atmosphere (continuous profiling), and along the air–sea interface; a network of water stable isotopologue measurements; targeted tasking of satellite remote sensing; and modeling with a new generation of weather and climate models. In addition to providing an outline of the novel measurements and their composition into a unified and coordinated campaign, the six distinct scientific facets that EUREC4A explored – from North Brazil Current rings to turbulence-induced clustering of cloud droplets and its influence on warm-rain formation – are presented along with an overview of EUREC4A's outreach activities, environmental impact, and guidelines for scientific practice. Track data for all platforms are standardized and accessible at https://doi.org/10.25326/165 (Stevens, 2021), and a film documenting the campaign is provided as a video supplement.