Sensitivity to Model Choices

The purpose of this study is to demonstrate that during periods when SuperDARN velocity measurements are available over a large portion of the convection zone the particular choice of statistical model has little effect on the resulting global potential pattern. By way of example, we perform the fitting technique using the APL model statistical patterns for IMF magnitude 6$\le$B_T$\le$12 nT and each of the eight IMF orientations (Figure 7, [Ruohoniemi and Greenwald, 1996]). The patterns are then compared to the solution obtained using the reference model (Figures 3 and 4a), and the differences are attributed to the statistical models used in the fittings.

Figure 5 shows residual potential contours for fittings using the APL model for the eight different IMF orientations illustrated compared with the reference solution. As expected, the largest change in potential is evident in the comparision with the IMF B_z+ model. The APL statistical model for this IMF orientation and magnitude range is most different from the B_z-/B_y- model used in the fitting. The dawn cell for the B_z+ model is virtually nonexistent and contains only 3 kV of potential variation, while the dusk cell is very contracted and contains 12 kV, resulting in $\Phi_{\sf PC}$ = 15 kV, as compared to $\Phi_{\sf PC}$ = 61 kV for the reference model (Figures 3 and 4a). Any change in the global solution due to the statistical model data should be obvious in the comparision between the fittings using these two models.

Figure 5: Contour maps showing the residual electrostatic potential for APL statistical models corresponding the IMF orientation indicated by the location of the plot. The reference pattern is computed using the APL model corresponding to IMF orientation B_z-/B_y-, shown in Figures 3 and 4a.

Figure 5b shows a region in the postmidnight/dawn sector where the residual potential is the largest. The region is located over northern Siberia and is characterized by only a few, isolated LOS Doppler measurements from the furthest range gates of the radar network. The maximum residual potential in this region is $\sim$11 kV. While it is true that the model vectors influence the solution in this area, the effect is small, localized, and entirely expected in a region with only statistical data available to define the solution.

The residual potential in regions where velocity measurements exist is only a few kV or less and limited to a small region in the postnoon/dusk sector, which is the throat region and has structure that the model patterns cannot reproduce. The global solution is therefore well-defined by the measurements in this instance. Only nominal variations in the patterns exist at meso-scale and smaller orders mainly in the regions where the drastically different statistical models are used to guide the solution. The residual potential plots in Figure 5a, 5c-h, using the other statistical models, show even less deviation from the reference pattern.

The APL statistical convection patterns, as defined by Ruohoniemi and Greenwald, [1996], are also sorted by three categories of IMF magnitude: 0$\le$B_T$\le$4 nT, 4$\le$B_T$\le$6 nT, and 6$\le$B_T$\le$12 nT. Residual potential contours (not shown) resulting from the comparison of the reference solution (Figures 3 and 4a) and the fitted pattern using the same IMF orientation but IMF magnitude 0$\le$B_T$\le$4 nT, show only minor variations of less than a few kV in potential present only in the largest region that is lacking velocity measurements. The general features of the APL statistical models tend to scale with the IMF magnitude so the effect of changing the model based on IMF magnitude alone are minor and limited to regions containing only statistical data.

While there is minor meso-scale variation of the convection pattern due to different model selection, the total potential variation across the polar cap, $\Phi_{\sf PC}$, is remarkably constant regardless of the chosen statistical model. The range of $\Phi_{\sf PC}$ for the fitted patterns is only 56 kV to 61 kV, while $\Phi_{\sf PC}$ varies in the statistical patterns from 15 kV to 77 kV. Clearly, the LOS measurements during this period adequately constrain the determination of $\Phi_{\sf PC}$.

It is instructive to consider the reason for the insensitivity of the $\Phi_{\sf PC}$ determination to the selection of statistical model data. The area of observations apparently encompass the positions of the potential extrema and the flows in the intervening region. Thus, the total potential variation is fixed by the observation of convection velocity through the polar cap. This important characteristic is reproduced by the fitting regardless of the nature of the sparse model data used to constrain the global solution. We can anticipate making definitive estimates of $\Phi_{\sf PC}$ when this condition prevails. Most often this will be realized when observations extend across much of the dayside region, as in this case.

We demonstrate how incompleteness in this coverage introduces a measure of ambiguity in the solution. We repeat the fitting but exclude Goose Bay data, which bridged an important portion of the postnoon convection pattern (see Figure 3). The larger dots in Figure 6b represent the grid cells at which the Goose Bay radar contributes LOS measurements. These cells occur between the dawn and dusk cells just poleward of the throat region where large flow velocities are seen across the dawn-dusk meridian in Figure 3.

Figure 6: a) Electrostatic potential contour map derived using the same IMF model as Figure 4a but without using the LOS data from the Goose Bay radar, and the resulting residual potential from Figure 4a and Figure 6a). Larger dots represent grid cells where the Goose Bay radar contributes data.

Figure 6a shows the potential pattern that results when these critical measurements are missing. Large residual potentials ($\sim$20 kV) are shown in Figure 6b resulting from comparing the pattern achieved using all the LOS data (Figure 4a) and that obtained without the Goose Bay data (Figure 6a). The potential across both cells is dramatically reduced without the Goose Bay data, resulting in $\Phi_{\sf PC} =$ 43 kV, far less than that obtained by fitting all the radar data with any choice of statistical model. The sensitivity to the selection of statistical model data is a consequence of the insufficiency of the measurements (without the Goose Bay radar) to fix $\Phi_{\sf PC}$.