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NASA/TP—2007–215079
Prediction of Geomagnetic Activity and Key Parameters in High-Latitude Ionosphere—Basic ElementsW. Lyatsky Oak Ridge Associated Universities, Oak Ridge, Tennessee
G.V. KhazanovMarshall Space Flight Center, Marshall Space Flight Center, Alabama
October 2007
National Aeronautics andSpace AdministrationIS20George C. Marshall Space Flight CenterMarshall Space Flight Center, Alabama35812
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NASA/TP—2007–215079
Prediction of Geomagnetic Activityand Key Parameters in High-LatitudeIonosphere—Basic ElementsW. Lyatsky Oak Ridge Associated Universities, Oak Ridge, Tennessee
G.V. KhazanovMarshall Space Flight Center, Marshall Space Flight Center, Alabama
October 2007
Nat�onal Aeronaut�cs andSpace Adm�n�strat�on
Marshall Space Fl�ght Center • MSFC, Alabama 35812
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Ava�lable from:
NASA Center for AeroSpace Informat�on7115 Standard Dr�ve
Hanover, MD 21076 –1320301– 621– 0390
Th�s report �s also ava�lable �n electron�c form at<https://www2.st�.nasa.gov>
Acknowledgments
We are grateful to Aaron R�dley for k�ndly prov�d�ng us w�th data on cross-polar cap potent�al and total hem�spher�c Joule heat�ng �n the Northern Hem�sphere computed w�th the ass�m�lat�ve mapp�ng of �onospher�c electrodynam�cs techn�que,
and Arjun Tan for fru�tful collaborat�on. We also gratefully acknowledge �nvaluable efforts of the Goddard Space Fl�ght Center staff, the Nat�onal Geophys�cal Data Center, the Dan�sh Meteorolog�cal Inst�tute, and the World
Data Center, Kyoto, Japan, �n prov�d�ng solar w�nd data, geomagnet�c act�v�ty �nd�ces, and data from geomagnet�c observator�es. Th�s study was part�ally funded from NASA grant NAG5–11995.
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TABLE OF CONTENTS
1. INTRODUCTION .......................................................................................................................... 1
2. POLAR MAGNETIC INDEX OF GEOMAGNETIC ACTIVITY ................................................ 3
2.1 Introduct�on ............................................................................................................................ 3 2.2 Polar Magnet�c Index Calculat�on Method ............................................................................. 4
3. COUPLING FUNCTION ............................................................................................................... 9
3.1 Ex�st�ng and New Coupl�ng Funct�ons ................................................................................... 9 3.2 Correlat�on Between Polar Magnet�c and Polar Cap Ind�ces and Var�ous Coupl�ng Funct�ons ................................................................................................................................ 11 3.3 Seasonal and Un�versal T�me Var�at�ons �n Correlat�on Between Polar Magnet�c and Polar Cap Ind�ces and Upstream Solar W�nd/Interplanetary Magnet�c F�eld Data ......... 14
4. CORRELATION WITH AURORAL ELECTROJET AL INDEX AND SUBAURORAL Kp INDEX ..................................................................................................................................... 19
4.1 Correlat�on W�th Auroral Electrojet AL Index ....................................................................... 19 4.2 Correlat�on W�th Subauroral Kp Index ................................................................................... 20
5. CORRELATION WITH CROSS-POLAR-CAP POTENTIAL DROP AND JOULE HEATING ................................................................................................................ 22
5.1 Introduct�on ............................................................................................................................ 22 5.2 Prel�m�nary Results ................................................................................................................. 22
6. CONCLUSIONS ............................................................................................................................. 26
REFERENCES .................................................................................................................................... 27
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LIST OF FIGURES
1. Correlat�on of the coupl�ng funct�on (F*) w�th hourly mean values of (a) magnet�c fields(Hb), (b) the PC �ndex, and (c) the PM �ndex for 2001 ............................................... 7 2. Correlat�on of the coupl�ng funct�on (F*) w�th hourly mean values of (a) magnet�c fields(Hb), (b) the PC �ndex, and (c) the PM �ndex for 2002 ............................................... 8
3. Correlat�on between PM/PC �nd�ces and upstream solar w�nd parameters for the Kan and Lee coupl�ng funct�on (a) and (b), and the Lyatsky et al. coupl�ng function(c)and(d),for2001.Onecanseeasignificantincreaseingoodness offit(R2) for the latter coupl�ng funct�on for both PM and PC �nd�ces ................................ 12
4. Correlat�on between PM/PC �nd�ces and solar w�nd parameters for the Kan and Lee coupl�ng funct�on (a) and (b), and the Lyatsky et al. coupl�ng funct�on (c) and (d) for2002.Again,asignificantincreaseisshowninthecorrelationbetweenthePM/PC �nd�ces and the latter coupl�ng funct�on ................................................................................ 13
5. Correlat�on of the PM/PC �nd�ces w�th a d�mens�onless coupl�ng funct�on (F*): (a) and (b) for 2001 and (c) and (d) for 2002. Th�s demonstrates an �ncrease inthecorrelation(againstthatshowninfigs.3and4)ofbothPMandPCindices w�th the F* funct�on .............................................................................................................. 14
6. Correlat�on between (a) the PM �ndex and coupl�ng funct�on (F*) and (b) the PC �ndex and coupl�ng funct�on (F*) for 1997—related to low solar act�v�ty ........................... 15
7. Correlat�on between (a) the PM �ndex and coupl�ng funct�on (F*) and (b) the PC �ndex and coupl�ng funct�on (F*) for 2000—related to h�gh solar act�v�ty .......................... 16
8. Solarcyclevariationincorrelation.Goodnessoffit(R2) of the correlat�on of PM, PC, and AL �nd�ces w�th coupl�ng funct�on (F*) �s shown for 10 yr (1995–2004). Correlat�on between PM and F*issignificantlyhigherthanthatforthePCandAL �nd�ces for all years. The average magn�tude of R2 for the correlat�on between the PM and F* funct�on �s ≈ 0.74,whichcorrespondstothecorrelationcoefficient R ≈ 0.86. Presented values of R2 are averages for 3 yr .......................................................... 17
9. Summerdropincorrelation.Goodnessoffit(R2) of the correlat�on of PM, AL, and PC �nd�ces w�th coupl�ng funct�on (F*) �s shown for summer months (May–August) for 1995–2004. Th�s demonstrates a dramat�c drop �n the correlat�on of the PC �ndex for the summer months wh�le the correlat�on between the PM �ndex and F* funct�on remainshighandclosetothatinfigure8.PresentedvaluesofR2 are averages for 3 yr ..... 17
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LIST OF FIGURES (Continued)
10. Un�versal t�me var�at�on �n correlat�on of PM/PC �nd�ces w�th coupl�ng funct�on (F*). Shown are mean values of R2 for 4-hr UT �ntervals, averaged for the follow�ng years: (a) 1995–1998 (low and moderate solar act�v�ty) and (b) 1999–2004 (h�gh solar act�v�ty). The curves are the fourth-order polynom�al fittothedata.CorrelationbetweenPCandF* has a strong UT var�at�on and fa�ls �n the �nterval of 10–20 UT wh�le the correlat�on between the PM and F* funct�on rema�ns h�gh or even �ncreases �n th�s UT sector ....................................... 18
11. Correlat�on of (a) the AL �ndex w�th coupl�ng funct�on (F*) and (b) the AL �ndex w�th the PM �ndex for 1995. Correlat�on between the AL and PM �nd�ces �s significantlyhigher(R2 ≈ 0.8 that corresponds to R ≈ 0.89) than that between the AL and coupl�ng funct�on (F*) ....................................................................................... 19
12. Correlat�on of (a) the AL �ndex w�th coupl�ng funct�on (F*) and (b) the AL �ndex w�th the PM �ndex for 1998—related to moderate solar act�v�ty. The correlat�on between the AL and PM �nd�ces rema�ns h�gh (R2 ≈ 0.73 that corresponds to R ≈ 0.86) ..................... 20
13. Correlat�on of (a) the Kp �ndex w�th the PM �ndex and (b) the Kp �ndex w�th the PC �ndex. Correlat�on between 3-hr values of Kp1.5 and PM/PC �nd�ces fortheyear2000—relatedtohighsolaractivity.Goodnessoffit(R2) between Kp1.5 and PM �s much better than that for Kp1.5 versus PC ........................................................... 21
14. Goodnessoffit(R2) of the correlat�on of Kp1.5 w�th AL, PM, and PC �nd�ces for 1995–2004. The correlat�on between Kp1.5andPMissignificantlybetter than that for the other two �nd�ces. Presented values of R2 are averages for 3 yr ................. 21
15. Correlat�on of hourly mean values of the AMIE CPC potent�al drop (U) w�th (a) the PM �ndex and (b) the PC �ndex for all days of 1998. The correlat�on �s much better for U versus the PM �ndex (R2 ≈ 0.78) than for U versus the PC �ndex (R2 ≈ 0.69) (data courtesy of Aaron R�dley, Un�vers�ty of M�ch�gan) ..................................................... 23
16. Correlat�on of hourly mean values of AMIE JH1/2 w�th (a) the PM �ndex and (b) the PC �ndex for all days of 1998. The correlat�on �s much better for JH1/2 versus the PM �ndex (R2 ≈ 0.75) than that for JH1/2 versus the PC �ndex (R2 ≈ 0.68) (data courtesy of Aaron R�dley, Un�vers�ty of M�ch�gan) ......................... 24
17. Correlat�on of the actual (AMIE) and pred�cted hourly mean values of the CPC voltage (U) and JH1/2 for all days of 1998. Th�s shows extremely h�gh correlat�on
(R2 ≈ 0.81–0.82) for both U voltage and JH1/2 (data courtesy of Aaron R�dley, Un�vers�ty of M�ch�gan) ........................................................................................................ 25
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LIST OF ACRONYMS
AE auroral electrojet �ndex of geomagnet�c act�v�ty
AL auroral electrojet �ndex of geomagnet�c act�v�ty
AMIE ass�m�lat�ve mapp�ng of �onospher�c electrodynam�cs
CPC cross-polar-cap (potent�al drop)
Dst low lat�tude �ndex of geomagnet�c act�v�ty
F funct�on a solar w�nd-geomagnet�c act�v�ty coupl�ng funct�on
F* funct�on a solar w�nd-geomagnet�c act�v�ty d�mens�onless coupl�ng funct�on
IMF interplanetarymagneticfield
JH Joule heat�ng
Kp subauroral �ndex (of geomagnet�c act�v�ty)
OMNI a mult�source, hourly resolut�on comp�lat�on of near-Earth energet�c part�cle andsolarwindmagneticfieldandplasmadata
PC polar cap �ndex of geomagnet�c act�v�ty
PM polar magnet�c �ndex of geomagnet�c act�v�ty
SuperDARN Super Dual Auroral Radar Network
TP Techn�cal Publ�cat�on
UT un�versal t�me
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NOMENCLATURE
A quant�ty
a coefficient
A0 measuredmagneticfield
B magneticfieldvector b coefficient
Bz IMF component along the z-ax�s �n solar-magnetospher�c frame
By IMF component along the y-ax�s �n solar-magnetospher�c frame IMF
Byz IMF component �n the y-z plane �n solar-magnetospher�c frame IMF
C constant
c coefficient
D day of year
E electricfield
eb a un�t vector correspond�ng to the best correlat�on
F solar w�nd-geomagnet�c act�v�ty coupl�ng funct�on
F* d�mens�onless solar w�nd-geomagnet�c act�v�ty coupl�ng funct�on
Fvisc coupl�ng funct�on account�ng for a contr�but�on from v�scous �nteract�on
f a funct�on
g correct�ve funct�on of season and UT
H geomagneticfieldvectormeasuredontheground
Hb geomagneticfieldcomponentofmagneticdisturbancesacrossthetranspolarequivalent�onospher�c current
H⊥ geomagneticfieldinthehorizontalplane
Hz geomagneticfieldcomponentalongthevertical(downward)direction
l a number—upper level of summ�ng
M a quant�ty
m arb�trary value
n solar w�nd plasma dens�ty number; arb�trary value
R correlationcoefficient
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NOMENCLATURE (Continued)
R2 goodnessoffit
r a number—upper level of summ�ng
t t�me
U electr�c potent�al drop
Vsw solar w�nd veloc�ty
ν power
X geomagneticfieldcomponentalongthex-ax�s
x horizontal(northward)axis
Y geomagneticfieldcomponentalongthey-ax�s
y azimuthalaxis
Z geomagneticfieldcomponentalongthez-ax�s
z vert�cal ax�s
α arb�trary value
∆ �ncrement
γ an exponent
ϕ clockangleinthehorizontalx-y plane on the ground
Λ geomagnet�c lat�tude
θ clock angle �n solar-magnetosphere frame �n the y-z plane between the z (northward) ax�s and the Byz vector
x
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TECHNICAL PUBLICATION
PREDICTION OF GEOMAGNETIC ACTIVITY AND KEY PARAMETERS IN HIGH-LATITUDE IONOSPHERE—BASIC ELEMENTS
1. INTRODUCTION
Pred�ct�on of geomagnet�c act�v�ty and related events �n the Earth’s magnetosphere and �onosphere �s an �mportant task of the Space Weather program. Relat�vely long-term (for several days and longer) pred�ct�on of geomagnet�c act�v�ty �s usually based on observat�ons of the Sun wh�le short-term (about 1–2hr)predictionisbasedonupstreamsolarwindandinterplanetarymagneticfield(IMF)data,measuredw�th spacecraft at the d�stance of about 100 to 200 Earth rad�� sunward. The last, more rel�able pred�ct�on method w�ll pr�mar�ly be used here.
In general form, the pred�ct�on formula can be expressed as:1
M t a M t m t b F t m tm mm
l
m
r( ) ( ) ( ) ,= − + −
==∑∑ ∆ ∆
01 (1)
where M �s a pred�cted value at the t�me (t), M (t – m ∆t) �s th�s value at a prev�ous t�me (t – m ∆t), F �s a funct�on that affects the M value and taken at (t – m ∆t), and am and bmaresomecoefficients.Inthelinearapproach,thecoefficientsam and bm are assumed to be constant, wh�le �n a nonl�near approach, thesecoefficientsmaybedependentonvaluesofM and F. The pred�ct�on �ncludes the determ�nat�on of the Ffunction,thecoefficientsam and bm, and the �ntegrat�on t�me. In the pred�ct�on of geomagnet�c act�v-�ty from solar w�nd data, d�fferent coupl�ng funct�ons (F) are used, wh�ch are the comb�nat�ons of solar w�nd parameters affect�ng the magnetosphere.1–6 The second term �n equat�on (1) �s related to a source. Thefirsttermisaccountingforthevalueunderinvestigationtakenforaprevioustimeinterval.
The pred�ct�on also �ncludes pred�ct�ng (evaluat�ng) some quant�t�es that cannot eas�ly be obta�ned but may be pred�cted from ava�lable exper�mental data us�ng results of correlat�on analys�s. For �nstance, thecross-polarcap(CPC)electricpotentialisakeyparameterthatshowsanelectricenergyfluxenteringthe days�de �onosphere from the solar w�nd. The CPC voltage cannot be rel�ably mon�tored. Comput�ng theCPCvoltageisaninverseproblemthatincludesacomplicatedtechniqueusinggeomagneticfielddatafrom many geomagnet�c observator�es.7,8 As a result, mon�tor�ng the CPC voltage at present �s not pos-s�ble; however, CPC voltage may be pred�cted w�th h�gh rel�ab�l�ty from upstream solar w�nd/IMF data and appropr�ate geomagnet�c act�v�ty �nd�ces.
Pred�ct�on rel�ab�l�ty �s dependent on both pred�ct�on method and the elements �ncluded. The two ma�n elements are an appropr�ate geomagnet�c act�v�ty �ndex and coupl�ng funct�on—the comb�nat�on of
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solarwindparametersprovidingthebest-fitcorrelationbetweenupstreamsolarwind/IMFdataandgeo-magnet�c act�v�ty. The appropr�ate cho�ce of these two elements �s �mperat�ve for any rel�able pred�ct�on model.Thefirstelement,ageomagneticactivityindex,shouldbeavailableinnear-realtimeandhaveaclear mean�ng as well as good, rel�able correlat�on w�th upstream solar w�nd/IMF data. The second ele-ment �s the coupl�ng funct�on, a comb�nat�on of solar w�nd/IMF parameters prov�d�ng the best correlat�on between upstream solar w�nd/IMF data and geomagnet�c act�v�ty �nd�ces.
ThepurposeofthisTechnicalPaper(TP)istoreanalyzeandimprovethesetwokeyelements—theappropr�ate geomagnet�c act�v�ty �ndex and the solar w�nd coupl�ng funct�on—wh�ch �s an �mportant step �n �mprov�ng the pred�ct�on rel�ab�l�ty of geomagnet�c act�v�ty and related events �n the Earth’s magneto-sphere, �onosphere, and thermosphere.
A new geomagnet�c act�v�ty �ndex has been developed that shows much better correlat�on w�th upstream solar w�nd/IMF data than other ex�st�ng �nd�ces. A new vers�on of the solar w�nd coupl�ng func-tion,whichaccountsforbothsolarwindelectricfield,penetratingintothemagnetosphere,andtheeffectof solar w�nd dens�ty and pressure, has been developed. Th�s coupl�ng funct�on shows h�gh, stable correla-t�on w�th geomagnet�c act�v�ty and related events �n the magnetosphere and �onosphere. Correlat�on of the new �ndex w�th the solar w�nd coupl�ng funct�on, other �nd�ces, such as the auroral electrojet (AL) and the subauroral (Kp) �nd�ces, and related d�sturbances �n the Earth’s �onosphere have been d�scussed. Rel�able pred�ct�on capab�l�t�es of some key parameters �n the Earth’s magnetosphere and �onosphere, such as the CPC voltage and total hem�spher�c Joule heat�ng (JH) �n the h�gh-lat�tude �onosphere, has been shown. These quant�t�es are used as �mportant �nput parameters for model�ng the magnetospher�c, �onospher�c, and thermospher�c processes, and the�r pred�ct�on rel�ab�l�ty �s very �mportant.
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2. POLAR MAGNETIC INDEX OF GEOMAGNETIC ACTIVITY
2.1 Introduction
Geomagnet�c act�v�ty �nd�ces, used for measur�ng the level of geomagnet�c act�v�ty, are calculated frommeasurementsofgeomagneticdisturbancesatspecificgeomagneticobservatories.Variousindicesshow d�fferent types of geomagnet�c act�v�ty.9–12 The auroral electrojet (AL and AE) �nd�ces show geo-magneticactivityintheauroralzonerelatedtosubstormactivity.Thesubauroral(Kp)indexshowsgeo-magnet�c act�v�ty at m�ddle lat�tudes. The low-lat�tude (Dst) �ndex shows the �ntens�ty of the r�ng current produced by energet�c part�cles �n the magnetosphere. The polar cap (PC) �ndex measures geomagnet�c activityproducedbyoverheadionosphericcurrentsandfield-alignedcurrentsinthenorthandsouthpolarcaps. S�nce the pr�mary source of geomagnet�c d�sturbances �s the solar w�nd, geomagnet�c act�v�ty �nd�-ces show the clear correlat�on w�th upstream solar w�nd/IMF data.
The ex�st�ng geomagnet�c act�v�ty �nd�ces were developed many years ago, when knowledge of the magnetosphereandionospherewasinsufficient,andimprovingthereliabilityofspaceweatherpredictionrequ�res the development of more appropr�ate �nd�ces. Ma�n requ�rements for �mprov�ng such �nd�ces are as follows:
• Should have a better, more stable correlat�on w�th upstream solar w�nd/IMF data.
• Should have good correlat�on w�th key �onospher�c and magnetospher�c parameters, such as CPC poten-t�al drop, Joule heat�ng, and others, wh�ch are used as �nput parameters for model�ng the processes �n the magnetosphere, �onosphere, and thermosphere.
• Should be ava�lable �n near real t�me.
In th�s TP, study results of a new, polar magnet�c (PM) �ndex of geomagnet�c act�v�ty �s shown. Thisindexwascomputedfrommagneticfieldmeasurementsfromtwonear-polegeomagneticobserva-tor�es—Thule, Greenland, and Vostok, Antarct�ca—the same observator�es that are used for der�v�ng the ex�st�ng PC �ndex, but a d�fferent method for der�v�ng the PM �ndex was used. As a result, the PM �ndex shows a much better correlat�on w�th the solar w�nd coupl�ng funct�on and related events than do other ex�st�ng �nd�ces, �nclud�ng the PC �ndex. Although the PM �ndex was computed from both observator�es �n two hem�spheres, the data from the Vostok Observatory are only part�ally ava�lable for the �nterval cons�dered (1995–2004), and �n th�s TP, only results obta�ned from the Thule Observatory—related to the Northern Hem�sphere—w�ll be cons�dered.
The most �mportant d�st�nct�on of the PM �ndex from the ex�st�ng PC �ndex cons�sts of account-
�ng for the contr�but�on from the transpolar (CPC) equ�valent �onospher�c current to geomagnet�c act�v-ityandrelatedevents,evenwhenthetranspolarcurrentdeviatessignificantlyfromitsaveragedirection.ThisleadstoasignificantincreaseinthecorrelationbetweenthePMindexandbothupstreamsolarwind
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data and key ground-measured parameters, such as CPC potent�al and Joule heat�ng �n the h�gh-lat�tude �onosphere, wh�ch are used as �nput parameters for model�ng the magnetospher�c, �onospher�c, and ther-mospher�c processes.
2.2 Polar Magnetic Index Calculation Method
The ex�st�ng PC �ndex was �ntroduced for measur�ng the transpolar equ�valent �onospher�c current, wh�ch �s an �mportant feature of h�gh-lat�tude geomagnet�c d�sturbances. Th�s �ndex �s calculated from measurements at two near-pole geomagnet�c stat�ons—Thule �n the Northern Hem�sphere (corrected geo-magnet�c lat�tude Λ ≈ 86.5°) and Vostok �n the Southern Hem�sphere (Λ ≈ –83.4°). The PC �ndex der�ved frommagneticfieldmeasurementsinthenorthpolarcapisrelatedmostlytogeomagneticactivityintheNorthernHemisphere,whiletheindexderivedfrommagneticfieldmeasurementsinthesouthpolarcap�s related mostly to the Southern Hem�sphere.
The transpolar current commonly po�nts between noon and dawn, so that the vector of magnet�c d�sturbances on the ground po�nts somewhere between noon and dusk. For der�v�ng the PC �ndex, the component of magnet�c d�sturbances (Hb) across a stat�st�cally-average d�rect�on of the transpolar electr�c current �s computed:11
Hb = H • eb , (2)
where Histhevectorofageomagneticdisturbanceinthehorizontalplaneandeb �s the un�t vector related tothetranspolarcurrentinaspecificuniversaltime(UT)andseason,anddirectedacrossthistranspolarcurrent. The ‘true’ d�rect�ons of the transpolar current and the eb vector are found when the Hb values show the best correlat�on w�th upstream solar w�nd/IMF data.
Thus, the PC �ndex shows the component of geomagnet�c perturbat�ons across an average d�rec-t�on of the transpolar current. Th�s method g�ves relat�vely good results when the d�rect�on of the trans-polarcurrentisclosetoitsaveragedirection.Inothercases,itleadstoasignificanterror.Therefore,forevaluat�ng the magn�tude of the transpolar current, another method �s used, wh�ch prov�des good results evenwhenthedirectionofthetranspolarcurrentdifferssignificantlyfromitsaveragedirection.
Equation(2),usedforcomputingthePCindex,suggeststhatthetranspolarcurrent,flowingacrossa stat�st�cally-average d�rect�on of th�s current, produces no geomagnet�c act�v�ty. Th�s approach under-est�mates the level of geomagnet�c act�v�ty pred�cted from the PC �ndex, s�nce the transpolar equ�valent ionosphericcurrentcontributes togeomagneticactivityevenwhenit issignificantlydeflectedfromitsaverage d�rect�on. To reduce th�s �ncorrectness, a new PM �ndex was computed.
Instead of us�ng equat�on (2) for the calculat�on of the PM �ndex, the Akasofu funct�on 2,5,13 was used, wh�ch der�ves the effect�veness of reconnect�on at days�de magnetopause when the IMF vector may besignificantlydeflectedfromthez-ax�s, mak�ng the problem close to the case under cons�derat�on. The follow�ng quant�ty was computed for der�v�ng the PM �ndex:
∆H = H⊥ s�nν (ϕ/2) , (3)
5
where H⊥ isatotalgeomagneticdisturbanceinthehorizontalplane; ϕ �s the angle measured from the d�rect�on, oppos�te the transpolar current, to �ts actual d�rect�on; and ν �s the power der�ved from exper�-mental data to prov�de the best correlat�on between ∆H and upstream solar w�nd/IMF data, wh�ch g�ves ν ≈ 3. The angle (ϕ) �s der�ved from exper�mental data for each UT hour and season. If the transpolar cur-rent �s along �ts averaged d�rect�on, ϕ = π. In th�s case, equat�on (3) co�nc�des w�th equat�on (2).
The ∆H quantitiesderived fromequation (3)maybesignificantlydifferent fromHb quant�t�es that areused for calculating thePC index.For instance, if the transpolar current isdeflected from itsaverage d�rect�on by the angle of π /2, Hb = 0 �s obta�ned from equat�on (2), wh�le from equat�on (3), ∆H ≈ 0.35 H⊥ �s obta�ned, so that the contr�but�on from the transpolar current to ∆Hremainsverysignificant.
The ∆H quant�ty may also be wr�tten as
∆H H H H H= ( /2) = 0.5 – /⊥ ⊥ ⊥( ) s�n s�n acos3 3ϕ b .. (4)
The values of ∆H may be used for a rough est�mate of the PM �ndex. The correlat�on w�th upstream solarwind/IMFdata,however,isbetterwhileaccountingforthemagneticfieldverticalHz component. Then,thefinaleformulaforthePMindexbecomesthefollowing:
PM = 0.5 a –H /H UT,bH H fz⊥ ⊥( ) +{ }s�n cos3 0 25. ( sseason) , (5)
where the factor 0.25 has been chosen to prov�de the best correlat�on of the result�ng PM �ndex w�th upstream solar w�nd/IMF data, and f (UT, season) �s a funct�on, reduc�ng the effect of UT and season, wh�ch are very strong at h�gh lat�tudes,14,15 on �onospher�c conductance and currents.
Geomagnet�c d�sturbances related to the s�gn (but not the absolute value) of the �nterplanetary magneticfield(IMFBy) related to the so-called Svalgaard-Mansurov effect,16,17 were reduced. Th�s effect �s assoc�ated w�th a s�ngle-current vortex located �n the polar cap and chang�ng �ts d�rect�on w�th the s�gn of IMF By.Thiscurrentdoesnotcontributetothetotaltranspolarcurrentbutproducesasignificantspread�n the correlat�on between computed ∆Hfieldsandupstreamsolarwinddata.
For calculat�on of the PM �ndex, the x, y, z coord�nate system was used, where �n the Northern Hem�sphere, the ax�s x �s northward, ax�s y �s eastward, and ax�s z �s downward. The secular and qu�et-day diurnalvariationsofthemagneticfieldwereremoved,andtheUT/seasonvariationsreduced.Toreducethe UT/season var�at�ons, a s�mple analyt�cal formula was used:
A = A0 f (UT, season) , (6)
where A0isanactualmeasuredmagneticfield,Aisacorrectedmagneticfield,andf (UT, season) �s as follows:
f D(UT, season) =1– 0.3 cos 2π( 174)/365 – −[ ] 00.5 cos 2π(UT–15.5)/24 ,[ ] (7)
where D �s the day of year and UT �s measured �n hours.
6
To account for the UT/seasonal var�at�on of the average d�rect�on of the transpolar current and Hb field,whencomputingtheHbfield,thefollowingexpressionwasused:
H X g Y gb = cos 2 UT– /24 + s�n 2 UT – /2π π( ) ( ) 44 , (8)
where X and Yare thecorrectedmagneticfielddisturbancesalong thex (northward) and y (eastward) axes, UT �s un�versal t�me �n hours, and g �s a correct�ve funct�on of season and UT that was der�ved from exper�mental data. The g funct�on was found from the follow�ng express�on: g D= + ( ) 7 2 0 5 0 12. . .cos 2π –174 /365 – cos 2 UTπ – 11.5 /24 .( ) (9)
Thecoefficientsinequation(9)werederivedtoprovidethebestcorrelationbetweenthePMindexandupstream solar w�nd/IMF data.
As ment�oned above, for der�v�ng the PC �ndex, only the Hbmagneticfieldswereused,whichunderestimatesarealCPCconvectionflowandarealtranspolarcurrentduetosignificantdeflectionsoftheconvectionflowandthetranspolarcurrentfromtheiraveragedirections.ThemethodusedforderivingthePMindexisaccountingforpossibledeflectionsofthetranspolarcurrentandrelatedmagneticfieldinthe polar cap from the�r average d�rect�ons. Th�s method prov�des a more accurate evaluat�on of the trans-polar current respons�ble for geomagnet�c act�v�ty not only �n the polar cap but also at lower lat�tudes.
F�gures 1 and 2 show two examples of the correlat�on of the HbfieldandPC/PMindiceswithupstreamsolarwind/IMFdata.Thesefiguresdemonstrateasignificantincreaseinthecorrelationbetweenthe PM �ndex and the coupl�ng funct�on (F*) as compared w�th the correlat�on of the Hbmagneticfieldand the PC �ndex w�th the same F* funct�on. The d�mens�onless coupl�ng funct�on (F*) prov�des the best correlat�on between geomagnet�c act�v�ty �nd�ces and upstream solar w�nd/IMF data. The explanat�on for th�s coupl�ng funct�on �s presented �n sect�on 3.
Figure1showsthecorrelationof(a)themagneticfield(Hb) w�th the coupl�ng funct�on (F*) and (b) the PC �ndex w�th the coupl�ng funct�on (F*) for 2001. The correlat�on patterns for Hb and the PC �ndex versus F*aresimilar,andcorrelationcoefficientsdiffer insignificantly.Panel(c)showsthecor-relat�on between the PM �ndex and the coupl�ng funct�on (F*). One can see that the correlat�on of the PM �ndex w�th the coupl�ng funct�on (F*)issignificantlyhigher.Goodnessoffit(R2) �ncreases to ∼0.71, whichcorrespondstothecorrelationcoefficientR ≈ 0.84.
F�gure 2 shows the correlat�on patterns for (a) Hb versus F* and (b) the PC �ndex versus F* for 2002. Panel (c) shows the correlat�on between the PM �ndex and the F* funct�on. Aga�n, the correlat�on of the PM �ndex versus the F*functionincreasessignificantly.R2 also �ncreases to ∼0.7.
The correlat�on between the PM �ndex and coupl�ng funct�on (F*) �s better than that between Hb/PC and the F*functionforeachyearfrom1995through2004,andthegoodnessoffit(R2) var�es from ∼ 0.8 (near solar m�n�mum) to ∼ 0.7 (near solar max�mum), wh�ch corresponds to the var�at�on of the cor-relationcoefficient(R) from ∼ 0.9 to ∼ 0.84.
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Coupling Function (F*) Coupling Function (F*)
R2=0.7062
R2=0.651 R2=0.617
(a)
(c)
(b)
F�gure 1. Correlat�on of the coupl�ng funct�on (F*) w�th hourly mean values of (a) magnet�c fields(Hb), (b) the PC �ndex, and (c) the PM �ndex for 2001.
In add�t�on to the h�gh correlat�on w�th upstream solar w�nd/IMF data, the PM �ndex also shows h�gh correlat�on w�th key parameters �n the magnetosphere and �onosphere, such as the Kp and Dst �nd�-ces, CPC potent�al drop, and Joule heat�ng released �n the h�gh-lat�tude �onosphere. These effects w�ll be covered �n the next sect�ons.
For comput�ng the PM �ndex, 1-hr, and for some cases, 15-m�n, measurements from h�gh-lat�tude Thule (corrected geomagnet�c lat�tude Λ ≈ 85°) and Vostok (Λ ≈ –83°) observator�es �n the Northern and Southern Hem�spheres were used, respect�vely, for 10 yr (1995–2004). Although the PM �ndex �n both polar caps was computed, the results obta�ned for the Northern Hem�sphere only are cons�dered here. (The magneticfieldmeasurementsfromtheSouthernHemispherearenotavailableforallyears.)ThemagneticfielddataandgeomagneticactivityindiceswereobtainedfromtheWorldDataCentersinKyoto,Japan, and the Dan�sh Meteorolog�cal Inst�tute, Denmark, at Web s�tes <http://swdcwww.kug�.kyoto-u.ac.jp> and <http://web.dm�.dk>, respect�vely. Also used were the OMNI solar w�nd/IMF data, ava�lable from Goddard Space Fl�ght Center at <ftp://nssdcftp.gsfc.nasa.gov/spacecraft_data/omn�/>. In th�s TP, the hourlymeanvaluesofthegeomagneticfieldandupstreamsolarwind/IMFdatawereusedforanalysis.
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Coupling Function (F*) Coupling Function (F*)
R2=0.7003
R2=0.647 R2=0.654
(a)
(c)
(b)
F�gure 2. Correlat�on of the coupl�ng funct�on (F*) w�th hourly mean values of (a) magnet�c fields(Hb), (b) the PC �ndex, and (c) the PM �ndex for 2002.
9
3. COUPLING FUNCTION
3.1 Existing and New Coupling Functions
To �mprove the pred�ct�on of geomagnet�c act�v�ty, �t �s also necessary to der�ve an appropr�ate solarwindcouplingfunction—acombinationofsolarwind/IMFparametersprovidingthebestfitwithgeomagnet�c act�v�ty. The most �mportant factors respons�ble for geomagnet�c act�v�ty are the solar w�nd veloc�ty (Vsw) and IMF Bz component, measured �n the solar-magnetospher�c coord�nate system. Add�-tionalparametersresponsibleforgeomagneticactivityaretheIMFazimuthalcomponent(IMFBy) and solar w�nd dens�ty (or pressure).
Most known coupl�ng funct�ons are the product of the solar w�nd speed and IMF Bz:
F V BV B sw zsw z× ×∼ , (10)
and the Akasofu coupl�ng funct�on:2,13
F V Bsw yzAkasofu ∼2 4 2s�n ( / ) ,θ (11)
where Byz �s the IMF �n the y-z plane and θ �s the clock angle between the z (northward) ax�s and the Byzvector.TheAkasofufunctionwasintroducedtomeasuretheenergyfluxfromthesolarwindtothemagnetosphere. Therefore, for the correlat�on of upstream solar w�nd/IMF data w�th ground magnet�c or electricfields,somemodificationsoftheAkasofufunctionarecommonlyused;e.g.,theKan-Leecouplingfunct�on:18
F V Bsw yzKan-Lee ∼ s�n ( / ) .2 2θ (12)
These coupl�ng funct�ons show relat�vely good correlat�on for some t�me �ntervals but fa�l for oth-ers. Recently, Lyatsky et al. proposed a theoret�cally-deduced coupl�ng funct�on l�nk�ng upstream solar w�nd data to geomagnet�c act�v�ty.5 They used the Perreault-Akasofu method13 and took �nto account a scalingfactordue topolarcapexpansionwhile increasinga reconnectedmagneticflux in thedaysidemagnetosphere. The coupl�ng funct�on obta�ned shows good correlat�on w�th geomagnet�c act�v�ty �nd�ces but �s dependent on the solar cycle. For moderate and h�gh solar act�v�ty, the coupl�ng funct�on may be wr�tten �n the follow�ng form:
F aV Bsw yzα θ= 1 2 2 2/ s�n ( / ) , (13)
where aisacoefficient.IfVsw �s measured �n km/s and ByzinnT,thecoefficienta = 0.01. The Fα coupl�ng funct�on �s d�fferent from coupl�ng funct�ons used earl�er, ma�nly by the power of Byz, wh�ch �s a result oftheconservationofreconnectedmagneticflux.Thiscouplingfunctionshowsaneffectiveionosphericelectricfield in the regionofopen (reconnected)field linescomputedwithaccounting for the scaling factor.
10
To test equat�on (13), Lyatsky et al. wrote a coupl�ng funct�on �n the general form5
F V Bswm
yzn
αα θ∼ s�n ( / ) ,2 (14)
where m, n, and αarearbitraryvalues.Thiscouplingfunctionisrelatedtoelectricandmagneticfieldsintheregionofopenmagneticfieldlines;therefore,thePCindexwaschosenfortheanalysiswhichshowsthemagneticfieldinthepolarcap.Then,thecorrelationcoefficientswerecomputedforthisindexversusth�s coupl�ng funct�on for d�fferent values of m, n, and α. They found that for moderate and h�gh solar act�v�ty, the best correlat�on between the Fα coupl�ng funct�on and the PC �ndex occurs near m ≈ 1 and n ≈ 0.5 for all values of α, wh�ch �s well cons�stent w�th the theoret�cal equat�on (13), and the max�mum R2 �s near α ≈ 2. That �s cons�stent w�th the coupl�ng funct�on, equat�on (13). However, the formula for the best-fitcouplingfunctionwasfoundtobedependentonthesolaractivitylevel.Forsolarminimum,thebest correlat�on w�th geomagnet�c act�v�ty takes place for Fαγ, where γ ≈1.4.
The Fα coupl�ng funct�on may be �mproved wh�le account�ng for the effect of solar w�nd pressure/v�scos�ty on geomagnet�c act�v�ty. Th�s effect was d�scussed earl�er by many researchers.19 The follow�ng coupl�ng funct�on was used:
F = Fα + Fvisc , (15)
where the term Fvisc = b n1/4 Vsw3/2 �s account�ng for a contr�but�on from v�scous �nteract�on of the
solarwindwiththegeomagneticfieldthatbecomesespeciallysignificantforsmallornorthwardIMF. TsurutaniandGonzalez19 reported that the v�scos�ty contr�buted up to 10% of the summary convect�on wh�le Borovsky and Funsten20 found th�s contr�but�on to be up to 20%. The formula for Fvisc has been der�ved from d�mens�onal arguments, wh�ch leads to Fvisc ∼ n1/4 Vsw
3/2. If the solar w�nd veloc�ety (Vsw), the IMF, and the solar w�nd number dens�ty (n) are measured �n km/s, nT, and cm–3,respectively,thecoefficientsa = 0.01 and b = 2 × 10–4. The coupl�ng funct�on (F)meansan‘effective’electricfieldinthepolarionosphere, measured �n mV/m.
The coupl�ng funct�on �n equat�on (15) shows better correlat�on w�th geomagnet�c act�v�ty �nd�ces than the coupl�ng funct�on �n equat�on (13). However, �t does not yet el�m�nate the dependence on the solar cycle. The coupl�ng funct�on (F) �n equat�on (15) �s appropr�ate for moderate and h�gh solar act�v�ty; how-ever, for solar m�n�mum, the better correlat�on w�th geomagnet�c act�v�ty �nd�ces takes place for F1.4.
The solar cycle effect may be significantly reduced while using the dimensionless coupling funct�on:
F* = c F2 / (F + C)2 , (16)
where F �s der�ved from equat�on (15), the factor c �s chosen equal to 100 (for conven�ence), and the factor C=26wasderivedfromexperimentaldatatoprovidethebest-fitcorrelationoftheF* funct�on w�th the PM and PC geomagnet�c act�v�ty �nd�ces. The coupl�ng funct�on (F*) prov�des very good correlat�on w�th geomagnet�c act�v�ty for any levels of solar and geomagnet�c act�v�ty as demonstrated �n the next sect�on. In th�s study, th�s d�mens�onless coupl�ng funct�on (F*) was used.
11
Note that the correct cho�ce of the coupl�ng funct�on �s very �mportant for �mprov�ng the correla-t�on of upstream solar w�nd parameters w�th geomagnet�c act�v�ty �nd�ces and related events �n the Earth’s magnetosphere and �onosphere.
3.2 Correlation Between Polar Magnetic and Polar Cap Indices and Various Coupling Functions
As ment�oned above, the ma�n d�fference between the PM �ndex and the ex�st�ng PC �ndex �s that the PM �ndex �s account�ng for the contr�but�on from the transpolar current to geomagnet�c activity even when the transpolar current is significantly deviated from its average direction. Thisleads to a strong �ncrease �n the correlat�on between the PM �ndex and both upstream solar w�nd/IMF data and key ground-measured parameters such as CPC potent�al and Joule heat�ng �n the h�gh- lat�tude �onosphere, as w�ll be shown.
For th�s analys�s, the hourly mean data of the PM and PC �nd�ces and upstream solar w�nd/IMF data, sh�fted to the magnetospher�c bow shock pos�t�on, were used. For comput�ng the coupl�ng funct�on, the OMNI dataset was used, wh�ch �ncludes the measurements of upstream solar w�nd/IMF data measured w�th the W�nd or the Advanced Compos�t�on Explorer satell�tes, located predom�nantly near the L1 l�bra-t�on po�nt toward the Sun. The PM/PC �nd�ces were compared w�th the coupl�ng funct�on(s) and averaged for the same and next hour; �.e., the correlat�on PM(t) or PC(t) w�th the coupl�ng funct�on (F) was �nves-t�gated where F = 0.5 [F(t) + F(t – 1 hr)], wh�ch prov�des the best correlat�on.
The correlat�on between the PM/PC �nd�ces and the Vsw Bz coupl�ng funct�on �s commonly worse thanthecorrelationwithothercouplingfunctions.Forinstance,goodnessoffitofthecorrelationbetweenthe PM and PC �nd�ces w�th Vsw Bz �s typ�cally about 0.4 to 0.5. Correlat�on of the PM and PC �nd�ces w�th other coupl�ng funct�ons, ment�oned above, �s better.
F�gures 3 and 4 show correlat�on patterns for (a) the PM �ndex and (b) the PC �ndex w�th the Kan-Lee18 coupl�ng funct�on, and (c) the PM �ndex and (d) the PC �ndex w�th the Lyatsky et al.5 coupl�ng funct�on for2001and2002yr,respectively.Goodnessoffit(R2) of the correlat�on of the PM and PC �nd�ces w�th the Kan and Lee coupl�ng funct�on �s about 0.59 and 0.51 for 2001, and 0.59 and 0.54 for 2002, respect�vely.GoodnessoffitofthecorrelationbetweenthePMandPCindiceswiththeLyatskyetal.couplingfunction�s about 0.67 and 0.61 for 2001, and 0.67 and 0.64 for 2002, respect�vely. F�gures 3 and 4 also show that the Fα coupl�ng funct�on, g�ven by equat�on (13), prov�des much better correlat�on w�th both the PM and PCindicesthantheKan-Leecouplingfunction.Thesefiguresalsoshowthatthecorrelationbetweenanycoupl�ng funct�on and PM �ndex �s better than the correlat�on between the same coupl�ng funct�on and PC �ndex.
F�gure 5 shows the correlat�on between the PM/PC �nd�ces and the d�mens�onless coupl�ng func-t�on (F*),derivedbyequation(16),for2001(a)and(b),and2002(c)and(d).Thisfigureincludessomeresultsfromfigures1and2.OnecanseethatthecorrelationbetweenthePMindexandcouplingfunction(F*)showsasignificantincreaseingoodnessoffit(R2) wh�ch reaches ∼0.7, correspond�ng to the correla-tioncoefficientR ∼0.84.ThegoodnessoffitforthePCindexversustheF*functionissignificantlyless(about 0.62–0.65).
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F�gure 3. Correlat�on between PM/PC �nd�ces and upstream solar w�nd parameters for the Kan and Lee18 coupl�ng funct�on (a) and (b), and the Lyatsky et al.5 coupl�ng function(c)and(d)for2001.Onecanseeasignificantincreaseingoodnessoffit (R2) for the latter coupl�ng funct�on for both PM and PC �nd�ces.
F�gures 6 and 7 show two add�t�onal examples of the correlat�on between the PM/PC �nd�ces and the coupl�ng funct�on (F*) for low and h�gh solar act�v�ty, respect�vely. F�gure 6 shows the correlat�on between (a) the PM �ndex and the coupl�ng funct�on (F*) and (b) the PC �ndex and the coupl�ng funct�on (F*)for1997nearsolarminimum.Thecorrelationisbetterthanthatinfigure5.Inthiscase,thegood-nessoffit(R2) reaches ∼0.78 for the PM �ndex and ∼0.75 for the PC �ndex. F�gure 7 shows the correlat�on between (a) the PM �ndex and the coupl�ng funct�on (F*) and (b) the PC �ndex and the coupl�ng func-t�on (F*)for2000(highsolaractivity).Thecorrelationisworsethaninfigure6butyethighenough;R2 reaches ∼0.76 for the PM �ndex and ∼0.69 for the PC �ndex.
An �ncrease �n the correlat�on of geomagnet�c act�v�ty �nd�ces w�th upstream solar w�nd/IMF parameters for low solar act�v�ty �s typ�cal. A poss�ble cause for th�s effect may be that the ranges of val-ues of geomagnet�c act�v�ty �nd�ces and the coupl�ng funct�ons for low solar act�v�ty are usually not large,
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F�gure 4. Correlat�on between PM/PC �nd�ces and solar w�nd parameters for the Kan and Lee18 coupl�ng funct�on (a) and (b), and the Lyatsky et al.5 coupl�ng function(c)and(d)for2002.Again,asignificantincreaseisshowninthe correlat�on between the PM/PC �nd�ces and the latter coupl�ng funct�on.
and the correlat�on between the �nd�ces and coupl�ng funct�on �s approx�mately l�near. Dur�ng the per�od of h�gh solar act�v�ty, the ranges of values of geomagnet�c act�v�ty �nd�ces and the coupl�ng funct�on increasesignificantly,whichmayprovidenonlineareffects,includingthewell-known‘saturation’effect�n geomagnet�c act�v�ty. It may reduce the correlat�on.
Figure8showsthedependenceofgoodnessoffit(R2) of the correlat�on between the PM, PC, and AL �nd�ces and the coupl�ng funct�on (F*) for the 10-yr per�od (1995–2004). To smooth the curves, the values of R2 inthisfigurewereaveragedfor3yr.ThePMindexshowsthebestcorrelationforallyears.Thegoodnessoffit(R2) for the PM �ndex versus F* var�es from ∼0.77 for solar m�n�mum to ∼0.7 for solar max�mum. For the PC and AL �nd�ces, R2 variesinasimilarwaybutissignificantlylessinmagnitude.
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F�gure 5. Correlat�on of the PM/PC �nd�ces w�th a d�mens�onless coupl�ng funct�on (F*): (a) and (b) for 2001 and (c) and (d) for 2002. Th�s demonstrates an �ncrease �n the correlat�on (aga�nst thatshowninfigs.3and4)ofbothPMandPCindiceswiththeF* funct�on.
Thus, one can see that the correlat�on between the PM �ndex and the coupl�ng funct�on (F*) �n figure8ishighenough(goodnessoffit(R2) �s not less than ∼0.71) and cons�derably h�gher than that for the other two �nd�ces for all years, and for low and h�gh solar act�v�ty.
3.3 Seasonal and Universal Time Variations in Correlation Between Polar Magnetic and Polar Cap Indices and Upstream Solar Wind/Interplanetary Magnetic Field Data
The ex�st�ng PC �ndex has a strong UT/season dependence �n �ts correlat�on w�th solar w�nd/IMF parameters. In contrast, the correlat�on of the PM �ndex w�th the coupl�ng funct�on (F*) shows aweakUT/seasondependence.Thisinterestingfeatureisdemonstratedinfigures9and10.
Figure9issimilartofigure8butisrelatedtofoursummermonthsonly(May–August).Thisfigurealsoshowsthedependenceofgoodnessoffit(R2) of the correlat�on of the PM, PC, and AL �nd�ces w�th the coupl�ng funct�on (F*)fortheperiodof10yr.Tosmooththecurvesinthisfigure,thevaluesofR2
were averaged for 3 yr. One can see a strong decrease �n R2 (wh�ch drops to ∼0.6) �n the correlat�on of the
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(b)
F�gure 6. Correlat�on between (a) the PM �ndex and coupl�ng funct�on (F*) and (b) the PC �ndex and coupl�ng funct�on (F*) for 1997—related to low solar act�v�ty.
PC �ndex w�th the F*functionforhighsolaractivity,whilethegoodnessoffitforthePMindexversusthecoupl�ng funct�on (F*)variesinsignificantlyandremainsatthelevelofR2 ≈ 0.7.
Figure10showsgoodnessoffitofthecorrelationbetweenthePM/PCindicesandthecouplingfunct�on (F*) as a funct�on of UT for the same 10 yr (1995–2004). Panel (a) �s related to low and moder-ate solar act�v�ty (1995–1998), wh�le panel (b) �s related to h�gh solar act�v�ty (1999–2004). Black c�rcles showgoodnessoffit(R2) computed for PM versus F* for each year, wh�le red c�rcles show R2 for the PC �ndex versus F*. The correlat�ons of the PM and PC �nd�ces w�th the coupl�ng funct�on (F*) are close �n the �nterval of ∼ 4–22 UT but strongly d�fferent �n the �nterval of 10–20 UT.
16
800
600
400
200
00 10 20 30 40 50
PCPM
(nT)
Coupling Function (F*)
Coupling Function (F*)
R2=0.764
(a)
12
8
4
0
–40 10 20 30 40 50
R2=0.693
(b)
F�gure 7. Correlat�on between (a) the PM �ndex and coupl�ng funct�on (F*) and (b) the PC �ndex and coupl�ng funct�on (F*) for 2000—related to h�gh solar act�v�ty.
17
0.78
0.74
0.7
0.66
0.62
0.581995 1996 1997 1998 1999 2000 2001 2002 2003 2004
PM vs F*
PC vs F*
AL vs F*Goo
dnes
s of
Fit
(R2 )
Year
Figure8.Solarcyclevariationincorrelation.Goodnessoffit(R2) of the correlat�on of PM, PC, and AL �nd�ces w�th coupl�ng funct�on (F*) �s shown for 10 yr (1995–2004). Correlat�on between PM and F*issignificantlyhigherthanthatforthePCandALindicesforall years. The average magn�tude of R2 for the correlat�on between the PM and F* funct�on �s ∼ 0.74,whichcorrespondstothecorrelationcoefficientR ≈ 0.86. Presented values of R2 are averages for 3 yr.
0.78
0.74
0.7
0.66
0.62
0.581995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Goo
dnes
s of
Fit
(R2 )
Year
PM vs F*
PC vs F*
AL vs F*
Figure9.Summerdropincorrelation.Goodnessoffit(R2) of the correlat�on of PM, AL, and PC �nd�ces w�th coupl�ng funct�on (F*) �s shown for summer months (May– August) for 1995–2004. Th�s demonstrates a dramat�c drop �n the correlat�on of the PC �ndex for the summer months wh�le the correlat�on between the PM �ndex and F*functionremainshighandclosetothatinfigure8.Presentedvalues of R2 are averages for 3 yr.
18
0.85
0.8
0.75
0.7
0.65
0.6
0.55
0.85
0.8
0.75
0.7
0.65
0.6
0.550 4 8 12 16 20 24 0 4 8 12 16 20 24
Goo
dnes
s of
Fit
(R2 )
Goo
dnes
s of
Fit
(R2 )
UT (hr)UT (hr)
R2 for (PM vs F*)R2 for (PC vs F*)
R2 for (PM vs F*)R2 for (PC vs F*)
(a) (b)
F�gure 10. Un�versal t�me var�at�on �n correlat�on of PM/PC �nd�ces w�th coupl�ng funct�on (F*). Shown are mean values of R2 for 4-hr UT �ntervals, averaged for the follow�ng years: (a) 1995–1998 (low and moderate solar act�v�ty) and (b) 1999–2004 (h�gh solar act�v�ty). Thecurvesarethefourth-orderpolynomialfittothedata.CorrelationbetweenPCand F* has a strong UT var�at�on and fa�ls �n the �nterval of 10–20 UT wh�le the correlat�on between the PM and F* funct�on rema�ns h�gh or even �ncreases �n th�s UT sector.
19
4. CORRELATION WITH AURORAL ELECTROJET AL INDEX AND SUBAURORAL Kp INDEX
4.1 Correlation With Auroral Electrojet AL Index
The AL �ndex �s based on measur�ng negat�ve (southward �n the Northern Hem�sphere) var�at�ons inthegeomagneticfieldhorizontalcomponentat12geomagneticobservatoriesspreadalonganaveragepositionoftheauroralzone.TheALindexshowssubstormactivityintheauroralzone,whichcontrib-utessignificantlythroughthesubstorm-related,field-alignedcurrentstothemagneticfieldinthepolarcap.12,21AlthoughtheALindexshowsmaximalnegativedeviationsin themagneticfield’snorthwardcomponent wh�le the PM �ndex shows rather an average geomagnet�c d�sturbance �n the polar cap, the correlat�on between the PM and AL �nd�ces �s very good for years of low solar act�v�ty but fa�ls for years of h�gh solar act�v�ty.
F�gures 11 and 12 show the correlat�on of the AL �ndex w�th (a) the coupl�ng funct�on (F*) and (b) the PM �ndex for 1995 (low solar act�v�ty) and 1998 (moderate solar act�v�ty), respect�vely. One can see the h�gh correlat�on between the AL and PM �nd�ces (R2 ≈0.8infig.11and≈0.73infig.12),whichiseven better than the correlat�on between the AL �ndex and the coupl�ng funct�on (F*).
0
–400
–800
–1,200
0 10 20
AL
(nT)
AL
(nT)
Coupling Function (F*) PM (nT)
R2=0.7
(a)
0
–400
–800
–1,200
0 100 200 300 400
R2=0.799
(b)
F�gure 11. Correlat�on of (a) the AL �ndex w�th coupl�ng funct�on (F*) and (b) the AL �ndex w�th thePMindexfor1995.CorrelationbetweentheALandPMindicesissignificantly h�gher (R2 ≈ 0.8 that corresponds to R ≈ 0.89) than that between the AL and coupl�ng funct�on (F*).
The correlat�on between the AL and PM �nd�ces decreases dur�ng solar max�mum, probably due to theexpansionoftheauroralzoneoutoffthepositionofgeophysicalobservatoriesresponsibleforprovid-�ng the AL �ndex.9,10 For h�gh solar act�v�ty, the PM �ndex—calculated us�ng data from both overhead and remotefield-alignedcurrents—mayprovidemorereliableinformationonauroralelectrojetthantheAL�ndex does for these per�ods.
20
0
–400
–800
–1,200
–1,600
0 10 20 30 40 50
AL
(nT)
AL
(nT)
Coupling Function (F*) PM (nT)
R2=0.684
(a)
0
–400
–800
–1,200
–1,600
0 200 400 600
R2=0.734
(b)
F�gure 12. Correlat�on of (a) the AL �ndex w�th coupl�ng funct�on (F*) and (b) the AL �ndex w�th the PM �ndex for 1998—related to moderate solar act�v�ty. The correlat�on between the AL and PM �nd�ces rema�ns h�gh (R2 ≈ 0.73 that corresponds to R ≈ 0.86).
4.2 Correlation With Subauroral Kp Index
The three-hourly Kp �ndex shows geomagnet�c act�v�ty at subauroral and m�ddle lat�tudes. Th�s �ndex �s w�dely used as an �mportant �nput parameter for model�ng magnetospher�c and �onospher�c pro-cesses. The Kp �ndex, however, shows low correlat�on w�th other ex�st�ng geomagnet�c act�v�ty �nd�ces. It �s �nterest�ng that the Kp �ndex shows good correlat�on w�th the PM �ndex. Note that the Kp �ndex �s a nonl�near (log) funct�on of geomagnet�c act�v�ty, and wh�le compar�ng �t w�th other �nd�ces, the best cor-relat�on takes place not just for the Kp �ndex but for Kp1.5.
An example of the correlat�on between (a) Kp1.5 and the PM �ndex and (b) Kp1.5 and the PC indexisshowninfigure13,relatedtotheyear2000(highsolaractivity).Onecanseethatthecorrelationbetween the 3-hr mean values of Kp1.5 and the related 3-hr mean PM/PC �nd�ces �s much better for the PMindex.Goodnessoffit(R2) between Kp1.5 and PM �s ∼0.67; that �s much h�gher than that for Kp1.5 versus the PC (∼0.57).
Figure14showsgoodnessoffit(R2) of the correlat�on of Kp1.5 w�th the AL, PM, and PC �nd�ces for 1995–2004. The correlat�on between Kp1.5andPMissignificantlybetterthanfortheothertwoindi-ces.Tosmooththecurvesinthisfigure,thevaluesofR2 were averaged for 3 yr. F�gure 14 demonstrates once more that the PM �ndex �s more appropr�ate for measurement and pred�ct�on of global geomagnet�c act�v�ty.
21
40
30
20
10
00 200 400 600
Kp1.
5
Kp1.
5
PM (nT) PC
R2=0.668
(a)
30
20
10
0–4 0 4 8 12
R2=0.572
(b)
F�gure 13. Correlat�on of (a) the Kp �ndex w�th the PM �ndex and (b) the Kp �ndex w�th the PC �ndex. Correlat�on between 3-hr values of Kp1.5 and PM/PC �nd�ces for theyear2000—relatedtohighsolaractivity.Goodnessoffit(R2) between Kp1.5 and PM �s much better than that for Kp1.5 versus PC.
0.75
0.7
0.65
0.6
0.551995 1996 1997 1998 1999 2000 2001 2002 2003 2004
PM
PC
AL
Goo
dnes
s of
Fit
(R2 )
Year
Figure14.Goodnessoffit(R2) of the correlat�on of Kp1.5 w�th AL, PM, and PC �nd�ces for 1995–2004. The correlat�on between Kp1.5andPMissignificantlybetter than that for the other two �nd�ces. Presented values of R2 are averages for 3 yr.
22
5. CORRELATION WITH CROSS-POLAR-CAP POTENTIAL DROP AND JOULE HEATING
5.1 Introduction
The CPC electr�c potent�al and Joule heat�ng of h�gh-lat�tude �onosphere are two key parameters that are w�dely used for model�ng the magnetosphere, �onosphere, and thermosphere.7,8,22–24 The CPC voltageshowselectricenergyfluxenteringthedaysideionospherefromthesolarwind.Thetotalhemi-sphericJouleheatingshowstheenergyfluxreleasedintheionosphereandheatingtheneutralatmosphere.Jouleheatingintheionosphereproducestheexpansionoftheatmospherethatsignificantlyaffectsther-mospher�c dynam�cs and satell�te orb�ts. Accord�ng to Kn�pp et al.,25 the solar extreme ultrav�olet rad�a-t�on on average prov�des ∼78%, the Joule heat�ng ∼16%, and energet�c part�cle prec�p�tat�on about 5%–8% of the total power com�ng to the Earth’s �onosphere, wh�le dur�ng strong geomagnet�c d�sturbances, the contr�but�on from Joule heat�ng becomes a predom�nant source of atmospher�c heat�ng. Therefore, the pred�ct�on of both CPC voltage and global Joule heat�ng �s h�ghly �mportant.
Permanent measurements of the CPC voltage and total Joule heat�ng are not yet poss�ble. The SuperDARN Doppler measurements of the E × B �onospher�c plasma dr�ft cannot prov�de permanent monitoringof ionospheric convectiondue to the strongdependenceof radiowave reflectionon iono-sphericconditions.Anyradarprovidesareliableconvectionfluxthroughthepolarcapinsomepercentofoperat�on t�me only. Other methods, �nclud�ng measurements w�th spacecraft, are also unable to prov�de permanent mon�tor�ng for both CPC voltage and total Joule heat�ng.
Model�ng the CPC voltage and Joule heat�ng �s more successful. The ass�m�lat�ve mapp�ng of �onospher�c electrodynam�cs (AMIE) techn�que,7,26,27basedoninversionofgeomagneticfieldmeasure-ments from a large number of geomagnet�c observator�es, �s w�dely accepted as one of the best methods for der�v�ng both CPC voltage and Joule heat�ng. However, s�nce th�s method requ�res ass�m�lat�on of data from a large number of geomagnet�c observator�es, model�ng results are not ava�lable �n real t�me. Therefore, pred�ct�on of these two �mportant parameters—CPC voltage and total Joule heat�ng—us�ng the upstream solar w�nd/IMF data and appropr�ate geomagnet�c act�v�ty �nd�ces,24,28,29 rema�ns the most rel�-able method of near real-t�me mon�tor�ng these parameters. Us�ng the PM �ndex and the new vers�on of the couplingfunctionmaysignificantlyimprovethepredictionreliabilityinforecastingtheseparameters.
5.2 Preliminary Results
Prel�m�nary results relat�ng to the correlat�on of the PM �ndex w�th CPC potent�al drop and Joule heat�ng, computed w�th the AMIE techn�que, w�ll be shown (hourly mean values of CPC potent�al drop and total hem�spher�c Joule heat�ng for each day of 1998 prov�ded by A. R�dley, Un�vers�ty of M�ch�-gan).
23
F�gure 15 shows the correlat�on of hourly mean values of the AMIE CPC potent�al drop (U) w�th (a) the PM �ndex and (b) the PC �ndex for all days of 1998. One can see that the correlat�on �s much better for U versus the PM �ndex (R2 ≈ 0.78) than that for U versus the PC �ndex (R2 ≈ 0.69).
300
250
200
150
100
50
00 100 200 300 400 500 600
U (k
V)U
(kV)
PM (nT)
PC
R2=0.784
(a)
300
250
200
150
100
50
0–5 0 5 10 15
R2=0.691
(b)
F�gure 15. Correlat�on of hourly mean values of the AMIE CPC potent�al drop (U) w�th (a) the PM �ndex and (b) the PC �ndex for all days of 1998. The correlat�on �s much better for U versus the PM �ndex (R2 ≈ 0.78) than for U versus the PC �ndex (R2 ≈ 0.69) (data courtesy of Aaron R�dley, Un�vers�ty of M�ch�gan).
F�gure 16 shows the correlat�on of hourly mean values of the root square of the AMIE total hem�-spher�c Joule heat�ng w�th (a) the PM �ndex and (b) the PC �ndex for all days of 1998. The correlat�on �s much better for JH1/2 versus the PM �ndex (R2 ≈ 0.75) than that for JH1/2 versus the PC �ndex (R2 ≈ 0.68).
24
60
50
40
30
20
10
0
0 10 20 30 40 50
JH1/
2 (G
W)
JH1/
2 (G
W)
PM (nT)
PC
R2=0.75
(a)
60
50
40
30
20
10
0–5 0 5 10 15
R2=0.675
(b)
F�gure 16. Correlat�on of hourly mean values of AMIE JH1/2 w�th (a) the PM �ndex and (b) the PC �ndex for all days of 1998. The correlat�on �s much better for JH1/2 versus the PM �ndex (R2 ≈ 0.75) than that for JH1/2 versus the PC �ndex (R2 ≈ 0.68) (data courtesy of Aaron R�dley, Un�vers�ty of M�ch�gan).
The correlat�on may be even more �mproved wh�le account�ng for both the PM �ndex and upstream solar w�nd/IMF data. The compar�son of pred�cted and actual values of the CPC voltage and Joule heat-ingispresentedinfigure17.Thisfigureshowsthecorrelationbetweentheactualandpredictedhourlymean values of the CPC voltage (U) and total hem�spher�c Joule heat�ng (JH1/2) for all days of 1998. Shown here �s the extremely h�gh correlat�on between the pred�cted and actual values (R2 ∼ 0.81 to 0.82 thatcorrespondtothecorrelationcoefficientR ≈ 0.9 and more) for both U voltage and JH1/2. For der�v�ng the pred�cted values of the CPC voltage (U) and total hem�spher�c Joule heat�ng, the follow�ng s�mple pred�ct�on funct�ons were used:
25
300
200
100
0
0 50 100 150 200 250 300
Act
ual J
H1/
2 (G
W)
Act
ualU
(kV)
Predicted U (kV)
Predicted JH1/2 (GW)
R2=0.811
(a)
50
40
30
20
10
00 10 20 30 40 50
R2=0.819
(b)
Figure 17. Correlation of the actual (AMIE) and predicted hourly mean values of the CPC voltage (U) and JH1/2 for all days of 1998. This shows extremely high correlation (R2 ≈ 0.81–0.82) for both U voltage and JH1/2 (data courtesy of Aaron Ridley, University of Michigan).
Upredict (kV) = 15 + 0.28 (PM + 9 F*) (17)
JH (GW) = 0.9 + 0.046 PM + 9 * ,predict
2F( ) (18)
where the PM index is measured in nT and F* is the dimensionless coupling function derived from equa-tion (16).
26
6. CONCLUSIONS
Pred�ct�on of geomagnet�c act�v�ty and related events �n the Earth’s magnetosphere and �onosphere �s an �mportant task of the Space Weather program. Pred�ct�on rel�ab�l�ty �s dependent on a pred�ct�on method and elements �ncluded �n the pred�ct�on scheme. Two ma�n elements are a su�table geomagnet�c act�v�ty �ndex and coupl�ng funct�on—the comb�nat�on of solar w�nd parameters prov�d�ng the best cor-relat�on between upstream solar w�nd data and geomagnet�c act�v�ty. The appropr�ate cho�ce of these two elements �s cruc�al for any rel�able pred�ct�on model.
ThePMindexwascomputedfromthemagneticfieldmeasurementsfromthenear-polegeomag-net�c observator�es—Thule, Greenland, and Vostok, Antarct�ca, the same observator�es that are used for der�v�ng the ex�st�ng PC �ndex, but a d�fferent method for comput�ng the PM �ndex was used. In th�s study, only the PM �ndex computed �n the Northern Hem�sphere was used. The most �mportant d�st�nct�on of the PM �ndex from the ex�st�ng PC �ndex was �n account�ng for the contr�but�on from the transpolar (CPC) equ�valent �onospher�c current to geomagnet�c act�v�ty and related events even when the transpolar cur-rentdeviatessignificantlyfromitsaveragedirection.Thisleadstoasignificantincreaseinthecorrelationbetween the PM �ndex and both upstream solar w�nd/IMF data and related events �n the Earth’s magneto-sphere and �onosphere.
The PM �ndex shows much better correlat�on w�th the solar w�nd coupl�ng funct�on and related events than do the other �nd�ces. The correlat�on of the PM �ndex w�th upstream solar w�nd/IMF data was investigatedfora10-yrperiod(1995–2004).Thecorrelationcoefficientsforhourlymeanvaluesareveryh�gh (∼0.87 to ∼0.88) for low and moderate solar act�v�ty but the correlat�on becomes worse w�th �ncreas-�ng solar act�v�ty.
The correlat�on of the PM �ndex w�th the AL and Kp �nd�ces, and such key �onospher�c parameters as CPC voltage and Joule heat�ng, calculated w�th the AMIE techn�que, was also �nvest�gated. These two parameters are w�dely used as �mportant �nput parameters for model�ng the magnetospher�c, �onospher�c, and thermospher�c processes. The correlat�on between the PM �ndex and the AL and Kp �nd�ces �s h�gh forlowsolaractivity.Thecorrelationcoefficient(R) for the PM �ndex versus the AL �ndex �s ∼0.9 but decreases w�th �ncreas�ng solar act�v�ty.
The pred�ct�on funct�on for pred�ct�ng CPC voltage and Joule heat�ng based on us�ng both the PM indexandupstreamsolarwind/IMFdataallowsasignificantincreaseinthereliabilityofthepredictionoftheseimportantparameters.Thecorrelationcoefficientsbetweentheactualandpredictedvaluesoftheseparameters are ∼0.9 and h�gher. Thus, the new polar magnet�c �ndex of geomagnet�c act�v�ty and the new vers�on of the coupl�ng functionprovideasignificantincreaseinthereliabilityofpredictinggeomagneticactivityandsuchkeyparameters as CPC voltage and total Joule heat�ng �n a h�gh-lat�tude �onosphere, wh�ch play an �mportant role �n the development of geomagnet�c and other act�v�t�es �n the Earth’s magnetosphere and are w�dely used as key �nput parameters �n model�ng magnetospher�c, �onospher�c, and thermospher�c processes.
27
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29
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REPORT DOCUMENTATION PAGE Form ApprovedOMB No. 0704-0188
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NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)Prescribed by ANSI Std. 239-18298-102
Unclassified Unclassified Unclassified Unl�m�ted
Pred�ct�on of Geomagnet�c Act�v�ty and Key Parameters�n H�gh-Lat�tude Ionosphere—Bas�c Elements
W.Lyatsky*andG.V.Khazanov
George C. Marshall Space Fl�ght CenterMarshall Space Fl�ght Center, AL 35812
Nat�onal Aeronaut�cs and Space Adm�n�strat�onWash�ngton, DC 20546–0001
PreparedbytheScienceandExplorationResearchOffice,ScienceandMissionSystemsOffice*Oak R�dge Assoc�ated Un�vers�t�es, Oak R�dge, TN
Unclassified-UnlimitedSubject Category 46Ava�lab�l�ty: NASA CASI 301–621–0390
Pred�ct�on of geomagnet�c act�v�ty and related events �n the Earth’s magnetosphere and �onosphere �s an �mpor-tant task of the Space Weather program. Pred�ct�on rel�ab�l�ty �s dependent on the pred�ct�on method and elements �ncluded �n the pred�ct�on scheme. Two ma�n elements are a su�table geomagnet�c act�v�ty �ndex and coupl�ng func-t�on—the comb�nat�on of solar w�nd parameters prov�d�ng the best correlat�on between upstream solar w�nd data and geomagnet�c act�v�ty. The appropr�ate cho�ce of these two elements �s �mperat�ve for any rel�able pred�ct�on model. The purpose of th�s work was to elaborate on these two elements—the appropr�ate geomagnet�c act�v�ty �ndex and the coupl�ng funct�on—and �nvest�gate the opportun�ty to �mprove the rel�ab�l�ty of the pred�ct�on of geomagnet�c act�v-�ty and other events �n the Earth’s magnetosphere. The new polar magnet�c �ndex of geomagnet�c act�v�ty and the new versionofthecouplingfunctionleadtoasignificantincreaseinthereliabilityofpredictingthegeomagneticactivityand some key parameters, such as cross-polar cap voltage and total Joule heat�ng �n h�gh-lat�tude �onosphere, wh�ch play a very �mportant role �n the development of geomagnet�c and other act�v�ty �n the Earth’s magnetosphere, and are w�dely used as key �nput parameters �n model�ng magnetospher�c, �onospher�c, and thermospher�c processes.
40
M–1205
Techn�cal Publ�cat�onOctober 2007
NASA/TP—2007–215079
space weather pred�ct�on, geomagnet�c act�v�ty �ndex, solar w�nd, interplanetarymagneticfield,cross-polarcappotentialdrop
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NASA/TP—2007–215079
Prediction of Geomagnetic Activity and Key Parameters in High-Latitude Ionosphere—Basic ElementsW. Lyatsky Oak Ridge Associated Universities, Oak Ridge, Tennessee
G.V. KhazanovMarshall Space Flight Center, Marshall Space Flight Center, Alabama
October 2007
National Aeronautics andSpace AdministrationIS20George C. Marshall Space Flight CenterMarshall Space Flight Center, Alabama35812