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- Author or Editor: Jielun Sun x

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## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## 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.

## Abstract

Drainage of cold air down a small valley and associated near-surface wind maxima are examined from 20 stations with sonic anemometers at 1 m and from a 20-m tower that includes six sonic anemometers in the lowest 5 m, deployed in the Shallow Cold Pool Experiment (SCP). The small valley is about 270 m wide and 12 m deep with a downvalley slope of 2%–3%. The momentum budget indicates that the flow is driven by the buoyancy deficit of the flow and opposed primarily by the stress divergence while the remaining terms are estimated to be at least an order of magnitude smaller. This analysis also reveals major difficulties in quantifying such a budget due to uncertainties in the measurements, sensitivity to choice of averaging time, and sensitivity to measurement heights.

Wind maxima occur as low as 0.5 m in the downvalley drainage flow—the lowest observational level. The downvalley cold air drainage and wind maxima are frequently disrupted by transient modes that sometimes lead to significant vertical mixing. On average, the downvalley drainage of cold air occurs with particularly weak turbulence with stronger turbulence above the drainage flow. The momentum flux profile responds to the shear reversal at the wind maximum on a vertical scale of 1 m or less, suggesting the important role of finescale turbulent diffusion.

## Abstract

Drainage of cold air down a small valley and associated near-surface wind maxima are examined from 20 stations with sonic anemometers at 1 m and from a 20-m tower that includes six sonic anemometers in the lowest 5 m, deployed in the Shallow Cold Pool Experiment (SCP). The small valley is about 270 m wide and 12 m deep with a downvalley slope of 2%–3%. The momentum budget indicates that the flow is driven by the buoyancy deficit of the flow and opposed primarily by the stress divergence while the remaining terms are estimated to be at least an order of magnitude smaller. This analysis also reveals major difficulties in quantifying such a budget due to uncertainties in the measurements, sensitivity to choice of averaging time, and sensitivity to measurement heights.

Wind maxima occur as low as 0.5 m in the downvalley drainage flow—the lowest observational level. The downvalley cold air drainage and wind maxima are frequently disrupted by transient modes that sometimes lead to significant vertical mixing. On average, the downvalley drainage of cold air occurs with particularly weak turbulence with stronger turbulence above the drainage flow. The momentum flux profile responds to the shear reversal at the wind maximum on a vertical scale of 1 m or less, suggesting the important role of finescale turbulent diffusion.

## Abstract

Relationships among the horizontal pressure gradient, the Coriolis force, and the vertical momentum transport by turbulent fluxes are investigated using data collected from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99). Wind toward higher pressure (WTHP) adjacent to the ground occurred about 50% of the time. For wind speed at 5 m above the ground stronger than 5 m s^{−1}, WTHP occurred about 20% of the time. Focusing on these moderate to strong wind cases only, relationships among horizontal pressure gradients, Coriolis force, and vertical turbulent transport in the momentum balance are investigated. The magnitude of the downward turbulent momentum flux consistently increases with height under moderate to strong winds, which results in the vertical convergence of the momentum flux and thus provides a momentum source and allows WTHP.

In the along-wind direction, the horizontal pressure gradient is observed to be well correlated with the quadratic wind speed, which is demonstrated to be an approximate balance between the horizontal pressure gradient and the vertical convergence of the turbulent momentum flux. That is, antitriptic balance occurs in the along-wind direction when the wind is toward higher pressure. In the crosswind direction, the pressure gradient varies approximately linearly with wind speed and opposes the Coriolis force, suggesting the importance of the Coriolis force and approximate geotriptic balance of the airflow. A simple one-dimensional planetary boundary layer eddy diffusivity model demonstrates the possibility of wind directed toward higher pressure for a baroclinic boundary layer and the contribution of the vertical turbulent momentum flux to this phenomenon.

## Abstract

Relationships among the horizontal pressure gradient, the Coriolis force, and the vertical momentum transport by turbulent fluxes are investigated using data collected from the 1999 Cooperative Atmosphere–Surface Exchange Study (CASES-99). Wind toward higher pressure (WTHP) adjacent to the ground occurred about 50% of the time. For wind speed at 5 m above the ground stronger than 5 m s^{−1}, WTHP occurred about 20% of the time. Focusing on these moderate to strong wind cases only, relationships among horizontal pressure gradients, Coriolis force, and vertical turbulent transport in the momentum balance are investigated. The magnitude of the downward turbulent momentum flux consistently increases with height under moderate to strong winds, which results in the vertical convergence of the momentum flux and thus provides a momentum source and allows WTHP.

In the along-wind direction, the horizontal pressure gradient is observed to be well correlated with the quadratic wind speed, which is demonstrated to be an approximate balance between the horizontal pressure gradient and the vertical convergence of the turbulent momentum flux. That is, antitriptic balance occurs in the along-wind direction when the wind is toward higher pressure. In the crosswind direction, the pressure gradient varies approximately linearly with wind speed and opposes the Coriolis force, suggesting the importance of the Coriolis force and approximate geotriptic balance of the airflow. A simple one-dimensional planetary boundary layer eddy diffusivity model demonstrates the possibility of wind directed toward higher pressure for a baroclinic boundary layer and the contribution of the vertical turbulent momentum flux to this phenomenon.