DEFINITION, CALCULATION, AND PROPERTIES OF THE Dst INDEX

R.L. McPherronInstitute of Geophysics and Planetary Physics

University of California Los Angelesrmcpherron@igpp.ucla.edu

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!