JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A1, 1005, doi: /2002ja009429, 2003

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. A1, 1005, doi: /2002ja009429, 2003 High-latitude ionospheric electric field variability and electric potential derived from DE-2 plasma drift measurements: Dependence on IMF and dipole tilt Tomoko Matsuo, 1 Arthur D. Richmond, and Kristine Hensel High Altitude Observatory, National Center for Atmospheric Research, Boulder, Colorado, USA Received 3 April 2002; revised 31 July 2001; accepted 5 September 2002; published 3 January [1] In this study the characteristics of electric field variability are investigated by using the sample standard deviations estimated from plasma drift measurements obtained during the Dynamics Explorer 2 (DE-2) mission. The spatial distribution of the standard deviation over the area poleward of 45 magnetic latitude and its climatological behavior with respect to the magnitude and orientation of the interplanetary magnetic field (IMF) and the dipole tilt angle (season) are examined. In comparison with past studies based on ground-based measurements and with results from a data assimilation model, this study quantifies the electric field variability with more complete spatial coverage and with more extensive climatological information and therefore is of importance to the problem of the global Joule heating estimation in thermospheric general circulation modeling. In general, the magnitude of the standard deviation exceeds the strength of the mean electric field in most of the polar area, especially under northward IMF conditions. In contrast to the climatological electric field, whose magnitude tends to be most intense in the polar cap, the standard deviation generally intensifies in the vicinity of the convection reversal and the cusp. Under most IMF clock angles the area of the largest electric field variability lies near the cusp; under the southward B Z condition the area extends toward the potential maximum on the dawn side and toward the region of strong sunward convection in the afternoon, while under the positive B Y condition the area extends poleward of the potential maximum on the dawn side. The analysis reveals that electric field variability varies with magnetic latitude, magnetic local time, IMF, and season in a manner distinct from that of the climatological electric field. This indicates that empirical models and data assimilation models designed to reproduce the average electric potential or the average electric fields correctly are not necessarily well-suited to represent the squared electric fields or the electric field variability correctly. INDEX TERMS: 2411 Ionosphere: Electric fields (2712); 2431 Ionosphere: Ionosphere/magnetosphere interactions (2736); 2784 Magnetospheric Physics: Solar wind/ magnetosphere interactions; 2463 Ionosphere: Plasma convection; KEYWORDS: DE-2, high-latitude ionosphere, electric field variability, electrical potential, Joule heating, climatological (background) error covariance Citation: Matsuo, T., A. D. Richmond, and K. Hensel, High-latitude ionospheric electric field variability and electric potential derived from DE-2 plasma drift measurements: Dependence on IMF and dipole tilt, J. Geophys. Res., 108(A1), 1005, doi: /2002ja009429, Also at Institute for Terrestrial and Planetary Atmospheres, State University of New York, Stony Brook, New York, USA. Copyright 2003 by the American Geophysical Union /03/2002JA Introduction [2] The electric field in the Earth s polar ionosphere as observed by ground-based radars and in situ instruments on satellites exhibits a significant amount of variability due to the dynamic nature of the interaction among the solar wind, the interplanetary magnetic field (IMF), and the terrestrial intrinsic magnetic field, as well as due to associated impulsive magnetospheric processes. There have been continuing efforts to describe the configuration of the ionospheric electric potential according to the IMF and solar wind conditions or geomagnetic activity indices with empirical or theoretical electric potential models [Foster, 1983; Foster et al., 1986; Friis-Christensen et al., 1985; Hairston and Heelis, 1990; Heelis et al., 1982; Heelis, 1984; Heppner, 1977; Heppner and Maynard, 1987; Papitashvili et al., 1994, 1999; Papitashvili and Rich, 2002; Rich and Maynard, 1989; Rich and Hairston, 1994; Ruohoniemi and Greenwald, 1996; Weimer, 1995, 1996, 2001]. [3] The configuration of the electric field in the polar ionosphere is dominated largely by the orientation and magnitude of IMF, as conceptually explained by, for example, Reiff and Burch [1985], and to a lesser extent by geomagnetic dipole tilt toward or away from from the Sun SIA 1-1

2 SIA 1-2 MATSUO ET AL.: DE-2 ELECTRIC FIELD VARIABILITY (season), in combination with the IMF orientation [Crooker and Rich, 1993]. In addition, the unloading process of the magnetosphere affects the nightside convection during high geomagnetic activity. The observational evidence for the seasonal variation of the ionospheric convection was reported by de la Beaujardière et al. [1991], Ruohoniemi and Greenwald [1995], Weimer [1995], and Papitashvili and Rich [2002], but the speculated role of the ionospheric conductivity in causing seasonal variation of the ionospheric convection is not conclusively understood. [4] In spite of the success of empirical models in capturing the realistic climatological behavior of the electric field, when it comes to representing the instantaneous state of the ionospheric electric field, even a well-tuned empirical electric field model leaves a residual of considerable magnitude, often as large as the magnitude of the modeled field [Codrescu et al., 2000; Matsuo et al., 2002]. The term electric field variability in the high-latitude ionosphere is used here to designate the component of the electric field not captured as the climatological electric fields by an empirical model like one of those cited above, that is, the residual electric field left after subtraction of the climatological fields, which itself may vary with external conditions like changes in the IMF. The standard deviation, which is almost invariably used to characterize the degree of the dispersion in a given population in statistics, serves as a summary measure of the deviations of the observations from the mean for a given set of samples; the larger these deviations, the greater the standard deviation. [5] This study is mainly motivated by the following two reasons. First of all, accurate knowledge of how electric field variability contributes to the squared electric field is crucial in the problem of the global Joule heating estimation in thermospheric general circulation modeling, as has been originally pointed out by Codrescu et al. [1995]. By taking into account the electric field variability, the estimated amount of Joule heating in the thermosphere, which is proportional to the square of the total electric field, can be significantly altered. Codrescu et al. [2000] estimated the electric field variability associated with the Millstone Hill electric field model [Foster et al., 1986], using the plasma drift velocity measurements obtained from the Millstone Hill radar for the period It has been shown by the same study that this estimated magnitude of electric field variability is significant enough to make as much contribution to the total amount of the global Joule heating as the climatological electric fields do. This effect of electric field variability has shed light on the outstanding problem of a systematic bias in the general circulation modeling of responses of the thermosphere-ionosphere system to magnetospheric inputs, which can be attributed to insufficient Joule heating estimates in the models. Secondly, a reliable quantification of the electric field variability is important for the estimation of the background error covariance for data assimilation procedures such as Assimilative Mapping of Ionospheric Electrodynamics (AMIE) technique of Richmond and Kamide [1988]. An accurate representation of the background error covariance is key to optimizing the data assimilation analysis. [6] The primary goal of the present study is to quantify the electric field variability as the sample standard deviation of the electric field with respect to magnetic latitude (mlat) and magnetic local time (MLT) over the area poleward of 45 magnetic latitude and to characterize its climatological behavior in terms of the orientation and magnitude of the IMF and dipole tilt angle. For this purpose, we use DE-2 plasma drift measurements and the climatological electric fields specified with the empirical high-latitude ionospheric electric potential model of Weimer [2001]. The ion drift measurements (0.5 or 0.25 Hz) were taken by the Retarding Potential Analyzer (RPA) [Hanson et al., 1981] and the Ion Drift Meter (IDM) [Heelis et al., 1981] on board the DE-2 satellite. The model of Weimer [2001] was derived from the electric potential, which was obtained by integrating the along-track electric field measurements, taken by the the Vector Electric Field Instrument (VEFI) [Maynard et al., 1981] also on board the DE-2 satellite. The VEFI directly measured the electric field using the double-probe technique. A second goal of this study is to quantify the seasonal and IMF variations of the electric potential derived from the DE-2 IDM/RPA data, in order to examine how features of the potential patterns and their variations relate to features of the electric field variability. [7] Foster et al. [1983] have presented the high-latitude distribution of the squared electric field as a function of geomagnetic activity and season, on the basis of the statistical analysis of the plasma drift measurements (15 s average) from the Atmospheric Explorer C (AE-C) satellite mission. The electric field variability has been shown to be dependent on the season and geomagnetic activity by Codrescu et al. [2000]. It was found to be large near the convection reversal boundary, and the largest variability was estimated to exceed 20 mv/m (400 m/s in terms of plasma velocity) just poleward of the auroral region. In addition, there have been recent attempts, by Crowley and Hackert [2001] and McHarg [2001], to estimate the electric field variability using electric fields estimated from the AMIE procedure. [8] In reality, the variability consists of a spectrum of various scales in time and space. For large spatial scales, Crowley and Hackert [2001] performed a spectrum analysis using the AMIE fields with temporal resolution of 10 min and spatial resolution of 2 mlat and 1-hour MLT (200 km 500 km) and concluded that most of the variability arises from variations with periods of less than 1 hour. For scales larger than 2 km at least up to 100 km, it is known that fluctuating electric fields prevail more in winter than in summer [e.g., Heppner, 1972; Golovchanskaya et al., 2002]. Furthermore, Heppner et al. [1993] have shown that this seasonal effect extends to at least the Hz band (20 m), using high-frequency measurements of Alternating Current (AC) electric field from the VEFI on board the DE-2 satellite. The intensity of AC electric fields falls with increasing frequency, ranging from mv/m in the 4 8 Hz band (1 km) to nearly zero in the Hz band (10 m). Golovchanskaya et al. [2002] found from the statistical analysis of electric field measurements taken by the VEFI that the fluctuating electric fields are most common for a scale of 11 km and gradually decrease with increasing scale. The analysis of how different scales of variability contribute to the total electric field variability is beyond the scope of the present study and is deferred to future studies. This spatial-scale information will also be important for the accurate repre-

3 MATSUO ET AL.: DE-2 ELECTRIC FIELD VARIABILITY SIA 1-3 sentation of the background error covariance used in data assimilation. 2. Data Set and Binning [9] The DE-2 data set used in this study includes the complete bulk ion drift velocity V, which was obtained by combining the along-track velocity from the RPA with the cross-track velocities from the IDM, whose resolution is every 2 or 4 s (14 or 28 km). The RPA essentially measured the energy spectrum of the ambient thermal ions in the spacecraft frame of reference, and the bulk ion velocity in the direction of spacecraft motion (along-track velocity) was derived from the ion number flux versus energy relation (current-voltage curve) obtained by sweeping or stepping the voltage applied to the internal retarding grids of the RPA instrument [Hanson et al., 1981]. Uncertainty in the determination of the along-track velocity is considerable because knowledge of the spacecraft potential and the relative ratios of light and heavy ion species is required, but these could only be estimated [Hanson et al., 1993; Anderson et al., 1994]. The IDM measured the angle of arrival of thermal ions with respect to the direction of spacecraft motion, determined from the ratio of the currents to the different collector segments of the IDM sensor. The cross-track velocities are determined from this angle of arrival in conjunction with the the along-track velocity derived from the RPA measurement [Heelis et al., 1981]. [10] Most of the data obtained during the DE-2 mission, between August 1981 and March 1983, are used. Prior to the statistical analysis, a careful visual inspection of the data from every satellite pass was conducted to eliminate obviously bad data points. The plasma velocity V is then combined with the model magnetic field B 0 calculated using the International Geomagnetic Reference Field (IGRF), in order to obtain the electric field E according to E = V B 0. After all the quantities are converted to modified M(110) magnetic Apex coordinates [Richmond, 1995], the along-track component (E IDM 1 ) and the crosstrack component (E RPA 2 )ofe in the horizontal plane are obtained from the IDM measurements, and from the combined RPA and IDM measurements, respectively. Furthermore, E IDM 1 is corrected for baseline offsets by subtracting a constant value such that the integral along a track between the low-latitude limits at 45 magnetic latitude, representing the potential difference between those points, vanishes. No baseline correction is applied to E RPA 2. Owing to the orbital geometry of the geographically polar-orbiting DE-2 satellite, E IDM 1 and E RPA 2 are directed mostly in the magnetic north-south and east-west directions, respectively, for magnetic latitude below 75, though not necessarily so at higher latitudes. In order to examine whether the larger measurement errors for E RPA 2 relative to E IDM 1 may produce noticeable influences on our results, we leave the electric field in these two components instead of converting to eastward and northward directions. [11] The IMF data are hourly averages from the NSSDC OMNIWeb ( composed of both Interplanetary Monitoring Platform 8 (IMP- 8) and International Sun-Earth Explorer 3 (ISEE-3) satellite measurements. Hourly IMF data and solar wind velocity and density data, also from the NSSDC OMNIWeb, are Table 1. Criteria for Binning by the IMF Clock Angle, the Angle of the IMF Vector in the GSM Y-Z Plane imf_angle, degrees a Bin Description N S 1 Northward B Z Positive B Y Southward B Z Negative B Y a imf_angle = arctan (B Y /B Z ). employed in order to sort the DE-2 data and also to invoke the electric potential model of Weimer [2001]. The 1-min Auroral Electrojet (AE) indices are obtained from the WDC- C2 Kyoto AE index service ( ac.jp/index.html). [12] All data points are binned by M(110) magneticlatitude (mlat) and magnetic-local-time (MLT). Bins are 5 wide in mlat, and MLT resolution is latitude-dependent, ranging from 1-hour MLT at the lowest latitude of 45 mlat to 8-hour at 85 mlat. Initially, the data from the Northern and Southern Hemispheres are binned separately. The data are further categorized by the IMF conditions and the dipole tilt angle. The binning criteria are shown in Table 1 for imf_angle: the angle of the IMF vector in the Geocentric Solar-Magnetospheric (GSM) Y-Z plane which is called the IMF clock angle; in Table 2 for Btrans: the magnitude of the IMF component in the GSM Y-Z plane; and in Table 3 for dipole_t: the dipole tilt angle toward the Sun in the GSM X- Z plane. The climatology according to these three parameters is studied by sorting the data (1) by imf_angle, (2) by combinations of Btrans and imf_angle, and (3) by combinations of dipole_t and imf_angle. The signs of IMF B Y and the dipole tilt are reversed for the Southern Hemisphere so that the data from both hemispheres are categorized under the equivalent geophysical conditions, which are representative of the effective IMF clock angle and dipole tilt angle for the Northern Hemisphere. We shall refer to 36.9 < dipole_t < as winter, < dipole_t < as equinox, and < dipole_t < 36.9 as summer (see Table 3). [13] The numbers of the DE-2 satellite passes selected for a given imf_angle criterion are 308 for the northward IMF case, 521 for the B Y -positive case, 330 for the the southward IMF case, and 518 for the B Y -negative case. Further sorting of the data either by Btrans or by dipole_t approximately divides the passes by three. Because the DE-2 satellite orbit precesses through local time sectors over the course of 1 year, a given geographic local time sector is sampled only during two seasons 6 months apart. Sorting the data by the dipole tilt angle affects the local time coverage more than sorting by the IMF parameters. However, a reasonable magnetic local time coverage is achieved by combining the data from both hemispheres, especially because in the Southern Hemisphere the offset of the magnetic pole from the geographic pole is larger than in the Northern Hemisphere (explained later). 3. Method 3.1. Electric Field Variability [14] First of all, the value of the climatological electric field for a given DE-2 observation is calculated by finite

4 SIA 1-4 MATSUO ET AL.: DE-2 ELECTRIC FIELD VARIABILITY Table 2. Criteria for Binning by Btrans, the Magnitude of the IMF in the GSM Y-Z Plane a Bin Description Btrans, nt 1 Small Medium qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Large 7 20 a Btrans ðb Y Þ 2 þðb Z Þ 2. differences from the electric potential specified with the model of Weimer [2001], which is invoked under the corresponding IMF, dipole tilt angle, solar wind velocity, and density conditions at the time the DE-2 measurements were taken, using the hourly IMF and solar wind data. No consideration is given to the ionospheric convection response time to IMF variations, as was carefully done by Weimer [2001] using an appropriate time averaging window applied to 5-min resolution IMF data. However, Weimer [2001] reported that the results are not sensitive to different time IMF averaging windows. When the IMF data are not available, the DE-2 observations are excluded from further statistical analysis. On the other hand, if IMF data are available but solar wind plasma data are missing, then the median values of 440 km/s and 8 cm 3 are substituted for the solar wind velocity and density parameters as the model inputs, respectively. This is justified because the model is less sensitive to these parameters than to the IMF parameters [Weimer, 2001]. Note that the AL index, an optional controlling parameter of the model to represent the influence of magnetospheric substorms, is not used in this study, except for one case (explained later). The relationship of the climatological electric fields to the total electric fields of the DE-2 observations E DE are expressed as: E DE 2¼ E IDM 2þ 1 E RPA 2; 2 E IDM 1 ¼ E W 1 þ E0 1 ; ð1þ E RPA 2 ¼ E W 2 þ E0 2 ; where E W 1 and E W 2 denote the climatological electric field, specified with the Weimer [2001] model, and E 0 1 and E 0 2 are the residual electric field components. [15] For a given selection of geophysical binning criteria from Tables 1 3, the sample standard deviation of the DE-2 electric field s m in the mth mlat/mlt bin is calculated by combining E1 0 and E 0 2 as follows: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P Nm E 0 2 P Nm 1nm E 0 2 u t 2nm n n s m ¼ þ ; ð2þ N m where E1nm 0 and E 0 2nm are the nth residual electric field values, out of N m, in the mth mlat/mlt bin. The relationship of the standard deviation s m to the climatological electric fields E W and the DE-2 electric fields E DE is expressed approximately as h RMS E DE i 2¼ h i 2þs RMS E W 2 ; ð3þ m where RMS E DE m ¼ m N m m vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P Nm E IDM 2 P Nm 1nm E RPA 2 u t 2nm n n þ ; ð4þ N m N m RMS E W m ¼ vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P Nm E W 2 P Nm 1nm E W 2 u t 2nm n n þ : ð5þ Equation (3) holds exactly if the residual field is uncorrelated with the climatological field specified with the model of Weimer [2001], which is approximately true. [16] The standard deviation s m, the root-mean-square of DE-2 electric fields RMS(E DE ) m, and the root-meansquare of climatological electric fields RMS(E W ) m, which are originally estimated independently for each hemisphere, are combined (root-mean-squared) with the estimates of the same quantities at the corresponding mlat/mlt bin from the other hemisphere in order to obtain better statistics in the final presentation with the exception of one case (explained below). The general features of combined results remain similar to the hemispherically independent results except for a few localized features. [17] In order to achieve a reasonable spatial coverage, when the data are sorted by combinations of imf_angle and dipole_t, the estimates of s m, of RMS(E DE ) m, and of RMS(E W ) m from the two hemispheres are not root-meansquared at all mlat/mlt bin locations. Instead, in case the estimate from one hemisphere is missing, the estimate from the other hemisphere is used to fill in that mlat/mlt bin Electric Potential [18] The average electric potential patterns are estimated separately for the DE-2 electric fields and the climatological electric fields by linear regression analysis of E IDM 1 and E RPA 2, and of E W 1 and E W 2, respectively, with respect to a linear combination of basis functions. The data from both hemispheres are used. The solution to the linear regression analysis is expressed in matrix form as ^b ¼ X T 1X X T y; ð6þ where X is a J K matrix which contains a set of K basis functions evaluated at J observational locations, y is a J column vector which contains the electric field data, and ^b is a K column vector which contains the least square estimates of the coefficients of the basis functions. (Superscript T indicates matrix transpose and superscript 1 denotes matrix inversion.) For the X basis functions, linear combinations of the basis functions designed for the AMIE procedure given by Richmond and Kamide [1988] are used. A total of 50 basis functions (K = 50) are constructed from the 244 basis functions (I = 244) used in the AMIE procedure using the 50 primary eigen vectors l i, k of the background error covariance matrix C u which was also developed in that Table 3. Criteria for Binning by dipole_t, the dipole Tilt Angle in the GSM X-Z Plane a Bin Description N S 1 Winter Equinox Summer N m N m dipole_t, degrees a The dipole tilt angle dipole_t is the angle from the north magnetic pole to the GSM Z axis and is positive when the north magnetic pole is tilted toward the Sun.

5 MATSUO ET AL.: DE-2 ELECTRIC FIELD VARIABILITY SIA 1-5 Figure 1. The dependence of the standard deviation s m on the IMF clock angle (imf_angle). study. This is the same set of basis functions used in the empirical orthogonal function (EOF) analysis of DE-2 electric field data by Matsuo et al. [2002]. The results are insensitive to a particular choice of the basis functions. The basis functions {X k k =1! 50} at locations j, which form the columns of matrix X in equation (6) are thus given by X k X 244 q j ; f j ¼ i l i;k!! Ei q j ; f j lj ; ð7þ where! l j denotes an unit vector in the direction of the jth electric field observation and! E j (q j, f j ) is a basis function for the electric field defined by Richmond and Kamide [1988], which are related to the basis functions i for electric potential by E! i = r i. The expression for i was given as equation (39) by Richmond and Kamide [1988], which was constructed by combining generalized associated Legendre functions at high latitudes with suitable extensions to lower latitudes. 4. Results 4.1. Electric Field Variability IMF Clock Angle (imf_angle) [19] The dependence of s m on the four imf_angle parameters (see Table 1) is shown in Figure 1, with the IMF northward case plotted at the top and with the rest of the cases plotted progressively clockwise. The maximum value

6 SIA 1-6 MATSUO ET AL.: DE-2 ELECTRIC FIELD VARIABILITY Figure 2. The dependence of the root-mean-square of the DE-2 electric fields RMS(E DE ) m on the IMF clock angle (imf_angle). The over-plotted contours show the electric potential. The contour interval is 5 kv. of s m and its mlat/mlt location are indicated at the lower right side of each plot, along with the root-mean-square value of s m above 60 mlat. (We shall refer the root-meansquare value above 60 mlat as a polar average. ) In addition, RMS(E DE ) m and RMS(E W ) m, defined by equations (4) and (5), are shown in Figures 2 and 3 respectively. In Figures 2 and 3 the over-plotted contours show the electric potential, obtained from the linear regression analysis described by equation (6), of the corresponding data. The maximum and minimum values of the estimated electric potential are shown at the upper right side of each plot. The negative gradient of this potential yields the average electric field vector, and the contours represent streamlines of average ionospheric convection. [20] Of course, the magnitude of the average electric field vector is not the same as the root-mean-square electric field defined by equations (4) and (5), and therefore the color plots in Plates 2 and 3 do not correspond to the gradients of the overplotted potentials. Only in regions where the electric field is fairly steady for the data that went into the bin average does the root-mean-square electric field magnitude approximate the magnitude of the average electric field vector. That tends to be the case in the region of strong anti-sunward convection over the polar cap. It is clearly not

7 MATSUO ET AL.: DE-2 ELECTRIC FIELD VARIABILITY SIA 1-7 Figure 3. The dependence of the root-mean-square of the climatological electric fields RMS(E W ) m on the IMF clock angle (imf_angle). The over-plotted contours show the electric potential. The contour interval is 5 kv. the case around the convection reversals where the northsouth electric field and the east-west convection vanish. (In fact, at the maximum and minimum of the average potential the magnitude of the average electric field vanishes, but the magnitudes of the electric-field samples going into the bin averages generally are not zero; it is only the vectorial average of these samples that vanishes.) [21] For all IMF clock angles the magnitude of s m dominates that of RMS(E W ) m over most of the polar region, and thus s m is similar to RMS(E DE ) m. In the area of the potential maximum and minimum as well as in the cusp region, s m becomes especially dominant relative to RMS(E W ) m.in comparison with RMS(E DE ) m, RMS(E W ) m tends to become comparable over the polar cap where the ionospheric convection is more uniform and tends to be significantly weaker in the vicinity of the convection reversals. For the northward IMF case s m and RMS(E DE ) m are strongest at magnetic latitudes higher than 80. As the IMF B Z component becomes increasingly negative, it is evident that the areas of strong s m and RMS(E DE ) m expand toward lower latitudes, while s m in the polar area weakens. For southward B Z the maximum of RMS(E W ) m is on the morning side of the polar cap, while the maxima of s m and RMS(E DE ) m lie close to the dawnside potential maximum and convection

8 SIA 1-8 MATSUO ET AL.: DE-2 ELECTRIC FIELD VARIABILITY Figure 4. The behavior of the polar average of the standard deviation s m above 60 mlat under geophysical conditions represented by combinations of Btrans and imf_angle, along with the polar average values of the root-mean-square of the DE-2 electric fields RMS(E DE ) m and the root-meansquare of the climatological electric fields RMS(E W ) m. reversal, while secondary maxima of s m, RMS(E DE ) m, and RMS(E W ) m appear in the afternoon region of strong Sunward convection. Regarding IMF B Y variations, the regions of strong s m and RMS(E DE ) m shift from the dawnside to the duskside as B Y changes sign from positive to negative. For both positive and negative B Y, RMS(E W ) m is strongest in the region of strong anti-sunward convection over the polar cap, while the maxima of s m and RMS(E DE ) m appear in the cusp area. In addition, the regions of strong s m and RMS(E DE ) m extend poleward of the dawnside potential maximum and equatorward of the duskside potential maximum for positive B Y. No sign of influences of nightside processes like substorms is apparent even in the southward IMF case. [22] The polar average of s m is larger than the polar average of RMS(E W ) m (183% for the northward IMF case, 130% for the B Y -positive case, 118% for the southward IMF case, and 136% for the B Y -negative case), and it is comparable to the polar average of RMS(E DE ) m (93% for the northward IMF case, 81% for the B Y -positive/negative cases and 77% for the southward IMF case). Comparing Figure 2 with Figure 3, we see that the root-mean-square electric field strength predicted by the model of Weimer [2001] represents from 50% to 60% of that of the DE-2 IDM/RPA electric fields, while the average cross polar cap potential drops are similar IMF Clock Angle and Magnitude (imf_angle and Btrans) [23] In Figure 4 the polar average value of s m, obtained from the data sorted by combinations of imf_angle and Btrans (see Tables 1 and 2), is shown along with the polar averages of RMS(E DE ) m and RMS(E W ) m. [24] The spatial distribution of s m for a given IMF clock angle remains similar over the whole range of Btrans, although the magnitude changes. All of the polar-average quantities intensify with increasing magnitude of Btrans and for imf_angle toward 180 (southward IMF). This behavior is consistent with the way the cross-polar-cap potential behaves with the magnitude of transverse IMF [Weimer, 1995; Burke et al., 1999]. Even though all of the polar average quantities behave in a similar way with respect to the IMF clock angle and magnitude, it is noticeable that the dependence on the clock angle is slightly less for s m than for RMS(E W ) m and RMS(E DE ) m IMF Clock Angle and Season (imf_angle and dipole_t) [25] The dipole tilt angle dependence of s m, RMS(E DE ) m, and RMS(E W ) m is examined for each of the four IMF clock angle cases, sorting the data by combinations of imf_angle and dipole_t (see Tables 1 and 3). The polar averaged quantities are shown in Figure 5, while the spatial distribution is shown in Figure 6 only for IMF B Y -positive case. The first row of Figure 6 depicts the dipole tile angle dependence of s m, while RMS(E DE ) m and RMS(E W ) m are shown in the second and third rows, respectively. The over-plotted contours show the electric potential obtained from the linear regression analysis of equation (6). [26] RMS(E W ) m exhibits little variation with season, in terms of both the polar average and the spatial distribution, as shown in Figures 5 and 6, respectively. In general, s m and RMS(E DE ) m become larger with decreasing dipole tilt angle (i.e., highest in winter and lowest in summer) and with increasingly negative IMF B Z, as indicated in terms of the polar average value in Figure 5. Under the southward IMF conditions, the polar average values of s m and RMS(E DE ) m at equinox are only marginally smaller than in winter. [27] In the winter and equinox cases the spatial distributions of s m and RMS(E DE ) m generally resemble those in the all season cases shown in Figures 1 and 2, respectively, where s m and RMS(E DE ) m are intense in the vicinity of the dawnside convection reversal and the cusp. On the other hand in summer, both s m and RMS(E DE ) m depart from the all-season case. The magnitudes of s m and RMS(E DE ) m remain strong only in the cusp region, while they significantly weaken in the convection reversal region. This

9 MATSUO ET AL.: DE-2 ELECTRIC FIELD VARIABILITY SIA 1-9 Figure 5. The behavior of the polar average of the standard deviation s m above 60 mlat under geophysical conditions represented by combinations of dipole_t and imf_angle, along with the polar average values of the root-mean-square of the DE-2 electric fields RMS(E DE ) m and the root-meansquare of the climatological electric fields RMS(E W ) m. seasonal variation in the spatial distribution of s m and RMS(E DE ) m can be seen for all but southward IMF conditions. This indicates that the variability in the cusp region is driven by a different mechanism from that in the convection reversal regions, and remains strong even in summer Seasonal Variation of Electric Potential IMF Clock Angle and Season (imf_angle and dipole_t) [28] For the purpose of examining the seasonal variation of the electric potential for a given IMF clock angle, the cross-polar cap potentials, which are obtained from the linear regression analysis (equation (6)) of the DE-2 electric fields E IDM 1 and E RPA 2 and of the climatological electric fields E W 1 and E W 2, are plotted in Figures 7a and 7b, respectively. The data are sorted by combinations of imf_angle and dipole_t (see Tables 1 and 3). [29] Although the potential drops in Figures 7a and 7b are usually quite similar, the equinox value for southward B Z in Figure 7a is considerably larger than that in Figure 7b. The dipole tilt angle dependence of the cross-polar cap potentials estimated from the IDM and RPA data does not resemble that of the polar average RMS(E DE ) m in Figure 5b. The cross-polar cap potential generally becomes large with increasingly negative IMF B Z in all seasons, most strongly so at equinox, as can be seen in Figure 7a. [30] This equinoctial peak for southward IMF is confirmed to be robust, to the extent that it remains even when excluding DE-2 data for AE greater than 1000 nt (excluding 17% of the data sorted into the equinox and southward IMF case) or Btrans greater than 10 nt (excluding 10% of the data) as well as when including only the along-track component of the electric field E IDM 1. The locations of the potential maximum and minimum are well covered by both the RPA and the IDM measurements under all the conditions defined by combinations of imf_angle and dipole_t, even though because of the way in which the DE-2 satellite orbit precesses through local time sectors over the course of 1 year, a geographic noon-midnight meridian sector is mainly sampled during equinox. On the other hand, the seasonal variation is insignificant for the cross-polar cap potentials estimated from E 1 W and E 2 W, as shown in Figure 7b. This is consistent with the results by Weimer [1995] in which the electric potentials are estimated from the VEFI measurements. Note that this strong peak is not seen even when the model of Weimer [2001] is invoked with the AL index option. The exact causes of the discrepancy between Weimer [1995] and this study are not clear and should be investigated further. [31] Regarding the asymmetry in the shape and ratio of the dawn and dusk cells, which should be most pronounced under summer and IMF B Y -positive conditions due to the overdraped lobe-cell generation and the daynight conductivity effects [Crooker and Rich, 1993], both electric potential patterns estimated from E 1 W and E 2 W and from E 1 IDM and E 2 RPA capture this feature well as shown in Figure Discussion [32] The use of the sample standard deviation as the measure of the electric field variability requires caution. First, the standard deviation is estimated from a limited number of samples. In this study the number of samples per mlat/mlt bin generally decreases with latitude, and especially at latitudes below 60 mlat the sample standard deviation becomes unreliable. Second, the standard deviation would be an ideal unbiased measure of the spread of the observations about the mean if the data were constituted of samples from a normal distribution: a symmetric distribution with well-behaved tails. In reality, histograms of the DE-2 data sometimes suggest a distribution with strong tails, and hence the standard deviation could be distorted by extreme values in the tails. Third, because the variability of the electric field consists of a whole spectrum of various

10 SIA 1-10 MATSUO ET AL.: DE-2 ELECTRIC FIELD VARIABILITY Figure 6. The dependence of the standard deviation s m on the dipole tilt angle (dipole_t) under the IMF B Y -positive case, along with the root-mean-square of the DE-2 electric fields RMS(E DE ) m and the root-mean-square of the climatological electric fields RMS(E W ) m. scales in time and space, the estimation of the standard deviation is surely susceptible to artificial factors such as the size of the mlat/mlt bin and to the way the observations are sorted over time, as has been discussed by Codrescu et al. [2000]. Therefore the generality of the quantitative estimate of the electric field variability described in this study is limited to some extent. Future statistical studies with a larger data base are necessary to settle questions such as those regarding the magnetospheric or ionospheric origins of the electric field variability.

11 MATSUO ET AL.: DE-2 ELECTRIC FIELD VARIABILITY SIA 1-11 Figure 7. The behavior of the cross polar cap potential drops obtained from the DE-2 electric fields E IDM 1 and E RPA 2 and from the climatological electric fields E W 1 and E W 2, under geophysical conditions represented by combinations of dipole_t and imf_angle. [33] The possibility of overestimation of the electric field variability owing to the observational error, which is attributed mostly to the uncertainty in RPA measurements [Anderson et al., 1994; Hanson et al., 1993], cannot be excluded. We believe that the observational error is relatively small, on the basis of the fact that the standard deviations of the alongtrack component E 1 IDM and of the cross-track component E 2 RPA are very comparable at latitudes higher than 80, as shown for the IMF B Y -positive case in Figure 8. At these latitudes both E 1 IDM and E 2 RPA are, on the average, composed of comparable contributions from the north-south electric field and east-west electric field due to the wobbling of the polar-orbiting satellite track around the geomagnetic pole over the course of a day and a year. [34] The maximum value of the electric field variability exceeds 50 mv/m and reaches up to 78 mv/m under southward IMF and winter conditions, and it is significantly larger than the estimate of 20 mv/m based on the statistical analysis of the plasma drift velocity measurements by the Millstone Hill Incoherent Scatter (IS) radar given by Codrescu et al. [2000]. At least two reasons can be pointed out for the possible underestimation of the electric field variability by Codrescu et al. [2000]. The temporal and spatial resolution of the IS radar observations (5-min and km 3 ) may not be fine enough to capture a highfrequency component of the variability, which is included in this study up to 0.5 or 0.25 Hz (14 28 km). In addition, the fact that only the line-of-sight component of the plasma drift velocity is used in the analysis of Codrescu et al. [2000] contributes to the underestimation. Related to this, we note that the estimate of the standard deviation using only one component of the electric field, shown in Figure 8, is about 70% 80% as large as that estimated using both components of the electric field, shown in Figure 1 on the right-hand side. [35] In comparison with the results of Crowley and Hackert [2001], our estimate of the electric field variability Figure 8. The standard deviation of either E IDM RPA 1 or E 2 under the IMF B Y -positive case, whose root-mean-square is approximately the middle right plot in Figure 1.

12 SIA 1-12 MATSUO ET AL.: DE-2 ELECTRIC FIELD VARIABILITY is about a factor of 3 larger. Even though the AMIE procedure attempts to capture a part of the variability, by incorporating various types of simultaneous observations into the objective analysis of the electrodynamic quantities, the coverage of the observations is never perfect and therefore the procedure is unable to reproduce more structured electric fields, which exist in reality, in data void regions. Furthermore, the AMIE procedure has limited spatial resolution owing to the finite number of basis functions it uses. For these reasons the analysis of the AMIE fields cannot take account of all of the variability which is present. The polar averages of RMS(E DE ) m and of RMS(E W ) m shown in Figures 2 and 3 suggest that the root-mean-square of climatological electric fields, which are specified with the model of Weimer [2001], are about 50% 65% as large as the root-mean-square of DE-2 electric fields. In fact, the comparison of root-mean-square values of the AMIE electric fields, based on the study by Chun et al. [2002], to those of the DE-2 electric fields indicated a similar ratio (M. G. McHarg, private communication, 2001). The fact that the range of variability estimated with data assimilation procedures is dependent on the background error covariance, which to date has been modeled only very approximately based on limited data, means that the use of the AMIE fields for estimation of the electric field variability, as has been conducted by Crowley and Hackert [2001] and McHarg [2001], requires caution. [36] The standard deviations of the electric potential were estimated by Weimer [1995] to be relatively small: 15% 18% of the corresponding polar cap potential drops. This is much smaller than the polar average of the standard deviation of the DE-2 electric field s m relative to the root-meansquare of the mean electric field RMS(E W ) m (118% 183%). As far as the part of the variability controlled by the solar wind is concerned, our use of hourly solar wind data may have prevented the model of Weimer [2001] from reflecting the realistic solar wind conditions to some extent. The electric potential by nature deemphasizes the small spatial scale variability while the electric field emphasizes it, and therefore the smoothing of small scale variability or high-frequency fluctuations in the data during fitting to a finite number of basis functions was inevitable in the studies by Weimer [1995, 2001]. This fact suggests that models designed to reproduce the electric potential correctly are not necessarily well-suited to represent the intensity of electric fields, or more specifically, the average squared electric fields and the electric field variability, correctly. A further implication of this fact for the general circulation modeling of responses of the thermosphere-ionosphere system to magnetospheric inputs is that the mean squared electric fields may be an appropriate form of the input to the energy equation in order to help overcome the problem of insufficient Joule heating estimates in the models. [37] The interpretation regarding the causes of the electric field variability is complicated because both highly fluctuating electric fields and the variability associated with the large scale electric field could yield large residual fields. The electric field variability is often relatively strong in the vicinity of the climatological convection reversals. Northsouth movement of the convection reversals will contribute to this variability, to the extent that the movement is not fully captured by the climatological model. In addition, as Golovchanskaya et al. [2002] pointed out that the strong fluctuating electric fields on the scale ranging from a few km to 100 km are typically located in the vicinity of the convection reversals, the strong electric field variability may be attributed to small-scale electric fields in these regions. Furthermore, we cannot rule out the possibility that the model of Weimer [2001] underestimates the climatological variability of the electric field, as would any statistical electric potential model that is based on a limited number of observations and that to some extent tends to smooth out small-scale features, including ones that may exist in the convection reversal regions. Unfortunately, from the analysis conducted in this study we cannot quantify how much of the variability is associated with larger versus smaller scales; to do this will require a comprehensive spectrum analysis of the electric field data. [38] Under northward IMF conditions the polar average of s m becomes particularly dominant: 183% relative to the polar average of RMS(E W ) m. When the IMF is northward, the ionospheric convection is known to be less organized [e.g., Lu et al., 1994], and therefore the climatological electric fields, which are reproduced with the model of Weimer [2001], are weaker and result in the larger ratio of the electric field variability to the mean electric field intensity. This effect is manifested also as the flatter change of s m over the IMF clock angle, in comparison with the change of RMS(E DE ) m over the IMF clock angle, as shown in Figure 4. [39] In Figures 1 and 2 the regions of the strong s m and RMS(E DE ) m do not always overlap the convection reversal regions: for southward B Z they appear equatorward of the duskside convection-reversal region, and for positive B Y they are located poleward of the dawnside convectionreversal region. It is known, in the vicinity of aurora arcs, that the north-south electric field reaches its peak value just equatorward of the arc and drops below the typical convection electric field magnitude inside the arc on the dusk side, while on the dawn side it is again weakened below the typical convection electric field magnitude inside the arc but reaches its peak value poleward of the arc, as summarized by Kamide and Baumjohann [1993]. Cumulative effects of this spatial relationship between the electric field and the auroral precipitation in the vicinity of aurora arcs may be manifested in the statistical study of the convection electric field with respect to auroral particle precipitation by Foster et al. [1986]; as pointed out by Kamide and Richmond [1987], the area of most intense precipitation lies equatorward/poleward of the strongest electric fields on the dawn/dusk side. In addition, Heelis et al. [1980] showed, based on the statistical analysis of simulataneous measurements of the particle precipitation and the plasma drift by Atmospheric Explorer that the convection reversal lies equatorward of the discrete, highly structured Boundary Plasma Sheet (BPS) precipitation zone on the duskside, while on the dawnside it lies in the middle of BPS precipitation zone and poleward of the extended Central Plasma Sheet (CPS) precipitation zone. The apparent anticorrelation of the areas of the strong conductivity and the regions of the strong s m and RMS(E DE ) m may be related to a speculated role of the large conductance in reducing the magnitude of electric field needed to maintain electric current continuity in the ionosphere.

13 MATSUO ET AL.: DE-2 ELECTRIC FIELD VARIABILITY SIA 1-13 [40] Even under southward IMF conditions, no region of the strong electric field variability is observed on the nightside, where substorm influence should be greatest. Since less than 10% of the total DE-2 satellite passes are identified as being measured during substorms [Weimer, 1999], the observations during substorms are likely outweighed by the rest of the observations. [41] The semiannual variation of geomagnetic activity, whose mechanism was first theorized by Russell and McPherron [1973], may be related to the large cross-polar cap potential under the southward IMF equinox conditions seen in Figure 7a. For the southward B Z cases, the average of IMF B Z is about 10% higher during equinox, which might be expected according to the theory of Russell and McPherron [1973]. The histogram of the AE index does suggest higher geomagnetic activity during these conditions, and a positive correlation between the AE index and the cross-polar cap potential had been established by Reiff et al. [1981] and Weimer et al. [1990] from satellite measurements; by Weimer et al. [1990] using the VEFI measurements; by Ahn et al. [1984, 1992] for equinox and solstice events, using the Kamide, Richmond, and Matsushita (KRM) algorithm [Kamide et al., 1981]; and by Richmond et al. [1990], Cooper et al. [1995], and Lu et al. [1998] for three different solstice events, using the AMIE procedure. [42] However, the generality of the seasonal and IMF clock angle variation of the cross-polar cap potential found in this study needs to be verified by further studies with larger data sets. For example, the statistical study of the Defense Meteorological Satellite Program (DMSP) data from 1993 to 1996 by Papitashvili and Rich [2002] showed that the winter cross-polar cap potentials were larger than those in equinox and summer for both hemispheres. Whether or not seasonal variation of the cross-polar cap potential depends on the solar cycle is an interesting question, as the data used by Papitashvili and Rich [2002] are from the solar minimum period in contrast to the solar maximum period during which our DE-2 data are taken. On the other hand, the solstice event study by Lu et al. [1994] found almost identical cross-polar cap potentials in both hemispheres under IMF B Z negative conditions, larger cross-polar cap potentials in the summer hemisphere during positive B Z and B Y >B Z conditions due to the enhanced lobe cell convection, and also a large cross-polar cap potential in the summer hemisphere during positive B Z and B Y <B Z conditions. This behavior is consistent with our result except for the IMF B Y positive case shown in Figure 7a. [43] In winter, the electric field variability becomes large owing to the prevailing fluctuating electric fields [e.g., Heppner, 1972; Golovchanskaya et al., 2002], which may be caused by the low conductivity in the dark hemisphere (winter) tending to require larger electric fields in order to maintain electric current continuity in the ionosphere. The polar average electric field variability is also large under equinox and IMF southward conditions in Figure 5a, associated with the larger electric potential under these conditions. Under these conditions, RMS(E DE ) m becomes almost as large as in the winter case, as seen in Figure 5b. In this case the large polar average value of RMS(E DE ) m is accompanied by a large cross-polar cap potential as seen in Figure 7a, which is suggestive of the increase in the organized ionospheric convection. The seasonal variation of the electric field variability reported by Codrescu et al. [2000], in which a large magnitude of electric field variability was found during moderate geomagnetically disturbed conditions in winter and during severely disturbed conditions in spring, could be interpreted as a manifestation of the same climatological behavior of electric field variability found in this study. Foster et al. [1983] also reported a similar seasonal variation in the hemisphere-integrated squared electric field: strongest in winter, weakest in summer, and in equinox marginally weaker than winter. 6. Conclusions [44] We have quantified the electric field variability as the sample standard deviation s m over magnetic latitude (mlat) and magnetic local time (MLT), including its dependence on IMF and season, using DE-2 plasma drift measurements and the climatological electric fields specified with the empirical electric potential model of Weimer [2001]. Despite some limitations, the standard deviation is the most common way to characterize the variability, and it can help to infer the average effect of electric field variability on the Joule heating estimation. In addition, it is directly useful for the estimation of the variances needed to help construct the background error covariance models used in data assimilation procedures such as AMIE. An accurate knowledge of electric field variability or the squared electric field is crucial in the problem of the global Joule heating estimation in thermospheric general circulation modeling, as has already been discussed by Codrescu et al. [1995, 2000], Crowley and Hackert [2001], and McHarg [2001]. [45] We conclude that empirical models and also data assimilation models designed to reproduce the average electric potential or the average electric fields correctly generally underestimate the electric field variability that is present in the DE-2 IDM/RPA data (14 28 km). Regarding general circulation modeling, a further implication of this fact is that in conjunction with the conventional use of an average electric potential model in the momentum equation to obtain the ion-drag term for the acceleration of neutral winds, the use of an appropriate model for the squared electric field in the energy equation in order to estimate the Joule heating rate correctly, may enable us to overcome the problem of insufficient Joule heating estimates in those models. [46] The electric field variability is estimated to exceed 20 mv/m above 60 mlat on average and to reach up to 78 mv/ m under southward IMF and winter conditions, which is quantitatively significantly larger than the results by Codrescu et al. [2000], Crowley and Hackert [2001], and McHarg [2001]. The polar average of the standard deviation s m is significantly larger than the polar average of the rootmean-square climatological fields RMS(E W ) m (183% for the northward IMF case, 130% for the B Y -positive case, 118% for the southward IMF case, and 136% for the B Y - negative case). [47] The electric field variability is shown to depend on the IMF clock angle imf_angle and the transverse IMF magnitude Btrans. Under most IMF clock angles the area of the largest electric field variability lies near the cusp. Under the southward B Z condition the area of large electric field variability extends toward the potential maximum on