Tropospheric Ducting Research Articles

Lee Wave Vertical Structure Monitoring Using Height–Time Analysis of VHF ST Radar Vertical Velocity Data

Abstract The strong lee wave event of intensive observation period 3 (14–15 October 1990) of the Pyrenean experiment was studied using a single VHF stratospheric–tropospheric radar installed 35 km downstream from the Pyrenean chain axis. This instrument obtained time series of the air vertical velocity with a time resolution of 4 min 50 s for altitudes ranging from 2250 to 15000 m mean sea level with a 750-m step. Maximum amplitudes of 5–6 m s−1 were measured between 3750 and 5250 m. Temporal variability of the vertical velocity was observed showing that the wave can be nonstationary at timescales on the order of 5–10 min. A classic signal processing technique using the calculation of height–time cross-correlation coefficient in a 2-h moving window was applied to the radar time series and allowed the wave vertical structure to be monitored with a time resolution of 2 h. The lee wave was found to be trapped in a tropospheric duct having an upper limit of 8000 m. The observed wave activity was found to be w...

Sea echo in tropospheric ducting environments

Path loss formulas for sea surface backscatter are developed for horizontally stratified tropospheric ducting environments. First‐order Bragg backscatter results coupled with ray and waveguide formalism serve as the basis for the development. Two features of composite model formalism, namely shadowing and tilting of the surface normal in the plane of incidence, are included in the development. Though developed for hh polarization, conventional composite model modifications for vertical polarization and depolarization can be incorporated into the echo models. Comparisons are made with previously generated parabolic equation results and with empirical model results generated by Engineers Refractive Effects Prediction System. These comparisons are for a frequency of 9.6 GHz for the standard atmosphere and for 14‐ and 28‐m evaporation ducts. Results apply to wind speeds of 10, 20, 30, and 40 knots (≈ 5, 10, 15, and 20 m/s).

Hybrid ray-mode parametrization of high frequency propagation in an open waveguide with inhomogeneous transverse refractive index: formulation and application to a bilinear surface duct

The authors discuss a general complex spectral approach to representing high-frequency source-excited fields in open guiding environments characterized by a continuously varying refractive index in the cross section transverse to the propagation direction. The authors use problem parameters that are motivated by electromagnetic wave propagation in the Earth's atmosphere, in particular, a tropospheric surface duct adjacent to the Earth's surface. The main objective is the development of an observable-based algorithm that self-consistently incorporates various wave objects that synthesize the high-frequency propagation process in a numerically efficient and physically incisive manner. The authors concentrate on ray fields and mode fields, either individually or, most generally, in a rigorous self-consistent hybrid combination. Explicit solutions are generated for a bilinear refractive index profile that generates a leaky surface duct. For numerical results see ibid., vol.39, no.6, p.789-97 (1991). >

Modelling tropospheric ducting effects on VHF/UHF propagation

The application of the parabolic equation method to range-independent and range-dependent tropospheric propagation modelling problems is demonstrated. The parabolic equation is an approximation to the Helmholtz wave equation which allows progressive calculation of the propagated electromagnetic field as solution is stepped out in range. The solution method described is derived from a technique developed by R.H. Hardin and F.D. Tappert (1973) for application to underwater acoustics problems. This split step Fourier solution involves the discretization of the field with respect to height and the use of the fast Fourier transform at successive range points. The solution is stable, with errors being dependent on wavenumber, range step size, and the gradients of refractive index with respect to height and range. Advantages of this method over other methods used to evaluate the effects of ducting layers on tropospheric propagation are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A Structured Review of Propagation Conditions in Tropospheric Ducts

Different mathematical models suggested for prediction of duct propagation have been critically examined and the problems associated with them have been discussed in this paper. It was found that finite difference method is most suitable to define the complexity of the tropospheric medium poses to radiowave propagation in ducting environment where as other methods suffer from certain limitations.

Analysis of wideband signal propagation in a three layer tropospheric medium

Abstract The propagation of wideband signals through a tropospheric ducting medium is examined analytically. A three layer troposphere on a flat earth model is employed. By considering only the guided modes a channel model is derived for the ducting medium. The performance of a phase shift keying (PSK) system is analysed in detail. The dependence of the bit error probability on propagation characteristics is examined.

Attenuation rates of coastal radar signals at 25 MHz

The attenuation rate of the ground wave signal with range is a factor limiting the performance of coastal radars. We show that observed attenuation rates are less than theoretically predicted rates at 25 MHz. This result, contrary to earlier findings at lower frequencies, suggests the onset of tropospheric ducting above 20 MHz. The attenuation rates for various sea states and distances are tabulated to allow estimates of system performance near 25 MHz.

Propagation of vertically and horizontally polarized waves excited by distributions of electric and magnetic sources in irregular stratified spheroidal structures of finite conductivity – generalized field transforms

Transform pairs for the electromagnetic fields in radially stratified spherical structures are derived. These field transforms are used to convert Maxwell's equations into generalized telegraphists' equations for the scalar wave amplitudes. Arbitrary distributions of electric and magnetic sources are considered and the full-wave expansions account for both vertically and horizontally polarized waves. The analysis in this paper also provides the basis for the complete expansion of the electromagnetic fields in irregular spheroidal structures (bodies of revolution) in which the medium is varying as a function of the radial distance and the latitude. This work can be applied to propagation in irregular ionospheric and tropospheric ducts.

Scattering and depolarization of electromagnetic waves in irregular stratified spheroidal structures of finite conductivity – full wave analysis

Scattering and depolarization of electromagnetic waves in irregular stratified, spheroidal structures (bodies of revolution) are investigated. Using complete expansions for the electromagnetic fields, Maxwell's equations are converted into sets of first order coupled differential equations for the forward and backward wave amplitudes. To obtain these generalized telegraphists' equations, exact boundary conditions are imposed at each of the interfaces between the irregular layers of the structure and Green's theorems are used to avoid term-by-term differentiation of the complete expansions. The electromagnetic parameters of the medium are assumed to vary as functions of the radial distance and the latitude. Excitations by arbitrary distributions of electric and magnetic sources are considered. Thus, this work can be applied to propagation in irregular ionospheric and tropospheric ducts. The solutions are shown to satisfy duality and reciprocity relationships in electromagnetic theory.

Duct propagation modelling for the Integrated-Refractive-Effects Prediction System (IREPS)

This paper reviews IREPS and some of its major products, and follows with a description of a recent effort to improve IREPS signal-prediction capabilities in tropospheric ducting environments. The IREPS products discussed are the altitude-versus-range coverage display, the path-loss-versus-range display, and a new historical propagation-conditions summary display derived from a computer-based refractivity climatology. In the GHz range elevated tropospheric layers are multimode systems, and practical beyond-the-horizon field calculations for system applications such as IREPS require simplified procedures. These simplified procedures could involve approximations directed towards speeding up waveguide calculations, or could take the form of replacing waveguide methods by ray methods or by a hybrid mixture of waveguide and ray concepts. Involved in each of these alternatives, and within the context of the modified refractivity formalism, is the need for calculating plane-wave reflection coefficients or their equivalents for layered media. The modelling effort discussed in this paper deals with the feasibility of using asymptotic forms of the plane-wave reflection coefficients for the purpose of waveguide analysis for a trilinear ducting environment.

High-frequency propagation in an elevated tropospheric duct

High-frequency propagation in an elevated tropospheric duct above the earth is analyzed conventionally by normal mode summation, which may be inefficient and often of questionable accuracy because of the large number of modes required. Ray-optical methods, which have been employed, are likewise subject to limitations. The present study explores a new method that combines a judiciously chosen mixture of ray-optical and normal mode fields plus a remainder field that is usually small. The modes may be guided along the concave side of the duct boundary or between this boundary and the earth's surface. By retaining the advantages of both the modal and ray formulations, the hybrid scheme generally requires far fewer rays and modes than the number of modes in a conventional normal mode representation. The hybrid method is applied here to the Green's function problem for a two-dimensional model of the duct formed by a refractive index discontinuity above a perfectly conducting earth. Field values for various locations of source and observation points are computed from the normal mode formulation, which is used as a reference solution, and from the hybrid formulation. The features of these alternative computational methods are discussed in detail and reveal the advantages of the hybrid scheme. Physical interpretation of the hybrid ray-mode field is emphasized throughout and grants new insight into various wave processes.

A model to calculate em fields in tropospheric duct environments at frequencies through SHF

Free‐space field levels are common in a tropospheric duct environment even at distances well beyond the horizon, when the frequency of propagation is above the minimum trapping frequency of the duct. Thus the likelihood of experiencing such a field enhancement is greater at higher propagation frequencies as long as molecular absorption does not become appreciable. A formulation of the wave‐guide duct problem is described which facilitates numerical solution without encountering the numerical difficulties for higher frequencies reported by previous investigators. Field predictions are shown to compare favorably with measurements for 2.201‐GHz propagation in an elevated duct environment.

Conversion of radiation modes to trapped modes due to lateral inhomogeneity of a simple elevated layer

It often happens that tropospheric ducts produced by elevated layers have a modal system in the microwave range consisting of many virtually lossless modes. These weakly attenuated modes have their energy localized about the layer and are insignificantly excited by sources far removed from the layer where the modal height gains are characteristically evanescent. Despite such an unfavorable geometry for direct excitation of these essentially loss‐free modes, they may be indirectly excited within the line of sight region by mode conversion processes associated with lateral inhomogeneity of the layer. In this paper an approximate theory is developed for the mode conversion produced within the line of sight region by large‐scale lateral inhomogeneity of an idealized, vertically homogeneous layer. The theory is applied to a 3‐GHz case study with the following results: (1) lateral inhomogeneity associated with layers of low elevation is more effective for converting to lossless modes than is lateral inhomogeneity associated with layers of high elevation; and (2) lateral inhomogeneity near the horizon is more effective than lateral inhomogeneity near the transmitter for converting to lossless modes.

大気中のインフラソニック波の研究

This paper presents a study of infrasonic waves generated by the explosions of the volcano Sakura-jima, and detected by the microphone array in Kariya, at a distance of about 710km. The geometric ray analyses using the rawinsonde and rocketsonde data show that these infrasonic waves are channeled mainly in the tropospheric duct, formed by the strong westerly wind in the upper troposphere. The propagation in the stratospheric duct which is also significant in winter season, is less frequent owing to the occasional destruction of the winter westerlies by the stratospheric Aleutian anticyclone over Japan.The infrasonic signals may provide a tool to monitor the upper stratospheric flow, if combined with the temperature data from satellite observations.

Roots of the modal equation for em wave propagation in a tropospheric duct

The solution of the modal equation for electromagnetic wave propagation in a tropospheric duct, having a trilinear refractivity profile, shows the existence of two sets of roots in the complex propagation plane. One of these is of the whispering gallery type with very low attenuation and the other is of the waveguide variety with relatively high attenuation. When the contrast in refractive index is small, the lower‐order waveguide modes have an attenuation comparable with the attenuation of the whispering gallery modes. A large contrast in refractive index causes the whispering gallery modes to dominate (surface or elevated ducts). Several examples of the altitude charts for the modal equation for propagation at 200 MHz through a medium having various contrasts in the refractive index give some physical insight into these two classes of modes.

Excitation of elevated tropospheric duct by electromagnetic field of a groundbased source scattered at sound wave

Excitation of elevated tropospheric duct by electromagnetic field of a groundbased source scattered at sound wave

Propagation in a tropospheric duct with a single-step discontinuity in the refractive index in the direction of propagation

A Green’s function approach is used to derive an expression for the field inside a laterally inhomogeneous duct. The laterally inhomogeneous duct is assumed to have a single step, and convergence criteria for the step size and number of modes are discussed.

Influence of refractive index fluctuations on the attenuation of the field in a tropospheric duct

Influence of refractive index fluctuations on the attenuation of the field in a tropospheric duct

Roots of the modal equation for em wave propagation in a tropospheric duct

The solution of the modal equation for electromagnetic wave propagation in a tropospheric duct, having a trilinear refractivity profile, shows the existence of two sets of roots in the complex propagation plane. One of these is of the Whispering Gallery type with very low attenuation and the other is of the creeping wave variety with relatively high attenuation. When the contrast in refractive index is small (the so-called linear atmosphere) the creeping wave modes dominate. A large contrast in refractive index causes the Whispering Gallery modes to dominate (surface or elevated ducts). Several examples of the altitude charts for the modal equation for propagation at 200 MHz through a medium having various constrasts in the refractive index give some physical insight into these two classes of modes. In addition, asymptotic solutions for the Whispering Gallery Modes are derived and used as initial choices in Newton’s method for the solution of the modal equation.

Coupled mode analysis for a nonuniform tropospheric wave guide

We employ a two‐dimensional cylindrical model to analyze the normal modes in a laterally nonuniform tropospheric duct. The utilization of the impedance boundary condition at the earth's surface permits us to use a complete field representation in terms of discrete modes only. These modes are chosen to be locally orthogonal so that a tapered‐type nonuniformity can be handled with a systematic accounting of the mode conversion. Explicit formulas are given for the coupling coefficients. It is shown that the general coupled mode analysis reduces to the appropriate form when dealing with an abrupt but small lateral change of the refractive index structure. This step model had been treated previously using a nonrigorous mode matching procedure that neglected reflected waves at the outset.