Oblique Ionograms Research Articles

Model study of the effect of the main ionospheric trough on oblique HF radiowave propagation

The purpose of this paper is to study the effect of the main ionospheric trough location on the form of oblique sounding ionograms on the Murmansk-St. Petersburg subauroral radio path. Using a mathematical model of the high-latitude ionosphere, we have calculated four different distributions of electron density along the radio path. One of the distributions has been obtained when the trough is absent, and the remaining three distributions contain troughs of approximately identical depth and width but located at different distances from the ends of the radio path. Using the program of two-dimensional ray tracing, we numerically synthesized oblique-incidence ionograms for each of the four obtained distributions of electron density. The calculations have shown that the location of the main ionospheric trough affects considerably the shape of oblique-incidence ionograms.

Simulation of off‐great circle HF propagation effects due to the presence of patches and arcs of enhanced electron density within the polar cap ionosphere

Observations over recent years have established that large‐scale electron density structures are a common feature of the polar cap F region ionosphere. These structures take the form of convecting patches and arcs of enhanced electron density which form tilted reflection surfaces for HF radiowaves, allowing off‐great circle propagation paths to be established. Numerical ray tracing has been employed to simulate the effects of these structures on the ray paths of the radiowaves. The simulations have reproduced the precise character of experimental observations of the direction of arrival over a propagation path within the polar cap and of oblique ionograms obtained over the same path.

Oblique ionogram features associated with off-great circle HF propagation at high and sub-auroral latitudes

Oblique ionograms received over northerly paths are often difficult to interpret, with many features not being of the form observed on the more familiar mid-latitude soundings. In particular, the ionograms contain unusual traces at frequencies close to and above the conventional or basic maximum usable frequency, i.e. above the junction frequency of the high and low angle modes. A series of experiments have been undertaken over a period of several years to investigate off-great-circle propagation mechanisms over high latitude and sub-auroral oval paths. In addition to measurements of the signal direction of arrival, oblique ionograms were also recorded over several of the paths. By these means, the characteristic ionogram signatures associated with off-great-circle propagation effects arising due to the presence of convecting patches of enhanced ionisation or sun-aligned arcs within the polar cap ionosphere, or to the presence of steep gradients to the side of the path within the mid-latitude trough region, have been identified.

Application of radio tomographic imaging to HF oblique incidence ray tracing

Radio tomography is a technique for generating images of the spatial structure of ionospheric electron density over a wide area. This paper assesses the potential use of radio tomography in HF oblique propagation and ray tracing applications. Synthetic ionograms produced by ray tracing through tomographic images and ionospheric models have been compared with experimental oblique ionograms from six paths lying close to the image plane in the United Kingdom. In particular, study has been made of the effects of various types of input information used to constrain the vertical electron density structure in the tomographic reconstructions. It was found that use of a fine height resolution (5 km) and incorporation of information from one vertical ionosonde in the reconstruction process makes significant improvements to the overall reliability of the tomographic image. As expected, E layer propagation is better defined using a climatological model than by tomography. However, in comparison with three ionospheric models, use of tomographic images can significantly reduce the RMS error in the determination of the F2 layer maximum usable frequency.

Validation of electron density profiles derived from oblique ionograms over the United Kingdom

Inversion algorithms are available to derive the vertical electron density profile at the midpoint of an oblique sounder path. The techniques open up the possibility of monitoring the ionosphere at otherwise inaccessible locations, such as over sea or inhospitable terrain. A new method of monitoring the ionosphere based on radio tomography can be used to create two‐dimensional images of electron density. The results in this paper compare midpoint profiles derived from oblique ionograms with corresponding profiles obtained from tomographic images of electron density and from a vertical ionospheric sounder. The comparisons illustrate the oblique sounder inversion technique and its inherent limitations. The results provide useful information on the complementary nature of the separate ionospheric measurement techniques and have implications for the use of these measurements as inputs to real‐time ionospheric models.

Implicit polynomials, orthogonal distance regression, and the closest point on a curve

Implicit polynomials (i.e., multinomials) have a number of properties that make them attractive for modeling curves and surfaces in computer vision. The paper considers the problem of finding the best fitting implicit polynomial (or algebraic curve) to a collection of points in the plane using an orthogonal distance metric. Approximate methods for orthogonal distance regression have been shown by others to be prone to the problem of cusps in the solution and this is confirmed here. Consequently, this work focuses on exact methods for orthogonal distance regression. The most difficult and costly part of exact methods is computing the closest point on the algebraic curve to an arbitrary point in the plane. The paper considers three methods for achieving this in detail. The first is the standard Newton's method, the second is based on resultants which are making a resurgence in computer graphics, and the third is a novel technique based on successive circular approximations to the curve. It is shown that Newton's method is the quickest, but that it can fail sometimes even with a good initial guess. The successive circular approximation algorithm is not as fast, but is robust. The resultant method is the slowest of the three, but does not require an initial guess. The driving application of this work was the fitting of implicit quartics in two variables to thinned oblique ionogram traces.

Analysis of data‐driven parametric models of the vertical ionospheric profile for use in oblique propagation studies

This paper compares parameterization techniques used for modeling the vertical profile of the ionosphere. In particular, comparisons of three‐layer parameterizations driven by ionosonde data are performed. Quasi‐parabolic, Chapman, and polynomial vertical profile models of the ionosphere are investigated. Optimization techniques applied at varying stages of the sensor output, ranging from direct inversion from the digital ionogram image to fitting to true height output for the estimation of parameters, are described. A Kalman‐based filter is optionally used to track and filter the parameters. The performance of the various methods in producing the parameterized profile is analyzed through the comparison of predicted versus measured values of the F2 O‐mode maximum observable frequency (MOF) on a 1250‐km midlatitude oblique path. As a further benchmark, the monthly median model, FIRIC, is also used to generate oblique ionograms. It is found that three‐layer parameterized models perform well and can increase prediction accuracy over the median model, with the ability to reduce the rms error in MOF estimation from 2.38 MHz to 0.83 MHz.

Mid-point electron density profiles from oblique ionograms

A computationally efficient technique for the inversion of oblique ionograms into mid-point electron density profiles is described. The profile is given as the sum of quasi-parabolic functions suitable for ray tracing. The CPU time for a 486 desk top computer is 30 s.

Arrival of Ionospheric Troughs and Oblique Spread-F in the Wake of Large-Scale Travelling Ionospheric Disturbances During the Intense Auroral Storms of August 22 and 23, 1990.

A modem digital ionosonde (Digisonde 256) recording the amplitude, angle-of-arrival, Doppler shift, and polarisation of MF and HF (1-10 MHz) echoes from the ionosphere was operated at the mid-latitude station of Beveridge (geographic 37.5°S, 144.9°E), located 40 km north of Melbourne, Australia, during the intense auroral storms of August 22 and 23, 1990. We changed the digisonde antenna design to permit the alternate recording of near-vertical angle-of-arrival ionograms, and southward-looking Doppler ionograms sensitive to oblique echoes at great ranges. This experimental design permitted us to track the equatorward migration of radio aurora associated with the poleward wall of the mid-latitude trough, the small-scale “slant-F” irregularities and medium-scale travelling ionospheric disturbances (TIDs) detected within the trough, and distinctive oblique spread-F patches located in proximity to the equatorward edge of the auroral zone; all arriving in response to large auroral electrojet activity. These observations graphically illustrate the processes by which the magnetosphere dumps energy into the high-latitude ionosphere when the geomagnetic index is high (ΣKp = 46 on August 23), leading to the generation of large-scale TIDs which precede the arrival of, and possibly contribute to the production of, the aforementioned menagerie of high mid-latitude irregularities. We illustrate the five forms (broadly speaking) of spread-F observed and offer plausible explanations for their cause. We corroborate our interpretation of oblique ionogram measurements by using DMSP/F8 and F9 precipitating particles satellite data, magnetometer measurements at Canberra (Δ = 45.9°S) (geomagnetic latitudes hereafter) and at Macquarie Is. (64.4°S) in the auroral zone, and routine ionograms (i.e., limited sensitivity to oblique echoes, and no angle-of-arrival or Doppler shift information) recorded at other mid-latitude stations. For example, during the night of August 23, radio aurora were observed to move equatorwards towards Beveridge (48.0°S) where a severe spread-F event occurred due to TIDs generated in the region defined by Macquarie Island north to Hobart (53.7°) (i.e., the source location probably changed in latitude as the aurora moved equatorward). The TIDs observed at Beveridge were also observed at Canberra (where mild spread-F was observed), and as far north as Norfolk Island (36.0°S) where they had little impact on the ionosphere.

Inversion of oblique ionograms including the Earth's magnetic field

A technique for determining ionospheric electron distribution from oblique ionograms is presented, based on the inversion method of Reilly and Kolesar ( Radio Sci. 24, 575, 1989). It makes use of an equivalent operating frequency and an additional term to account for magnetoionic effects associated with the Earth's magnetic field. The technique is demonstrated by application to synthetic oblique ionograms, and to an experimentally obtained ionogram.

Analytic calculation of the ordinary (O) and extraordinary (X) mode nose frequencies on oblique ionograms

On oblique ionograms, the maximum frequencies of the ordinary and extraordinary modes are referred to as nose frequencies. The difference in the nose frequencies depends on parameters such as the length of the propagation circuit and the direction of propagation. In this paper, the difference in nose frequencies is studied using the frequency scaling technique of Bennett et at. [(1991) Appl. Comput. Electromagn. Soc. Jl 6, 192]. For long paths, an explicit formula is obtained which gives the difference approximately as a function of the local magnetic dip and azimuth of propagation at the ray mid point. For shorter paths, it is shown how analytic ray tracing can be used to determine the difference.

On the spectral width of chirpsounder signals

A formula has been derived that relates the slope of the group time delay curve of an oblique ionogram to the spectral width of a sampled chirpsounder signal over the same path. In comparisons with experimental data recorded during smooth ionospheric conditions, the formula shows good agreement with reality when it is possible to resolve the O- from the X-wave. Results of numerical simulations of the chirpsounder signal are also discussed. These are based on an analytic expression derived in this paper for the dechirped receiver signal, with the addition of various sampling windows.

Synthesis of oblique ionograms from vertical ionograms using quasi-parabolic segment models of the ionosphere

This paper describes a method of synthesizing oblique ionograms from vertical ionograms based on representing the ionosphere by multiple quasi-parabolic segments (QPS). The advantage of this approach is that it allows analytical solutions to be obtained for several ray parameters when the Earth's magnetic field is neglected and the ionosphere is spherically stratified. The no-field results are representative of the ordinary mode. In addition, results for the extraordinary mode can be obtained by introducing a perturbation to the effective frequency and modifying the no-field results. The method is illustrated by comparing synthesized oblique ionograms with observed ionograms and with results obtained for the ordinary mode using the classical method.

Upgrades for efficient three‐dimensional ionospheric ray tracing: Investigation of HF near vertical incidence sky wave effects

An earlier, three‐dimensional ray‐tracing program has been upgraded to include magnetic field effects, variable step sizes, improved propagation loss computation, and efficient homing and focusing computation algorithms. A combination of fourth‐order Runge‐Kutta and Adams methods, with error control and extension to variable step size, has been included. The program is applied to an investigation of high‐frequency near vertical incidence sky wave (NVIS) effects. Model simulations of oblique ionograms are found to be consistent with experiment. Implications for NVIS geolocation are discussed.

A method for real height analysis of oblique ionograms

A method is presented for the conversion of an HF oblique ionogram to an ionospheric density true height profile, within the usual approximations of spherical symmetry and no magnetic field. It is a lamination method for inversion of the equations for group path delay and sounder range, which are treated on equal footing, similarly to an earlier method by Rao. A reentrant procedure has been added to alleviate the problem of valley ambiguity. Use of the method and its clear improvement over other methods, which invoke further approximations, are demonstrated by calculations on oblique ionograms from known, model daytime profiles. Future directions are indicated.

Ionospheric true height profiles from oblique ionograms

An improved technique for the reduction of an HF oblique ionogram to an ionospheric true height profile is presented. It is based on a more accurate generalization of the Breit‐Tuve theorem to curved earth and ionosphere geometries. The improvement over previous methods is demonstrated by means of calculations on known cases.

A method for inverting oblique sounding data in the ionosphere

We have developed in this paper a method of inverting backscatter leading edge ionograms and fixed distance oblique ionograms to obtain ionization profiles. The problem of ionogram inversion is first formulated in such a way that the Backus‐Gilbert technique can be applied. This inversion technique starts by assuming an initial profile based on available knowledge. Oblique group paths are computed by using this initial profile and are compared with the experimental data. The discrepancy in group path is used as a basis for improving the profile and thus an iterative procedure is developed. This iteration is continued until an optimum solution is found. As is well known, when ionograms are given at discrete frequencies there may exist an infinite number of profiles that will yield the observed group path data. Among this infinite number of solutions there is an optimum one in the sense that its fractional departure from the initially assumed profile is a minimum in terms of value at boundaries and in terms of the profile curvature. The method is then applied to the special vertical incidence case and reasonably fast convergence is obtained. This success demonstrates the promise of this method in inverting oblique sounding data.

Analysis of discrete oblique ionogram traces in sweep‐frequency sky‐wave high resolution backscatter

A method is presented for the analysis of discrete oblique ionogram traces observed in high resolution sweep‐frequency sky‐wave backscatter technique to obtain quasiparabolic ionospheric layer parameters. The method employs three data points on the oblique ionogram with one of the data points being the point of coincidence of the oblique ionogram trace with the leading edge of the backscatter. The method is applied to the analysis of an experimental oblique ionogram trace and the validity of the results is examined.

A note on the analysis of oblique ionograms

A previously reported method of analysis of oblique ionograms is reformulated to enable an exact ray-calculation analysis of the oblique ionograms using only the assumptions of spherically symmetric ionosphere concentric with the Earth and neglect of the Earth's magnetic field.

Ionospheric structure from oblique‐backscatter soundings

Oblique ionograms are made monostatically by using an HF sounder to record the delay times of echoes from known ground targets as a function of operating frequency. Cooperative sources, such as repeaters, or distinctive terrain features, such as cities, serve effectively as known ground targets. An analytic method is developed to transform oblique‐backscatter ionograms into the h'‐f curves recorded by conventional ionosondes at vertical incidence, from which ionospheric electron‐density profiles can be derived. The validity of the transformation technique is demonstrated by comparing h'‐f data recorded simultaneously at oblique incidence and at vertical incidence near the midpoint of the oblique path.