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## 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*′ and *T*′). The turbulent fluxes (e.g., *w*′*T*′) 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*′ and *T*′). The turbulent fluxes (e.g., *w*′*T*′) are then averaged over 1 h to reduce random sampling errors.

## Abstract

The mixing lengths for heat and momentum are computed from seven levels of eddy correlation data during the Cooperative Atmosphere–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 Atmosphere–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 Risø Air Sea Experiment and Microfronts95 and aircraft data from the Boreal Ecosystem–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 Risø Air Sea Experiment and Microfronts95 and aircraft data from the Boreal Ecosystem–Atmosphere Study.

## 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 atmospheric–oceanic boundary in light wind, fair weather conditions during TOGA COARE (Tropical Ocean Global Atmosphere Coupled Ocean–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 2° × 2° 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 atmospheric–oceanic boundary in light wind, fair weather conditions during TOGA COARE (Tropical Ocean Global Atmosphere Coupled Ocean–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 2° × 2° 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

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 Ocean–Atmosphere Response Experiment (COARE) bulk flux scheme, the simple model (i) does not use Monin–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 Monin–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 Ocean–Atmosphere Response Experiment (COARE) bulk flux scheme, the simple model (i) does not use Monin–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 Monin–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^{−1}) where *C*
_{DN10} is a constant, strong winds (10 to 20 m s^{−1}) where *C*
_{DN10} increases linearly with increasing wind speed, and very strong winds (20 to 24 m s^{−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^{−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^{−1}) where *C*
_{DN10} is a constant, strong winds (10 to 20 m s^{−1}) where *C*
_{DN10} increases linearly with increasing wind speed, and very strong winds (20 to 24 m s^{−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^{−1}.

## 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

*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

^{−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*–

_{*}*U*

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

*U*

_{N}_{10}. Third, this relation depends only weakly on Monin–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 × 10

^{−3}. Hurricane modelers and the air–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 wind–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

^{−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*–

_{*}*U*

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

*U*

_{N}_{10}. Third, this relation depends only weakly on Monin–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 × 10

^{−3}. Hurricane modelers and the air–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 wind–wave coupling.

## Abstract

The variation of the sea surface sensible heat flux is investigated using data from the Gulf of Tehuantepec Experiment (GOTEX) and from eight additional aircraft datasets representing a variety of surface conditions. This analysis focuses on near-neutral conditions because these conditions are common over the sea and are normally neglected, partly because of uncertain reliability of measurements of the small air–sea temperature difference. For all of the datasets, upward heat flux is observed for slightly stable conditions. The frequency of this “countergradient” heat flux increases with increasing wind speed and is possibly related to sea spray or microscale variations of surface temperature on the wave scale. Upward area-averaged sensible heat flux for slightly stable conditions can also be generated by mesoscale heterogeneity of the sea surface temperature (SST). Significant measurement errors cannot be ruled out.

The countergradient heat flux for weakly stable conditions is least systematic for weaker winds, even though it occurs with weak winds in all of the datasets. In an effort to reduce offset errors and different SST processing and calibration procedures among field programs, the authors adjusted the SST in each field program to minimize the countergradient flux for weak winds. With or without this adjustment for the combined dataset, the extent of the upward heat flux for weakly stable conditions increases with increasing wind speed.

## Abstract

The variation of the sea surface sensible heat flux is investigated using data from the Gulf of Tehuantepec Experiment (GOTEX) and from eight additional aircraft datasets representing a variety of surface conditions. This analysis focuses on near-neutral conditions because these conditions are common over the sea and are normally neglected, partly because of uncertain reliability of measurements of the small air–sea temperature difference. For all of the datasets, upward heat flux is observed for slightly stable conditions. The frequency of this “countergradient” heat flux increases with increasing wind speed and is possibly related to sea spray or microscale variations of surface temperature on the wave scale. Upward area-averaged sensible heat flux for slightly stable conditions can also be generated by mesoscale heterogeneity of the sea surface temperature (SST). Significant measurement errors cannot be ruled out.

The countergradient heat flux for weakly stable conditions is least systematic for weaker winds, even though it occurs with weak winds in all of the datasets. In an effort to reduce offset errors and different SST processing and calibration procedures among field programs, the authors adjusted the SST in each field program to minimize the countergradient flux for weak winds. With or without this adjustment for the combined dataset, the extent of the upward heat flux for weakly stable conditions increases with increasing wind speed.

## Abstract

The scale dependence of velocity variances is studied using data collected from a grassland site, a heather site, and four forested sites. The dependence of velocity variances on averaging time, used to define the fluctuation quantities, is modeled. The crosswind velocity variance is emphasized, because it is more difficult to model than the other two components and is crucial input for applications such as dispersion modeling. The distinction between turbulence and mesoscale variances is examined in detail. Because mesoscale and turbulence motions are governed by different physics, meaningful study of the behavior of velocity variances requires adequate separation of turbulence and mesoscale motions from data. For stable conditions, the horizontal velocity variances near the surface exhibit a spectral gap, here corresponding to a very slow or nonexistent increase of variance with increasing averaging time. This “gap region,” when it occurs, allows separation of mesoscale and turbulence motions; however, the averaging times corresponding to this gap vary substantially with stability. A choice of typical averaging times for defining turbulent perturbations, such as 5 or 10 min, leads to the capture of significant mesoscale motions for very stable conditions and contributes to the disagreement with turbulence similarity theory. For unstable motions, the gap region for the horizontal velocity variances shrinks or becomes poorly defined, because large convective eddies tend to “fill in” the gap between turbulence and mesoscale motions. The formulation developed here allows turbulence and mesoscale motions to overlap into the same intermediate timescales. The mesoscale variances are less predictable, because a wide variety of physical processes contribute to mesoscale motions. Their magnitude and range of timescales vary substantially among sites. The variation of the behavior of turbulence variances among sites is significant but substantially less than that for the mesoscale motions.

## Abstract

The scale dependence of velocity variances is studied using data collected from a grassland site, a heather site, and four forested sites. The dependence of velocity variances on averaging time, used to define the fluctuation quantities, is modeled. The crosswind velocity variance is emphasized, because it is more difficult to model than the other two components and is crucial input for applications such as dispersion modeling. The distinction between turbulence and mesoscale variances is examined in detail. Because mesoscale and turbulence motions are governed by different physics, meaningful study of the behavior of velocity variances requires adequate separation of turbulence and mesoscale motions from data. For stable conditions, the horizontal velocity variances near the surface exhibit a spectral gap, here corresponding to a very slow or nonexistent increase of variance with increasing averaging time. This “gap region,” when it occurs, allows separation of mesoscale and turbulence motions; however, the averaging times corresponding to this gap vary substantially with stability. A choice of typical averaging times for defining turbulent perturbations, such as 5 or 10 min, leads to the capture of significant mesoscale motions for very stable conditions and contributes to the disagreement with turbulence similarity theory. For unstable motions, the gap region for the horizontal velocity variances shrinks or becomes poorly defined, because large convective eddies tend to “fill in” the gap between turbulence and mesoscale motions. The formulation developed here allows turbulence and mesoscale motions to overlap into the same intermediate timescales. The mesoscale variances are less predictable, because a wide variety of physical processes contribute to mesoscale motions. Their magnitude and range of timescales vary substantially among sites. The variation of the behavior of turbulence variances among sites is significant but substantially less than that for the mesoscale motions.