DEFINITION, CALCULATION, AND PROPERTIES OF THE Dst INDEX

1
DEFINITION, CALCULATION, AND PROPERTIES OF THE
Dst INDEX
Presentation at GEM 1998 WorkshopSnowmass,
ColoradoJune 15-19, 1998

• R.L. McPherron
• Institute of Geophysics and Planetary Physics
• University of California Los Angeles
• rmcpherron_at_igpp.ucla.edu

2
MINOR MAGNETIC STORM RECORDED AT SAN JUAN -
11/24/96
3
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

4
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 observers location
• X component is towards geographic north pole
• Y component is east along a circle of latitude
• Z component is radially inward or down

5
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

6
SCHEMATIC ILLUSTRATION OF EFFECTS OF RING CURRENT
IN H COMPONENT
Projection of a uniform axial field onto Earths
surface
Magnetic effects of a symmetric equatorial ring
current
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MAGNETIC EFFECT OF A RING CURRENT AT EARTHS
CENTER

• Axial field from a circular ring current

Z

• Field at center of ring

X
LRRe
Westward RingCurrent

• Convenient units

8
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

9
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

10
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

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DESSLER-PARKER-SCKOPKE DERIVATION
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THE DESSLER-PARKER-SCKOPKE RELATION
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CONTRIBUTIONS TO THE VARIATION IN THE H COMPONENT
14
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

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EFFECTS OF MAGNETOPAUSE ON THE Dst INDEX
10

• Balance magnetic pressure against dynamic pressure

8
6
4
Neutral
Point
2
Z (Re)
0
-2
Solar
-4
Wind
-6
-8
-10
0
5
10
15
X (Re)
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A SHEET CURRENT MODEL OF EFFECT OF TAIL CURRENT
ON Dst

• Magnetic Effects

• Tail Current Model

xxx
x
x
x
Ri
Ro
Bz
xxx
x
x
x
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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

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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

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ESTIMATION OF THE SECULAR TREND INH COMPONENT AT
SAN JUAN
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REMOVAL OF SECULAR TREND FROM HOURLY VALUES OF H
AT GUAM DURING STORM
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COMPARISON OF GUAM H WITH SECULAR TREND IN 1986
x 10
395.5
Secular Trend
3.59
3.585
Observed H (nT)
3.58
3.575
115
120
125
130
135
140
DEVIATION OF GUAM H FROM SECULAR TREND IN 1986
50
0
-50
Transient H (nT)
-100
115
120
125
130
135
140
Day in 1986
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REMOVAL OF STORM EFFECTS IN QUIET DAY (Sq)
ESTIMATION
COMPARISON OF DETRENDED GUAM H TO MIDNIGHT SPLINE
50
0
-50
Disturbance (nT)
Midnight Spline
-100
H Comp
115
120
125
130
135
140
DETRENDED AND STORM CORRECTED GUAM H IN 1986
80
60
40
Residual H (nT)
20
0
-20
115
120
125
130
135
140
Day in 1986
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QUIET VALUES DURING STORM USED IN QUIET DAY (Sq)
ESTIMATION
80
Flagged Point
Quiet Value
70
60
50
40
30
Transient H (nT)
20
10
0
-10
-20
115
120
125
130
135
140
Day in 1986
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Sq FOR H AT SAN JUAN IN 1978 AS FUNCTION OF DAY
OF YEAR AND UT
-5
350
-5
0
10
0
300
20
25
15
0
5
250
0
20
200
Day of Year
15
0
0
5
0
0
150
10
15
25
20
30
31.1
100
50
20
25
0
-5
5
0
5
10
15
20
UT Hour
-5
0
5
10
15
20
25
30
Diurnal Variation (nT)
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QUIET GUAM H TRACE AT EQUINOX AND SOLSTICE 1986
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COMPARISON OF SEVERAL OBSERVED AND PREDICTED
QUIET DAYS AT GUAM IN 1986
Observed
Quiet
Disturbance (nT)
Residual
40
41
42
43
44
45
46
47
48
49
50
Day in 1986
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CORRECTED H AT GUAM DURING RECOVERY FROM A
MAGNETIC STORM
60
40
20
0
Quiet H
-20
-40
Disturbance (nT)
-60
-80
Corrected H
-100
Observed H
-120
-140
40
41
42
43
44
45
46
47
48
49
50
Day in 1986
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DELTA H AT MIDLATITUDES DURING MAGNETIC STORM
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MAJOR SUBSTORMS DURING MAGNETIC STORM OF APRIL
3-5, 1979
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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 12, 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!