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## Abstract

Two types of vanes that were used to measure the angle of the airstream with respect to an aircraft are described, analyzed and compared. One type is a rotating vane that is free to align itself with the airstream and the angle is sensed by an angle transducer. The other type is constrained from rotating and the angle is obtained by measuring the force exerted on the vane by the airstream and dividing by the pitot-static pressure. The free vane measures the angle directly and is not sensitive to acceleration, while the constrained vane has a faster response time and has no bearing friction. At an aircraft speed of 70 m sec^{−1}, both vanes are able to resolve changes in angle of less than 0.02°, which corresponds to a gust velocity of about 2 cm sec^{−1}, and respond to within 5% of a step-function change in angle in a distance of less than 5 m. An inflight comparison between the two vanes indicates that they both measure the same angle with a correlation coefficient of 0.97.

## Abstract

Two types of vanes that were used to measure the angle of the airstream with respect to an aircraft are described, analyzed and compared. One type is a rotating vane that is free to align itself with the airstream and the angle is sensed by an angle transducer. The other type is constrained from rotating and the angle is obtained by measuring the force exerted on the vane by the airstream and dividing by the pitot-static pressure. The free vane measures the angle directly and is not sensitive to acceleration, while the constrained vane has a faster response time and has no bearing friction. At an aircraft speed of 70 m sec^{−1}, both vanes are able to resolve changes in angle of less than 0.02°, which corresponds to a gust velocity of about 2 cm sec^{−1}, and respond to within 5% of a step-function change in angle in a distance of less than 5 m. An inflight comparison between the two vanes indicates that they both measure the same angle with a correlation coefficient of 0.97.

## Abstract

A model is proposed for the variation with height of the terms in the turbulence kinetic energy budget throughout an unstably stratified barotrople planetary boundary layer. The model is based upon aircraft measurements throughout the boundary layer that are presented here and previous results from surface layer measurements. The model assumes that at the limit of neutral stability, the transport term in the budget equation is at a minimum. When the height above the ground is greater than about ten times the absolute value of the Obukhov length, the shear-generation term is negligible, while the rate of dissipation of turbulence energy becomes almost constant, and the transport term increases almost linearly with height to balance the almost linear decrease of the buoyancy-generation term. Measurements of the ratio of the vertical flux of the horizontal part of the turbulence kinetic energy to the vertical part show good agreement with a model based upon surface layer observations and a laboratory tank experiment.

One set of observations was taken over a lake from just downwind of the shore to about 30 km offshore and the assumption of horizontal homogeneity was found to be unjustified.

## Abstract

A model is proposed for the variation with height of the terms in the turbulence kinetic energy budget throughout an unstably stratified barotrople planetary boundary layer. The model is based upon aircraft measurements throughout the boundary layer that are presented here and previous results from surface layer measurements. The model assumes that at the limit of neutral stability, the transport term in the budget equation is at a minimum. When the height above the ground is greater than about ten times the absolute value of the Obukhov length, the shear-generation term is negligible, while the rate of dissipation of turbulence energy becomes almost constant, and the transport term increases almost linearly with height to balance the almost linear decrease of the buoyancy-generation term. Measurements of the ratio of the vertical flux of the horizontal part of the turbulence kinetic energy to the vertical part show good agreement with a model based upon surface layer observations and a laboratory tank experiment.

One set of observations was taken over a lake from just downwind of the shore to about 30 km offshore and the assumption of horizontal homogeneity was found to be unjustified.

## Abstract

Aircraft measurements of sensible and latent heat fluxes, surface and air temperature, mean wind and humidity were used to examine the boundary layer structure over the Great Lakes for two cases in late fall when the water was warmer than the air above. The sensible and latent vertical turbulent heat fluxes at the surface were in the range 5–10 mW em^{−2}, and 6–15 mW em^{−3}, respectively. Estimates of the mean vertical velocity at the interface between the mixed layer (where the equivalent potential temperature lapse rate was ∼1C km^{−1} and the mixing ratio was effectively constant) and the stable air above were obtained from the equations for the rate of change of sensible plus latent heat and of water vapor in the boundary layer. The values obtained by this method appear to be reasonable when compared with estimates obtained from the wind field. Using this mean vertical velocity, the vertical fluxes of latent and sensible heat and liquid water in the cloud layer just below the top of the mixed layer can be determined. The downward buoyancy flux at this level was found to be <8% of the upward surface buoyancy flux.

Sensible and latent heat fluxes were found to vary by as much as a factor of 2 along the flight path across Lake Michigan at 147 m because of variation in the lake surface temperature. The maximum wind speed in a set of measurements at four heights, from 30 to 308 m above the lake, near the upwind end was at the lowest level. It is shown that this peculiarity may be due to the thermal wind.

## Abstract

Aircraft measurements of sensible and latent heat fluxes, surface and air temperature, mean wind and humidity were used to examine the boundary layer structure over the Great Lakes for two cases in late fall when the water was warmer than the air above. The sensible and latent vertical turbulent heat fluxes at the surface were in the range 5–10 mW em^{−2}, and 6–15 mW em^{−3}, respectively. Estimates of the mean vertical velocity at the interface between the mixed layer (where the equivalent potential temperature lapse rate was ∼1C km^{−1} and the mixing ratio was effectively constant) and the stable air above were obtained from the equations for the rate of change of sensible plus latent heat and of water vapor in the boundary layer. The values obtained by this method appear to be reasonable when compared with estimates obtained from the wind field. Using this mean vertical velocity, the vertical fluxes of latent and sensible heat and liquid water in the cloud layer just below the top of the mixed layer can be determined. The downward buoyancy flux at this level was found to be <8% of the upward surface buoyancy flux.

Sensible and latent heat fluxes were found to vary by as much as a factor of 2 along the flight path across Lake Michigan at 147 m because of variation in the lake surface temperature. The maximum wind speed in a set of measurements at four heights, from 30 to 308 m above the lake, near the upwind end was at the lowest level. It is shown that this peculiarity may be due to the thermal wind.

## Abstract

Measurements of air velocity and temperature from an airplane in the planetary boundary layer with strong surface heating are used to calculate vertical heat, momentum and energy fluxes, as well as spectral densities and probability distributions of velocity and temperature. Airplane traverses parallel to the wind are compared to crosswind traverses and a definite elongation of the heat transporting eddies, or thermals, parallel to the wind is observed. The terms in the turbulent kinetic energy balance equation (with the exception of the pressure fluctuation term) and the temperature variance balance equation are estimated. The turbulent kinetic energy dissipation is almost constant with height between the lowest flight level of 100 m above the surface, and the highest flight level of 1000 m, which is just below the top of the boundary layer, while the generation term due to the buoyancy force decreases and the divergence of the vertical transport of kinetic energy increases with height to maintain an approximate balance. The temperature variance dissipation decreases rapidly with height and the generation of temperature variance and the divergence of the vertical transport of temperature variance become small above 100 m.

## Abstract

Measurements of air velocity and temperature from an airplane in the planetary boundary layer with strong surface heating are used to calculate vertical heat, momentum and energy fluxes, as well as spectral densities and probability distributions of velocity and temperature. Airplane traverses parallel to the wind are compared to crosswind traverses and a definite elongation of the heat transporting eddies, or thermals, parallel to the wind is observed. The terms in the turbulent kinetic energy balance equation (with the exception of the pressure fluctuation term) and the temperature variance balance equation are estimated. The turbulent kinetic energy dissipation is almost constant with height between the lowest flight level of 100 m above the surface, and the highest flight level of 1000 m, which is just below the top of the boundary layer, while the generation term due to the buoyancy force decreases and the divergence of the vertical transport of kinetic energy increases with height to maintain an approximate balance. The temperature variance dissipation decreases rapidly with height and the generation of temperature variance and the divergence of the vertical transport of temperature variance become small above 100 m.

## Abstract

Measurements of air temperature with an immersion thermometer from an aircraft are invariably affected by the increased temperature of the decelerated air in the vicinity of the element. For dry air and a dry thermometer this effect is well known and usually taken into account. However, the evaporation of water from an element which has been wetted either intentionally (as in a wet-bulb thermometer) or unintentionally (by cloud or rain droplets) reduces this temperature increase. The psychrometric equation generalized for high-speed flow is used to calculate the aerodynamic correction factor for a wet temperature sensor. As an example of the magnitude of the evaporation effect, the temperature difference between a wet and a dry thermometer in a saturated airstream moving at 70 m sec^{−1}>1C.

Aircraft measurements in clouds from 3 different temperature sensors are discussed. The temperature differences between an exposed and a protected thermometer are found to be as large as 1C in conditions where the exposed thermometer is wet and the protected thermometer is dry. More importantly, the outputs of the two sensors are well correlated in clear air but are uncorrelated in cloud. Humidity measured with a wet-bulb depression sensor is found to compare very well with the output of a dewpoint hygrometer in clear air. This sensor is also a good cloud indicator since the wet-bulb depression is ∼0 only when the dry-bulb thermometer is completely wet.

## Abstract

Measurements of air temperature with an immersion thermometer from an aircraft are invariably affected by the increased temperature of the decelerated air in the vicinity of the element. For dry air and a dry thermometer this effect is well known and usually taken into account. However, the evaporation of water from an element which has been wetted either intentionally (as in a wet-bulb thermometer) or unintentionally (by cloud or rain droplets) reduces this temperature increase. The psychrometric equation generalized for high-speed flow is used to calculate the aerodynamic correction factor for a wet temperature sensor. As an example of the magnitude of the evaporation effect, the temperature difference between a wet and a dry thermometer in a saturated airstream moving at 70 m sec^{−1}>1C.

Aircraft measurements in clouds from 3 different temperature sensors are discussed. The temperature differences between an exposed and a protected thermometer are found to be as large as 1C in conditions where the exposed thermometer is wet and the protected thermometer is dry. More importantly, the outputs of the two sensors are well correlated in clear air but are uncorrelated in cloud. Humidity measured with a wet-bulb depression sensor is found to compare very well with the output of a dewpoint hygrometer in clear air. This sensor is also a good cloud indicator since the wet-bulb depression is ∼0 only when the dry-bulb thermometer is completely wet.

## Abstract

A model for the growth of a convectively mixed layer is derived by layer integrating the basic equations and parameterizing unknown terms in the mixed layer turbulence kinetic energy equation by means of free convection similarity theory. When shear generation of turbulence energy is neglected in the turbulent inversion layer capping the mixed layer, the model essentially reduces to that of Tennekes. This shear generation is found to be important only in cases of significant baroclinicity and shallow mixed layer depth or small free flow stratification.

## Abstract

A model for the growth of a convectively mixed layer is derived by layer integrating the basic equations and parameterizing unknown terms in the mixed layer turbulence kinetic energy equation by means of free convection similarity theory. When shear generation of turbulence energy is neglected in the turbulent inversion layer capping the mixed layer, the model essentially reduces to that of Tennekes. This shear generation is found to be important only in cases of significant baroclinicity and shallow mixed layer depth or small free flow stratification.

## Abstract

Isolated cumuli penetrating through marine stratocumulus clouds were documented during the Atlantic Stratocumulus Transition Experiment. This paper aims at understanding the role of the penetrating cumulus in regulating stratocumulus and boundary-layer structure through analysis of data from the NCAR Electra aircraft. When penetrating cumulus clouds are present, the boundary layer is generally decoupled from the near-surface air except in the cumulus region. Therefore, air in the cumulus region includes air entrained at the cloud top, as well as air modified by surface processes. In the stratocumulus region, however, entrained inversion air and moist surface air are confined to separate layers. As a result, large horizontal variations are found in scalars, such as ozone and water vapor. Turbulence statistics and conditional sampling of entrainment events in the cumulus and stratocumulus regions indicate that stronger entrainment may occur at the cumulus top compared to the surrounding stratocumulus. This analysis is, however, complicated by insufficient sampling of cloud-top jump conditions in both regions.

Convergent flow in the lower boundary layer and compensating diverging flow in the upper boundary layer were identified along the flight trark. This flow field, together with the vertical coupling of surface air with the cloud layer in the cumulus region, helps to transport moisture upwards from the sea surface and disperse it to the surrounding stratocumulus sheet, thus helping to maintain the stratocumulus cover.

## Abstract

Isolated cumuli penetrating through marine stratocumulus clouds were documented during the Atlantic Stratocumulus Transition Experiment. This paper aims at understanding the role of the penetrating cumulus in regulating stratocumulus and boundary-layer structure through analysis of data from the NCAR Electra aircraft. When penetrating cumulus clouds are present, the boundary layer is generally decoupled from the near-surface air except in the cumulus region. Therefore, air in the cumulus region includes air entrained at the cloud top, as well as air modified by surface processes. In the stratocumulus region, however, entrained inversion air and moist surface air are confined to separate layers. As a result, large horizontal variations are found in scalars, such as ozone and water vapor. Turbulence statistics and conditional sampling of entrainment events in the cumulus and stratocumulus regions indicate that stronger entrainment may occur at the cumulus top compared to the surrounding stratocumulus. This analysis is, however, complicated by insufficient sampling of cloud-top jump conditions in both regions.

Convergent flow in the lower boundary layer and compensating diverging flow in the upper boundary layer were identified along the flight trark. This flow field, together with the vertical coupling of surface air with the cloud layer in the cumulus region, helps to transport moisture upwards from the sea surface and disperse it to the surrounding stratocumulus sheet, thus helping to maintain the stratocumulus cover.

## Abstract

Observations of stratiform clouds in a region several hundred kilometers west of the southern California coast were made from the NCAR Electra research aircraft in the summer of 1987 during the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment (FIRE). Examples are shown of how heating or cooling of air by the sea and the evaporation of precipitation affect the stability of the temperature profile above the surface layer, which in turn affects the vertical moisture transports and the resulting cloud formation. We expect that sea-surface heating leads to the formation of stratus layers, while sea-surface cooling or cooling from evaporation of precipitation may produce fields of cumuli. The observations lead to a conceptual model of the life cycle of a stratus layer, starting as a thin, rather homogeneous layer, which grows and becomes patchy with time, produces precipitation, followed by formation of small cumuli below, and finally disintegrates, leaving a field of cumuli behind.

## Abstract

Observations of stratiform clouds in a region several hundred kilometers west of the southern California coast were made from the NCAR Electra research aircraft in the summer of 1987 during the First ISCCP (International Satellite Cloud Climatology Project) Regional Experiment (FIRE). Examples are shown of how heating or cooling of air by the sea and the evaporation of precipitation affect the stability of the temperature profile above the surface layer, which in turn affects the vertical moisture transports and the resulting cloud formation. We expect that sea-surface heating leads to the formation of stratus layers, while sea-surface cooling or cooling from evaporation of precipitation may produce fields of cumuli. The observations lead to a conceptual model of the life cycle of a stratus layer, starting as a thin, rather homogeneous layer, which grows and becomes patchy with time, produces precipitation, followed by formation of small cumuli below, and finally disintegrates, leaving a field of cumuli behind.

## Abstract

Data taken during the Air Mass Transformation Experiment (AMTEX) by the NCAR Electra aircraft have proven useful for investigating the structure of thermals penetrating into the turbulent inversion layer which caps the convective mixed layer. On 16 February 1975, two flight legs, one upwind and one crosswind, and each about 12 min long (∼80 km in length), were flown at a nominally constant altitude at about the level of the turbulent inversion layer. Because of the variations in height of this relatively thin layer, the airplane spent about equal amounts of time above and below the inversion layer. These two legs are further split into six sections for statistical analyses, each with somewhat different characteristics. Variances, co-variances, spectra and cospectra of potential temperature, the three air velocity components, and humidity are computed to illustrate the dynamic processes occurring in this region. Two spectral maxima occur in vertical velocity and temperature: one at a wavelength of about 1.5 times the mixed layer depth and the other at about 200–300 m, which seems to be related to the characteristic size of a penetrating thermal.

## Abstract

Data taken during the Air Mass Transformation Experiment (AMTEX) by the NCAR Electra aircraft have proven useful for investigating the structure of thermals penetrating into the turbulent inversion layer which caps the convective mixed layer. On 16 February 1975, two flight legs, one upwind and one crosswind, and each about 12 min long (∼80 km in length), were flown at a nominally constant altitude at about the level of the turbulent inversion layer. Because of the variations in height of this relatively thin layer, the airplane spent about equal amounts of time above and below the inversion layer. These two legs are further split into six sections for statistical analyses, each with somewhat different characteristics. Variances, co-variances, spectra and cospectra of potential temperature, the three air velocity components, and humidity are computed to illustrate the dynamic processes occurring in this region. Two spectral maxima occur in vertical velocity and temperature: one at a wavelength of about 1.5 times the mixed layer depth and the other at about 200–300 m, which seems to be related to the characteristic size of a penetrating thermal.

## Abstract

It is determined how long a time series must be to estimate covariances and moments up to fourth order with a specified statistical significance. For a given averaging time *T* there is a systematic difference between the true flux or moment and the ensemble average of the time means of the same quantities. This difference, referred to here as the systematic error, is a decreasing function of *T* tending to zero for *T*→∞. The variance of the time mean of the flux or moment, the so-called error variance, represents the random scatter of individual realizations, which, when *T* is much larger than the integral time scale *T* of the time series, is also a decreasing function of *T*. This makes it possible to assess the minimum value of *T* necessary to obtain systematic and random errors smaller than specified values. Assuming that the time series are either Gaussian processes with exponential correlation functions or a skewed process derived from a Gaussian, we obtain expressions for the systematic and random errors. These expressions show that the systematic error and the error variance in the limit of large *T* are both inversely proportional to *T*, which means that the random error, that is, the square root of the error variance, will in this limit be larger than the systematic error. It is demonstrated theoretically, as well as experimentally with aircraft data from the convective boundary layer over the ocean and over land, that the assumption that the time series are Gaussian leads to underestimation of the random errors, while derived processes with a more realistic skewness and kurtosis give better estimates. For fluxes, the systematic and random errors are estimated when the time series are sampled instantaneously, but the samples separated in time by an amount Δ. It is found that the random error variance and the systematic error increase by less than 8% over continuously sampled data if Δ is no larger than the integral scale obtained from the flux time series and the cospectrum, respectively.

## Abstract

It is determined how long a time series must be to estimate covariances and moments up to fourth order with a specified statistical significance. For a given averaging time *T* there is a systematic difference between the true flux or moment and the ensemble average of the time means of the same quantities. This difference, referred to here as the systematic error, is a decreasing function of *T* tending to zero for *T*→∞. The variance of the time mean of the flux or moment, the so-called error variance, represents the random scatter of individual realizations, which, when *T* is much larger than the integral time scale *T* of the time series, is also a decreasing function of *T*. This makes it possible to assess the minimum value of *T* necessary to obtain systematic and random errors smaller than specified values. Assuming that the time series are either Gaussian processes with exponential correlation functions or a skewed process derived from a Gaussian, we obtain expressions for the systematic and random errors. These expressions show that the systematic error and the error variance in the limit of large *T* are both inversely proportional to *T*, which means that the random error, that is, the square root of the error variance, will in this limit be larger than the systematic error. It is demonstrated theoretically, as well as experimentally with aircraft data from the convective boundary layer over the ocean and over land, that the assumption that the time series are Gaussian leads to underestimation of the random errors, while derived processes with a more realistic skewness and kurtosis give better estimates. For fluxes, the systematic and random errors are estimated when the time series are sampled instantaneously, but the samples separated in time by an amount Δ. It is found that the random error variance and the systematic error increase by less than 8% over continuously sampled data if Δ is no larger than the integral scale obtained from the flux time series and the cospectrum, respectively.