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  • Author or Editor: R. Atlas x
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R. C. Srivastava and D. Atlas

Abstract

Equations relating the mean of the Doppler spectrum and the distribution of point velocities, and their spectra are derived under the assumptions that: 1) the scatterers follow the air motion faithfully, 2) the reflectivity is constant, and 3) the beam illumination function is separable. It is found that the three-dimensional spectral density function is strongly attenuated at scales small compared to the beam dimensions, and essentially unaffected at scales large compared to the beam dimensions. Relationships between the one-dimensional longitudinal and transverse spectra of the mean velocity and the three-dimensional spectrum of the point velocities are derived. Numerical computations with a model Kolmogorov-Obukhov turbulence spectrum are performed to illustrate the effects of filtering. Energy at scales small compared to the beam dimensions is attenuated. Energy at scales large compared to the beam dimensions is also reduced, in the case of the one-dimensional spectrum, because small scales in the orthogonal directions contributing to the energy are attenuated by the filtering. The energy depleted from the spectrum of the mean velocity appears as an increased variance of the Doppler spectrum. The ratio of the total energy under the measured spectrum to that under the spectrum of the point velocities is computed as a function of beam dimensions. An equivalent rectangular filter approximation is proposed for computing the one-dimensional spectra. Analytical results are obtained for the longitudinal spectrum and are shown to be in excellent agreement with the numerical results for the actual filter. The use of a spherical volume equal to that of the actual radar pulse volume is shown to be invalid.

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David Atlas, Kenneth R. Hardy, and Keikichi Naito

Abstract

A general analysis is made of the turbulent refractivity spectrum in and beyond the limiting microscale and a relation derived for its scattering reflectivity in either the back or bistatic directions. Radar reflectivity is computed as a function of wavelength for regions of CAT. The results are compared to the minimum detectable reflectivity of airborne radars having optimum state of the art characteristics at each wavelength. It is shown that the best radars now feasible can barely detect the most reflective CAT at 10 n mi (i.e., 1 minute warning). A 20-db improvement in sensitivity is required for detection of most CAT, which appears to be just attainable by pre-detection integration. The optimum wavelength to implement is 5–6 cm. The best radar at this wavelength will also detect circus clouds reliably. Whether detecting clouds or chaff a measure of the echo fluctuation (or Doppler) spectrum is required to identify the intensity of CAT. However, in the case of high altitude clear air echoes, there is an indication that the reflectivity in excess of some minimum threshold value is a sign of some degree of mechanical turbulence. It is also demonstrated that a ground-based forward-scatter link holds great promise for reliable CAT detection. A tentative quantitative classification of CAT severity is also proposed.

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E. Stratmann, D. Atlas, J. H. Richter, and D. R. Jensen

Abstract

A method of calibrating a fixed vertically pointing radar is presented. The technique involves the firing of B-B shot of known radar cross section through the beam while making successive trajectory corrections until the absolute maximum signal is attained. The results agree closely with an independent calibration of antenna gain. The approach is particularly suited to an FM-CW radar with high range resolution because the pellets reach heights well in excess of the minimum range and errors in range are negligible. Corrections are presented for the reduction in maximum two-way gain resulting from intersecting beams whose full gain is attained only at the point of intersection. It is also shown that Probert-Jones’ k 2 factor is significantly smaller for this system, and possibly for others, than the generally accepted value of unity. The method can be readily extended to any sufficiently sensitive pulsed radar by using small elevation angles and direct measurements of range rather than those obtained from the echoes.

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David Atlas, R. C. Srivastava, and P. W. Sloss

Abstract

Other investigators have discussed the effects of wind and reflectivity gradients across the radar beam on Doppler measurements, but have either estimated their magnitude from a simple approximation or set them aside as negligible. This paper deals with the component of the shear vector along the beam. Exact solutions and simple approximations for both the mean and variance of the Doppler spectrum are derived for two types of reflectivity gradients combined with a linear velocity, gradient. In the case of an exponential reflectivity, gradient it is found that the “effective” beam (i.e., the reflectivity-weighed two-way illumination pattern) remains Gaussian with identical beamwidth to the real beam, but its mean is shifted to an angle ϕm on the high-reflectivity side of the actual beam. With a linear velocity profile in the ϕ direction, the approximate solution shows that the mean Doppler velocity, is then shifted to the scatterer velocity found at ϕm. This approximation is shown to be valid for most physically realizable conditions. Moreover, the spectra variance is found to be essentially independent of the reflectivity gradient and Lhermitte's simple approximation is also generally valid. Analogous results are obtained for a reflectivity profile varying as exp(cR 2ϕ2) where R is range. The effects of reflectivity gradients on the beam-averaged echo power are also discussed.

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L. P. Riishøjgaard, R. Atlas, and G. D. Emmitt

Abstract

Through the use of observation operators, modern data assimilation systems have the capability to ingest observations of quantities that are not themselves model variables but are mathematically related to those variables. An example of this is the so-called line-of-sight (LOS) winds that a spaceborne Doppler wind lidar (DWL) instrument would provide. The model or data assimilation system ideally would need information about both components of the horizontal wind vectors, whereas the observations in this case would provide only the projection of the wind vector onto a given direction. The estimated or analyzed value is then calculated essentially as a weighted average of the observation itself and the model-simulated value of the observed quantity. To assess the expected impact of a DWL, it is important to examine the extent to which a meteorological analysis can be constrained by the LOS winds. The answer to this question depends on the fundamental character of the atmospheric flow fields that are analyzed, but, just as important, it also depends on the real and assumed error covariance characteristics of these fields. A single-level wind analysis system designed to explore these issues has been built at the NASA Data Assimilation Office. In this system, simulated wind observations can be evaluated in terms of their impact on the analysis quality under various assumptions about their spatial distribution and error characteristics and about the error covariance of the background fields. The basic design of the system and experimental results obtained with it are presented. The experiments were designed to illustrate how such a system may be used in the instrument concept definition phase.

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