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  • Author or Editor: Jielun Sun x
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Jielun Sun

Abstract

An investigation on vertical variations of the mixing lengths for momentum and heat under neutral and stable conditions was conducted using the data collected from the Cooperative Atmosphere–Surface Exchange Study in 1999 (CASES-99). By comparing κz with the mixing lengths under neutral conditions calculated using the observations from CASES-99, the vertical layer where the Monin–Obukhov similarity theory (MOST) is valid was identified. Here κ is the von Kármán constant and z is the height above the ground. On average, MOST is approximately valid between 0.5 and 10 m. Above the layer, the observed mixing lengths under neutral conditions are smaller than the MOST κz and can be approximately described by Blackadar’s mixing length, κz/[1 + (κz/l )], with l = 15 m for up to z ~ 20 m for the mixing length for momentum and up to the highest observation height for the mixing length for heat. Above ~20 m, the mixing length for momentum approaches a constant. Both MOST κz and Blackadar’s formula systematically overestimate the mixing length for momentum above ~20 m, leading to overestimates of turbulence.

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Jielun Sun

Abstract

Conservation of total, kinetic, and thermal energy in the atmosphere is revisited, and the derived thermal energy balance is examined with observations. Total energy conservation (TEC) provides a constraint for the sum of kinetic, thermal, and potential energy changes. In response to air thermal expansion/compression, air density variation leads to vertical density fluxes and potential energy changes, which in turn impact the thermal energy balance as well as the kinetic energy balance due to the constraint of TEC. As vertical density fluxes can propagate through a large vertical domain to where local thermal expansion/compression becomes negligibly small, interactions between kinetic and thermal energy changes in determining atmospheric motions and thermodynamic structures can occur when local diabatic heating/cooling becomes small. The contribution of vertical density fluxes to the kinetic energy balance is sometimes considered but that to the thermal energy balance is traditionally missed. Misinterpretation between air thermal expansion/compression and incompressibility for air volume changes with pressure under a constant temperature would lead to overlooking important impacts of thermal expansion/compression on air motions and atmospheric thermodynamics. Atmospheric boundary layer observations qualitatively confirm the contribution of potential energy changes associated with vertical density fluxes in the thermal energy balance for explaining temporal variations of air temperature.

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Jielun Sun
and
L. Mahrt

Abstract

This study relates surface fluxes to remotely sensed variables over well-defined variations of surface wetness and vegetation. The surface fluxes are estimated from repeated Twin Otter aircraft flights at 33 m above the surface after correcting for advection and local storage between the aircraft level and the surface. An extensive analysis of flux errors due to finite sample size over heterogeneous terrain is performed. The resulting surface energy budget seems to balance only if mesoscale fluxes are included. The spatial variation of the surface fluxes and atmospheric temperature and moisture are well predicted for these specific surface conditions by a model based on the normalized difference of vegetation index and brightness temperatures of channels 4 and 5 from the NOAA-11 Advanced Very High Resolution Radiometer.

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Larry Mahrt
,
Dean Vickers
,
Jielun Sun
, and
J. Harry McCaughey

Abstract

This study estimates area-averaged fluxes over the Boreal Ecosystem–Atmosphere Study (BOREAS) region using tower and aircraft data. The dependence of the area-averaged flux on various assumptions and external flow characteristics is examined.

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Jielun Sun
,
Volker Wulfmeyer
,
Florian Späth
,
Holger Vömel
,
William Brown
, and
Steven Oncley

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 Statement

It 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.

Open access
Jielun Sun
,
Sean P. Burns
,
Anthony C. Delany
,
Steven P. Oncley
,
Thomas W. Horst
, and
Donald H. Lenschow

Abstract

A unique set of nocturnal longwave radiative and sensible heat flux divergences was obtained during the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99). These divergences are based on upward and downward longwave radiation measurements at two levels and turbulent eddy correlation measurements at eight levels. In contrast to previous radiation divergence measurements obtained within 10 m above the ground, radiative flux divergence was measured within a deeper layer—between 2 and 48 m. Within the layer, the radiative flux divergence is, on average, comparable to or smaller than the sensible heat flux divergence. The horizontal and vertical temperature advection, derived as the residual in the heat balance using observed sensible heat and radiative fluxes, are found to be significant terms in the heat balance at night. The observations also indicate that the radiative flux divergence between 2 and 48 m was typically largest in the early evening. Its magnitude depends on how fast the ground cools and on how large the vertical temperature gradient is within the layer. A radiative flux difference of more than 10 W m−2 over 46 m of height was observed under weak-wind and clear-sky conditions after hot days. Wind speed variation can change not only the sensible heat transfer but also the surface longwave radiation because of variations of the area exposure of the warmer grass stems and soil surfaces versus the cooler grass blade tips, leading to fluctuations of the radiative flux divergence throughout the night.

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