Volume 51, Issue 7 p. 1131-1141
Research Article
Free Access

Effect of time-dependent 3-D electron density gradients on high angle of incidence HF radiowave propagation

K. A. Zawdie

Corresponding Author

K. A. Zawdie

Space Science Division, Naval Research Laboratory, Washington, District of Columbia, USA

Correspondence to: K. A. Zawdie,

[email protected]

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D. P. Drob

D. P. Drob

Space Science Division, Naval Research Laboratory, Washington, District of Columbia, USA

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J. D. Huba

J. D. Huba

Plasma Physics Division, Naval Research Laboratory, Washington, District of Columbia, USA

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C. Coker

C. Coker

Space Science Division, Naval Research Laboratory, Washington, District of Columbia, USA

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First published: 07 July 2016
Citations: 10


One of the challenges for the utilization of HF radiowaves in practical applications is to understand how the signals propagate in time- and range-dependent multipath environments. For typical quiescent ionospheric conditions it is often reasonably straightforward to interpret received HF signals. For disturbed ionospheric conditions, however, such as in the presence of large tilts, irregularities, and medium-scale traveling ionospheric disturbances (MSTIDs), data interpretation and utilization often becomes challenging. This paper presents a theoretical HF propagation modeling study that exploits the capabilities of a first principles, mesoscale resolution ionosphere code, SAMI3 (Sami3 is Another Model of the Ionosphere) and a new implementation of the 3-D ray trace equations, MoJo-15 (Modernized Jones Code) in order to examine the relationship between various HF propagation observables and MSTID characteristics. This paper demonstrates the implications of MSTIDS on high angle of incidence HF propagation during typical low-latitude, postsunset ionospheric conditions and examines the spatiotemporal evolution of multiple propagation paths that may connect a given source and receiver.

Key Points

  • Three-dimensional ionospheric gradients and ray tracing are necessary to model the effects of MSTIDs
  • Three propagation modes are a common feature during MSTID propagation
  • The raypath of the propagation mode changes significantly during HF propagation

1 Introduction

Traveling ionospheric disturbances (TIDs) are common in the ionosphere and have been detected for many decades. The typical signature for a TID is a propagating density perturbation near the F peak height that is organized into bands at an angle to the magnetic equator. They can be classified according to their velocity, wavelength, and wave period (or frequency). Medium-scale TIDs (MSTIDs) typically have a period of 10–60 min, and the wavelength is on the order of 100 km [Garcia et al., 2000; Shiokawa et al., 2003].

A particular type of MSTID is an electrodynamic MSTID, which is similar to a typical MSTID, but is associated with changes in the electric field [Crowley and Rodrigues, 2012]. The E × B drifts from the electric field cause drifts of the plasma, which form into bands of perturbed densities that travel at speeds of approximately 100 m/s. In the Northern Hemisphere, the waves propagate southwest toward the equator with the wavefronts typically aligned from northwest to southeast. These types of perturbations typically occur late at night or after midnight at low and midlatitude. Since they are electrified, and the conductivity along the magnetic field line is very large, they often have a signature in the conjugate hemisphere.

The electrodynamic MSTID is believed to be generated by the Perkins instability, which was outlined by Perkins [1973]. He hypothesized that there must be a force balance between the gravitational effects and electric fields in the night time F region and that if the balance was upset by a north-south component of the electric field, then unstable electric field modes would develop. Recent modeling studies, however, indicate that the growth rate for the Perkins instability is slow, so while it is clearly a contributing influence, it cannot fully account for the generation of electrodynamic MSTIDs in the ionosphere [Duly et al., 2014]. It has been suggested that gravity waves are responsible for triggering the instability and increasing the growth rate above the nominal Perkins instability growth rate [Crowley and Rodrigues, 2012].

In section 2 we outline the methodology of this study, specifically the Sami3 is Another Model of the Ionosphere/equatorial spread F (SAMI3/ESF) and MoJo models and their configuration options. In section 3 the calculation results are presented. To keep the paper manageable, direct comparison to observations is left for future work. In section 6, we provide a theoretical discussion and summary of the conclusions. It should be noted that multiple TIDs and/or gravity wave-induced ionospheric gradients in the E and F regions may result in extreme multipath environments resulting from the presence of many waves, but it is not considered in this paper in order to better focus specifically on the temporal evolution of TID-induced ionospheric perturbations.

2 Previous Work

Some of the earliest work in identifying and understanding TIDs was presented by Munro and Heisler in a series of papers published in the 1950s [Munro, 1950, 1953; Munro and Heisler, 1956a, 1956b]. The first paper by Munro described a method for examining the disturbances in the ionosphere and identified the speed, direction, and seasonality of TIDs. His second paper identified and categorized different types of reflections resulting from the passage of TIDs and related the reflections to different types of curved surfaces in the ionosphere [Munro, 1953]. Munro's joint work with Heisler in 1956 connected the cusp-type anomalies in ionograms with horizontal gradients in the ionosphere and demonstrated that the separation of the O and X mode provides useful information in determining the qualities of TIDs [Munro and Heisler, 1956a, 1956b].

Subsequent understanding of the influence of TIDs on HF propagation was obtained by examination of the ground backscatter observed by over-the-horizon radars (OTHR). Georges and Stephenson [1969] presented some of the first evidence that OTHR observables could provide information to better understand TID phenomena. This early study, however, neglected the effects of the magnetic field. The idea was later revisited by Bristow and Greenwald [1995], who established that TID parameters could be estimated from the backscatter signature using 2-D ray tracing. Soon after, Stocker et al. [1999] demonstrated another possible method for using the backscatter signature to determine properties of TIDs, but the method neglected the effects of the magnetic field.

Another early advance in understanding the influence of TIDs on HF radio wave propagation came from Lobb and Titheridge [1977] , who demonstrated that the “U-shaped” features that sometimes overlap the main trace of ionograms are the result of horizontal gradients in the ionosphere resulting from MSTIDs. These horizontal gradients from MSTIDs result in multipath propagation (i.e., more than one raypath connects the receiver and the transmitter at a given frequency), which leads to multiple traces on the ionogram. While they were able to successfully calculate multipathing that occurs during the passage of an MSTID, their model was 2-D, and the effect of the magnetic field was neglected. In addition, they assumed a very simple Gaussian-perturbed parabolic layer for the TID perturbation, such that gradients in the background ionosphere were neglected and the TID did not evolve self-consistently with the background ionosphere.

Recently, Cervera and Harris [2014] examined the influence of TIDs on quasi-vertical ionograms (QVIs) utilizing a detailed 3-D ionospheric ray trace code, which also includes the effects of the magnetic field. Importantly, however, Cervera and Harris [2014] demonstrated that a 3-D ray trace calculation is actually required to accurately explain typical TID disturbance features observed in QVIs. The Cervera and Harris [2014] study utilized the Hooke model [Hooke, 1968] to represent the TID perturbations, which assumes that atmospheric gravity waves are the perturbing mechanism. The background ionospheric gradients were neglected, and the time evolution of the ionosphere was solely determined by the Hooke model.

3 Methodology

3.1 SAMI3/ESF Mesoscale Ionospheric Specifications

In this study the mesocale version of SAMI3 (SAMI3/ESF) is utilized to generate the time-dependent ionosphere specifications, including the TID perturbation. This mesoscale version of SAMI3 was developed to study the physics of the formation of equatorial spread F (ESF) [e.g., Huba et al., 2008], as well as the perturbing effects of large-scale gravity waves propagating into the ionosphere from below [Huba et al., 2015]. SAMI3/ESF solves the three-dimensional, time-dependent equations mass and momentum equations for the evolution of seven major ionospheric species (H+, He+, O+, urn:x-wiley:rds:media:rds20414:rds20414-math-0001, N+, urn:x-wiley:rds:media:rds20414:rds20414-math-0002, and NO+). Radiative recombination and 21 chemical reactions are also included. The plasma is simulated along the entire dipole magnetic field line. The code also solves the electron and ion temperature equations for three ion species: H+, He+, and O+. Quasi-neutrality is assumed, so the electron density is determined by summing the densities of each ion species.

The neutral composition and temperature are specified by the empirical NRLMSISE00 model [Picone et al., 2002]. The neutral winds are assumed to be constant for the purposes of this study, but the horizontal wind model (HWM14) [Drob et al., 2015] can be used to account for climatologically varying average tidal background winds. The grid is a nonorthogonal, nonuniform, fixed grid that is periodic in longitude and simulates a 4° longitudinal wedge of the ionosphere. To simplify the SAMI3/ESF ionospheric calculations, a nontilted dipole magnetic field is assumed as described in Huba et al. [2000], but for the actual HF ray tracing calculations a full but simple 3-D magnetic field model based on observations and lower order spherical harmonic expansion is utilized.

The type of TID that we focus on in this work is the electrodynamic TID, which is described in section 1. This particular type of TID is of interest as it may be able to trigger equatorial spread F bubbles in the ionosphere [Krall et al., 2011], and it differs from many other TID simulations in that the TID is on the bottomside of the F region peak rather than at the peak itself. To generate a realistic electrodynamic TID in SAMI3/ESF, a traveling sinusoidal in situ electric field is superimposed on the computed E × B drift as described by Krall et al. [2011]. The in situ wave-driven electric field is defined in terms of the vertical (p) and horizontal (h) directions as

Here x and y are Cartesian coordinates corresponding to the longitudinal and latitudinal directions, respectively. The wave numbers kx and ky are defined as urn:x-wiley:rds:media:rds20414:rds20414-math-0004 and urn:x-wiley:rds:media:rds20414:rds20414-math-0005. The magnitude of the wave number vector, k, is defined as k = 2π/λ, where λ is the wavelength. The propagation angle, θTID, is defined as the angle between k and the magnetic equator. A propagation angle of 0° is equivalent to a bearing of −90°, which implies westward propagation parallel to the equator and wave crests that are aligned with the magnetic field. A propagation angle of 90° (or bearing of −180°) implies southward propagation perpendicular to the equator. Following Krall et al. [2011], we set the maximum E × B drift amplitude (UTID) to 50 m/s, the wavelength to 250 km, the period to 1 h, and the propagation direction to southwestward. The electric field is imposed over the altitude region ranging from 200 to 400 km, from 4 to 16° in latitude, and from −1.5° to 1.5 ° in longitude.

The initial conditions for the SAMI3/ESF calculations are provided by output from SAMI2 (the two-dimensional version of SAMI3) [Huba et al., 2000]; in this case for day of year 80 (equinox) with F10.7 = F10.7a = 150 and Ap = 4. The longitudinal extent of the SAMI3/ESF simulation is 4°, centered on 0°, and extends to ±35° in latitude. The SAMI3/ESF simulations consider the ionosphere's evolution, starting at 19:30 local time (LT), which is after the lifting of the F layer by the prereversal enhancement; and ends at 20:30 LT. Snapshots of the time evolving 3-D electron density field are saved at 1 min intervals for the HF propagation calculations.

Three different SAMI3/ESF simulations were run that only differed in the MSTID parameters. The first of these is the control that does not have an MSTID perturbation. The second simulation includes an MSTID with a bearing of −110° (θTID = 20°) and the third a bearing of −140° (θTID = 50°). In each of these simulations the typical peak density ranges from about 2.9 e6/cm3 to 3.1 e6/cm3, corresponding to a critical frequency range of about 15–16 MHz. The peak density occurs around 450 km altitude; thus, the imposed MSTID, which is imposed between 200 and 400 km altitude, is only on the bottomside of the ionosphere and does not reach the peak density. The vertical electron density profiles of all three simulations, as shown in Figure 1, are qualitatively very similar. This is because the MSTID primarily creates horizontal gradients rather than simply modifying the electron density profiles. As will be shown, the horizontal gradients in electron density resulting from the presence of MSTIDs are responsible for significant changes in the HF propagation path from a given source to a given receiver.

Details are in the caption following the image
Electron density as a function of altitude at the location of the transmitter at four different times during the simulation. (left) The background case, (middle) the MSTID with −110° bearing, and (right) the MSTID with −140° bearing.

Figure 2 shows the (log10) electron density at 290 km altitude as a function of latitude and longitude for four different times during the simulation. The background case (Figure 2, left column) has a gradient in the latitudinal direction due to the typical variations in the ionospheric background but it is smooth and (unsurprisingly) much less pronounced than the horizontal gradients introduced by the MSTID simulations. The −110° bearing case (Figure 2, middle column) has gradients in both directions, but the largest horizontal gradients are in the longitudinal direction. In the −140° bearing case (Figure 2, right column) the large horizontal gradients are at an angle. As time progresses, the MSTID in both cases progresses toward the southwest. As expected, in both of the MSTID cases, the minimum (maximum) of the density crests are lower (higher) than in the background case, and the horizontal gradients are at a much smaller scale than the background case.

Details are in the caption following the image
Electron density as a function of latitude and longitude (in degrees) at 290 km altitude at four different times during the simulation. (left column) The background case, (middle column) the MSTID with −110° bearing, and (right column) the MSTID with −140° bearing.

3.2 MoJo HF Ray Trace Calculations

MoJo-15 (Modernized Jones code) is a new implementation of the original computational algorithm of Jones and Stephenson [1975] for detailed 3-D HF ray tracing. MoJo was rewritten from the ground up in order to capitalize on modern programming practices and computational architectures. MoJo provides a ray trace engine written in FORTRAN-90 with the main function interfaces directly callable from high-level interactive scripting languages (Python and MATLAB) for calculation automation.

For this paper MoJo-15 integrates the 3-D Haselgrove HF ray trace equations [Haselgrove and Haselgrove, 1960] in spherical 3-D coordinates, assuming the Appleton-Hartree dispersion relation with collision and the Earth's magnetic field using a fourth-order Runge-Kutta scheme. The gradients of the electron density and magnetic field are calculated in all three directions for the Jacobian of the ray trace equations at every step of the numerical integration. Although MoJo-15 can also do this for the electron collision frequency, for the calculations herein only an altitude dependent electron collision frequency model is used for simplicity.

One major feature of MoJo-15 (not included in the original Jones and Stephenson code) is the capability to quickly calculate exact modes to machine precision via the nonlinear Levenberg-Marquardt [Levenberg, 1944; Marquardt, 1963] algorithm, given a reasonable first guess of azimuth and elevation for a fixed frequency and propagation mode (O or X). If only one mode exists connecting the source, and receiver MoJo-15 will always find this ray. In very complicated multipath environments it is a nontrivial problem to quickly identify and locate every possible mode, particularly in time-evolving environments. The simplest brute-force approach is to integrate a very dense distribution of rays over an extended domain of azimuths and elevations and identify any clusters of rays that land within some tolerance distance (∼1 km), from the receiver. In a more elegant approach, Cervera and Harris [2014] integrate a tessellated triangular mesh of rays and identify those triangles with landing points that encompass a given receiver. Once these multiple clusters are determined, a representative first guess can be provided to the MoJo homing algorithm to find the exact eigenvalues for the mode.

Here a novel technique to elucidate how MSTIDs warp all possible propagation paths from a given transmitter to the set of all possible ground receiver locations is presented. In this technique, a series of rays is traced with initial elevation angles ranging from −35° to +35° from zenith in the north-south plane to create a fan, which could also be described as a two-dimensional beam. The angles could be chosen to reflect the performance of a particular system but, in this case, are chosen to cover the area of interest. Next, a series of Euler rotations is applied to the ray fan in order to tilt the fan at various angles (beta angles) away from the zenith; first in the north-south plane and after a 90° azimuthal rotation in the east-west direction. Three fan configurations are shown in Figure 3. The purple fans are pointed directly overhead (0° beta angle). The blue fan is defined similarly to the other north-south purple fan, but it is tilted off zenith by −15°, so that it illuminates an area of the ground farther west in longitude. Note that the red dot indicates the position of the transmitter, and the lines at 0 km altitude illustrate the landing points of the ray fan.

Details are in the caption following the image
Three example ray fans that are used to generate the grid mesh pattern on the ground. The two purple ray fans are the north-south and east-west aligned ray fans with a beta angle of 0°. The blue fan has a beta angle of −15°. The thick lines at 0 km altitude indicate the landing position of the ray fan on the ground as a function of latitude and longitude (in degrees).

A spherical distribution of rays over regular azimuth and elevation intervals maps to series of concentric circles and radial lines, which can be potentially offset from the transmitter due to ionospheric tilts and magnetic inclinations. The series of tilted linear 2-D ray fans maps to a nearly orthogonal rectangular grid of landing points in the region surrounding the transmitter, assuming that no significant ionospheric gradients are present.

An example of this mapping is shown in Figure 4 (left), for the SAMI3/ESF ionospheric control case at 20:10 UT, where a hypothetical transmitter broadcasting at 3.125 MHz with O mode polarization is located at 10.5°N, 0.0°E. Each blue line represents the landing points of the series of rays from a given fan, where each fan is defined by the tilt with respect to zenith. In the control case, with only global-scale horizontal gradients, this results in a nearly orthogonal rectangular pattern. The landing location of the vertically incident east-west aligned ray fan is indicated by the horizontal purple line. It is located ∼0.5° southward of the transmitter, due to the magnetic inclination angle and the global-scale ionospheric gradients (see Figure 2) in the control case. The vertical purple line indicates the landing location for the vertically aligned north-south ray fan. Again, the landing locations are slightly offset from the transmitter location due a slight magnetic declination in the ionospheric control case. It should be noted that at ranges much farther away from the transmitter (i.e., for very low transmission elevations) these lines eventually diverge as a result of the Earth curvature).

Details are in the caption following the image
(left) The landing points of a series of ray fans launched from a transmitter at 10.5° latitude, 0.0° longitude (denoted by the red dot). The purple lines illustrate the landing points of the two vertical ray fans. (middle and right) The 3.125 MHz O mode paths between the same transmitter and a receiver at 9.5° latitude and 0° longitude (blue dot) at 20:10 LT for the background case.

It should be apparent from this figure that for a hypothetical receiver located at 9.5°N, 0.0°E (the blue dot), there is only one mode for 3.125 MHz O mode propagation. Figure 4 (middle and right) shows the path of the single mode as a function of latitude and altitude (middle) and as a function of longitude and altitude (right). The grey contours indicate lines of constant electron density. In Figure 4 (middle) there is a clear tilt in the latitude direction due to the global-scale gradient. In Figure 4 (right) there no horizontal gradients in the longitude direction, but the mode is necessarily offset from the vertical due the effects of the magnetic field (a slight declination) which is accounted for in MoJo-15.

4 Simulation Results

4.1 Two-dimensional Versus 3-D

For each of the three time-dependent 3-D SAMI3/ESF simulations described in section 3, MoJo-15 is used to calculate the time evolution of high angle of incidence HF propagation during the passage of an MSTID. Before describing the main results regarding the time evolution of modes, the effect of the presence of an MSTID the east-west aligned vertical 2-D ray fan is considered. The propagation of this ray fan through the different modeled ionospheres at 20:00 LT is shown in Figure 5. In all three cases, the rays do not deviate from initial latitude-altitude plane until they reach the reflection point. Thus, in the longitude-latitude plots (Figure 5, bottom row), only the lines from the reflected portion of the rays are distinguishable. Figure 5 (left column) shows the control case. As expected there is no significant ray bending or focusing, in this case, and the rays reflect uniformly at a height of ∼300 km altitude.

Details are in the caption following the image
Raypaths from a single transmitter (3.125 MHz, O mode) as a function of (top row) longitude-altitude and (bottom row) longitude-latitude for each of the three simulations. (left column) The background case, (middle column) the case with a −110° bearing MSTID, and (right column) the case with −140° bearing MSTID.

Figure 5 (middle column) shows the results for the MSTID propagating with a bearing of −110°. Here the effect of the MSTID-induced horizontal gradients are apparent. First, the rays reflect at different altitudes. Second, the longitude versus altitude panel shows focusing around 0°. This is often interpreted as a caustic, which is expected for horizontal gradients. The latitude and longitudes of the landing points shown in Figure 5 (bottom row), however, clearly illustrates that this focusing is a mirage. While a large number of rays land on the ground near 0°, they are dispersed in latitude, with offsets ranging from 9.5° to 10.5°N, or distances approaching nearly 100 km.

Figure 5 (right column) shows the case for the MSTID propagating at a bearing of −140°. The effects of horizontal gradients are also clearly noticeable. The rays launched westward reflect at a lower altitude than those launched eastward. Again, the rays deviate significantly from the original 2-D plane of propagation.

Both of these examples highlight a limitation of 2-D ray trace calculations, which ignore the magnetic field and out of plane deviations caused by horizontal gradients. For examples of 2-D ray tracing, see Coleman [1997] and Coleman [1998]. In both of the MSTID cases the rays deviate significantly from the initial plane; thus, the group path delay would be underestimated with a 2-D model. In addition, signal amplitudes would be overestimated in the regions of caustics for the −110° MSTID propagation case. These examples also highlight a potential limitation for accurately modeling HF sky wave propagation in the presence of 3-D ionospheric gradients using 2-D parabolic and full wave methods, which calculate the variation of the full electromagnetic field of a radio wave in space [Barnes, 1997]. Specifically, 2-D full wave and parabolic codes that ignore the loss of wave energy to out of plane propagation may erroneously overpredict field strengths in these regions.

4.2 The Time Evolution of the Modes

The section describes the main results of the time evolution of the reflected high angle of incidence HF propagation during the passage of an MSTID. Figure 6 (left column) shows the effect of the −140° bearing MSTID's passage on the mapping of the reflected 3.125 MHz O mode propagation paths at four different times.

Details are in the caption following the image
The landing points of a series of ray fans launched from a transmitter at (left column) 10.5° latitude, 0.0° longitude, see text for details. ( middle and right columns) The corresponding 3.125 MHz O mode propagation modes at different times for the −140° bearing MSTID case.

In this case, the MSTID-induced gradients in the ionosphere results in a strikingly different mesh pattern. Instead of a rectilinear grid, the mesh is warped and folds in on itself. In locations where the mesh is folded over, a triad of modes exists as explained by Davies and Baker [1966] and Chum et al. [2010]. The time series of maps shown in Figure 6 (left column) reveals the prominant spatial aspects, as well as distinct time evolution of the MSTID-induced gradients on HF propagation. Figure 6 (middle column) shows the mode paths as a function of latitude and altitude connecting the hypothetical transmitter and receiver at the four different times. Figure 6 (right column) shows the same modes over longitude and altitude. As before the grey lines indicate the lines of constant electron density.

Figure 6 (first row) corresponds to a simulation time of 20:00 LT. Although there are some horizontal gradients in the ionosphere associated with the approaching MSTID, there is still only one mode connecting the transmitter and receiver. Note that in the far left panel, the region of multipathing has not yet reached the location of the receiver. As compared to control case shown in Figure 4, the location of the mode refection point is shifted ∼0.5 westward and ∼0.5 southward, almost 70 km. This is almost as large as the wavelength of the specified MSTID. As noted by Chum et al. [2010] this has important repercussions for the accuracy of HF Doppler sounding techniques to measure MSTID propagation velocity, wave period, and wavelength parameters, which rely upon the assumption that HF Doppler sounding point occurs at midpoint between the transmitter and receiver.

Not only does this location vary in space, but it also varies in time. The second row corresponds to 20:10 LT. Now the MSTID has moved further to the southwest (see also Figure 2). Now the hypothetical receiver is located in the region where multipath propagation occurs. Figure 6 (middle and right columns) shows the calculated raypaths for the three distinct modes. The latitude and longitude of each mode reflection point varies significantly.

Figure 6 (third row) shows the configuration at 20:20 LT. There are still three distinct modes. At this time, however, two of them reflect at a significantly lower latitude (∼100 km), and they have a greater longitudinal offset (∼50 km) than the other modes. From Figure 6 (left column), the multipath region has nearly passed the receiver, so that it is expected that soon these two modes will merge then promptly disappear.

Figure 6 (fourth row) shows the configuration at 20:30 LT. As expected, there is no more multipathing. The single ray remaining is quite different from the initial ray at 20:00 LT. This ray, however, is fairly similar to the single eigenvalue that exists in the case of the background simulation. This suggests that the effects of the MSTID have for the most part passed by the receiver at this time.

It is evident that these results are both fully consistent with, and explain the characteristic “S” shape in HF doppler soundings during the passage of a wavelike disturbance, as originally explained in the conceptual hypothesis by Jones (unpublished) as described in Davies and Baker [1966] and also recently revisited by the work of Chum et al. [2010]. Chum also importantly notes the formation of the S trace for a given transmitter to receiver direction depends of the orientation of the MSTID bearing with the great circle path connecting a given transmitter and receiver. For example, if the MSTID bearing is orthogonal to the great circle path connecting the transmitter and receiver, a characteristic S trace of HF doppler with any significant duration is not expected to occur, though a brief instant of multipathing propagation and step in HF doppler should occur.

4.3 The Time Evolution of Observed Group Path Delays

Typically, HF radiowave ionospheric sounding techniques can only measure the observed characteristics of a received signal from which the actual raypath must be inferred given some set of physical assumptions. One such typical observable is group path delay, or virtual height. Figure 7 shows how the virtual height for the hypothetical scenario evolves over time. Again, there is only one observed group path until the formation of the multipath triad occurs, and then after some time the triad disappears. While two of the three paths (one of which is the original) have a virtual height that increases with time, both of these eventually disappear. The new and surviving raypath has a virtual path that decreases with time.

Details are in the caption following the image
The virtual height for each of the modes in the previous figure as a function of time.

The calculations show the changes in virtual height can vary by as much as 40 km over an hour and are clearly associated with the changes in reflection point between the source and receiver. The variations, however, result from deviations of the raypath from the direct line of bearing between the source and receiver, which by simple geometry results in a longer actual propagation path length and group delay, not just a change in the altitude of the reflection point. For HF Doppler sounders deployed to measure ionosphere MSTID characteristics, consideration of the simultaneous measurement of the signal group delays may provide one way to diagnose where the assumptions of the stationarity of the HF Doppler sounding midpoint location breaks down and thus indicate when key MSTID wave parameters are very likely to be spurious [Nickisch et al., 2006].

Also of interest is how the ray changes as a function of frequency. Figure 8 (left) shows an example QVI for the background case. Here there is no multipathing, and the QVI is very smooth. The red indicates O mode, and the blue indicates the X mode. Figure 8 (right) shows an example QVI (O mode trace only) for the −140° bearing MSTID case at the same time. The colors correspond to rays in Figure 6. The trace from the red eigenray is smooth and continuous. It is very similar to the O mode trace in the background case. The traces from the other two eigenmodes differ significantly. We note that similar perturbations in the QVI have been seen in measurements Cervera and Harris [2014].

Details are in the caption following the image
(left) A QVI for the background case at 20:10 LT; in this panel, the red trace indicates the O mode, and the blue trace indicates X mode. (right) The multipathing that occurs for the O mode trace of a QVI in the −140° bearing MSTID case. The colors match the scheme in Figure 6.

5 Discussion and Conclusion

For the first time, a realistic, full physics, time-dependent, mesoscale ionospheric model (SAMI3) simulation of an MSTID has been used in connection with a full physics 3-D HF ray trace code (MoJo-15) to predict the spatiotemporal evolution of high angle of incidence HF ionospheric sounding observables. The advantage to this approach is that horizontal gradients in all directions and time evolution of the perturbation are taken into account. The main results show that these horizontal gradients have a profound effect on the path of the HF rays resulting in out-of-plane propagation that cannot be properly accounted for assuming only 2-D propagation. Accounting for both three-dimensional propagation and three-dimensional ionospheric gradients is necessary to accurately capture the complexity of radiowave propagation through the ionosphere.

Through the mapping of a mesh of tilted and rotated 2-D ray fans the influence of the passage of an MSTID on the mapping of the set of all possible transmission paths to the ground from a given transmitter was shown. The folding of the grid, in the presence of the horizontal gradients, occurs for MSTIDs propagating at all angles. In general, the rays tend to refract both in plane and out of plane along the direction of propagation. The simulations show that three modes are a common feature during an ionospheric disturbance as hypothesized by Jones as described in Davies and Baker [1966] [see also Chum et al., 2010]. This is also consistent with the observations of Munro, who identified multimode propagation characteristics from curved surfaces in the ionosphere [Munro, 1953]. In the future, the arrival angle and group path delay information of propagation paths should also be examined to understand the correlation between the characteristics of HF doppler sound observables and MSTIDs.

Clearly, the actual ionospheric structure can be more complicated as shown by the recent HF doppler traces presented by Chum et al. [2010], where tilts are observed and up to five different propagation paths, each manifesting itself with a different HF doppler trace. For the simple, yet typical MSTID propagation characteristics selected for this study, the HF raypaths through the perturbed ionosphere varied widely as the MSTID propagates over the transmitter. The reflection location varied as much as 100 km during the course of the simulation. Currently, HF doppler systems are being developed and deployed to detect MSTIDs in the ionosphere, but one of the assumptions in the algorithm is that the raypath does not vary significantly [Crowley and Rodrigues, 2012]. This assumption may only be valid for TIDs with a large wavelength (>300–350 km) since the horizontal gradients would not be as steep. Future modeling work to directly simulate the HF doppler should be undertaken, which would provide additional insights into the correlation between HF doppler signatures and the path of the radio waves through the ionosphere. In addition, colocation of 630 nm images [e.g., Garcia et al., 2000] with HF doppler signatures would allow for validation of the length, direction, and wave periods of the MSTIDs. This is particularly important since HF Doppler observations have been used to support the hypothesis of secondary gravity waves propagating in the thermosphere as described in Vadas and Crowley [2010].


The authors acknowledge support from the Chief of Naval Research (CNR) under the NRL 6.1 Base Program. This work is from a dissertation to be submitted to the Graduate School, University of Maryland, by Katherine Zawdie in partial fulfillment of the requirements for the PhD degree in Physics. Data are available upon request from the lead author.