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CALCULATION OF THE Dst INDEX

CALCULATION OF THE Dst INDEX. Presentation at LWS CDAW Workshop Fairfax, Virginia March 14-16, 2005. R.L. McPherron Institute of Geophysics and Planetary Physics University of California Los Angeles rmcpherron@igpp.ucla.edu. Dipole is tilted and inverted relative to rotation axis

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CALCULATION OF THE Dst INDEX

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  1. CALCULATION OF THE Dst INDEX Presentation at LWS CDAW WorkshopFairfax, VirginiaMarch 14-16, 2005 R.L. McPherron Institute of Geophysics and Planetary Physics University of California Los Angeles rmcpherron@igpp.ucla.edu

  2. 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 GEOGRAPHIC COORDINATES USED IN MAGNETIC MEASUREMENTS

  3. 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 LOCAL VIEW OF VARIOUS COORDINATE SYSTEMS USED IN GEOMAGNETISM

  4. 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 DISTRIBUTION OF RING CURRENT AND ITS PERTURBATION IN A MERIDIAN

  5. Moos, N.A.F., Colaba Magnetic Data, 1846 to 1905, 2, The Phenomena and its Discussion, Central Government Press, Bombay, 1910. Figure below taken from the following reference to illustrate work by Moos Chapman, S., and J. Bartels, Geomagnetism, Vol 1, Clarendon Press, Oxford, 1962. Use a large set of storms with start time uniformly distributed in local time For each hour after an ssc (storm time) find the average departure of H at a single station from its mean value in the corresponding months (disturbance) obtaining the disturbance versus storm time or Dst Separate the storms by the local time at which the ssc occurred to illustrate the asymmetry of the development as seen by a single station Origin of Dst

  6. = + + + ( i ) ( i ) ( i ) ( i ) ( i ) H ( t ) H ( t ) Sq ( t ) L ( t ) D ( t ) 0 Main field and its secular variation Secular Variation from average IGY Average IGY Calculation of Dst Measured field at ith station Disturbance Variation Lunar Variation Solar Quiet Day Variation Main Field Variation

  7. Average Variation over Longitudinal Chain For each hour average the preceding equation over 8 stations around the world at fixed latitude Average Disturbance Average Lunar variation ~ 0 Average Sq at 8 stations Average secular variation at 8 stations Round-world average variation at time t

  8. Average Sq Variation • For ith station in month m take the average of the five international quiet days (25 hours) defined by Greenwich time • From this average quiet day subtract a linear trend connecting midnight at the two ends of the Greenwich day • For each month average the quiet day variations over all stations • Model the residual average Sq variation with a double Fourier series in time T and month M. Estimate up to 6th harmonic. • Use this series to estimate the average Sq variation at any hour of any day of year. Subtract the estimate fromDH(t).

  9. Average Secular Variation • Plot the residual variation versus time. Found that there was no trend in its baseline, i.e. the average secular variation was constant • Determine the average level of the baseline during quiet intervals not affected by magnetic storms • Subtract this constant from the previous residual obtaining • Assume that the last term in {} is approximately zero so that • Assume that only the ring current contributes to the average disturbance so that we have found the disturbance as a function of storm time

  10. Use four stations distributed in longitude near 25 magnetic latitude SECULAR VARIATION For each station calculate annual means from the 5 quiet days of each month Use current and four preceding annual means to determine a polynomial fit to the quiet days. Let t be time relative to some reference epoch. Use the preceding 5-year fit to predict the baseline value on first day of current year. Include this value as a data point in the current 5-year fit Create the deviation of H from the secular trend for each hour of current year QUIET DAY VARIATION Use the five local days closest to the Greenwich monthly five quiet days plus 1-hour at each end of these days At each hour calculate monthly averages of the local quiet days Subtract a linear trend passing through average of first and last hours Fit a double Fourier transform in hour of day and day of year to the 12 sets of 24 hourly values Use the fit coefficients to calculate the quiet day variation at every hour of year Subtract the estimated Sq variation from the deviation time series Calculate Dst as the latitude weighted average disturbance variation Modern Dst CalculationSugiura, M., and T. Kamei, Equatorial Dst index 1957-1986, IAGA Bulletin No 40, pp. 7-14, ISGI Publications Office, Saint-Maur-des-Fosses, France, 1991.

  11. Creation of the Secular Variation • For every calendar month select 10 international quiet days • Determine the monthly median value at local midnight (red dots) • Take 2-year running average of midnight medians • Fit a cubic smoothing spline to the filtered data (black line)

  12. Creation of Monthly Quiet Day Curve • Create ensemble of the 10 international quiet days for a month • Subtract value at local midnight • Subtract linear trend through left and right local midnight • Calculate median variation as function of time

  13. Solar Cycle Effects on Sq Variation • Calculate monthly median quiet day for each month of four solar cycles (44 years) • For each year of an 11-year solar cycle calculate mean of four monthly medians • Compare all means (all years in lower right panel) • There appears to be little effect of solar cycle on the median quiet day • We can ignore effect of phase of solar cycle in Sq

  14. KakiokaMonthlyQuiet Days1960 to 2004 • For each month in 44 years find median Sq of 10 quiet days • Find median of each month for all years • Arrange as a map of variation as function of local time and month • Use coefficients of two-dimensional Fourier transform to calculate Sq

  15. Fourier Synthesis of Arbitrary Quiet Day • Use data from four solar cycles • Find the median quiet day for each month • Load data into a 12 month by 24 hour 2-D array • Perform a double Fourier transform • Expand array to 366 by 24 and move the Fourier coefficients to correct location • Inverse transform to obtain quiet day for each day of year

  16. Removal of Secular and Quiet Variations • Select the portion of the secular variation curve for the interval • Synthesize the quiet day variation for the appropriate days of year • Subtract both from the original data to obtain the disturbance variation for the given station component

  17. 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 LONGITUDINAL PROFILE OF Bj FROM MAGNETOSPHERIC CURRENTS

  18. Relation of Dst to Stream Interface • The figure shows the relation of several solar wind and magnetospheric variables to CIRs The main stream interface at leading edge of high speed stream is taken as epoch zero in a superposed epoch analysis • The colored patches show upper and lower quartiles of the variable as function of epoch time • The heavy red line is the median curve • Stream interfaces cause weak storms

  19. 70 60 50 40 30 20 10 0 -10 -20 -30 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

  20. CORRECTED H AT GUAM DURING RECOVERY FROM A MAGNETIC STORM 60 40 20 0 Quiet H -20 -40 Disturbance (nT) -60 -80 CorrectedH -100 Observed H -120 -140 40 41 42 43 44 45 46 47 48 49 50 Day in 1986

  21. The End!

  22. SCHEMATIC ILLUSTRATION OF EFFECTS OF RING CURRENT IN H COMPONENT Magnetic effects of a symmetric equatorial ring current Projection of a uniform axial field onto Earth’s surface

  23. In Out

  24. 4 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 REMOVAL OF SECULAR TREND FROM HOURLY VALUES OF H AT GUAM DURING STORM

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

  26. THE DESSLER-PARKER-SCKOPKE RELATION

  27. CONTRIBUTIONS TO THE VARIATION IN THE H COMPONENT

  28. 4 x 10 2.74 2.735 80% Point Fourth Order Trend 2.73 2.725 2.72 H (nT) 2.715 2.71 Daily Average 2.705 2.7 1978 1983 1988 Year ESTIMATION OF THE SECULAR TREND INH COMPONENT AT SAN JUAN

  29. 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

  30. 60 Spring 50 Summer Fall 40 Winter 30 Pred Quiet H (nT) 20 10 0 -10 0 5 10 15 20 Local Time QUIET GUAM H TRACE AT EQUINOX AND SOLSTICE 1986

  31. 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)

  32. 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

  33. 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 CURRENTS CONTRIBUTING TO MIDLATITUDE MAGNETIC PERTURBATIONS

  34. Balance magnetic pressure against dynamic pressure EFFECTS OF MAGNETOPAUSE ON THE Dst INDEX 10 8 6 4 Neutral Point 2 Z (Re) 0 -2 Solar -4 Wind -6 -8 -10 15 10 5 0 X (Re)

  35. Tail Current Model Magnetic Effects 0 -5 Normal Tail -10 Total -15 Bz (nT) -20 Inner Edge -25 -30 Earth -35 -6 -4 -2 0 2 4 6 -Xgsm (Re) A SHEET CURRENT MODEL OF EFFECT OF TAIL CURRENT ON Dst xxx x x x Ri Ro Bz xxx x x x

  36. 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 MAGNETIC EFFECTS OF A SUBSTORM CURRENT WEDGE

  37. 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

  38. Magnetograms from several midlatitude stations during storm

  39. 1000 125 1610 2118 252 1143 2200 900 1641 627 1803 2351 757 1702 700 1032 2147 0 AU and AL index (nT) -1000 -2000 0 12 24 36 48 60 72 100 125 1610 2118 252 1143 2200 900 1641 627 1803 2351 757 1702 700 1032 2147 0 Dst Index (nT) -100 -200 0 12 24 36 48 60 72 Time from 0000 UT on April 3 MAJOR SUBSTORMS DURING MAGNETIC STORM OF APRIL 3-5, 1979

  40. 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!

  41. EXAMPLE OF MIDLATITUDE MAGNETIC DATA DURING MAGNETIC STORM

  42. 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

  43. Axial field from a circular ring current MAGNETIC EFFECT OF A RING CURRENT AT EARTH’S CENTER Z • Field at center of ring X LRRe Westward RingCurrent • Convenient units

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

  45. DESSLER-PARKER-SCKOPKE DERIVATION

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