DEFINITION, CALCULATION, AND PROPERTIES OF THE Dst INDEX R.L. McPherron Institute of Geophysics and Planetary Physics University of California Los Angeles [email protected] Presentation at GEM 1998 Workshop Snowmass, Colorado June 15-19, 1998
Dec 16, 2015
DEFINITION, CALCULATION, AND PROPERTIES OF THE Dst INDEX
R.L. McPherronInstitute of Geophysics and Planetary Physics
University of California Los [email protected]
Presentation at GEM 1998 WorkshopSnowmass, Colorado
June 15-19, 1998
MINOR MAGNETIC STORM RECORDED AT SAN JUAN - 11/24/96
24 24.25 24.5 24.75 25 25.25 25.5 25.75 2627100
27120
27140
27160
27180
27200
Day of November 1996
H C
om
po
ne
nt (
nT
)
SAN JUAN H COMPONENT NOVEMBER 24-25, 1996
Disturbed
Quiet
22:2508:45
INTERPLANETARY MAGNETIC FIELD, AE AND Dst INDICES DURING STORM
Coronal mass ejection produce intervals of strong southward Bz at the earth
Magnetic reconnection drives magnetospheric convection
Convection drives currents along field lines and through ionosphere
Ground magnetometers record effects of ionospheric currents in H and other components
H traces are used to construct the AE and Dst index
GEOGRAPHIC COORDINATES USED IN MAGNETIC MEASUREMENTS
Dipole is tilted and inverted relative to rotation axis
Dipole field lines are nearly vertical above 60 latitude
Cartesian geographic coordinates are defined in a plane tangent to earth at observer’s location
X component is towards geographic north pole
Y component is east along a circle of latitude
Z component is radially inward or down
LOCAL VIEW OF VARIOUS COORDINATE SYSTEMS USED IN GEOMAGNETISM
Origin is located at observer X points north, Y points east, Z
points down in the local tangent plane
F is the total vector field H is the horizontal projection of
the vector F D is the east declination of H
from geographic north in tangent plane
I is the inclination of F below the tangent plane
X, Y, Z are the geographic Cartesian components of F
SCHEMATIC ILLUSTRATION OF EFFECTS OF RING CURRENT IN H COMPONENT
Projection of a uniform axial field onto Earth’s surface
Magnetic effects of a symmetric equatorial ring current
SymmetricRing
Current
Dipole Axis
MagneticFieldLines
AxialMagneticField
i
ii
HB
cos
i
i
i
H
B
ii
i
North
MAGNETIC EFFECT OF A RING CURRENT AT EARTH’S CENTER
Axial field from a circular ring current
Field at center of ring
Convenient units
2
322
20
e
e
Rz
IRB
BI
L RR e
0
2
B nTI MA
LR( )
( )
100
X
B
WestwardRingCurrent
View Meridional
EquatorLRRe
Z
LONGITUDINAL PROFILE OF Bj FROM MAGNETOSPHERIC CURRENTS
Symmetric ring should create nearly constant longitudinal profile in H component Local time average of H at equator approximates B at center of Earth But other magnetospheric currents create local time dependent deviations from
symmetry Assume asymmetric component has zero mean when averaged over local time Define the disturbance storm time index Dst as local time average of observed H
profile
j
N
j j
jst B
H
ND
1 cos
1
Local Time0012 18 06 12
Dst
B
oo
o
o
DISTRIBUTION OF RING CURRENT AND
ITS PERTURBATION IN A MERIDIAN
Most of the current is concentrated close to the equator
Eastward current inside and westward outside
Perturbations curl around the volume of current
The perturbation over the earth is nearly uniform and axial
THE SOLENOIDAL EFFECT OF THE RADIATION BELT CURRENTS
A more realistic model of the ring current
Shows the magnetic perturbations
Shows the distortion of dipole current contours
Perturbation field from ring current
DESSLER-PARKER-SCKOPKE DERIVATION
Drift Velocity of an Equatorial Ion in Dipole Field
The Equatorial Ring Current of the Ion
The Magnetic Effect of the Equatorial Ring
where is the ion energy and is its charge
and is the distance from the earth's dipole
vE r
qM
E q
r M
Iqv
r
BI
r
E
M
d
d
3
2
2
3
4
2
10 0
The Magnetic Effect of Ion's Gyration
The Total Magnetic Effect at Earth's Center
Express as Fraction of Surface Field
where is the total field energy outside earth
Br
E
M
B B BE
M
B
B
E
U
Us
20
30
1 20
4 4
2
2
3
THE DESSLER-PARKER-SCKOPKE RELATION
D t B E t E
D t
B
E t
E
dE t
dtU t
E t
U t
D t
dtQ t
D t
Q t
Q t
st m
st
m
st st
*
*
* *
( ) / ( ) /
( )
( )
( )( )
( )
( )
( )( )
( )
( )
( )
0
0
2 3
2
where is the effect of ring current
is the average equatorial surface field
is the total energy of the ring current particles
is the total energy in dipole field outside earth
where is the rate of energy input to the ring current
and is the ring current decay time
where is called the ring current injection function
Note
B
EU t nT
J U tm
0 14
32 5 10
( ) . ( ) in MKS units
CONTRIBUTIONS TO THE VARIATION IN THE H COMPONENT
CURRENTS CONTRIBUTING TO MIDLATITUDE MAGNETIC PERTURBATIONS
View is from behind and aabove earth looking toward Sun
Current systems illustrated– Symmetric ring current
– Dayside magnetopause current
– Partial ring current
– Tail current
– Substorm current wedge
– Region 1 current
– Region 2 current
Current systems not shown– Solar quiet day ionospheric current
– Secular variation within earth
– Main field of Earth
EFFECTS OF MAGNETOPAUSE ON THE Dst INDEX
Balance magnetic pressure against dynamic pressure
051015
0
-10
-8
-6
-4
-2
2
4
6
8
10
X (Re)
Z (R
e)SolarWind
NeutralPoint
k v
aB
Bk
av
B nT P nPdyn
22
0
2 02
2
2
35
( ) ( )
A SHEET CURRENT MODEL OF EFFECT OF TAIL CURRENT ON Dst
-6 -4 -2 0 2 4 6-35
-30
-25
-20
-15
-10
-5
0
-Xgsm (Re)
Bz
(nT
)
Normal Tail
Inner Edge
Total
Earth
Tail Current Model Magnetic Effects
Bz
xxx
xxx
x x x
x x x
i
osz R
RBB ln
Ri Ro
MAGNETIC EFFECTS OF A SUBSTORM CURRENT WEDGE
Transverse currents in the magnetosphere are diverted along field lines to the ionosphere
Viewed from above north pole the projection of the current system has a wedge shape
Midlatitude stations are primarily affected by field-aligned currents and the equatorial closure (an equivalent eastward current)
The local time profile of H component is symmetric with respect to the central meridian of wedge
The D component is asymmetric with respect to center of wedge
STEPS IN THE CALCULATIONOF Dst INDEX
Define the reference level for H component on a monthly basis Fit a polynomial to reference H values (secular variation) Adjust H observed on a given day by subtracting secular variation Identify quiet days from same season and phase of solar cycle Remove storm effects in quiet values and offset traces so that there is zero
magnetic perturbation at station midnight Flag all values recorded during disturbed times and interpolate from adjacent
quiet intervals Create some type of smoothed ensemble average of all quiet days Subtract average quiet day from adjusted daily variation to obtain disturbance
daily variation for station Repeat for a number of stations distributed around the world at midlatitudes Project the local H variations to obtain axial field from ring current and
average over all stations
ESTIMATION OF THE SECULAR TREND INH COMPONENT AT SAN JUAN
1978 1983 19882.7
2.705
2.71
2.715
2.72
2.725
2.73
2.735
2.74x 10
4
Year
H (
nT)
Fourth Order Trend
Daily Average
80% Point
REMOVAL OF SECULAR TREND FROM HOURLY VALUES OF H AT GUAM DURING STORM
115 120 125 130 135 1403.575
3.58
3.585
3.59
395.5x 104
Ob
serv
ed H
(n
T)
COMPARISON OF GUAM H WITH SECULAR TREND IN 1986
115 120 125 130 135 140
-100
-50
0
50
Day in 1986
Tra
nsi
ent
H (
nT
)
DEVIATION OF GUAM H FROM SECULAR TREND IN 1986
Secular Trend
REMOVAL OF STORM EFFECTS IN QUIET DAY (Sq) ESTIMATION
Day in 1986
115 120 125 130 135 140
-100
-50
0
50
Dis
turb
ance
(nT
)
COMPARISON OF DETRENDED GUAM H TO MIDNIGHT SPLINE
115 120 125 130 135 140-20
0
20
40
60
80
Res
idua
l H (
nT)
DETRENDED AND STORM CORRECTED GUAM H IN 1986
Midnight Spline
H Comp
QUIET VALUES DURING STORM USED IN QUIET DAY (Sq) ESTIMATION
115 120 125 130 135 140
-20
-10
0
10
20
30
40
50
60
70
80
Day in 1986
Tra
nsi
ent
H (
nT
)
Flagged Point Quiet Value
Sq FOR H AT SAN JUAN IN 1978 AS FUNCTION OF DAY OF YEAR AND UT
5 10 15 20
50
100
150
200
250
300
350
UT Hour
Day
of
Yea
r
-5
-5
-5
0
0
0
0
0
0
0
0
0
05
5
5
10
1015
15
15
20
20
20
20
25
25
25
3031.1
-5 0 5 10 15 20 25 30
Diurnal Variation (nT)
QUIET GUAM H TRACE AT EQUINOX AND SOLSTICE 1986
Spring
Summer
Fall
Winter
0 5 10 15 20-10
0
10
20
30
40
50
60
Local Time
Pre
d Q
uie
t H
(n
T)
COMPARISON OF SEVERAL OBSERVED AND PREDICTED QUIET DAYS AT GUAM IN 1986
40 41 42 43 44 45 46 47 48 49 50
-30
-20
-10
0
10
20
30
40
50
60
70
Day in 1986
Dis
turb
ance
(n
T)
Observed
Quiet
Residual
CORRECTED H AT GUAM DURING RECOVERY FROM A MAGNETIC STORM
40 41 42 43 44 45 46 47 48 49 50-140
-120
-100
-80
-60
-40
-20
0
20
40
60
Day in 1986
Dis
turb
ance
(n
T) Quiet H
Observed H
Corrected H
DELTA H AT MIDLATITUDES DURING MAGNETIC STORM
MAJOR SUBSTORMS DURING MAGNETIC STORM OF APRIL 3-5, 1979
0 12 24 36 48 60 72-2000
-1000
0
1000
AU
an
d A
L i
nd
ex
(n
T) 125
6271610
18032118
2351252
7571143
17022200
700900
10321641
2147
0 12 24 36 48 60 72-200
-100
0
100
Time from 0000 UT on April 3
Ds
t In
de
x (
nT
)
125627
16101803
21182351
252757
11431702
2200700
9001032
16412147
CONCLUSIONS
The Dst index is defined to be linearly proportional to the total energy of particles drifting in the radiation belts (symmetric ring current)
Dst must be estimated from surface measurements of the horizontal component of the magnetic field
Surface field measurements include effects of many electrical currents other than the symmetric ring current
These effects must be estimated or eliminated by the algorithm that calculates the Dst index
Extraneous currents include: secular variation, Sq, magnetopause, tail, Region 1&2, partial ring current, substorm current wedge, magnetic induction
There are numerous assumptions and errors involved in Dst calculations and the index contains systematic and random errors as a consequence
Be aware of these problems and take them into account in interpreting Dst!