A technique for determining key ionospheric parameters from high-frequency (HF) over-the-horizon radar ground scatter data is investigated using two Southern Hemisphere SuperDARN radars and also a Northern Hemisphere SuperDARN radar with reliable elevation angle-of-arrival capability. Ground scatter data are analyzed over a range of frequencies from 8 to 18 MHz to determine the maximum usable frequency and the vertical critical frequency over a wide geographical area within the radar field of view. The technique is shown to be well suited to middle to high latitudes where backscatter echoes from the ground dominate over those from ionospheric scattering targets. However, the technique is shown to break down during the winter months and away from solar maximum. It is shown that the use of reliable elevation angles can greatly enhance such methods allowing discrimination between ground scatter propagating via the E and F regions. It is also shown that contamination from very low velocity ionospheric scatter and ground scatter originating from the back lobe of the radar can be effectively filtered out, with the use of reliable elevation angles. This greatly improves the reliability of the ionospheric data products and allows for a high degree of automation of the process.
Real-time monitoring of ionospheric conditions is of particular importance to high-frequency (HF) radio communications and ionospheric research. Critical users of HF communications include defense, commercial airlines, remote area emergency services, and maritime fleets. Conditions in the ionosphere can vary greatly as space weather conditions change, over short time scales of just a few minutes up to the longer time scales associated with the approximately 11 year solar cycle.
A key ionospheric parameter of interest to HF communicators is the maximum usable frequency (MUF) associated with a particular HF circuit. The MUF is the highest frequency supported by the ionosphere for an oblique propagation circuit between two geographic locations. Closely related to the MUF is the vertical critical frequency of the F2 region, or foF2, which is the maximum frequency reflected by the F region ionosphere at vertical incidence at a particular geographic location. The foF2 parameter is used for the provision of frequency advice to HF communicators, for the determination of the electron density and total electron content of the ionosphere, for modeling the refraction of RF signals, and in the development of realistic ionospheric models [e.g., Anderson et al., 1987; Cander, 2008; Belehaki et al., 2009; Bilitza et al., 2011].
Across the Australasian region, the foF2 parameter is determined in real time by a network of ionosondes. Historical ionospheric maps and propagation models are then used to determine MUFs for particular HF circuits. Geographical coverage of foF2 data is limited by the number of ionosondes operating within a given area. Over many regions of Australia the geographical foF2 coverage is quite sparse and is absent over the oceans, requiring a high degree of interpolation in the use of foF2 data. Due to the spatial variation of ionospheric conditions this can lead to significant errors.
We have implemented a technique developed by Hughes et al.  for determining the ionospheric parameters MUF and foF2 using ground backscatter from the Super Dual Auroral Radar Network (SuperDARN) [Greenwald et al., 1995; Chisham et al., 2007]. In this paper we test the feasibility of this technique for the Tasman International Geospace Environment Radars (TIGER), which form part of the SuperDARN network and cover the middle- to high-latitude subauroral zone to the south of Australia. The TIGER system presently consists of two radars with partially overlapping fields of view: Bruny Island, with geographic coordinates 43.40°S, 147.20°E (54.8°S, 133.2°W geomagnetic) and Unwin, with geographic coordinates 46.51°S, 168.38°E (54.4°S, 106.2°W geomagnetic). We also use data from a SuperDARN radar located in Saskatoon, Canada, to investigate the potential for elevation angle-of-arrival information to improve the accuracy of the MUF and foF2 data products determined using this technique. The Saskatoon radar has geographic coordinates 52.16°N, 106.53°W (60.9°N, 43.8°W geomagnetic).
The Super Dual Auroral Radar Network (SuperDARN) is a global network of high-frequency, coherent scatter radars designed to detect backscatter from plasma density irregularities in the ionosphere and backscatter from the ground propagating via specular reflection in the ionosphere. SuperDARN radars operate in the frequency range 8–20 MHz, employing a linear phased-array of 16 antennas to create a narrow, steerable beam. Most SuperDARN radars also have an auxiliary linear array with fewer antennas, displaced from the main array, which acts as an interferometer for the calculation of the elevation angle of arrival. Elevation angle measurements are critical for determining the propagation modes of received backscatter and the altitude in the ionosphere from which backscatter originated.
The interferometer data obtained from many SuperDARN radars, including the Bruny Island and Unwin radars, are considered unreliable [McDonald et al., 2013]. For this reason, we have investigated in detail the calculation of ionospheric parameters from SuperDARN data in the absence of direct angle-of-arrival measurements. Elevation angle measurements from the Saskatoon SuperDARN radar are considered reliable and their use in the calculation of ionospheric parameters will be discussed in section 3.
The primary data products of the SuperDARN radars are power (signal-to-noise ratio), line-of-sight Doppler velocity, and Doppler spectral width of the received backscatter. These data products are derived using the SuperDARN data analysis software (FITACF), which fits model functions to complex autocorrelation functions (ACF) of time lags generated by a multipulse sequence [Greenwald et al., 1985]. The spectral width parameter is a measure of the spread of velocities within the scattering volume and thus has units of velocity. The Doppler velocity V and spectral width W parameters are used to differentiate ionospheric backscatter from ground backscatter. In this work we use ground backscatter, which we identify as any backscatter for which both |V| and W are less than 50 m s−1 and that also satisfies the SuperDARN ground scatter condition,
where Vmax=30 m s−1 and Wmax=90 m s−1 are empirically derived constants used in the SuperDARN data analysis software. Since SuperDARN radars are designed primarily for observing ionospheric backscatter, algorithms for discriminating between ground scatter and ionospheric scatter tend to focus on minimizing the contamination of ionospheric backscatter with ground scatter, rather than the other way around [e.g., Chisham and Pinnock, 2002; Blanchard et al., 2009; Ribeiro et al., 2011]. Therefore, ground scatter echoes identified using condition (1) are often contaminated with considerable amounts of low-velocity ionospheric scatter. We will return to this later.
1.2 MUF and foF2 Using SuperDARN Radars
The method presented here for determining MUF and foF2 using SuperDARN radars is based on methods developed by Hughes et al.  using five SuperDARN radars located in North America. In our implementation, the Bruny Island and Unwin SuperDARN radars were operated in a “sounding mode” for which complete scans of the field of view (beams 0–15) were performed at a number of well-spaced frequencies in the 8–20 MHz range. A sampling time of 3 s per azimuthal direction was used, which corresponds to a total scan time of 1 min per frequency to sample all 16 azimuthal directions. The range resolution used was 45 km, which is the value used in the most common mode of operation for SuperDARN radars. Backscatter identified as ground scatter is analyzed in time intervals of typically 10–15 min. This sets the temporal resolution of the calculated ionospheric parameters.
Histograms of the average fitted ACF power versus range are generated for each azimuthal direction to determine the skip distance associated with each frequency in the sounding mode. The skip distance is the minimum possible ground range that a signal of a given frequency can achieve following specular reflection by the ionosphere. Peaks in the power versus range profiles correspond to particular propagation modes, with the leading edge of each peak corresponding to the skip distance associated with that mode (see Figures 1a–1e).
A modified Gaussian function of the form,
is fitted to each power profile, where x is the range and A0, x0 and ω are free fitting parameters. The factor S(x) allows for an asymmetric or skewed Gaussian profile, with s a free parameter describing the degree of asymmetry about x0, the center of the distribution. The skip distance is estimated as the point at which the fitted distribution G(x) falls below a specified value on the lower range side of x0. Skip distances determined in this way are shown as vertical lines in Figure 1.
A virtual-height model [e.g., Chisham et al., 2008] is used to convert each skip distance from slant range, the group path of the propagating signal, to ground range, the distance from the radar to the ground scattering location. For each azimuthal direction, a straight line is fitted to plots of frequency versus skip distance which then defines a maximum usable frequency (MUF) for any ground range along that azimuth (Figure 1f).
The MUF values (oblique critical frequencies) are converted to vertical critical frequencies (e.g., foF2) over the field of view of the radar using the relationship,
where fc is the vertical critical frequency, f0 is the oblique critical frequency and Δ0 is the elevation angle of arrival at the radar corresponding to the skip distance, which we shall refer to as the critical angle. In the absence of elevation angle-of-arrival measurements from the radar, the critical angle is determined using a virtual height model, based on the slant range of the critical ray associated with the skip distance.
2 Determining Ionospheric Parameters at Bruny Island and Unwin
We present the results of our implementation of the method described in section 1.2 on the Bruny Island and Unwin radars for the 24 h interval commencing at 12:00 UT on 12 September 2010. During this time the radar sounding mode consisted of five fixed frequencies: 9050, 10,190, 12,190, 14,390, and 16,350 kHz, each transmitted within a nominal 3 kHz channel. Figure 2 is a range-time plot showing ground backscatter obtained with the Bruny Island radar during this time period for azimuthal beam 8, which is the beam closest to the center of the azimuthal field of view. Echoes detected at each frequency are plotted separately and are color coded according to the backscatter power. The solid black lines indicate the day-night terminator. Dawn and dusk occur at approximately 20:30 UT and 07:30 UT respectively.
From an HF communications perspective, we are typically most interested in 1-hop F region (1F) propagation via specular reflection in the ionosphere. This propagation mode accounts for the broad population of ground backscatter from 21:00 to 11:00 UT at 9050 kHz in Figure 2. As the frequency increases, signals undergo less refraction in the ionosphere and so the echoes from the 1F mode are observed at increasingly greater ranges from the radar. At 00:00–07:30 UT, which corresponds to local nighttime, the 1F mode at 9050 kHz and 10,190 kHz is observed at approximately 2500–3000 km in range. No ground scatter echoes were detected from 00:00 to 07:30 UT for frequencies greater than 12 MHz. This indicates that either the ionosphere could not support radio propagation at these frequencies or that the ground backscatter did not follow a suitable path to be detectable by the radar.
In addition to the 1F propagation mode, echoes from several other modes are apparent in Figure 2. Backscatter from meteor plasma trails was detected at ranges up to 450 km at all frequencies, with greater occurrence rates at the lower frequencies. In the afternoon (∼03:00–08:00 UT), 2-hop F region (2F) ground scatter was observed at 9050, 10,190, and 12,190 kHz at approximately double the range of the 1-hop F region scatter for that frequency. The backscatter indicated by the circle at 09:00–12:00 UT for each frequency is low-velocity ionospheric scatter that has nevertheless satisfied the Doppler velocity and spectral width criteria for ground scatter presented in section 1.1. This is a well-known problem with analyzing SuperDARN data [de Larquier et al., 2013] and will be addressed in section 3.1. In contrast to the ground scatter, the range of the low-velocity ionospheric scatter in Figure 2 does not appear to vary significantly with frequency; the decreased refraction through the ionosphere of higher-frequency signals does not contribute significantly to the group path for ionospheric scatter. Ground backscatter from the 1-hop E region (1E) propagation mode is frequently observed by many SuperDARN radars during daylight hours [e.g., Dyson et al., 2003; Milan et al., 1997a]. It is likely that echoes associated with the 1E and 1F modes are observed at similar ranges for the time period shown in Figure 2 and so the 1-hop E region ground scatter has been obscured. The relative ground range of 1E and 1F backscatter returns in power versus range profiles and distinguishing between them is critical to the practicality of extracting ionospheric parameters from SuperDARN data.
2.1 Ground Scatter Power and Skip Distance
We analyze the average ground backscatter power detected at each range gate in 10 min intervals. For the sounding mode described above, this corresponds to two complete scans of the azimuthal field of view for all five frequencies. It is necessary to average the backscatter power over a sufficient number of scans for it to be possible to fit a function to the power versus range profile and hence determine the skip distance.
In each 10 min interval, we generate a power versus range profile for each beam and each frequency. A sample of these power profiles is shown in Figures 1a–1e. To determine skip distances, we use a nonlinear least squares fitting algorithm [Markwardt, 2009] with equation (2) with initial parameter values chosen to achieve convergence over a wide range of conditions. The initial parameters used in this study were A0 equal to twice the maximum power of the raw power versus range profile, x0 equal to the range at which the power maximum occurs, ω = 200 km and s = 0. The skip distance is estimated as the point at which the fitted distribution G(x) falls below 20% of the maximum value, on the lower range side of x0. We also fit a symmetric Gaussian with s = 0 (S(x) = constant) since the asymmetric form of G(x) often fails to converge for the highest frequencies and sparsest data sets. The initial parameters for the fitting of the symmetric Gaussian were slightly different, with A0 equal to the maximum power and ω = 200 km.
The red curves in Figures 1a–1e are the asymmetric Gaussian fits to the data, while the dark blue curves are the symmetric Gaussian fits with s = 0. The skip distance for each profile is indicated by the blue vertical line. If the fitted function for s = 0 has width parameter ω exceeding 500 km, or if the height A0 of the fitted function is less than half the maximum power of the raw data distribution, this indicates a near uniform or very sparse power versus range profile and the fit is rejected. Fits for s ≠ 0 are required to have ω < 400 km and s > 0, which ensures that the tail of the distribution is to the right. Similarly, where the skip distances determined using the Gaussian fits with s ≠ 0 and s = 0 do not closely coincide (to within 300 km in our implementation), both are rejected. It is observed that a symmetric Gaussian function tends to fit the region with the greatest number of echoes while the asymmetric Gaussian function, fitted to the data using a nonlinear least squares fitting algorithm [Markwardt, 2009], fits the region of maximum power.
For many power versus range profiles, multiple peaks are present which correspond to different propagation modes. For example, power peaks corresponding to the 1F and 2F propagation modes are apparent in Figures 1a–1b. To accurately measure the skip distance for a particular propagation mode and frequency, the correct peak corresponding to that propagation mode must be fitted. This is not always straightforward and has been identified in the present study as a significant challenge of the technique. We will return to this in section 2.4.
For each of the 16 azimuthal beam directions we have a number of measured skip distances at different frequencies. We can estimate the MUF over the range of the radar by fitting a line to the skip distance values as a function of frequency. An example of this fitting for azimuthal beam 8 is shown in Figure 1f. Figure 3 shows an example of the calculated MUF for circuits between the radar site and every point within the radar field of view for the Bruny Island (tig) and Unwin (unw) radars.
2.3 F Region Critical Frequency (foF2)
Using elevation angle-of-arrival estimates of the critical ray, the ray that is backscattered by the ground at the skip distance, it is possible to convert our MUF values to foF2 values over the field of view of the radar using equation (3). In this way, we can determine one foF2 value for each available skip distance measurement. The foF2 values are calculated at the ionospheric reflection point, which we assume to be at half the range to the skip distance. foF2 values for the Bruny Island and Unwin radars are shown as filled circles in Figure 3. These values were calculated using a virtual height model to estimate the elevation angle of arrival of the critical ray.
Figure 4 shows the diurnal variation in foF2, averaged over all beams, for the Bruny Island and Unwin radars for the 24 h interval commencing at 12:00 UT on 12 September 2010. Also shown are the foF2 values for the same time interval measured by a digital ionosonde located at Macquarie Island operated by Ionospheric Prediction Service (IPS) Radio and Space Services. The ionosonde is located within the field of view of the Unwin radar and is shown as a diamond in Figure 3. The foF2 values obtained by each radar agree well with the ionosonde data, although differences of up to ∼1 MHz are apparent in some instances.
2.4 Correct Fitting of Peaks
During the daytime, particularly close to local noon, power versus range profiles often show a double-peaked structure close to the skip distance (see Figures 5a and 5d). These two closely spaced peaks are due to ground scatter propagating via the 1E and 1F modes, as indicated by the arrows in Figures 5a and 5d. Also present is a peak due to meteor scatter at ranges below 500 km in Figures 5a, 5b, and 5d. During the summer months, an additional peak may be present when the daytime F1 region forms [Davies, 1990; Dyson et al., 2000]. To accurately measure the skip distance associated with a particular propagation mode, it is necessary to identify which of these peaks corresponds to which mode. Hughes et al.  identify 1-hop F region power peaks based on the following: (1) larger slant ranges achieved by F region ground scatter due to reflection from a higher altitude and (2) the tendency of F region ground scatter to arrive at the radar at elevation angles within the region of greatest antenna gain, resulting in an enhanced power for F region ground scatter. We will discuss each of these criteria in turn to show that they may be effective for distinguishing ionospheric propagation modes only under specific ionospheric conditions.
Figure 5 shows a selection of power versus range profiles for the Bruny Island and Unwin radars obtained during daylight hours when both E region and F region ground scatter are expected to occur. Accompanying each power profile is a ray tracing plot showing the predicted raypaths for that time interval and frequency. The raypaths were computed using code based on a two-dimensional formulation of Fermat's principle in the propagation plane [Coleman, 1998] with input parameters taken from the International Reference Ionosphere [Bilitza et al., 2011] (see: http://vt.superdarn.org/Ray-tracing). Simulated rays are calculated at elevation angles ranging from 5° to 55° to the horizontal. The black-shaded region in each ray tracing plot indicates locations in the ionosphere where the wave-vector is perpendicular to the geomagnetic field to within 1°; this is the “aspect-angle condition” for ionospheric backscatter scatter to be detectable by the radar [Ponomarenko et al., 2009].
We first consider the relative slant ranges of E region and F region ground scatter for the examples in Figure 5. Due to the presence of the relatively short-lived molecular ions in the E region, the E region electron density is strongly coupled to the solar zenith angle and therefore peaks in the summer months and around local noon. In the midlatitude to high-latitude F region, the electron density peaks at solar maximum due to the increased amount of EUV radiation and also in winter due to the winter anomaly [Torr and Torr, 1973]. Therefore, in the spring and summer months, both the E region and F region ionosphere are able to support reflection of rays with similar angles of incidence. This results in E region ground scatter occurring at shorter ranges than F region ground scatter due to the large difference in reflection altitude for the two modes. This is shown in our results in Figure 5a and has been observed previously using the TIGER radars [Norman et al., 2004]. The results in Figure 5a were obtained from the Bruny Island radar on 24 February 2009. The ray tracing plot for this time interval indicates that the power peak at 700–1100 km range corresponds to 1-hop E region ground scatter and the power peak at 1200–1550 km corresponds to 1-hop F region ground scatter. The range difference between the two modes is expected to be most pronounced away from solar maximum when the F region is at its weakest. In contrast, in winter near solar maximum, electron densities increase in the F region and decrease in the E region. Therefore, for a signal of a given frequency, the F region ionosphere can support specular reflection at angles much closer to the vertical compared to the E region ionosphere. This was also noted by Norman et al. . This results in 1-hop F region ground scatter occurring at similar or shorter ranges than 1-hop E region ground scatter, as shown in Figure 5b. This figure shows a power versus range profile from the Bruny Island radar on 6 May 2011, approaching the Southern Hemisphere winter, at solar maximum. Close to solar maximum the F region may become so strongly ionized that the 1F power peak may occur at a similar or shorter range than the 1E power peak even during the summer months. This is shown in Figure 5c for the Unwin radar on 14 February 2012.
We have also observed that as the frequency is increased, 1E ground scatter increases in range more slowly than 1F ground scatter. This is shown for the Unwin radar in Figure 6 for the time interval 23:00–23:24 UT on 28 October 2011. For each power profile in Figure 6 the longer-range peak corresponds to 1F ground scatter, which gradually separates in range from the 1E power peak as the frequency increases. This effect is commonly observed in ground scatter studies which sound the ionosphere at a wide range of frequencies [e.g., Dyson et al., 2000, 2003], and we attribute this behavior to the narrow vertical extent of the E region. The height of the maximum electron density in the F2 layer also exhibits a seasonal dependence [e.g., Zhang et al., 1999] which may affect the slant range of radar backscatter. Clearly, it is not possible to use the slant range to distinguish between E region and F region ground scatter under all ionospheric conditions.
Next we consider the relative power of E region and F region ground scatter. For the Unwin radar we observe that the maximum power of the 1F peak often exceeds that of the 1E peak, which might be expected when E region ground scatter arrives at the radar at low angles where the antenna gain is reduced [Hughes et al., 2002]. However, we have found this effect is not reliable enough to consistently distinguish the F region peak from the E region peak based on power alone. For the Bruny Island radar we observe that the power of the 1E peak is often similar to or greater than the power of the 1F peak. For example, the peak in Figure 5a corresponding to the 1E mode at 700–1100 km range has a greater power than the 1F peak at 1200–1500 km range. In Figure 5d, the 1E peak at 1000–1300 km range and the 1F peak at 1300–1600 km range exhibit similar power. In Figure 5d we have included the results of the Gaussian fitting algorithm, which show that the 1E and 1F power peaks have been interpreted as a single-backscatter distribution. This leads to a ∼500 km error in the F region skip distance. The elevation angle of arrival of backscatter for a particular propagation mode depends on both the radar operating frequency and the local ionospheric conditions, and the power depends strongly on the elevation angle of arrival due to the nonuniform antenna gain. This means that the backscatter power does not provide a reliable method for identifying propagation modes, as the peak of maximum power may correspond to propagation via any one of the E, F1, or F2 regions.
The process of identifying the F region power peak is also complicated by the presence of low-velocity ionospheric scatter in the ground scatter data. Figure 7 (left) shows a power profile from the Bruny Island radar for the time interval 10:00–10:20 UT on 27 January 2011, close to local dawn. A ray tracing simulation for this time period is shown in the Figure 7 (right). As described above, the black-shaded region in the ray tracing plots indicates the locations in the ionosphere where ionospheric backscatter is expected to be detectable by the radar, should a scattering target be present. The range to the black-shaded region in Figure 7 is similar to the range of the power peak at 700–900 km in the left panel, strongly suggesting that this peak is ionospheric backscatter. The ray tracing indicates that the F region ground scatter power peak occurs at 1500–1900 km range, which can be seen in the radar data. However, the algorithm has fitted the ionospheric scatter instead. This results in an error of ∼800 km in the skip distance. Low-velocity ionospheric scatter is frequently observed by the TIGER radars close to dawn and dusk. It is particularly difficult to distinguish ground scatter from low-velocity ionospheric scatter at these times because the ground scatter undergoes a rapid increase in range at dusk as the ionospheric electron density decreases, and a rapid decrease at dawn as the electron density rises (see Figure 2). During disturbed geomagnetic conditions when midlatitude SuperDARN radars observe an increased proportion of ionospheric backscatter due to the expansion of the auroral oval, it is expected to be even more challenging to isolate F region ground scatter from the data based on slant range and power alone.
The above results illustrate the impact of seasonal and solar cycle variability in ionospheric conditions on the performance of an automated fitting algorithm for the determination of ionospheric parameters from SuperDARN data. Initial attempts to manage the fitting process by excluding backscatter from very short ranges, where F region ground scatter is not expected to occur, met with some success. The range below which echoes were excluded was defined separately for day and night and also for each frequency. For example, we required that the skip distance for a 10 MHz signal be greater than 500 km during the day and greater than 1000 km at night. At 14 MHz, we required that the skip distance be greater than 800 km during the day and greater than 1600 km at night. This approach was effective near local noon in the summer months and away from solar maximum, when E region skip distances are significantly shorter than F region skip distances. It was not effective, however, at times when E region and F region ground scatter were observed at similar ranges. It was also not effective when a significant amount of low-velocity ionospheric scatter was present. Additional information is required to automate the identification of different propagation modes under a broad range of ionospheric conditions. Elevation angle-of-arrival measurements from the radar interferometer array provide a possible solution. This will be explored in section 3.
3 Incorporating Elevation Angle-of-Arrival Data
We have investigated the use of direct elevation angle-of-arrival measurements from SuperDARN radars to improve the accuracy of the MUF and foF2 data products. We used the Saskatoon SuperDARN radar operating a sounding mode where the frequency was cycled sequentially at 1 min intervals through eight frequencies in the range 9–18 MHz, each with a 300 km bandwidth. This mode was operated continuously over the period 1–4 August 2012.
We have used elevation angle-of-arrival measurements to (1) reliably identify backscatter associated with the 1-hop F region propagation mode, (2) estimate the critical angle Δ0 associated with each skip distance, and (3) identify cases where ground scatter may have originated from the rear field of view of the radar.
3.1 HF Propagation Modes
Prior to implementing the curve fitting procedure described in section 1.2, we use the elevation angle-of-arrival and slant range to identify the propagation modes of backscattered signals. Our algorithm is designed to remove 1-hop E region ground scatter (1E), -hop F region ionospheric scatter () and meteor scatter from the data set based on the estimated virtual height of reflection.
To identify 1E ground scatter, we calculate the virtual height hv of each echo assuming a 1-hop propagation mode; that is, we assume that the group range r to the ionospheric reflection point is equal to one half of the total measured slant range. The virtual height is then calculated using a triangle of sides r, RE=6371 km (the average radius of the Earth) and RE+hv such that
where Δ is the elevation angle of arrival measured by the radar. We classify echoes with a virtual reflection height below 140 km as ground scatter via the E region. Meteor echoes will also satisfy this criterion due to their short slant range. The 140 km threshold value is well below the expected virtual height of reflection in the F region [Koustov et al., 2007; Chisham et al., 2008; Liu et al., 2012], so 1F ground scatter is not expected to satisfy this criterion.
To identify low-velocity ionospheric backscatter contaminating the ground scatter data, we calculate the virtual height of each echo again using equation (4), this time assuming -hop propagation, with the range to the ionospheric reflection point equal to the total measured slant range. We then compare the calculated virtual height with the value given by the SuperDARN empirical virtual height model [Chisham et al., 2008]. This model is based on a statistical study of 5 years of elevation angle-of-arrival data for ionospheric scatter from the Saskatoon SuperDARN radar. The empirical virtual height model (EVHM) gives the expected distribution of ionospheric backscatter echoes in slant range-virtual-height space and is expected to provide a reasonable estimate of this distribution for all SuperDARN radars [Chisham et al., 2008]. We classify echoes as ionospheric backscatter if the virtual height calculated using equation (4) falls within ±150 km of the virtual height predicted by the EVHM. This criterion was chosen based on the statistical distribution of ionospheric backscatter used to create the EVHM; at any given slant range, -hop F region echoes are distributed over about 300–400 km in virtual height, with the mean virtual height increasing at greater ranges from the radar [see Chisham et al., 2008, Figure 4]. If the echo is ionospheric scatter then the virtual height calculated with equation (4) should be comparable to that predicted by the EVHM. If the echo is in fact ground scatter, then the virtual height will be greatly overestimated and exceed that predicted by the EVHM by more than 150 km. For the 4 days of Saskatoon data studied, there was no indication of ground backscatter being identified as ionospheric scatter for a value of 150 km as described above (see Figure 8).
The tests described above for 1E and backscatter are applied only to echoes that were classified as ground scatter. Echoes which do not meet the Doppler velocity and spectral width criteria for ground scatter, condition (1), are also discarded from the analysis.
Figure 8 shows all backscatter echoes detected by the Saskatoon SuperDARN radar on 1 August 2012 that were classified as ground scatter based on the Doppler velocity and spectral width criteria of section 1.1. The echoes are color coded according to the propagation mode as determined by the virtual height criteria described above. In addition to the 1-hop F region ground scatter (shown in blue), significant amounts of low-velocity ionospheric scatter (red), and meteor scatter at ranges up to ∼500 km (green) were detected. Ground scatter echoes reflected in the F1 region may also be present at 900–1100 km range from 18:00 to 22:00 UT. Echoes from this mode are expected to exhibit different slant range and elevation angle-of-arrival characteristics to F2 region ground scatter. However, we have not attempted to exclude F1 region ground scatter from the data set. MUF and foF2 may be overestimated when significant echoes from the F1 region are used as input for the Gaussian fitting algorithm.
3.2 Critical Angle
We estimate the critical angle associated with each skip distance by performing a least squares linear fit to the elevation angle data as a function of slant range. The value of the fitted line at the skip distance is used as the critical angle. An example of this fitting procedure is shown in Figure 9. Elevation angle-of-arrival measurements from the radar are shown as asterisks and are plotted as a function of range. The red line indicates the least squares linear fit to the elevation angle data, and the blue vertical line indicates the skip distance. Outlying elevation angles, which may have been aliased [e.g., Milan et al., 1997b; McDonald et al., 2013], are excluded from the fitting procedure.
Figure 10 is a field-of-view plot showing foF2 and MUF measured by the Saskatoon SuperDARN radar for the time interval 22:00–22:24 UT (16:00–16:24 LT) on 1 August 2012, utilizing direct angle-of-arrival measurements from the radar. The MUF values are calculated for HF communication circuits between the radar site and every point within the field of view of the Saskatoon radar. The filled circles indicate the foF2 values measured by the radar. The foF2 values are plotted at the ionospheric reflection point, assumed to be at half the range to the skip distance.
3.3 Ground Scatter From Behind the Radar
We have observed that the Saskatoon SuperDARN radar routinely detects ground scatter from the backward look direction. The “front” field of view for SuperDARN radars is defined by the boresight direction, which for most SuperDARN radars is directed poleward. The “rear” field of view is located equatorward of the radar site. Log-periodic antennas such as those installed on the Saskatoon radar, the TIGER radars and several other SuperDARN radars exhibit significant back lobes in the antenna gain pattern, particularly in the lower part of the HF band [Custovic et al., 2013]. This effect has been observed previously in SuperDARN data at the CUTLASS SuperDARN radars and elsewhere and is identifiable by a characteristic variation in the measured angle of arrival with azimuth [Milan et al., 1997b]. Since elevation angles are calculated assuming that the signal arrived from the forward direction, large errors in the angle of arrival occur when backscatter from behind the radar dominates the data. It is possible to correct for this when calculating the critical angle. foF2 values determined using backscatter from the rear field of view then correspond to the ionosphere in the geographical region behind the radar.
We have introduced a test to determine the backscatter direction of arrival in real time. When critical angles have been determined for at least five beams at a given frequency, we calculate the standard deviation of these critical angles. A large standard deviation indicates significant variation in the critical angle with azimuth, which is characteristic of backscatter arriving from the rear field of view. When the standard deviation exceeds a threshold value, the algorithm recalculates all the elevation angle values obtained at this frequency assuming that the backscatter originated from the rear field of view. The critical angle for each beam is then determined again using the corrected angle-of-arrival values. If the standard deviation of the critical angles is still large following this correction, this indicates a mixture of scatter from in front and behind the radar. In this case, all critical angle values for this frequency are rejected and foF2 is not determined. Figure 11 is a field-of-view plot showing MUF and foF2 for a time period where ground scatter from the rear field of view was observed at multiple frequencies. The foF2 values correspond to the ionosphere in the geographical region approximately 1000 km equatorward of the radar site.
Figure 12 shows the diurnal variation in average foF2 for 3 August 2012 as measured by the Saskatoon SuperDARN radar. The blue line shows the foF2 averaged over all beams in the forward look direction, and the red line shows the foF2 averaged over all beams in the backward look direction. A longer averaging interval of 32 min was chosen to better represent the long-term trends in the data and to improve the performance of the Gaussian fitting algorithm at nighttime when the ground scatter echo occurrence was low. During the daytime, most of the foF2 values correspond to the forward look direction, while during local nighttime, all of the foF2 values correspond to the backward look direction. In the early morning, foF2 values were determined in both the forward and backward look directions. Over the 24 h interval, the average foF2 reaches a maximum during the daytime and a minimum shortly before dawn. This is consistent with the expected diurnal variation in ionospheric electron density. We emphasize that very large errors in the foF2 would have resulted during local nighttime if the backscatter direction of arrival had not been taken into account.
The above method relies on the accuracy of the EVHM used in order to successfully remove low-velocity ionospheric backscatter from the data. At times when the correspondence between elevation angles and slant ranges of ionospheric echoes differs significantly from that predicted by the EVHM, this method does not work. This may account for the population of echoes in Figure 8 at 14:00–00:00 UT at ranges of around 800 km that appear to be correlated with the ionospheric echoes shown in red but have been identified as 1-hop F region ground scatter (blue). For these slant ranges the Chisham et al.  EVHM predicts an elevation angle of 23° for -hop ionospheric backscatter. However, the echoes are observed to have elevation angles in the range 30–40°. This is shown in Figure 13 (left), which is a histogram of elevation angles for 14:00–00:00 UT at ranges 500–1000 km. Figure 13 (right), which shows simulated ionospheric backscatter returns for the same time interval, confirm that the elevation angles are in the 30–40° range. Thus, it is not always possible to identify low-velocity ionospheric backscatter even when elevation angle measurements are available. However, the removal of most of the low-velocity ionospheric backscatter from the data is observed to greatly improve the accuracy of the MUF and foF2 data products. Ribeiro et al.  have developed a depth-first-search algorithm for use with the SuperDARN radars which is effective at identifying discrete populations of ionospheric backscatter in the data. However, their technique requires the analysis of data sets spanning many hours so it is not applicable when the data are to be analyzed in real time.
When determining foF2 values using the techniques described above, the foF2 estimate is highly sensitive to errors in the critical angle, the elevation angle of arrival associated with the skip distance. Errors in foF2 of order 500–1000 kHz may arise when the estimated critical angle differs from the true critical angle by just a few degrees. This may account for the variation of foF2 with range apparent in Figure 10. The foF2 values at the furthest ranges correspond to skip distances for the highest frequencies, and hence have the lowest critical angles. The relationship between phase lag and angle of arrival is highly nonlinear. Particularly at low elevation angles, a small error in the measured phase difference results in a large error in the angle of arrival [McDonald et al., 2013]. However, much larger errors in foF2 are expected when the critical angle is estimated using a virtual height model. This is the approach taken by Hughes et al. , who assume a constant virtual reflection height of 400km. Whenever the actual virtual reflection height differs significantly from this value, large errors in the associated critical angle will result. For example, if the slant range to the ionospheric reflection point is 700 km, equation (4) predicts that the associated critical angle would be 27.3°, 32.3°, or 37.6° assuming virtual reflection heights of 350 km, 400 km, and 450 km respectively. We suggest that virtual height models are effective at determining the location in the ionosphere from which backscatter originated but using the elevation angle directly leads to significant errors in foF2.
A further limitation of the virtual height models presently used in conjunction with SuperDARN radar data is that they assume a minimum slant range for F region echoes, typically 800 km to the ionospheric reflection point, or 1600 km to the ground scattering location [e.g., Chisham et al., 2008; Liu et al., 2012]. For ground scatter slant ranges below 1600 km, virtual height models assume propagation via the E region. Thus, during daylight hours when skip distances are reduced, the slant range of the F region critical raypath is often too low for the use of standard virtual height models for all but the highest operating frequencies (see Figure 1). During the winter months and toward solar maximum, the slant range of the F region critical raypath is further reduced, making it particularly difficult to apply a virtual height model at these times. The use of a sounding mode with a large spread of frequencies over the 8–20 MHz band maximizes the chance that F region skip distance data with slant ranges greater than 1600 km will be available at all times of the day. When angle-of-arrival data are available, there is no such restriction on the slant range and foF2 can be determined at a much larger number of locations within the radar field of view. Also, it becomes possible to use data from the most common mode of operation of SuperDARN radars, at around 10–12 MHz. At these lower frequencies, chosen to maximize the occurrence of backscatter from ionospheric irregularities, F region skip distances are particularly low during daylight hours.
Elevation angle-of-arrival data provide two further insights into the validity of this technique for determining MUF and foF2. First, we confirm that the minimum slant range for each frequency observed in power versus range profiles does indeed correspond to the slant range to the skip distance. Detailed modeling of the gain pattern of SuperDARN antennas [Milan et al., 1997b; Custovic et al., 2011, 2013] indicates that the radar is capable of detecting signals at elevation angles greater than those associated with the skip distance. This is evident in Figure 14, which shows 6 h histograms of elevation angle data from the Saskatoon SuperDARN radar centered around local noon (09:00–15:00 local time), for three different frequencies. The peak in elevation angle occurrence is well below the maximum detectable angle by the radar in all cases. Therefore, it is clear that the minimum slant range for each frequency is determined by the path of the critical ray, rather than by the upper elevation limit of the antenna gain.
Secondly, the availability of angle-of-arrival data makes it possible to identify cases where ground backscatter originated from the rear field of view of the radar. Knowledge of the signal ground scattering location allows the correct geographic coordinates to be assigned to the foF2 values. It also increases the total geographical area over which foF2 and MUF can potentially be determined, since backscatter can be detected from both the front and rear field of view. However, identifying cases where ground scatter originated from behind the radar in real time is not straightforward because a comparison of elevation angles across many beams in the field of view is required. Particularly at nighttime, ground scatter echoes may be too sparse to determine the critical angle for enough azimuthal directions to permit such a comparison. The twin terminated folded dipole (TTFD) antennas installed on most post-2005 SuperDARN radars exhibit a much smaller ratio of backward gain to forward gain than the traditional log-periodic antennas used on older SuperDARN radars such as Saskatoon [Custovic et al., 2013]. Therefore, for radars fitted with TTFD antennas, ground scatter from behind the radar is not expected to affect the measurement of MUF and foF2 using the techniques presented here.
We have implemented and investigated a technique suggested by Hughes et al.  for determining MUF and foF2 on the Bruny Island and Unwin SuperDARN radars. These data products are expected to complement the existing vertical and oblique ionosonde network in the Australasian region, particularly over land and sea regions where ionosonde coverage is sparse.
The technique is most effective at times when backscatter associated with the 1-hop F region propagation mode is clearly discernible. Particularly, in the winter months and away from solar maximum, we found that the technique described by Hughes et al.  was unable to reliably identify the 1-hop F region propagation mode based only on the slant range and power of backscattered signals. This results in very large errors in skip distance measurements and hence MUF and foF2.
Large errors in foF2 can also be expected when the critical angle associated with ground scatter at the skip distance is estimated using a virtual height model. When the radar is operating in the common mode during daylight hours, it is generally not possible to apply a virtual-height model at all.
To address these problems, we have incorporated elevation angle-of-arrival measurements into the technique. Elevation angle measurements provide an effective tool for identifying the propagation mode of individual echoes, which helps to isolate the 1-hop F region ground scatter echoes that are used in this technique. Additionally, we have used elevation angles to estimate the critical angle associated with each skip distance. This eliminates the reliance on virtual height models, which may not accurately represent the real-time HF propagation characteristics of the ionosphere and are often not valid. Angle-of-arrival measurements also provide a means of recognizing when backscatter has originated from the rear field of view, which is important for assigning the correct geographical coordinates to the MUF and foF2 data products.
Andrew McDonald is supported by a postdoctoral fellowship through the Department of Defence, Defence Science Technology Organisation (DSTO) and by an ARC LIEF grant LE0989069 in partnership with IPS Radio and Space Services. Emma Bland receives support from DSTO and from an Australian Postgraduate Award. The authors thank Kathryn McWilliams and Dieter André, University of Saskatchewan, for the use of the Saskatoon SuperDARN radar. SuperDARN data are freely available by contacting the authors or through the SuperDARN website at Virginia Polytechnic Institute and State University (http://vt.superdarn.org/).
Alan Rodger thanks Gerard Blanchard and an anonymous reviewer for their assistance in evaluating this paper.