Starting in fall 2006, we have added the ability for the user to obtain the calculated cross polar cap potential from a polar pass of a DMSP. As shown in the figure on the left below, once you have selected a DMSP orbit, you are given the option of obtaining the potential from either the northern or southern polar pass.

If you click on the link for the northern hemisphere pass, you get the figure on the right above which shows (from top to bottom) the vertical and horizontal crosstrack along with the potential plot for this polar pass. The magnitude and location of the maximum and minimum potential along this pass are printed at the bottom of the figure. The calculations and the figure here are generated by a program called NADIAWEB.

The NADIAWEB procedure on this website is a limited demonstration project designed to produce a first-order (though not necessarily definitive) calculation of the potential drop over the polar cap observed during a given pass of the DMSP spacecraft. It is based on the procedure NADIA developed by UTD for the Air Force to provide estimates of the polar cap potential drop for space weather environmental monitoring and modeling. NADIAWEB is a simplified version and it works in the following manner.

The potential in the ionosphere is determined by using the frozen in flux equation

**E = -(v x B)**

to calculate the electric field at the spacecraft's location and then integrating
along the spacecraft’s path. For the DMSP data provided on this website,
the crosstrack ion flows, both horizontal (Vy) and vertical (Vz) components,
are averaged into four-second bins. NADIAWEB takes each four-second value of
these flows along with the vertical and horizontal magnetic field at that location
to calculate the electric field parallel to the spacecraft’s track (Ex).
Thus

**Ex = -Vy Bz + Vz By**

The magnetic field data comes from the IGRF magnetic field model. Once the electric
field is calculated, it is multiplied by the distance the spacecraft traveled
during that four-second period (~29 km) to determine the potential change along
that segment of the path.

The calculation starts at the first four-second data point past 50º magnetic latitude as the spacecraft heads poleward. The program keeps a running sum of the potentials for each four-second step until the spacecraft passes the 50º magnetic latitude on the other side of the pole. We chose 50º magnetic latitude as our endpoints because for the majority of the cases these endpoints are far enough equatorward that the ion flows are essentially zero and we can safely assume that the potential is zero at both points. (There are exceptions where the endpoints should be further equatorward, and that will be discussed later.) In an ideal world the flow pattern would remain completely stable during the time of the pass and the running total of the potential would return to zero by the time the spacecraft reached the endpoint. In reality the convection pattern (and hence the potential distribution pattern) is continually changing as the drivers of the flow pattern (the IMF, magnetospheric-ionospheric interactions, etc.) are continually changing. Even when the drivers are relatively steady there are still some variations in the flow patterns during the 15-25 minutes it takes a DMSP to traverse the polar region. Thus the running sum of the potential never returns exactly to zero at the stopping endpoint, not even during periods when the IMF and other drivers are steady.

The final potential at the stopping endpoint is referred to as the offset, that is, the offset is the difference between the potential at the end of the calculation and zero. Obviously, the magnitude of the offset gives a rough indication of the variation of the convection pattern during the spacecraft’s polar pass. Our “rule of thumb” is that we have a high confidence level in any pass where the offset is less than 25% of the total potential difference calculated along this pass. In other words the offset < 0.25 * (PHI_corrected maximum – PHI_corrected minimum). Passes where the offset exceeds the 25% level are treated on a case-by-case basis. In order to normalize the potential and force both ends of the pass to zero potential we do a linear correction the entire array of potential values where we remove some fraction of the offset based on the position of the array point from the starting point. In other words, assume that there are N data points along the path from the starting endpoint (point 1) to the stopping endpoint (point N) and the running calculation of the potential at the stopping endpoint is P, thus the offset is P. We then take the array of calculated potential values (PHI_calculated) and make a new array of corrected potential values (PHI_corrected) using the formula

PHI_corrected(i) = PHI_calculated(i) – {[(i-1)/(N-1)] * P}

Note that what is plotted on the figure on the website is the corrected potential, and the values for the potential maximum and minimum given on the plot are taken from corrected potentials, not the original calculated potentials.

Now that the basics of the calculations have been explained, we can explore some of the more detailed questions about the analysis and its use for research purposes.

**Q.** Is the total potential drop given on the plot the same
as the cross polar cap potential?

No. The total potential drop given on the plot (PHI_corrected maximum –
PHI_corrected minimum) is just the potential drop seen along the spacecraft’s
track through the potential distribution. You can think about it as a cross
section through the potential distribution pattern.

In the
figure here we take a typical two-cell pattern from the Weimer model (taken
from Weimer D. R., *J. Geophys. Res., 106,* p. 407, 2001) and draw a
typical pass for F13 (red) and a typical pass for F15 (blue). Assuming this
pattern was steady during the time of the two spacecraft passes, we note several
things. First, neither one passed over the location of the true potential maximum
and minimum of this pattern (shown as the tiny cross and diamond on the figure).
Thus both report a potential drop that is less than the true cross polar cap
potential (PHI_true maximum – PHI_true minimum). Second, the path for
F13 goes closer to the true potential maximum and minimum than the F15 path
does. Thus the observed potential seen by F13 is larger than the observed potential
seen by F15. So the general rule is that 99% of the time the F13 potential (from
the near dawn-dusk orientation) is always larger than the potential observed
by a similtaneous F15 pass (or any other spacecraft in the evening-morning orientation).

So while the observed potential from DMSP is not the same as the true polar cap potential drop, it does serve as lower bound on the true polar cap potential drop. Further, you can use some of the potential drop data from F13as a proxy for the true polar cap potential drop.

**Q.** So how close did a given pass get to the true maximum and
minimum potential and how do I use the F13 observation as a proxy for the true
cross polar cap potential drop?

Good questions, and we have spent over 15 years trying to get good answers,
but unfortunately we aren’t there yet. The problem is this: without knowing
for certain what the true potential distribution pattern is during a pass, we
cannot make a truly accurate estimate of how close the spacecraft’s track
got to the true absolute maximum and minimum and thus what sort of correction
can be made to the observed potential drop to get the true total potential drop.
The user is free to take whatever model patterns they have confidence in and
use those to estimate the true potential drop based on the DMSP’s observations.

**Q.** What are skimmers and why should I be concerned about them?

The DMSP spacecraft are in polar orbits that precess one complete 360 degree
turn per year. The result is that the plane of their orbit remains fixed with
respect to the local time below their orbits. However, the Earth’s magnetic
dipole is tilted with respect to its spin axis and thus the dipole axis rocks
back and forth once per day relative to the spacecraft’s orbital plane.
Because the magnetic coordinate system is tied to the magnetic dipole that means
it too rocks back and forth once a day underneath the spacecraft’s orbital
plane. Thus if we plot one day’s worth of spacecraft tracks in the magnetic
latitude / magnetic local time coordinate system as seen in the two plots below
(one for the dawn-dusk (F13) orientation and one for the evening-morning (F15)
orientation) the tracks “wander” back and forth and form a band
of passes in this system. (Note that the dashed circles are there to indicate
the range of a nominally sized polar cap.)

This is useful for scientific studies since it gives us a swath of possible areas of the potential patterns to study. But it is also problematic since it means that part of the time, the DMSP pass misses the potential distribution pattern altogether. We refer to such passes as “skimmers” and must discard most of them. Generally DMSP passes which occur between roughly 0200 and 0800 UT (regardless of which spacecraft) miss most of the pattern. When the polar cap is extremely contracted, then entire path is outside of the potential distribution pattern and no flow is observed at all. The F13 passes below show such cases, and obviously the results of the NADIAWEB procedure here would report an observed potential drop of essentially zero.

On the other hand, during storm times the polar cap expands equatorward and a pass which would have been a skimmer now cuts through a significant section of ionospheric flow. Below are examples from a few days later which cover the same path as the skimmers shown above, but now observe a potential drop of 110 kV in the north and 52.38 kV in the south.

But that takes us back to the question just before. Since this is an expanded and highly distended pattern (in fact, it occurs during the 31 March 2001 superstorm), what was the true total potential drop? Without a reliable model of the pattern to use, we cannot make a fully reliable estimate of true total potential drop. All we can say for certain is that the true total potential drop must be something in excess of 110 kV during the time of the northern polar pass. So in general any pass which occurs between about 0200 and 0800 UT should be ignored except for cases when the polar cap has expanded, and even those should be used with caution.

**Q.** Can I get the potential calculations using different starting
and stopping points?

As explained in the preceding question, this project was of limited scope and
as such this current version is a “one-size-fits-all” routine. Users
are welcome to take the flow data from the website and do their own calculations
with whatever endpoints they choose.

**Q.** I would like to examine the set of potentials for a large
period of time rather than on a pass by pass basis. Can I get the data for this
period directly?

Unfortunately, no. Because of the limitations and uncertainties in the results
(as explained above) we realized long ago that simply running all the data through
the NADIA routine without examining the results tended to produce a significant
percentage of bad passes within the dataset, and it was not easily apparent
which passes were the bad ones. Producing such a large database would indeed
be quite useful, but sadly my time and funding for such work are extremely limited.
Instead we have opted for producing datasets for short periods where there is
a strong scientific interest, such as particular storms and campaign periods.
For those I have been able to run the NADIA procedure, check each pass by eye
and, if necessary, rerun certain passes to improve the quality of the results
and/or discard particular passes if they are unusable. Thus the data from these
periods are verified as quality results and can be used in publication. If you
have a specific time period you are interested in, please contact Dr.
Marc Hairston about it and I will see if I either have the data already
processed or, if possible, I can produce it for you.

**Q**. Why is there no quality flag on these potential calculations?

We agree there should be some indication of quality for each pass. However,
as you can tell from the questions above, a single quality flag for each pass
is not possible. Ideally there should be a flag to tell how close to the magnetic
pole a given pass got (thus separating skimmers from non-skimmer passes), a
flag to indicate the quality of the pass with respect to the offset, a flag
to warn of the quality of the flow data being used in the calculations, and
so forth. Again, this was a first-order demonstration project and we did not
have the time or funding to develop such quality flags. We would prefer that
the users do what we do: look at the passes on a case by base basis and use
their eyes and experience to determine which are the ones that are suitable
for research use.

**Q.** Will there be any upgrades or improvements to this data
product?

We certainly hope that someday we will have the chance to improve this site
as described above and provide a more robust and complete dataset for that community.
If you find our site helpful in you research, please write
and let us know. Also if you have any specific requests or suggestions for
improvements, please write and tell us.
We reserve the right to include any such letters and emails in future funding
proposals as evidence for the need of upgrading this site.

*Last update December 2006*