This paper illustrates the importance of understanding and taking into account the presence of various structural features in the polar ionosphere (in particular, patches and arcs of enhanced electron density) when planning and operating HF radio links. These features result in radio waves propagating over paths well displaced from the great circle direction and impact on almost any HF communications system where the signal reflects from the ionosphere within the region poleward of the subauroral trough. The off–great circle mechanisms give rise to propagation at times that are not predicted by current prediction codes and may also suppress propagation at times that are expected. Techniques to account for this type of propagation are therefore required. A ray-tracing model that accurately reproduces many of the direction of arrival features observed in experimental measurements has been developed. Particular attention will be given in this paper to area coverage estimations undertaken by means of the ray-tracing model.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 Extensive HF propagation measurements have been made by the University of Leicester and colleagues at northerly latitudes over a number of years [see, e.g., Warrington et al., 1997; Zaalov et al., 2003; Rogers et al., 1997, 2003; Siddle et al., 2004a, 2004b]. Of particular relevance to this paper, measurements undertaken in the polar cap found that the presence of convecting patches and Sun-aligned arcs of enhanced electron density can lead to signals arriving in directions displaced from the great circle path by up to 100° [Warrington et al., 1997; Zaalov et al., 2003]. Patches are formed in the dayside auroral oval [see, e.g., MacDougall and Jayachandran, 2007] during periods of southward directed Interplanetary Magnetic Field (IMF) (Bz < 0) and the associated high levels of geomagnetic activity and generally convect in an antisunward direction across the polar cap into the nightside auroral oval, whereas arcs occur when geomagnetic activity is low and the IMF is directed northward (Bz > 0) and drift in a duskward direction [Buchau et al., 1983]. It was also found that the signals can arrive at the receiver over a range of directions with, for example, azimuthal standard deviations of up to 35° at frequencies of 2.8, 4.0 and 4.7 MHz being observed on one path from Isfjord, Svalbard to Alert [Warrington, 1998]. Similar measurements have also been undertaken at auroral latitudes [Warrington et al., 2006]. Although initially driven by direction finding interests, the measurements of direction of arrival undertaken in these experiments give insight into the complex propagation mechanisms present at high latitudes.
 Much progress has been made with the development of a ray-tracing model that accurately reproduces many of the direction of arrival features observed in the experimental measurements [Zaalov et al., 2003, 2005]. A major outcome of the ray-tracing simulations is that paths other than those subject to experimental investigation can readily be assessed. Furthermore, the model can used to estimate the geographic area covered by a transmitter and hence enable an improvement in prediction capability over current techniques (e.g., VOACAP [Sweeney et al., 1993]). Although the model is currently being developed, the aim is to provide accurate forecasts of HF propagation conditions suitable for transpolar airline operations. This paper is particularly concerned with modeling within the polar cap.
2. Ionospheric Model
 The simulations make use of a numerical ray tracing code [Jones and Stephenson, 1975] to estimate the raypaths through a model ionosphere. The background ionosphere comprises two Chapman layers, the main parameters of which (critical frequency, critical height, vertical scale height of each layer) are determined from vertical ionospheric soundings. Values based on the International Reference Ionosphere (IRI) [Bilitza, 1990] have also been employed when not considering a specific day. Other models, such as NeQuick [Leitinger et al., 2005], could also be used. The background model is then perturbed to include the various ionospheric features of interest (i.e., patches, arcs, the trough, etc). Note that the perturbations are formed from a number of Gaussian features, thus ensuring that the functions describing the electron density (and hence the refractive index) and its first derivative are continuous as required by the ray tracing code [Jones and Stephenson, 1975].
2.1. Convecting Patches
 Patches of enhanced electron density associated with high geomagnetic activity are modeled as an arbitrary number of Gaussian distributions with approximately equal longitudinal and latitudinal scale. The temporal evolution of the patches relative to the propagation path is simulated by means of a convection flow scheme coupled with the rotation of the Earth beneath the convection pattern, the precise form of which depends upon the components of the IMF. In practice, the shape, size and number of patches in the convection flow area depends upon many geophysical parameters, not only upon the instantaneous values but also upon their history. By using up to four vortices based on the modeled convection flow patterns associated with the various IMF orientations presented by Lockwood , many realistic situations may be simulated. Work by Dandekar  indicated that vertical ionosondes observe 6–8 patches per day at high sunspot activity and 3 per day at low sunspot activity in the polar cap. However, this does not necessarily indicate the total number of patches present in the polar region as some patches may lie outside the field of view of the ionosondes. In the current model, Doppler shifts due to patch motion are not incorporated.
2.2. Sun-Aligned Arcs
 The shape of each Sun-aligned arc is defined within the model by a small number of three-dimensional Gaussian perturbations in electron density of different spatial scales (altitude, longitude and latitude) randomly distributed near to the center of the arc. Several Gaussian perturbations were combined in defining the shape of each modeled arc in order to prevent the shapes of the arcs being too stylized. For all arcs away from close proximity to the dawn or dusk auroral oval, the plasma strands are elongated for several hundreds or thousands of kilometers with a latitudinal scale which is significantly larger than the longitudinal scale. Many such arcs can be included in the simulation with their positions being randomly distributed in an area centered on the geomagnetic pole and bounded by the auroral oval. The magnitude of the electron density perturbation of each of the elements forming the arcs is randomly distributed about a specified average value. Evolution of the structures relative to the propagation path is determined by the rotation of the Earth beneath the arcs and by the movement of the arcs in the dawn-dusk direction. In this paper, for simplicity, the modeled results presented only include patches.
3. Point-to-Point Measurements and Simulations
 Examples of the azimuth deviations produced by the presence of patches are given in Figure 1 for a 4.6 MHz signal transmitted from Qaanaaq and received at Alert in December 2010. The direction of arrival measurements are typical of those received on other days during that month, and also of those made in earlier measurement periods previously reported [e.g., Warrington et al., 1997]. Simulations for the same period are reproduced in Figure 2. While the nature of the simulated variations are reminiscent of the measurements, it is important to note that the number of patches and their positions in reality and in the simulation are not the same, hence the detailed variations are not expected to be in agreement. Comparisons between measurement and simulation (with the data presented in Figures 1 and 2 and many others) do however indicate that the assumed propagation mechanism is appropriate, and that the model can be used as the basis for further development.
4. Area Simulations
 The area coverage to be expected from a transmitter at a given location can be estimated by ray tracing through model ionospheres containing patches and arcs of enhanced ionization. A large number of rays launched in an azimuth/elevation grid from the transmitter are traced through the model ionosphere, and the signal strength at the receiver estimated by determining the ray density in the area around the receive antenna. (ignoring absorption effects and antenna radiation patterns, both of which can be subsequently accounted for by assigning different power levels to each ray depending upon its launch and reception angles at the antennas, and on the path each ray takes through the D region).
 An example outcome of this process is illustrated in Figure 3. Figure 3a shows a modeled electron density distribution at a height of 250 km and a time of 1800 UT (the dayside ionosphere is positioned in Figure 3aaround the bottom right quadrant). Patches of enhanced ionization have been randomly positioned within the model ionosphere, as described previously. The outcome of the ray-tracing process is illustrated inFigures 3b–3d for a signal frequency of 12 MHz for a transmitter located at Cambridge Bay. Figure 3b indicates the ground coverage to be expected for the background ionosphere without patches present. Focusing of the rays at the 1, 2 and 3 hop skip zone ranges is clearly evident. Figure 3c indicates the expected area coverage when the patches are taken into account. It is interesting to note that the presence of the patches severely distorts the background pattern on the ground, that coverage is reduced in places, and that coverage is obtained in areas where it was not present without the presence of the patches. Figure 3d shows the coverage with a different patch distribution.
 In considering the effect of the presence of the patches, it is important to remember that the patch distribution used in the above simulations is only illustrative and that in reality the patches will be distributed differently, and that as time progresses the patches will move in accordance with the prevailing convection cell pattern (a function of the geomagnetic conditions). To estimate the effect of the patches on a statistical basis, a large number of simulations have been undertaken, and the median and decile signal strengths calculated for the same configuration as that of Figure 3. The outcome of this is presented in Figure 4, from which it is evident that coverage is expected over a much greater area when the patches are present. It is interesting to note the good agreement for the one-hop mode with predictions produced by VOACAP (seeFigure 5).
 In addition to area coverage, when a digital communications system is being employed the multipath delay spread and Doppler spread are important parameters as these can form limiting factors in the operation of particular types of modem. The model is capable of producing estimates of the multipath delay spread, in this case from the first and last arrival times of rays arriving in each pixel. Examples corresponding to the scenarios of Figure 3 are presented in Figure 6.
5. Concluding Remarks
 Currently available prediction codes such as ITU-R Recommendation 533 [International Telecommunication Union, 2012] and VOACAP [Lane, 2001] do not include the effects of off–great circle propagation [see Stocker et al., 2007]. VOACAP, for example, defines a number of control points along an assumed great circle path and uses these to define the electron density profiles at the reflection points based on hourly monthly median and decile maps. The simulations presented here indicate that significant improvements may be made by incorporating off–great circle mechanisms into prediction techniques, and this is a major aim of the current work. Integration of additional measured parameters (e.g., patch intensity) from data sources such as ionosondes, GPS TEC measurements, etc is a future development. The model is also capable of estimating parameters of relevance to data communication systems: the current model is capable of estimating the multipath delay spread, and the modeling and incorporation of Doppler spread is anticipated as a future development.
 The work presented here concentrates on estimates of where the rays launched from a transmitter reach the ground, and the associated spread in the times of arrival. Absorption of the signals in the D region plays a critical role in HF propagation. In addition to the normal diurnal variation, ionospheric D region absorption has three components associated with X-ray flux, proton precipitation and auroral electron precipitation. The NOAA DRAP-2 [Sauer and Wilkinson, 2008] product provides an absorption prediction model for two of these three components, but does not take into account electron precipitation. An example of a solar proton event is presented in Figure 7, where for this event there is a good agreement between the prediction of absorption and the observed loss of HF signal. Honary et al.  discuss the need for an auroral absorption model, and collaborative developments in this area will be integrated with the propagation model presented here.
 A new, extensive set of observations of HF propagation in the high-latitude region is about to commence [seeDanskin et al., 2011]. These measurements will allow the predictions obtained from the model to be validated and improvements to the model made.
 The authors would like to thank the EPSRC for supporting the modelling work and later experimental work upon which this paper is based, and the Royal Society for supporting continued collaboration between N. Y. Zaalov and the researchers at the University of Leicester.