Example of Fitting Technique

Figure 2 shows the LOS velocity data from all seven operational SuperDARN radars in the northern hemisphere during a standard 2 min scan from 1924 to 1926 UT on January 12, 2000. This period occurred before the Prince George radar was operational. The LOS data from each radar have been mapped into a grid of geomagnetic coordinates described by Ruohoniemi and Baker [1998]. Each grid cell containing data shows the average velocity for each radar contributing to the cell. The velocity magnitude is represented by the greylevel of the dot that marks the cell location and the direction is indicated by a tail on the dot which points in the direction of the observed flow. LOS Doppler measurements for this period are observed >60 $^\circ\Lambda$ and from $\sim$7 to 24 MLT, encompassing roughly 3/4 of the convection zone.

Figure 2: Line-of-sight (LOS) Doppler velocity data from seven SuperDARN HF radars in the northern hemisphere on January 12, 2000, 1924-1926 UT.

The LOS Doppler measurements can be used to construct a global solution of the electrostatic potential. Figure 3 shows fitted velocity vectors and potential contours derived from the LOS measurements shown in Figure 2 using the technique described by Ruohoniemi and Baker [1998] with two improvements described in the Appendix. The fitting of the potential was carried out to order 8 (L = 8) in the spherical harmonic expansion (see the Appendix for an explanation of the fitting order) and the APL model corresponding to IMF magnitude 6$\le$B_T$\le$12 nT and IMF orientation B_z-/B_y- was chosen to augment the LOS data.

Figure 3: Fitted velocity vectors and electrostatic potential contours from the LOS measurements in Figure 2 using the technique described by Ruohoniemi and Baker [1998] to order 8 with the APL model for IMF magnitude 6${\le}B_T$$\le$12 nT, IMF orientation B_z-/B_y-, and the improvements discussed in the Appendix.

Observations from a solar wind monitoring satellite, ACE, indicated that the IMF conditions impacting the magnetopause during this period were $\sim$6 nT with roughly equal B_z- and B_y- components. The fitted velocity vectors in Figure 3 describe a pattern consisting of two large-scale convection cells in the dawn and dusk sectors, which is typical of periods of southward IMF [Heppner and Maynard, 1987]. The moderate-to-large flow velocities, generally $\le$1 km/s with some areas >1 km/s, and significant potential variations, 27 kV across the dawn cell and 34 kV across the dusk cell, suggest that a moderate to strongly southward IMF condition exists at the dayside magnetopause. The effect of the observed IMF B_y- condition is evident in the strong (>1 km/s) duskward flow across the noon meridian near 78$^\circ\Lambda$ which is part of a sharp rotation of flows in the post noon sector [Heppner, 1972,Heelis, 1984,Greenwald et al., 1990]. Also, the larger and more circular dawn cell as compared to the more crescent shaped dusk cell suggest an IMF B_y- condition [Reiff and Burch, 1985,Crooker, 1979]. The pattern is quite similar to the DE model of Heppner and Maynard, [1987] for IMF B_y- conditions, particularly in the dayside.

While the features of the convection pattern for this period are consistent with the IMF 6$\le$B_T$\le$12 and B_z-/B_y- APL model, there are significant differences. Figure 4 shows greyscale shaded potential contours with dark dots marking grid cells that contain LOS measurements. The fitted pattern from Figure 3 is reproduced in Figure 4a for comparison with the statistical model data shown in Figure 4b.

Figure 4: Electrostatic potential contours for IMF magnitude 6 ${\le}B_T\!\!\!\le$12 nT and IMF orientation B_z-/B_y-, a) order 8 fitted solution from Figure 2, b) APL statistical model after Ruohoniemi and Greenwald [1996], and c) the residual potential of a) and b), $\Delta\Phi$. Note the different greyscale levels for c).

The convection patterns in Figures 4a and 4b are similar in the largest-scale features, the two-cell morphology, and $\Phi_{\sf PC}$. Potential variations in the dawn and dusk cells are 27 kV and -34 kV ( $\Phi_{\sf PC} =$ 61 kV), respectively, for the fitted patterns, and -33 kV and 28 kV ( $\Phi_{\sf PC} =$ 61 kV), respectively, for the statistical model data. Several interesting differences exist between these potential patterns. The largest difference in the patterns occurs in the dayside where the throat region, located in the prenoon sector of the statistical data, is rotated to the postnoon sector in the fitted solution. The resulting dawn cell in the fitted solution extends much further into the dusk region ($\sim$15 MLT) than the statistical model data predicts. In addition, the dusk cell of the fitted pattern has two regions of large negative potential that extend over a broader range of MLT than shown in the statistical pattern.

Figure 4c shows the residual potential which we define as the difference in the potential shown in Figures 4a and 4b, in this case the change from the statistical pattern to the fitted pattern. Note that the greyscale levels used in all the residual potential plots are different by a factor of two from those used in plot of the potential solutions to dramatize changes or lack thereof. The residual potential in Figure 4c shows that the largest differences between the two patterns occur in a region of the dayside between the MLTs where the throat is located in the two patterns, and the premidnight sector into which the dusk cell of the fitted pattern extends. The existence of large residuals ($\sim$35 kV) demonstrate that the LOS Doppler measurements determine the solution in these regions.

Smaller-scale features present in the fitted pattern (Figure 4a) but absent from the statistical model (Figure 4b) are due in part to the lower order (6) fit used by Ruohoniemi and Greenwald, [1996] in constructing the statistical patterns, and to the tendency of statistical constructions to supress finer-scale features.