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## Abstract

A top-down/bottom-up diffusion Model is used to evaluate the relative contributions of humidity temperature, and their cross correlation to the radar refractive index structure function paramer *C _{n}*

^{2}in the cloud-free, convective planetary boundary layer (PBL). Profiles of

*C*

_{n}^{2}can be measured continuously in the clear air with Doppler radars. Extraction of information about PBL dynamical parameters is more straightforward if

*C*

_{n}^{2}is dominated by either moisture (

*C*

_{q}^{2}) or temperature (

*C*

_{T}^{2}). In the lower part of the PBL the surface Bowen ratio β

_{0}determines this dominance. In the upper part of the PBL the inversion Bowen ratio β

_{1}is the primary determining factor. The model suggests that humidity accounts for at least 75% of

*C*

_{n}^{2}over tropical and midlatitude oceans. Polar oceans, where β

_{0}often exceeds 0.5, may not be dominated by either temperature or moisture. Over land β

_{0}can easily vary from 0.1 to 10. Geographical regions with β

_{0}<0.3 will be dominated by

*C*

_{q}^{2}in the lower PBL; regions with β

_{0}>5 will be dominated by

*C*

_{T}^{2}. Even for large values of β

_{0}, the upper part of the PBL will often be dominated by humidity.

## Abstract

A top-down/bottom-up diffusion Model is used to evaluate the relative contributions of humidity temperature, and their cross correlation to the radar refractive index structure function paramer *C _{n}*

^{2}in the cloud-free, convective planetary boundary layer (PBL). Profiles of

*C*

_{n}^{2}can be measured continuously in the clear air with Doppler radars. Extraction of information about PBL dynamical parameters is more straightforward if

*C*

_{n}^{2}is dominated by either moisture (

*C*

_{q}^{2}) or temperature (

*C*

_{T}^{2}). In the lower part of the PBL the surface Bowen ratio β

_{0}determines this dominance. In the upper part of the PBL the inversion Bowen ratio β

_{1}is the primary determining factor. The model suggests that humidity accounts for at least 75% of

*C*

_{n}^{2}over tropical and midlatitude oceans. Polar oceans, where β

_{0}often exceeds 0.5, may not be dominated by either temperature or moisture. Over land β

_{0}can easily vary from 0.1 to 10. Geographical regions with β

_{0}<0.3 will be dominated by

*C*

_{q}^{2}in the lower PBL; regions with β

_{0}>5 will be dominated by

*C*

_{T}^{2}. Even for large values of β

_{0}, the upper part of the PBL will often be dominated by humidity.

## Abstract

A model for inversion layer turbulence properties of a cloud-free entraining mixed-layer with wind shear at the top is developed. Using the approach of Wyngaard and LeMone (1980), expressions for the average values of ε and σ_{w}
^{2} in the entrainment region are developed in terms of a mixed layer scaling velocity *W _{m}*, the entrainment velocity

*W*and several mean profile scaling parameters including the flux Richardson numberwhere Δ

_{e}*S*is the inversion wind shear, Γ the lapse rate of θ

_{k}_{v}above the inversion and Δθ

_{v}the buoyancy jump at the inversion. Deardorff's empirical relation for

*W*/ σ

_{e}_{w}is used to close the set of equations and to obtain a parameterization for

*W*which applies it

_{e}*R*is greater than a critical value approximately equal to one-half. The wind shear enhancement of entrainment leads to an increase in the refractive index structure parameter,

_{f}*C*

_{N}^{2}, in the interfacial region. This increase in

*C*

_{N}^{2}may be significant under conditions of strong geostrophic forcing combined with a low-level inversion or large baroclinic effects associated with horizontal gradients of mixed-layer temperature or inversion height.

## Abstract

A model for inversion layer turbulence properties of a cloud-free entraining mixed-layer with wind shear at the top is developed. Using the approach of Wyngaard and LeMone (1980), expressions for the average values of ε and σ_{w}
^{2} in the entrainment region are developed in terms of a mixed layer scaling velocity *W _{m}*, the entrainment velocity

*W*and several mean profile scaling parameters including the flux Richardson numberwhere Δ

_{e}*S*is the inversion wind shear, Γ the lapse rate of θ

_{k}_{v}above the inversion and Δθ

_{v}the buoyancy jump at the inversion. Deardorff's empirical relation for

*W*/ σ

_{e}_{w}is used to close the set of equations and to obtain a parameterization for

*W*which applies it

_{e}*R*is greater than a critical value approximately equal to one-half. The wind shear enhancement of entrainment leads to an increase in the refractive index structure parameter,

_{f}*C*

_{N}^{2}, in the interfacial region. This increase in

*C*

_{N}^{2}may be significant under conditions of strong geostrophic forcing combined with a low-level inversion or large baroclinic effects associated with horizontal gradients of mixed-layer temperature or inversion height.

## Abstract

A model of scalar structure function parameters in the entraining, convective boundary layer is developed based on a top-down and bottom-up diffusion approach. The behavior of the structure function parameters is obtained from the large eddy simulations of the scalar variance budget equations given by Moeng and Wyngaard. The conventional convective scaling formalism is augmented with an additional scaling parameter, *R _{c}*, which is the ratio of the entrainment flux of the scalar variable,

*C*, to the surface flux. The model is compared to atmospheric measurements of the structure function parameters for temperature (

*C*

_{T}^{2}) and humidity (

*C*

_{Q}^{2}). Two types of comparisons are done: average profiles from several well known measurement campaigns (e.g., Minnesota and AMTEX) and individual profiles from twenty soundings by a light aircraft. The model appears to fit the

*C*

_{Q}^{2}data better than it fits the

*C*

_{T}^{2}data, particularly for the average profiles. There is a tendency for the model to underestimate the structure function parameters in the upper mixed-layer, particularly for

*C*

_{T}^{2}.

## Abstract

A model of scalar structure function parameters in the entraining, convective boundary layer is developed based on a top-down and bottom-up diffusion approach. The behavior of the structure function parameters is obtained from the large eddy simulations of the scalar variance budget equations given by Moeng and Wyngaard. The conventional convective scaling formalism is augmented with an additional scaling parameter, *R _{c}*, which is the ratio of the entrainment flux of the scalar variable,

*C*, to the surface flux. The model is compared to atmospheric measurements of the structure function parameters for temperature (

*C*

_{T}^{2}) and humidity (

*C*

_{Q}^{2}). Two types of comparisons are done: average profiles from several well known measurement campaigns (e.g., Minnesota and AMTEX) and individual profiles from twenty soundings by a light aircraft. The model appears to fit the

*C*

_{Q}^{2}data better than it fits the

*C*

_{T}^{2}data, particularly for the average profiles. There is a tendency for the model to underestimate the structure function parameters in the upper mixed-layer, particularly for

*C*

_{T}^{2}.

## Abstract

Measurements of the momentum, heat, moisture, energy, and scalar variance fluxes are combined with dissipation estimates to investigate the behavior of marine surface layer turbulence. These measurements span a wide range of atmospheric stability conditions and provide estimates of *z*/*L* between −8 and 1. Second- and third-order velocity differences are first used to provide an estimate of the Kolmogorov constant equal to 0.53 ± 0.04. The fluxes and dissipation estimates are then used to provide Monin–Obukhov (MO) similarity relationships of the various terms in the turbulent kinetic energy (TKE) and scalar variance (SV) budgets. These relationships are formulated to have the correct limiting forms in extremely stable and convective conditions. The analyses concludes with a determination of updated dimensionless structure function parameters for use with the inertial–dissipation flux method.

The production of TKE is found to balance its dissipation in convective conditions and to exceed dissipation by up to 17% in near-neutral conditions. This imbalance is investigated using the authors’ measurements of the energy flux and results in parameterizations for the energy flux and energy transport term in the TKE budget. The form of the dimensionless energy transport and dimensionless dissipation functions are very similar to previous parameterizations. From these measurements, it is concluded that the magnitude of energy transport (a loss of energy) is larger than the pressure transport (a gain of energy) in slightly unstable conditions.

The dissipation of SV is found to closely balance production in near-neutral conditions. However, the SV budget can only be balanced in convective conditions by inclusion of the transport term. The SV transport term is derived using our estimates of the flux of SV and the derivative approach. The behavior of the derived function represents a slight loss of SV in near-neutral conditions and a gain in very unstable conditions. This finding is consistent with previous investigations.

The similarity between these functions and recent overland results further suggests that experiments are generally above the region where wave-induced fluctuations influence the flow. The authors conclude that MO similarity theory is valid in the marine surface layer as long as it is applied to turbulence statistics taken above the wave boundary layer.

## Abstract

Measurements of the momentum, heat, moisture, energy, and scalar variance fluxes are combined with dissipation estimates to investigate the behavior of marine surface layer turbulence. These measurements span a wide range of atmospheric stability conditions and provide estimates of *z*/*L* between −8 and 1. Second- and third-order velocity differences are first used to provide an estimate of the Kolmogorov constant equal to 0.53 ± 0.04. The fluxes and dissipation estimates are then used to provide Monin–Obukhov (MO) similarity relationships of the various terms in the turbulent kinetic energy (TKE) and scalar variance (SV) budgets. These relationships are formulated to have the correct limiting forms in extremely stable and convective conditions. The analyses concludes with a determination of updated dimensionless structure function parameters for use with the inertial–dissipation flux method.

The production of TKE is found to balance its dissipation in convective conditions and to exceed dissipation by up to 17% in near-neutral conditions. This imbalance is investigated using the authors’ measurements of the energy flux and results in parameterizations for the energy flux and energy transport term in the TKE budget. The form of the dimensionless energy transport and dimensionless dissipation functions are very similar to previous parameterizations. From these measurements, it is concluded that the magnitude of energy transport (a loss of energy) is larger than the pressure transport (a gain of energy) in slightly unstable conditions.

The dissipation of SV is found to closely balance production in near-neutral conditions. However, the SV budget can only be balanced in convective conditions by inclusion of the transport term. The SV transport term is derived using our estimates of the flux of SV and the derivative approach. The behavior of the derived function represents a slight loss of SV in near-neutral conditions and a gain in very unstable conditions. This finding is consistent with previous investigations.

The similarity between these functions and recent overland results further suggests that experiments are generally above the region where wave-induced fluctuations influence the flow. The authors conclude that MO similarity theory is valid in the marine surface layer as long as it is applied to turbulence statistics taken above the wave boundary layer.

## Abstract

This paper focuses on the study of momentum flux between ocean and atmosphere in light winds and is based on the data collected during several field campaigns, the Atlantic Stratocumulus Transition Experiment, the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment, and the San Clemente Ocean Probing Experiment. Weak wind at sea is frequently accompanied by the presence of fast-traveling ocean swell, which dramatically affects momentum transfer. It is found that the mean momentum flux (*uw* covariance) decreases monotonically with decreasing wind speed, and reaches zero around a wind speed *U* ≈ 1.5–2 m s^{−1}, which corresponds to wave age *c*
_{p}/*U* ≈ 10 for wave/swell conditions of the experiments in this study. Further decrease of the wind speed (i.e., increase of the wave age) leads to a sign reversal of the momentum flux, implying negative drag coefficient. Upward momentum transfer is associated with fast-traveling swell running in the same direction as the wind, and this regime can be treated as swell regime or mature sea state. In the swell regime the surface stress vector is nearly opposite to wind and swell directions, and the wind is roughly aligned in the swell direction. Thus, a weak wind over ocean swell can be frequently associated with upward momentum transfer (i.e., from ocean to atmosphere).

## Abstract

This paper focuses on the study of momentum flux between ocean and atmosphere in light winds and is based on the data collected during several field campaigns, the Atlantic Stratocumulus Transition Experiment, the Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment, and the San Clemente Ocean Probing Experiment. Weak wind at sea is frequently accompanied by the presence of fast-traveling ocean swell, which dramatically affects momentum transfer. It is found that the mean momentum flux (*uw* covariance) decreases monotonically with decreasing wind speed, and reaches zero around a wind speed *U* ≈ 1.5–2 m s^{−1}, which corresponds to wave age *c*
_{p}/*U* ≈ 10 for wave/swell conditions of the experiments in this study. Further decrease of the wind speed (i.e., increase of the wave age) leads to a sign reversal of the momentum flux, implying negative drag coefficient. Upward momentum transfer is associated with fast-traveling swell running in the same direction as the wind, and this regime can be treated as swell regime or mature sea state. In the swell regime the surface stress vector is nearly opposite to wind and swell directions, and the wind is roughly aligned in the swell direction. Thus, a weak wind over ocean swell can be frequently associated with upward momentum transfer (i.e., from ocean to atmosphere).

## Abstract

Recent measurements made onboard the R/P *FLIP* in the San Clemente Ocean Probing Experiment in September 1993 and onboard the R/V *Moana Wave* during Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment are used to evaluate the direct dependence between the Monin–Obukhov stability parameter (ratio of height to Obukhov length) *ζ* and the bulk Richardson number Ri_{b} derived from standard meteorological mean observations of water surface temperature, wind speed, air temperature, and humidity. It is found that in the unstable marine surface layer, *ζ* = *C* Ri_{b}(1 + Ri_{b}/Ri_{bc})^{−1}, where the numerical coefficient *C* and the saturation Richardson number Ri_{bc} are analytical functions of the standard bulk exchange coefficients. For measurements at a height of 10–15 m, *C* is about 10 and Ri_{bc} is about −4.5. Their values are insensitive to variations of Ri_{b} and *ζ* over three decades. Thus, a simple dependence between *ζ* and Ri_{b} has a much wider range of applicability than previously believed. The authors show that this behavior is the result of the effects of “gustiness” driven by boundary layer–scale convective eddies. The derived relationship can be used as a first guess for *ζ* in bulk flux routines and reduces or eliminates the need for lengthy iterative solutions. Using this approximation yields errors in the latent heat flux of a few watts per square meter, compared to the full iterative solution.

## Abstract

Recent measurements made onboard the R/P *FLIP* in the San Clemente Ocean Probing Experiment in September 1993 and onboard the R/V *Moana Wave* during Tropical Ocean Global Atmosphere Coupled Ocean–Atmosphere Response Experiment are used to evaluate the direct dependence between the Monin–Obukhov stability parameter (ratio of height to Obukhov length) *ζ* and the bulk Richardson number Ri_{b} derived from standard meteorological mean observations of water surface temperature, wind speed, air temperature, and humidity. It is found that in the unstable marine surface layer, *ζ* = *C* Ri_{b}(1 + Ri_{b}/Ri_{bc})^{−1}, where the numerical coefficient *C* and the saturation Richardson number Ri_{bc} are analytical functions of the standard bulk exchange coefficients. For measurements at a height of 10–15 m, *C* is about 10 and Ri_{bc} is about −4.5. Their values are insensitive to variations of Ri_{b} and *ζ* over three decades. Thus, a simple dependence between *ζ* and Ri_{b} has a much wider range of applicability than previously believed. The authors show that this behavior is the result of the effects of “gustiness” driven by boundary layer–scale convective eddies. The derived relationship can be used as a first guess for *ζ* in bulk flux routines and reduces or eliminates the need for lengthy iterative solutions. Using this approximation yields errors in the latent heat flux of a few watts per square meter, compared to the full iterative solution.

## Abstract

We examine the consequences of using a vertical wavenumber spectral model to describe variations of vertical profiles of atmospheric variables (horizontal and vertical wind, temperature, and other scalars) about a mean profile. At high wavenumbers the model exhibits a wavenumber to the -3 dependence, which is characteristic of a continuum of internal gravity waves whose amplitudes are controlled by a breaking process.

By employing a random phase between wavenumber amplitude components, a reverse fourier transform of the spectrum yields simulated profiles of velocity and thermal variability as well as shear and Brunt–Väisälä frequency variability. Individual components of the vertical shear of the horizontal wind and the Brunt–Väisälä frequency exhibit Gaussian distributions; the square of the magnitude of the shear exhibits a Rice–Nakagami distribution. Assuming regions with Ri < 0.25 are turbulent, we can examine a number of aspects of the occurrence of clear-air turbulent breakdown in the stratified free atmosphere. For a typical tropospheric condition, the average turbulent layer thickness turns out to be about 35 m and about 20% of the troposphere appears to be actively turbulent. The majority of the turbulent layers appear to be due to autoconvective overturning instead of Kelvin-Helmholtz dynamic instability. Computations of profiles of the refractive index structure function parameter, *C*_{n}^{2}*ε*, are found to be quite sensitive to the assumptions of the relationship of turbulent length scale to layer thickness, the growth of turbulent layers after breakdown, and the threshold sensitivity and sampling strategy of measurement systems (e.g., clear-air radar).

## Abstract

We examine the consequences of using a vertical wavenumber spectral model to describe variations of vertical profiles of atmospheric variables (horizontal and vertical wind, temperature, and other scalars) about a mean profile. At high wavenumbers the model exhibits a wavenumber to the -3 dependence, which is characteristic of a continuum of internal gravity waves whose amplitudes are controlled by a breaking process.

By employing a random phase between wavenumber amplitude components, a reverse fourier transform of the spectrum yields simulated profiles of velocity and thermal variability as well as shear and Brunt–Väisälä frequency variability. Individual components of the vertical shear of the horizontal wind and the Brunt–Väisälä frequency exhibit Gaussian distributions; the square of the magnitude of the shear exhibits a Rice–Nakagami distribution. Assuming regions with Ri < 0.25 are turbulent, we can examine a number of aspects of the occurrence of clear-air turbulent breakdown in the stratified free atmosphere. For a typical tropospheric condition, the average turbulent layer thickness turns out to be about 35 m and about 20% of the troposphere appears to be actively turbulent. The majority of the turbulent layers appear to be due to autoconvective overturning instead of Kelvin-Helmholtz dynamic instability. Computations of profiles of the refractive index structure function parameter, *C*_{n}^{2}*ε*, are found to be quite sensitive to the assumptions of the relationship of turbulent length scale to layer thickness, the growth of turbulent layers after breakdown, and the threshold sensitivity and sampling strategy of measurement systems (e.g., clear-air radar).

## Abstract

Humidity variability at the top of the marine atmospheric boundary layer and in the overlying free troposphere was examined using data collected during the marine stratocumulus phase of the First Regional Experiment (FIRE) of the International Satellite Cloud Climatology Program. A time series of the humidity structure-function parameter *C*
_{q}
^{2} derived from Doppler wind profiler reflectivity data is compared to a concurrent time series of specific humidity *q*. Both *q* and its vertical gradient were calculated from rawinsonde data obtained from sondes launched within 500 m of the profiler. Time-height correlation analysis between log(*C*
_{q}
^{2}) and log(∂*q*/∂*z*)^{2} shows that the two time series are highly correlated at and just above the inversion base, with *r* approximately equal to 0.7. The correlation is slightly lower in the free troposphere where *r* is about 0.5 (a value of *r* greater than 0.2 is significant at the 95% confidence level). There is also correlation between log(*C*
_{q}
^{2}) and log(*q*), which is maximized at an offset in height between the two instruments.

Closer analysis of a short-lived clearing event shows locally reduced values of *C*
_{q}
^{2} in a region of enhanced ∂*q*/∂*z*. This apparent paradox can be explained by noting the absence of enhanced entrainment associated with cloud-top radiative cooling. The combined wind profiler-rawinsonde datasets were also used to estimate the entrainment velocity *w*
_{e} for clear and cloudy conditions. An average value of *w*
_{e} equal to 0.38 cm s^{−1} was obtained for cloudy conditions; for the clear case a value of 0.13 cm s^{−1} was obtained.

## Abstract

Humidity variability at the top of the marine atmospheric boundary layer and in the overlying free troposphere was examined using data collected during the marine stratocumulus phase of the First Regional Experiment (FIRE) of the International Satellite Cloud Climatology Program. A time series of the humidity structure-function parameter *C*
_{q}
^{2} derived from Doppler wind profiler reflectivity data is compared to a concurrent time series of specific humidity *q*. Both *q* and its vertical gradient were calculated from rawinsonde data obtained from sondes launched within 500 m of the profiler. Time-height correlation analysis between log(*C*
_{q}
^{2}) and log(∂*q*/∂*z*)^{2} shows that the two time series are highly correlated at and just above the inversion base, with *r* approximately equal to 0.7. The correlation is slightly lower in the free troposphere where *r* is about 0.5 (a value of *r* greater than 0.2 is significant at the 95% confidence level). There is also correlation between log(*C*
_{q}
^{2}) and log(*q*), which is maximized at an offset in height between the two instruments.

Closer analysis of a short-lived clearing event shows locally reduced values of *C*
_{q}
^{2} in a region of enhanced ∂*q*/∂*z*. This apparent paradox can be explained by noting the absence of enhanced entrainment associated with cloud-top radiative cooling. The combined wind profiler-rawinsonde datasets were also used to estimate the entrainment velocity *w*
_{e} for clear and cloudy conditions. An average value of *w*
_{e} equal to 0.38 cm s^{−1} was obtained for cloudy conditions; for the clear case a value of 0.13 cm s^{−1} was obtained.

## Abstract

Eddy correlation measurements of the vertical fluxes of particles, momentum, heat and water vapor, were conducted over a partially snow covered field in central Pennsylvania during December 1985. The PMS ASASP-300 and CSASP-100-HV optical counters were used as sensors to measure particle-number fluxes. Overall, average dry deposition velocities for 28 half-hour runs were found to be 0.034 ± 0.014 and 0.021 ± 0.005 cm s^{−1} for particles in two size ranges, 0.15–30 and 0.5–1.0 μm, respectively. The average deposition velocity was close to results from prior wind-tunnel and theoretical investigations. These results were also comparable with those reported by other authors over grass. Relatively large sampling rates reduced the effects of counting noise on deposition measurements of 0.5–;1.0 μm particles. Small correlation coefficients between vertical velocity and the particle concentration were found even after corrections for the effects of counting noise. The normalized average surface deposition velocity *v _{ds}*/

*u*

_{*}for particles in diameter of 0.15–0.30 and 0.5–1.0 μm appeared to be 0.006 and 0.002, respectively, in nearly neutral and stable conditions.

## Abstract

Eddy correlation measurements of the vertical fluxes of particles, momentum, heat and water vapor, were conducted over a partially snow covered field in central Pennsylvania during December 1985. The PMS ASASP-300 and CSASP-100-HV optical counters were used as sensors to measure particle-number fluxes. Overall, average dry deposition velocities for 28 half-hour runs were found to be 0.034 ± 0.014 and 0.021 ± 0.005 cm s^{−1} for particles in two size ranges, 0.15–30 and 0.5–1.0 μm, respectively. The average deposition velocity was close to results from prior wind-tunnel and theoretical investigations. These results were also comparable with those reported by other authors over grass. Relatively large sampling rates reduced the effects of counting noise on deposition measurements of 0.5–;1.0 μm particles. Small correlation coefficients between vertical velocity and the particle concentration were found even after corrections for the effects of counting noise. The normalized average surface deposition velocity *v _{ds}*/

*u*

_{*}for particles in diameter of 0.15–0.30 and 0.5–1.0 μm appeared to be 0.006 and 0.002, respectively, in nearly neutral and stable conditions.

## Abstract

Hot wires respond to temperature as well as to velocity, whereas cold wires respond to velocity as well as to temperature. The static and dynamic response characteristics are summarized and it is shown that the frequency transfer functions for the four different responses in general are different. The influence of the transfer characteristics on measurements of turbulence statistics is discussed; it is shown that the nonideal response behavior influences, most strongly, statistics involving the correlation between velocity and temperature and here, most seriously, parameters involving small-scale turbulence.

## Abstract

Hot wires respond to temperature as well as to velocity, whereas cold wires respond to velocity as well as to temperature. The static and dynamic response characteristics are summarized and it is shown that the frequency transfer functions for the four different responses in general are different. The influence of the transfer characteristics on measurements of turbulence statistics is discussed; it is shown that the nonideal response behavior influences, most strongly, statistics involving the correlation between velocity and temperature and here, most seriously, parameters involving small-scale turbulence.