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## Abstract

The mixing lengths for heat and momentum are computed from seven levels of eddy correlation data during the Cooperative Atmosphereâ€“Surface Exchange Study-1999 (CASES-99). A number of formulations of the mixing length are evaluated, including surface layer similarity theory, several hybrid similarity theories, a formulation based on the Richardson number, and a formulation based on the local shear. A formulation of the mixing length is examined, which approaches *z*-less similarity for large *z* and surface layer similarity close to the ground surface. A generalized version includes a dependence on boundary layer depth, which approaches the usual boundary layer height dependence for neutral conditions. However, for many of the observational cases, a boundary layer did not exist in the usual sense, in that turbulence was generated primarily above the surface inversion layer and occasionally extended downward toward the surface. For these cases, inclusion of *z*-less turbulence is crucial.

## Abstract

The mixing lengths for heat and momentum are computed from seven levels of eddy correlation data during the Cooperative Atmosphereâ€“Surface Exchange Study-1999 (CASES-99). A number of formulations of the mixing length are evaluated, including surface layer similarity theory, several hybrid similarity theories, a formulation based on the Richardson number, and a formulation based on the local shear. A formulation of the mixing length is examined, which approaches *z*-less similarity for large *z* and surface layer similarity close to the ground surface. A generalized version includes a dependence on boundary layer depth, which approaches the usual boundary layer height dependence for neutral conditions. However, for many of the observational cases, a boundary layer did not exist in the usual sense, in that turbulence was generated primarily above the surface inversion layer and occasionally extended downward toward the surface. For these cases, inclusion of *z*-less turbulence is crucial.

## Abstract

A series of automated tests is developed for tower and aircraft time series to identify instrumentation problems, flux sampling problems, and physically plausible but unusual situations. The automated procedures serve as a safety net for quality controlling data. A number of special flags are developed representing a variety of potential problems such as inconsistencies between different tower levels and the flux error due to fluctuations of aircraft height.

The tests are implemented by specifying critical values for parameters representing each specific error. The critical values are developed empirically from experience of applying the tests to real turbulent time series. When these values are exceeded, the record is flagged for further inspection and comparison with the rest of the concurrent data. The inspection step is necessary to either verify an instrumentation problem or identify physically plausible behavior. The set of tests is applied to tower data from the RisÃ¸ Air Sea Experiment and Microfronts95 and aircraft data from the Boreal Ecosystemâ€“Atmosphere Study.

## Abstract

A series of automated tests is developed for tower and aircraft time series to identify instrumentation problems, flux sampling problems, and physically plausible but unusual situations. The automated procedures serve as a safety net for quality controlling data. A number of special flags are developed representing a variety of potential problems such as inconsistencies between different tower levels and the flux error due to fluctuations of aircraft height.

The tests are implemented by specifying critical values for parameters representing each specific error. The critical values are developed empirically from experience of applying the tests to real turbulent time series. When these values are exceeded, the record is flagged for further inspection and comparison with the rest of the concurrent data. The inspection step is necessary to either verify an instrumentation problem or identify physically plausible behavior. The set of tests is applied to tower data from the RisÃ¸ Air Sea Experiment and Microfronts95 and aircraft data from the Boreal Ecosystemâ€“Atmosphere Study.

## Abstract

An alternative method to Fourier analysis is discussed for studying the scale dependence of variances and covariances in atmospheric boundary layer time series. Unlike Fourier decomposition, the scale dependence based on multiresolution decomposition depends on the scale of the fluctuations and not the periodicity. An example calculation is presented in detail.

Multiresolution decomposition is applied to tower datasets to study the cospectral gap scale, which is the timescale that separates turbulent and mesoscale fluxes of heat, moisture, and momentum between the atmosphere and the surface. It is desirable to partition the flux because turbulent fluxes are related to the local wind shear and temperature stratification through similarity theory, while mesoscale fluxes are not. Use of the gap timescale to calculate the eddy correlation flux removes contamination by mesoscale motions, and therefore improves similarity relationships compared to the usual approach of using a constant averaging timescale.

A simple model is developed to predict the gap scale. The goal here is to develop a practical formulation based on readily available variables rather than a theory for the transporting eddy scales. The gap scale increases with height, increases with instability, and decreases sharply with increasing stability. With strong stratification and weak winds, the gap scale is on the order of a few minutes or less. Implementation of the gap approach involves calculating an eddy correlation flux using the modeled gap timescale to define the turbulent fluctuations (e.g., *w*â€² and *T*â€²). The turbulent fluxes (e.g., *w*â€²*T*â€²) are then averaged over 1 h to reduce random sampling errors.

## Abstract

An alternative method to Fourier analysis is discussed for studying the scale dependence of variances and covariances in atmospheric boundary layer time series. Unlike Fourier decomposition, the scale dependence based on multiresolution decomposition depends on the scale of the fluctuations and not the periodicity. An example calculation is presented in detail.

Multiresolution decomposition is applied to tower datasets to study the cospectral gap scale, which is the timescale that separates turbulent and mesoscale fluxes of heat, moisture, and momentum between the atmosphere and the surface. It is desirable to partition the flux because turbulent fluxes are related to the local wind shear and temperature stratification through similarity theory, while mesoscale fluxes are not. Use of the gap timescale to calculate the eddy correlation flux removes contamination by mesoscale motions, and therefore improves similarity relationships compared to the usual approach of using a constant averaging timescale.

A simple model is developed to predict the gap scale. The goal here is to develop a practical formulation based on readily available variables rather than a theory for the transporting eddy scales. The gap scale increases with height, increases with instability, and decreases sharply with increasing stability. With strong stratification and weak winds, the gap scale is on the order of a few minutes or less. Implementation of the gap approach involves calculating an eddy correlation flux using the modeled gap timescale to define the turbulent fluctuations (e.g., *w*â€² and *T*â€²). The turbulent fluxes (e.g., *w*â€²*T*â€²) are then averaged over 1 h to reduce random sampling errors.

## Abstract

Bulk aerodynamic formulas are applied to meteorological data from low-altitude aircraft flights to obtain observational estimates of the subgrid enhancement of momentum, sensible heat, and latent heat exchange at the atmosphericâ€“oceanic boundary in light wind, fair weather conditions during TOGA COARE (Tropical Ocean Global Atmosphere Coupled Oceanâ€“Atmosphere Response Experiment). Here, subgrid enhancement refers to the contributions of unresolved disturbances to the grid-box average fluxes at the lower boundary of an atmospheric general circulation model. The observed subgrid fluxes increase with grid-box area, reaching 11%, 9%, 24%, and 12% of the total sensible heat, latent heat, scalar wind stress, and vector wind stress magnitude, respectively, at a grid-box size of 2Â° Ã— 2Â° longitude and latitude.

Consistent with previous observational and modeling studies over the open ocean, most of the subgrid flux is explained by unresolved directional variability in the near-surface wind field. The authors find that much of the observed variability in the wind field in the presence of fair weather convective bands and patches comes from contributions of curvature and speed variations of simple larger-scale structure across the grid box.

Inclusion of a grid-scale-dependent subgrid velocity scale in the bulk aerodynamic formulas effectively parameterizes the subgrid enhancement of the sensible heat flux, latent heat flux, and vector stress magnitude, and to a lesser degree the subgrid enhancement of the scalar wind stress. An observational estimate of the subgrid velocity scale derived from one-dimensional aircraft flight legs is found to be smaller than that derived from a two-dimensional grid-box analysis. The additional enhancement in the two-dimensional case is caused by the nonhomogeneous and nonisotropic characteristics of the subgrid-scale wind variability. Long time series from surface-based platforms in the TOGA COARE region suggest that measures of convective activity, in addition to geometric grid-scale parameters, will be required to more accurately represent the subgrid velocity scales.

## Abstract

Bulk aerodynamic formulas are applied to meteorological data from low-altitude aircraft flights to obtain observational estimates of the subgrid enhancement of momentum, sensible heat, and latent heat exchange at the atmosphericâ€“oceanic boundary in light wind, fair weather conditions during TOGA COARE (Tropical Ocean Global Atmosphere Coupled Oceanâ€“Atmosphere Response Experiment). Here, subgrid enhancement refers to the contributions of unresolved disturbances to the grid-box average fluxes at the lower boundary of an atmospheric general circulation model. The observed subgrid fluxes increase with grid-box area, reaching 11%, 9%, 24%, and 12% of the total sensible heat, latent heat, scalar wind stress, and vector wind stress magnitude, respectively, at a grid-box size of 2Â° Ã— 2Â° longitude and latitude.

Consistent with previous observational and modeling studies over the open ocean, most of the subgrid flux is explained by unresolved directional variability in the near-surface wind field. The authors find that much of the observed variability in the wind field in the presence of fair weather convective bands and patches comes from contributions of curvature and speed variations of simple larger-scale structure across the grid box.

Inclusion of a grid-scale-dependent subgrid velocity scale in the bulk aerodynamic formulas effectively parameterizes the subgrid enhancement of the sensible heat flux, latent heat flux, and vector stress magnitude, and to a lesser degree the subgrid enhancement of the scalar wind stress. An observational estimate of the subgrid velocity scale derived from one-dimensional aircraft flight legs is found to be smaller than that derived from a two-dimensional grid-box analysis. The additional enhancement in the two-dimensional case is caused by the nonhomogeneous and nonisotropic characteristics of the subgrid-scale wind variability. Long time series from surface-based platforms in the TOGA COARE region suggest that measures of convective activity, in addition to geometric grid-scale parameters, will be required to more accurately represent the subgrid velocity scales.

## 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 airâ€“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 fetchâ€“height cross sections of the mean flow and momentum flux that are suitable for future verification of numerical models.

## 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 airâ€“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 fetchâ€“height cross sections of the mean flow and momentum flux that are suitable for future verification of numerical models.

## Abstract

*u*is the measured friction velocity, and

_{*}*U*

_{N}_{10}is the neutral-stability wind speed at a reference height of 10 m. This relation is fitted to

*U*

_{N}_{10}values between 9 and 24 m s

^{âˆ’1}. A drag relation formulated as

*u*versus

_{*}*U*

_{N}_{10}has several advantages over one formulated in terms of

*U*

_{N}_{10}has smaller experimental uncertainty than do determinations of

*C*

_{DN}_{10}. Second, scatterplots of

*u*versus

_{*}*U*

_{N}_{10}are not ill posed when

*U*

_{N}_{10}is small, as plots of

*C*

_{DN}_{10}are;

*u*â€“

_{*}*U*

_{N}_{10}plots presented here suggest aerodynamically smooth scaling for small

*U*

_{N}_{10}. Third, this relation depends only weakly on Moninâ€“Obukhov similarity theory and, consequently, reduces the confounding effects of artificial correlation. Finally, with its negative intercept, the linear relation produces a

*C*

_{DN}_{10}function that naturally rolls off at high wind speed and asymptotically approaches a constant value of 3.40 Ã— 10

^{âˆ’3}. Hurricane modelers and the airâ€“sea interaction community have been trying to rationalize such behavior in the drag coefficient for at least 15 years. This paper suggests that this rolloff in

*C*

_{DN}_{10}results simply from known processes that influence windâ€“wave coupling.

## Abstract

*u*is the measured friction velocity, and

_{*}*U*

_{N}_{10}is the neutral-stability wind speed at a reference height of 10 m. This relation is fitted to

*U*

_{N}_{10}values between 9 and 24 m s

^{âˆ’1}. A drag relation formulated as

*u*versus

_{*}*U*

_{N}_{10}has several advantages over one formulated in terms of

*U*

_{N}_{10}has smaller experimental uncertainty than do determinations of

*C*

_{DN}_{10}. Second, scatterplots of

*u*versus

_{*}*U*

_{N}_{10}are not ill posed when

*U*

_{N}_{10}is small, as plots of

*C*

_{DN}_{10}are;

*u*â€“

_{*}*U*

_{N}_{10}plots presented here suggest aerodynamically smooth scaling for small

*U*

_{N}_{10}. Third, this relation depends only weakly on Moninâ€“Obukhov similarity theory and, consequently, reduces the confounding effects of artificial correlation. Finally, with its negative intercept, the linear relation produces a

*C*

_{DN}_{10}function that naturally rolls off at high wind speed and asymptotically approaches a constant value of 3.40 Ã— 10

^{âˆ’3}. Hurricane modelers and the airâ€“sea interaction community have been trying to rationalize such behavior in the drag coefficient for at least 15 years. This paper suggests that this rolloff in

*C*

_{DN}_{10}results simply from known processes that influence windâ€“wave coupling.

## Abstract

A Rutan Aircraft Factory Long-EZ aircraft flew numerous low-level slant soundings on two summer days in 2001 off the northeastern coast of the United States. The soundings are analyzed here to study the nonstationary vertical structure of the wind, temperature, and turbulence. An error analysis indicates that fluxes computed from the aircraft slant soundings are unreliable. The first day is characterized by a weakly stable boundary layer in onshore flow capped by an inversion. A low-level wind maximum formed at about 100 m above the sea surface. The second day is characterized by stronger stability due to advection of warm air from the upwind land surface. On this more stable day, the wind maxima are very sharp and the speed and height of the wind maxima increase with distance from the coast. Although trends in the vertical structure are weak, variations between subsequent soundings are large on time scales of tens of minutes or less. The vertical structure of the wind and turbulence is considerably more nonstationary than the temperature structure, although the existence of the wind maximum is persistent. Causes of the wind maxima and their variability are examined but are not completely resolved.

## Abstract

A Rutan Aircraft Factory Long-EZ aircraft flew numerous low-level slant soundings on two summer days in 2001 off the northeastern coast of the United States. The soundings are analyzed here to study the nonstationary vertical structure of the wind, temperature, and turbulence. An error analysis indicates that fluxes computed from the aircraft slant soundings are unreliable. The first day is characterized by a weakly stable boundary layer in onshore flow capped by an inversion. A low-level wind maximum formed at about 100 m above the sea surface. The second day is characterized by stronger stability due to advection of warm air from the upwind land surface. On this more stable day, the wind maxima are very sharp and the speed and height of the wind maxima increase with distance from the coast. Although trends in the vertical structure are weak, variations between subsequent soundings are large on time scales of tens of minutes or less. The vertical structure of the wind and turbulence is considerably more nonstationary than the temperature structure, although the existence of the wind maximum is persistent. Causes of the wind maxima and their variability are examined but are not completely resolved.

## Abstract

Over 5000 aircraft eddy-covariance measurements from four different aircraft in nine different experiments are used to develop a simple model for the friction velocity over the sea. Unlike the widely used Coupled Oceanâ€“Atmosphere Response Experiment (COARE) bulk flux scheme, the simple model (i) does not use Moninâ€“Obukhov similarity theory (MOST) and therefore does not require an estimate of the Obukhov length, (ii) does not require a correction to the wind speed for height or stability, (iii) does not require an estimate of the aerodynamic roughness length, and (iv) does not require iteration. In comparing the model estimates developed in this work and those of the COARE algorithm, comparable fitting metrics for the two modeling schemes are found. That is, using Moninâ€“Obukhov similarity theory and the Charnock relationship did not significantly improve the predictions. It is not clear how general the simple model proposed here is, but the same model with the same coefficients based on the combined dataset does a reasonable job of describing the datasets both individually and collectively. In addition, the simple model was generally able to predict the observed friction velocities for three independent datasets that were not used in tuning the model coefficients. Motivation for the simple model comes from the fact that physical interpretation of MOST can be ambiguous because of circular dependencies and self-correlation. Additional motivation comes from the large uncertainty associated with estimating the Obukhov length and, especially, the aerodynamic roughness length.

## Abstract

Over 5000 aircraft eddy-covariance measurements from four different aircraft in nine different experiments are used to develop a simple model for the friction velocity over the sea. Unlike the widely used Coupled Oceanâ€“Atmosphere Response Experiment (COARE) bulk flux scheme, the simple model (i) does not use Moninâ€“Obukhov similarity theory (MOST) and therefore does not require an estimate of the Obukhov length, (ii) does not require a correction to the wind speed for height or stability, (iii) does not require an estimate of the aerodynamic roughness length, and (iv) does not require iteration. In comparing the model estimates developed in this work and those of the COARE algorithm, comparable fitting metrics for the two modeling schemes are found. That is, using Moninâ€“Obukhov similarity theory and the Charnock relationship did not significantly improve the predictions. It is not clear how general the simple model proposed here is, but the same model with the same coefficients based on the combined dataset does a reasonable job of describing the datasets both individually and collectively. In addition, the simple model was generally able to predict the observed friction velocities for three independent datasets that were not used in tuning the model coefficients. Motivation for the simple model comes from the fact that physical interpretation of MOST can be ambiguous because of circular dependencies and self-correlation. Additional motivation comes from the large uncertainty associated with estimating the Obukhov length and, especially, the aerodynamic roughness length.

## Abstract

The 10-m neutral drag coefficient (*C*
_{DN10}) over the sea is calculated using a large observational dataset consisting of 5800 estimates of the mean flow and the fluxes from aircraft eddy-covariance measurements. The dataset includes observations from 11 different experiments with four different research aircraft. One of the goals is to investigate how sensitive *C*
_{DN10} is to the analysis method. As such, *C*
_{DN10} derived from six unique processing schemes that involve different methods for averaging the surface stress and the wind speed are compared. Especially in weak winds, the resulting *C*
_{DN10} values depend on the choice of processing.

Four distinct regimes of *C*
_{DN10} are identified: weak winds where calculating *C*
_{DN10} is not well posed, moderate winds (4 to 10 m s^{âˆ’1}) where *C*
_{DN10} is a constant, strong winds (10 to 20 m s^{âˆ’1}) where *C*
_{DN10} increases linearly with increasing wind speed, and very strong winds (20 to 24 m s^{âˆ’1}) where *C*
_{DN10} steadily decreases with increasing wind speed. However, as this last regime is based on data from a single experiment, additional data are needed to confirm this apparent decrease in *C*
_{DN10} for winds exceeding 20 m s^{âˆ’1}.

## Abstract

The 10-m neutral drag coefficient (*C*
_{DN10}) over the sea is calculated using a large observational dataset consisting of 5800 estimates of the mean flow and the fluxes from aircraft eddy-covariance measurements. The dataset includes observations from 11 different experiments with four different research aircraft. One of the goals is to investigate how sensitive *C*
_{DN10} is to the analysis method. As such, *C*
_{DN10} derived from six unique processing schemes that involve different methods for averaging the surface stress and the wind speed are compared. Especially in weak winds, the resulting *C*
_{DN10} values depend on the choice of processing.

Four distinct regimes of *C*
_{DN10} are identified: weak winds where calculating *C*
_{DN10} is not well posed, moderate winds (4 to 10 m s^{âˆ’1}) where *C*
_{DN10} is a constant, strong winds (10 to 20 m s^{âˆ’1}) where *C*
_{DN10} increases linearly with increasing wind speed, and very strong winds (20 to 24 m s^{âˆ’1}) where *C*
_{DN10} steadily decreases with increasing wind speed. However, as this last regime is based on data from a single experiment, additional data are needed to confirm this apparent decrease in *C*
_{DN10} for winds exceeding 20 m s^{âˆ’1}.

## Abstract

This study estimates area-averaged fluxes over the Boreal Ecosystemâ€“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.

## Abstract

This study estimates area-averaged fluxes over the Boreal Ecosystemâ€“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.