Ground-based optical determination of the b2i boundary:

A basis for an optical MT-index

E. F. Donovan,1,2 B. J. Jackel,1,2 I. Voronkov,3 T. Sotirelis,4 F. Creutzberg,5

and N. A. Nicholson1,2

Received 30 November 2001; revised 25 January 2002; accepted 30 January 2002; published 14 March 2003.

[1] The equatorward boundary of the proton aurora corresponds to a transition fromstrong pitch angle scattering to bounce trapped particles. This transition has beenidentified as the b2i boundary in Defense Meteorological Satellite Program (DMSP) iondata [Newell et al., 1996]. We use ion data from 29 DMSP overflights of the CanadianAuroral Network for the OPEN Program Unified Study (CANOPUS) Meridian ScanningPhotometer (MSP) located at Gillam, Canada, to develop a simple algorithm to identifythe b2i boundary in latitude profiles of proton auroral (486 nm) brightness. Applyingthis algorithm to a ten year set of Gillam MSP data, we obtain �250,000 identifications ofthe ‘‘optical b2i,’’ the magnetic latitude of which we refer to as b2i�. We intercompare�1600 near-simultaneous optical and in situ b2i�, concluding that the optical b2i� is areasonable basis for an optical equivalent to the MT-index put forward by Sergeevand Gvozdevsky [1995]. Using �17,000 simultaneous measurements, we demonstrate astrong correlation between the optical b2i� and the inclination of the magnetic field asmeasured at GOES 8. We develop an empirical model for predicting the GOES 8inclination, given theuniversal time, dipole tilt, and the optical b2i�, as determined atGillam. We also show that in terms of information content, the b2i boundary is an optimalboundary upon which to base such an empirical model. INDEX TERMS: 2455 Ionosphere:

Particle precipitation; 2704 Magnetospheric Physics: Auroral phenomena (2407); 2716 Magnetospheric

Physics: Energetic particles, precipitating; 2744 Magnetospheric Physics: Magnetotail; 2764 Magnetospheric

Physics: Plasma sheet; KEYWORDS: proton aurora, isotropy boundary, b2i boundary, magnetotail stretching,

magnetic mapping

Citation: Donovan, E. F., B. J. Jackel, I. Voronkov, T. Sotirelis, F. Creutzberg, and N. A. Nicholson, Ground-based optical

determination of the b2i boundary: A basis for an optical MT-index, J. Geophys. Res., 108(A3), 1115, doi:10.1029/2001JA009198, 2003.

1. Introduction

[2] Ion distribution functions measured at low altitudes(i.e., �1000 km) on magnetic field lines threading the CPS(Central Plasma Sheet) are typically isotropic outside of themostly empty upgoing loss cone. A meridional profile of thedistribution functions typically shows such single loss conedistributions from near the polar cap boundary, and equator-ward through much of the CPS, and then a transition fromisotropy to anisotropy at lower latitudes. This transitionmarks the equatorward boundary of significant ion precip-itation. Equatorward of the transition region, the ion dis-tribution function is isotropic outside of the mostly empty

upgoing and downgoing loss cones. This picture is compli-cated by local acceleration, transverse heating, convection,and other phenomena. Nevertheless, low altitude observa-tions of ion distributions and energy spectra from tens of eVto tens of KeV, spanning a wide range of geomagneticlatitudes, and under a variety of geophysical conditions, aregenerally consistent with this picture [Imhof et al., 1977;Sergeev and Tsyganenko, 1982; Imhof, 1988; Gvozdevskyand Sergeyev, 1995].[3] A single loss cone distribution indicates strong pitch

angle diffusion due to scattering [Ashour-Abdalla andThorne, 1978] that results in proton precipitation, ultimatelyproducing diffuse auroral luminosity. This region of diffuseauroral precipitation, and hence strong pitch angle diffusion,corresponds to latitudes where single loss cone distributionsare observed. Equatorward of this, the double loss conedistributions indicate bounce trapped ions with little or nopitch angle scattering. The transition between bounce trap-ping and strong pitch angle scattering occurs at what hasbeen called the ion isotropy boundary, or simply the ‘‘IB’’[e.g., see Sergeev et al., 1983]. The IB is readily identifiedin data from satellite instruments that measure energy fluxesboth orthogonal to, and parallel to, the local magnetic field[see, e.g., Imhof et al., 1977, Figure 2].

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A3, 1115, doi:10.1029/2001JA009198, 2003

1Department of Physics and Astronomy, University of Calgary, Calgary,Alberta, Canada.

2Institute for Space Research, University of Calgary, Calgary, Alberta,Canada.

3Department of Physics, University of Alberta, Edmonton, Alberta,Canada.

4Applied Physics Laboratory, Johns Hopkins University, Greenbelt,Maryland, USA.

5Keometrics, Ottawa, Ontario, Canada.

Copyright 2003 by the American Geophysical Union.0148-0227/03/2001JA009198$09.00

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[4] The data set that has been most extensively used forthe determination of precipitation boundaries is from theDefense Meteorological Satellite Program (DMSP) iondetectors, which measure energy fluxes along the fielddirection [Hardy et al., 1984]. Under the assumption thatsignificant ion precipitation corresponds to a full loss cone,it is reasonable to equate the equatorward termination ofthat precipitation to the IB, and hence to infer the IB latitudefrom the DMSP data. Newell et al. [1998] used NationalOceans and Atmospheres Administration (NOAA) andDMSP data to demonstrate the equivalence of the IB andlocation of the peak energy flux of 3 – 30 KeV ions asmeasured by DMSP. The location of the peak energy flux isreferred to as the ‘‘b2i boundary’’ [Newell et al., 1996]. Inthe evening sector, this peak is usually near the equatorwardedge of precipitating 3 – 30 KeV ions. Toward dawn thepeak tends to be less well pronounced. Therefore, a slightlymodified definition of the b2i will be used in this paper: itwill be the low latitude edge of a plateau in the 3 – 30 keVion energy flux (which usually coincides with a peak if thereis one). This new procedure seems to work well, though itsperformance has not yet been fully demonstrated. Thelatitude of the IB, and b2i boundary (herein referred to as‘‘IB�’’, and ‘‘b2i�’’, respectively), are functions of bothenergy and magnetic local time (MLT), with variations thatreflect the recent time history of magnetospheric dynamics.[5] Whatever the cause of the pitch angle scattering, the

IB is an important marker of a transition between twodifferent magnetospheric regions. Poleward of the IB,plasma conditions support strong diffusion. Equatorwardof it, they do not. The two most likely causes of thescattering are wave-particle interactions [e.g., Ashour-Abdalla and Thorne, 1978] and breaking of the first adia-batic invariant due to highly curved field lines in the vicinityof the neutral sheet [Sergeev et al., 1983]. The dependence ofIB� on energy is often consistent with the scattering being aconsequence of field line curvature, at least for higher energy(i.e., >30 KeV) protons [Imhof et al., 1977; Gvozdevsky andSergeyev, 1995]. Furthermore, the results of simulations ofparticle motions in realistic magnetic field models indicatethat inner CPS field lines, in the vicinity of the neutral sheet,have small enough radii of curvature to cause enough pitchangle scattering to fill the relatively small loss cone [Tsyga-nenko, 1982; Sergeev et al., 1983]. On this basis, it has beensuggested that the IB is the signature of the transitionbetween regions of adiabatic and nonadiabatic ion motionin the neutral sheet region, and that the nonadiabaticity is dueprimarily to field line radii of curvature that are on the orderof the ion gyroradii (the actual criterion for pitch anglescattering is that the radius of curvature is smaller than abouteight times the ion gyroradius [Sergeev and Tsyganenko,1982; Sergeev and Gvozdevsky, 1995]).[6] If the pitch angle scattering is due to field line

curvature, then the latitude of the boundary contains infor-mation about the curvature of magnetic field lines near theequatorial plane [see, e.g., Wing and Newell, 1998; Wanlisset al., 2000]. Sergeev and Gvozdevsky [1995] carried out acomparison between the latitude of the IB� and the incli-nation of the geomagnetic field in the geosynchronousregion, demonstrating a good correlation between the twoquantities: in general, the more equatorward the IB, thegreater the magnetic field inclination. Sergeev and Gvoz-

devsky [1995] suggested that IB� is therefore a meaningfulindicator of the state of the inner magnetosphere, anddeveloped an IB-based Magnetotail (MT) index.[7] In situ measurements of IB� are available directly

from auroral zone crossings of the FAST and NOAAspacecraft, and indirectly (i.e., through the b2i) from DMSP.On any given day, literally dozens of IB� measurements areprovided by such spacecraft. In order to develop the MT-index, it was deemed necessary to devise an empiricalmethod for comparing IB� measurements from differentMLTs. In order to do so, Sergeev and Gvozdevsky [1995]carried out a statistical study of the MLT dependence ofIB�. More specifically, they used a straightforward auroraloval shape, characterized by two parameters, to estimate theIB� at magnetic midnight, based on a measurement of thisquantity at some other MLT. The estimated midnight IB� isthe MT-index (or ‘‘MT’’):

MT ¼ IB� � A1 � 1� cosp12

MLT�MLToð Þ� �h i

ð1Þ

Here, the IB� is observed at local time MLT, and theconstants A1 and MLTo were determined statistically to be4.3� and 23.1 hours, respectively.[8] Precipitation of magnetospheric protons leads to

auroral emissions at wavelengths corresponding to a num-ber of hydrogen electronic transitions. Figure 1 is a keogramof hydrogen Balmer-b (herein ‘‘486 nm’’) intensity obtainedby the Canadian Auroral Network for the OPEN ProgramUnified Study (CANOPUS) Meridian Scanning Photometer(MSP) located at Gillam, Canada. Some typical eveningsector proton auroral properties are evident here. In partic-ular, significant emissions occur over several degrees oflatitude, move equatorward during a growth phase, andbrighten at the time of a substorm onset (that here occursat roughly 0315 UT). At 0300 UT on 8 January 1997,DMSP F12 passed almost directly overhead of Gillam. InFigure 2, we have plotted the integrated ion energy fluxfrom DMSP F2 and the proton auroral brightness from thephotometer at Gillam, as functions of magnetic latitude. Wehave also identified the b2i� (obtained from the DMSP fluxdata). As well, proton auroral intensities are shown for thefive successive MSP scans which take place during the fiveminutes around the F12 overflight. The data shown here istypical. The proton auroral brightness profile does notchange significantly on a five minute time scale, exceptduring dynamic events such as substorm onsets. As well,the brightness profile is often reasonably well fit by a simpleGaussian. Finally, the brightness profile correlates fairlywell with that of the integrated ion energy flux. This singleexample suggests that the equatorward edge of the protonaurora can reasonably be expected to correspond to the b2iboundary.[9] Long term data sets of Hb emissions have been

produced by MSPs located in Canada at Fort Smith, RankinInlet, Gillam, and Pinawa [Rostoker et al., 1995], as well asin Alaska, at Poker Flat [Deehr, 1994], Scandinavia, atLongyearbyen and in Finland, and in Antarctica [Kaila etal., 1997]. Thus, there is a possibility of building up a largeset of optically inferred b2i boundaries. Moreover, thisoptical b2i boundary could form the basis of an opticalMT, an index that would have some distinct advantages over

SMP 10 - 2 DONOVAN ET AL.: OPTICAL MT-INDEX

satellite measurements. For instance, the b2i boundary couldbe monitored continuously over many hours by a groundstation, thus allowing for near-continuous monitoring offield line stretching in the inner magnetosphere and midtailregion (via the MT). As well, having long periods of timeduring which the b2i� is known would greatly increase thenumber of simultaneous determinations of the b2i� at severallocal times and latitudes. There are also distinct disadvan-tages to using optical data for monitoring the b2i boundary:Hb emissions are weak, and virtually impossible to detect atauroral latitudes during the summer months. Even during the

winter months, optical determination of this boundary willonly be possible on the night side, and within the field ofview of an appropriate MSP. Furthermore, clouds, moonlight, twilight, aerosol contamination and filter leakage allconspire to reduce the number of hours of good Hb data thatone can obtain from ground-based MSPs.[10] Any intercomparison of the MSP and in situ data

requires assigning latitudes to emissions which are strictlyobserved at known photometer elevation angles. In all ofour work, we assume an emission altitude of 110 km. Thisis in line with measured altitude profiles [i.e., Strickland et

Figure 1. Keogram of 486 nm emissions obtained by the CANOPUS Gillam MSP on 8 January 1997.The latitudes correspond to a presumed emission altitude of 110 km.

Figure 2. DMSP overflight of Gillam at �0300 UT on 8 January 1997. This is a comparison of DMSPmeasured ion energy flux with hb intensity. The dotted curves indicate Hb intensity from meridionalscans during the DMSP overflight. The smooth curve is a Gaussian fit to the average intensity profile (ie,during the overflight). The vertical line indicates the b2i� inferred from the DMSP flux data.

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al., 2001, Plate 1; Omholt, 1971, section 3.2.7], and modelsof auroral emissions resulting from typical proton precip-itating energy fluxes and characteristic energies [i.e., Koze-lov, 1995, Figure 2]. Some uncertainties are introduced intoour analysis by assuming the fixed height of the emissions.These result from the fact that the presumed height willdiffer from the actual height of the peak brightness, and thatthe emissions are in reality from an extended height range.These uncertainties have no effect on our inferred latitude atmagnetic zenith, and progressively larger effects for lowerelevation angles.[11] In what follows, we use a number of DMSP over-

flights of Gillam to develop a simple algorithm for inferringthe b2i� from the MSP data. Using only data from Gillam,we then apply this algorithm, thereby creating a large dataset of optical b2i�. Using a large number of simultaneousoptical and DMSP-based b2i� values, and presuming thatthe locus of points that make up the b2i boundary is of theform given in equation (1), we estimate the quantities A1

and MLTo. Finally, we demonstrate that the latitude of theproton aurora correlates well with the inclination of themagnetic field at geosynchronous orbit, as measured byGOES 8. Our principal message is that the optical b2i�contains the essential ingredients necessary for the con-struction of an optical MT-index, and that this new indexcan provide valuable information about the state of the innermagnetosphere which will compliment that provided by thein situ MT-index.

2. Optical b2i�

[12] We used the DMSP and MSP data sets for themonths of September to April for the years 1990 (Sep-tember) to 1999 (April). There were 29 instances where aDMSP satellite passed within one half hour of magneticlocal time of Gillam during times of good viewing con-ditions, and during which the region of significant proton

auroral emission was well within the field of view of theGillam MSP. This search for conjunctions was inspired byBlanchard et al. [1995], who used DMSP particle andCANOPUS MSP 630 nm data to develop an algorithm foridentifying the polar cap boundary using the optical data.For each nearly coincident overflight we fit a Gaussian tothe brightness profile from the MSP, and determined theb2i� from the DMSP data. The location of the b2iboundary, relative to the peak in the brightness profile,was then determined in units of standard deviations (ie, interms of the width of the region of significant protonauroral emissions). Results are shown in Figure 3. In allcases, the b2i boundary was south of the peak in bright-ness. In all but one case, the b2i boundary was between 0.6and 2.2 standard deviations south of the peak. The meanlocation (for all 29 cases) was roughly 1.4 standarddeviations south of the peak. For reference, the standarddeviations range from roughly 50 kilometers to roughly150 km, assuming that the emissions come from an altitudeof 110 km.[13] Considering the results summarized in Figure 3, we

suggest that a reasonable algorithm for determining theoptical b2i� is as follows. Fit a Gaussian to the Hb bright-ness profile. If that Gaussian is ‘‘well’’ within the field ofview of the MSP, then a reasonable estimate of the b2i� is1.4 standard deviations south of the peak in brightness. Forour purposes, we consider this criterion to be satisfied if thepeak of the best-fit Gaussian is more than one standarddeviation from the edge of the field of view. Although attimes the brightness profile is not be well fit by a Gaussian,this algorithm is straightforward to implement, test, andreproduce.

3. Optical MT-Index

[14] The Gillam MSP operates continuously betweensunset and sunrise, delivering meridional scans of 486 nm

Figure 3. Distribution of b2i boundary locations, relative to the peak in Hb intensity for 29 DMSPoverflights of Gillam (see text). The histogram shows the distribution of the 29 b2i locations with ashaded Gaussian included for reference. Negative values indicate locations equatorward of the peak inbrightness.

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intensity at a rate of one per minute. We applied ouralgorithm for determining the optical b2i� to the MSP dataobtained during the months of September to April, begin-ning in the fall of 1990, and ending in the spring of 1999,restricting our attention to MLTs between 1830 and 0530.We obtained a data set of roughly 250000 optical b2i�values. The optical b2i� values are ordered surprisingly wellby Kp (see scatterplot of Nicholson et al. [2003]). Theaverage values of b2i�, as a function of MLT, and binned byKp, are plotted in Figure 4. The statistical local timedependence is qualitatively similar to the statistical ovalshape used by Sergeev and Gvozdevsky [1995] as a basis forinferring the b2i� at magnetic midnight from a b2i�determined at some other MLT. As discussed above, thisinferred b2i� at magnetic midnight is the MT-index.[15] A more quantitative test for the equivalence of an

optical MT-index (i.e., one inferred from the optical b2i�)and that of Sergeev and Gvozdevsky [1995] was carried outas follows. From our set of �250000 optical b2i� values,we identified �1600 instances when there was a nearlysimultaneous in situ b2i identification obtained by a DMSPpass. The criterion we applied for ‘‘near-simultaneous’’ wasthat the b2i boundary determinations occurred within twominutes of each other. Presuming that the instantaneouslocus of points making up the b2i boundary is roughly ofthe form given in equation (1), these 1600 points provideus with an excellent opportunity to infer, through a least-squares fit, the quantities A1, and MLTo. Carrying out thisfit, we obtain values of A1 and MLTo of, 3.6 and 23.2hours, respectively. These are in good agreement with thevalues of these parameters provided by Sergeev andGvozdevsky [1995]. Of the 1600 near-simultaneous b2iboundary identifications, half had MLT separationsbetween the spacecraft and MSP in excess of 5.1 hours.However, even such widely separated measurements showremarkably good agreement. This is illustrated in thescatterplots of Figure 5 comparing in situ and optical

MT-indices determined from the roughly 1600 near-simul-taneous DMSP and MSP observations.

4. Geostationary B-Field Inclination

[16] The MT-index is the latitude of the b2i boundary atmagnetic midnight, estimated on the basis of an observationof b2i� at some other local time. This index providesquantitative information about the state of the inner magne-tosphere, based on a demonstrated correlation between theMT-index and the inclination of the geomagnetic field atgeostationary orbit [Sergeev and Gvozdevsky, 1995; Newellet al., 1998]. In section 2 we suggested an algorithm for theoptical determination of b2i� and used this algorithm to inferroughly 250000 optical b2i� values from good observationtimes during the period 1990 – 1999. This data set providesus with an excellent opportunity to explore the correlationbetween the inclination of the magnetic field at geosynchro-nous orbit and the latitude of the equatorward boundary ofsignificant proton precipitation. In this section, we presentthe results of a comparison between our optical b2i� values,and the geosynchronous magnetic field inclination.[17] In order to examine the degree of stretching of the

near-Earth magnetic field, we use simultaneously obtainedGOES 8 magnetic field data and our optical b2i� data base.Throughout the years from 1996 to 1999, GOES 8 waslocated over the East coast of Hudson Bay, roughly 1 hourof local time east of Gillam. As pointed out by Newell et al.[1998], a geosynchronous satellite at the longitude ofGOES 8 is located well above (roughly 0.8 Earth radii)the magnetic equatorial plane. As such, GOES 8 is ideallylocated in terms of providing information about the degreeof stretching of the magnetic field in the inner magneto-sphere. With the exception of substorm onsets, the latitudeof the proton aurora does not change appreciably on a timescale of several minutes or longer. With this in mind, wegrouped our b2i� data set into five minute bins. The same

Figure 4. Mean geomagnetic latitudes of the optical b2i�, where the values are binned according by Kp.

DONOVAN ET AL.: OPTICAL MT-INDEX SMP 10 - 5

binning was also applied to the GOES 8 magnetic field data.Furthermore, the inclination of the GOES 8 magnetic fieldwas defined to be

IG8 ¼ arctan Bz=Br� �

ð2Þ

Here, Bz and Br are the Solar Magnetic z and radial (iesqrt(Bx

2+By2)) components of the magnetic field, respectively

(see Russell [1971] for a definition of SM coordinates).Figure 6 is a plot of the GOES 8 inclination, the Gillamproton auroral data, and the optical b2i�s for one night. In

Figure 6. GOES 8 magnetic field inclination (top) and Gillam proton auroral data (bottom) for 0200–1100 UT on 24 March 1996. Five minute averages of the locations of the optical b2i, determined with thealgorithm discussed in section 2, are indicated with the red diamonds on the keogram.

Figure 5. Comparison of MT-indices inferred from near-simultaneous identification of b2i� from theMSP (optical) and DMSP (in situ) data. The top and bottom panels show the events where the MLTseparation of the DMSP spacecraft and the MSP were greater than, and less than, 5.1 hours, respectively.There are 817 cases each of large and small MLT separation. The linear correlation coefficients are 0.77(small separation) and 0.66 (large separation).

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the time period from 1996 to 1999, there were 219 nightsduring which there were relatively long and continuousperiods during which we could obtain optical b2i� valuesand the GOES 8 inclination. Overall, we obtained roughly17000 simultaneous five minute averages of these twoquantities. This data set is the basis of our comparison.[18] GOES 8 magnetic field inclination varies with local

time, dipole tilt, and the distribution of the cross-tail currentin the inner magnetosphere. The distribution of the cross-tailcurrent affects the mapping between the inner magneto-sphere and the ionosphere, and, presumably, the location ofthe earthward boundary of the region in which the strongpitch angle scattering causes the proton auroral precipitation(see section 1). One therefore expects some correlationbetween the inclination of the magnetic field in the innermagnetosphere and the latitude of the b2i boundary (or theIB) in the same local time sector. In this section, we developan empirical model of the GOES 8 inclination as a functionof optical b2i�, dipole tilt and universal time. Our immedi-ate goal is to minimize the root-mean-square (RMS) differ-ence between the model inclination, and the observedinclination.[19] The average inclination for our data set is 58.06�

with a RMS deviation from the average of 8.64�. As statedabove, the deviation is due to the combined local time anddipole tilt effects, and geomagnetic activity. We first devel-oped a model of the inclination that depended only on theb2i boundary. In particular, a third order polynomial in b2i�fit the inclination with an RMS deviation of only 5.8�.However, the model errors showed clear dependence onlocal time and dipole tilt angle. In order to remove theseeffects we developed a simple model that depended only ondipole tilt and universal time (and hence local time). Weexperimented with a number functional forms, and settledon a model that is linear in dipole tilt, and quadratic in

universal time. A linear least squares fit between the modeland the �17000 GOES 8 inclinations yielded the following:

IG8 ¼ 49:5� 0:29� tiltþ 0:25 UT� 3:5ð Þ2 ð3Þ

The RMS deviation between the observed and modelinclinations is 7.35�. It should be noted that this model isbased on a subset of GOES 8 data from the winter monthsand the interval 0 – 12 UT, and is unlikely to be valid forsummer and dayside locations.[20] We detrended the data using equation (3) and fit the

residuals to a quadratic in b2i�. The resulting combinedmodel

IG8 ¼ 61:8� 0:43 b2i� � 71:5ð Þ2�0:29� tiltþ 0:25 UT� 3:5ð Þ2

ð4Þ

has an RMS error of 5.07�. For reference, a general modelto 3rd degree in all parameters has an RMS error of 4.62�.The model given in 4 provides nearly as good a fit, and hasa much simpler form, so we will use it for all furtheranalysis. Figure 7 is a scatterplot of the observed andpredicted GOES 8 magnetic inclination (with equation (4)),based on our data set of �17000 simultaneous optical b2i�and GOES 8 observations. The very high correlation (r =0.815) indicates a strong relationship between geostation-ary magnetic field and the location of proton auroralemissions.[21] We have developed a way of predicting the inclina-

tion of the magnetic field at the location of GOES 8 from aground-based observation. These results are similar to thoseof Sergeev and Gvozdevsky [1995] and Newell et al. [1998].If we were to consider only the RMS deviations discussedabove, one might question the value of this exercise. Afterall, in going from a model that was based only on local time

Figure 7. Predicted and observed inclinations at GOES 8. Points shown are for 16878 simultaneousobservations of the optical b2i� and the GOES 8 inclination. The predictions are based on equation (4).The linear correlation coefficient between the observed and predicted values is 0.815.

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and dipole tilt (equation (3)) to one that also utilizes theoptical b2i�, we reduced the RMS deviation from 7.35� to5.07�. The correlation between the predicted and observedinclinations demonstrated in Figure 7 is impressive; how-ever a similar scatterplot (not shown) based on inclinationspredicted with equation (3) demonstrates a significant (r =0.53) correlation.[22] The advantage of the optical b2i� is that it provides

information about the short term variability of inclinationat geostationary orbit. In Figure 8, we have plotted theobserved GOES 8 inclinations for the night of 24 March1996 as well as the inclinations predicted by equations (3)and (4). For this night, the RMS deviation between theobserved inclinations and those predicted using equations(3) and (4) are �8� and �3�, respectively. It is clear thatthe short term variability of the inclination at geosta-tionary orbit and the latitude of the optical b2i arestrongly related. The night of 24 March 1996 was trulytypical in terms of the variability of the proton aurora, theGOES 8 inclination, as well as the quality of fit providedby both models. On some of the 219 nights, there wasgreater systematic discrepancy between the modelled andobserved inclinations. On other nights, there was greatersystematic agreement.[23] We wish to explore one final question concerning the

relationship between the optical b2i�, as inferred from thesimple algorithm presented in section 2, and the inclinationof the magnetic field at GOES 8. The optical b2i� is

b2i� ¼ �peak � 1:4s ð5Þ

where �peak and s are the latitude of the peak and thestandard deviation of the Gaussian fit to the brightness

profile, respectively. We proposed this algorithm based onour comparison of data from the 29 DMSP-Gillamconjunctions. The use of this algorithm is supported byour comparison of optical and in situ b2i� values obtainedsimultaneously at different MLTs (i.e., Figure 5), and thefact that we find a similar correlation between theinclination of the magnetic field at geosynchronous orbitand the latitude of the optically inferred b2i� as do Sergeevand Gvozdevsky [1995] and Newell et al. [1998] (i.e., Figure7). In our view, we have presented a compelling case thatthe algorithm in equation (5) is at least a reasonable way ofinferring the optical b2i� from the brightness profile. Thereis certainly a strong correlation between the inclination atgeosynchronous orbit and the b2i�. The use of the b2iboundary (or the IB) as a basis for the MT-index was at leastpartially based on this correlation.[24] Undoubtedly, b2i� conveys important information

about how relatively stretched field lines near the earthwardedge of the current sheet are. It is not clear, however,whether or not the b2i boundary is the single ion precip-itation boundary that provides the most information in thisregard. For example, there are other variables related to theproton precipitation that could be used to parameterize anempirical model of the inclination of the magnetic field atgeostationary orbit. Examples include the latitudes of thepeak in brightness and poleward boundary of the protonauroral intensity, as well as the integrated brightness, width,and peak intensity of the proton aurora. In this paper we donot explore all of these variables in terms of their value aspredictors of the geostationary magnetic field inclination.We have, however, carried out a straightforward numericalexperiment that allows us to at least partially explore thequestion of whether b2i� is the optimal single ion precip-

Figure 8. Observed (solid diamonds) and modelled (open triangles) GOES 8 inclinations for the nightof 24 March 1996 (proton auroral data and optical b2i� values for this night are given in figure 6). Modelvalues are obtained using equation (4). For comparison purposes, the dashed curve shows the GOES 8inclination from the best fit model based solely on dipole tilt and universal time (equation (3)).

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itation boundary, in terms of information content about thestate of the inner magnetosphere.[25] We define a more general boundary, referred to as

b�, in the following way:

b� ¼ �peak � as ð6Þ

Here, �peak and s have the same meaning as in equation (5),and a is a constant. If a is set to 1.4, then this more generalboundary is our optical b2i�. We then determine, using b�,dipole tilt and universal time as the parameters in anempirical model of GOES 8 inclination, what value of awill provide the lowest RMS deviation between theobserved and model inclinations. We assert that this valueof a will correspond to the optimal boundary of the formgiven in equation (6), in terms of information content aboutthe state of the inner magnetosphere. To explore this, RMSdeviations were determined for values of a ranging from 0to 2.5, with results shown in Figure 9. The optimal values ofa are 1.46 and 1.14 for separate and simultaneous fitsrespectively, where separate means we first fit the UT,dipole tilt, and then the b�, and simultaneous means we fitall variables together. This result has important implications:if we decided to develop an empirical model of the GOES 8inclination parameterized with information obtained fromthe MSP at Gillam, then consideration only of informationcontent would lead us to use a parameter that is somethinglike 1 or 1.5 standard deviations south of the peak in protonauroral brightness. In other words, in terms of informationcontent, the optimal proton aurora based boundary fromwhich to infer the inclination at geosynchronous orbit isessentially b2i�.[26] In this section, we have shown that the optical b2i�

correlates well with the inclination of the magnetic field atgeosynchronous orbit. In doing so, we developed a simplemodel that can be used to predict the inclination at GOES 8,based on the latitude of the optical b2i, measured at Gillam

(equation (4)). We have further demonstrated that, in termsof information content about the state of the inner magneto-sphere, the b2i� is the best of a family of simple parametersthat can be derived from the Gillam MSP proton auroraldata.

5. Discussion

[27] The b2i boundary (alternatively, the IB) is theequatorward edge of significant proton precipitation, andhence of field lines threading the region of the magneto-sphere in which there is at least one mechanism causingstrong pitch angle scattering of CPS protons. In this paper,we have presented a method of identifying this boundaryusing data obtained from the CANOPUS MSP located atGillam, Canada. We call the latitude of this opticallydetermined boundary the optical b2i�. We have shown thatthis optical boundary contains similar information to the insitu b2i, and that it correlates well with the inclination of themagnetic field, as measured at the location of GOES 8.Consequently, the optical b2i� can be used as the basis of anoptical MT-index.[28] We obtained �250000 optical b2i� values from a

survey of ten years of Gillam MSP data. This is anenormous number of boundary determinations, a pointhighlighted by the fact that we were able to obtain roughly1600 near-simultaneous identifications of the in situ b2iboundary and the ground-based optical b2i�. Data fromother MSPs operating in Alaska, Canada, Scandinavia, andthe Antarctic should provide similarly large numbers ofoptical b2i� and MT-index values. Boundary identificationsfrom all of the MSPs, as well as the DMSP, NOAA, FAST,and other spacecraft, will comprise an enormous data set ofb2i� values. It is reasonable to think of the b2i boundary asa surface in the magnetosphere, stretching from the iono-sphere in one hemisphere, along magnetic field lines, to theconjugate hemisphere. The possibility exists for near-simul-

Figure 9. RMS model error as a function of a. Solid curve is best fit of b2i� to detrended inclination,while the dashed curve is produced by simultaneous fitting of quadratics in all parameters. Vertical linesindicate location of minima.

DONOVAN ET AL.: OPTICAL MT-INDEX SMP 10 - 9

taneous identification of the b2i boundary from one or moreground-based MSPs, and one or more low altitude space-craft (i.e., the DMSP and NOAA satellites), and possiblyhigher altitude spacecraft (i.e., POLAR). Simultaneousmultipoint identifications of this boundary will be a power-ful tool for increasing our knowledge of magnetospherictopology, and testing magnetic field models.[29] The optical b2i� and MT-index and their in situ

counterparts provide complimentary information. The opti-cal indices are often available continuously over periods ofseveral hours or more. The in situ indices are available onlyonce for any given satellite transit of the auroral oval. Thus,monitoring of these indices on time scales corresponding tosubstorm dynamics, or the transient effects of solar windpressure pulses, is possible only through the optical data.On the other hand, there is an ever increasing number ofspacecraft capable of delivering the data required for theidentification of the in situ indices. At present, the numberof useful auroral oval transits per day is upwards of fifty. Insitu boundary identification is not hampered by viewingcondition, and the result is continuous delivery of datapoints that are spaced by (more or less) tens of minutes.Many magnetospheric processes (i.e., storms and longsteady magnetospheric convection periods) take place overtens of hours or longer. Semicontinuous monitoring of theb2i� and MT-index over periods of tens of hours or days isonly possible with the in situ data. Furthermore, in manysituations, the sample rate of this boundary provided bysatellites is more than sufficient. For example, a ten day plotof the equatorward edge of the proton aurora, for the periodcovering the November 1993 geomagnetic storm, is givenin Figure 2 of Knipp et al. [1998]. Optical and in situ b2i�sprovide complimentary information regarding differentimportant temporal scales.[30] We developed an empirical model relating the incli-

nation of the magnetic field at GOES 8 to the optical b2i�,obtained with data from the Gillam MSP. We found that wecan reliably predict the GOES 8 inclination using theoptical b2i�. Moreover, we found that the b2i� is arguablysuperior to other boundaries that one might identify withthe proton auroral data, in terms of information contentconcerning how stretched the magnetic field is at geo-synchronous orbit.[31] In summary, we have (1) developed an algorithm for

inferring the b2i� from proton auroral MSP data, suggestednaming this the optical b2i�, and generated a data set of�250000 optical b2i� values; (2) shown that the opticalb2i� is very well ordered by Kp; (3) compared �1600 near-simultaneous in situ and optical observations of the b2i�,and demonstrated that the optical b2i� can form the basis ofan optical MT-index; (4) demonstrated that the magneticfield inclination at GOES 8 is highly correlated with b2i�;(5) developed an empirical model that predicts the GOES 8inclination, based on the dipole tilt, universal time, and theb2i� as measured at Gillam; and (6) shown that the opticalb2i� is an optimal boundary for predicting the inclination atGOES 8, in terms of information content.[32] In the future, we intend to expand on this work in

several ways. Weiss et al. [1997] used electron data toidentify 138 times when a DMSP spacecraft was magneti-cally conjugate to a Los Alamos National Laboratoriesgeosynchronous satellite. With these DMSP ‘‘underflights’’

of the LANL spacecraft, they carried out an observationaltest of the Tsyganenko 1989 [Tsyganenko, 1989] magneticfield model. This same data set would allow for a determi-nation of the location of the b2i boundary, as identified inthe DMSP data, compared to that of the geosynchronousspacecraft. Our work correlating the optical b2i� with theinclination at geosynchronous orbit was limited in scope.We used only Gillam MSP and GOES 8 magnetic field data.As such, we are limited to times of moderate geomagneticactivity: the equatorward most b2i� values that can beobtained with the Gillam MSP are �63�. In times of intensegeomagnetic activity (i.e., during the growth phase of manysubstorms and during moderate storms), the optical b2i�moves well equatorward of the Gillam MSP field of view,and on occasion (i.e., during intense storms and otherextreme activity), equatorward of the Pinawa MSP, whichis located �6� south of Gillam. At other times near dawnand dusk and during extremely quiet periods the b2i� movespoleward of the field of view of the Gillam MSP, and intothat of the Rankin Inlet MSP, which is located �6� north ofGillam. Our work should be extended to include theseextremely active, or quiet times.[33] Finally, we used SM coordinates in calculating the

GOES 8 inclination and as a measure of field line stretching.This stretching is, however, relative to the current sheet,which in general does not correspond to the SM equatorialplane, even in the inner magnetosphere. Current sheetwarping in the inner magnetosphere depends on bothmagnetic activity and dipole tilt [Lopez, 1990]. Skone etal. [1995] developed a coordinate system based on theshape of the current sheet, with the specific objective ofbetter understanding perturbations of the magnetic field atgeosynchronous orbit. A logical extension of our presentwork is to consider the relationship between the b2i� andthe magnetic field inclination, relative to the local orienta-tion of the current sheet, rather than the SM equatorialplane.

[34] Acknowledgments. Funding for the operation of the CANOPUSMSP located at Gillam is provided by the Canadian Space Agency. GOES-8magnetic field data were obtained from CDAWeb. DMSP data wereprovided by D. Hardy and P. Newell. This research was supported in partby NSERC operating grants, and Canadian Space Agency CANOPUScontracts. EFD and BJJ acknowledge their use of the infrastructure of theUniversity of Calgary Institute for Space Research. EFD acknowledgesuseful discussions with D. Knudsen, K. Kauristie, J. Wanliss, and J.Samson.[35] Arthur Richmond thanks Victor Sergeev and Simon Wing for their

assistance in evaluating this paper.

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�����������������������F. Creutzberg, Keometrics, 9 Massey Lane, Ottawa, Ontario, Canada K1J

6C7.E. F. Donovan, B. J. Jackel, and N. A. Nicholson, Department of Physics

and Astronomy, University of Calgary, Calgary, Alberta, Canada T2N 1N4.(eric@phys.ucalgary.ca)T. Sotirelis, Applied Physics Laboratory, Johns Hopkins University, 1100

Johns Hopkins Road, Laurel, MD 20723, USA.I. Voronkov, Department of Physics, University of Alberta, Edmonton,

Alberta, Canada T6G 2E9.

DONOVAN ET AL.: OPTICAL MT-INDEX SMP 10 - 11