Two modifications have been made to the mapping technique of
*Ruohoniemi and Baker* [1998].
The fitted convection patterns now produced by the
APL group, including those presented in this paper, incorporate these
modifications unless otherwise specified. Here we describe the changes and
the reasons for adopting them.

The first concerns the specification of the equatorward boundary of the
convection zone. In
*Ruohoniemi and Baker* [1998]
this boundary, referred to here
as
,
was taken to be a circle of constant invariant
latitude. We use the value of
at midnight MLT,
,
to identify this circular boundary. The actual value of
was either set to a constant (usually 60)
or varied
from scan to scan to accommodate the varying size of the convection zone.
The equatorward boundary was specified as a circle in the derivation of the
statistical convection model of
*Ruohoniemi and Greenwald* [1996]
and this has been the
accepted convention in studies of this kind. However, we have found that the
SuperDARN data invariably indicate that the convection boundary is located
at higher latitudes on the dayside than on the nightside. The definition of
the boundary used in the fitting should reflect this character. As a practical
matter, we have found that using a circular boundary that accommodates the
flow on the nightside allows the flow on the dayside to extend to
unrealistically low latitudes.

The solution is to introduce an MLT dependence in the specification of the
boundary latitude. We have explored several options for the boundary,
including a global shifting of the coordinate flows so that the convection
pattern is centered on a point 4
equatorward of the magnetic pole
towards the nightside. In the end, we adopted a solution based on the work
of
*Heppner and Maynard* [1987].
These authors studied the dependence of the latitude
of the boundary on MLT and geomagnetic activity level using electric field
measurements from the DE satellite. Their Figure 10 indicates that this
boundary, referred to here as
,
has a similar shape
through all activity levels, but expands and contracts. Figure A1
shows several examples of
boundaries for varying
sizes of the convection zone.
The boundary is almost circular on the nightside but rises steeply
in latitude after crossing the dawn and dusk meridians, reaching a highest
latitude near the 11 MLT meridian.We characterize the size of the boundary by referring to the latitude of its
intercept with the midnight MLT meridian,
.
For a given
scan, a value of
is determined such that all the
significant convection observations are contained within the boundary. Some
freedom remains in choosing the limit to what defines significant flow, but
100 m/s is a typical value.

The spherical harmonic fitting continues to be performed over the entire region poleward of , where numerically . Grid cells in the crescent-shaped region on the dayside located between the latitude of and (see Figure A1) are padded with zero velocity vectors. Our implementation of allows some small, but non-zero, potential contours to exist equatorward of the HMB boundary (see for example, Figure 3). The resulting patterns more closely reproduce the character of convection at lower latitudes.

A consequence of using the lower latitude convection boundary defined by
is a minor difference in the statistical model data
used in the fitting.
A careful inspection of Figure
4b reveals subtle differences from the statistical model
of
*Ruohoniemi and Greenwald* [1996].
The patterns derived by of
*Ruohoniemi and Greenwald* [1996]
were
fitted using a circular lower latitude convection boundary ()
corresponding to 60.
When the fitting technique of
*Ruohoniemi and Baker* [1998].
is used,
is determined by the extent of
the LOS observations and the statistical model is scaled accordingly, thus
modifying the pattern somewhat.

The second improvement over the original fitting technique described by
*Ruohoniemi and Baker* [1998]
is a weighting scheme which reduces the tendency for
the statistical model data to dominate the global solution of
at higher
order fittings. By the order of the fitting we refer back to the expansion of
used by
*Ruohoniemi and Baker* [1998]
in terms of spherical harmonic functions
of order *L* and degree *M*. The values of *L* and *M* determine the resulting
spatial filtering of the velocity data.

The original technique of
*Ruohoniemi and Baker* [1998]
weighted the statistical
model data relative to the LOS velocity data without regard to the order of
the fitting. The weight assigned to a velocity value from the model was set
to the geometric mean of the radar velocity measurements. Fittings at higher
order required progressively more statistical model vectors ()
in
order to constrain the behavior of the greater number of terms in the
spherical harmonic expansion over the regions of no radar observations. A
fixed weighting scheme, therefore, causes the solution to be more influenced
by the statistical data at higher orders. The consequence was an undesirable
compromise in selecting the order of the fitting at a level high enough to
adequately reproduce finer-scaled features in areas where data were present,
but low enough so the statistical model didn't dominate the solution.

An improvement has been made whereby the weight of the statistical data is
adjusted according to the order of the fitting. The result is that the degree
to which the model vectors affect the solution is less dependent on the order
of the fit. In essence, the weight defined above as the geometric mean of the
radar velocity measurements is reduced by the factor 4^{2}/*L*^{2}. The effect is
to roughly equalize the contribution of the statistical model to the fitting
solution for
(fittings of order *L* < 4 are not considered
useful). The cost associated with this progressive de-weighting might be the
emergence of erratic behavior in the patterns over the areas of no radar
observations. However, we have found the results to be quite satisfactory with
these settings, at least up to fittings of order *L* = 10.
Higher order fittings can now be used to reproduce smaller-scale features
described by the LOS measurements and the statistical model data simply
guide the solution realistically in regions where no radar data are available.

Figure A2 shows residual potentials for varying orders of fit
(*L* = 4,6,8,10 from top to bottom) for both the fixed and varied (left and
right column) weighting schemes. Inspection of the residuals in the left
column of Figure A2 shows the problem of using a high order fit
with the fixed weighting scheme of
*Ruohoniemi and Baker* [1998].
Increasingly large
(>12 kV) residual contours are evident as the order is increased. In this
example, the increasing fitting order is inadvertently causing the global
solution to converge on the solution defined by the statistical model.

The right column of Figure A2 reveals a slight trend toward larger residuals with increasing fitting order, implying that the statistical data is influencing the solution to a greater extent in the higher order fittings. However, in regions where LOS velocity data are present (e.g., 15-18 MLT and 75-85 ), the maximum deviation in the residual is 3 kV. Such minor change in the residual contours from order 4 to 10 demonstrates that the improved weighting scheme allows the fitting technique to be virtually independent of order in regions were velocity data are present. Larger residual deviations (up to 10 kV) are seen in the postmidnight-dawn region where no velocity measurements exist. Such a trend is expected at higher orders. The additional statistical data used in the higher order fittings causes the differences between model patterns to become more evident in locations where no data exists.

Contrasting the right column in Figure A2 with the left column shows the marked improvement the adjusted weighting scheme has on reducing the impact of the statistical model at higher orders. Smaller-scale features present in the velocity data can now be reproduced in the global patterns without significant influence from the statistical model data.