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- Author or Editor: Donald H. Lenschow x

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## Abstract

Airplanes have been used to estimate the magnitude and shape of thunderstorm updrafts by assuming that the airplane follows the updraft when the thrust, mass and pitch angle are held constant. This assumption is shown to be satisfactory, using simplified airplane equations of motion, for a Beechcraft Queen Air and a North American T-28, if the updraft is large with respect to the contribution of the drift of the pitch angle reference to the airplane vertical velocity. For thunderstorms, where updrafts >8 m s^{−1} with a diameter of ∼3 km are expected, the airplanes should follow the updraft closely enough that a “smooth” updraft profile can be distinguished from a “top hat” profile. The contribution to the vertical airplane velocity from horizontal wind variations is less than 20% of the horizontal wind variation if the pitch angle is held constant. If, instead, the airspeed is held constant, the contribution to the vertical airplane velocity would be as much as 100% of the horizontal wind variation.

A Queen Air, instrumented with a complete air motion sensing system, was flown through the updraft over an isolated mountain peak, which was similar in size and shape to a thunderstorm updraft, to check the analysis. The results verified the desirability of flying at constant pitch angle.

## Abstract

Airplanes have been used to estimate the magnitude and shape of thunderstorm updrafts by assuming that the airplane follows the updraft when the thrust, mass and pitch angle are held constant. This assumption is shown to be satisfactory, using simplified airplane equations of motion, for a Beechcraft Queen Air and a North American T-28, if the updraft is large with respect to the contribution of the drift of the pitch angle reference to the airplane vertical velocity. For thunderstorms, where updrafts >8 m s^{−1} with a diameter of ∼3 km are expected, the airplanes should follow the updraft closely enough that a “smooth” updraft profile can be distinguished from a “top hat” profile. The contribution to the vertical airplane velocity from horizontal wind variations is less than 20% of the horizontal wind variation if the pitch angle is held constant. If, instead, the airspeed is held constant, the contribution to the vertical airplane velocity would be as much as 100% of the horizontal wind variation.

A Queen Air, instrumented with a complete air motion sensing system, was flown through the updraft over an isolated mountain peak, which was similar in size and shape to a thunderstorm updraft, to check the analysis. The results verified the desirability of flying at constant pitch angle.

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## Abstract

We show that the error variance contributed by random uncorrelated measurement noise can be merged with the error variance contributed by real variations in the atmosphere to obtain a single expression for the total error variance when the sampling time is much less than the integral scale of atmospheric variability. We assume that the measured signal is a representation of a variable that is continuous on the scale of interest in the atmosphere. The characteristics of this noise are similar, but not identical, to quantization noise, whose properties are briefly described. Uncorrelated noise affects the autocovariance function (or, equivalently, the structure function) only between zero and the first lag, while its effect is smeared across the entire power spectrum. For this reason, quantities such as variance dissipation may be more conveniently estimated from the structure function than from the spectrum.

The modeling results are confirmed by artificially modifying a test time series with Poisson noise and comparing the statistics from ten realizations of the modified series with the predicted error variances. We also demonstrate applications of these results to measurements of aerosol concentrations. A “figure of merit” is defined which is used to specify when instrument counting noise contributes more to measurement error than does atmospheric variability. For example, for measuring the vertical flux of a trace species for a small surface resistance to deposition, the specified counting rate is about 100 counts s^{−1} for measuring flux in the surface layer and about 10^{3} counts s^{−1} for measuring flux throughout the convective boundary layer.

## Abstract

We show that the error variance contributed by random uncorrelated measurement noise can be merged with the error variance contributed by real variations in the atmosphere to obtain a single expression for the total error variance when the sampling time is much less than the integral scale of atmospheric variability. We assume that the measured signal is a representation of a variable that is continuous on the scale of interest in the atmosphere. The characteristics of this noise are similar, but not identical, to quantization noise, whose properties are briefly described. Uncorrelated noise affects the autocovariance function (or, equivalently, the structure function) only between zero and the first lag, while its effect is smeared across the entire power spectrum. For this reason, quantities such as variance dissipation may be more conveniently estimated from the structure function than from the spectrum.

The modeling results are confirmed by artificially modifying a test time series with Poisson noise and comparing the statistics from ten realizations of the modified series with the predicted error variances. We also demonstrate applications of these results to measurements of aerosol concentrations. A “figure of merit” is defined which is used to specify when instrument counting noise contributes more to measurement error than does atmospheric variability. For example, for measuring the vertical flux of a trace species for a small surface resistance to deposition, the specified counting rate is about 100 counts s^{−1} for measuring flux in the surface layer and about 10^{3} counts s^{−1} for measuring flux throughout the convective boundary layer.

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## Abstract

We calculated integral scales for horizontal and vertical velocity components, temperature, humidity and ozone concentration, as well as for their variances and covariances from aircraft measurements in the convective atmospheric boundary layer over both ocean and land surfaces. We found that the integral scales of the second-order moment quantities are 0.67± 0.09 that of the variables themselves. Consequently, only the second-order moment integral scales are presented here. These results are used to calculate the averaging lengths necessary to measure second-order moment quantities to a given accuracy. We found that a measurement length of 10 to 100 times the boundary-layer height is required to measure variances to 10% accuracy, while scalar fluxes require a measurement length of 10^{2} to 10^{4} and stress a measurement length of 10^{3} to 10^{5} times the boundary layer height. We also show that the ratio of the wavelength of the spectral peak to the integral scale can be used to estimate the sharpness of the spectral peak.

## Abstract

We calculated integral scales for horizontal and vertical velocity components, temperature, humidity and ozone concentration, as well as for their variances and covariances from aircraft measurements in the convective atmospheric boundary layer over both ocean and land surfaces. We found that the integral scales of the second-order moment quantities are 0.67± 0.09 that of the variables themselves. Consequently, only the second-order moment integral scales are presented here. These results are used to calculate the averaging lengths necessary to measure second-order moment quantities to a given accuracy. We found that a measurement length of 10 to 100 times the boundary-layer height is required to measure variances to 10% accuracy, while scalar fluxes require a measurement length of 10^{2} to 10^{4} and stress a measurement length of 10^{3} to 10^{5} times the boundary layer height. We also show that the ratio of the wavelength of the spectral peak to the integral scale can be used to estimate the sharpness of the spectral peak.

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## Abstract

We discuss procedures for analyzing dual aircraft formation flights using time-lapse photographs of one aircraft from the other, combined with inertial navigation system position measurements, to estimate the displacement vector between the two aircraft. We show that accuracies of a few percent of the separation distance can be readily achieved, and we develop a technique for aligning the datasets from the two aircraft to correct for variations in the longitudinal component of the displacement vector. We then derive an expression for the variance of the difference between measurements of the same variable on each aircraft as a function of averaging time and separation distance. An example of data from a series of formation flights over eastern Colorado is used to demonstrate the techniques for estimating the displacement vector, aligning the datasets, and calculating. lateral coherences and phase angles.

## Abstract

We discuss procedures for analyzing dual aircraft formation flights using time-lapse photographs of one aircraft from the other, combined with inertial navigation system position measurements, to estimate the displacement vector between the two aircraft. We show that accuracies of a few percent of the separation distance can be readily achieved, and we develop a technique for aligning the datasets from the two aircraft to correct for variations in the longitudinal component of the displacement vector. We then derive an expression for the variance of the difference between measurements of the same variable on each aircraft as a function of averaging time and separation distance. An example of data from a series of formation flights over eastern Colorado is used to demonstrate the techniques for estimating the displacement vector, aligning the datasets, and calculating. lateral coherences and phase angles.

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## Abstract

Few sensors have perfectly linear dynamic response. Because the atmosphere is inherently turbulent, nonlinear sensor response can lead to errors in measured means. We discuss a technique for estimating this error for both first- and second-order systems involving only a single input and output. We find that the error has two distinct sources: one due to nonlinearity of the response, the other due to nonlinearity of the calibration. We then apply the technique developed here to three examples: a Pilot tube, which we approximate by a first-order dynamic equation, and a thrust anemometer and the CSIRO liquid water probe, which are both considered to be second-order systems. The Pilot tube, and to some extent, the thrust anemometer overestimate the mean in a way similar to a cup anemometer, which has been discussed previously. In particular, the square of the relative turbulence intensity determines the upper limit of this positive bias. We also show that the CSIRO probe may, in some situations, have a significant negative bias.

## Abstract

Few sensors have perfectly linear dynamic response. Because the atmosphere is inherently turbulent, nonlinear sensor response can lead to errors in measured means. We discuss a technique for estimating this error for both first- and second-order systems involving only a single input and output. We find that the error has two distinct sources: one due to nonlinearity of the response, the other due to nonlinearity of the calibration. We then apply the technique developed here to three examples: a Pilot tube, which we approximate by a first-order dynamic equation, and a thrust anemometer and the CSIRO liquid water probe, which are both considered to be second-order systems. The Pilot tube, and to some extent, the thrust anemometer overestimate the mean in a way similar to a cup anemometer, which has been discussed previously. In particular, the square of the relative turbulence intensity determines the upper limit of this positive bias. We also show that the CSIRO probe may, in some situations, have a significant negative bias.

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## Abstract

A conically scanning Doppler lidar technique for measuring air motions from an aircraft is proposed in the companion paper (Keeler et al.). A theoretical analysis of this technique shows that, assuming isotropic turbulence, the technique is feasible for measuring air motions to woes small enough that the velocity spectra in a convective atmospheric boundary layer can be resolved well into the inertial subrange, and most of the turbulent motions that contribute to the vertical fluxes can be resolved. A scanning beam range of 10 m was selected to ensure that flow distortion induced by the aircraft will not significantly affect the velocity measurement. Thus, the technique offers improved accuracy over presently used immersion air motion sensors. An additional feature is the possibility of measuring mean vertical wind shear.

## Abstract

A conically scanning Doppler lidar technique for measuring air motions from an aircraft is proposed in the companion paper (Keeler et al.). A theoretical analysis of this technique shows that, assuming isotropic turbulence, the technique is feasible for measuring air motions to woes small enough that the velocity spectra in a convective atmospheric boundary layer can be resolved well into the inertial subrange, and most of the turbulent motions that contribute to the vertical fluxes can be resolved. A scanning beam range of 10 m was selected to ensure that flow distortion induced by the aircraft will not significantly affect the velocity measurement. Thus, the technique offers improved accuracy over presently used immersion air motion sensors. An additional feature is the possibility of measuring mean vertical wind shear.

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The authors use a 1998 workshop titled “Observations, Experiments, and Large-Eddy Simulation” as a springboard to begin a dialogue on the philosophy of simulation as well as to examine the relationship of large eddy simulation (LES) of geophysical flows to both observations and experiments.

LES is shown to be perhaps the simplest representative of a broad class of activity in the geosciences, wherein the aggregated properties of fluids are solved for using approximate, or conjectural equation sets. To distinguish this type of activity from direct fluid simulation, the terms pseudofluid and pseudofluid simulation are introduced. Both direct and pseudofluid simulation introduce methodological changes into the science as they propose to provide synthetic, yet controlled, descriptions of phenomena that can then be used to help shape ideas regarding the behavior of real fluids. In this sense they differ from more traditional theoretical activities, whose goal is to provide better/simpler explanations of observed phenomena. However, because pseudofluids, by their very nature, demand testing, they supplant neither observations nor experiments. Instead they define additional opportunities and challenges for these well-established scientific methodologies.

Such challenges and opportunities primarily manifest themselves as tests, which are categorized into two types: (i) tests that attempt to justify the method a priori and (ii) tests of hypotheses that are derived from the method. LES is shown to be particularly amenable to both types of tests whether they be implemented using observations or experiments. Moreover, the recent developments in laboratory and remote sensing technologies are shown to provide exciting opportunities for realizing such tests. Last, efforts to better understand LES will have peripheral benefits, both because LES shares common features with, and because LES is increasingly used as a tool to further develop, other types of pseudofluids in the geosciences. For these reasons institutional initiatives to develop symbiotic relationships between observations, experiments, and LES would be timely.

The authors use a 1998 workshop titled “Observations, Experiments, and Large-Eddy Simulation” as a springboard to begin a dialogue on the philosophy of simulation as well as to examine the relationship of large eddy simulation (LES) of geophysical flows to both observations and experiments.

LES is shown to be perhaps the simplest representative of a broad class of activity in the geosciences, wherein the aggregated properties of fluids are solved for using approximate, or conjectural equation sets. To distinguish this type of activity from direct fluid simulation, the terms pseudofluid and pseudofluid simulation are introduced. Both direct and pseudofluid simulation introduce methodological changes into the science as they propose to provide synthetic, yet controlled, descriptions of phenomena that can then be used to help shape ideas regarding the behavior of real fluids. In this sense they differ from more traditional theoretical activities, whose goal is to provide better/simpler explanations of observed phenomena. However, because pseudofluids, by their very nature, demand testing, they supplant neither observations nor experiments. Instead they define additional opportunities and challenges for these well-established scientific methodologies.

Such challenges and opportunities primarily manifest themselves as tests, which are categorized into two types: (i) tests that attempt to justify the method a priori and (ii) tests of hypotheses that are derived from the method. LES is shown to be particularly amenable to both types of tests whether they be implemented using observations or experiments. Moreover, the recent developments in laboratory and remote sensing technologies are shown to provide exciting opportunities for realizing such tests. Last, efforts to better understand LES will have peripheral benefits, both because LES shares common features with, and because LES is increasingly used as a tool to further develop, other types of pseudofluids in the geosciences. For these reasons institutional initiatives to develop symbiotic relationships between observations, experiments, and LES would be timely.

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## Abstract

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## Abstract

The problems and advantages of the bolometric method of measuring surface temperature from an airplane are discussed. It is shown that the airborne bolometer measures a weighted area-mean temperature which is a function of the surface temperature distribution and emissivity. For the employed wavelength of radiation (in the atmospheric “window”), the effect of atmospheric absorptivity is negligible under ordinary conditions for altitudes of 300 m or less, but can be an important consideration for flight levels above 300 m. From a series of flights over Southwestern Wisconsin it is concluded that the diurnal variation of surface temperature is greatest in flat farmland and sandy field areas, where a maximum difference of 29C occurred. Hilly woods and fields showed the smallest diurnal variation, with a maximum of 14C. The maximum standard deviation occurred in flat farmland area, with a value of 6C. A swampy area had a maximum value of 2C for a standard deviation.

## Abstract

The problems and advantages of the bolometric method of measuring surface temperature from an airplane are discussed. It is shown that the airborne bolometer measures a weighted area-mean temperature which is a function of the surface temperature distribution and emissivity. For the employed wavelength of radiation (in the atmospheric “window”), the effect of atmospheric absorptivity is negligible under ordinary conditions for altitudes of 300 m or less, but can be an important consideration for flight levels above 300 m. From a series of flights over Southwestern Wisconsin it is concluded that the diurnal variation of surface temperature is greatest in flat farmland and sandy field areas, where a maximum difference of 29C occurred. Hilly woods and fields showed the smallest diurnal variation, with a maximum of 14C. The maximum standard deviation occurred in flat farmland area, with a value of 6C. A swampy area had a maximum value of 2C for a standard deviation.

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## Abstract

This paper considers the accuracy of divergence estimates obtained from aircraft measurements of the horizontal velocity field and points out an error that appears in these estimates that has heretofore not been addressed. A procedure for eliminating this error is presented. The divergence and vorticity are estimated from the coefficients of a least squares fit to a wind field obtained from the Second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) circular flight legs. These estimates are compared with estimates from numerical models and satellites and with airplane estimates based on tracer budgets and the temporal changes in cloud-top height. The estimates are consistent with expectations and estimates using other methods, albeit somewhat high. Furthermore, significant differences occur among the cases, likely due to the large differences in the techniques. The results indicate that the wind field technique is a viable approach for estimating mesoscale divergence if the wind measurements are accurate. The largest source of wind field systematic error may be the result of flow distortion effects on the air velocity measurement and limitations of in-flight calibrations. Because of flow distortion, the only way the current systems can be calibrated is by flight maneuvers, which assume a steady-state homogeneous nonturbulent atmosphere. Analysis of the errors in this technique suggests that wind field measurements with minimal systematic errors should provide estimates of divergence with much greater accuracy than is now possible with other existing methods.

## Abstract

This paper considers the accuracy of divergence estimates obtained from aircraft measurements of the horizontal velocity field and points out an error that appears in these estimates that has heretofore not been addressed. A procedure for eliminating this error is presented. The divergence and vorticity are estimated from the coefficients of a least squares fit to a wind field obtained from the Second Dynamics and Chemistry of Marine Stratocumulus (DYCOMS-II) circular flight legs. These estimates are compared with estimates from numerical models and satellites and with airplane estimates based on tracer budgets and the temporal changes in cloud-top height. The estimates are consistent with expectations and estimates using other methods, albeit somewhat high. Furthermore, significant differences occur among the cases, likely due to the large differences in the techniques. The results indicate that the wind field technique is a viable approach for estimating mesoscale divergence if the wind measurements are accurate. The largest source of wind field systematic error may be the result of flow distortion effects on the air velocity measurement and limitations of in-flight calibrations. Because of flow distortion, the only way the current systems can be calibrated is by flight maneuvers, which assume a steady-state homogeneous nonturbulent atmosphere. Analysis of the errors in this technique suggests that wind field measurements with minimal systematic errors should provide estimates of divergence with much greater accuracy than is now possible with other existing methods.