Large-scale imaging of high-latitude convection with Super Dual

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. A9, PAGES 20,797-20,811, SEPTEMBER 1, 1998 Large-scale imaging of high-latitude convection with Super Dual Auroral Radar Network HF radar observations J. M. Ruohoniemi and K. B. Baker Applied Physics Laboratory, Johns Hopkins University, Laurel, Maryland Abstract. The HF radars of the Super Dual Auroral Radar Network (SuperDARN) provide measurements of the E x B drift of ionospheric plasma over extended regions of the highlatitude ionosphere. With the recent augmentation of the northern hemisphere componento six radars, a sizable fraction of the entire convection zone (approximately one-third) can be imaged nearly instantaneously (-2 min). To date, the two-dimensional convection velocity has been mapped by combining line-of-sight velocity measurements obtained from pairs of radars within common-volume areas. We describe a new method of deriving large-scale convection maps based on all the available velocity data. The measurements are used to determine a solution for the distribution of electrostatic potential,, expressed as a series expansion in spherical harmonics. The addition of data from a statistical model constrains the solution in regions of no data coverage. For low-order expansions the results provide a gross characterization of the global convection. We discuss the processing of the radar velocity data, the factors that condition the fitting, and the reliability of the results. We present examples of imaging that demonstrate the response of the global convection to variations in the interplanetary magnetic field (IMF). In the case of a sudden polarity change from northward to southward IMF, the convection is seen to reconfigure globally on very short (<6 min) timescales. 1. Introduction The plasma of the high-latitude ionosphere responds to electric fields of magnetospheric origin by convecting according to v = E x BIB 2, where E is the ionospheric electric field and B is the geomagnetic field. The motion of the plasma can be measured by a variety of techniques, including rockets, satellites, and radars. With certain assumptions, magnetic perturbation data collected on the ground can also be used to estimate ionospheric plasma drifts. All of the techniques have their limitations, for example, a rocket or satellite is restricted to measurements along a flight path, a radar typically observes only over a limited area centered on the radar site, and the interpretation of geomagnetic perturbation data generally requires the adoption of a conductivity model of unknown validity. Paper number 98JA /98/98JA reconnection paradigm is not completely accepted [Heikkila, 1997]. The large-scal electric fields generated by these processes at the magnetospheric boundary map along geomagnetic field lines to the ionosphere with little attenuation and a substantial shrinkage in spatial dimension. The resulting ionospheric convection is an important clue to the nature of the so- lar wind-magnetosphere interaction. Recently, the need for information on convection on global scales has received heightened attention. This is due in part to the National Space Weather Program and related initiatives, which have the goal of describing the integrated electrodynamics of the solar wind-magnetosphere-ionosphere system in both real-time and predictive modes. Electric fields are a critical input for the dynamical space weather models that are under development. The global convection electric field, or, equiva- Despite several decades of study, the causes of high-latitude convection are still not well understood. Magnetospheric conlently, the distribution of electrostatic potential,, implied by E = -V, is extremely useful both for specifying the current vection is a dissipative process in the ionosphere because of Joule heating and hence is associated with the transfer of enstate of the high-latitude ionosphere and projecting its future condition. Maps of electrostatic potential will likely have a ergy from the source regions. It is commonly thought that reconnection of the magnetic field carried by the solar wind value for space weather analogous to those of barometric pressure for tropospheric weather. with geomagnetic field lines on the dayside is one source [Dungey, 1961]; an analogous process of reconnection in the One goal of the observational community is to map convection over the entire high-latitude region. A sophisticated analymagnetotail on the nightside conserves magnetospheric flux and sis known as assimilative mapping of ionospheric electrodyrepresents another source. It is also believed that momentum in namics (AMIE) has been developed that combines observations the solar wind that streams by the Earth's dawn and dusk from disparate instruments and models to synthesize global flanks is transferred across the magnetospheric boundary by a maps of electrodynamic parameters, including the electrostatic kind of "viscous" interaction [Axford and Hines, 1961]. Alpotential [Richmond and Kamide, 1988]. The value of this apthough numerous studies have interpreted convection in terms proach has been demonstrated in a wide array of studies of of these solar wind-magnetosphere interactions, even the basic convection dynamics [e.g., Lu et al., 1996; Ridley et al., 1997]. The most pressing problems require this large-scale view of the convection, both to establish the global state of the ionosphere Copyright 1998 by the American Geophysical Union. and to relate separated local effects. 20,797 The greatest observational requirement is for mapping of convection over large areas with high spatial and temporal

2 20,798 RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION resolution. Preferably, the measurements relate directly to the E X B drift of the ionospheric plasma. The capabilities of the research community in this regard have been significantly increased with the realization of the Super Dual Auroral Radar Network (SuperDARN) system. SuperDARN consists of networks of coherent-scatter HF radars extended in longitude, one in each of the northern and southern hemispheres. The configuration in the northern hemisphere is shown in Plate 1. The technical aspects of the operation of the radar have been described by Greenwald et al. [1985]. The radars measure the convection velocity by observing the drift of small-scale irregularities in the F region [Ruohoniemi et al., 1987]. The spatial resolution roughly averages 50 km X 100 km, and the scan repeat time is usually 2 min. One aspect of the SuperDARN geometry is the pairing of radars such that observations in common-volume areas are bidirectional and the two-dimen- sional E X B velocity can be resolved unambiguously. By combining measurements from all the radars in the northern hemisphere, direct mapping of the convection can be extended to almost 12 hours of magnetic local time (MLT). The measurements in the southern hemisphere add a conjugate dimension. The fields of view of the radars extend poleward from about 65øA; thus the potential for mapping convection with SuperDARN extends to nearly half of the convection region. This development suggests the feasibility of "imaging" the instantaneous large-scale convection with SuperDARN, where we make an analogy to the imaging of auroral luminosity performed by satellite-borne detectors. Toward this end, we have derived a method of filtering, combining, and reducing line-ofsight velocity data from the SuperDARN radars that optimizes the mapping of the large-scale convection pattern. The results of the mapping analysis have already been applied in a number of research projects. The method has also been modified to run in real time using data transferred from the radars over Internet links. This paper provides the technical description of the technique to support these and future applications. We also illustrate certain interplanetary magnetic field (IMF) dependencies in the large-scale convection and, in one particularly clear example, examine the rapidity of the convection response to a sudden polarity change in the IMF z component. 2. The Data SuperDARN is an international collaborative project. The affiliations and other vital information about the radars in the northern hemisphere are provided in Table 1. The operation of the overall system is described by Greenwald et al. [1995, and references therein]. Here we provide a brief summary of the most pertinent characteristics. The radars operate on a 24-hour, 365-days-a-year basis, under the control of a computer program that specifies the operating mode. By agreement of the SuperDARN principal investigators, at least 50% of the time each month is designated to run common-time mode, which provides for standardized settings of several operating parameters. In the current version of this mode, the radar scans are synchronized to start on 2-min boundaries beginning with 0000 UT. A scan consists of steering the radar beam through 16 successive azimuthal settings separated by 3.3 ø with an integration period per setting of 7 s. The additional period at the end of the 2-min interval is made up with computer processing tasks and idle time. The radar transmits on a selected frequency lying in the 8- to 20-MHz interval, and the backscatter returns are range-gated in steps of 45 km. Backscattering occurs from HF rays that come in contact with decameter-scale field-aligned irregularities while propagating orthogonally to the geomagnetic field lines. A recent analysis of observations performed by the Goose Bay HF radar over a 5-year period demonstrated the scattering rates that can be expected [Ruohoniemi and GreenwaM, 1997]. For conditions of solar cycle maximum, the likelihood of observing backscatter varies with MLT from 45% on the dayside to 80% on the nightside. Scattering rates vary widely with season and geomagnetic activity level. The Doppler shift in the backscattered signal provides an estimate of the line-of-sight component of the E X B (convection) velocity. SuperDARN measurements of convection velocity are possible only if suitable irregularities are present and illuminated by the HF radar transmissions under the orthogonal-to-b propagation condition. The amount of scatter can sometimes be increased by changing the operating frequency. 3. Preprocessing The autocorrelation functions of the backscattered signal are evaluated in real time by on-site computers, and various parameters (e.g., signal-to-noise ratio, velocity, and spectral width) are recorded as functions of time, beam number (0-15), and range gate (0-74). The velocity analysis begins with a sequence of scan data from the HF radars. Velocities with error estimates greater than 200 m/s are dropped. In addition, the class of scatter that is due to scattering from the ground after reflection from the ionosphere ("groundscatter") must be excluded; we drop velocity values that are flagged as groundscatter on the basis of their velocity magnitudes and spectral widths. Despite these tests, velocity values contaminated by interference or groundscatter are sometimes passed. Velocity data from a single radar scan can be mapped directly into geographic or geomagnetic coordinates using standard SuperDARN mapping algorithms and the magnetic coordinate system of Baker and Wing [1989]. We have found it useful to first filter the velocity data in the basic radar beam/gate coordinates. After some testing, we determined that the most satisfactory results were obtained by performing a "boxcar" filtering involving both temporal and spatial sampling. For a scan collected at time t,, the filtering sample includes the scans per- formed at t,-1 and t,+l, where the subscripts indicate the scan order. The spatial sampling is performed over a 3 X 3 beam/ gate template centered on the cell of interest. Thus the filtering sample for a cell indexed b for beam number and g for gate number, i.e., (b,g) k, encompasses the velocity data' contaihed in the 3 x 3' beam/gate template centered on this cell through the three successive scans centered on k. (The sampling is modified if a limiting scan, beam, or gate is encountered.) Weights are assigned to favor the samples collected at the. exact position of the target cell (b,g) or at the target time, t,. The sample is median-filtered to produce a "best" estimate of the line-of-sight velocity for the target cell. (The particular merit of medianfiltering over simple averaging in this application is its rejection of anomalous data.) The assignment of a velocity value to the target cell depends on the (weighted) number of velocity values obtained for the sampling; if too low, no value is determined, and the cell is turned off; if sufficiently high, a value is determined, and the cell is turned on. This filtering results in a marked improvement in the smoothness of the velocity maps. An example is shown in Figure 1. The data were collected by the Goose Bay radar on December 14, The figure shows three successive input

3 RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION 20,799 Table 1. SuperDARN Radars in the Northern Hemisphere Radar Location Affiliation Latitude, øn Longitude, øe Start Saskatoon Saskatchewan, Canada University of Sept Saskatoon Kapuskasing Goose Bay Stokkseyri Ontario, Canada Labrador, Canada Iceland Johns Hopkins University Applied Physics Laboratory Johns Hopkins University Applied Physics Laboratory Centre National de la Recherche Scientifique Pykkvibaer Iceland University of Leicester Hankasalmi Finland University of Leicester Sept June Oct Dec April 1995 scans starting at 2001:25, 2003:04, and 2004:44 UT (scanning was not yet synchronized to 2-min boundaries) and the filtered velocity for the middle scan. From the three input scans, it is clear that the velocity data are characterized by variability. Some of this is due to interference (e.g., beams 9 and 15 of the 2001:25 UT scan and beam 12 of the 2004:44 UT scan), and some is due to marginal velocity data. However, there is considerable point-to-point variability even within extensive areas of E x B drift measurements. The signal-to-noise ratio associated with the activity in this interval exceeded 30 db, and the average uncertainty in the line-of-sight velocity determination was just 11 m/s, with 95% of the values associated with uncertainties less than 50 m/s. As this example illustrates, the plasma drift on small spatial and temporal scales typically shows much variability while conforming on larger scales to relatively simple configurations with smooth gradients. Evidence of small-scale electric field variability has also been presented by Codrescu et al. [1995] on the basis of incoherentscatter measurements of convection velocity. We defer further discussion of this interesting property to future studies. Here we remark that our algorithm for deriving large-scale convection patterns filters the velocity data on spatial scales that are large compared with the resolution available in the basic radar measurement. Thus the elimination of small-scale variations in the velocity field by boxcar filtering entails no loss of useable information. It is desirable to assign uncertainties to the filtered velocity values. We have seen that the nominal uncertainty in the basic line-of-sight velocity measurement does not characterize the noise-like variability in that measurement. We have encountered similar difficulties with using spectral width as a proxy for this uncertainty. A more appropriate measure appears to be the variability that is characteristic of the velocity sample used for the boxcar filtering. The standard deviation of the entire velocity sample is first calculated. Points that are more than two standard deviations from the sample mean are dropped, and the standard deviation is recalculated. This is assigned as the uncertainty on the filtered velocity value. Note that this characterization of the velocity variability is made on spatial scales set by the beam and range gate dimensions of the boxcar filter, which are typically 200 km x 150 km. Thus the uncertainty estimate gauges the velocity variability in the small-scale domain. For a selected time interval, the data from each radar are processed through the boxcar filter as described above and written to a holding file. The velocity values are matched with the magnetic coordinates of the radar cells. The next step is to combine the data from the individual radar holding files into a single file. For this purpose we define a global grid for spatial averaging and a time step for temporal averaging period which may be as short as the scan repeat rate, i.e., 2 min or less. After some consideration, we decided on a grid defined by the spatial scale of 1ø of latitude, or about 111 km projected to the surface of the Earth. For each integral interval of 1 o in colatitude, 0, the number of grid cells distributed in longitude, n(o), is set by the requirement that the step in longitude projected to the Earth's surface be as close to 111 km as possible for integer n(o), i.e., n(o) = NINT[360 sin(o)] (1) where 0 is the central colatitude of the 1 ø interval and NINT is the "nearest-integer" function. A plot of the grid is shown in Plate 2. The set of line-of-sight velocity vectors discussed in relation to the velocity filtering (Figure 1) is also shown. We briefly discuss the merits of this construction. It is preferable to average the radar velocity data rather than work directly with the individual velocity values because the latter would lead to oversampling of the near-radar regions relative to the far-radar regions. With reference to Plate 2, the distribution of field points produces many estimates of the velocity within the grid cells at near ranges; this does not add significantly to the definition of the velocity pattern on global scales but would tend to skew a solution that counted all the velocity inputs equally. We also consider that there will be a need to compare the convection velocities with other types of measurements, such as imager data. This is made much easier if data are plotted to a common format. We note that this particular grid nearly equalizes cell areas, while the more conventional choice of a grid defined by fixed steps in latitude and longitude has the disadvantage of a severe latitudinal variation in cell area. Finally, we add that the fitting analysis described in the following implies a spatial filtering of the velocity data on scales that are usually larger than those of the grid defined here. One could instead define a grid using the dimensions of the spatial filter. While feasible, this would make the input velocity map dependent on the selection of fitting parameters and introduce other complications. Plate 3 shows the line-of-sight velocity data from the four radars that were operating on December 14, 1994, mapped into

4 20,800 RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION gC 20:1:25 UT <30> m/s gC 20:3:4 UT <30> m/s (a) 60 ß e-- = : - : _ ß khz khz gC 20:4:44 UT <30> m/s gC 20:3:4 UT <30> m/s I ' " ' ' I ' ' ' ' I... I I... I... I... I' (c) (d) I,,,, I,,,, I,,,, I khz I,,,, I i I I I i I I khz Figure 1. (a)-(c) A sequence of line-of-sight velocity data collected during successive scans with the Goose Bay HF radar on December 14, The scanstart at 2001:25, 2003:04, and 2004:44 UT. The plotting coordinates are beam number (0-15) and range gate (0-74), and the line-of-sight velocity vectors are rotated to the horizontal for clarity; the leftwardirected arrows correspond to motions toward the radar. (d) The filtered velocity data obtained for the scan beginning at 2003:04 UT as explained the text. the grid for the period UT. An average velocity and eral scans, the determination of the occurrence rate has a ternits uncertainty were obtained a given grid cell for a given poral dimension. The filtering by occurrence rate roughly radar if at least 25% of the radar samplings within that cell re- equalizes the statistical significance of the average velocities by turned a velocity value. Since the averaging period spans sev- eliminating more marginal data. The file of mastered velocity

5 ß, RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION 20,801 SuperDARN HF Rad '% Magnetbmeter Chains Operationat... ' / ß Alaska....Greenland ß Planned". - /,.... ß CANOPUS ß MAGIC ß 15.LT... /... 9.LT..'""..,..,......*.... 'J'...""-..,.../ '"'.. "" '" 'i:..."mac.cs ß I.MACE..".." %...,: ' ' ', : /... / '... [] '..m/s,.".,,"..."'l, % ' :' i;'... /..._ '"'... I o :.'22,-'..' _,-... I '. '..,:.. ;..,...,.,..,i.2 ' ' <_,,--... '"'":".: '""'-.., '.._ '!...-.o ß.: ß /.',: %.. '6 ß "'..-'" '"-...' "';'.... ' ß...'.. b ,."' 12/14/ T2 LT :06: :12:00 UT... '... 't"... ' ',T i ': '. b.,;. x....,!.. i}300 L T : : :/; :, ; ,,,',. :' '.. '/._I...X...; : /! oo :..,"/./, ',;/,/d. '.. '-...'.:.' :..,.,½/ :c, :.. "7 '"l"-" ::,.., I '. '..:',',:"..,'"-.../... l. o.--. :::-...' l'øø'" "...W '"",.., '""'"'," ""'"";,:'"'"'.-'"'"'1.:'"" '"""'"'" ',. 1000m/s b'"'" Plate 1. Fields of view of the Super Dual Auroral Radar Network (SuperDARN) radars in the northern hemisphere (yellow). The prospective fields of view of three radars planned for western North America are also shown (orange). The sites of collocated magnetometers are indicated (blue), and their affiliations are listed in the legend. Plate 3. Plot of the averaged line-of-sight velocity values obtained from the SuperDARN radars on December 14, 1994, UT. The longitude positions of the contributing radars are indicated by the letters distributed along the 60øA contour: T, Saskatoon; K, Kapuskasing; G, Goose Bay; and W, Stokkseyri. (The letter codes for the remaining northern radars are E, Pykkvibaer, and F, Hankasalmi.) 12/14/94 20:03:04-20:04:43 UT m/s m/s 5OO 4OO oo oo foo 12/14/ LT :06:00 - '... /... 20:12:00 UT '"'"'" '... I"... '... ' 15 1, I... "9 LT _ '"" N...'... [...'... "'-.../ '"-. ' 000m/s."",.""'"... 'L - '... //2..,.-".m/s..."""",... /... "... t. f - V' '/'*/-? '-/. "X', 1, /...".. 4oo: /...'"'..."...',:.:.<... '......, ß "..."... :7... '-i" /'-.., "'., " ': ß. i.! oo i ;.. '., i '.. Plate 2. Plot of the grid for spatial averaging of the line-of- Plate 4. Plot of convection velocity vectors obtained by mergsight velocity data as described in the text. A sample of veloc- ing the overlapping line-of-sight velocity values of Plate 3. ity data from the Goose Bay radar is overlain (December 14, 1994; :43 UT). The outer dashed circle corresponds to a magnetic latitude of 60 ø, and 3-hour magnetic local time (MLT) meridians are shown, with 1200 MLT at the top. The position of the radar in magnetic longitude is indicated on the 60øA contour by letter G. The velocity data are scaled to the length of the reference arrow and are also color-coded by magnitude.

6 20,802 RUOHONIEMI AND BAKER' IMAGING OF HIGH-LATITUDE CONVECTION data shown in Plate 3 represents the processed set of highconfidence velocity estimates that will be used to derive twodimensional convection patterns. coefficients Aim and B!m are real-valued. The relations between the electrostatic potential, convection electric field, and velocity are the familiar 4. Imaging the Large-Scale Convection In this section we present the results of solving the data of Plate 3 for estimates of the large-scale convection pattern. We begin with a demonstration of solving for two-dimensional velocity vectors by directly merging the line-of-sight data, a solution which has been the standard approach in SuperDARN studies to date. In accordance with the original SuperDARN concept, the radars are arranged in pairs and oriented to look over large common-volume areas (e.g., Plate 1). For the radars shown in Plate 3, the common-volume pairs are Saskatoon-Kapuskasing and Goose Bay-Stokkseyri. However, a considerable number of grid cells in this example (approximately one-third) are sampled by three radars, and a few are sampled by all four. On the other hand, about half of the sampled grid cells are sampled only once. The standard mapping of the two-dimensional convection velocities is generated by merging the lineof-sight velocity data wherever they intersect. The solution is shown in Plate 4, where, for the overdetermined cases (e.g., more than two velocity inputs), the velocity vector has been determined by a least squares fitting of the variation of the line-of-sight velocity with radar look direction. Overall, the impression is of sunward flow on the duskside at lower latitudes that turns poleward before the noon meridian is crossecl A strong shear is imaged in the zonal flow in the MLT sector over the 77ø-81 ø latitude interval. Although we obtain a reasonable representation of the large-scale convection, a large fraction (-50%) of the available velocity information cannot be merged and therefore remains unused. We now discuss the new technique of mapping the global convection with the SuperDARN measurements. The twodimensional velocity at a point can be unambiguously resolved only if two or more radars make simultaneous measurements there. However, all the available line-of-sight velocity data serve to constrain the possibilities for the large-scale convection pattern. The pattern that is most consistent with the measurements can be determined by mathematical fitting procedures. This philosophy is similar to the approach taken in the derivation of some statistical convection models [i.e., Weimer, 1995; Ruohoniemi and Greenwald, 1996] and in the AMIE procedure [Richmond and Kamide, 1988]. We expand the electrostatic potential in terms of spherical harmonic functions, Ytm, according to [e.g., Jackson, 1962] L M CI)(0, ) =. ' mlmylm(o,d)) (2) l=om=-m where the Aim are complex-valued coefficients and L and M are the order and degree of the expansion, respectively, with M -< L. It is conveniento make ci> purely real and rewrite this equation in the form L ci)(0, ) = y, AtoPl ø (cos 0) /=0 l + Z (Alm cosm( + Blm sin mc )p/m (cos 0) m=l where the Pl m are the associated Legendre functions and the (3) E =-Vcb; ExB V= a2 (4) The filtered line-of-sight velocity values have been converted to the mapping grid, furnishing a set of N velocity values and their uncertainties, Wi and o'i. The quantity to be minimized is 1 12 X 2 = i=1 o [V[/]. [/]- W/ where V[i] is the fitted velocity vector at the grid cell position associated with i and the dot product provides the projection of this velocity onto the line-of-sight direction. The set of coefficients (A!m,B!m) specifies the best fit convection pattern. Although these equations are a complete formulation of the problem, it is conveniento replace colatitude 0 with an effective colatitude O' defined by (5) ('rr/2- Ao) (6) where A0 is an assumed low-latitude limit to the convection. The effect of this variable transformation is to map the latitude interval of the convection zone over the full 'rr range of the colatitude parameter. The values of L and M determine the spatial filtering performed on the velocity data. The global-scale character of the pattern is resolved by expansions of relatively low order and degree; often we use L = 4 and M = 4. The method of singular value decomposition [e.g., Press et al., 1992] is used to find the set of coefficient values that minimizes X 2. In the examples presented here, the degree of the expansion is equal to the order, i.e., M = L. The fitting procedure can be applied direc[ly to the set of velocity data shown in Plate 3, rendering a set of coefficients that reproduces the input values as nearly as possible in the sense defined by (5). In principle, the set of coefficients can then be solved for ci> over the entire global grid through (3). This amounts to an extrapolation of the fitting solution obtained over the limited area covered by measurements to the uncovered portions of the high-latitude zone. However, the results may be unphysical over areas that are distant from the input velocity data. This outcome is not altogether surprising, as the fitting was constrained only over the region of data coverage. It is desirable in many applications to obtain a global picture of the convection that is consistent with all the available input data in a mathematically optimal sense. We have tried several approaches to the extrapolation of a localized solution to a global pattern. Our favored approach is to fold in velocity information from a statistical convection model. It will be easily appreciated that a very few points over the uncovered areas of the plot of Plate 3 will suffice to constrain the global solution for ci>. We have settled on a minimalist treatment. In brief, we sample the prediction of the statistical model at the least number of grid positions that is required to bound each term in the spherical harmonic expansion of ci>. For a given expansion order L, a set of sampling points can be determined (see the appendix for details). If fewer points are taken, instability related to the effect of unconstrained extrapolation creeps in; if more points are taken, the global solution owes more of its character to the input from the statistical model than is neces-

7 RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION 20,803 sary to achieve stabilization. This approach balances the need for stabilization against the desire to base the global solution as much as possible on actual measurements. The assignment of uncertainties on the model velocities requires special consideration (see the appendix). The ensemble of measurements and model data are then fit according to the criterion of (5) to obtain a best fit set of coefficients. The result for the example described in Plate 3 with L = 4 and A0 = 60 ø is shown in Plate 5. The model data have been taken from a statistical model [Ruohoniemi and Greenwald 1996] (hereinafter called the APL model) for conditions of low IMF magnitude (0-4 nt) in the GSM y-z plane, Bz-, B3.+, and IByl IBzl. As indicated by observations the WIND satellite, these IMF conditions had prevailed over the preceding 1- hour period. Fitted velocity vectors are plotted at those cell positions where constraining velocity information was used from either measurements or the model. Since no measurements were available over the MLT sector, the vectors plotted there indicate the density of sampling of the statistical model. The contours of constant electrostatic potential also represent convection streamlines. The overall pattern is two-cell, with the details of the dusk cell largely determined by direct the case of consistency and a large number of degrees of freedom is Xr 2 1. For the analysis of Plate 5 we have Xr 2 = 0.5. This indicates that the offsets between the measured and fitted velocities are considerably less than would have been expected on the basis of the assigned uncertainties. The fitting is satisfactory in the sense that the velocity inputs are reproduced to within the confidence limits. With increase of Xr 2 through values greater than 1, the fitting would become progressively less satisfactory. One cause of excessive offsets might be the existence of spatial or temporal structure in the velocities that is not resolved at the scale sizes selected for the fitting. Such a discrepancy could be reduced by appealing to a higher-order ex- pansion or a shorter averaging period. In particular, structure in the mesoscale range (-500 km x 500 km) would tend to adversely impacthe Xr 2 determination in a low-order fitting. That is because variability at these scales is not resolved by the fitting but also does not contribute to the uncertainty determination, which is carried out at smaller scales. We have found that Xr 2 is typically -< 1 during periods of stable IMF but more variable when IMF is changing, especially after a southward turning. This is consistent with some studies that have described enhanced mesoscale structure during active periods [e.g., Greenwald et al., 1996]. We discuss this point further in one of the case studies. By propagating the uncertainties through the calculations we can obtain point-by-point specifications of the uncertainties on the potential values and convection velocities. However, we generally prefer to analyze the entire velocity pattern while taking cognizance of the confidence limits applicable to each. As an example of the difficulty of characterizing uncertainty in a fitted pattern, we observe that for the result depicted in Plate 5, measurements. The velocity shear near 78øA is associated with the convection reversal boundary across this cell, and the associated potential extremum is near 1630 MLT. The depicted dawn cell owes relatively more to input from the statistical convection model. The total cross polar cap potential variation, ci:,pc, estimated for this pattern is 52 kv. For an expansion of this order, the spatial scales associated with the fitting are 6 ø in latitude and 45 ø in longitude; finer details of the velocity variations are suppressed. We consider how the solution varies with a change in the order of the spherical harmonic expansion to L = 7, which increases the resolution of the fitting to 4 ø in latitude and 26 ø in longitude. The result is shown in Plate 6. Overall, the pattern is not greatly changed from the lower-order solution (ci:,pc= 53 kv versus 52 kv for L = 4). As expected, more of the details in the velocity distribution can be accommodated, for example, the line of the latitudinal velocity shear on the duskside is more elongated in longitude and matches more closely the merged result of Plate 4. The pattern from the higher-order fitting has perhaps produced an improved estimate of the overall pattern as well, in that it depicts a simpler, less convoluted distribution of flow streamlines, especially at lower latitudes in the prenoon sector. The pattern has been altered more on the dawnside, with the increase in expansion order due to the denser sampling of the statistical model output. (More model data are required in order to constrain the values of the additional terms in the expansion.) The increase in the statistical constraining measurements over some areas came from multiple radars, over others from only single radars, and over the remainder from none. We perceive that there are significant decreases in the reliability of the VcI:, determination through the three cases, which, while quantifiable according to various schemes, are perhaps best appreciated in terms of the differences in data coverage, the sensitivity of the results to reasonable variation of the fitting parameters, and comparison with independent measurements. The selection of the A0 parameter is an additional complication. Ideally, the latitudinal limit of the convection region could be determined for every period and every MLT. No such source of definitive measurements of this parameter exists. The statistical convection models provide some gauge of the size of the convection region, but the relation of statistical convection boundaries to instantaneous boundaries is not clear. Instead, we usually adopt an empirical approach whereby we preview a map of line-of-sight velocity data for a given period and judge model contribution with increase in L reduces the usefulness of the likely low-latitude limit of the convection region. Although working in higher expansion orders. The choice of expansion somewhat subjective, the velocity data do tend to identify order in mapping the global convection involves a trade-off between higher spatial resolution and increased dependence on the statistical model. The plots include a quality-of-fit parameter that is related to X 2. This is the reduced chi-square, Xr 2, obtained by dividing X 2 by the number of degrees of freedom, v, in the fitting. The reduced chi-square is shown explicitly as a fraction with v as the denominator. If the measurements are physical (i.e., can be represented as the gradient of a scalar potential) and the measurement errors are distributed normally, Xr 2 gauges the degree to which the distribution of offsets (i.e., the differences between the fitted and measured velocities) is consistent with the uncertainties assigned to the measurements. The expected value in boundaries, especially along the dawn and dusk flanks. In a statistical study of backscatter occurrence, Ruohoniemi and Greenwald [1997] in fact found a strong correlation between the equatorward limits of HF backscattering and the boundary of the Feldstein oval. In addition, when geomagnetic activity increases, the equatorward expansion of echo activity (and velocity measurements) tends to occur at all MLTs. This approach is the most workable of those we have tried so far. The main effect of varying the value of A0 (within reasonable limits) is to vary the size of the convection region and the magnitude of CI)pc. The dependence of CI)pc on this value is typically not large' for the example of Plate 5, CI)pc = 53 kv for A0 = 55 ø, while CI)pc = 51 kv for A0 = 65 ø.

8 20,804 RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION 12/14/ :06:00-20:12:00 UT 000 m/s 18t order = 4!at_min = 60 X /499 = 0,5 Plate 5. Solution for the global convection pattern obtained by fitting the line-of-sight velocity data of Plate 3 and data from a statistical convection model to a low-order expansion (L = 4) of the electrostatic potential in spherical harmonics. The low-latitude limit of the convection zone was assumed to be A0: 60 ø. The solid (dotted) contours are associated with negative (positive) values of electrostatic potential, and the contour interval is 6 kv. Velocity vectors implied by the fitting are plotted at points where constraining velocity data were provided by either measurements or the model. The cross polar cap potential variation implied by this solution is (I:'],c: 52 kv, and the reduced chi-square for the fitting is Xr2= 0.5 (see text). Plate 7. Plot of the global convection pattern produced by the fitting analysis described in the text (L- 4) using the prediction of the APL convection model for the interplanetary magnetic field (IMF) conditions prevailing during the period of Plate 5. The statistical pattern was sampled at the points indicated by fitted velocity vectors. 12/14/ LT. APL MODEL 20:06:00... ß <BT<4 Bz4By+ 20:12:00UT LT _ "... \.x,' / "/";?"- E,> J :..,...',' o,.., ''-.. / '... ß... '-... / -- /.. ""- '"' "F<'... '... " 5 <" /57s,a,_m::oo = o.4... Plate 6. Same as in Plate 5 except that the fitting has been performed to higher order (L = 7).

9 RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION 20,805 The greater uncertainty in the estimation of ti)pc is due to the use of a statistical model. As discussed above, the sampling scheme we have adopted minimizes the amount of model input; still, when measurements are scarce the fitting will more nearly reproduce the model pattern. To the extent that the statistical models differ, the same input data will lead to different results. The sensitivity to model characteristics is particularly pronounced where measurements are lacking. We have found, however, that when measurements extend over most of the dayside region of flows entering the polar cap, a low-order fitting is very effectively constrained and reasonable variation of the model inputs (e.g., switching between APL model patterns) has little effect on the results. We stress that for the purposes described here, any statistical model may be applied but uncertainties are introduced due to the largely unknown accuracy of the model as a predictor of the instantaneous convection. Of course, the most desirable way to reduce this uncertainty is through continued expansion of the SuperDARN measurement area. the configurations of the solar wind and the magnetospheric cavity, and a model of the propagation of IMF transients from the bow shock to the magnetopause. The validity of the result is not always clear. We can measure the time delay more reliably by identifying the impact of IMF transitions in the SuperDARN data. The rotation of the IMF vector to slightly southward that occurred at the satellite just after 1750 UT was followed by an intensification of dayside flows. Examination of the 2-min velocity data (not shown) indicates that this response was apparent by 1812 UT. The steeper southward turning that took place at the satellite near 1805 UT produced a second, larger intensification that was apparent by 1824 UT. Thus we obtain an effective delay of about 20 min between IMF conditions at the satellite and the ionospheric response. Plate 8 shows a sequence of six global convection images obtained for the period UT. All six northern radars contribute to the data set, which has been averaged over 6-min intervals. We have applied a low-order expansion (L = 4) and shifted the assumed low-latitude limit of the convection zone To conclude this discussion, we compare the convection ' from A = 68 ø to 65 ø between the second and fifth time interpattern of Plate 5 with the corresponding convection pattern vals to follow the expansion of the convection zone. The fitfrom the APL model for the IMF conditions described above. tings were seeded with statistical model data appropriate to the The model pattern was resolved over the global grid into zonal and meridional components and fitted to a spherical harmonic expansion of ti) of the same order (i.e., L = 4) as the fitting of Plate 5. The result is shown in Plate 7. The similarity between prevailing IMF conditions as discussed in the preceding section. To emphasize the coverage from measurements, we have plotted fitted vectors only where measurements were available. Schematics of the average IMF vector in the GSM y-z plane the patterns on the dawnside is not too surprising considering are shown, where the IMF data have been delayed by 20 min the origin of the input velocity data there. On the duskside, on the other hand, the pattern of Plate 5 is dominated by measurements. The model fitting reproduces the overall morphology of the convection in this region, including the location of the potential extremum near 1630 MLT, 78øA and the line of the convection reversal boundary. One difference that does emerge is the magnitude of the potential gradients on the duskside, which are larger in the model pattern (note the greater value of the potential extremum). Combined with a weaker dawn cell, the total potential variation, ti)p½, obtained for the model pattern is virtually the same (51 versus 52 kv). We conclude that the convection observed in this period was largely consistent with the prediction of the APL convection model keyed to the prevailing IMF conditions. and averaged over 6-min intervals. The bulk of the measurements were obtained on the dayside. The first two images (which are characteristic of the preceding 1-hour period) show a pattern that is characterized by small velocities on the noon meridian and a dayside throat of higher velocities that is markedly displaced toward the dusk side. The serpentine nature of the contours in the postnoon sector is consistent with expectations based on statistical models for IMF By- conditions. It is obvious that the convection state changes dramatically in the UT interval, when a more pronounced two-cell pattern emerges. The continuing displacement of the throat toward the dusk side of the noon meridian suggests continued merging under B3.- conditions. Beß ginning in the UT interval, the pattern changes to one more characteristic of Bz-; note especially that the throat 5. Case Study: January 10, 1996 As a demonstration of the application of this analysis to the study of IMF dependencies in high-latitude convection, we examine a period of prolonged and extensive scatter observed by the SuperDARN radars on January 10, The IMF data shifts toward the dawn side of the noon meridian. We associate the first development with the change in IMF from Bz+ to B z- under strong By- conditions, which occurred at the satellite just after 1750 UT. The second change appears to be the result of the sudden turning of the IMF to almost pure Bz-, which occurred just after 1800 UT at the satellite. collected at the WIND satellite in the UT interval It is worth noting that the patterns are not greatly changed are shown in Figure 2. A number of transitions took place in the IMF y-z component; the most dramatic occurred just after 1800 UT at the satellite when B z turned strongly negative and By dropped to zero from moderate negative values. Just prior to 1800 UT a significant change occurred when the IMF vector rotated to negative Bz and more negative By. A third, more gradual transition occurred between 1600 and 1730 UT when the IMF y-z component turned from predominantly By+ to predominantly By-. We ask how these changes influenced the high-latitude convection seen by SuperDARN. First we determine the time delay between the IMF transitions observed at the satellite and the response of the ionospheric convection. It is usual to estimate this parameter on the basis of the satellite position, solar wind velocity, models of when different delay times are used, owing to the strong constraints placed on the fitting over the dayside by the measurements. This constraint extends to the specification of the total cap potential variation because the measurementspan most of the region of antisunward flow; ti)pc increased from 30 kv before the arrival of the first IMF transition to 57 kv by the end of this period. We have generated potential patterns for the entire UT period with seeding by the APL convection model keyed to the IMF conditions at the WIND satellite at a 20-min delay. Figure 3 shows a time series of the resulting total cross polar cap potential variation. ti)pc approximately doubled as a result of the IMF southward turning. The potential variation then dropped as the impact of a northward rotation of the IMF

10 20,806 RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION 40 '20_- n- - o_ _ 10'- - I ' I I R X Ry 8 m 4 0 : :,, : ' : : I ', : : I : : : : : I ' ' ' ' t ' ' ' I ' : : I ', : '. : ', o x UT (hours) Figure 2. IMF data recorded at the position of the WIND satellite on January 10, 1996, UT. The top panel indicates the position of the satellite in GSM (X, Y,Z) coordinates. was felt after 1900 UT. The dashed trace in the plot shows a 6. Case Study: Response to a Sudden Southward time series of CI)pc predicted on the basis of the statistical Turning of the IMF model alone. The success of the model as a predictor of the convection of course depends on the degree to which the con- In this section we examine a particularly dramatic example vection is a function solely of the time-delayed IMF measured of the high-latitude convection responding to a transition in the at the satellite. Where the two traces coincide, it can be in- IMF. Observations the individual radar showed a high deferred that the measurements and model data more nearly gree of simultaneity in the transient associated with a southagree. In the period immediately preceding the arrival of the ward turning. By imaging the global convection through the insouthward turning ( UT) the model consistently pre- terval using the technique outlined here, we can characterize dicts greater CI)pc than was indicated by the measurements; the the initial and final states of the convection and find that the difference is typically 5 to 10 kv. In the period following the reconfiguration can be described as a global, nearly instantatransition ( UT) the model again substantially under- neous process. This finding contradicts a substantial body of estimates CI)pc from the measurements. However, during the pc- work that suggests a pronounced MLT dependence [e.g., riod bounded by the sharp rotations of the IMF B z component Bargatz et al., 1985; Hairston and Heelis, 1995]. It is more ( UT) the traces are more nearly in agreement, with consistent with the findings of Ridley et al. [1997], and this exdifferences typically less than 5 kv. We conclude that the ample provides a global response time (<6 min) that is the model was more successful in predicting the overall convection shortest yet reported. in the immediate aftermath of the southward IMF turning. This The IMF data recorded at the WIND satellite during the result is perhaps not altogether surprising; the IMF factor might event is shown in Figure 4. The IMF vector had been northbe expected to register most strongly when there is a distinct ward with a magnitude of 6 nt when it suddenly switched to change of state brought on by enhanced merging after a pro- southward with the same magnitude just after 2040 UT. The longed period of nonnegative B z. transition began at 2043:25 UT and was completed in less than

11 RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION 20,807! it I --I I I I I ; 1 I II 2.5 min. B z was notably stable both before and after the transition. We have established that the appropriate time delay for relating the IMF transition at the satellite and the related convection transient in the SuperDARN data is 27 min. We have applied our mapping technique to estimate the global convection through this interval. Input line-of-sight velocity maps and output fitted patterns are shown in Plate 9 for the two 6-min periods, UT and UT, that bounded the time of arrival of the IMF transient. The line-of- sight velocity data show dramatic changes in the flows both in the postnoon ( MLT) and premidnight ( MLT) sectors. The fitted maps show that the overall convection immediately preceding the arrival of the IMF transient was characterized by sunward flows on the noon meridian associated with a reverse dayside convection cell. With the change in B z the pattern changes dramatically; the flows on the noon meridian reverse to antisunward, the convection zone expands to lower latitudes, and two dominant cells emerge. (Note that the o 16:oo 18:oo 20:00 22:00 UT (hours) Figure 3. Time series of the total cross polar cap potential variation obtained from the fitting analysis performed on velocity data from measurements and the statistical model (solid line) and from model data alone (dashed line) for the period of January 10, 1996, UT. loo._. 50 R X lo 8 i- 6 v co , i i! I,, UT (hours) Figure 4. IMF data recorded at the position of the WIND satellite on November 24, 1996, UT. The top panel indicates the position of the satellite in GSM (X, Y,Z) coordinates.

12 20,808 RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION low-order fitting reduces the magnitude of the effect in the velocities compared with the input line-of-sight velocities because of the spatial filtering effect.) The arrival of the IMF transient is felt simultaneously on the dayside and the nightside. Instead of showing the progression of a transient in MLT, the convec- (with plans to upgrade to all six in the northern hemisphere). A proxy value of the IMF is determined by finding the best match between the measurements and the patterns of the APL model. The measurements and related model pattern are solved for a global convection map. The convection map, IMF proxy value, and total polar cap potential variation are then output to the Web page. The delay between current time and plot time is typically 5 min. The maps have value as space weather maps of the plasma winds that can be incorporated into ionospheric tive plasma drift from the SuperDARN HF radars. The lineof-sight velocity data are carefully filtered and mapped onto a polar grid. The coverage provided by the radars approaches 12 hours of MLT and 20 ø of invariant latitude. The velocity data are fit to an expansion of the electrostatic potential in spherical harmonics. Some selection of fitting criteria is required, including the order of the expansion and the low-latitude limit of the convection zone. Information from a statistical model is used to tion "snaps" into a new configuration at all MLTs. The reconfiguration of the global convection in this event was completed in less than 6 min. This example also shows an abrupt increase Xr 2 after the stabilize the solution in regions were no measurements are IMF tums southward, from 0.9 to 1.4. It is probable that this is related to the onset of mesoscale structuring in the convection pattern, as was discussed earlier. We have examined time series of the input line-of-sight velocities from the individual radars and easily identified numerous localized transients in the convection in this latter period. In contrast to the response to the IMF southward turning, these show clear propagation characteristics. Data from the nightside magnetometers (not shown) indicated a clear substorm onset near 2230 UT. Thus the period after the southward turning can be characterized as active (likely growth phase) and may have been particularly susceptible to such processes at mesoscale dimensions as vortex formation [Greenwald et al., 1996] and flow bursts triggered by pulsed reconnection [Rodger and Pinnock, 1997]. In this example the emergence of mesoscale structure is effectively flagged by the elevation of the value of Xr 2. available. The gross character of the global convection is often effectively determined by a low-order fitting of the electrostatic potential, provided the measurements are sufficiently widespread. We have derived numerous examples of time series of the global convection. Here we have presented examples that showed the response to variations in the IMF. Effective IMF propagation delay times were determined by comparing IMF changes at the WIND satellite with the onset of apparent responses in the convection observed by the SuperDARN radars. We identified an event with a particularly abrupt polarity change in IMF B z and found that the convection responded nearly simultaneously at all MLTs and reconfigured globally in a very short time (<6 min). More detailed study of the manner in which the global convection responds to changes in the IMF is left to future work. The extraction of global convection maps on the basis of 7. Related Work SuperDARN plasma drift measurements has immediate value for a range of studies. Since the SuperDARN radars operate The method of mapping global convection with continuously, this information can be generated for almost any SuperDARN data has already found application in a number of period. The temporal resolution afforded by the radar scan rate research projects. The new results include a study of convecof 2 min is sufficient to image most of the effects of interest. tion during a period of presumably weak interaction between In addition, patterns are calculated in near-real time using data the solar wind and magnetosphere [Bristow et al., 1998], a piped down from the radars over Intemet connections. Thus it comparison of MHD modeling and large-scale convection (R. is possible to run the analysis in a space weather mode with A. Greenwald and P. Janhunen), analyses of the redistribution nowcasting of the global convection. The interested reader of high-latitude plasma structure for varying IMF (D. Decker is directed to the links to the various SuperDARN data prodand J. Sojka), and the penetration of high-latitude electric fields during a substorm in[erval [Buonsanto et al., 1998]. ucts that can be found at the APL Website ( The mapping method is being used to generate maps of glo- With the continued expansion of the SuperDARN networks bal convection nearly in real time. These are displayed at the in both the northern and southern hemispheres the scope of the Applied Physics Laboratory (APL) SuperDARN Website. Data are transferred over Internet links from three of the radars imaging studies will further increase. Coverage in the northern hemisphere will soon exceed 12 hours of MLT, making possible simultaneous, extended observations of the convection over the dayside and nightside regions of plasma flow into and out of the polar cap. Such coverage will make it possible to rely almost entirely on direct convection velocity measurements to map global patterns. Appendix: Necessity of Using a Model In an ideal situation, the coefficients of the fit could be demodels as the ionospheric convection component. termined entirely from observed data. Unfortunately, the We are also proceeding with studies that compare the global SuperDARN radar network does not cover the full range of convection mappings with related effects in currents and parmagnetic local times. This means that a significant portion of ticle precipitation. In one effort, data from imagers carried by the full range of magnetic local times is unconstrained by meathe Polar satellite are plotted onto the convection grid defined surements. A least squares fitting of the available data reprohere (H. Gallagher). The distribution of ionospheric conductivduces this input in a best fit sense by considering all possible ity is inferred from a combination of model and imager data. combinations of values for the expansion coefficients. The end Ionospheric currents can then be calculated and used to predict result is the minimization of X 2 over the region where measuregeomagnetic perturbations and Joule heating. rhents were made by combining terms with different orders and degrees such that the fit of the line-of-sight velocities is the 8. Summary best in the region of data, but the total solution may be beyond We have derived a new technique for imaging the global all physical reason. For example, the degree-0 terms might convection on the basis of direct measurements of the convec- have an order-1 term with a maximum value of 500 kv, while

13 RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION 20, /lgg tdlt.... APL MODEL 01/10/lgg dl.... APL MODEL 18:00: < T_ <a 18:05: '... 4<BT<6 18:05:00 UT '... uy- 18:12:00 LIT '... By-,.. ¾... I... " -, ':... ".. : :... "'%.../ '-,.,,.. 1La:)0 m/$... ' /...:...: '":: ::.,. ' ' -.., '::: ",...;;';' -, ,.! /.'//I/..Z,', I;';: :,,," \ I i,,," - :: i i! il ' :'. / "/ :x x x! \ \ \\\ "',/ t"!['"(,i,1 ' i \ \ ".,.. '.. '.-,._ ', :...,.',,,',:o: \ \ V" L....'. "'..?,i!, o! L. "-.. "... i/. -?' :'" i \ \,,... :".-" = /,..,', ß : -... %.. / /.....*,.... "../....,, \,.,'.",.,.,., :?: -::::....,...,... 2'...?... ' L.-'""'" "! I':T. i "'" 1.. :,i 7"0'"'.... "' nt}... ß... :', mm =ea _min=ee... I ; O... ' s, = o.,... Ol IL!... ; e = 30 kv (- rain) = 01/10/1gg (L.T... APL MODEL 01/10/lgg vllt.. APL MODEL 18:12:00 - ""'... /... ' 4<BT<6, e<bt< 12 18:24:00 UT,,...-"... -,,.,. 18:18:00 UT...,..-'""'... "t'"' "'"'"'"" By- 18:18.' X 'I-:" '... /...,, '" '... " ' '"':" '- ß ":.-'" '"'" / '"".,.,,, "'-. ":,, /',.---..!..:...,. :,,..,,... /'...-' _.,,,!,...,-:'- -,-z',.. '..,-.,......, ,.,,., / //?" _.,- : ', -';,-:;...:,.,," ",,., :'.-' z/... v," w. m,./,, vo '.. i il! tit '::. "i', i L ' : L..:!.: "I I' ' ":! O "/ '/ f / I [/ \'.. i;... ' k' " " \ ' / /... r.j..,. /// /' /......%,......::,/...;,, :..:I '...,,...' \ '.. '...,, I.. '....-".." ',./ :' "',. f., " ß... : I, :;;"'...'....r.'r ß.,.. (.,,,,... '../ '/ '..- " -,"'...).;z/.. -' %"_X,"... :.... x.',,,..<.,,,,, order= 4 '"" '! '... '... +Y order '... \ lat_m = e7 lalmin-... ':.. "....,.,. l... '.V :,,,.,..._ "'" 01 I.L'T kv (- m ) /40,,, OJ I... = 45 k¾ (ø20 rain) X"/3. -' 0, / /d:'l MODEL 18:30: :36:00 UT "...11< "' '/,.., - Bz- i," /..,./' '..,.,. '", " / / a../.,?,:-:', '". ',,o / / ß i..'! i,: \ \ ',.\ - -; ':.//"-/-.../.. /.. "":"L )',//, o/,,. L_,X..//'iI.. 7.-,,...,-/,',.,,,',,.' "..,., ',.'-- 4 e. = :... ' e = 57 kv (-20 ) Plate 8. Sequence of global convection patterns obtained by fitting velocity data obtained with the SuperDARN radars on January 10, 1996, UT. The 2-min scan data have been averaged over 6-min intervals. A schematic of the IMF vector in the GSM y-z plane corresponding to each time interval is shown in the lower right-hand comer of each plot.

14 20,810 RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION 150: order = 4 X /513 = o.g 11/24/ TLT_... 11/24/ LT... APL MODEL 21:12: J... 21:12: J... 6<BT<12 21:18:00 UT '....J-... ' '.. 21:18:00 UT ,,... [...", -, ' --"'... [... ß... "v', -.-'......,..' : ".. /--...,. m,, '""..."..." '-.. ". s...-' r.-' j (--' "' s." -" '.-" '7 - '... ' "- ', ' '.'.', ' "- '. ', 7s6 :.'" 't ' '".. ':; :.' '"; :i:: '""' -. - l e ' '.,"" '""*.: ' / J '",' 9? e /..z.'. "-,. "?'... ß.,-...-.,... ß..., -.,:... ß.....,..,: L: -%,-- ""'-._.....' ':..:... ::... '.., '" ; i :,... o =... Plate 9. Plots of (left) the line-of-sight velocities and (right) the fitted global convection patterns for two 6-min intervals on November 24, 1996, that bound the period of reconfiguration of the convection due to a change in the polarity of B..

15 RUOHONIEMI AND BAKER: IMAGING OF HIGH-LATITUDE CONVECTION 20,811 the order-2 term has a maximum (negative) value of -520 kv. References In the region where them is data the result is a quite reason- Axford, W. I., and C. O. Hines, A unifying theory of high-latitude able value of the order of tens of kilovolts, but elsewhere the geophysical phenomena, Can. J. Phys., 39, , potential is utterly unphysical. Baker, K. B., and S. Wing, A new magnetic coordinate system for In order to eliminate this problem it is necessary to provide conjugate studies of high latitudes, J. Geophys. Res., 94, , some constraints on the potential in the regions lacking obser- Bargatze, L. F., D. N. Baker, R. L. McPherron, and E. W. Hones Jr., vations. Fortunately, this is quite easy to do. In essence, we Magnetic impulse response to many levels of geomagnetic activity, sample a statistical convection model over a set of points so J. Geophys. Res., 90, , that each term in the expansion of the potential is realistically Bristow, W. A., J. M. Ruohoniemi, and R. A. Greenwald, Super Dual bounded. Consider an expansion of order 7 in both degree and Auroral Radar Network observations of convection during a period of small-magnitude northward IMF, J. Geophys. Res., 103, order. The Legendre polynomial P77 has a single maximum 4061, (actually a minimum) at O'='rr/2. The coefficients for Buonsanto, M. J., S. Gonzales, X. Pi, J. M. Ruohoniemi, M. Sulzer, p77[cos(0')][a77 cos(7 ) + B77 sin(7q0] can be completely con- W. Swartz, J. Thayer, and D. N. Yuan, Radar chain study of the strained by choosing seven vectors or 14 line-of-sight velocities May 1995 storm, J. Atm. Terr. Phys., in press, from the model equally spaced in MLT at 0'= 'rr/2. Similarly, Codrescu, M. V., T. J. Fuller-Rowell, and J. C. Foster, On the importance of E-field variability for Joule heating in the high-latitude to constrain the degree-6 terms we have to consider the posi- ionosphere, Geophys. Res. Len., 22, , tions of the maximand minima of P76. For the order/degree-7 Dungey, J. W., Interplanetary magnetic field and the auroral zones, Phys. Rev. Len., 6, 47-48, Greenwald, R. A., K. B. Baker, R. A. Hutchins, and C. Hanuise, An HF phased-array radar for studying small-scale structure in the case we find that by using 13 equally spaced positions in O' from 0 to 'rr, with 14 line-of-sight values at 'rr/2, 12 at 'rr/2_+ 'rr/12, 10 at 'rr/2 _+'rr/6, etc., we can constrain the coefficients of the expansion with the least number of model input values. In the more general case of order/degree Ama x we must divide the polar cap into a grid with 2Amax + 1 values of 0'. The circle at 'rr/2 must have 2Amax line-of-sight velocities specified by the model, while the number of velocities for each of the other circles decreases by 2 for each step away from 'rr/2. The data from the statistical model are keyed to prevailing IMF conditions or, if this information is unavailable, taken from a default pattern characteristic of average (i.e., weak two-cell) convection. These preceding considerations determine the manner of sampling the model for velocity values. We now consider the assignment of uncertainties to the model velocities. It is not clear how, in general, the model predictions should be weighted relative to the measured velocities. A resolution of this question would require a detailed analysis of the validity of the statistical model as a predictor of convection. Given that this is unknown, we assign uncertainty on the basis of the minimalist principle enunciated in the text. We have described the minimum sampling of points that is required to stabilize the solution if all points are given equal weight. For the general case of unequal uncertainties, we retain the same sampling of the model for velocities but assign an uncertainty, cr m, that gives each model term in the solution of (5) a weight that is equal to the average weight of the data terms, i.e., 1 _1 1 tym 2 - ' i=1 cr' '.2 (A1) Obviously, the higher the order of the expansion, the more model vectors that must be supplied. Thus as one goes to higher orders, the results of the expansion are able to fit ever finer spatial details of the observed data, but at the same time, the result becomes ever more dependent on the model. We currently use the APL convection model, but any model could be used. high-latitude ionosphere, Radio Sci., 20, 63-79, Greenwald, R. A., et al., DARN/SuperDARN: A global view of highlatitude convection, Space Sci. Rev., 71, , Greenwald, R. A., J. M. Ruohoniemi, W. A. Bristow, G. J. Sofko, J.-P.Villain, A. Huuskinen, S. Kokubun, and L. A. Frank, Mesoscale dayside convection vortices and their relation to substorm phase, J. Geophys. Res., 101, 21,697-21,713, Hairston, M. R., and R. A. Heelis, Response time of the polar ionospheric convection pattern to changes in the north-south direction of the IMF, Geophys. Res. Lett., 22, , Heikkila, W. J., Interpretation of recent AMPTE data at the magnetopause, J. Geophys. Res., 102, , Jackson, J. D., Classical Electrodynamics, John Wiley, New York, Lu, G., et al., High-latitude ionospheric electrodynamics as determined by the assimilative mapping of ionospheric electrodynamics procedure for the conjunctive SUNDIAL/ATLAS1/GEM period of March 28-29, 1992, J. Geophys. Res., 101, 26,697-26,718, Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, 2nd ed., 994 pp., Cambridge Univ. Press, New York, Richmond, A.D., and Y. Kamide, Mapping electrodynamic features of the high-latitude ionosphere from localized observations: Technique, J. Geophys. Res., 93, , Ridley, A. J., G. Lu, C. R. Clauer, and V. O. Papitashvili, Ionospheric convection during nonsteady interplanetary magnetic field conditions, J. Geophys. Res., 102, 14,563-14,579, Rodger, A. S., and M. Pinnock, The ionospheric response to flux transfer events: The first few minutes, Ann. Geophys., 15, , Ruohoniemi, J. M., and R. A. Greenwald, Statistical patterns of highlatitude convection obtained from Goose Bay HF radar observations, J. Geophys. Res., 101, 21,743-21,763, Ruohoniemi, J. M., and R. A. Greenwald, Rates of scattering occurrence in routine HF radar observations during solar cycle maximum, Radio Sci., 32, , Ruohoniemi, J. M., R. A. Greenwald, K. B. Baker, J.-P. Villain, and M. A. McCready, Drift motions of small-scale irregularities in the high-latitude F region: An experimental comparison with plasma drift motions, J. Geophys. Res., 92, , Weimer, D. R., Models of high-latitude electric potentials derived with a least error fit of spherical harmoni coefficients, J. Geophys. Res., 100, 19,595-19,607, Acknowledgments. This work was supported by the National Science Foundation (NSF) Office of Polar Programs under NSF grant OPP and the Division of Aeronomy under NSF grant ATM We thank R. A. Greenwald and W. A. Bristow for valuable discussions. The Editor thanks Gang Lu and another referee for their assistance in evaluating this paper. K. B. Baker and J. M. Ruohoniemi, Applied Physics Laboratory, The Johns Hopkins University, Johns Hopkins Road, Laurel, MD ( kile_baker@jhuapl.edu; mike_ruohoniemi@jhuapl.edu) (Received October 9, 1997; revised April 10, 1998; accepted April 10, 1998.)