A Neural Network Model Relating H at a Single Station to Dst
T. P. O’Brien and R. L. McPherron
Institute for Geophysics and Planetary Physics, 405 Hilgard, UCLA, Los Angeles, CA 90095-1567
The operational goal of real-time estimation of the Dst index from single-station H requires a good understanding
of how H depends on local time, storm conditions, and season of year. In this investigation artificial neural
networks are trained on several years of data for the San Juan magnetometer. One neural network produces H
given Dst, local time, day of year; the other additionally requires Solar Wind dynamic pressure and interplanetary
electric field. The neural networks illustrate the local time, seasonal, and storm modulation of the nearly linear
relationship between Dst and H. We present evidence that a seasonal offset may be present in the Dst index. We
also demonstrate that the partial ring current, as measured by the asymmetry index, persists, after the interplanetary
electric field has vanished, for larger values of Dst during northern winter, and that this asymmetry is linearly
proportional to Dst.
The Dst index is intended to be a direct measure of the symmetric ring current [Chapman and Bartels, 1962; Knecht
and Shuman, 1985; Lincoln, 1967; Rostoker, 1972]. It is calculated from several (4 to 6) ground stations by
removing the quiet day variation from the H (North) component of the magnetic field at the Earth’s surface current
[Iyemori et al., 1992; Sugiura, 1964; Sugiura and Kamei, 1991]. The deviation from the quiet day at a single station
is referred to as H. Dst is calculated as a weighted arithmetic average of several H measurements. The asymmetry
index, ASY, is intended to measure the magnitude of the partial ring current, and is defined as the range of H
values measured around the Earth [Crooker and Siscoe, 1971, Clauer et al. 1983, Kawasaki and Akasofu, 1971]. By
its very definition, Dst depends on a particular H in a linear fashion; ASY has no such inherent relation to the
magnitude of H or Dst. Figure 1 suggests that in this time interval there is a direct relation between D st and ASY.
We will show that in an average sense ASY does indeed vary directly with Dst.
Since models of the magnetosphere often require Dst as an input, the real-time specification of Dst is an important
operational goal. One method for estimating Dst in real time is the use of a single H rather than a global average.
This simple estimate can be quiet good. However, the relationship between H and Dst depends strongly on local
time and also depends on season, storm phase, and even the magnitude of Dst. Although our primary interest is
estimating Dst from H at a single station, we have built models of H rather than Dst, because such models tell us
directly about the local current systems that give rise to differences between H and Dst.
We have used hourly data from the OMNI data set in combination with USGS magnetometer data for the years
1979 and 1985-1992. The models we have built are single hidden layer, feed forward, artificial neural networks,
trained using a combination of Newton’s method and gradient descent. The final model for each combination of
inputs was chosen from a large pool of competing models based on out of sample performance. Models for both
Guam and San Juan were built, but the San Juan (SJG) models were significantly better, and have been used
exclusively. Two different models were generated for San Juan. Model SJGa describes H as a function of local
time (lt), day of year (DOY), and Dst; model SJGb describes H as a function of local time, day of year, Dst, Solar
Wind dynamic pressure (Psw), and interplanetary
electric field (VBs). The out of sample rms error for
SJGa is 11.2 nT, for SJGb 10.5 nT. Throughout this
discussion, Dst, H, and ASY will be presented in
nT, Psw in nPa, and VBs in mV/m.
After training the networks on real data, we fed them
artificial data so that we could isolate interesting
behavior. In particular, we tend to vary only one of
the inputs (e.g. local time) while holding the others
fixed. This allows us to get a clear idea of how one
particular parameter effects the system. Although it is Fig. 1. The variations in Dst and ASY are correlated in
physically impossible for Dst to remain constant for a time and magnitude. The substorm activity in the first
day while the Earth rotates beneath the current disturbed period seems to prevent Dst from recovering.
systems in the magnetosphere, our empirical model In the second period, the recovery is more rapid.
allows us to simulate this situation. Since we can
arbitrarily specify the local time we are interested in, we can, in effect, have San Juan at all longitudes
simultaneously. We are not making any dynamic simulations, but merely varying parameters that we typically
associate with time which are, in fact, spatial. That is, local time is merely a measure of the spatial location of the
station relative to the Earth-Sun line, and season is just a measure of the position of the Earth in its orbit, and
consequently, the orientation of its rotation axis to the Solar equator.
First, we will investigate the seasonal effects in the H-Dst mapping. We will show that the offset in the best linear
fit to the neural network output for Dst below –40 nT varies in a regular way with season. We will also show that
the variation in the slope of this relation with season is less pronounced. We choose to make the linear fit to Dst  40 nT because the H-Dst relationship is extremely linear in this regime. Although the neural network produces H
as a function of Dst, we have inverted the relation and created least-squared-error linear fits of Dst as a function of
H. In Figure 2 left, the horizontal contour lines show us that the seasonal dependence of the slope is insignificant,
except at 1800 hours, where the change is limited to the range 0.7-0.8. In contrast the local time variation of the
slope is much larger ranging between 0.8-1.4 late in the year. Local time and seasonal changes in the offset plotted
in the right panel are comparable covering a range –10 to +15 nT. This offset is not large compared to the Dst index
during a large storm, but it is large enough to seriously effect estimates of the recovery rate late in a storm.
There are two possible causes of this dependence: incorrect quiet days and genuine seasonal dependence. The first
could arise from the standard method used in calculating the quiet days for the Dst index. The H values are the
hourly deviations from the quiet day field of the Earth. The Dst index is the weighted average of these H values.
We use the standard Dst index, but calculate our own hourly H values. The standard technique and the technique
we employ for calculating the quiet day are essentially the same, but we use a longer time window in defining the
secular variation of the Earth’s magnetic field, and we use a slightly different technique to remove storm effects.
While the differences in technique could give rise to some systematic difference in our H and those used to
calculate the standard Dst, there is no reason to suggest that the differences between these two techniques would
give rise to a coherent seasonal variation. The second possible cause of the seasonal dependence could be the result
of some interplay between the geomagnetic coordinate system and the day-night asymmetry in the ionospheric
conductivity, which is tied to the geographic coordinates. This could be confirmed by building a similar H model
for a Southern Hemisphere station, but has not been done at this time.
The next issue we will address is the disappearance of the partial ring current in the storm recovery phase. It is
generally believed that that the partial ring current always vanishes when the interplanetary magnetic field Bz turns
northward, or, equivalently, VBs = 0 [see examples in Kawasaki and Akasofu, 1971]. Because we can hold all the
Fig. 2. For the slope of the linear Dst-H
relationship, it is clear that the local time
dependence dominates. For the offset, however, the
seasonal variation is significant, weighing in at
nearly 10 nT peak to peak for some local times.
Fig. 3. In northern summer (DOY 151), the
asymmetry drops below 20 nT when VBs shuts off. In
the winter (DOY 331), it persists at more than 40 nT
until Dst recovers to –40 nT.
other variables constant and only change the local time, we can simulate ASY as the range of H we get out of our
model if we apply it to 24 hours of local time while holding all other parameters fixed. In Figure 3, we have done
this for several values of VBs, several values of Dst, and 2 days of the year. Surprisingly, we find that during
northern winter, the simulated ASY index can be quite large for VBs = 0. For example at Dst = -40 nT, the ASY is
about 40 nT at DOY 331 (late November) for VBs = 0. However, for the same conditions on DOY 151 (late May),
the simulated ASY index is less than 20 nT. This suggests that somehow, during northern winter, the partial ring
current does not decay soon after the IMF Bz turns northward, but that during northern summer the decay is more
In Figure 3, it is also apparent that the asymmetry determined by the neural network depends strongly on the
magnitude of Dst. Figure 4 shows that the H values at different local times spread with stronger Dst. This spread is
the asymmetry, and its dependence on Dst is linear for both the main and recovery phases. A linear dependence of
the ASY is essential to making a good model of Dst given only one H. Figure 4 also demonstrates that the neural
network model is fitting a meaningful difference in the behavior at different local times. This result was so
surprising we checked it by plotting the WDC-C2 ASY-H versus SYM-H at one-minute resolution. There is an
obvious linear dependence between the two with a correlation coefficient ~ 0.7
The persistence of ASY beyond the time when VBs shuts off can most likely be explained by one of two
mechanisms. First, it is possible that the asymmetry persists because of a neutral flywheel effect where the neutrals
provide an inertia, which keeps the partial ring current system going after the driver has shut off. Second, it is
possible that a local ionospheric current is actually contaminating the H measurements, and that this current is
related directly to the storm intensity, and therefore Dst. The latter would be consistent with the observed seasonal
variation in the less accurate Guam models.
We have built a neural network model of H from Dst, local time, day of year, and Solar Wind conditions. With this
model, we have shown that a significant seasonal offset exists in the linear relation between H and Dst, which
SJGb vs Dst (Psw = 3) (VB s = 3) (DOY = 331)
SJGb vs Dst (Psw = 3) (VB s = 0) (DOY = 331)
+,-. lt = 1800
H = 1.22*Dst + -1.78
o,-- lt = 0600
H = 0.84*Dst + -4.08
+,-. lt = 1800
H = 1.21*Dst + -17.49
 H (nT)
 H (nT)
o,-- lt = 0600
H = 0.72*Dst + 1.64
Fig. 4. The H-Dst relation is shown for recovery phase (VBs = 0) and main phase (VBs = 3). The dashed and
dashed-dotted line represent neural network fits, and the ‘o’ and ‘+’ indicate real data at approximately the same
values of Dst, VBs, etc., at dawn and dusk, respectively. The H-Dst relation is linear for Dst below -40 nT. The
spread (ASY) grows linearly below this point.
suggests that Dst itself may have a seasonal offset. We have also shown the partial ring current, as measured by the
ASY index, does not shut off immediately when VBs drops to zero, but, at least in parts of the year, persists until
Dst itself decays. The first of these results suggests either an error in the calculation of the quiet day or a seasonally
dependent storm-time feature of the ionosphere. The second result suggests either a neutral flywheel providing
inertia to the partial ring current or, again, a seasonally dependent storm-time feature of the ionosphere. The
possibility of a seasonally dependent storm-time feature of the ionosphere could be tested by the investigation of
the H-Dst relationship for a Southern Hemisphere ground station.
We would like to thank the USGS and NGDC and WDC-C2 for providing the data that we have used in this
analysis. This work is supported by NSF grant ATM 96-13667
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