A practical tropospheric scatter model using the parabolic equation

Hitney, H. V.

doi:10.1109/8.237621

Cited by 30 publications

(24 citation statements)

References 8 publications

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“…By 120 km, the levels computed with the 2-D refractivity field from LES are approximately 37 dB above the levels computed with only the mean profile. In addition, at ranges from 120 to 150 km the levels are 7-10 dB above the -50 dB level computed by Rogers [1996] using a standard atmosphere and the troposcatter model of Hitney [1993]. It is apparent that at 0.263 GHz, refractivity fluctuations at the capping inversion significantly affect EM intensity levels in a geometric shadow zone.…”

Section: Parabolic Equation Calculations For Em Propagation Through Rmentioning

confidence: 82%

Electromagnetic wave propagation through simulated atmospheric refractivity fields

Gilbert¹,

Xiao²,

Khanna³

et al. 1999

Radio Science

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Abstract. Large-eddy simulation (LES) provides three-dimensional, time-dependent fields of turbulent refractivity in the atmospheric boundary layer on spatial scales down to a few tens of meters. These fields are directly applicable to the computation of electromagnetic (EM) wave propagation in the megahertz range but not in the gigahertz range. We present an approximate technique for extending LES refractivity fields to the smaller scales needed for calculating EM propagation at gigahertz frequencies. We demonstrate the technique by computing refractivity fields through 128 3 LES, extending them to smaller scales in two dimensions, and using them in a parabolic equation EM propagation model. At 0.263 GHz the very small scale structure in the extended fields has a negligible effect on the predicted EM levels. At 2 GHz, however, it increases the predicted levels by 15-25 dB. We relate these results to the refractivity structure sampled by EM waves at 0.263 and 2 GHz. We also show that at long range an EM field calculated through an LES-based refractivity field is generally less coherent and significantly weaker than one computed from a "plywood" (i.e., stratified, range-independent) model of the small-scale refractivity field. We give a physical explanation for the differences in the EM fields computed in these two ways. Finally, although the plywood model gives results that fit the EM levels observed in the recent Variability of Coastal Atmospheric Refractivity (VOCAR) experiment, it is not physically realistic. The instantaneous top of the atmospheric boundary layer is known to be sharp and horizontally varying, and we show that using such a top also yields a fit to the VOCAR data. IntroductionThe research discussed here is an interdisciplinary effort between boundary-layer meteorologists and physicists working in electromagnetic (EM) propagation. The purpose of the collaboration was to use large-eddy simulation (LES) methods and a parabolic equation ( Large-Eddy SimulationTurbulence is characterized by three-dimensional, stochastic motions (eddies) of a wide range of spatial scales. These motions generate corresponding stochastic structure in advected scalars such as refractive index. The largest eddies in the turbulent atmospheric boundary layer scale with the integral scale, which is of the order of the boundary-layer depth zi (-1 km). The smallest eddies scale with the Kolmogorov microscale, which is typically of the order of 1 mm. A direct numerical solution of the governing equations for such a turbulent flow is far beyond the present or expected capabilities of computers. 1413

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Section: Parabolic Equation Calculations For Em Propagation Through Rmentioning

confidence: 82%

Electromagnetic wave propagation through simulated atmospheric refractivity fields

Gilbert¹,

Xiao²,

Khanna³

et al. 1999

Radio Science

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“…The differential and are in terms of the spatial frequency components and . The matrix exponential is then expanded in the power series (16) each term of which is allowed to operate on the Fourier basis function . This operation creates a new matrix in which the differential operators are replaced according to , and .…”

Section: Discussionmentioning

confidence: 99%

“…A class of numerical path integral propagation methods, often described as parabolic wave equation methods, has become increasingly popular primarily due to the Fourier split-step algorithm introduced by Hardin and Tappet [15]. There have been several improvements in this method, including hybrid solutions such as what can be described as the path-integral/radio-physical optics hybrid model for tropospheric propagation recently reported by Hitney [16]. For lower atmosphere propagation, Dockery and Kuttler [17] developed an improved impedance-boundary algorithm.…”

Section: Introductionmentioning

confidence: 99%

A path integral time-domain method for electromagnetic scattering

Nevels

Miller

2000

IEEE Trans. Antennas Propagat.

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A new full wave time-domain formulation for the electromagnetic field is obtained by means of a path integral. The path integral propagator is derived via a state variable approach starting with Maxwell's differential equations in tensor form. A numerical method for evaluating the path integral is presented and numerical dispersion and stability conditions are derived and numerical error is discussed. An absorbing boundary condition is demonstrated for the one-dimensional (1-D) case. It is shown that this time domain method is characterized by the unconditional stability of the path integral equations and by its ability to propagate an electromagnetic wave at the Nyquist limit, two numerical points per wavelength. As a consequence the calculated fields are not subject to numerical dispersion. Other advantages in comparison to presently popular time-domain techniques are that it avoids time interval interleaving and it does not require the methods of linear algebra such as basis function selection or matrix methods.

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“…The effects of air turbulence has been studied by applying a perturbation technique in a mode theory [12], or applying a phase-screen method in an SSF model [13,14]. The results of different models have been compared over a series of over-water measurements, in a nearly standard atmosphere [14].…”

Section: Introductionmentioning

confidence: 99%

Ducting and Turbulence Effects on Radio-Wave Propagation in an Atmospheric Boundary Layer

Chou¹,

Kiang²

2014

PIER B

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Abstract-The split-step Fourier (SSF) algorithm is applied to simulate the propagation of radio waves in an atmospheric duct. The refractive-index fluctuation in the ducts is assumed to follow a twodimensional Kolmogorov power spectrum, which is derived from its three-dimensional counterpart via the Wiener-Khinchin theorem. The measured profiles of temperature, humidity and wind speed in the Gulf area on April 28, 1996, are used to derive the average refractive index and the scaling parameters in order to estimate the outer scale and the structure constant of turbulence in the atmospheric boundary layer (ABL). Simulation results show significant turbulence effects above sea in daytime, under stable conditions, which are attributed to the presence of atmospheric ducts. Weak turbulence effects are observed over lands in daytime, under unstable conditions, in which the high surface temperature prevents the formation of ducts.

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A practical tropospheric scatter model using the parabolic equation

Cited by 30 publications

References 8 publications

Electromagnetic wave propagation through simulated atmospheric refractivity fields

Electromagnetic wave propagation through simulated atmospheric refractivity fields

A path integral time-domain method for electromagnetic scattering

Ducting and Turbulence Effects on Radio-Wave Propagation in an Atmospheric Boundary Layer

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