Download Uncertainty in Ring Current Parameters Due to the

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 85,
NO. A2, PAGES 633-643,
FEBRUARY 1, 1980
UNCERTAINTY IN RING CURRENT PARAMETERS DUE TO THE QUIET MAGNETIC FIELD
VARIABILITY
C. Robert
Department
Abstract.
Clauer,
R. L.
AT
McPherron,
Ground observations
provided
that
the magnetic
[Kane, 1978].
effects
error, we have performed a statistical
study
using 2 years of quiet data (AE < .100 ¾),
acquired at 27 mid-latitude
magnetic observatories.
We have empirically
determined the average quiet magnetic' field at each observatory,
and the uncertainty
of that field
as a function
of season and local
time.
Since the Sq currents
are confined primarily
to the dayside,
the uncertainty
of the Sq diurnal variation
changes
as a function
of local time.
During disturbed
periods the quiet field
is subtracted from the
a worldwide
chain
of
field,
mid-
near local midnight.
At dusk the uncertainty
is
near +13 ¾.
These uncertainties
represent
uncertainty
in the quiet field.
The uncertainty
can be greatly
reduced by examining the changes
occur
in
some
interval
of
time.
This
is
done by subtracting
the local time profile
obtained at time t 1 from the profile
obtained at
time t2.
For time intervals
less than 3 hours
the quiet day errors are generally
strongly
correlated,
and the errors are eliminated
by the
subtraction.
The error in the difference
profile
is typically
about +6 ¾. Thus for individual events the local time profile
can be used to
obtain parameters
such as the magnitude,
extent,
and central
meridian,
which accurately
characterize the magnetic disturbance
attributed
to a
particular
current
system, provided the duration
of
the
event
is
less
than
3 hours.
The
which includes the Sq variation
given by Chapmanand Bartels
and secu-
[1940] is statisti-
cal:
the mean variation
obtained by averaging
the mean hourly values of the magnetic elements
for the five international
quiet days of each
month.
When this process is performed for many
stations,
it is possible
to determine the Sq
currents.
Figure 1 shows the average Sq currents
inferred
from
such
mean
variation
curves
for
the
three seasons: D (November, December, January,
February), J (May, June, July, August), and E
(March, April, September, October) [after
Matsushita, 1967].
The average position of the
more
general mid-latitude
indices,
such as Dst and
the dawn-dusk asymmetry, are less accurate,
but
they are still
useful,
provided the disturbance
is sufficiently
large.
center,
is near
or focus,
30 ø north
hemisphere
when
Introduction
observed
hemisphere
of
the
focus
of the northern
current
vortex
latitude.
In the northern
the currents
from
the
flow
sun.
a ground observer
would
see
a
counterclockwise,
Thus
in
the
positioned
decrease
in
the
northern
poleward
X com-
ponent (geographic north) of the geomagnetic
field as he rotated under the system, while an
observer equatorward of the focus would see an
enhancement of X.
The solar quiet daily variation,
or Sq variation, is an ever present feature of the geomagnet-
Copyright 1980 by the American Geophysical Union.
Paper number 9A1409.
01480227/80/009A1409501.00
To use ground magnetic observations
lar variation
at 27 mid-latitude
magnetic observatories,
for the period 1967-1968.
In addition,
we investigate
the error associated
with
our empirical
model.
The method employed in
this analysis
provides a mean quiet field
and
a statistical
scatter
at a given observatory
and
local
time without
regard to the cause.
It has
pragmatic advantages over conventional
statistical studies which have modeled Sq using harmonic
analysis,
since our concern is with the consequences of the quiet field
uncertainty
in terms
of using mid-latitude
magnetic data to quantify
the size and location
of the magnetic disturbances caused by substorms and by the ring current.
The observatories
used in this study, and
their
coordinates,
are listed
in Table 1.
The original
definition
of the Sq variation
latitude
magnetic observatories
to reveal the
magnetic effects of substorms and the partial
ring current.
To obtain a smooth local time
profile
of the magnetic disturbance,
we produce
a least squares fit to the resulting
data values, using a series of cubic spline functions.
Profile
uncertainty
is estimated to range from
approximately +23 ¾ near local noon, to +10 ¾
which
Physics
to study the temporal and spatial
development of
magnetospheric
disturbances,
the quiet magnetic
field,
including
the Sq variation,
must be removed from the data.
At high latitudes,
where
substorm perturbations
are large and the time
scale for change is short relative
to Sq, the
presence of the quiet diurnal variation
is not
a problem.
At mid-latitudes,
however, variability
of the Sq variation
may produce magnetic
perturbations
comparable to the magnetic effects
of the partial
ring current
on comparable time
scales.
Thus the accuracy with which the quiet
magnetic field,
including
the Sq variation,
may
be subtracted
from mid-latitude
magnetic observations limits
the use of these data for identifying the effects
of magnetospheric
current
systems.
In this paper we report
the results
of an empirical
determination
of the quiet magnetic
latitudes,
variability
of Sq currents
may produce magnetic perturbations
comparable to the
magnetic effects
of the partial
ring current on
comparable time scales.
Thus it is important
to know the error associated
with the quiet
field
used as a reference
to obtain
the magnetic
effects
of the ring current.
To determine this
from
and Planetary
90024
ic field.
Other transient
magnetic perturbations,
such as those due to magnetospheric
substorms and
storms, are superposed upon the Sq variation
of magnetic
of the quiet time ionospheric currents, known
as Sq, can be removed from the data.
At mid-
observations
and M. G. Kivelson
of Earth and Space Sciences and Institute
of Geophysics
University
of California,
Los Angeles, California
perturbations can be used to study the spatial
and temporal development of magnetospheric disturbances,
MID-LATITUDES
633
634
Clauer
TABLE 1.
et al.:
Locations
Uncertainty
of Mid-Latitude
in Ring Current
Observatories
Parmmeters
Used in
This
Geographic
Station
Code
W Longitude
Station
16058 '
63ø53'
65o19 '
66o09 '
Fredericksburg
77o22'
Cuba
Dallas
Boulder
Tucson
82 008 '
96ø45'
105 ø14 '
110ø50'
NT
Newport
116o59'
48ø16'N
300.2 ø
55.1 ø
TA
HO
Tahiti
Honolulu
149o37 '
158o00 '
17o33 ' S
21ø19'N
282.7 ø
266.5 ø
-15.3 ø
21.1 ø
PM
TO
Port Moresby
Toolangi
212o51'
214032'
9ø24'S
37o32' S
217.9 ø
220.8 o
-18.6 ø
-46.7 ø
GU
KA
YA
Guam
Kakioka
Yakutsk
215o08 '
219o49 '
230o16 '
13ø35'N
36ø14'N
62ø01'N
212.9 ø
206.0 ø
193.8 ø
4.0 ø
26.0 ø
50.9 ø
GN
PY
HY
YB
VD
Gnangara
Patrony (Irkutsk)
Hyderabad
Yangi-Bazar (Tashkent)
Vysokaya Dubrava
244ø03'
255o33'
281o27'
290o22'
298o55'
31ø47' S
52ø10'N
17ø25'N
41ø18'N
56ø42'N
185.8 o
174.7 ø
148.9 ø
144.0 ø
140.7 ø
-43.2 o
40.7 ø
7.6 ø
32.3 ø
48.5 ø
DT
Dusheti
315o17 '
42ø04'N
122.0 ø
36.6 ø
ST
NU
Stepanovka (Odessa)
Nurmijarvi
329o07'
340o24'
46ø46'N
60ø30'N
111.1 ø
112.5 ø
43.6 ø
57.8 ø
HR
FU
Hermanus
Furs tenf eldbruck
340o46 '
348 ø43 '
34ø25'S
48 ø10 ' N
80.5 ø
93.3 o
-33.3 ø
48.8 o
(Tbilisi)
the
posiseain
Sq cur-
Hasegawa [1936] concluded
or south from one day to another.
[1975] has studied deformation of the Sq
scale.
Thus even on very quiet days at any particular
station,
there can be considerable
day-to-day
variability
in the amplitude and phase of the
diurnal
variation.
Figure 2 shows superposed
plots of the H components, measured at two midlatitude
observatories
during quiet periods and
arranged according to season.
These data from
1967 and 1968 were selected
according to the
criterion
AE < 100 ¾. The Sq variation
appears
to have a distinctive
shape, with some variability in phase and amplitude.
In addition,
the
variation
seems to be superposed upon a base
line which is nearly constant in local time, but
whose value may change from day to day.
An Empirical
Sq Model
14ø24'N
31ø40' S
43ø15'S
18ø07'N
ø
ø
ø
ø
-21.3 ø
-20.2ø
-31.8 ø
29.6 ø
38ø12'N
349.8 ø
49.6 ø
22068 'N
32ø59'N
40 o08 ' N
32 ø15 ' N
345.4
327.7
316.5
312.2
34.1
43.0
49.0
40.4
xj=.
J
o
ø
o
o
o
ø
o
o
+ [:J +PJ +r J ]
J
whereMj is the main geomagneticfield, Rj is
the field due to ring current, Ij is the field
due to ionospheric(Sq) currents, Pj is the field
due to magnetopause
currents, and Tj is the field
due to tail current.
The quantity
in the brackets produces a diurnal variation,
while the remaining terms are quasi-steady
and symmetric.
It is useful, then, to represent Xj in terms of
a symmetricfield Bj and a diurnal variation
field Vj. That is,
Xj = Bj + Vj
whereBj = M- + R_-andVj = I. +
The
results
oft•iss•udy
areval•es
Po•
+1.Tj.Includof the stations
listed
in Table
B and
V
for
each
ed
in
iation
our
of
determination
the
main
of
B is the secular
varobserved
at each ob-
field
servatory over the 2 years of data used in the
study.
The mean diurnal variation
V at each
station
is
determined
for
each
of
the
three
sea-
sons.
Determination
of
the
Diurnal
Variation
The proper reference
level from which to
measure Sq variations
has been investigated
by
several
On a magnetically
quiet day the magnetic field
X, observed at some observatory
j, will
be composed of the following
terms:
55.0
4.6
3.2
3.1
Latitude
CE
DS
BD
TU
system on an hourly basis and reports movement
of the focus position
by several
degrees on that
time
E Longitude
FR
that the Sq focus could move as muchas 15ø of
Marriot
Latitude
M'Bour
Pilar
Trelew
San Juan
rents also exists.
north
Geomagnetic
MB
PI
TW
SJ
It can also be seen from Figure 1 that
strength
of the Sq current
system and the
tion of the focus change appreciably
with
son.
A great deal of day-to-day
variability
the shape, position,
and strength
of the
latitude
Investigation
researchers.
the daily
line;
that
Without
other
information
mean would be an appropriate
however,
theoretical
arguments
the current
responsible
for the
base
suggest
Sq magnetic
Clauer et al.'
D
MONTHS
75 ø
E
NP
Uncertainty
for
MONTHS
75 ø
in Ring Current Parameters
each
of
the
635
24 local
time
hours.
Minimum
variance indicated the best parallelism
or greatest similarity
between stations within a group.
His results demonstrate that the midnight-to-dawn
NP
•0o•.•.
45o,4,'
hours are the least affected
by local
and can be safely used as a base line
to compute
Sq variations.
In this
,"•L',, ,'%<•'•: ;,' ',','
•,?,'•. '--' .-'.-'.,,,',V
',,,,,,, ,, •:
•
/ ,',,,,,
', V,".".'.-Z.-".'L:'2"
MONTHS
NP
75 ø
60ø
45ø
External Sq currentsduring
30,•
"]/(l
00o'
.-'' . ;-
.-:--:::--:::::L•-'•
,"
-
: ' ,' *
day to
be used
To de-
x
variation
V on each day,
residuals
reference
were
from
this
calculated.
and 10 percentile
curves for the ensemble of
superposed data.
The source of the dayside variability,
appar-
by
tude winds [Hasegawa, 1960; Gupta, 1967; Kane,
1972; Schlapp, 1968]; however, changes in iono-
,' /
conductivity
may also play an important
role [Brownand Williams, 1969; Chapmanand
Bartels, 1940]. Other sources in the magneto-
in the southern hemisphere the
counterclockwise
numbers
near
current
as viewed
from
cross
marks are
the
intensity
of each vortex
in
units of 103 A. The current intensity between
consecutive lines is 25 x 103 A [after
Matsushita,
value.
ent in Figures 3 and 4, has been investigated
equatorial
plane at the solar noon meridian.
In the northern hemisphere the currents flow
the total
reference
many researchers.
The variability
appears most
closely related to changes in local high-alti-
and equinox (E), viewed from the magnetic
flow
The
line
viewed from the sun.
AfterMatsushita,
1967
SP
currents
the sun.
a base
the IGY for the threeseasons
Fig. 1. Average ionospheric currents during the
IGY for the three seasons, winter (D), summer
clockwise;
as
termine the diurnal
spheric
(J),
study we have computed the mean field
between 00 and 02 hours LT on each quiet
Figures 3 and 4 show the superposed residuals of
the X component computed for the same data shown
in Figure 2.
The panels to the right of the
superposed plots show the mean, 90 percentile,
SP
J
sources
from which
sphere or interplanetary
space which could affect Sq variability
have not been ruled out.
Matsushita [1975], for example, suggests that
the interplanetary
magnetic field polarity
may
influence the latitude
of the Sq current focus.
Nevertheless,
the
results
of
these
studies
not adequate to enable one to predict
ically
at any particular
time.
are
Sq analyt-
Consequently, we
have chosen to determine
empirically
the mean
seasonal
each of the
27 observ-
Sq variation
1967].
at
MAGNETIC
DIURNAL
VARIATIONS
QuietPeriods(AE< lOOT) During1967-1968
perturbation
lit
side.
flow primarily
To justify
during the night
propriate
on the earth's
the use of the mean field
hours (2100-0300
base line
reference,
on the sunlit
HONOLULU
TUCSON
(21.90N, 158.0 øW)
(32.250N, IlO.•!øW)
LT) as an ap-
Price
[1964] argue that (1) ionization
is much greater
H Component
sun-
and Stone
in the E region
portion
25•50
of the
earth, decaying rapidly at the terminator,
(2)
in situ observations
using rocket-borne
magnetometers
indicate
dayside,
and (3) during magnetically
currents
exclusively
on the
quiet peri-
]]20X
ods, the magnetic changes occurring during the
daylight
hours are much greater
than the changes
during the night hours.
A statistical
investigation
to determine
the
appropriate
Sq reference
line was reported by
Kane [1971].
%
20X
25850
He reasoned that stations spread
over a large region in latitude
and longitude
would exhibit
nearly parallel
responses to
changes in distant
magnetospheric
currents,
while the effects
of changes in local ionospheric
or
earth
induction
currents
would
not
be
well
correlated
between stations.
To quantify
the
quiet time station
behavior
at different
local
times, he computed the monthly mean quiet field
for 67 stations
at each hour in local
time, over
the period January through December 1958.
The
stations
were grouped into regions within
latitude and longitude boundaries.
For each group
he statistically
measured the variance
of individual station observations
from the group mean
0
6
12
18
24
LOCAL
0
6
12
18
24
TIME
Fig. 2.
Superposed magnetic variations
of the
H component observed at Tucson and Honolulu
durlng qulet tlmes (AE < 100 y) for 2 years
(1967 and 1968).
The data are arranged according
to season.
division.
Vertical
scale
is
20 y per
636
Clauer
et al.:
Uncertainty
in Ring Current
Parameters
MAGNETIC DIURNALVARIATION AT HONOLULU (21.9 N,158.0 W)
QUIET DATA (AE<1007') DURING 1967 - 1968
AX COMPONENT
ri i i i i i i i , i i
X'XL.10
Perce•ile
•
L/I
i
I
i
i
i
o•
O0
06
i
i
12
i
i
i
I
I
I
I
I
I
I
I
I
I
IIIIIIIIIII__..•
i
i
18
24
LOCAL
i
i
i
i
i
i
i
I
i
i
.....,•,,
O0
06
TIME
12
18
24
Fig. 3. Superposed daily quiet variations of X component observed at Honolulu during
1967 and 1968.
(Left) Residuals from the field averaged between 00 and 02 hours LT on
each day. Data are arranged according to season. (Right) Mean, 90 percentile,
and 10
percentile
curves computed from the superposed data.
The vertical
scale is 12 ¾ per
division.
atories listed
in Table 1. Quiet periods were
selected from 2 years of data (1967 and 1968),
according
to the criterion
AE < 100 ¾. On each
quiet day the field
average between 00 and 02
hours
LT was
used
as
a reference
to
determine
the residual
Sq variation
at each station.
These
variations
were arranged according to season, in
the way illustrated
in Figures 3 and 4.
The mean
variation
then
at
each
station
for
each
season
the X component the scatter
ring
current
and tail
Calculating
the
Main
Field
Base
station
to
current.
field
base
line
at
each
Line
which
can be determined
at
any day in the period 1967-1968 for any of the
27 observatories used in this analysis.
The
second degree polynomial
The
is
the Model quiet- Field
The model quiet
of
the fit
was
computed.
Determination
about
typically
within +10 ¾, while the secular variation of X is roughly 55 ¾ over a 3-year interval.
The base line determined this way reflects
the
main field and some average configuration
of the
the
model Sq variation
is added was obtained as follows.
The monthly average field between 00 and
02 hours LT during quiet times (AE < 100 ¾) was
computed at each station using several years of
data.
These averages were then fit with a second
degree polynomial to approximate the main field
and secular variation
at each station.
Figure 5
shows the results
of this procedure for the X
and Y components of the field
at Honolulu.
For
the
base
line
field
B.
is used to determine
This
value
is
added
to
the variation
V for the season, component, and
local time selected.
Figure 6 compares the X
component
tions with
of
the model
the actual
field
field
at
a number of
sta-
observed on February
6, 1968. February 6 was classified QQ. The mean
AE on this day was 43 ¾, and Ap = 2. The upper
trace is the model quiet field,
while the lower
trace is the measured field.
Local midnight is
indicated
above each trace,
and a base line is
Clauer et al.:
Uncertainty in Ring Current Parameters
637
drawn through the midnight value.
While there is
general agreement between the predicted and actu-
mean.
al quiet day, differences
ly means of the 90 percentile and 10 percentlie
values.
Figure 7 shows the mean error in the Sq
differences
stations.
from
the
do exist.
model
For example,
are
while
tween the model and actual
at
some stations,
it
is
In addition,
not
similar
at
the difference
base lines
16 ¾ at
all
be-
local
San Juan.
tions,
of Quiet
Field
obtained
in our estimate
seasons.
by averaging
of
The error
seasons
field
re-
sult from (1) uncertainty of the Sq variation and
(2) uncertainty of the Sq base line.
In this
section we will quantify these errors, discussing
and varies
source
of
affected
contributors.
local
noon,
and the
To estimate
the model Sq variation,
least
the quiet
the hour-
for
of
field
average
To quantify
we have used the 90 and
computed
10 percentile curves of the ensemble of Sq variations observed at each observatory. and illus-
the
00 and
years
lies
0200 LT of
in
the
The variability
of quiet
variability,
of
LT at
I
i
i
we have
the model base
field,
each
station
(1967-1968).
i
I
I
I
I
for
The result
i
the
is a
i
24
'
I
I
I
I
I
06
I
I
I
I
I
I
I
,,,jj
I
i
i
'-I
,ii
I
12
i
,..• •
I
I
18
I
i
24
LOCAL
Fig. 4.
Sameformat as Figure 3.
observed
at Tucson during
00
06
12
18
24
TIME
Superposed daily quiet variations
1967 and 1968.
line
averaged between
where
I
of
the quiet time ring
being the predominant
QUIET DATA (AE.<1007')DURING1967 - 1968 AX COMPONENT
I
uncer-
measured between 00 and
MAGNETIC DIURNALVARIATIONAT ;=';•J•ON (32.25 N,110.8W)
00
all
a maximum near
error
the base line
02 hours
of data
matrix Dij,
••11
three
the same for
from
differences
from the measured quiet
trated in Figures 3 and 4.
In general,
these
percentlie
curves lie symmetrically
about the
sta-
the
02 hours LT thus represents variability
near
the uncertainty
of
over all
time
by Sq disturbances.
greatest
near
each hour of
tainty
of the base line computed for each station.
We assume that during quiet times, the
magnetic field
between 00 and 02 hours LT is not
magnetospheric currents,
current and tail current
midnight.
local
is nearly
first
the uncertainty
of the Sq variation.
Since the Sq currents are confined primarily
to the dayside, the uncertainty
of the Sq variation is a function
of local time, being the
local
during
difference
1100 LT of +22 ¾ to a minimum near
about +4 ¾.
Model
of the quiet
the
as a function
The second
Errors
the error
to be half
variation,
is only 1 ¾
three
Uncertainty
We estimate
time
of X component
2
638
Clauer et al.'
Uncertainty
in Ring Current Parameters
Averoge
Monthly
Midnight
QuietMognetic
Fieldot Honolulu
50
there were periods with AE < 100 ¾. This matrix,
with our statistical
analysis,
is schematically
illustrated
in Figure 8.
To describe the D matrix statistically,
we
_
40
•
50
ZO
_
I0
ß
XComponent
_
ß
calculated
the mean and standard
deviation
for
each row and column.
The mean and standard
deviation
of each column
characterize
the individ-
_
;27400
90
_
_
ual station
80
_
70
6O
periods.
ß
row
_
27350 iiiiiiiiiii
iiiiiiiiiii
5630[-
56•0•.•.•..•
561o•
56oo•
.
iiiiiiiiiii
trix,
¾Component
1967
quiet day.
2 shows five
deviation
of
each
stations
on
a
of
example rows of the D ma-
the column statistics,
that
1968
1969
and a summaryof the
given by the meanand standard de-
Month
the
secular
the stations
are,
in general,
behaving sire-
ilarly.
The mean of each row characterizes
the
average field
deviation
from the model seen by
several stations,
and reflects
the strength of
the quiet time ring current on that day.
That
is, the row mean represents
a base level
on a
particular
day relative
to the predicted
base
value.
Uncertainty
of this base line exists
be-
Fig. 5.
Monthly average quiet magnetic field
at
Honolulu averaged between 00 and 02 hours LT.
Solid curve is a second degree polynomial
fit
to
the data.
The average long-term
change in the
termed
ensemble
ßß ß ßßßßßßß ß .
viation
oftherow
means
andstandard
deviations
-'•ß'ß''-'"•ßß The
column
statistics
aresimilar,
suggesting
1966
is
the
row statistics
JFMAMJJA$ONDJFMAMJJA$ONDJFMj•
field
characterize
particular
Table
iiiiii11111
behavior over the ensemble of quiet
The mean and standard
variation.
cause
the station
differences
Dij are
not theof
same across
the
row.
The standard
deviation
the
Dij = Oij - Pij
ity
Oij
observedquiet field averagedbetween
00 and 02 hours
LT;
values
in
each
characterize
the
uniform-
a second
matrixRi• hasbeencomputed
by subtractingthe
row mean from
Pij
row
of the station
observations.
To remove the ring current
effects,
each value
in
the row.
That
is,
model quiet base line field prediction.
Rij = Dij - <rowj>
Columns of the D matrix
represent
different
stations,
while rows represent
days during which
PREDICTED
The standarddeviation of all the values Rij
AND
ACTUAL
MAGNETIC
FIELD
AT SEVERAL MID-LATITUDE OBSERVATORIES
FOR QUIET DAY FEBRUARY6, 1968
I'1'1'1'1'1'1'1'1'1'1'1'1
I'1'1'1'1'1'1'1'1'1'1'1'1
ß
SAN
JUAN
-
I
•GNANGARA
1
PIeR
•
I
__.T
1
2518t
t ----
'•'-"-
•
{
1,1,1,1,1,1,1,1,1,1,1,1,1
0
4
8
11%31
I"--•--•""--"'"'-•' ....
1,1,1,1,1,1,1,1,1,1,1,1,1
12
16
10
24
UNIVERSAL
0
4
8
12
16
10
TIME
Fig. 6.
(Top) predicted and (bottom) actual magnetic field at several
for quiet day, February 6, 1968.
Dots above each trace indicate
local
base line is drawn through
to the left.
The vertical
24
the midnight value of each trace,
scale is 20 ¾ per division.
and its
observatories
midnight.
A
value
is
indicated
Clauer
et al.'
Uncertainty
in Ring Current
characterize
the base line uncertainty.
This
standard deviation
was computed to be 4.7 ¾. A
stringent
estimate
of the base line error is
given by plus or minus 2 standard deviations,
or
about +9 ¾.
The
combination
Evariation
moae-
of
errors
E,
•.
Da
e,•
639
STATION(J)
DAY
(I)•
A
1
and
e
Parameters
producea total uncer•amn•y
in the
B
œ ...
D•A D•B D•c . . . <R0Wl>
(•R0Wl)
2
D2A D2B D2c, . , <ROW
2> (O'ROW
2)
]• .
D3A D3B D3C, , , <ROW
]•>(O'ROW
......
qumeu
rmela
graven
Dy
......
Etota
1 = (Evariation
2
<mL
^>
+ E•aseline)
ß
This result
is plotted
in Figure
tainty varies from a minimum of
LT, to a maximum of about +23 ¾
At dusk the uncertainty
is about
should be mentioned that this is
gent estimate
of the uncertainty,
on +2 standard
deviations
of the
used to calculate
the empirical
9.
The uncer+10 ¾ near 0100
near local noon.
+15 ¾. It
a fairly
strinbased roughly
spread in data
quiet field
model.
Fig. 8.
Schematic illustration
of D matrix used
to estimate base line uncertainty
in the quiet
field
model.
Rows of the matrix
correspond
to
quiet days, and columns correspond to stations.
Each D component is the difference
between the
actual field
average between 00 and 02 LT, and
the
model
of Quiet
Field
base
line
at
the
indicated
station
and
day.
The matrix can be described
statistically
by computing the mean and standard deviation
each
Application
c> .
row
and
of
column.
Model
where
In Figure
from
10 we illustrate
a worldwide
chain
of
the use of data
mid-latitude
observa-
W.
=
1
tories
to determine
a local
time profile
of a
magnetic disturbance.
Plotted
on the left
side
of the figure
are several
hours of data from
Xi_1 - Xi+1
X1 - X
February 11, 1967, along with the model quiet
field,
for each observatory.
We have indicated
the difference
between the quiet curve and the
W1= X1
- X2
- X
n
field
measurement at 0600 UT, and these values
are plotted• as a function
of the local time position
of the observatory
on the right
of the
figure.
The error
bars on each difference
value
were determined
from Figure 9.
The smooth curve
through the data points was computed using a
least squares cubic spline technique.
The discontinuity
near 00 LT is at the day boundary of
the spline fit.
The spline-fitting
technique
8Yi = Y1
- S.
uses a program from the IMSL Library i
The technique
and
matches
fits
the
cubic
first
splines
and
[1975].
within
second
intervals
derivatives
of
the spline
at the interval
boundaries
or knots as
they are commonly called.
The positions
of the
knots influence
the fit,
so we therefore
use
several knot arrays and select
the best fit
based
on a weighted rms error.
The splines are fitted
so as to minimize the error given by
E=
n
(r•
•Y2. W. )
i=l
z
%
1
ERROROF QUIETDAY
DIURNALVARIATION
i=2
X1
Xn-1 - Xn
W
n = X1 - Xn
1
spline
value at Xi.
In the profile
based
on
two
standard
deviations
I
,
i
i
i
i
L•AL
i
TI•E
,
,
i
,
i
i
I
i
i
(HRS.)
FiE. 7.
predicted
•Enitude
of the uncertainty
of the
daily quiet variation
as a function
of
time
local
and
season.
of
the
data
used
to compute the mean quiet day field.
Frequently,
one is interested
in determining
the change which occurs during a specific
interval of time, e.g.,
during the expansion phase of
a substorm.
This can be accomplished
by sub-
tracting the profile at time t 1 from the profile
at time t 2. Substantial error reduction in the
resulting
difference
profile
is obtained.
The
procedure is illustrated
in Figure 11.
On February 11, 1967, a substorm onset occurred at 0515 UT, and the expansion phase
reached its maximum at 0600 UT.
The top panel
of Figure 11 shows the local time profile
of the
magnetic disturbance
at 0515 UT.
The uniform
depression suggests an enhancement of the symmetric ring current.
The wiggles in the profile
smaller
values,
than
the
and are
errors
associated
not meaningful.
panel shows the profile
This is the same profile
Figure 10.
0
shown, E =
5.7 ¾. Since this error is less than the error
in the data values used to obtain the profile,
we estimate
the uncertainty
of the profile
to be
equal to the uncertainty
in the data.
Recall
that this uncertainty,
shown in Figure 9, is
data
4
1
where Yi is the data value at Xi and Si is the
are
o
n-
n
with
the
The center
obtained at 0600 UT.
discussed earlier
in
The solid line in the bottom panel was obtained by subtracting
the 0515 UT profile
from
the 0600 UT profile,
and represents
the effects
of currents
which developed during the substorm
expansion.
There is a 20-¾ enhancement of the
field
centered near 0400 LT, due to the substorm
expansion current,
and a -30-¾ perturbation
centered near dusk, due to the development of the
640
Clauer et al.'
Uncertainty
in Ring Current Parameters
-•O monthsUNCERTA_INT.Y
OF PREDICTED
co
c•
o
co
o
4
•2 ' I'0.......
8
6
i , 0i i 212, 20i , I; .....
16
4
2
LOCAL TIME
o
i4
12
(HRS)
•
Fig. 9. Magnitude of the uncertainty of the
predicted quiet field as a function of local
o
•o
time
•
and
season.
o
partial
ring current.
Because errors in the
quiet day model at a particular
observatory are
highly correlated over time periods of several
hours, the subtraction
of the profiles
removes
•j
much of the uncertainty
file.
For time periods
correlation
coefficient
in the difference
proof 2 hours or less the
is greater than 0.8.
It
is
to
reasonable
therefore
estimate
the
uncer-
tainty in the difference
profile
by considering
only the rms residual errors of the profiles
at
times t 1 and t2, providing the separation is less
•j
than
2 or 3 hours.
of the profiles
ent, we obtain
file
Assuming that
the rms errors
at 0515 and 0600 UT are independan uncertainty
of +6 ¾ in the pro-
shown in the bottom panel.
The data values shown in the bottom panel
Figure 11 were obtained by subtracting
values
at
0515
UT from
the
values
The dashed curve is a spline
o
•
values.
The
is 4.7
rms
error
of
the
¾, which is consistent
fit
at
of
the data
0600
UT.
to the data
dashed
with
curve
fit
our error
estimate.
o
it
the
For time separations of greater than 3 hours
becomes risky to subtract data values,
since
station
has
moved
in
local
time.
The
use
of
the profile
overcomes this difficulty
by transforming from the rotating
frame of the earth to
one fixed with respect to the earth-sun line.
•o
Discussion
o
o
o
•
•D
To develop parameters
and indices
using mid-
latitude
data which characterize
geommgnetic
substorm and ring current disturbances,
it is
necessary to separate and remove the magnetic
effects of quiet time sources from the disturbance field
with known uncertainty.
A technique
for removing the quiet magnetic field from disturbed data has been described
in this report.
The technique predicts th• quiet field at a midlatitude
observatory based on the mean diurnal
quiet variation
observed at the station over
many quiet days grouped according to season, and
a base line determined by the monthly mean quiet
field
o
•
•
o
measured
between
00
and
02
hours.
LT
at
the
observatory.
A conservative
estimate of the
accuracy of the predicted
field
is given in
Figure 9 and is based approximately on 2 standard
deviations
of the data use d in the analysis.
The criterion
used to select quiet periods was
based on the AE index introduced
by Davis and
Sigiura
[1966].
The index is created using 10
auroral zone observatories
nearly equally spaced
in longitude in the northern hemisphere and indicates the strength of the auroral electrojets.
Periods defined by AE < 100 ¾, however, do not
Clauer et al.'
necessarily
represent
a quiet
Uncertainty
'ground state'
in Ring Current
of
shown
a quiet day
mid-latitude
mated by the
computed at
ranges from
These
We have
the
absolute
deviation
are
based
on 2 standard
95% confidence
level.
a
also
shown
that
events
devia-
with
2O
-20
-40
-60
from
can only be roughly determined using
magnetograms.
The error is estiuncertainty
of the mean quiet field
27 mid-latitude
observatories,
and it
+23 ¾ at 12 LT to +10 ¾ at 00 LT.
estimates
and have
tions
that
641
FEBRUARY 11, 1967
40
the magnetosphere,
since no condition
was set on
previous magnetospheric
activity.
For example,
the period following
the main phase of a magnetic
storm is often very quiet by the criterion
AE < 100 ¾, although the ring current is typically enhanced and decaying slowly.
Nevertheless,
the quiet field
at each observatory generated by
this model is useful,
since it references
disturbances to a model with known uncertainty.
We have
Parameters
U3 2O
' 'o'oo'
U'T
...... J...........
x•
I,O• o
0 -20
time
dura-
-4O
tions of less than 3 hours may be characterized
much more accurately.
Since the errors
in the
estimate of the quiet field at time t 1 correlate
2O
Feb. 11,1967
Local
Time
X Component
'
'
i
i
Profile
0600
i
'
'
'
i
,
,
,
i
,
,
UT
,
,
i
!
i
i
i
i
,
14
"6•2
'1•4
'1•
'1'8
'2'0
'2'2
'24
'62
'64
'•'•8
'1•)
'12
TO
16
_
LOCAL
18
Fig. 11.
latitude
_
_
_
TU
20
22 .c:
Local time profiles
magnetic disturbance
.-
•SJIHI
...........
•
02 •
o
04
('HOURS)
of
in
the midthe X component
on February 11, 1967:
(Top) profile at substorm onset at 0515 UT, (middle) profile
at the
end of the substorm expansion
(bottom) the result
24
TIME
at
of subtracting
0600 UT, and
the 0515 UT
profile
from the 0600 UT profile
(solid line).
The dots were obtained by subtracting
the •X
values
at
0515
from
the
•X values
at
0600
UT.
Dashed line is a least squares spline fit to
the dots.
Bottom panel shows the magnetic perturbations
due to currents which develop in the
interval
0515-0600
UT.
O6
08
10
_
,
03
06
09
•
-60
]
i
-40
Universal Time (hrs)
,
,
•
i
-20
,
,
i
i
0
i
i
[
20
i
i
i
12
40
AX (gamma)
Fig. 10. (Left) Mid-latitude
observations of
north-south component (solid line) and model
quiet magnetic field (dashed line) on February 11,
1967.
Vertical
line
at
0600 UT indicates
ence between observation and quiet field
observatory.
(Right) Local time profile
differ-
at each
of AX
component at 0600 UT, the end of the substorm
expansion phase.
Dots correspond to the deviation from the quiet field
at each station.
Error bars represent
the uncertainty
of the
quiet field
at each local
time.
The smooth
curve is a least squares fit to the data points,
using
a series
of cubic
splines.
Discontinuity
in the curve at 2400 LT is the result
boundary.
of the day
with the errors at time t2, the error in the
difference
profile
is less than the error of
either
of the subtracted
profiles.
The uncertainty
of the difference
profile
is typically
about +6 ¾ for time periods of 2 hours or less.
These errors
are important
to know in order to
evaluate
indices or parameters which are determined from local time profiles
of the mid-latitude magnetic disturbance.
In particular,
we
have been interested
in isolating
and parameter-
izing
the magnetic disturbances which result
from
the substorm expansion phase current
and the partial
ring current.
This is illustrated
schematically
in Figure 12.
The top of the figure
shows
the magnetic signature
of these currents
as a
function
of local time or position
around the
earth.
The north-south
and east-west
perturbations are indicated
by AX and AY, respectively.
The substorm expansion current produces an enhancement in the northward field
in the night
region,
while the partial
ring current
produces
a depression
in the northward field,
centered
near dusk.
The AX profile
can be used to compute
642
Clauer
et al.'
Uncertainty
in Ring Current
Only with more complete data sets from space will
the configuration
of the currents
which are responsible
for the mid-latitude
magnetic distur-
MIDLATITUDE LOCAL TIME PROFILE PARAMETERIZATION
Field Aligned Currents
In
Out
In•,,
I Partial
Ring
Current
;iubstorrn
Expansion
Current
bance
// AX-•',
,i•
'•:;•.
•'
"• Extent
Central
Central
/
! •'i;
Meridian
/
be
determined.
Work presently
in progress uses the mid-latitude disturbance
parameters to study the development of the partial
ring current
and its relationship
to interplanetary
and substorm parameters.
Preliminary
results
were reported
by
Ay..•//•--'"•\•-Magmtude
Merid•an•
Parameters
/
Clauer and McPherron [1978],
results
Extent
SIZE
=Magnitude
xExtent
Uagmtude•
•'
I
I
I
i
i
i
will
be published
Acknowledgments.
i
work was supported
Local Time (hours)
and more detailed
soon.
The major portion
by the Office
of this
of Naval
Re-
search under grant ONR N00014-75-C-0396.
Partial
support was also provided by NASA grant NGL 05007-004 and NSF grant ATM 76-17035.
The regents
of the University
of California
provided partial
support of the computing costs.
All of the digitized
data was provided by the World Data Center
A for Geomagnetism.
We also gratefully
acknowledge the helpful
comments on earlier
versions of
12
this
manuscript
by R. J. Walker.
The Editor
thanks S. Matsushita
for their
assistance
in evaluating
EquatorialProjectionof Inferred Currents
Fig.
12.
(Top) Schematic illustration
parameters
obtained
of
from the mid-latitude
local
time profile of the north-south (AX) geomagnetic
disturbance.
Parameters
extent,
central
meridian,
turbation.
(Bottom) Equatorial projection of a
pansion phase current and partial
ring current
which could be inferred
from the magnetic
t ions.
parameters
which characterize
These include
the magnitude,
central
meridian
of
the
the disturbance.
extent,
size,
and
disturbances
due
to
both
the substorm and the partial
ring current.
The
magnitude
is determined
by the maximum or minimum
of the profile;
the extent is given by the full
width at half
maximum (or minimum) of the pertur-
bation;
the size is given by the product of the
magnitude and extent;
and the central
meridian
is
the
local
time
of
the
maximum
or
minimum
value.
Figure 10 illustrates
the creation
of such a
AX profile
at the peak of a substorm expansion.
Figure 11 illustrates
how improvement to the
profile
can be obtained by subtra•cting
the profile
determined
at
the
References
include
the magnitude,
and size of the per-
simplefield-aligned modelof the substorm
ex-
ob s erva
and M. Sugiura
this paper.
substorm
onset
from
the
profile
at the peak of the expansion.
The profile
in the bottom panel is very similar
to the
schematic illustration
in Figure 12.
We have
estimated
that the uncertainty
in the disturbance
magnitude determined from such a profile
is
roughly +6 ¾. The uncertainty
in the central
meridian
and extent
is roughly +1 hour.
The method described
in this report
examines
the degree to which the quiet mid-latitude
field
can be removed from magnetic data to isolate
disturbances
of presumable magnetospheric
origin.
One should note, however, that the use of ground
data alone does not permit one to unambiguously
specify
the source of the disturbance.
For example, a portion
of the disturbance
attributed
to a
partial
ring current
or a substorm expansion may
indeed be the result
of the disturbance
dynamo
current produced by winds which develop in response to Joule heating at auroral
latitudes.
Brown,G. M., and W. R. Williams, Someproperties
of the day-to-dayvariability of Sq (H), Planet.
Space Sci., 17, 455, 1969.
Chapman, S.,
University
and J. Bartels,
Geomagnetism, Oxford
Press, New York, 1940.
Clauer,
C. R., and R. L. McPherron,
On the relationship
of the partial
ring current
to substorms and the interplanetary
magnetic field,
J. Geomagn. Geoelec., 30, 195-196,
1978.
Davis. T. N., and M. Sugiura,
Auroral
activity
index AE and its universal
tions,
J. Geophys.. Res., 71,
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time varia-
785-801,
1966.
Gupta, J., Relative importanceof solar rJdiation
in causing
geomagnetic
variations,
and gravitational
J. Geophys..Res.., 72,
tide
1583, 1967.
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of terrestrial
On the type of diurnal
magnetism on quiet
variations
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Imp. Acad. Tokyo, 12, 88, 1936.
Hasegawa, M., On the position
of the focus of the
geomagnetic Sq current system, J.. Geophys. Res.,
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1, Edition
5,
International
Libraries,
Kane, R. P.,
Mathematical
and
Statistical
7500 Bellaire
Blvd.,
Houston, Texas.
Baseline
for. Sq studies,
Ann.
Geophys., 27(2),
229, 1971.
Kane, R. P., Day-to-day variability
of the quiet
day daily range of equatorial
geomagnetic field
and its relationship
with ionospheric
dynamics,
J. Atmos. Terr.
Kane, R. P.,
Phys., 34, 73, 1972.
Sq variation
at low latitudes
during
geomagnetic storms, J. Geophys. Res., 83, 5312,
1978.
Marriot,
R. T., The quiet time equatorial
counterelectrojet,
M.S. thesis,
Univ. of Calif.,
Los
Angeles, 1975.
Matsushita,
S., Solar quiet and lunar daily variation fields,
Phy.sics of Geomagnetic Phenomena,
edited by Matsushita
and Campbell, Academic,
New York, 1967.
Matsushita,
S., IMF polarity
effects
on the Sq
Clauer et al.'
current
focus location,
Uncertainty
J. Geophys. Res., 8__0,
4751, 1975.
Price,
A. T., and D. J. Stone, The quiet day
magnetic variations
during the IGY, Ann. IGY,
3__5,63, 1964.
Schlapp,D. M., World-widemorphology
of day-to-
in Ring Current Parameters
day variability
of Sq, J. Atmos. Terr.
30, 1761, 1968.
(Received August 10, 1979;
revised October 2, 1979;
accepted October 3, 1979.)
643
Phys.,