An evaluation of range accuracy in the Super Dual Auroral Radar Network over‐the‐horizon HF radar systems

The Super Dual Auroral Radar Network (SuperDARN) of over‐the‐horizon HF radars forms a powerful diagnostic of large‐scale ionospheric and magnetospheric dynamics in the Northern and Southern Hemispheres. Currently, the ground location of the HF radar returns is routinely determined by a simple range‐finding algorithm, which takes no account of the prevailing HF propagation conditions. This is in spite of the fact that both direct E and F region backscatter and 1½‐hop E and F region backscatter are commonly used in geophysical interpretation of the data. Here HF radar backscatter which has been artificially induced by the high‐power RF facility (ionospheric heater) operated by the European Incoherent Scatter Scientific Association at Tromsø is used to provide a range calibration for the SuperDARN radars. The known ground range, the measured radar slant range, and the group path calculated by a ray‐tracing simulation are compared. The standard algorithm for backscatter ground range location is found to be accurate to within 16 km and 60 km for direct and 1½‐hop backscatter, respectively.

(1/2-hop) propagation to E and F region ionospheric irregularities and ll/2-hop propagation to both the E and F region commonly observed by the radar systems. Previous studies have adopted a ray-tracing simulation [Villain et al., 1984;Baker et al., 1986] or velocity field cross-correlation [Ruohoniemi et al., 1987;Andr• et al., 1997] approach to assess the accuracy of range-finding using the straight line approximation. These studies suggested agreement between the ground range and radar range within -15 km over a l/2-hop path.
Early studies with HF radars either used HF radar data alone or combined HF radar data with data from instruments such as ground magnetometers, which had a limited spatial resolution and are often only available from arrays which are sparsely populated in comparison to radar fields of view. However, the growing importance of combined ground-spacecraft measurements and multi-instrument studies from the ground have led to numerous coordinated studies with instruments of a high spatial resolution, such as meridian scanning photometers, all sky cameras, and auroral imagers. In these studies the location of the radar 801 backscatter is a crucial element in the study. In addition, spacecraft overpasses, where the magnetic conjugate points are computed to a high precision using geomagnetic field models, require high accuracy in the location of the HF radar backscatter.
A illustrative example is found in the recent studies made of the footprint of the magnetospheric cusp. Optical signatures associated with dayside reconnection have been extensively investigated from the ground in the visible wavelengths of 630.0 nm and 557.7 nm associated with auroral activity [e.g. Lockwood et al., 1993Lockwood et al., , 1995Sandholt et al., 1996]. HF radars observe pulsed ionospheric flows in the cusp region, which are the response to this transient reconnection at the magnetopause [e.g. Pinnock et al., 1993Pinnock et al., , 1995Provanetal., 1998Provanetal., , 1999  ].
In this paper, HF radar backscatter which has been artificially induced at a precisely known location by the high-power RF facility (ionospheric heater) operated by the European Incoherent Scatter (EISCAT) Scientific Association at Troms0 is used to provide a range calibration for the Super Dual Auroral Radar Network (SuperDARN) radars. The known ground range, the measured radar slant range, and the group path calculated from a ray-tracing simulation are compared. This demonstrates an excellent agreement between the measured radar slant range and the calculated group path and allows the quantification of the deduced range accuracy to be made for 1/2-, 11/2 -and 21/2-hop backscatter modes over paths of -850 and -1800 km.

Instrumentation
The data presented here result from the generation of artificial ionospheric HF coherent backscatter. It is well known that the EISCAT heating facility at Troms0, Norway [Rietveld et al., 1993], is capable of generating artificial field-aligned irregularities using high-power HF radio waves [e.g., Robinson, 1989]. These irregularities are detectable by both incoherent and coherent scatter radars [e.g., Robinson et al., 1997]. The Co-operative U.K. Twin Located Auroral Sounding System (CUTLASS) radar is a pair of HF coherent backscatter radar systems located at Hankasalmi, Finland, and Pykkvibasr, Iceland, and forms part of the SuperDARN array. Details of SuperDARN are given by Greenwald et al. [1995] and details of the CUTLASS systems at Hankasalmi and Pykkvibasr are given by Milan et al. [1997]. The CUTLASS radars' locations and the Troms0 heater's ionospheric interaction location are given in Table 1  Here data are presented from the Observations of ULF waves with CUTLASS and the Heater (SP-UK-OUCH; Wright and Yeoman [1999]) experiment. In this experiment the CUTLASS radars run in a high-temporalresolution and high-spatial-resolution mode, with Hankasalmi running a six-beam scan (scanning beams 7 through 2, inclusive) with an integration time of 1 s, while Pykkvibasr runs a three-beam scan (beams 13-15) with a 2 s integration period. Thus both radars produce data with a temporal resolution of 6 s. Both run in a high-spatial-resolution mode, with each radar having 75 range gates of 15 km length, centered on the heated volume at Troms0 (the distance to the first range gate being set at 480 and 1470 km for the Hankasalmi and Pykkvibasr radars, respectively). The EISCAT heater was in continuous operation at 50% power (using 6 X 80 kW transmitters, an Effective Radiated Power (ERP) of -•130 MW), at a frequency of =4-5 MHz for 4 hour intervals. Observations with the heater aligned along the magnetic field and employing a _+30 ø beam swing at a frequency of 1 Hz, centered vertically, have been recorded, with the resulting backscatter detected by both radars of the CUTLASS system. The heater produces artificial electron density irregularities in the F region ionosphere, which act as targets for the HF radar. The artificial targets result in very high returned backscatter power in comparison to naturally occurring irregularities. This allows a short integration time to be run on the radar, providing higher time resolution than is normally available. hours and 40 min of Pykkvib•r radar backscatter for which stron• radar returns were obtained over a number of radar ran•½ •at½s for periods of •rcatcr than 1 hour. In addition to stron• returns we also require that the radar was opcratin• consistently at one soundin• frequency. Data from an example run of SP-UK-OUCH will be presented in detail, alon• with statistical analysis of the entire data set, from both radar systems.

Plate 1 presents data from a section of an SP-UK-OUCH run from 1210 to 1250 UT on October 15, 1998, an interval when the heater was operating in its beam swinging mode. Returned backscatter power and elevation angle are plotted as a function of time and range gate for the Hankasalmi radar beam 5 (Plates l a and lb) and Pykkvibasr radar beam 15 (Plates 1 c and ld)
which overlie the heater location. During this interval the Hankasalmi radar was operating between 19.415 and 19.680 MHz, and the Pykkvibasr radar was operating b'6tween 12.105 and 12.235 MHz, both frequency bands having been selected at the beginning of the experiment to optimize the returned backscatter power. In Plate la a broad band of high-power radar returns, generated by the TromsO heater, can be seen between range gates 25 and 35. Lower power backscatter is also visible beyond range gate 50, but these data have been identified by the radar, via their Doppler velocity and spectral width, as ground scatter: radiowaves that have refracted in the ionosphere and backscattered from the ground. The elevation angles for the heater-induced scatter (Plate lb) are centered at 10 ø, with the nearer ranges exhibiting slightly higher elevation angles than the farther ranges, as expected for a constant irregularity height. The backscattered power from Pykkvibasr is displayed in Plate l c. In this case a threshold of 6 dB has been applied to the data, in order to reduce clutter from lowpower ground backscatter returns. Again, a band of high backscatter power is visible, this time between range gates 33 and 38. The Pykkvibasr data for this interval are not as clear as the Hankasalmi data, and the unstructured low-power returns surrounding the artificial backscatter region are due to ground scatter. A second structured region of backscatter is visible centered on range gate 56. The elevation angles for the two structured regions of backscatter (Plate l d) are centered on 18 ø and 31 ø for the nearer range and farther range regions, respectively. The origins of these two regions of backscatter will be discussed below in Sections 4.2 and 4.3.

Hankasalmi Radar Performance
In order to assess the performance of the radar system range evaluation the data from the interval presented in Section 3.1 and the overall SP-UK-OUCH data set from beam 5 of Hankasalmi and beam 15 of Pykkvibasr require a more statistical analysis. In order to assess the overal! performance and consistency of the radars the occurrence of backscatter with a power of >10 dB has been quantified as a function of the geographic latitude and longitude determined by the radar range-finding algorithm. Figure 2 presents the results of such an analysis for the Hankasalmi radar. The occurrence of radar backscatter at power levels above 10 dB is plotted as a function of geographic latitude derived from the standard radar rangefinding algorithm, with occurrence denoted on the left hand y axis labels. Also plotted is the actual latitude of the TromsO field line as a function of altitude, denoted on the right hand y axis labels, taking into account the dip angle of the geomagnetic field.  Table 2. backscatter, the main heater signature being located at apparent longitudes of 22ø-23øE, and the farther range scatter being located at apparent longitudes of 29ø-30øE. The entire data set is plotted in Figure 3b, showing a peak occurrence at 23øE, where over 3600 datapoints have been accumulated.

Ray-tracing Simulation
In order to gain a more detailed understanding of the propagation conditions .prevailing during the experiment of October 15 1998, a ray-tracing simulation has been undertaken. A modified version of the ray-tracing code developed by Jones and Stephenson [1975] has been used in which the angle between the k vector and the magnetic field has been used to identify regions where backscatter is likely to occur in the presence of density irregularities. An example ionogram from the Troms½ dynasonde is illustrated in Figure 4, together with a real height profile, as calculated by the Polan inversion algorithm, and the two-o•-Chapman-layer model which was used in the ray-tracing simulation. The critical frequencies of the two layers have been determined from the ionosonde measurements, and the ionospheric parameters for the two o•-Chapman layers employed in the simulation are given in Table 2. The critical and scale heights of the layers have also been chosen to be in

I:,ykkvib•er, near the centers of the narrow radaroperating-frequency bands. It was assumed that the backscattered power would return to the radar on the same path as on the outward leg (i.e., reciprocity is assumed to hold). The results obtained from the raytracing simulation of three propagation paths (one from
Hankasalmi-Troms0 and two from I:,ykkvib•er-Troms0) are presented in Plate 2. For the case of the Hankasalmi radar, orthogonality occurs just prior to reflection while for the Pykkvib•er radar orthogonality takes place close to or at the reflection point.

Discussion
Artificial coherent HF radar backscatter generated by the EISCAT ionospheric heating facility at Troms0 has provided a high-power signature at a known ground range which can be used to calibrate the range assessment of the SuperDARN radar facilities. Case study and statistical analysis of runs of the SP-UK-OUCH experiment have provided a database to assess both the accuracy and variability of the standard SuperDARN range-finding algorithm. Here the data presented above will be compared with ray-tracing results to assess the propagation paths concerned. Three regions of structured artificial backscatter (one measured by the Hankasalmi radar and two measured by the I:,ykkvib•er radar) are analyzed in terms of three propagation paths: direct ionospheric backscatter from the Hankasalmi-Troms0 path (hereafter referred to as the 1/2-hop path), ionospheric backscatter from a l l/2-hop mode across the I:,ykkvib•er-Troms0 path (hereafter referred to as the 11/2-hop path), and ionospheric backscatter from a 21/2-hop mode across the Pykkvib•er-Troms0 path (hereafter referred to as the 21/2-hop path).

Half-Hop Path Propagation
The artificial scatter observed from the Hankasalmi radar presented in Plate 1 and Figure 2 resulted from a radar frequency of 19 MHz, with a heater interaction height of 210 km and with radar elevation angles of -10 ø. A ray trace for this situation is presented in Plate 2a. The HF rays achieve the orthogonality required for HF backscatter at ground ranges of-850 km, prior to reflection, and hence the propagation path for this scatter can be determined with confidence. The ground range, the calculated group path, and the measured radar slant range for the three propagation paths are summarized in Table 3. The field-aligned data from Figure 2b are used for this comparison, as this is the most appropriate mode for this purpose, with the heater beam aligned with the Troms0 field line. In this case the strongest heating effects (due to field-aligned heating [Robinson, 1989]) will occur in a very well defined location. The ray trace reveals a difference between the ground range and the group path for this mode of 50 km and a difference between the measured radar slant range and the calculated group path of only 1.6 km (radar slant range here has a resolution of 15 km). The range-finding algorithm then calculates the backscatter ground latitude at 69.06 ø . This agrees with the known ground latitude of the Troms0 heater interaction height at 210 km altitude within 16 km, in practice an accuracy of one 15 km range gate, well within the 45 km range gates used in standard radar operations. Comparing the field-aligned heater measurements in Figure 2b with the measurements resulting from heater beam-swinging operations in Figure 2a, the beam swinging can be seen to result in a broader patch of heater-induced irregularities, which are centered between a location vertically above the heater (the center of the heater beam swinging) and the field-aligned position where heating is at its most effective.

One-and-One-Half-Hop Path Propagation
The main band of artificial scatter observed from the Pykkviba•r radar presented in Plate 1 and Figure 3 resulted from a radar frequency of 12 MHz, with radar elevation angles of--18 ø. A ray trace for this situation is presented in Plate 2b. The HF rays achieve orthogonality at ground ranges of--1800 km, and thus the propagation path for this scatter can again be determined with confidence (the rays also achieve orthogonality at their 1/2-hop position, but this lies outside the radar field of view in this case). The parameters deduced for this propagation path and the data presented in Figure 3a are summarized in Table 3. The raytrace reveals a difference between the ground range and the calculated group path for this mode of 157 km and a difference between the measured radar slant range and the group path of only 1 km. The rangefinding algorithm then calculates the backscatter ground longitude at 22.2 ø . This differs from the known ground longitude of the Troms0 heater by 114 km, an accuracy of seven 15 km range gates, or just over two 45 km range gates as used in standard radar operations.

Two-and-One-Half-Hop Path Propagation
The second population of artificial scatter observed from the Pykkvibaer radar at farther range gates was observed with radar elevation angles of-31 ø. A ray trace for this situation is presented in Plate 2c. The HF rays again achieve orthogonality at ground ranges of -1800 km, and thus the propagation path for this scatter can again be determined with confidence. The parameters deduced for this propagation path are summarized in Table 3. The ray trace reveals a difference between the ground range and the calculated group path for this mode of 380 km and a difference between the measured radar slant range and the calculated group path of 67 km. The latter discrepancy results from accumulated errors in the ray trace calculation and inaccuracies in the (uniform) ionospheric models employed. The range-finding algorithm then calculates the backscatter ground longitude at 29.5 ø. This differs from the known ground longitude of the Troms0 heater by 390 km, an accuracy of twenty-six 15 km range gates, or eight 45 km range gates, as used in standard radar operations.

Implications for Radar Operations
The comparison presented in Sections 4.1-4.3 shows an excellent agreement between the calculated ray trace results and the measured radar slant range. This gives confidence in the accuracy of the model ionospheres employed and the propagation modes inferred. It also demonstrates the accuracy of the radar elevation angle determination. The comparison between the known target ground location and the ground location inferred from the range-finding algorithm can then be used to evaluate the performance of the algorithm under more general conditions. For the 1/2-hop path over a ground range of 825 km the range-finding algorithm has an accuracy of well within the standard 45 km range gate of a SuperDARN radar. In fact, the accuracy of the range finding over such a path is close to the narrowest range gate such systems are capable of at present. The HF propagation to the point of backscatter under these conditions at 19 MHz is close to straight line propagation, so this result is perhaps unsurprising. The agreement between the ground range and radar range within -15 km is fully in accord with the results of Ruohoniemi et al. [1987], who employed a ray-tracing analysis and a velocity field cross-correlation technique between the Goose Bay HF radar and the Sondrestrom incoherent scatter facility for a 1500 km 1/2-hop path. It also confirms the results of Andrd et al. [1997], who performed a similar velocity field analysis to determine the relative accuracies of various HF radar frequencies over a i/2-hop path, again finding an accuracy of 15 km. Andr• et al. [1997] suggested an optimum assumed height for 1/2-hop propagation paths of 200-300 km, which is in accord with the results presented here.
For the 11/2-hop path over 1830 km an overestimate of the radar range of--100 km is deduced as a consequence of the group path of the HF rays exceeding that of the straight line propagation assumed in the range-finding algorithm. In the standard use of the range-finding algorithm, a height of 300-400 km is assumed to offset the expected difference between the group path and ground range. This altitude leads to a reduced range offset, 60 km. The results presented here suggest that an additional offset of-60 km (or an assumed height of 500 km) would improve the performance further for 11/2-hop backscatter.
The 21/2-hop path exhibits even more significant range errors, with the range-finding algorithm overestimating the length of the 1830 km path by 390 km. In contrast to the ll/2-hop path no simple adjustment of the assumed backscatter height can be employed to compensate for the range offset, with the adoption of an assumed target altitude of 500 km only reducing the range offset to 300 km. Two-and-one-half-hop paths are not observed in natural scatter, because of their low power, so this is not in practice a problem for standard radar operations. It does, however, suggest that care should be taken in the use of high-elevation-angle scatter. Baker and Greenwald [1988] demonstrated a relative range error of 120 km between 15 ø and >20 ø elevation angle backscatter, with ionospheric tilts thought to be responsible for the different propagation paths observed. The artificial backscatter data presented in Figures 2 and 3 are extremely consistent, suggesting that the range offsets determined here are highly systematic. No detectable variation is seen in the location of the artificial backscatter in the Hankasalmi field of view, over the 850 km, 1/2-hop path. A variability of only two 15 km range gates is seen in the 1830 km, l l/2-hop path from Pykkvibaer to Troms0. This stability in the measured range gates of the artificial scatter persists even when the location of naturally occurring ground backscatter varies by at least 20 range gates (300 km) during 4 hour runs of SP-UK-OUCH, indicating changes in the prevailing ionospheric conditions. This observation offers experimental confirmation of the modeling of Andrd et al. [1997], who suggested a group path change of <10 km due to a change in the altitude of the F region peak by 50 km. It also demonstrates that the accuracy in radar range is maintained to within 30 km for 11/2-hop paths.
Thus the accuracy in the determination of the location of the backscatter is only weakly controlled by variations in the ionosphere between the radar and target ionosphere. Under most conditions the use of a full ray tracing analysis based on ionosonde observations or on predictive models of the ionosphere is not required for the range accuracy needed for geophysical interpretation of HF radar data.

Summary
An evaluation of the absolute range finding accuracy of current routine analysis of the SuperDARN network of over-the-horizon HF radars has been performed, comparing ground range, calculated group path, and measured radar slant range of backscatter artificially excited at a known location by the EISCAT heating facility at Troms0. HF propagation over a 1/2-hop path, a 11/2-hop path, and a 21/2-hop path has been examined for the first time. The radar slant range and the calculated group paths are in excellent agreement for all three paths. The standard algorithm for backscatter ground range location is found to be accurate to within 16 km and 114 km for 1/2-hop and l l/2-hop backscatter, respectively, when using the true backscatter height, and these range offsets are extremely consistent. Using an assumed backscatter height of 200-300 km for 1/2-hop paths thus gives an accurate range determination, to within -15 km, as suggested by Andrd et al. [1997]. The standard assumption of 400 km height for far range backscatter reduces the error for 11/2-hop backscatter to 60 km, but the adoption of an additional range offset of 60 km (or the adoption of an assumed backscatter altitude of 500 km) seems desirable for 11/2-hop paths. Two-and-onehalf-hop paths, although not seen in practice, would introduce significant range errors, and suggest that highelevation-angle backscatter should be interpreted with caution.