A Neural Network Model Relating H at a Single Station to D

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A Neural Network Model Relating


a琠a⁓楮杬e⁓ a瑩潮⁴漠
D
st



T. P. O’Brien

and
R. L. McPherron


Institute for Geophysics and Planetary Physics, 405 Hilgard, UCLA, Los Angeles, CA 90095
-
1567




ABSTRACT


The operational goal of real
-
time estimation of t
he D
st

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 J
uan magnetometer. On
e neural network produces

H
given D
st
, 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 modulatio
n of the nearly line
ar
relationship between D
st

and

H. We present evidence that a
seasonal offset
may be present
in the D
st

index. We
also demonstrate that the partial ring current, as measured by the asymmetry index, persists, after the interplanetary
el
ectric field ha
s vanished, for larger values of D
st

during northern winter, and that this asymmetry is linearly
proportional to D
st
.



INTRODUCTION


The D
st

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
. D
st

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 v
ery definition, D
st

depends on a particular

H

in a linear fashion; ASY has no such inherent relation to the
magnitude of

H
or D
st
. Figure 1 suggests that in this time interval there is a direct relation between D
st

and ASY.
We will show that in an averag
e sense ASY does indeed vary directly with D
st
.


Since models of the magnetosphere often require D
st

as an input, the real
-
time specification of D
st

is an important
operational goal. One method for estimating D
st

in real time is the use of a single

H rath
er than a global average.
This simple estimate

can be quiet good. However, the relationship between

H and D
st

depends strongly on local
time and also depends on season, storm phase, and even the magnitude of D
st
.
Although our
primary interest

is
estimat
ing

Dst from


H

at

a single station, w
e have bui
lt models of

H rather than D
st
, because such models tell us
directly about the local current systems that give rise to differences between

H and D
st
.


We have used hourly data from the OMNI data set in combination with USGS magnetometer data for the year
s
1979 and 1985
-
1992. The model
s 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 po
ol 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
d
escribes


H as a function of local
time (
lt
), day of year (DOY), and D
st
;
model
SJGb
describes


H as a function of local time, day of year, D
st
, Solar
Wind dynamic pressure (P
sw
), and interplanetary
electric field (VB
s
). The out of sample rms error for
SJG
a is 11.2 nT, for
SJGb 10.5 nT. Throughout this
discussion, D
st
,

H, and ASY will be presented in
nT, P
sw

in nPa, and VB
s

in mV/m.


After training the networks on real data, we fed them
artificial data so that we could isolate interesting
behavior. In pa
rticular, we tend t
o 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
physically impossible for D
st

to remain constant for a
day while the Earth rotates beneath the current
systems in the magnetosphere, our empirical model
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 Eart
h
-
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.



SEASONAL EFFECTS ON THE MAPPING OF

H TO
D
st


First, we will investigate the seasonal
effects

in the


H
-
D
st

mapping
. We will
show that

the offset in the best linear
fit to the neural network output for D
st

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 pronou
nced
. We choose
to make
the linear fit to D
st



-
40 nT because the

H
-
D
st

relationship is extremely linear in this regime. Although the neural network produces

H
as a function of D
st
, we have
inverted the relation and
created least
-
squared
-
error linear fi
ts of D
st

as a function of

H. In Figure 2

left
, the horizontal contour lines show us that the sea
sonal 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 large
r

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. Th
is offset is not large compared to the D
st

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 calc
ulating the quiet days for the D
st

index.

The

H

values are
the
hou
r
l
y
d
eviations from the quiet day field of the Earth
. The

D
st

index
is the weighted average of these

H values
.

We use the standard D
st

index
, but calculate our own
hourly

H

values
.

The

st
andard 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
D
st
,
t
here

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 depende
n
ce
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 coordinate
s. This could be confirmed by building a similar

H model
for a Southern Hemisphere station, but has not been done at this time.



THE
DISAPPEARANCE OF THE
PARTIAL RING CURRENT
DURING STORM RECOVERY


The next issue we will address is the disappearance of t
he partial ring current in the storm recovery phase. It is
generally believed that tha
t the partial ring current
always
vanishes when the interplanetary magnetic field B
z

turns
northward, or, equivalently, VB
s
= 0
[
see examples in
Kawasaki

and Akasofu
, 197
1
]
. Because

we can hold all the


Fig. 1. The variations in D
st

and ASY are correlated in
time and magnitude. The substorm activity in the first
disturbed period seems to prevent D
st

from recovering.
In the second period, the re
covery is more rapid.


Fig. 2. For the slope of the linear D
st
-

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 pea
k to peak f
or some local times.



Fig. 3. In northern summer (DOY 151), the
asymmetry drops below 20 nT when VB
s

shuts off. In
the winter (DOY 331), it persists at more than 40 nT
until D
st

recovers to

40 nT.

other variables constant and only change the local time, we can simulate ASY as the range of

H we g
et 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 VB
s
, several values of D
st
, and 2 days of the year. Surprisingly, we find that during
northern winter, the simulated ASY index can be quite large for VB
s

= 0. For example at D
st

=
-
40 nT, the ASY is
about 40 nT at DOY 331 (l
ate November) for VB
s

= 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 B
z

turns northward
, but that during northern summer the decay is more
immediate.


In Figure 3, it is also apparent that the asymmetry
determined by the neural network
depends strongly on the
magnitude of D
st
. Figure 4 shows that the

H values at different local times spr
ead with stronger D
st
. This spread is
the asymmetry, and its dependence on D
st

is linear for both the main and recovery phases. A linear dependence of
the ASY is essential to making a good model of D
st

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 A
SY
-
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 VB
s

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 curren
t is actually contaminating the

H measurements, and that this current is
related directly
to the storm intensity, and therefore D
st
. The latter would be consistent with the observed seasonal
variation in the less accurate Guam models.




DISCUSSION


We have

built a neural network model of

H from D
st
, local time, day of year, and Solar Wind con
ditions. With this
model, we have shown that a
significant
seasonal offset exists in the linear relation between

H and D
st
, which


Fig.
4
. The

H
-
D
st

relation is shown for recovery phase (VB
s

= 0) and main phase

(VB
s

= 3). T
he dashed and
dashed
-
dotted line represent neural network fits, and the ‘o’ and ‘+’ indicate real data at approximately the same
values of D
st
, VB
s
, etc., at dawn and dusk, respectively. The

H
-
D
st

relation is linear for D
st

below
-
40 nT. The

spread (ASY)

grows linearly below this point.

suggests that D
st

itself
may have

a seasonal offset.
We have also shown the partial ring current, as measured by the
ASY inde
x, does not shut off immediately when VB
s

drops to zero, but, at least in parts of the year, persists until
D
st

itself decays. The first of these results suggests either an error in the calculation of the quiet day or a seasonally
dependent storm
-
time feat
ure 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 io
nosphere. The
possibility of a seasonally dependent storm
-
time feature o
f the ionosphere could be tested by the investigation of
the

H
-
D
st

relationship for a Southern Hemisphere ground station.


ACKNOWLEDGEMENTS


We would like to thank the USGS and NGDC

and WDC
-
C2

for providing the data that we have used in this
analysis. Thi
s work is supported by NSF

grant

ATM 96
-
13667


REFERENCES


Chapman, S., and J. Bartels,
Geomagnetism, Vol 1
, Clarendon Press, Oxford, 1962.

Clauer, C.R., R.L. McPherron, and C. Searls, Solar wind control of the low
-
latitude asymmetric magn
etic
disturbance field,
J. Geophys. Res.
,
88
(A4), 2123
-
2130, 1983.

Crooker, N.U., and G. Siscoe, A tudy of the geomagnetic disturbance field asymmetry,
Radio Sci.
,
6
, 495
-
501,
1971.

Iyemori, T., T. Araki, T. Kamei, and M. Takeda, Mid
-
latitude geomagnetic i
ndices ASY and SYM (provisional),
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Japan, 1992.

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-
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-
latitude DS component of geomagnetic storm field,
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,
76
(10), 2396
-
2405, 1971.

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,
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-
1 to 4
-
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Lincoln, J.V., Geomagnetic
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, edited by S.M.a.W.H. Campbell, pp.
67
-
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-
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