DEFINITION, CALCULATION, AND PROPERTIES OF THE Dst INDEX R.L. McPherron Institute of Geophysics and Planetary Physics University of California Los Angeles Presentation at GEM 1998 Workshop Snowmass, Colorado June 15-19, 1998

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

INTERPLANETARY MAGNETIC FIELD, AE AND Dst INDICES DURING STORM n Coronal mass ejection produce intervals of strong southward Bz at the earth n Magnetic reconnection drives magnetospheric convection n Convection drives currents along field lines and through ionosphere n Ground magnetometers record effects of ionospheric currents in H and other components n H traces are used to construct the AE and Dst index

GEOGRAPHIC COORDINATES USED IN MAGNETIC MEASUREMENTS n Dipole is tilted and inverted relative to rotation axis n Dipole field lines are nearly vertical above 60  latitude n Cartesian geographic coordinates are defined in a plane tangent to earth at observer’s location n X component is towards geographic north pole n Y component is east along a circle of latitude n Z component is radially inward or down

LOCAL VIEW OF VARIOUS COORDINATE SYSTEMS USED IN GEOMAGNETISM n Origin is located at observer n X points north, Y points east, Z points down in the local tangent plane n F is the total vector field n H is the horizontal projection of the vector F n D is the east declination of H from geographic north in tangent plane n I is the inclination of F below the tangent plane n 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

MAGNETIC EFFECT OF A RING CURRENT AT EARTH’S CENTER n Axial field from a circular ring current n Field at center of ring n Convenient units X Westward Ring Current LRReLRRe Z

LONGITUDINAL PROFILE OF  B j FROM MAGNETOSPHERIC CURRENTS n Symmetric ring should create nearly constant longitudinal profile in H component n Local time average of  H at equator approximates  B at center of Earth n But other magnetospheric currents create local time dependent deviations from symmetry n Assume asymmetric component has zero mean when averaged over local time n Define the disturbance storm time index Dst as local time average of observed  H profile

DISTRIBUTION OF RING CURRENT AND ITS PERTURBATION IN A MERIDIAN n Most of the current is concentrated close to the equator n Eastward current inside and westward outside n Perturbations curl around the volume of current n The perturbation over the earth is nearly uniform and axial

THE SOLENOIDAL EFFECT OF THE RADIATION BELT CURRENTS n A more realistic model of the ring current n Shows the magnetic perturbations n Shows the distortion of dipole current contours n Perturbation field from ring current

DESSLER-PARKER-SCKOPKE DERIVATION

THE DESSLER-PARKER-SCKOPKE RELATION

CONTRIBUTIONS TO THE VARIATION IN THE H COMPONENT

CURRENTS CONTRIBUTING TO MIDLATITUDE MAGNETIC PERTURBATIONS n View is from behind and aabove earth looking toward Sun n Current systems illustrated –Symmetric ring current –Dayside magnetopause current –Partial ring current –Tail current –Substorm current wedge –Region 1 current –Region 2 current n Current systems not shown –Solar quiet day ionospheric current –Secular variation within earth –Main field of Earth

EFFECTS OF MAGNETOPAUSE ON THE Dst INDEX n Balance magnetic pressure against dynamic pressure X (Re) Z (Re) Solar Wind Neutral Point

A SHEET CURRENT MODEL OF EFFECT OF TAIL CURRENT ON Dst Xgsm (Re) Bz (nT) Normal Tail Inner Edge Total Earth n Tail Current Model n Magnetic Effects BzBz xxx xxx xxx RiRi RoRo

MAGNETIC EFFECTS OF A SUBSTORM CURRENT WEDGE n Transverse currents in the magnetosphere are diverted along field lines to the ionosphere n Viewed from above north pole the projection of the current system has a wedge shape n Midlatitude stations are primarily affected by field-aligned currents and the equatorial closure (an equivalent eastward current) n The local time profile of H component is symmetric with respect to the central meridian of wedge n The D component is asymmetric with respect to center of wedge

STEPS IN THE CALCULATION OF Dst INDEX n Define the reference level for H component on a monthly basis n Fit a polynomial to reference H values (secular variation) n Adjust H observed on a given day by subtracting secular variation n Identify quiet days from same season and phase of solar cycle n Remove storm effects in quiet values and offset traces so that there is zero magnetic perturbation at station midnight n Flag all values recorded during disturbed times and interpolate from adjacent quiet intervals n Create some type of smoothed ensemble average of all quiet days n Subtract average quiet day from adjusted daily variation to obtain disturbance daily variation for station n Repeat for a number of stations distributed around the world at midlatitudes n Project the local H variations to obtain axial field from ring current and average over all stations

ESTIMATION OF THE SECULAR TREND IN H COMPONENT AT SAN JUAN x 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 x 10 4 Observed H (nT) COMPARISON OF GUAM H WITH SECULAR TREND IN Day in 1986 Transient H (nT) DEVIATION OF GUAM H FROM SECULAR TREND IN 1986 Secular Trend

REMOVAL OF STORM EFFECTS IN QUIET DAY (Sq) ESTIMATION Day in Disturbance (nT) COMPARISON OF DETRENDED GUAM H TO MIDNIGHT SPLINE Residual H (nT) DETRENDED AND STORM CORRECTED GUAM H IN 1986 Midnight Spline H Comp

QUIET VALUES DURING STORM USED IN QUIET DAY (Sq) ESTIMATION Day in 1986 Transient H (nT) Flagged Point Quiet Value

Sq FOR H AT SAN JUAN IN 1978 AS FUNCTION OF DAY OF YEAR AND UT UT Hour Day of Year Diurnal Variation (nT)

QUIET GUAM H TRACE AT EQUINOX AND SOLSTICE 1986

COMPARISON OF SEVERAL OBSERVED AND PREDICTED QUIET DAYS AT GUAM IN Day in 1986 Disturbance (nT) Observed Quiet Residual

CORRECTED H AT GUAM DURING RECOVERY FROM A MAGNETIC STORM Day in 1986 Disturbance (nT) Quiet H Observed H Corrected H

DELTA H AT MIDLATITUDES DURING MAGNETIC STORM

MAJOR SUBSTORMS DURING MAGNETIC STORM OF APRIL 3-5, 1979

CONCLUSIONS n The Dst index is defined to be linearly proportional to the total energy of particles drifting in the radiation belts (symmetric ring current) n Dst must be estimated from surface measurements of the horizontal component of the magnetic field n Surface field measurements include effects of many electrical currents other than the symmetric ring current n These effects must be estimated or eliminated by the algorithm that calculates the Dst index n Extraneous currents include: secular variation, Sq, magnetopause, tail, Region 1&2, partial ring current, substorm current wedge, magnetic induction n 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!