Saturation of the ionospheric polar cap potential during the

October––November 2003 superstorms

Marc R. Hairston and Kelly Ann DrakeCenter for Space Sciences, University of Texas at Dallas, Richardson, Texas, USA

Ruth SkougLos Alamos National Laboratory, Los Alamos, New Mexico, USA

Received 25 October 2004; revised 18 March 2005; accepted 29 March 2005; published 28 July 2005.

[1] The question of whether the cross polar cap potential drop in the Earth’s ionospheresaturates under conditions of extreme electric field in the solar wind has been testedobservationally during the past several years. The challenge to proving the existence ofthis phenomenon is that periods of such extreme electric fields in the solar wind arerelatively rare. The three superstorms of October and November 2003 provided ideal casesfor testing this idea. We first review the earlier evidence of the saturation seen by theDMSP-F13 spacecraft during the 31 March 2001 superstorm and other storm eventsduring the 1998–2002 time period. Then we present observations from the DMSP-F13spacecraft during the October and November 2003 superstorms that show definiteevidence of this saturation. In addition, some of the electric fields during thesesuperstorms were almost twice as large as the largest fields previously studied, thusincreasing the range of our sample set and further increasing our confidence in theexistence of the saturation phenomenon. The data are compared with the saturatedpotentials predicted by the Hill-Siscoe model to test its validity. The DMSP measurementsindicate that the saturation limit of the cross polar cap is about 260 kV.

Citation: Hairston, M. R., K. A. Drake, and R. Skoug (2005), Saturation of the ionospheric polar cap potential during the

October–November 2003 superstorms, J. Geophys. Res., 110, A09S26, doi:10.1029/2004JA010864.

1. Introduction

[2] The connection between the solar wind drivers, theinterplanetary magnetic field (IMF) and the solar windram pressure, with the electric fields and convectionpatterns in Earth’s polar ionosphere has been studiedextensively for the past 2 decades and, for the southwardIMF conditions, is very well understood [e.g., Heelis,1984; Heppner and Maynard, 1987; Richmond andKamide, 1998; Rich and Hairston, 1994; Weimer, 1995;1996; Boyle et al., 1997; Ruohoniemi and Baker, 1998,and references therein]. As the IMF flows past the Earth,a cross-magnetospheric electric field is generated alongthe magnetopause. During southward IMF conditions theIMF couples directly with the Earth’s magnetosphere andthus part of this electric field maps down to the polarionosphere. This creates the cross polar cap potential inthe ionosphere which can be directly measured by satel-lite and radar observations [Hairston and Heelis, 1996;Greenwald et al., 1995]. As the solar wind velocity and/or the magnitude of the southward component of the IMFincreases, then this cross-magnetospheric electric fieldincreases, so in turn the ionospheric cross polar cappotential should also increase.

[3] Work by several researchers [e.g., Reiff and Luhman,1986; Weimer, 1995, 1996] comparing the observed polarcap potential to the solar wind conditions resulted in a seriesof empirical relationships where the polar cap potential is alinear function of the solar wind speed and the magnitude ofthe z-component of the IMF. In the most thorough analysiscomparing 3 1/2 years of Defense Meteorological SatelliteProgram (DMSP) observations of the polar cap potential tosolar wind parameters, Boyle et al. [1997] obtained thefollowing best empirical fit:

%B ¼ 10�4 v2SW þ 11:7 B sin3 q=2ð Þ; ð1Þ

where %B is the ionospheric polar cap potential in kV, vSWis the solar wind speed in km/s, B is the y-z planecomponent of the IMF field in nT, and q is the clock angleof the IMF in the y-z plane where 0� is northward and 180�is southward.[4] Hill et al. [1976] and later Hill [1984] predicted that

once the induced electric field from the solar wind reached acertain magnitude the ionospheric potential would stopincreasing and saturate. In this model the solar wind-induced region 1 currents in the magnetosphere wouldcreate a magnetic field that opposes the Earth’s dipole field,effectively reducing the amount of magnetic flux availableon the dayside magnetopause for reconnection with theIMF. In effect, the magnetosphere would reach a point

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110, A09S26, doi:10.1029/2004JA010864, 2005

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where no matter how large the solar wind electric fieldbecame, there would be no more magnetic flux available inthe magnetosphere to reconnect with the increased flux inthe solar wind, thus the magnitude of the polar cap potentialcould not increase any further. The difficulty in testing thismodel is that such saturation only occurs under extremesolar wind conditions. Under nominal conditions, evenduring routine magnetic storms, the polar cap potentialresponds linearly to the increase in the magnitude of thesolar wind induced electric field. Boyle et al. [1997]checked their data set of DMSP observations for anyevidence of saturation but found none. However, becauseof the severe restrictions they placed on their data to ensurethe IMF was steady for an extended time period, the highestsolar wind electric field they observed was about 8 mV/m.Also, their data set did not include any periods of extremelyhigh solar wind velocities that might have exhibited thesaturation effect.[5] Early efforts using limited data sets of polar cap

potentials potential measurements from AE-C, AE-D, S3-2, and S3-3 spacecraft performed by Reiff et al. [1981],Cowley [1984], and Reiff and Luhman [1986] showed someindication of possible saturation. Later efforts to test theidea of saturation using larger and better data sets were doneby Russell et al. [2001] and Shepherd et al. [2002]. Russellet al. [2001] used the AMIE procedure based on magne-tometer, spacecraft, and radar observations from five largestorms to calculate the polar cap potential. These eventsincluded periods where the solar wind electric field datareached 10mV/m and indicated saturation beginning to occurat this point. Shepherd et al. [2002] looked at 3 years ofSuperDARN data and the inferred polar cap potential basedon these observations. Their work (see specifically Figure 4in the work of Shepherd et al. [2002]) covered data for solarwind electric fields of up to 110 kV/RE (17.27 mV/m) andshowed evidence of saturation beginning with solar windelectric fields as small as 20 kV/RE (3.14 mV/m) and showedno potentials larger than 120 kV. However there was someambiguity about these results which will be discussed inmoredetail in the final section of this paper.[6] Hill et al. [1976] and Hill [1984] only gave the form

of a function where the polar cap potential would saturate.Siscoe et al. [2002] expanded on Hill’s idea to formulate anexact prediction of the polar cap potential as a function ofthe solar wind parameters and the ionospheric Pedersenconductivity. The saturation formula given by Siscoe et al.is

Fpc ¼ 57:6 Esw P1=3sw D4=3 F qð ÞP1=2sw Dþ 0:0125 x SEsw F qð Þ

ð2Þ

where %pc is the polar cap potential in kV, ESW is the solarwind electric field (ESW = jvSW � BSWj), PSW is the rampressure exerted by the solar wind in nPa (PSW = rSWvSW

2 ),D is the strength of the Earth’s dipole field normalized to 1for the present value, F(q) is a function of the clock angle ofthe IMF to account for the geometry of reconnection (hereF(q) = sin2(q2), i.e. F(q) = 0 for IMF northward and 1 forIMF southward), x is a dimensionless coefficient between 3and 4 that depends on the geometry of currents in theionosphere [Crooker and Siscoe, 1981], and S is the height-integrated Pedersen ionospheric conductivity (assumed to

be uniform throughout the polar region for simplicity’ssake) measured in S. From MHD simulations, Siscoe et al.obtained the relation

x ¼ 4:45� 1:08 log S=1Sð Þ ð3Þ

to compute the value of the x coefficient to use in theformula. They compared the predictions from this formulawith polar cap potentials generated from an MHDsimulation and found a good agreement. It should be notedthat all the variables in equation (2) can be measureddirectly except for the Pedersen conductivity, so the analysispresented here will use nominal values of 5 and 10 S for theconductivity. From here on, equation (2) will be referred toas the Hill-Siscoe model and equation (1) will be referred toas the Boyle formula. Siscoe et al. [2004] expanded on thiswork in an attempt to test four explanations (including theHill-Siscoe model above) of the causes of saturation. Theyshowed all four were consistent with current observationsand models but could not specifically rule out any of themat this point.

2. Previous Work With DMSP

[7] The DMSP satellites are in polar orbits with periodsbetween 100 and 105 min. In general there are two to fouroperational satellites at all times situated in two orbitalorientations: 0545–1754 LT (essentially dawn-dusk) and0930–2130 LT. The two-cell distribution of potential duringsouthward IMF conditions is such that generally the space-craft in the dawn-dusk orientation passes closest to theabsolute maximum and minimum of the potential. Thusfor analysis of the cross polar cap potential we restrictourselves to using data from the dawn-dusk DMSP satellite:F13. Each DMSP spacecraft carries a Special Sensor–Ions,Electrons, and Scintillation (SSIES) package which mea-sures several parameters of the thermal plasma including thebulk ion velocity. Combining the cross-track ion flow withthe magnetic field data, we calculate the electric fieldparallel to the spacecraft’s track. Starting at the subauroralregion on one end of the spacecraft’s polar pass and going tothe other side, we integrate the electric field along the trackto get the electrostatic potential. Because of changes in flowpattern during the time of the pass (generally about 15 to20 min) the integrated potential rarely returns to zero at thefar end of the path. This remaining potential at the end ofthe pass (called the offset) is redistributed linearly across allthe potential data to force both ends to zero. The differencebetween the maximum and minimum potential in thiscorrected set of data is what we use as the observedpotential drop and one half of the offset is what we use asthe uncertainty of the potential drop. Under nominal iono-spheric conditions there a period each day from roughly0200 to 0800 UTwhere the magnetic dipole is tilted furthestaway from the spacecraft’s ground track and the spacecraftonly skims the edges of the potential distribution pattern.During storm times the polar cap expands equatorwardenough that a substantial part of the pattern is still observedby the spacecraft passes between 0200 and 0800 UT. Still,there is the uncertainty about how close the spacecraft did ordid not come to the true maximum and minimum of thepotential, so for our analysis we prefer to use passes from

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the other times of the day when there is greater confidencethat the observed potential drop is very close to the actualpotential drop. A more complete description of this analysisis given by Hairston and Heelis [1996] and Hairston et al.[1998].[8] The superstorm of 31 March 2001 provided an

excellent chance to use the DMSP observations to test forthe existence of cross polar cap potential saturation. Duringthe period from 1300 UT to 2200 UT on that date the IMFwas strongly southward with BZ (in GSM coordinates)changing slowly from �30 to �20 nT. During this period,DMSP-F13 made six southern polar passes that were veryclose to the magnetic pole. The proximity to the poleensures that the observed potential difference was close tothe true cross polar cap potential and the repeated passesdemonstrated that the observed patterns were stable and nottransitory. A full report of this work was presented byHairston et al. [2003], and Figure 1 here is an adaptationof Figure 3 from that paper. We plotted the observedpotential drops as a function of the corresponding observedsolar wind electric field (ESW = v � B). The vertical bars onthe data points show the uncertainty of the observedpotentials based on the offset described above. The straightline labeled %B is the potential predicted by the Boyleformula, while the two curved lines are the Hill-Siscoemodel predictions for2 = 5 and 10 S. The range of the solarwind induced electric field during this event extends to justover 20 mV/m. The observed potentials show that even afteraccounting for the uncertainty of the measurements, theyhave definitely saturated far below where the levels wherethe linear predictions of Boyle et al. [1997] would placethem. As pointed out above, all of the data used in the Boylemodel occurred when the solar wind electric field was lessthan 8 mV/m. Examining the Boyle and Hill-Siscoe modelpredictions in Figure 1 shows that they generally overlap inthe region below 8 mV/m. Thus the Boyle formula for the

polar cap potential is valid for the vast majority of the timewhen solar wind conditions are nominal and the solar windelectric field is <8 mV/m. It should be emphasized here thatthe line for the Boyle formula plotted here and in thesubsequent figures is a simplification where the values forthe solar wind velocity and are set to constants using theiraveraged values for that period and only the value of thesolar wind electric field is changed. This is done not as anexact comparison of the observations to the Boyle formulabut as a first-order guide to show the difference between theobserved saturated potentials and the magnitude of thepotentials were they to increase linearly with the solar windelectric field.[9] After this work was complete we undertook a search

for further passes which occurred during extreme solar windconditions. We first searched the ACE database for periodswhen the IMF was strongly southward (BZ < �20 nT) andsteady for 1 or more hours. In the period from 1998 throughearly 2002 we identified about 50 possible events. We thenexamined the DMSP-F13 database to see if there were anyusable passes that occurred during these events. We dis-carded all events where no DMSP-F13 polar passes over-lapped a period where ER > 8 mV/m or where there wereonly skimmer passes. After this we were left with 22 passesfrom eight events that should show evidence of saturation.Figure 2 is a plot of these passes along with the original sixpasses from the 31 March 2001 storm (noted by the letterson the figure) in the same format as Figure 1 but with onesignificant difference. The x-axis now shows ER, the recon-nection electric field in the solar wind, here defined as ER =ESW sin2(q/2), where q is the same clock angle as inequations (1) and (2). This takes into account the reconnec-tion factor of the IMF, since obviously a 10 mV/m electricfield in the solar wind would have very different results ifthe IMF orientation was completely north versus completelysouth. For the 31 March 2001 storm the IMF was almostcompletely southward during the six polar passes, so forthat event ER � ESW, but this was not the case for many ofthe new passes. Thus we rescaled the solar wind electricfield to make the comparisons valid.[10] Out of the 22 new passes, three of them were passes

where DMSP barely reached 75� magnetic latitude. Nor-mally, these would be discarded as skimmer passes withsmall observed potentials as described above; however,these three occurred during major storms when the polarcap had expanded significantly equatorward. Thus thesethree DMSP passes crossed enough of the potential distri-bution to measure large potential drops ranging from 134 to218.kV. Because these passes tracked so far from thelocations of the true maximum and minimum, we knowthat the true potential drops were larger than the observeddrops, but we have no way of definitively calculating themagnitude of those true potential drops. However, scalingthe size of the standard potential distribution up to the sizeof the patterns measured by the endpoints of these DMSPpasses and then comparing the potential along the track withthe total potential in the scaled up pattern shows that anincrease of 20% would be a reasonable estimate. Thus weplot these three passes on Figure 2 using potentials 20%greater than the measured potential drops and denote thesepasses by plotting their error bars with dotted lines. For theupper error bar on these three passes we used one-half of the

Figure 1. Adapted from Figure 3 from Hairston et al.[2003], this figure shows the data from the six prime DMSPpasses during the 31 March 2001 storm. The observedpotentials are plotted as a function of the solar wind electricfield and demonstrate that the potential saturates underconditions of large electric fields in the solar wind. Thestraight line labeled %B is the predicted potential fromthe Boyle formula, while the two curves labeled %H-S arethe predicted potential from the Hill-Siscoe model using thenominal values of 2 = 5 and 10 S.

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offset, thus matching all the other passes plotted here.However, for these three passes we extended the lowererror bar down to the original measured potential to includethe actual observation and to show the wider range ofuncertainty. The first one (at ER = 10.03 mV/m, extrapo-lated potential = 161 kV) falls in the middle of severalclosely spaced points and is difficult to see. The second one(at ER = 12.68 mV/m; extrapolated potential = 203 kV) iseasier to see and, because of its small offset relative to the20% correction, the location of data point is very asymmet-ric relative to the error bars. The third point is clearly visibleon the far right of the figure. This pass occurred between0457 and 0524 UT on 4 May 1998 during a period whenBZ = �31 nT. Although DMSP-F13 did not go above75.23� magnetic latitude, it still observed a potential dropof 218.28 kV and that is plotted here at 262 kV to includethe estimated 20% extra potential. This was only one ofthese additional 18 passes where the ER value exceeded thehighest value from the earlier 31 March 2001 event, so it isparticularly frustrating that the true potential for this pass isso uncertain. While the true potentials of these three pointscould be larger than the values plotted here, anything over30% larger is unrealistic, and even were the true potentialthat large it would still be much smaller than the expectedpotential from the linear Boyle model. Even after includingthis extra estimated potential, these three data points stillappear to fall within the range described by the rest of thedata points.[11] In the plot we have left the predicted line from the

Boyle formulation and the two Hill-Siscoe model predictioncurves based on the 31 March 2001 storm conditions toserve as a baseline. The figure shows the observed poten-tials as a function of the reconnection electric field in thesolar wind (which depends on the solar wind velocity, IMF

magnitude, and clock angle) but the Hill-Siscoe modelpredicted potential curves also depend on the ram pressure(which depends on the solar wind density and the solar windvelocity), the Pedersen conductivity, as well as an extra termof the sine of the clock angle. Varying the average solarwind velocity and clock angle would slightly change theslope and intercept of the line from the Boyle formulation.Likewise, varying the pressure, conductivity, and clockangle would move the curves of the Hill-Siscoe model upand down. Thus a range of nominal values for thesevariables would not produce a single line but a set ofHill-Siscoe curves forming a band on the plot. Mixing theseobservations from several different events occurring underdifferent solar wind conditions would not result in a set ofpoints forming a line; rather such data would form a band ofpoints. This is exactly what we see in the data shown inFigure 2: a band of points that show clear evidence ofsaturation.

3. Data From the October and November 2003Superstorms

[12] The three superstorms of October and November2003 served as ideal tests for the Hill-Siscoe model. Inthe space of 3 days we almost doubled the number of passesin the data set and extended the range of the reconnectionelectric field in the solar wind from just over 20 mV/m toalmost 40 mV/m. We start by examining the solar wind datafor the October storms. The superstorm of 29–31 October2003 was actually two sequential storms caused by twoseparate coronal mass ejections (CME). Figure 3 shows thedata from ACE during this period and a more completedescription of this data set is given by Skoug et al. [2004].The most outstanding feature of the first storm was the solar

Figure 2. Plot of the same six data points along with data from an additional 22 DMSP passes duringthe 1988–2002 time period that also show evidence of saturation. The line showing the predictedpotential from the Boyle formulation (here labeled %B) and the predicted potential from the Hill-Siscoemodel (using nominal values of2 = 5 and 10 S) based on the 31 March 2001 conditions are included as abaseline.

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wind speed (second panel) which exceeded 2000 km/s for aperiod starting at 0759 UT after the first shock passed theACE spacecraft at about 0620 UT on 29 October. This isonly the second time solar winds speeds in excess of 2000km/s have been directly observed (the other was observedon 4–5 August 1972 by Prognoz 2 and HEOS 2), thoughthere are several storms from the 19th and earlier 20thcenturies (such as the Carrington event of 1859) where suchhigh speeds can be inferred [Skoug et al., 2004]. The toppanel in Figure 3 shows the solar wind ion density observedby the Solar Wind Electron Proton Alpha Monitor (SWE-PAM) instrument on board the ACE spacecraft. Normally,SWEPAM measures the solar wind speed and ion densityevery 64 s in its ‘‘track’’ mode and every 33 min it takes onemeasurement in a ‘‘search’’ mode. However, from 1241 UTon 28 October to 0051 UT on 31 October the penetratingradiation from the energetic particles caused the trackingalgorithm to fail. Thus during this period only the 33-minresolution ‘‘search’’ mode data were usable. Also, duringthe period from 0600 UT on 29 October to 0400 UT on30 October the calculated ion densities from SWEPAMappear to be too low. Comparing the densities calculatedfrom ACE to the electron densities calculated from thePlasma Wave Instrument (PWI) later on Geotail (200 RE

further downstream) show good agreement until 0600 UT

on 29 October at ACE. After this time the correspondingGeotail densities are 2 to 5 times higher. Although the exactcause of this disagreement is unknown, it was determinedthat the Geotail plasma density data were less uncertain thanthe ACE density data, while the solar wind velocity calcu-lations from ACE remained valid for this period [Skoug etal., 2004]. Thus the region bounded by vertical bars andplotted with a heavy line on the top panel of Figure 3denotes the period where Geotail data rather than ACE dataare used for the solar wind density (after being timeshiftedforward to account to the transit time from ACE to theposition of Geotail.) After 0400 UT on 30 October, Geotailwas in the magnetotail, so after that time we revert to usingthe ACE density data. At 1100 UT on 31 October Geotailreemerged from the magnetotail (during the recovery phaseof the second storm), and the density measurements be-tween it and ACE once again agreed. So from 0400 UT 30October to 1100 UT 31 October there is no independentcheck on the quality of the ACE density calculations.However, we believe the data became more reliable towardthe end of this period as the storm recovery progressed[Skoug et al., 2004].[13] It is clear from the Geotail data that there was an

enhancement in the density just after the shock passed ACE.The bottom two panels show the BY and BZ components (in

Figure 3. This figures shows the solar wind density, solar wind velocity, and the BY and BZ

components (in GSM coordinates) of the IMF observed by the ACE spacecraft during the 29–30October 2003 CMEs. Note that the heavy trace in the density panel between the vertical bars at0600 UT on 29 October and 0400 UT on 30 October represents the substitution of GEOTAIL densitydata for the suspect ACE density data during this period. The short horizontal dashes in bottom paneldenote the times corresponding to the DMSP polar passes used in this study. The letters denotewhether the pass was a Northern or Southern Hemisphere pass.

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the GSM coordinate system) of the IMF measured by themagnetometer on board ACE. The two shocks from the twosequential CMEs can clearly be seen in the data in Figure 3.The first shock arrived at ACE at 0558 UT on 29 Octoberbased on the variability of IMF data. At the next SWEPAMobservation at 0620 there is a sudden increase in the solarwind speed in the top panel of Figure 3 and the ACE plasmadensity (not shown here). The second shock arrived at ACEat 1630 UT on 30 October and again is shown by theincrease in the solar wind speed and the variability of themagnetic field components; however, there is no apprecia-ble increase in the solar wind ion density. It is not clear whythere was no increase in the density following the secondshock. It could be there was an increase, but the densityalgorithm on SWEPAM was still failing and did notproperly detect it. Or the SWEPAM data could be accurate,indicating that the first shock had swept most of the plasmaout ahead of it, and there simply was not enough plasmaremaining behind for the second shock to create a densitypulse.[14] The IMF oscillated sharply between north and south

for the first few hours after the first shock, then turned steadilynorthward at 0841 UT on 29 October, and stayed steadilynorthward until 1746 UT. After that time the IMF turnedstrongly southward (BZ ranging from �27 to �10 nT) fornearly 9 hours until 0238 UT on 30 October. This extendedperiod of strong steady southward IMF provided the idealconditions for DMSP observations of the saturated potential.After 0238 UT the IMF turned moderately northward (BZ +10 nT) and the storm recovery began. At about 1630 UTthe second shock reached ACE and after a short period of

northward IMF BZ turned southward (�5 to �15 nT) forabout 30 min. BZ then hovered around zero until about1820 UT when it turned strongly southward (�20 to�35 nT) for about 4 hours. Again the conditions during thisperiod of steady southward IMF were ideal for testing thesaturation model. After this period BZ oscillated betweennorthward and southward periods for the next 4 hours.[15] During this period the DMSP-F13 spacecraft made a

polar pass every 51 min and measured the potential dropalong its track during each of these passes. Figure 4 showsthe history of the potential observation for the 3-day periodof 29–31 October. Because of the offset of the Earth’smagnetic dipole the spacecraft crosses a different part of thepotential distribution in each hemisphere, thus seeing dif-ferent observed potential drops even when the pattern is thesame. If all the potential measurements are plotted sequen-tially, this creates an artifact where the potential appears tojump back and forth between each hemisphere’s measure-ment. Instead, as in Figure 4, we connect all the NorthernHemisphere measurements sequentially (the solid line) andconnect all the Southern Hemisphere measurements sequen-tially (the dashed line). This gives two different lines thatclearly trend with each other rather than matching eachother exactly. In Figure 4 we can trace the history of the twostorms quite clearly. There is a sharp jump to 160 kV duringthe northern pass centered on 0643 UT as a response to theinitial shock and the strong negative BY and southward BZ

immediately after the shock. Note that this huge potentialoccurs during the time when DMSP would normally onlyskim the polar cap region. After that the potential decreasesto lower values (70 to 100 kV), corresponding to the

Figure 4. This figure shows the history of the potentials observed by DMSP-F13 during the 29–31 October 2003 superstorms. The solid line traces the potentials observed in the northern polar passesand the dashed line traces the potentials observed in the southern polar passes.

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following period of northward IMF. During the period from1500 UT to 0300 UT on 30 October there are largepotentials (most passes between 150 and 225 kV) measuredin both hemispheres. A period of small potentials followfrom 0300 UT to 1700 UT corresponding to the period ofsmall magnitudes of the IMF. From 1700 UT to 0100 UTthere is a second set of large potentials (most between 150and 210 kV) in response to the second shock and the periodof southward IMF following that. After that the potentialreturns to nominal values for the remainder of 31 October.A plot of the potentials from DMSP-F15 for this period (notshown) demonstrates a similar history. However, since theorbit orientation of F15 is 0930–2130 local time, its pathdoes not get as close to the true potential maximum andminimum as F13’s path does, and it observed smallerpotentials than F13 did. The largest potential drops mea-sured by F15 were 173.5 kV during the first storm and162.5 kV during the second storm.[16] For the analysis, we selected all the DMSP passes

during these storms with potentials greater than 140 kVresulting in 20 passes. In Figure 3 we have placed horizontalbars on the bottom panel (BZ) showing the times of these 20passes relative to the solar wind inputs, after having time-shifted them appropriately. The amount of time shifting wasdone individually for each pass and was based on the transittime of the solar wind from ACE to the magnetopause usingthe corresponding solar wind speed and then adding anadditional 10 min to account for the response time of theionosphere. Because of the different solar wind conditions,primarily the different densities and ram pressures leadingto different predictions for the Hill-Siscoe model, we chose

to plot these data in two groups, one for each storm. Figure 5shows the data for the 13 passes from the first storm usingthe same format as Figure 2 where the observed potentialand uncertainty are plotted against the reconnection electricfield in the solar wind. The prediction for the Boyle formulaand the two Hill-Siscoe curves (for S = 5 and 10 S) are alsoplotted on the figure. These predictions are based on thefollowing averages for the periods of the twelve passes:VSW = 1222.3 ± 172.9 km/s; P = 15.969 ± 7.896 nPa; F(q) =0.7883 ± 0.2199. The data points cover the reconnectionelectric field range from 7.73 to 30.22 mV/m with thehighest measured potential being 225 kV. The data clearlyshow the saturation effect compared to the prediction of theBoyle formula. The seven data points with a box around thecentral point denote the seven polar passes occurringbetween 2000 UT 29 October and 0135 UT 30 Octoberwhich corresponds to the period in Figure 3 of 1927 UT to0101 UT at ACE, a time of steady strong BZ negative and BY

positive conditions. Thus these are the points in which wehave the highest confidence. The fact that all of these sevenhigh-confidence points fall below the Hill-Siscoe curve forS = 10 S indicates that the overall average conductivityduring these passes was greater than 10 S. However, itshould be noted that since the pressures here are based onthe extrapolated densities from the Geotail, the accuracy ofthe Hill-Siscoe curves on this plot are somewhat uncertain.[17] In Figure 6 we plot the data from the seven DMSP

passes picked from the second storm. Here the Boyleformula and the Hill-Siscoe curves are calculated usingthese averages from the periods of these passes: VSW =1357.9 ± 181.6 km/s; P = 5.668 ± 2.701 nPa; F(q) = 0.8382 ±

Figure 5. Plot of the observed potentials versus the reconnection electric field in the solar wind for thefirst superstorm during 29–30 October 2003. The eight passes with the highest confidence level aredenoted by small boxes around the data points. The line for the predicted potential from the Boyleformulation (%B) and two representative Hill-Siscoe model curves are presented using the averagedvalues of other parameters during this period. The averaged parameters during this period were VSW =1222.3 ± 172.9 km/s; P = 15.969 ± 7.896 nPa; F(q) = 0.7883 ± 0.2199.

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0.2093. The slight increase in the average velocity causesthe line for the Boyle formula to move slightly upward.Meanwhile, the decrease in the pressure causes the two Hill-Siscoe curves to migrate significantly downward relative totheir locations in Figure 5. Here the data points for thereconnection electric field range from 7.74 mV/m all theway to 39.78 mV/m, with the highest measured potentialbeing 209.87 kV. Again the data clearly show saturation.The fact that three of these points are above 35 mV/m,nearly twice as large as the highest electric field prior tothese storms, yet still show no significant increase in theirpotential serve as conclusive evidence for the reality of thesaturation of the potential. In fact, the four passes in whichwe have the highest confidence are the four data pointsfarthest to the right in Figure 6. They correspond to theperiod of steady strong southward IMF between 1832 UTand 2130 UT at ACE in Figure 3. This time five of the sevenpoints appear to trend about the S = 10 S Hill-Siscoe curve,while the remaining two indicate a lower conductivity.Again, it should be noted that the density data for thisperiod comes from ACE during the period while Geotailwas in the magnetotail. As stated above, there is someuncertainty about the quality of the plasma density dataduring this period. However, we feel the quality of theSWEPAM data improved as the event progressed, so we arefairly certain about the position of the Hill-Siscoe curves forthis period.[18] Twenty-two days after the first superstorm hit the

Earth, another large CME from that same active site on thesun struck the Earth on 20 November 2003. This timethe CME did not swamp the SWEPAM, so there is highconfidence in all of the solar wind density and velocitydata for this event. Figure 7 show the solar wind data for

this event in the same format as Figure 3. There areseveral major differences between this event and the twoOctober CMEs. First the velocity increase is not asdramatic as the two shocks in October, but is more inline with a typical shock jumping from roughly 440 to620 km/s. Second, the solar wind densities are muchhigher this time after the shock, sometimes going over30 protons/cc. Third, the magnetic fields are much largerin magnitude. After the shock arrived, BZ oscillatedbetween north and south for about 90 min, then spent about50 min strongly northward (ranging from 13 to 37 nT). At1059 UT BZ turned sharply southward and began a 12-hourperiod when it remained strongly southward. BZ reached aminimum of �53 nT at 1435 UT then slowly increased toabout �10 nT over the next 9 hours. This extended periodof strongly southward IMF provided us with 12 morepasses occurring during large solar wind electric fieldswhere the potential should saturate. As in Figure 3 thetimes of 12 passes are denoted by the locations ofthe horizontal bars on the bottom panel (BZ). As before,the passes have been shifted forward in time so that theymatch the solar wind conditions that were in effect at thetime of that DMSP polar pass.[19] Figure 8 shows the history of the observed potentials

for 20–21 November in the same format as Figure 4. Again,the Northern and Southern Hemisphere histories trend alongwithout matching each other exactly. The potential sharplyincreases after about 1200 UT to over 200 kV. It reaches amaximum of 224 kV during the 1405–1435 UT southernpass (corresponding to the conditions in the solar wind justbefore BZ reached its minimum), then slowly decreased overthe next 8 hours. Again the measured potentials fromDMSP-F15 (not shown) mirror this history but do not

Figure 6. This figure follows the format of Figure 5 in plotting the observed potentials vs. thereconnection electric field in the solar wind for the second superstorm during 30–31 October 2003. Thefour passes with the highest confidence level are denoted by small boxes around the data points.The averaged parameters during this period were VSW = 1357.9 ± 181.6 km/s; P = 5.668 ± 2.701 nPa;F(q) = 0.8382 ± 0.2093.

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go as high as F13 with the largest F15 potential being175.5 kV.[20] Figure 9 shows the observed potentials for these 12

passes plotted against the corresponding reconnection elec-tric field in the solar wind that was driving the magneto-sphere during that pass. Like Figures 5 and 6, the line forthe Boyle formula and the two curves for the Hill-Siscoemodel (S = 5 and 10 S) are also shown on the plot. Theaveraged values of the solar wind parameters that were usedin calculating these were: VSW = 590.18 ± 34.39 km/s; P =8.405 ± 3.892 nPa; F(q) = 0.8881 ± 0.0912. The lower solarwind speed significantly reduces the value of the interceptin the Boyle formula line compared with Figures 5 and 6.This time the reconnection electric field in the solar windranges from 9.61 to 32.93 mV/m while the highest potentialwas the 224.45 kV pass mentioned above. While the rangeof data is not as great as the range during the earlier storms,these data do help fill in the middle region of the recon-

nection electric field. Again, it is obvious that the potentialshave saturated even as the electric field increases.

4. Discussion and Conclusions

[21] If there were any residual doubt about the reality ofthe saturation of the potential, the evidence from thesesuperstorms should finally put that to rest. Figure 10combines all the data from Figures 2, 5, 6, and 9 to showthe complete set of all 50 passes. We now have observationsunder solar wind electric field conditions almost all the wayout to 40 mV/m, about 2 1/2 times further out than the dataset in the work of Shepherd et al. [2002], which previouslyhad the largest coverage. All the data show clear evidence ofsaturation for conditions where the reconnection electricfield in the solar wind is above about 8 mV/m.[22] The next question is: what is the maximum value of

the saturated potential? Although the theoretical value under

Figure 7. Plot of the solar wind parameters measured by the ACE spacecraft during the 20 November2003 superstorm in the same format as Figure 3.

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the Hill-Siscoe model varies with the size of the electricfield, the ram pressure, and the Pedersen conductivity, itappears from these data that the maximum saturationpotential during these large storms is generally somewherebetween 160 and 250 kV. It should noted here that whilethese results agree with the results of Shepherd et al. [2002]to the extent that saturation exists and begins to manifestitself when the solar wind electric field becomes large, their

work showed no potentials above 120 kV. While this mayappear to establish a value for the saturation potential thatdiffers from ours, it is actually an artifact of the restriction ofthe SuperDARN observation to latitudes greater than 60�magnetic latitude. Under disturbed storm conditions such asthese where the convection pattern has expanded well below60� magnetic latitude, SuperDARN is unable to image theentire convection pattern, so their observed potential drop islikely less than the true potential (J. M. Ruohoniemi,personal communication, 2004). As to the size of themaximum saturation potential, we have searched the entiredatabase of DMSP-F8 (1987–1994) and F13 (1994–present) which are the two dawn-dusk DMSP spacecraft.Out of the roughly 170,000+ polar passes from these twospacecraft, there are only 27 passes where the observedpotential drop exceeded 200 kV. Two passes tied for highestobserved potential of 258 kV, one during the 31 March2001 storm and the other during the 10 April 1990 storm.(Unfortunately, there were no solar wind data during theApril 1990 event.) This points out two facts: first that it isunlikely that we will ever observe potential drop much(if any) in excess of 260 kV and second, how extremelyrarely these superstorm conditions occur.[23] We wish to point out two future avenues of research.

First, there is the question of the Pedersen conductivity termin the Hill-Siscoe model. While all the other terms inequation (2) can be measured directly, the Pedersen con-ductivity cannot. Thus for any given polar pass, we cansolve for this one remaining free variable to obtain the Hill-Siscoe prediction of the Pedersen conductivity, and whilethat result may fall within the range of nominal values forthe conductivity, without a way to test independently for the

Figure 8. Plot of the potentials observed by DMSP-F13during the 20–21 November 2003 superstorm in the sameformat as Figure 4.

Figure 9. Plot of the observed potentials versus the reconnection electric field in the solar wind for the20–21 November 2003 superstorm in the same format as Figures 5 and 6. The averaged parametersduring this period were VSW = 590.18 ± 34.39 km/s; P = 8.405 ± 3.892 nPa; F(q) = 0.8881 ± 0.0912.

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actual magnitude of the conductivity, there is no way todetermine conclusively if the Hill-Siscoe model is valid ornot. Although there is no way to directly measure theconductivity over the entire polar cap, the AMIE procedurecan produce a map of predicted conductivities based onobservations from ground magnetometers, radars, and sat-ellite observations [Lu et al., 2001]. We are currentlyconducting a study of the AMIE results from the Octoberand November 2003 superstorms to compare the predictedHill-Siscoe conductivities with the AMIE derived conduc-tivities. The results of this study will be the subject of afuture paper. Second, we have focused on the extremes ofthe solar wind to find if the saturation phenomenon existedor not. As a result, we have ignored all the data from themiddle region where the solar wind reconnection electricfield is between 4 and 8 mV/m. Since there are more dataavailable as the electric field decreases, we should be able toexamine that subset of the database to determine clearlywhere the ‘‘turnover’’ occurs between the simple linearfunction obtained by Boyle et al. [1997] and the saturatedregion of the Hill-Siscoe model. Such a study is part of ourfuture plans for research.[24] Last, it should be noted that despite all the discus-

sions of the uncertainty in the October ACE density data,this has no real effect on the argument for saturation. The ER

versus observed potential plots are not affected by thisuncertainty; only the position of the prediction curve ofthe Hill-Siscoe model are affected. Thus the uncertainly ofthe densities only affects the question of whether the Hill-Siscoe model is the correct description of saturation, notwhether the saturation phenomenon itself is occurring.

[25] Acknowledgments. We thank the ACE magnetometer group andCharles Smith at UNH for the magnetometer data used in this work. Wealso thank K. Ishisaka, H Kojima, H. Matsumoto, and T. Terasawa forproviding us with the electron density data from Geotail. The first authorwould like to thank J. Kozyra, M. Liemohn, G. Siscoe, T. Hill, and J. M.Ruohoniemi for their encouragement and discussions about this work.Work at the University of Texas at Dallas was done under the grantsNSF ATM-0101118 and NASA NAG5-9297. Work at Los Alamos wasperformed under the auspices of the U. S. Department of Energy, withfinancial support from the NASA ACE program.

[26] Arthur Richmond thanks George Siscoe and another reviewer fortheir assistance in evaluating this paper.

ReferencesBoyle, C. B., P. H. Reiff, and M. R. Hairston (1997), Empirical polar cappotentials, J. Geophys. Res., 102, 111.

Cowley, S. W. H. (1984), Solar wind control of magnetospheric convection,in Proceedings of Conference on Achievements of the IMS, 26–28 June1984, Graz, Austria, ESA SP-271, Eur. Space Agency, Paris.

Crooker, N. U., andG. L. Siscoe (1981), Birkeland currents as the cause of thelow-latitude asymmetric disturbance field, J. Geophys. Res., 86, 11,201.

Greenwald, R. A., W. A. Bristow, G. J. Sofko, C. Senior, J.-C. Ceriser, andA. Szabo (1995), SuperDual Auroral Radar Network radar imaging ofdayside high-latitude convection under northward interplanetary mag-netic field: Toward resolving the distorted two-cell versus multicell con-troversy, J. Geophys. Res., 100, 19,661.

Hairston, M. R., and R. A. Heelis (1996), Analysis of ionosphericparameters based on DMSP SSIES data using the DBASE4 and NADIAprogram, Tech. Rep., PL-TR-96-2078, Phillips Lab., Geophys. Dir.,Hanscom Air Force Base, Mass.

Hairston, M. R., R. A. Heelis, and F. J. Rich (1998), Analysis of the iono-spheric cross polar cap potential drop usingDMSP data during the NationalSpace Weather Program study period, J. Geophys. Res., 103, 26,337.

Hairston, M. R., T. W. Hill, and R. A. Heelis (2003), Observed saturation ofthe ionosphereic polar cap potential during the 31 March 2001 storm,Geophys. Res. Lett., 30(6), 1325, doi:10.1029/2002GL015894.

Heelis, R. A. (1984), The effects of interplanetary magnetic field orientationon dayside high-latitude ionospheric convection, J. Geophys. Res., 89,2873.

Heppner, J. P., and N. C. Maynard (1987), Empirical high-latitude electricfield models, J. Geophys. Res., 92, 4467.

Hill, T. W. (1984), Magnetic coupling between the solar wind and magneto-sphere: Regulated by ionospheric conductance?, Eos Trans. AGU, 65,1047.

Hill, T. W., A. J. Dessler, and R. A. Wolf (1976), Mercury and Mars: Therole of ionospheric conductivity in the acceleration of magnetosphericparticles, Geophys. Res. Lett., 3, 429.

Lu, G., A. D. Richmond, J. M. Ruohoniemi, R. A. Greenwald, M. Hairston,F. Rich, and D. S. Evans (2001), An investigation of data and modelinputs on assimilative mapping of ionospheric electrodynamics, J. Geo-phys. Res., 106, 10,883.

Reiff, P. H., and J. G. Luhman (1986), Solar wind control of the polar cappotential, in Solar Wind-Magnetospheric Coupling, edited by Y. Kamideand J. A. Slavin, p 453, Terra Sci., Tokyo.

Reiff, P. H., R. W. Spiro, and T. W. Hill (1981), Dependence of polar cappotential drop on interplanetary parameters, J. Geophys. Res., 86, 7639.

Rich, F. J., and M. Hairston (1994), Large-scale convection patternsobserved by DMSP, J. Geophys. Res., 99, 3827.

Richmond, A. D., and Y. Kamide (1998), Mapping electrodynamic featuresof the high-latitude ionosphere from localized observations: Technique,J. Geophys. Res., 93, 5741.

Figure 10. Combination of all the data points from Figures 2, 5, 6, and 9 to give the entire set of50 points showing saturation during the 1998 through 2003 period.

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Ruohoniemi, J. M., and K. B. Baker (1998), Large-scale imaging of high-latitude convection with Super Dual Auroral Radar Network HF radarobservation, J. Geophys. Res., 103, 20,797.

Russell, C. T., J. G. Luhmann, and G. Lu (2001), Nonlinear response ofthe polar ionosphere to large values of the interplanetary electric field,J. Geophys. Res., 106, 18,495.

Shepherd, S. G., R. A. Greenwald, and J. M. Ruohoniemi (2002), Crosspolar cap potentials measured with SuperDARN during quasi-steady so-lar wind and IMF conditions, J. Geophys. Res., 107(A7), 1094,doi:10.1029/2001JA000152.

Siscoe, G. L., G. M. Erickson, B. U. O. Sonnerup, N. C. Maynard, J. A.Schoendorf, K. D. Siebert, D. R. Weimer, W. W. White, and G. R. Wilson(2002), Region 1 current-voltage relation: Test of Hill model, saturation,and dipole-strength scaling, J. Geophys. Res., 107(A6), 1075,doi:10.1029/2001JA000109.

Siscoe, G., J. Raeder, and A. J. Ridley (2004), Transpolar potential satura-tion models compared, J. Geophys. Res., 109, A09203, doi:10.1029/2003JA010318.

Skoug, R. M., J. T. Gosling, J. T. Steinberg, D. J. McComas, C. W. Smith,N. F. Ness, Q. Hu, and L. F. Burlaga (2004), Extremely high speed solarwind: 29–30 October 2003, J. Geophys. Res., 109, A09102, doi:10.1029/2004JA010494.

Weimer, D. R. (1995), Models of high-latitude electric potentials derivedwith a least error fit of spherical harmonic coefficients, J. Geophys. Res.,100, 19,595.

Weimer, D. R. (1996), A flexible, IMF dependent model of high-latitudeelectric potentials having ‘‘space weather’’ applications, Geophys. Res.Lett., 23, 2549.

�����������������������K. A. Drake and M. R. Hairston, Center for Space Sciences, University of

Texas at Dallas, P. O. Box 830638, MS FO22, 2601 North Floyd Road,Richardson, TX 75083-0688, USA. (hairston@utdallas.edu)R. Skoug, Space Science and Applications, Los Alamos National

Laboratory, Group ISR-1, MS D466, Los Alamos, NM, 87545, USA.

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