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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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Jielun Sun
and
L. Mahrt

Abstract

This study examines the bulk aerodynamic method for estimating surface fluxes of heat and moisture using the surface radiative temperature. The surface rediative temperature is often the only available surface temperature from field measurements. Models typically predict heat fluxes from the surface radiative temperature computed from the surface energy balance. In this study, the corresponding radiometric exchange coefficient and radiometric roughness height are computed from tower- and low-level aircraft data taken during four different field programs. The data analysis shows that the radiometric exchange coefficient does not increase with increasing instability. This is because the radiometric exchange coefficient must compensate for the large vertical temperature difference resulting from use of the surface radiative temperature.

The data analysis and scaling arguments indicate that the radiometric exchange coefficient for heat in the bulk aerodynamic formulation is closely related to θ*/Δθ for both stable and unstable conditions, where Δθ is the difference between the surface radiative temperature and the air temperature and θ* is the negative of the heat flux divided by the surface friction velocity. Application of Monin–Obukhov similarity theory with surface radiative temperature also reduces to a relatively circular internal relationship between the radiometric roughness height and θ*/Δθ. This roughness height is flow dependent and not systematically related to the roughness height for momentum.

As an additional complication, the observed radiometric exchange coefficient for heat depends on the relationship between the measured surface radiative temperature and the microscale distribution of surface radiative temperature in the footprint of the heat flux measurement. Analogous problems affect the prediction of the moisture flux based on the saturation vapor prssure at the surface radiative temperature.

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L. T. Mahrt
and
Jielun Sun

Abstract

The exchange coefficients for area-averaged surface fluxes can become anomalously large when the large-scale flow is weak and significant fluxes of heat and moisture are driven by mesoscale motions within the averaging or subgrid area. To prevent this erratic behavior of the exchange coefficient, the “subgrid velocity scale” must be included to account for generation of turbulent fluxes by subgrid mesoscale motions. This velocity scale is obtained by spatially averaging the local time-averaged velocity used in the bulk aerodynamic relationship. The subgrid velocity scale is distinct from the free convection velocity scale included in the bulk aerodynamic relationship to represent transport induced by convectively driven boundary-layer-scale eddies (Godfrey and Beljaars; Beljaars).The formulation of Godfrey and Beljaars is derived by time averaging the velocity scale of the bulk aerodynamic relationship.

The behavior of the subgrid velocity scale is explored using data from five different field programs. Ubiquitous “nameless” mesoscale motions of unknown origin are found in all of the datasets. The addition of the subgrid velocity scale reduces the dependence of the exchange coefficients on grid size. Based on the data analysis, the subgrid velocity scale increases with grid size and contains a contribution due to surface heterogeneity.

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Ronald B. Smith
and
Jielun Sun

Abstract

Nonlinear steady-state solutions for stratified two-layer flow over a ridge are found. In parameter space, these solutions lie between the interfacial case of Long and the constant stratification case of Smith. The solutions predict the depth of the layer which will descend and accelerate. Qualitative agreement with Bora and Boulder observations is found.

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Jielun Sun
and
Jeffrey R. French

Abstract

Air–sea interactions are investigated using the data from the Coupled Boundary Layers Air–Sea Transfer experiment under low wind (CBLAST-Low) and the Surface Wave Dynamics Experiment (SWADE) over sea and compared with measurements from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99) over land. Based on the concept of the hockey-stick transition (HOST) hypothesis, which emphasizes contributions of large coherent eddies in atmospheric turbulent mixing that are not fully captured by Monin–Obukhov similarity theory, relationships between the atmospheric momentum transfer and the sea surface roughness, and the role of the sea surface temperature (SST) and oceanic waves in the turbulent transfer of atmospheric momentum, heat, and moisture, and variations of drag coefficient C d (z) over sea and land with wind speed V are studied.

In general, the atmospheric turbulence transfers over sea and land are similar except under weak winds and near the sea surface when wave-induced winds and oceanic currents are relevant to wind shear in generating atmospheric turbulence. The transition of the atmospheric momentum transfer between the stable and the near-neutral regimes is different over land and sea owing to the different strength and formation of atmospheric stable stratification. The relationship between the air–sea temperature difference and the turbulent heat transfer over sea is dominated by large air temperature variations compared to the slowly varying SST. Physically, C d (z) consists of the surface skin drag and the turbulence drag between z and the surface; the increase of the latter with decreasing V leads to the minimum C d (z), which is observed, but not limited to, over sea.

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Dean Vickers
,
L. Mahrt
,
Jielun Sun
, and
Tim Crawford

Abstract

The horizontal and vertical structure of the mean flow and turbulent fluxes are examined using aircraft observations taken near a barrier island on the east coast of the United States during offshore flow periods. The spatial structure is strongly influenced by the surface roughness and surface temperature discontinuities at the coast. With offshore flow of warm air over cool water, the sea surface momentum flux is large near the coast and decreases rapidly with increasing offshore distance or travel time. The decrease is attributed to advection and decay of turbulence from land. The rate of decrease is dependent on the characteristic timescale of the eddies in the upstream land-based boundary layer that are advected over the ocean. As a consequence, the air–sea momentum exchange near the coast is influenced by upstream conditions and similarity theory is not adequate to predict the flux.

The vertical structure reveals an elevated layer of downward momentum flux and turbulence energy maxima over the ocean. This increase in the momentum flux with height contributes to acceleration of the low-level mean wind. In the momentum budget, the vertical advection term, vertical flux divergence term, and the horizontal pressure gradient term are all of comparable magnitude and all act to balance large horizontal advection. An interpolation technique is applied to the aircraft data to develop fetch–height cross sections of the mean flow and momentum flux that are suitable for future verification of numerical models.

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Jielun Sun
,
Steven K. Esbensen
, and
L. Mahrt

Abstract

The authors reconsider the problem of estimating the sensible heat transfer at the earth's surface from direct measurements of turbulent fluxes in the atmospheric boundary layer. For simplicity, only horizontally homogeneous conditions are considered for a thin atmospheric layer containing no liquid water, adjacent to the earth's ground surface. Applying the first law of thermodynamics to the thin interfacial layer, an expression is obtained for thermal conduction at the surface in terms of the traditionally defined sensible heat flux by turbulence and a set of correction terms including the so-called moisture correction term. A scale analysis is presented to suggest that the magnitudes of the miscellaneous correction terms are usually negligible. Previous literature on estimation of the sensible heat flux is critically reviewed in light of the new result.

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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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