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Donald H. Lenschow

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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Bjorn Stevens and Donald H. Lenschow

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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Leif Kristensen and Donald H. Lenschow

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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Donald H. Lenschow and Leif Kristensen

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Donald H. Lenschow and Leif Kristensen

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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Leif Kristensen and Donald H. Lenschow

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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Donald H. Lenschow and Leif Kristensen

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 103 counts s−1 for measuring flux throughout the convective boundary layer.

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Yasushi Mitsuta, Nobutaka Monji, and Donald H. Lenschow

Abstract

During the field observation period of the Air Mass Transformation Experiment in 1975 (AMTEX ‘75), one of the boundary-layer research flights of the National Center for Atmospheric Research (NCAR) Electra aircraft was conducted in the vicinity of Tarama Island. A 50-m onshore observation tower was located on the southwestern coast of Tarama Island, and a 12-m offshore observation tower on the northern reef. We compare and discuss mean profiles of dry- and wet-bulb temperature, wind speed and direction, and turbulent fluxes of latent and sensible heat and momentum observed by these three observing platforms. We found that the 50.m onshore tower, which was about 3.5 km downwind of the shoreline, and the airplane flight legs over the island at 140 and 160 m height were in the island-modified air. This resulted in large differences between ocean and island measured fluxes, smaller differences in the variances and almost no differences in the means. Thus, we found that for the conditions of this experiment it is feasible to use the island-measured values of mean quantities as characteristic of the ocean. but the fluxes and variances are characteristic of the island.

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Donald H. Lenschow and Warren B. Johnson Jr.

Abstract

During three observational periods in the spring and summer of 1964, an experimental program was conducted over a forested area in northeastern Wisconsin in which airplane measurements in the planetary boundary layer were obtained in conjunction with simultaneous pilot-balloon observations of mean wind profiles up to a height of 2000 m and supporting surface-layer measurements. Sufficient data were obtained to permit the investigation of several features of boundary-layer structure. A strong dependence of horizontal and vertical velocity variances upon stability is found, and velocity spectra for stable and unstable conditions are quite different. A clear distinction between the eddy sizes responsible for momentum transport in near-neutral and unstable situations is shown by the co-spectral densities of horizontal and vertical velocities. Heat-flux profiles derived from the combined data are qualitatively similar to those found by previous investigators and to Ball's theory, in that the heat flux decreases steadily with height and tends to become negative in the upper portion of the boundary layer. However, the eddy-energy budget fails to show the strong transport of eddy energy to the inversion level that is required by Ball's model, indicating that if such a transport occurs, it must be at wavelengths longer than those measured. An approximate balance of the eddy-energy budget is possible when allowance is made for the bandwidth restrictions on the vertical flux measurements.

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Donald H. Lenschow, Volker Wulfmeyer, and Christoph Senff

Abstract

The authors derive expressions for correcting second- through fourth-order moments of measured variables that are contaminated by random uncorrelated noise. These expressions are then tested by applying them to an artificially produced time series as well as measurements from two upward-pointing ground-based lidar systems:a differential absorption lidar that measures water vapor density and a high-resolution Doppler lidar that measures vertical wind velocity. Both sets of measurements were obtained in a convective boundary layer, and contain sufficient noise to significantly affect measurements of second- and fourth-order moments (as well as integral scale and skewness) throughout the boundary layer. It is shown that the corrections derived here can be used to obtain useful measurements of these moments from instruments such as lidars, which are inherently noisy. The authors also obtain information on higher-order moments of the noise as well as the correlation between noise and atmospheric measurements.

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