Modeling of the global distribution of ionospheric electric fields based on realistic maps of field-aligned currents

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 111,, doi: /2005ja011465, 2006 Modeling of the global distribution of ionospheric electric fields based on realistic maps of field-aligned currents Renata Lukianova 1,2 and Freddy Christiansen 3 Received 10 October 2005; revised 6 December 2005; accepted 19 December 2005; published 17 March [1] A new approach for modeling the global distribution of ionospheric electric potentials utilizing high-precision maps of FACs derived from measurements by the Ørsted and Champ satellites as input to a comprehensive numerical scheme is presented. The boundary conditions provide a correct treatment of the asymmetry of conductivity and sources of electric potential between the northern and southern hemispheres. On the basis of numerical simulation the basic convection patterns developed simultaneously in both hemispheres for equinox and summer/winter solstices are obtained. A rather complicated dependence of the convection patterns on season linked with the sign of IMF B Y is found. In particular, the combinations of B Y > 0/summer and B Y < 0/winter produce the highest circular flow around the pole in comparison with the combinations of B Y < 0/summer and B Y > 0/winter. The model predicts that the summer cross-polar potentials are smaller than the winter potentials. The value of the ratio depends on the combination of season/imf B Y sign. The ratio is found to be greater for the combination of B Y > 0/southern summer and B Y < 0/northern summer. The smallest value is obtained for the combination of B Y < 0/southern summer and B Y > 0/northern summer under northward IMF conditions. At middle latitudes the main features of the MLT-profile of the westward and equatorward electric field components are reproduced. The model predicts that during solstice the equatorward component of the midlatitude electric field is negative at all local times for B Y < 0 and positive for B Y >0. Citation: Lukianova, R., and F. Christiansen (2006), Modeling of the global distribution of ionospheric electric fields based on realistic maps of field-aligned currents, J. Geophys. Res., 111,, doi: /2005ja Introduction [2] It has long been a goal of high-latitude experiments and modeling to describe the entire ionospheric convection system. Large-scale convection maps have been obtained by averaging data over time and/or space. Ground-based instruments usually provide good temporal but poor spatial coverage. For satellites, many passes are required before the whole polar region is covered. Heppner and Maynard [1987] synthesized a sketched convection pattern looking for characteristic signatures in the electric field from each pass of DE-2. Rich and Hairston [1994] used a spatial binning approach on several years of DMSP measurements. From chains of magnetometers data fitted to the IMF conditions using linear regression, Papitashvili et al. [1994] produced electric potential patterns. The AMIE procedure [Richmond and Kamide, 1988] is a comprehensive approach combining observations from multiple instruments simultaneously, which has the advantage of providing a snapshot of the convection pattern although 1 Department of Physics, St. Petersburg State University, St. Petersburg, Russia. 2 Also at Arctic and Antarctic Research Institute, St. Petersburg, Russia. 3 Danish National Space Center, Copenhagen, Denmark. Copyright 2006 by the American Geophysical Union /06/2005JA the method depends very much on the availability of coincident data from multiple locations. AMIE results are widely used in current research. Recently, a renewed interest in the generation of global convection models has showed up. Papitashvili and Rich [2002] extended the previous results to construct a new model in which the electric potential are scaled by DMSP satellite observations. Weimer [1995, 2005] used a spherical harmonic expansion to fit a pattern to sets of electric potentials from DE-2 binned by IMF angle and magnitude. Ruohoniemi and Greenwald [1996, 2005] averaged Super- DARN radar data and employed Laplace s equation to extrapolate the mapping. [3] The majority of existing convection models are statistical or semiempirical ones. Pure numerical models are less widely used. Two reasons for the lesser attention paid to numerical modeling of the ionospheric convection can be mentioned. First, there has until recently been a lack of realistic maps of Birkeland field-aligned currents (FAC) distribution that serve as a source of the electric potential. Second, there has been an absence of appropriate algorithms to utilize these maps. In order to calculate the electric potential pattern within the northern or southern hemispheres, most authors have used the total distribution of FACs flowing above the ionosphere in one hemisphere only. Mathematically, it implies the statement of a Dirichlet or Neumann boundary condition on the equatorial boundary of 1of11

2 Figure 1. Sketch illustrating the statement of boundary value problem for the ionospheric shells. Arrows represent the geomagnetic field lines. Calculation area is shaded. the high-latitude region. The effect of electrical coupling between hemispheres is generally neglected. However, an asymmetry in the interhemispheric distribution of FACs and/ or conductivity is a common feature of ionospheric electrodynamics. The IMF B Y component produces antisymmetric convection between the northern and southern polar caps, known as the Svalgaard-Mansurov effect. The IMF B Y is also responsible for an interhemispheric asymmetry in the FAC distribution with respect to the noon meridian [Taguchi et al., 1993; Papitashvili et al., 2002]. Additionally, significant difference in the northern and southern cap potential drops has been observed under jb Z /B Y j < 1 conditions [Lu et al., 1994], as well as under seasonal conditions of winter in one hemisphere and summer in the other [Papitashvili and Rich, 2002]. Thus a mutual influence of the opposite hemispheres and a penetration of the electric field to middle latitudes may be quite significant. [4] Up to now, none of the ionospheric convection models has utilized direct measurements of FACs as input. This implies that the main link of magnetosphere-ionosphere coupling has not been taken explicitly into account. Since the early results of Iijima and Potemra [1976], no comprehensive studies of FAC distributions were carried out, until the emergence of a new generation of low-orbiting satellites with high-precision magnetometers (Ørsted, Champ) and the low-precision multiple Iridium satellites. These spacecrafts are providing an enormous database of magnetic field variations above the ionosphere, resulting in the appearance of qualitatively new FAC models [Waters et al., 2001; Papitashvili et al., 2002] parameterized by the IMF direction/strength, by season, and by hemisphere. Currently, the technique of space measurements of FACs is developing rapidly. This motivates us to attempt a new approach for modeling the global distribution of the ionospheric electric potential utilizing the high-precision maps of FACs derived from measurements by modern constellation of satellites as an input for a comprehensive numerical scheme. The boundary conditions provide a correct treatment of the asymmetry of conductivity and sources of electric potential between hemispheres. Modeling the ionospheric electric fields in their interhemispheric conjugation allows us to obtain their variations at lower latitudes. Since the FAC model is fully parameterized by the IMF conditions, by season, and by hemisphere, the same parameterization can be further applied for the convection model. The modeled convection patterns are expected to be in accordance with ground and satellite observations of the ionospheric electric field. The validation of this can be provided by a comparison with results from existing models. [5] The outline of the paper is as follows. In the second section, we describe the model including the statement of the problem, the boundary conditions, and the algorithm. The modeling results are presented in the third section. We calculate the global electric potential distribution under different IMF conditions for equinox and solstice. In this section we obtain the basic convection patterns in both northern and southern polar region, and the results are compared to other models. We also discuss the electric fields located below the polar cap boundary. The final section is a summary of the modeling results. 2. Model Description [6] For an open model of the magnetosphere, electrical conjugation between polar cap ionospheres of northern and southern hemispheres via the geomagnetic field is negligible. Outside of the polar caps, however, this conjugation is important. The equation of electric current continuity: div J ¼ j 00 sin c; where J is the height-integrated horizontal ionospheric current, j 00 is the field-aligned current, and c is the magnetic inclination, is solved on a grid covering the twodimensional ionospheric shell with specified heightintegrated conductivity in spherical coordinate system (q is the geomagnetic colatitude, j is the geomagnetic longitude). Figure 1 gives a sketch of the ionospheric shell. According to the statement of the boundary value problem and the algorithm developed by Lukianova et al. [1997], we divide the ionospheric shell into three subregions (referred to as a = 1, 2, and 3) as follows. Northern (a = 1) and southern (a = 2) polar caps with boundaries at the colatitudes q 1 and q 2 = p q 1, respectively, are uncoupled with respect to electric potential. On the remaining portion of the sphere (a = 3) the Earth s closed magnetic field lines are taken to be equipotential for conjugate points on opposite hemispheres. This allows us to solve equation (1) on each half of the low-latitude subregion (a = 3). For definiteness, let it be the northern half from the polar boundary at q 1 to a specified equator boundary at q 3 (this area is denoted by N in the sketch). The boundary q 3 is set latitudinally away from the equator to avoid a division by zero in the expression for the components of conductivity tensor. The sum of conductivities and sources at conjugate points of N and S is used in every point. Further we omit the sign N for a = 3 subregion and obtain the following boundary value problem: ð1þ div J 1 ¼ j 1 for q q 1 ð2þ div J 2 ¼ j 2 for p q 1 q < p ð3þ div J 3 ¼ j 3 for q 1 q q 3 ð4þ 2of11

3 where J a is the height-integrated horizontal ionospheric current and j a is the radial component of FACs in the corresponding subregions. Three subregions (a = 1, 2, 3) are connected by the boundary conditions as follows: U 1 ðq 1 ; j Þ ¼ U 3 ðq 1 ; jþ ¼ U 2 ðq 2 ; jþ ð5þ J 1 ðq 1 ; jþ J 3 ðq 1 ; jþ ¼ J 2 ðq 2 ; jþ ð6þ J 3 ðq 3 ; jþ ¼ 0 ð7þ where U a is the ionospheric electric potential in the corresponding subregions. [7] Boundary condition (5) means that no discontinuity in the electric potential across the boundary of the polar cap and between the boundaries of opposite caps. Condition (6) means that any possible discontinuities of the longitudinal components of ionospheric currents across the boundaries of the northern and southern caps compensate each other through the currents leaking across these boundaries into the lower latitudes. Condition (7) means the absence of current across the equator. The quantities U a and J a are connected by Ohm s law: J a ¼ S a ð ru a Þ ð8þ where S a is the height-integrated conductivity tensor including both Hall and Pedersen conductivity. [8] Equations (2) (7) are solved numerically using an iteration technique. To obtain (2) (7) in iterative form, we use the term: Za ðnþ1þ ¼ Ua ðnþ1þ Ua ðnþ =t ðnþ1þ ð9þ where n is the number of iteration, t (n+1) is the relaxation parameter obtained by method adopted from Vladimirov (n) (n+1) [1981], and U a and U a are the electric potential distribution obtained at iteration n and (n+1), respectively. [9] Following the recommendation of Samarsky and Nikolaev [1978], we include into the left side of equations (2) (4) a regularizer R, specifically, the angular component of the Laplace operator, R divð rþ D ð10þ This is useful because R admits the separation of variables making the solution of the problem (2) (7) easier. Now in terms of Z a equations (2) (4) have the form: div rza ðnþ1þ þ div J ðþ a n ¼ j a ð11þ The boundary condition (5) is satisfied in each iteration step. In terms of Z a, it has the form (the vertical line means the boundary at corresponding q a ): Z ðnþ1þ 1 Z ðnþ1þ 1 Z ðnþ1þ ¼ q1 q2 2 Z ðnþ1þ ¼ q1 q3 3 U ðnþ 2 U ðþ n 3 U ðþ n q2 1 1 q1 U ðþ n q1 q1 ð Þ ð12aþ =t nþ1 ð Þ ð12bþ =t nþ1 The iterative counterparts of boundary conditions (6) (7) ðnþ1þ ðnþ1þ ðnþ1þ 3 ¼ J @q 1 J ðþ n 2 J ðþ n 3 q1 q2 q3 q1 q2 ðnþ1þ ¼ J ðþ n 3 q3 q3 ð13þ ð14þ It is obvious, if U a (n)! U a (n+1)! U* a as n!1, U* a is a solution of (2) (7). It is also obvious that if the iteration process converges (Z a (n+1)! 0) the solution of (11) (14) is equal to the solution of (2) (7). We can express the solution of (11) as a Fourier series: Za ðnþ1þ ¼ X k¼2m C k¼ 2m akðþ q e ikj ð15þ where C ak (q) are the complex-valued coefficients depending solely on the colatitude. Taking into account (8), by a finite difference scheme over a two-dimensional grid (q, j), we obtain an approximation for div J a and J a in (11) and (13) (14). Substitution of (15) into (11) (14) gives the onedimensional boundary value problem for Fourier coefficients. The corresponding three systems of linear algebraic equations are solved by the sweep method (Gauss method for the system of equations with three-diagonal matrix). In order to connect the subregions a = 1, 2, 3 the system of six equations containing a pair of boundary grid points from each of them is singled out and solved separately. Finally, we restore Z a (n+1) by inverse Fourier transform and obtain U a (n+1). Having the potential distribution we can calculate the zonal and meridional components of the electric field strength as follows: E q E j ¼ 1= sin ð16þ ð17þ The described technique needs the distribution of ionospheric conductivity. Both the solar UV conductance and the auroral precipitation-enhanced conductance contribute to S a. The solar UV contribution can be calculated from the 10.7 cm solar radio flux proxy and the zenith angle. Seasonal and diurnal variations are taken into account using the estimates by Robinson and Vondrak [1984]. The Kp-dependent model of Hardy et al. [1987] is used to calculate the auroral contribution. The auroral conductivity is combined with the solar radiation conductivity as the square root of the sum of the squares. Note that the effective numerical scheme allows a rather steep gradient of the conductivity and sources. Depending on the conductivity and FAC distribution, the solution (2) (7) gives the potential distribution. In particular, it can be substantially different but not independent in the two hemispheres. 3. Calculations 3.1. Patterns of Ionospheric Potentials [10] Recently, a new model of FACs has been derived from magnetic field measurements from the Ørsted and Champ satellites parameterized by IMF strength and direc- 3of11

4 Table 1. Numbers of the IMF Clock-Angle Orientation IMF B Z <0 =0 >0 IMF B Y <0 =0 >0 <0 =0 >0 <0 =0 >0 Number tion for summer, winter and equinox for both hemispheres [Papitashvili et al., 2002]. We use these FAC patterns as input for calculating of the global distribution of ionospheric electric potentials. In this paper we present convection patterns modeled for the IMF B T =(B Z 2 +B Y 2 ) 1/2 =5nT and eight IMF clock-angle orientation (Table 1) under conditions of December solstice and March equinox. For the calculation, the boundaries q 1, q 2 and the equatorial boundary q 3 were set at 30 and 60 of geomagnetic colatitude, respectively. The coordinate grid steps were Dq = 1 and Dj = (360/128). Average values of the parameters controlling the solar part of conductivity, specifically F 10.7 = 120, UT = 12, and day = 80 (equinox), day = 355 (solstice) were used. Taking into account the variation of average Kp with B Z, we choose Kp = 2 for B Z 0 and Kp = 3 for B Z <0. [11] First, we consider winter solstice conditions. Figure 2 gives the convection patterns obtained in the northern winter polar region. Figure 3 gives the result for the southern summer polar region. The plots in paired Figures 2 and 3 are arranged as follows. The first, second, and third rows present the maps of electric potential obtained for B Z >0, B Z = 0 and B Z < 0, respectively. The first, second, and third plots in each row present the maps obtained for B Y < 0, B Y = 0, and B Y > 0, respectively. Such an organization of the plots according to the IMF clock-angle in GSM Y-Z plane was used in previous works [e.g., Papitashvili et al., 2002; Weimer, 2005] For easy comparison we organize the plots in the same manner. One can see that the solstice convection patterns from Figures 2 and 3 show a significant seasonal effect. First, the convection cells in the winter hemisphere have more voltage than corresponding cells in the summer hemisphere. Also, the shape of the corresponding cells from the opposite polar caps is recog- Figure 2. Isolines of the electric potential calculated for December solstice in the northern winter hemisphere for nine IMF clock-angle orientations with contours every 5 kv (first and second rows) and 10 kv (third row). Minimum and maximum potentials are shown by number under each plot. Positive and negative potential are marked by solid and dashed lines, respectively. Noon is at the top, and dawn is to the right in each polar plot. Circles are drawn every 20 in magnetic latitude down to 50. 4of11

5 Figure 3. The same as Figure 2, but in the southern summer hemisphere. nizably different even for the same IMF orientation. A change of the IMF B Y sign does not produce a simple mirror antisymmetric change in convection patterns within the same hemisphere. Also, the paired patterns from opposite hemispheres, specifically the patterns for B Y > 0/northern and B Y < 0/southern (B Y < 0/northern and B Y > 0/southern) do not copy each other. It is worth to underline the following features. For the IMF = 0 pattern, the winter dusk cell dominates while in summer the positive dusk and the negative dawn cell are more symmetric. For the IMF B Z > 0 patterns, the winter dusk cell generally dominates irrespective of the IMF B Y sign. However, in the dayside near-pole region one can identify an isolated convection cell extended from the prenoon (B Y < 0) or postnoon (B Y >0) sector. During southern summer the convection vortex surrounds the pole. The ionospheric plasma flows clockwise or anticlockwise around the pole depending on the IMF B Y sign. For B Y > 0 the dawn cell strongly dominates while the dusk cell almost disappears. For B Y = 0, the convection system is marginal in winter cap and is barely structured in summer cap. The IMF B Z < 0 patterns from both hemispheres show a customary two-cell convection system slightly distorted according to the IMF B Y effect. [12] Figures 4 and 5 give the result of our calculation for equinox in the northern and southern hemispheres, respectively. One can see that the two-cell convection system is typical for all IMF orientations, although under northward IMF conditions an additional B Y -dependent vortex is developed near local noon. In contrast to solstice conditions, during equinox the B Y effect produces an antisymmetric distortion of the convection cells in the opposite hemispheres. Without any influence of the B Y component the convection patterns display interhemispheric symmetry. The peculiarity of the IMF B Z > 0 patterns is that the dusk cell always extends to the dawnside across the pole. Under southward IMF conditions a two-cell system with extended dusk vortex is developed. [13] From Figures 2 5 one can see that the patterns obtained under different IMF and seasonal conditions are in agreement with the commonly accepted understanding of large-scale convection. They also show some smallerscale but notable peculiarities caused by the combined action of different factors. Also, the convection vortices are not confined within the high-latitude region. The flow extends to lower latitudes where the electric potential is determined by the mutual electrodynamic influence 5of11

6 Figure 4. The same as Figure 2, but for the equinox in the northern hemisphere. of the opposite hemispheres. Indeed, below the boundary between the regions of open and closed geomagnetic field lines (denoted as q 1 and q 2 ) the electric potential isolines show some kind of fracture. The features of penetrated electric field will be considered in more details in section Comparison With Other Models [14] Convection patterns calculated for both northern and southern hemispheres show all the main features predicted by previous statistical models. Present modeling was undertaken for different seasons and for the test IMF/SW conditions, specifically the IMF B T = 5 nt, n = 5cm 3, V = 400 km/s. A quantitative comparison for one of the most representative parameters is given in Figure 6. This figure shows the voltage in the foci of the dawn positive and dusk negative convection cells for eight the IMF clock-angle orientations (see Table 1). We compare the voltage obtained from present calculation with the voltage predicted by DMSP and DISM models of Papitashvili and Rich [2002] and DE2 model of Weimer [1995]. From Figure 6 one can see that the voltage predicted by the various models responds to the IMF rotation in the same manner. The largest and the smallest values are achieved under the IMF B Z < 0, B Y = 0 and B Z > 0, B Y = 0 conditions, respectively. Some greater uncertainty is in the voltage of the southern dawn cell. The spread in results from different models increases in this case. In particular, one can suspect that during solstice the present model slightly underestimates the voltage. During equinox the southern dawn cell voltage shows too slight variations with the IMF rotation. However, overall the present model gives reasonable values of the voltage in the dawn and dusk convection cells. [15] Regarding the cross-polar potential it is interesting to estimate the seasonal and the IMF clockangle effect. Earlier, Papitashvili and Rich [2002] obtained the ratio 1.2 between the winter and summer cross-polar potential. Christiansen et al. [2002] obtained the summer/winter ratio 1.5 for the R1 FAC. The seasonal ratio for each IMF clock-angle (Table 1) derived from our model is presented in Figure 7. The upper panel shows the ratio between the northern winter and southern summer crosspolar potential (DU W and DU S, respectively) calculated under December solstice conditions. The second panel shows the same parameter for southern winter and northern summer during June solstice (corresponding convection patterns are not shown). One can see that the winter 6of11

7 Figure 5. The same as Figure 2, but for the equinox in the southern hemisphere. potential drop regularly exceeds the summer value. The ratio varies significantly from 1.0 to 1.7 with the average value of 1.3 for both the northern and southern winter. This is a bit larger compared to the results of Papitashvili and Rich [2002] who attributed the winter/summer potential difference mostly to the seasonal dependence of FACs. Figure 7 also shows that in the northern cap, the value of DU W /DU S is greater when the IMF B Y > 0 while in the southern cap this ratio is greater when the IMF B Y <0. The effect is more clearly seen under conditions of positive/zero B Z component. This is possibly caused by the dependence of FACs on the sign of B Y. Although the FAC distribution obtained in [Papitashvili et al., 2002] shows a general mirror asymmetry related to B Y polarity there is some difference in details especially for northward IMF. On the other hand, because of conductivity gradients resulting in an extension of the dusk convection cell, this is favorable for the strengthening of convection in the northern polar cap when the IMF B Y > 0, or in the southern polar cap when the IMF B Y < 0. The combined effect of seasonal and B Y dependence of FAC can cause changes in DU W /DU S. A similar effect was recently detected by Ruohoniemi and Greenwald [2005]. These results show greater variability of convection patterns than a traditional scheme Electric Field at Lower Latitudes [16] As it was pointed out by Weimer [2005], one of the unresolved problems of ionospheric modeling is the determination of the electric fields penetrating to middle latitudes, since this field is located below the outer boundary of the existed models. Although this aspect mostly concerns the electrodynamics of geomagnetic storms, the seasonal asymmetry in conductivity as well as the seasonal and the IMF dependence of FACs affects the distribution of the electric potential in the region of closed geomagnetic field lines. In our model we can calculate the electric field as low in latitude as from the equator. In this section we present the variations of zonal and meridional component of the electric field that determines the plasma motion along the latitude and longitude, respectively, obtained from the patterns considered above. The westward and equatorward electric field component was calculated. First, we focus on the seasonal effect and present the electric field variations at high and middle latitudes obtained for equinox and northern winter. To exclude the asymmetry caused by the B Y effect, 7of11

8 geomagnetic field lines where its behavior is controlled by the electric potential distribution in the opposite polar caps. As expected, the electric field decays more quickly during the day than at night. This effect is clearly seen during both equinox and solstice. The notable feature is that during northern winter, a strong winter electric field decays more rapidly with latitude than the weaker summer field. As a result, the electric field from summer high latitudes and the subauroral electric field from both hemispheres have comparable amplitudes. Figure 9 demonstrates with better resolution the profile of westward and equatorward components at middle latitudes (q =45 ). It is seen that the corresponding curves keep their form during both seasons. Figure 9 indicates that the electric fields are mostly eastward during the day, westward and poleward at night, equatorward near dawn. Westward and equatorward components peak just before dawn. The poleward electric field is strongest on the nightside. [17] When the seasonal interhemispheric asymmetry in conductivity and in FAC intensity is amplified with the B Y related redistribution of FACs, the plasma flow at middle latitude is also modified. Specifically, the flow is strongly affected by the corresponding summer polar cap convection pattern. Returning to Figures 2 and 3, one can see that under northward IMF conditions the B Y -related ionospheric plasma flows have the opposite direction in the northern winter and southern summer polar caps (e.g., B Y < 0 produces eastward (westward) flow in the northern (southern) polar cap). Although the most intensive vortices are confined within high-latitude regions, a recognizable Figure 6. The electric potential in the foci of the dawn positive and dusk negative convection cells for eight the IMF clock-angle orientation according Table 1 under December solstice (a) and March equinox (b) conditions. The upper and lower plot in panels (a) and (b) represent the northern and southern hemispheres, respectively. Results are represented as follows: the present model (thick line with squares), DMSP model (thin line with circles), IZMEM/ DMSP model (dotted line with triangles), DE2 model (dashed line with diamonds). the IMF conditions of B Z <0,B Y = 0 were chosen. The upper panel of Figure 8 shows the westward component in both polar caps (q = 15 ) and just below the boundary separating the regions of open and closed field lines (q = 30 ). The first and second plot in the panel gives the result for March and December, respectively. The lower panel of Figure 8, organized in the same manner, shows the equatorward component. Figure 8 indicates that both components effectively penetrate to the region of closed Figure 7. Histogram of the ratio between the winter and summer cross-polar potential for eight the IMF clock-angle under December (upper panel) and June (lower panel) solstice conditions. 8of11

9 Corresponding high-latitude convection patterns were given in the first row of Figures 2 3. From Figure 10 one can see that the behavior of the westward component which determines meridional plasma flow is similar regarding to B Y polarity. However, equatorward component which determines zonal flow is negative for B Y < 0 and positive for B Y > 0 at all local times. That implies opposite directions of plasma circulation at middle latitudes. For B Y <0(B Y >0) the vortex with clockwise (anticlockwise) flow is extended from the southern summer polar cap to the middle latitudes of the northern winter hemisphere. This result illustrates nicely that the mutual influence of opposite hemispheres can modify the global convection. 4. Discussion and Conclusion [18] We have performed numerical modeling of the global distribution of the ionospheric electric field. A new approach is to utilize realistic maps of FACs obtained from Ørsted and Champ satellites as an input for the calculation of convection systems which are developed simultaneously in both hemispheres. From the conductivity side, both the solar contribution and auroral precipitation contribution are included. The convection patterns we have obtained reproduce all common features inherent in statistical models. Besides that, some new remarkable features are seen. [19] Very recently, Ruohoniemi and Greenwald [2005] reported a rather complicated dependence of the convection patterns on season. Analyzing SuperDARN data, these authors found it necessary to link season with the sign of IMF B Y to fully characterize the dependence. In particular, Figure 8. Westward component of the electric field in the northern and southern polar caps (q = 15 ), and at subauroral latitudes (q = 30 ) for the equinox and northern winter (upper panel). The same for equatorward component (lower panel). portion of the electric field penetrates to middle latitudes. The electrodynamic coupling of opposite hemispheres shows itself in an expansion of the dominating direction of plasma flow from summer to winter hemisphere. To demonstrate this effect, in Figure 10 both components of midlatitude electric field (q =45 ) are presented. Upper and lower panels give the results for IMF B Y < 0 and B Y > 0, respectively. Figure 9. Westward and equatorward components of the electric field at middle latitudes (q = 45 ) for the equinox and northern winter. 9of11

10 Figure 10. Westward and equatorward components of the electric field at middle latitudes (q = 45 ) during northern winter under conditions of the IMF B Y < 0 (upper panel) and B Y > 0 (lower panel). the combinations of B Y > 0/summer and B Y < 0/winter produce the most circular flow around the pole in comparison with the combinations of B Y < 0/summer and B Y > 0/winter. In the frame of our model, the majority of the effects described by Ruohoniemi and Greenwald [2005] are nicely reproduced. An inspection of the B Z > 0 patterns of Figures 2 and 3 show that the circumpolar vortex is more pronounced in summer. The B Y > 0/summer conditions are the most favorable for the development of one-cell convection pattern in which the dawn cell dominates. There is no the equivalent response of the dusk cell with respect to B Y < 0. The pattern of B Y < 0/winter that is paired to B Y > 0/summer regarding to B Y effect, shows a tendency for the development of an isolated vortex of the dawn cell near noon. These peculiarities imply a greater variability in the convection cells associated with the combined influence of both the seasonal and IMF factors. Further investigation of hemispheric asymmetries is needed. [20] Our calculation of the cross-polar potential drop for the equinox, winter solstice, and summer solstice under different IMF conditions give the following results. During the equinox the northern and southern potential drops are found to be practically equal. During solstice the winter cross-polar potential (DU W ) drop regularly exceeds the summer one (DU S ), but the ratio between these values depends on the IMF conditions. There remains some disagreement between models regarding the value of cross-polar potential drop in northern and southern hemispheres. In particular, the models of Weimer [1995] and Ruohoniemi and Greenwald [2005] give an increase of potential drop from winter to summer. However, our result is generally consistent with the result of Papitashvili and Rich [2002]. These authors described an overall decrease of 15% in potential drop in passing from winter to summer. The effect was mostly attributed to the seasonal dependence of FACs that changes the topological properties of the dayside magnetopause. At the same time, our results do not contradict to the finding of Ruohoniemi and Greenwald [2005] pointed out that B Y < 0 conditions are favorable for an increase of DU S. Under B Y > 0 conditions the value of DU S was found to be smaller. Convection patterns from the first row of Figure 3 show the same regularity. More systematically, though more indirectly, this regularity is obtained from variations of the ratio DU W /DU S. To investigate the combined seasonal/imf effect, we examined the dependence of DU W /DU S on the IMF clock-angle rotation. The ratio is found to be greater for the combination of B Y > 0/southern summer and B Y < 0/northern summer. The smallest value of DU W /DU S is obtained for the combination of B Y < 0/southern summer and B Y > 0/northern summer (northward IMF). In other words, in the first two cases the value of the potential drop in the winter polar cap exceeds that of the summer polar cap more than in the last two cases. Because we consider the winter and summer hemispheres in their conjugation, the obtained regularity can be of the same nature as an increase of DU S for B Y < 0 and thus can be attributed to merging site asymmetries [Crooker, 1992]. [21] Convection patterns presented in Figures 2 5 are confined within 50 CGM latitude. Actual outer boundary of the region where we calculate the electric potential distribution is set at 30 CGM latitude. Taking into account the interhemispheric electrodynamic coupling allows us to simulate the behavior of the meridional and zonal components of the electric field at middle latitudes. Calculations give the following results. During equinox at middle latitudes the electric fields are westward at night and near dawn, mostly eastward during the day, poleward at night and near dusk, and equatorward near dawn. Westward and equatorward components are peaked near dawn. Poleward electric field is strongest on the nightside. The obtained variations are in good agreement with observation and modeling. Note that the MLT-profile of the westward and equatorward components obtained from the present model is similar to the variations derived from a Rise Convection Model [e.g., Fejer and Emmert, 2003], providing an independent check of our model. Examination of the electric field during solstice shows that although the electric field is stronger in the winter polar cap, it is mostly confined within high latitudes. In the summer polar cap and at middle latitudes the electric field has comparable amplitudes, implying a slower spatial decay. A combined influence of the seasonal and IMF asymmetry reinforces the global asymmetry in electric potential distribution. The simulation shows that during solstice the equatorward component of the mid-latitude electric field is negative at all local times for B Y < 0 and positive for B Y > 0. This component determines the zonal component of ionospheric plasma flow. Thus the vortex with clockwise (anticlockwise) flow can occupy the majority of the globe, although to our present knowledge there are yet no direct observations supporting this prediction. 10 of 11

11 [22] Finally, we would like to mention two key elements of the proposed model in the context of further work. First, it can utilize high-precision maps of FACs. We believe that further development of direct measurements of FACs will improve the accuracy of the ionospheric electric field modeling based on realistic FAC distribution. In particular, better understanding of conductivity variations in relation to FACs is needed. Second, taking into account the electrodynamic coupling of the opposite hemispheres, the model can handle the electric field far below the auroral latitudes. It allows a simulation of the electric field disturbances that originate at the polar regions but cover a broad range of latitudes in both hemispheres. [23] Acknowledgments. Work of RL was partly supported by the NATO grant PST.CLG We appreciate discussions with V. Pilipenko. [24] Arthur Richmond thanks Vladimir Papitashvili and Colin Waters for their assistance in evaluating this paper. References Christiansen, F., V. O. Papitashvili, and T. Neubert (2002), Seasonal variations of high-latitude field-aligned current system inferred from Ørsted and Magsat observations, J. Geophys. Res., 107(A2), 1029, doi: / 2001JA Crooker, N. (1992), Reverse convection, J. Geophys. Res., 97, 19,363. Fejer, B. G., and J. T. Emmert (2003), Low-latitude ionospheric disturbance electric field effects during the recovery phase of the October 1998 magnetic storm, J. Geophys. Res., 108(A12), 1454, doi: / 2003JA Hardy, D. A., M. S. Gussenhoven, R. Raistrick, and W. J. McNeil (1987), Statistical and functional representation of the pattern of auroral energy flux, number flux and conductivity, J. Geophys. Res., 92, 12,275. Heppner, J. P., and N. C. Maynard (1987), Empirical high-latitude electric field model, J. Geophys. Res., 92, Iijima, T., and T. A. Potemra (1976), Large-scale characteristics of field-aligned currents associated with substorm, J. Geophys. Res., 81, Lu, G., et al. (1994), Interhemispheric asymmetry of the high-latitude ionospheric convection pattern, J. Geophys. Res., 99, Lukianova, R., V. M. Uvarov, and B. A. Samokish (1997), Numerical simulation of the global distribution of electric potential over the Earth s ionosphere (in Russian), J. Comput. Math. Math. Phys., 37(7), 838. Papitashvili, V. O., and F. J. Rich (2002), High-latitude ionospheric convection models derived from Defense Meteorological satellite Program ion drift observations and parameterized by the interplanetary magnetic field strength and direction, J. Geophys. Res., 107(A8), 1198, doi: /2001ja Papitashvili, V. O., et al. (1994), Electric potential patterns in the Northern and Southern polar regions parametrized by the interplanetary magnetic field, J. Geophys. Res., 99, Papitashvili, V. O., F. Christiansen, and T. Neubert (2002), A new model of field-aligned currents derived from high-precision satellite magnetic field data, Geophys. Res. Lett., 29(14), 1683, doi: /2001gl Rich, F. J., and M. Hairston (1994), Large-scale convection patterns observed by DMSP, J. Geophys. Res., 99, Richmond, A. D., and Y. Kamide (1988), Mapping electrodynamic features of the high-latitude ionosphere from localized observations: Technique, J. Geophys. Res., 93, Robinson, R. M., and R. R. Vondrak (1984), Measurements of E region ionization and conductivity produced by solar illumination at high latitudes, J. Geophys. Res., 89, Ruohoniemi, J. M., and R. A. Greenwald (1996), Statistical patterns of high-latitude convection obtained from Goose Bay HF radar observations, J. Geophys. Res., 101, 21,743. Ruohoniemi, J. M., and R. A. Greenwald (2005), Dependencies of high-latitude plasma convection: Consideration of IMF, seasonal, and UT factors in statistical patterns, J. Geophys. Res., 110, A09204, doi: /2004ja Samarsky, A. A., and E. S. Nikolaev (1978), The Integration Methods of the Grid Equations (in Russian), Nauka, Moscow. Taguchi, S., M. Sugiura, J. D. Winningham, and J. A. Slavin (1993), Characterization of the IMF B Y -dependent field-aligned currents in the cleft region based on DE2 observations, J. Geophys. Res., 98, Vladimirov, V. S. (1981), Equations of Mathematical Physics (in Russian), Nauka, Moscow. Waters, C. L., B. J. Anderson, and K. Liou (2001), Estimation of global field-aligned currents using the Iridium system magnetometer data, Geophys. Res. Lett., 28, Weimer, D. R. (1995), Models of high-latitude electric potentials derived with a least error fit of spherical harmonic coefficients, J. Geophys. Res., 100, 19,595. Weimer, D. R. (2005), Improved ionospheric electrodynamic models and application to calculating Joule heating rates, J. Geophys. Res., 110, A05306, doi: /2004ja F. Christiansen, Danish National Space Center, Copenhagen, Denmark. R. Lukianova, Department of Physics, St. Petersburg State University, 38 Bering Street, St. Petersburg, Russia. (renata@aari.nw.ru) 11 of 11