## 1 Introduction

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 *F*_{2} region, or *f*_{o}*F*_{2}, which is the maximum frequency reflected by the *F* region ionosphere at vertical incidence at a particular geographic location. The *f*_{o}*F*_{2} 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 *f*_{o}*F*_{2} 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 *f*_{o}*F*_{2} data is limited by the number of ionosondes operating within a given area. Over many regions of Australia the geographical *f*_{o}*F*_{2} coverage is quite sparse and is absent over the oceans, requiring a high degree of interpolation in the use of *f*_{o}*F*_{2} 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.* [2002] for determining the ionospheric parameters MUF and *f*_{o}*F*_{2} 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 *f*_{o}*F*_{2} 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).

### 1.1 Instrumentation

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 *V*_{max}=30 m s^{−1} and *W*_{max}=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 *f*_{o}*F*_{2} Using SuperDARN Radars

The method presented here for determining MUF and *f*_{o}*F*_{2} using SuperDARN radars is based on methods developed by *Hughes et al.* [2002] 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 *A*_{0}, *x*_{0} 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 *x*_{0}, 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 *x*_{0}. 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., *f*_{o}*F*_{2}) over the field of view of the radar using the relationship,

where *f*_{c} is the vertical critical frequency, *f*_{0} is the oblique critical frequency and Δ_{0} 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.