Ground-based optical determination of the b2i boundary: A basis for an optical MT-index

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A3, 1115, doi: /2001ja009198, 2003 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. Nicholson 1,2 Received 30 November 2001; revised 25 January 2002; accepted 30 January 2002; published 14 March [1] The equatorward boundary of the proton aurora corresponds to a transition from strong pitch angle scattering to bounce trapped particles. This transition has been identified as the b2i boundary in Defense Meteorological Satellite Program (DMSP) ion data [Newell et al., 1996]. We use ion data from 29 DMSP overflights of the Canadian Auroral Network for the OPEN Program Unified Study (CANOPUS) Meridian Scanning Photometer (MSP) located at Gillam, Canada, to develop a simple algorithm to identify the b2i boundary in latitude profiles of proton auroral (486 nm) brightness. Applying this algorithm to a ten year set of Gillam MSP data, we obtain 250,000 identifications of the 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 a reasonable basis for an optical equivalent to the MT-index put forward by Sergeev and Gvozdevsky [1995]. Using 17,000 simultaneous measurements, we demonstrate a strong correlation between the optical b2i and the inclination of the magnetic field as measured at GOES 8. We develop an empirical model for predicting the GOES 8 inclination, given theuniversal time, dipole tilt, and the optical b2i, as determined at Gillam. We also show that in terms of information content, the b2i boundary is an optimal boundary 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: /2001ja009198, 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 the mostly empty upgoing loss cone. A meridional profile of the distribution functions typically shows such single loss cone distributions from near the polar cap boundary, and equatorward through much of the CPS, and then a transition from isotropy to anisotropy at lower latitudes. This transition marks the equatorward boundary of significant ion precipitation. Equatorward of the transition region, the ion distribution function is isotropic outside of the mostly empty 1 Department of Physics and Astronomy, University of Calgary, Calgary, Alberta, Canada. 2 Institute for Space Research, University of Calgary, Calgary, Alberta, Canada. 3 Department of Physics, University of Alberta, Edmonton, Alberta, Canada. 4 Applied Physics Laboratory, Johns Hopkins University, Greenbelt, Maryland, USA. 5 Keometrics, Ottawa, Ontario, Canada. Copyright 2003 by the American Geophysical Union /03/2001JA009198$09.00 upgoing and downgoing loss cones. This picture is complicated by local acceleration, transverse heating, convection, and other phenomena. Nevertheless, low altitude observations of ion distributions and energy spectra from tens of ev to tens of KeV, spanning a wide range of geomagnetic latitudes, and under a variety of geophysical conditions, are generally consistent with this picture [Imhof et al., 1977; Sergeev and Tsyganenko, 1982; Imhof, 1988; Gvozdevsky and Sergeyev, 1995]. [3] A single loss cone distribution indicates strong pitch angle diffusion due to scattering [Ashour-Abdalla and Thorne, 1978] that results in proton precipitation, ultimately producing diffuse auroral luminosity. This region of diffuse auroral precipitation, and hence strong pitch angle diffusion, corresponds to latitudes where single loss cone distributions are observed. Equatorward of this, the double loss cone distributions indicate bounce trapped ions with little or no pitch angle scattering. The transition between bounce trapping and strong pitch angle scattering occurs at what has been called the ion isotropy boundary, or simply the IB [e.g., see Sergeev et al., 1983]. The IB is readily identified in data from satellite instruments that measure energy fluxes both orthogonal to, and parallel to, the local magnetic field [see, e.g., Imhof et al., 1977, Figure 2]. SMP 10-1

2 SMP 10-2 DONOVAN ET AL.: OPTICAL MT-INDEX [4] The data set that has been most extensively used for the determination of precipitation boundaries is from the Defense Meteorological Satellite Program (DMSP) ion detectors, which measure energy fluxes along the field direction [Hardy et al., 1984]. Under the assumption that significant ion precipitation corresponds to a full loss cone, it is reasonable to equate the equatorward termination of that precipitation to the IB, and hence to infer the IB latitude from the DMSP data. Newell et al. [1998] used National Oceans and Atmospheres Administration (NOAA) and DMSP data to demonstrate the equivalence of the IB and location of the peak energy flux of 3 30 KeV ions as measured by DMSP. The location of the peak energy flux is referred to as the b2i boundary [Newell et al., 1996]. In the evening sector, this peak is usually near the equatorward edge of precipitating 3 30 KeV ions. Toward dawn the peak tends to be less well pronounced. Therefore, a slightly modified definition of the b2i will be used in this paper: it will be the low latitude edge of a plateau in the 3 30 kev ion energy flux (which usually coincides with a peak if there is one). This new procedure seems to work well, though its performance has not yet been fully demonstrated. The latitude of the IB, and b2i boundary (herein referred to as IB, and b2i, respectively), are functions of both energy and magnetic local time (MLT), with variations that reflect 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 two different magnetospheric regions. Poleward of the IB, plasma conditions support strong diffusion. Equatorward of it, they do not. The two most likely causes of the scattering are wave-particle interactions [e.g., Ashour- Abdalla and Thorne, 1978] and breaking of the first adiabatic invariant due to highly curved field lines in the vicinity of the neutral sheet [Sergeev et al., 1983]. The dependence of IB on energy is often consistent with the scattering being a consequence of field line curvature, at least for higher energy (i.e., >30 KeV) protons [Imhof et al., 1977; Gvozdevsky and Sergeyev, 1995]. Furthermore, the results of simulations of particle motions in realistic magnetic field models indicate that inner CPS field lines, in the vicinity of the neutral sheet, have small enough radii of curvature to cause enough pitch angle scattering to fill the relatively small loss cone [Tsyganenko, 1982; Sergeev et al., 1983]. On this basis, it has been suggested that the IB is the signature of the transition between regions of adiabatic and nonadiabatic ion motion in the neutral sheet region, and that the nonadiabaticity is due primarily to field line radii of curvature that are on the order of the ion gyroradii (the actual criterion for pitch angle scattering is that the radius of curvature is smaller than about eight 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 information about the curvature of magnetic field lines near the equatorial plane [see, e.g., Wing and Newell, 1998; Wanliss et al., 2000]. Sergeev and Gvozdevsky [1995] carried out a comparison between the latitude of the IB and the inclination of the geomagnetic field in the geosynchronous region, demonstrating a good correlation between the two quantities: in general, the more equatorward the IB, the greater the magnetic field inclination. Sergeev and Gvozdevsky [1995] suggested that IB is therefore a meaningful indicator of the state of the inner magnetosphere, and developed an IB-based Magnetotail (MT) index. [7] In situ measurements of IB are available directly from auroral zone crossings of the FAST and NOAA spacecraft, and indirectly (i.e., through the b2i) from DMSP. On any given day, literally dozens of IB measurements are provided by such spacecraft. In order to develop the MTindex, it was deemed necessary to devise an empirical method for comparing IB measurements from different MLTs. In order to do so, Sergeev and Gvozdevsky [1995] carried out a statistical study of the MLT dependence of IB. More specifically, they used a straightforward auroral oval shape, characterized by two parameters, to estimate the IB at magnetic midnight, based on a measurement of this quantity at some other MLT. The estimated midnight IB is the MT-index (or MT ): h p i MT ¼ IB A 1 1 cos ð 12 MLT MLT oþ Here, the IB is observed at local time MLT, and the constants A 1 and MLT o were determined statistically to be 4.3 and 23.1 hours, respectively. [8] Precipitation of magnetospheric protons leads to auroral emissions at wavelengths corresponding to a number of hydrogen electronic transitions. Figure 1 is a keogram of hydrogen Balmer-b (herein 486 nm ) intensity obtained by the Canadian Auroral Network for the OPEN Program Unified Study (CANOPUS) Meridian Scanning Photometer (MSP) located at Gillam, Canada. Some typical evening sector proton auroral properties are evident here. In particular, significant emissions occur over several degrees of latitude, move equatorward during a growth phase, and brighten at the time of a substorm onset (that here occurs at roughly 0315 UT). At 0300 UT on 8 January 1997, DMSP F12 passed almost directly overhead of Gillam. In Figure 2, we have plotted the integrated ion energy flux from DMSP F2 and the proton auroral brightness from the photometer at Gillam, as functions of magnetic latitude. We have also identified the b2i (obtained from the DMSP flux data). As well, proton auroral intensities are shown for the five successive MSP scans which take place during the five minutes around the F12 overflight. The data shown here is typical. The proton auroral brightness profile does not change significantly on a five minute time scale, except during dynamic events such as substorm onsets. As well, the brightness profile is often reasonably well fit by a simple Gaussian. Finally, the brightness profile correlates fairly well with that of the integrated ion energy flux. This single example suggests that the equatorward edge of the proton aurora can reasonably be expected to correspond to the b2i boundary. [9] Long term data sets of H b emissions have been produced by MSPs located in Canada at Fort Smith, Rankin Inlet, Gillam, and Pinawa [Rostoker et al., 1995], as well as in Alaska, at Poker Flat [Deehr, 1994], Scandinavia, at Longyearbyen and in Finland, and in Antarctica [Kaila et al., 1997]. Thus, there is a possibility of building up a large set of optically inferred b2i boundaries. Moreover, this optical b2i boundary could form the basis of an optical MT, an index that would have some distinct advantages over ð1þ

3 DONOVAN ET AL.: OPTICAL MT-INDEX SMP 10-3 Figure 1. Keogram of 486 nm emissions obtained by the CANOPUS Gillam MSP on 8 January The latitudes correspond to a presumed emission altitude of 110 km. satellite measurements. For instance, the b2i boundary could be monitored continuously over many hours by a ground station, thus allowing for near-continuous monitoring of field line stretching in the inner magnetosphere and midtail region (via the MT). As well, having long periods of time during which the b2i is known would greatly increase the number of simultaneous determinations of the b2i at several local times and latitudes. There are also distinct disadvantages to using optical data for monitoring the b2i boundary: H b emissions are weak, and virtually impossible to detect at auroral latitudes during the summer months. Even during the winter months, optical determination of this boundary will only be possible on the night side, and within the field of view of an appropriate MSP. Furthermore, clouds, moon light, twilight, aerosol contamination and filter leakage all conspire to reduce the number of hours of good H b data that one can obtain from ground-based MSPs. [10] Any intercomparison of the MSP and in situ data requires assigning latitudes to emissions which are strictly observed at known photometer elevation angles. In all of our work, we assume an emission altitude of 110 km. This is in line with measured altitude profiles [i.e., Strickland et Figure 2. DMSP overflight of Gillam at 0300 UT on 8 January This is a comparison of DMSP measured ion energy flux with hb intensity. The dotted curves indicate Hb intensity from meridional scans 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.

4 SMP 10-4 DONOVAN ET AL.: OPTICAL MT-INDEX Figure 3. Distribution of b2i boundary locations, relative to the peak in H b intensity for 29 DMSP overflights of Gillam (see text). The histogram shows the distribution of the 29 b2i locations with a shaded Gaussian included for reference. Negative values indicate locations equatorward of the peak in brightness. al., 2001, Plate 1; Omholt, 1971, section 3.2.7], and models of auroral emissions resulting from typical proton precipitating energy fluxes and characteristic energies [i.e., Kozelov, 1995, Figure 2]. Some uncertainties are introduced into our analysis by assuming the fixed height of the emissions. These result from the fact that the presumed height will differ from the actual height of the peak brightness, and that the emissions are in reality from an extended height range. These uncertainties have no effect on our inferred latitude at magnetic zenith, and progressively larger effects for lower elevation angles. [11] In what follows, we use a number of DMSP overflights of Gillam to develop a simple algorithm for inferring the b2i from the MSP data. Using only data from Gillam, we then apply this algorithm, thereby creating a large data set of optical b2i. Using a large number of simultaneous optical and DMSP-based b2i values, and presuming that the locus of points that make up the b2i boundary is of the form given in equation (1), we estimate the quantities A 1 and MLT o. Finally, we demonstrate that the latitude of the proton aurora correlates well with the inclination of the magnetic field at geosynchronous orbit, as measured by GOES 8. Our principal message is that the optical b2i contains the essential ingredients necessary for the construction of an optical MT-index, and that this new index can provide valuable information about the state of the inner magnetosphere which will compliment that provided by the in situ MT-index. 2. Optical b2i [12] We used the DMSP and MSP data sets for the months of September to April for the years 1990 (September) to 1999 (April). There were 29 instances where a DMSP satellite passed within one half hour of magnetic local time of Gillam during times of good viewing conditions, and during which the region of significant proton auroral emission was well within the field of view of the Gillam MSP. This search for conjunctions was inspired by Blanchard et al. [1995], who used DMSP particle and CANOPUS MSP 630 nm data to develop an algorithm for identifying the polar cap boundary using the optical data. For each nearly coincident overflight we fit a Gaussian to the brightness profile from the MSP, and determined the b2i from the DMSP data. The location of the b2i boundary, relative to the peak in the brightness profile, was then determined in units of standard deviations (ie, in terms of the width of the region of significant proton auroral emissions). Results are shown in Figure 3. In all cases, the b2i boundary was south of the peak in brightness. In all but one case, the b2i boundary was between 0.6 and 2.2 standard deviations south of the peak. The mean location (for all 29 cases) was roughly 1.4 standard deviations south of the peak. For reference, the standard deviations range from roughly 50 kilometers to roughly 150 km, assuming that the emissions come from an altitude of 110 km. [13] Considering the results summarized in Figure 3, we suggest that a reasonable algorithm for determining the optical b2i is as follows. Fit a Gaussian to the H b brightness profile. If that Gaussian is well within the field of view of the MSP, then a reasonable estimate of the b2i is 1.4 standard deviations south of the peak in brightness. For our purposes, we consider this criterion to be satisfied if the peak of the best-fit Gaussian is more than one standard deviation from the edge of the field of view. Although at times the brightness profile is not be well fit by a Gaussian, this algorithm is straightforward to implement, test, and reproduce. 3. Optical MT-Index [14] The Gillam MSP operates continuously between sunset and sunrise, delivering meridional scans of 486 nm

5 DONOVAN ET AL.: OPTICAL MT-INDEX SMP 10-5 Figure 4. Mean geomagnetic latitudes of the optical b2i, where the values are binned according by Kp. intensity at a rate of one per minute. We applied our algorithm for determining the optical b2i to the MSP data obtained during the months of September to April, beginning in the fall of 1990, and ending in the spring of 1999, restricting our attention to MLTs between 1830 and We obtained a data set of roughly optical b2i values. The optical b2i values are ordered surprisingly well by Kp (see scatterplot of Nicholson et al. [2003]). The average values of b2i, as a function of MLT, and binned by Kp, are plotted in Figure 4. The statistical local time dependence is qualitatively similar to the statistical oval shape used by Sergeev and Gvozdevsky [1995] as a basis for inferring the b2i at magnetic midnight from a b2i determined at some other MLT. As discussed above, this inferred 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 out as follows. From our set of optical b2i values, we identified 1600 instances when there was a nearly simultaneous in situ b2i identification obtained by a DMSP pass. The criterion we applied for near-simultaneous was that the b2i boundary determinations occurred within two minutes of each other. Presuming that the instantaneous locus of points making up the b2i boundary is roughly of the form given in equation (1), these 1600 points provide us with an excellent opportunity to infer, through a leastsquares fit, the quantities A 1, and MLT o. Carrying out this fit, we obtain values of A 1 and MLT o of, 3.6 and 23.2 hours, respectively. These are in good agreement with the values of these parameters provided by Sergeev and Gvozdevsky [1995]. Of the 1600 near-simultaneous b2i boundary identifications, half had MLT separations between the spacecraft and MSP in excess of 5.1 hours. However, even such widely separated measurements show remarkably good agreement. This is illustrated in the scatterplots of Figure 5 comparing in situ and optical MT-indices determined from the roughly 1600 near-simultaneous DMSP and MSP observations. 4. Geostationary B-Field Inclination [16] The MT-index is the latitude of the b2i boundary at magnetic midnight, estimated on the basis of an observation of b2i at some other local time. This index provides quantitative information about the state of the inner magnetosphere, based on a demonstrated correlation between the MT-index and the inclination of the geomagnetic field at geostationary orbit [Sergeev and Gvozdevsky, 1995; Newell et al., 1998]. In section 2 we suggested an algorithm for the optical determination of b2i and used this algorithm to infer roughly optical b2i values from good observation times during the period This data set provides us with an excellent opportunity to explore the correlation between the inclination of the magnetic field at geosynchronous orbit and the latitude of the equatorward boundary of significant proton precipitation. In this section, we present the 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 obtained GOES 8 magnetic field data and our optical b2i data base. Throughout the years from 1996 to 1999, GOES 8 was located over the East coast of Hudson Bay, roughly 1 hour of local time east of Gillam. As pointed out by Newell et al. [1998], a geosynchronous satellite at the longitude of GOES 8 is located well above (roughly 0.8 Earth radii) the magnetic equatorial plane. As such, GOES 8 is ideally located in terms of providing information about the degree of stretching of the magnetic field in the inner magnetosphere. With the exception of substorm onsets, the latitude of the proton aurora does not change appreciably on a time scale of several minutes or longer. With this in mind, we grouped our b2i data set into five minute bins. The same

6 SMP 10-6 DONOVAN ET AL.: OPTICAL MT-INDEX Figure 5. Comparison of MT-indices inferred from near-simultaneous identification of b2i from the MSP (optical) and DMSP (in situ) data. The top and bottom panels show the events where the MLT separation 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). binning was also applied to the GOES 8 magnetic field data. Furthermore, the inclination of the GOES 8 magnetic field was defined to be I G8 ¼ arctan B z =B r ð2þ Here, B z and B r are the Solar Magnetic z and radial (ie sqrt(b x 2 +B y 2 )) 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 Gillam proton 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 UT on 24 March Five minute averages of the locations of the optical b2i, determined with the algorithm discussed in section 2, are indicated with the red diamonds on the keogram.

7 DONOVAN ET AL.: OPTICAL MT-INDEX SMP 10-7 Figure 7. Predicted and observed inclinations at GOES 8. Points shown are for simultaneous observations 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 the time period from 1996 to 1999, there were 219 nights during which there were relatively long and continuous periods during which we could obtain optical b2i values and the GOES 8 inclination. Overall, we obtained roughly simultaneous five minute averages of these two quantities. 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 current in the inner magnetosphere. The distribution of the cross-tail current affects the mapping between the inner magnetosphere and the ionosphere, and, presumably, the location of the earthward boundary of the region in which the strong pitch angle scattering causes the proton auroral precipitation (see section 1). One therefore expects some correlation between the inclination of the magnetic field in the inner magnetosphere and the latitude of the b2i boundary (or the IB) in the same local time sector. In this section, we develop an empirical model of the GOES 8 inclination as a function of optical b2i, dipole tilt and universal time. Our immediate goal is to minimize the root-mean-square (RMS) difference between the model inclination, and the observed inclination. [19] The average inclination for our data set is with a RMS deviation from the average of As stated above, the deviation is due to the combined local time and dipole tilt effects, and geomagnetic activity. We first developed a model of the inclination that depended only on the b2i 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 on local time and dipole tilt angle. In order to remove these effects we developed a simple model that depended only on dipole tilt and universal time (and hence local time). We experimented with a number functional forms, and settled on a model that is linear in dipole tilt, and quadratic in universal time. A linear least squares fit between the model and the GOES 8 inclinations yielded the following: I G8 ¼ 49:5 0:29 tilt þ 0:25ðUT 3:5Þ 2 ð3þ The RMS deviation between the observed and model inclinations is It should be noted that this model is based on a subset of GOES 8 data from the winter months and the interval 0 12 UT, and is unlikely to be valid for summer and dayside locations. [20] We detrended the data using equation (3) and fit the residuals to a quadratic in b2i. The resulting combined model I G8 ¼ 61:8 0:43ðb2i 71:5Þ 2 0:29 tilt þ 0:25ðUT 3:5Þ 2 has an RMS error of For reference, a general model to 3rd degree in all parameters has an RMS error of The model given in 4 provides nearly as good a fit, and has a much simpler form, so we will use it for all further analysis. Figure 7 is a scatterplot of the observed and predicted GOES 8 magnetic inclination (with equation (4)), based on our data set of simultaneous optical b2i and GOES 8 observations. The very high correlation (r = 0.815) indicates a strong relationship between geostationary magnetic field and the location of proton auroral emissions. [21] We have developed a way of predicting the inclination of the magnetic field at the location of GOES 8 from a ground-based observation. These results are similar to those of Sergeev and Gvozdevsky [1995] and Newell et al. [1998]. If we were to consider only the RMS deviations discussed above, one might question the value of this exercise. After all, in going from a model that was based only on local time ð4þ

8 SMP 10-8 DONOVAN ET AL.: OPTICAL MT-INDEX Figure 8. Observed (solid diamonds) and modelled (open triangles) GOES 8 inclinations for the night of 24 March 1996 (proton auroral data and optical b2i values for this night are given in figure 6). Model values are obtained using equation (4). For comparison purposes, the dashed curve shows the GOES 8 inclination from the best fit model based solely on dipole tilt and universal time (equation (3)). and dipole tilt (equation (3)) to one that also utilizes the optical b2i, we reduced the RMS deviation from 7.35 to The correlation between the predicted and observed inclinations demonstrated in Figure 7 is impressive; however a similar scatterplot (not shown) based on inclinations predicted 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 inclination at geostationary orbit. In Figure 8, we have plotted the observed GOES 8 inclinations for the night of 24 March 1996 as well as the inclinations predicted by equations (3) and (4). For this night, the RMS deviation between the observed inclinations and those predicted using equations (3) and (4) are 8 and 3, respectively. It is clear that the short term variability of the inclination at geostationary orbit and the latitude of the optical b2i are strongly related. The night of 24 March 1996 was truly typical in terms of the variability of the proton aurora, the GOES 8 inclination, as well as the quality of fit provided by both models. On some of the 219 nights, there was greater systematic discrepancy between the modelled and observed inclinations. On other nights, there was greater systematic agreement. [23] We wish to explore one final question concerning the relationship between the optical b2i, as inferred from the simple algorithm presented in section 2, and the inclination of the magnetic field at GOES 8. The optical b2i is b2i ¼ peak 1:4s where peak and s are the latitude of the peak and the standard deviation of the Gaussian fit to the brightness ð5þ profile, respectively. We proposed this algorithm based on our comparison of data from the 29 DMSP-Gillam conjunctions. The use of this algorithm is supported by our comparison of optical and in situ b2i values obtained simultaneously at different MLTs (i.e., Figure 5), and the fact that we find a similar correlation between the inclination of the magnetic field at geosynchronous orbit and the latitude of the optically inferred b2i as do Sergeev and Gvozdevsky [1995] and Newell et al. [1998] (i.e., Figure 7). In our view, we have presented a compelling case that the algorithm in equation (5) is at least a reasonable way of inferring the optical b2i from the brightness profile. There is certainly a strong correlation between the inclination at geosynchronous orbit and the b2i. The use of the b2i boundary (or the IB) as a basis for the MT-index was at least partially based on this correlation. [24] Undoubtedly, b2i conveys important information about how relatively stretched field lines near the earthward edge of the current sheet are. It is not clear, however, whether or not the b2i boundary is the single ion precipitation boundary that provides the most information in this regard. For example, there are other variables related to the proton precipitation that could be used to parameterize an empirical model of the inclination of the magnetic field at geostationary orbit. Examples include the latitudes of the peak in brightness and poleward boundary of the proton auroral intensity, as well as the integrated brightness, width, and peak intensity of the proton aurora. In this paper we do not explore all of these variables in terms of their value as predictors of the geostationary magnetic field inclination. We have, however, carried out a straightforward numerical experiment that allows us to at least partially explore the question of whether b2i is the optimal single ion precip-

9 DONOVAN ET AL.: OPTICAL MT-INDEX SMP 10-9 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 lines indicate location of minima. itation boundary, in terms of information content about the state of the inner magnetosphere. [25] We define a more general boundary, referred to as b, in the following way: b ¼ peak as 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 general boundary is our optical b2i. We then determine, using b, dipole tilt and universal time as the parameters in an empirical model of GOES 8 inclination, what value of a will provide the lowest RMS deviation between the observed and model inclinations. We assert that this value of a will correspond to the optimal boundary of the form given in equation (6), in terms of information content about the state of the inner magnetosphere. To explore this, RMS deviations were determined for values of a ranging from 0 to 2.5, with results shown in Figure 9. The optimal values of a are 1.46 and 1.14 for separate and simultaneous fits respectively, where separate means we first fit the UT, dipole tilt, and then the b, and simultaneous means we fit all variables together. This result has important implications: if we decided to develop an empirical model of the GOES 8 inclination parameterized with information obtained from the MSP at Gillam, then consideration only of information content would lead us to use a parameter that is something like 1 or 1.5 standard deviations south of the peak in proton auroral brightness. In other words, in terms of information content, the optimal proton aurora based boundary from which to infer the inclination at geosynchronous orbit is essentially b2i. [26] In this section, we have shown that the optical b2i correlates well with the inclination of the magnetic field at geosynchronous orbit. In doing so, we developed a simple model that can be used to predict the inclination at GOES 8, based on the latitude of the optical b2i, measured at Gillam ð6þ (equation (4)). We have further demonstrated that, in terms of information content about the state of the inner magnetosphere, the b2i is the best of a family of simple parameters that can be derived from the Gillam MSP proton auroral data. 5. Discussion [27] The b2i boundary (alternatively, the IB) is the equatorward edge of significant proton precipitation, and hence of field lines threading the region of the magnetosphere in which there is at least one mechanism causing strong pitch angle scattering of CPS protons. In this paper, we have presented a method of identifying this boundary using data obtained from the CANOPUS MSP located at Gillam, Canada. We call the latitude of this optically determined boundary the optical b2i. We have shown that this optical boundary contains similar information to the in situ b2i, and that it correlates well with the inclination of the magnetic field, as measured at the location of GOES 8. Consequently, the optical b2i can be used as the basis of an optical MT-index. [28] We obtained optical b2i values from a survey of ten years of Gillam MSP data. This is an enormous number of boundary determinations, a point highlighted by the fact that we were able to obtain roughly 1600 near-simultaneous identifications of the in situ b2i boundary and the ground-based optical b2i. Data from other MSPs operating in Alaska, Canada, Scandinavia, and the Antarctic should provide similarly large numbers of optical b2i and MT-index values. Boundary identifications from all of the MSPs, as well as the DMSP, NOAA, FAST, and other spacecraft, will comprise an enormous data set of b2i values. It is reasonable to think of the b2i boundary as a surface in the magnetosphere, stretching from the ionosphere in one hemisphere, along magnetic field lines, to the conjugate hemisphere. The possibility exists for near-simul-

10 SMP DONOVAN ET AL.: OPTICAL MT-INDEX taneous identification of the b2i boundary from one or more ground-based MSPs, and one or more low altitude spacecraft (i.e., the DMSP and NOAA satellites), and possibly higher altitude spacecraft (i.e., POLAR). Simultaneous multipoint identifications of this boundary will be a powerful tool for increasing our knowledge of magnetospheric topology, and testing magnetic field models. [29] The optical b2i and MT-index and their in situ counterparts provide complimentary information. The optical indices are often available continuously over periods of several hours or more. The in situ indices are available only once for any given satellite transit of the auroral oval. Thus, monitoring of these indices on time scales corresponding to substorm dynamics, or the transient effects of solar wind pressure pulses, is possible only through the optical data. On the other hand, there is an ever increasing number of spacecraft capable of delivering the data required for the identification of the in situ indices. At present, the number of useful auroral oval transits per day is upwards of fifty. In situ boundary identification is not hampered by viewing condition, and the result is continuous delivery of data points that are spaced by (more or less) tens of minutes. Many magnetospheric processes (i.e., storms and long steady magnetospheric convection periods) take place over tens of hours or longer. Semicontinuous monitoring of the b2i and MT-index over periods of tens of hours or days is only possible with the in situ data. Furthermore, in many situations, the sample rate of this boundary provided by satellites is more than sufficient. For example, a ten day plot of the equatorward edge of the proton aurora, for the period covering the November 1993 geomagnetic storm, is given in Figure 2 of Knipp et al. [1998]. Optical and in situ b2i s provide complimentary information regarding different important temporal scales. [30] We developed an empirical model relating the inclination of the magnetic field at GOES 8 to the optical b2i, obtained with data from the Gillam MSP. We found that we can reliably predict the GOES 8 inclination using the optical b2i. Moreover, we found that the b2i is arguably superior to other boundaries that one might identify with the proton auroral data, in terms of information content concerning how stretched the magnetic field is at geosynchronous orbit. [31] In summary, we have (1) developed an algorithm for inferring the b2i from proton auroral MSP data, suggested naming this the optical b2i, and generated a data set of optical b2i values; (2) shown that the optical b2i is very well ordered by Kp; (3) compared 1600 nearsimultaneous in situ and optical observations of the b2i, and demonstrated that the optical b2i can form the basis of an optical MT-index; (4) demonstrated that the magnetic field inclination at GOES 8 is highly correlated with b2i ; (5) developed an empirical model that predicts the GOES 8 inclination, based on the dipole tilt, universal time, and the b2i as measured at Gillam; and (6) shown that the optical b2i is an optimal boundary for predicting the inclination at GOES 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 to identify 138 times when a DMSP spacecraft was magnetically conjugate to a Los Alamos National Laboratories geosynchronous satellite. With these DMSP underflights of the LANL spacecraft, they carried out an observational test of the Tsyganenko 1989 [Tsyganenko, 1989] magnetic field model. This same data set would allow for a determination of the location of the b2i boundary, as identified in the DMSP data, compared to that of the geosynchronous spacecraft. Our work correlating the optical b2i with the inclination 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 geomagnetic activity: the equatorward most b2i values that can be obtained with the Gillam MSP are 63. In times of intense geomagnetic activity (i.e., during the growth phase of many substorms 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 other extreme activity), equatorward of the Pinawa MSP, which is located 6 south of Gillam. At other times near dawn and dusk and during extremely quiet periods the b2i moves poleward of the field of view of the Gillam MSP, and into that of the Rankin Inlet MSP, which is located 6 north of Gillam. Our work should be extended to include these extremely 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 equatorial plane, even in the inner magnetosphere. Current sheet warping in the inner magnetosphere depends on both magnetic activity and dipole tilt [Lopez, 1990]. Skone et al. [1995] developed a coordinate system based on the shape of the current sheet, with the specific objective of better understanding perturbations of the magnetic field at geosynchronous orbit. A logical extension of our present work is to consider the relationship between the b2i and the magnetic field inclination, relative to the local orientation of the current sheet, rather than the SM equatorial plane. [34] Acknowledgments. Funding for the operation of the CANOPUS MSP located at Gillam is provided by the Canadian Space Agency. GOES-8 magnetic field data were obtained from CDAWeb. DMSP data were provided by D. Hardy and P. Newell. This research was supported in part by NSERC operating grants, and Canadian Space Agency CANOPUS contracts. EFD and BJJ acknowledge their use of the infrastructure of the University of Calgary Institute for Space Research. 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