Real-time Earth magnetosphere simulator with three-dimensional magnetohydrodynamic code

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1 SPACE WEATHER, VOL. 4,, doi: /2004sw000100, 2006 Real-time Earth magnetosphere simulator with three-dimensional magnetohydrodynamic code M. Den, 1 T. Tanaka, 2,3 S. Fujita, 4,5 T. Obara, 5,6 H. Shimazu, 5,6 H. Amo, 7 Y. Hayashi, 7 E. Nakano, 8 Y. Seo, 9 K. Suehiro, 7 H. Takahara, 8 and T. Takei 8 Received 25 June 2004; revised 10 February 2006; accepted 12 February 2006; published 16 June [1] We developed a real-time numerical simulator for the solar wind-- space-- magnetosphere-- ionosphere coupling system, adopting the three-dimensional (3-D) magnetohydrodynamic (MHD) simulation code developed by Tanaka. By using the real-time solar wind data, which is available from the ACE spacecraft every minute, as the upstream boundary conditions for density, temperature, flow speed, and interplanetary magnetic field, our MHD simulation system can numerically reproduce the global response of the magnetosphere and ionosphere at the same time as in the real world. We achieved realtime 3-D simulations of the solar wind--magnetosphere--ionosphere coupling system with a mesh size by adapting high-performance FORTRAN language with eight CPUs on a supercomputer system located at the National Institute of Information and Communications Technology (NICT). Simulated plasma temperature and density in geostationary orbit were also plotted as an index to predict satellite charging. In addition, we present real-time virtual AE indices obtained from simulation results that directly compare with geomagnetic field activities as well as real-time plasma temperature and density in geostationary orbit. Our real-time MHD simulator now runs routinely on NICT s supercomputer system. We will present a detailed configuration of the real-time simulator system in this paper. Some examples are presented from system output to show how solar wind variations result in geomagnetic disturbances. Citation: Den, M., et al. (2006), Real-time Earth magnetosphere simulator with three-dimensional magnetohydrodynamic code, Space Weather, 4,, doi: /2004sw Introduction [2] It is well known that space weather phenomena are manifestations of perturbations occurring in the solarterrestrial coupled system, which includes the Sun, interplanetary space, the magnetosphere, the ionosphere, and the thermosphere. Many numerical simulations have successfully developed in recent years to quantitatively treat complex coupling processes in this system. They can also 1 Computer and Information Network Center, National Institute for Fusion Science, Gifu, Japan. 2 Department of Physics, Kyushu University, Fukuoka, Japan. 3 Core Research for Evolutional Science and Technology, Japan Science and Technology Agency, Tokyo, Japan. 4 Meteorological College, Chiba, Japan. 5 Also at Core Research for Evolutional Science and Technology, Japan Science and Technology Agency, Tokyo, Japan. 6 Simulator Group, Applied Research and Standards Department, National Institute of Information and Communications Technology, Tokyo, Japan. 7 1st Computers Software Division, NEC Corporation, Tokyo, Japan. 8 High Performance Computing Marketing Promotion Division, NEC Corporation, Tokyo, Japan. 9 Internet Systems Research Laboratories, NEC Corporation, Tokyo, Japan. be a powerful approach to conducting physics-based predictions of space weather phenomena. Many numerical magnetohydrodynamic (MHD) simulation models have been developed in the last 20 years. The first global MHD simulations of the Earth s magnetosphere were presented in the early 1980s [e.g., LeBoeuf et al., 1981; Wu et al., 1981]. Thereafter, MHD models were developed into three-dimensional (3-D) models and have been used to study the solar wind-- magnetosphere-- ionosphere coupling system [Ogino, 1986; Watanabe and Sato, 1990; Usadi et al., 1993; Fedder et al., 1995; Tanaka, 1995; Janhunen, 1996; Gombosi et al., 1998; White et al., 1998; Song et al., 1999]. Comparing simulation results with measurements of calculated physical quantities has played a crucial role in evaluating the capabilities of MHD models. The magnetic field perturbations measured by ground-based magnetometers were calculated using global simulation results from magnetosphere models [e.g., Raeder et al., 2001a, 2001b; Shao et al., 2002; Wiltberger et al., 2003]. Raeder et al. [2001a] compared global simulation results for Earth s magnetosphere and ionosphere with polar cap potential and field-aligned current patterns obtained from assimilative mapping of ionospheric electrodynamics as well as with magnetometer data and plasma data obtained from Copyright 2006 by the American Geophysical Union 1of10

2 Figure 1. Outline of configuration for real-time Earth magnetosphere simulator. several spacecraft for the Geospace Environment Modeling substorm challenge event of 24 November Korth et al. [2004] also presented their finding on field-aligned current density obtained using global magnetospheric simulations and compared them with global distributions of field-aligned current (FAC) for two events with opposite directions of the interplanetary magnetic field B y. Furthermore, Wang et al. [2003] calculated the plasma depletion layer using global simulation of the solar wind-- magnetosphere--ionosphere system and compared it with Wind observations for two events on 12 January 1996 and 1 January All this work is quite important for evaluating simulation models, including the assumptions and parameters used in them and simulation techniques. [3] However, we aimed at real-time global simulations that would present geospherical space activities every day from the viewpoint that a space weather forecast system should be operated every day under all weather conditions as in ordinary weather forecasting. It can present the results under all solar-terrestrial conditions and can also provide quick look plots that provide intuition to some extent about real-time activities. Indeed, reproduction studies on severe events such as the Bastille Day event or other challenges are important for theoretical studies using numerical simulations, but our direction also includes investigations on all levels of activity. [4] We have recently developed a real-time global magnetosphere simulation system using 3-D MHD code [Tanaka, 1995] that adopts an unstructured grid system to cope with the different characteristic scales between the magnetosphere and ionosphere and a finite volume total variation diminishing (TVD) scheme to effectively capture discontinuities. We assigned part (one node, eight CPUs, 64 Gflops) of the supercomputer system located at the National Institute of Information and Communications Technology (NICT) exclusively for numerical space weather predictions. By reducing the numbers of grids used in the code to a necessary minimum and optimizing the parallelization and vectorization of the code, we achieved real-time speed in global simulations of the solar wind-- magnetosphere--ionosphere system with such limited computer resources. To obtain simulation results for the real magnetosphere at real-time speed, we adopted the real-time solar wind data obtained by Advanced Composition Explorer (ACE) as upstream boundary conditions. We also visualized the simulation results at real-time speed with the Real-time Visible System Library (RVSLIB) software system. Visualization data were produced every minute. [5] The main purpose of the space weather forecast project is to predict when and how space environment disturbances occur, how they develop, and to what extent they may negatively affect human systems. Our real-time MHD simulator can calculate the dynamical responses of the magnetosphere and ionosphere systems and can predict timing of geomagnetic disturbances and the extent they are developed. One-day movies in our database are useful for academic purposes, since they provide very clear causality between variations of the solar wind and geomagnetic disturbances. Using the simulation output of the magnetosphere, we calculated real-time AE indices as direct measurements of ground magnetic activities and plasma density and temperature in geostationary orbit, which can directly reveal magnetopause crossing, and found indices of satellite charging and input data for the simulation models. We expect to be able to predict the timing of sudden commencements and occurrences of the geomagnetically induced current associated with ground-based magnetic field disturbances for practical purposes. Furthermore, if electric field distribution in the ionosphere is obtained using our simulation output data, it can be used to predict GPS positioning errors and might possibly be applied to a flight control system. [6] We present a method of constructing the real-time space weather simulation system in this paper. Section 2 describes the system configuration and numerical results, 2of10

3 Table 1. Comparison of Performance of Two Cases, Using One CPU (FORTRAN90) and Eight CPUs (HPF) One CPU Eight CPUs (HPF) CPU, s Vectorization ratio, % and validation of simulations is discussed in section 3. Section 4 is devoted to the summary. 2. System Configuration [7] An outline of the present system configuration is given in Figure 1. NICT is one of the three receiving stations for the real-time solar wind data transmitted from the ACE spacecraft. Among these real-time data, density (n), velocity (v), temperature (T), and the z (B z ) and y (B y ) components of the interplanetary magnetic field (IMF) are sent to be calculated in real time to define the upstream boundary conditions for the MHD model. We adopted a 5-min average prepared from 64-s data for density, velocity, and temperature and 15-s data for the IMF. Computer resources of one node (eight CPUs) of NEC s SX-6 operated by NICT Japan was used for the realtime simulation. [8] The numerical model in Figure 1 solves the MHD equations using the finite volume TVD scheme for the solar wind--magnetosphere--ionosphere coupling process. The numerical scheme must work stably for all activity levels of the solar wind to enable steady and continuous operation of real-time simulation. To obtain sufficient numerical stability, the 3-D MHD code in Figure 1 used a TVD scheme with third-order accuracy in space for flux calculations [Tanaka, 1994]. In addition, we set the threshold value for each item of data to maintain stable calculations avoiding extreme inputs. At present, these threshold values are set as follows: 3.3 < n < 10 per cm 3, 124 < v < 899 km/s, 112,200 < T < 204,000 K, 7.5 < B y < 7.5 nt, and 13 < B z < 13 nt. Another important point with the numerical scheme is to decouple the intrinsic components of the magnetic field from the MHD equation system to enable precise calculation of FAC and convection electric fields. Unless this decoupling is done, the variable components of the magnetic field are contaminated by numerical errors generated during the calculation of the large total magnetic field. This code can save machine resources and can achieve the real-time simulations that visualize realistic responses of the magnetosphere-ionosphere system to real-time solar wind data observed by the ACE spacecraft. [9] Ohm s law is solved in the ionosphere to match the divergence of Pedersen and Hall currents with FAC. Ionospheric conductivity is calculated from the solar EUV flux, diffuse precipitation is modeled by pressure and temperature, and discrete precipitation is modeled by upward FAC. Hall conductivity was set to be twice the Pedersen conductivity. We followed Tanaka [2001] in calculating conductivity. A two-dimensional partial differential equation was solved on a sphere to obtain the ionospheric potential. Since this is an elliptic equation, it can be solved quite easily with the biconjugate residual method. [10] The x axis was pointing toward the Sun in the simulation, the y axis was pointing toward the opposite direction of Earth s orbital motion, and the z axis was pointing toward the north. The topological structure of the grid system was aligned to the spherical coordinate. The number of grids in this coordinate was (r q f). The grid spacing was nonuniform in the q direction. The coordinate was strictly spherical near Earth and was gradually modified to a cylindrical structure toward the tail region. The effective area covered by this grid system was R E (x y z), where R E is Earth s radius. This coordinate system enabled us to set the fine grids in regions where high resolution was needed such as the ionosphere, cusp, and plasma sheet; coarse grids covered the other regions [Tanaka, 2001]. [11] The simulation code must be written as vector and parallel code to obtain sufficient performance from the SX-6. The present simulation code is parallelized by high-performance FORTRAN (HPF) with an averaged vectorization ratio of 99.0%, providing sufficient speed for real-time simulation. HPF, an extension of FORTRAN language for parallel programming, was first defined in 1993 by the HPF Forum, which consists of major research laboratories and vendors of parallel processing [High Performance FORTRAN Forum, 1997; Seo et al., 2002; Sakagami et al., 2002]. Parallelization instructions in this language include data mapping, computation mapping, and communication. [12] The HPF compiler can perform computation mapping (parallelization) by automatically inserting necessary communications between processors on the basis of the data mapping specified by users. However, it is quite difficult to obtain sufficient performance only through automatic parallelization at the present levels of technology. The speed of parallel execution can be improved drastically by providing accurate information for computation mapping. It needs to be noted that the source FORTRAN programs do not need to be changed for HPF, although some directives need to be inserted to help parallel computation. We inserted 799 directive and associated declaration lines and 11,842 total lines in the source code. This means the ratio of additional lines for HPF is 6.7%. [13] Table 1 compares performance by computing with only one CPU and by HPF parallelizing. The relative speed of HPF parallelization with eight CPUs is about 4.6 times faster than that with one CPU. The effect parallelization has is not close to 8 times because there are not enough grids in the parallelized dimension to provide sufficient grids after division. If we have more grids, parallel efficiency will be improved. [14] In addition to high-performance computing, realtime and low-cost visualization must be achieved with limited computer resources. Visualization simultaneously 3of10

4 Figure 2. General configuration for the Real-time Visual Simulation Library (RVSLIB). occurs about every minute with calculation in a supercomputer system, and visualization data are also sent to the Web server about every minute. That is, we can obtain real-time global magnetosphere information within several minutes. Visualization is required to consume the least resources in a real-time run. We used NEC s Real- Time Visual Simulation Library (RVSLIB), which concurrently provides visualization on a supercomputer (Figure 2). We confirmed that the ratio of the CPU times for visualization to the total CPU times was less than 0.1%. The graphic outputs in our simulation system included three images, colored shading of pressure in the noonmidnight plane, a 3-D magnetic field configuration, and a polar plot including a colored contour of ionospheric conductivity and contour lines of the electric potential. They are generated at every time step that corresponds to about 1 min and are delivered to a World Wide Web server (Figure 3). The four plots (bottom right plots in the first set of images) display the latest 6-hour solar wind data, velocity, density, and the z and y components of the IMF used for upstream boundary conditions. The latest six pressure images at 20-min intervals and the list of the files for recent images, the same as the top image about every 15 min, are also presented. The data for the previous day are provided in a movie, which is available at www2.nict.go.jp/dk/c232/realtime/. 3. Validation of Simulation Results [15] Real-time pictures and 1-day movies in avi file format became available from 22 December 2003 on our Web site, The complex response of the magnetosphere-ionosphere system to real solar wind could be observed every day. Many changes are always repeated responding to various types of solar wind variations. More precisely, they do not happen to be the same IMF condition again. Figures 4, 5, and 6 show a sequence of these complex changes that occurred on 30 May [16] Figure 4 shows the output for real-time simulation at 0710:23 UT on 30 May At this time, the IMF was pointing toward the north (bottom right). The IMF then turned dawnward after 0710 UT. The ionospheric convection under IMF B y -dominant conditions at 0925:45 UT is shown in Figure 5. After 1055 UT, the IMF turned southward, with IMF B y staying dawnward. The simulation output at 1125 UT, 30 min after the IMF turned southward, is shown in Figure 6. [17] Although it is rather difficult to compare calculated magnetic configurations with observations, some typical configurations are known from previous simulation studies. A tadpole-shaped magnetosphere under due northward IMF conditions was proposed by Gombosi et al. [2000]. Magnetosphere structures under nonzero IMF B y conditions were modeled by Crooker et al. [1998] and Tanaka [1999]. The results shown in Figures 4 and 5 match with these previous models quite well. [18] It is quite difficult to further evaluate global magnetospheric configurations from direct observations. Determining global magnetospheric configurations through observations is extremely difficult because of the one-point nature of satellite observations. It is difficult even with careful statistical treatment, taking various conditions that control the problem into consideration. As an alternative, let us discuss ionospheric signatures for varying IMF. 4of10

5 [19] The present model output gives not only the response of magnetospheric structures but also 2-D ionospheric convection. Detailed morphologies of ionospheric convection have been derived from statistical analyses and case studies of data obtained by polar-orbiting satellites [Heppner and Maynard, 1987; Weimer, 1995] and ground-based high-frequency (HF) radars [Ruohoniemi and Greenwald, 1996]. They provide better references than magnetospheric observations by satellites in checking the validity of the present system. Much previous work has shown that ionospheric convection is not a mere projection of magnetospheric convection. [20] The ionospheric convection in the bottom left image of Figure 4 corresponds to the IMF conditions and exhibits the signature of reverse cell convection in the center of the contracted polar cap. The By-dominant case in Figure 5 shows quite a different pattern for ionospheric convection, which consists of a round cell on the morning side and a crescent cell on the evening side. As is well known, this convection structure has been confirmed for IMF By-dominant conditions from both observations [Heppner and Maynard, 1987; Weimer, 1995] and theory [Crooker et al., 1998; Tanaka, 1999]. Compared with the dawnward IMF case in Figure 5, the ionospheric cross -- polar cap potential increased 70% in Figure 6. At this time, the cell structure in the ionosphere consisted of a round cell on the dawn side and a crescent cell on the dusk side. This modified basic two-cell pattern under southward IMF is a well-known effect of negative IMF By [Heppner and Maynard, 1987; Weimer, 1995]. The present real-time simulation reproduced these signatures of ionospheric convection quite well. The dense ionospheric potential contour in Figure 6 corresponds to active geomagnetic conditions under southward IMF. [21] Fedder et al. [1998] showed that these ionospheric convection patterns can be reproduced fairly well by considering the global self-consistency throughout the whole convection system. By analyzing the dependence of nightside convection on IMF By and ionospheric conductivity, Tanaka [2001] also showed that the observed convection pattern could be reproduced if the magnetosphere-ionosphere coupling process was treated, including the Hall current closure of FAC through the Cowling channel. The present real-time simulation took these previous schemes Figure 3. Web images of real-time Earth magnetosphere simulation. Top four illustrations are the latest images of (top left) magnetic field lines, (top right) plasma pressure, (bottom left) ionospheric convection (white and black line) and electrical potential (colored contour), and (bottom right) input solar wind data for most recent 6 hours. The plots in the middle show (left) plasma temperature and (right) density at geostationary orbit and simulated AE indices. The bottom six images are recent color contour plasma pressures with 20-min intervals. 5 of 10

6 Figure 4. Snapshot of real-time simulation results at 0710:23 UT on 30 May Images are the same as in Figure 3 (top). sufficiently into account to obtain results that matched the observed features of ionospheric convection. [22] Another example of calculation concerned with the ground-based magnetic field is the case of plasmoid ejection on 15 June 2003, which we compared with the AE indices. Figure 7 is a snapshot of the magnetic field configuration and pressure (color contour) on 15 June Very clear ejection of the plasmoid can be seen there, which indicates that the activity in the magnetosphere was reproduced accurately by our simulation system. We used the geomagnetic H variations for AE index calculation obtained from the ionospheric Hall current in the magnetosphere to reduce computation time [Fujita et al., 2003]. Although the rotational ionospheric current producing ground magnetic variations is a more rigorous method [Raeder et al., 2001a], Fujita et al. [2003] successfully reproduced geomagnetic variations quite similar to those in a geomagnetic sudden commencement event. It needs to be noted that simulated AE indices were obtained by using H component variations at all grid points located at latitudes between 60 and 70, unlike the case for real AE indices based on ten selected AE stations. We confirmed that there were no essential differences between the simulated AE indices based on all grid point data and those from the ten grid points nearest the AE stations. Figure 8 plots calculated results for the AE indices (virtual AE indices) from our simulation data and the observed AE indices provided by Kyoto University. We can see a sharp decrease in the AL index associated with plasmoid ejection in both the virtual and real AE indices. In addition, there is overall agreement between the two AE indices although the amplitude of the simulated AE index is smaller than that based on the observation data. [23] Higher-resolution simulation in the radius direction is expected to reduce these differences; however, simulations at higher resolutions consumes CPU resources, and it is difficult to make them compatible with a real-time processing system at present. Detailed analyses of AE indices using this MHD code will be presented in a future paper. [24] As previously stated, we concluded that our simulation system can simulate the real-time response of a 6of10

7 Figure 5. Same as Figure 4 except for time 0925:45 UT. global magnetosphere-ionosphere system with appropriate accuracy and can be applied to space weather forecasting. Our system continues to operate with the threshold values for input data previously described from 17 November An extended version with the plots of plasma temperature, density, and AE indices was implemented beginning in February Summary [25] We developed a real-time global magnetosphere simulation system for space weather forecasting. Realtime simulations were achieved by assigning one node of the supercomputer system located at NICT and by optimizing the parallelization and vectorization of code. We adopted observed ACE solar wind data as upstream boundary conditions to obtain simulation results close to the real-time magnetosphere. We visualized the simulation data at the same time as calculation using RVSLIB, and the visualization data were renewed every minute. [26] The main purpose of the space weather forecast project was to predict when and how disturbances in the space environment occur, how they develop, and to what extent they may cause damage to human systems. Our real-time MHD simulator can calculate the dynamical response of the magnetosphere and can predict when geomagnetic disturbances occur and to what extent they develop. We showed AE indices obtained from real-time global MHD simulation ahead of the actual time by about an hour, indicating the activities of the magnetosphere about an hour in advance. The plasma temperature and density in the geostationary orbit are plotted about an hour in advance as an index of magnetopause crossing and as input data for the simulation model of satellite charge. We expect to be able to predict the timing of sudden commencements and occurrences of the geomagnetically induced current associated with ground-based magnetic field disturbances for practical purposes. Furthermore, if electric field distribution in the ionosphere is obtained using our simulation output data, it can be used to predict GPS positioning errors and might possibly be applied to a flight control system. Our real-time simulation is expected to become an essential approach to 7of10

8 Figure 6. Same as Figure 4 except for time 1125:31 UT. Figure 7. Simulation results of magnetic field lines and colored contour of pressure on 15 June 2003 as an example of clear plasmoid ejection. 8 of 10

9 Figure 8. Calculated AE indices for same day as in Figure 7 (right) obtained using real-time simulation data and (left) based on observation data provided by Kyoto University on 15 June forecasting space weather. Our MHD simulation code, developed by Tanaka [1994], could reproduce the magnetosphere activities with appropriate accuracy. We also confirmed that this code could continue running unless the solar wind conditions were intense, for example, B z < 20 nt. It should be noted that the intensity and region of the conductivity could be simulated qualitatively but that they are not in agreement with ground-based observation completely. The limited number of grids is one reason, and this is what should be overcome in future. [27] NICT is promoting the space weather forecast project and is one of the forecast centers belonging to the International Space Environment Service. The real-time magnetosphere simulations are utilized for daily space weather forecasts of geomagnetic activities at NICT. These real-time simulation results can be used not only for predicting space weather but for analyzing magnetospheric phenomena. [28] Acknowledgments. The authors greatly appreciate the ACE MAG and SWEPAM teams for real-time solar wind data. We also wish to thank the World Data Center for Geomagnetism in Kyoto for providing us with their quick look plots of AE indices. References Crooker, N. U., J. G. Lyon, and J. A. Fedder (1998), MHD model merging with IMF B y : Lobe cells, sunward polar cap convection, and overdraped lobes, J. Geophys. Res., 103, Fedder, J. A., J. G. Lyon, S. P. Slinker, and C. M. Mobarry (1995), Topological structure of the magnetotail as a function of interplanetary magnetic field direction, J. Geophys. Res., 100, Fedder, J. A., S. P. Slinker, and J. G. Lyon (1998), A comparison of global numerical simulation results to data for the January , 1992, Geospace Environment Modeling challenge event, J. Geophys. Res., 103, 14, ,810. Fujita,S.,T.Tanaka,T.Kikuchi,K.Fujimoto,K.Hosokawa,and M. Itonaga (2003), A numerical simulation of the geomagnetic sudden commencement: 1. Generation of the field-aligned current associated with the preliminary impulse, J. Geophys. Res., 108(A12), 1416, doi: /2002ja Gombosi, T. I., D. L. De Zeeuw, C. P. T. Groth, K. G. Powell, and P. Song (1998), The length of the magnetotail for northward IMF: Results of 3D MHD simulations, in Physics of Space Plasmas, vol. 15, edited by T. Chang and J. R. Jasperse, pp , MIT Press, Cambridge, Mass. Gombosi, T. I., K. G. Powell, and B. van Leer (2000), Comment on Modeling the magnetosphere for northward interplanetary magnetic field: Effects of electrical resistivity by Joachim Raeder, J. Geophys. Res., 105, 13, ,147. Heppner, J. P., and N. C. Maynard (1987), Empirical high-latitude electric field models, J. Geophys. Res., 92, of10

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(1999), Configuration of the magnetosphere-ionosphere convection system under northward IMF condition with nonzero IMF B y, J. Geophys. Res., 104, 14, ,690. Tanaka, T. (2001), Interplanetary magnetic field B y and auroral conductance effects on high-latitude ionospheric convection patterns, J. Geophys. Res., 106, 24, ,516. Usadi, A., A. Kageyama, K. Watanabe, and T. Sato (1993), A global simulation of the magnetosphere with a long tail: Southward and northward interplanetary magnetic field, J. Geophys. Res., 98, Wang, Y. L., J. Raeder, C. T. Russell, T. D. Phan, and M. Manapat (2003), Plasma depletion layer: Event studies with a global model, J. Geophys. Res., 108(A1), 1010, doi: /2002ja Watanabe, K., and T. Sato (1990), Global simulation of the solar windmagnetosphere interaction: The importance of its numerical validity, J. Geophys. Res., 95, 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, ,608. White, W. W., G. L. Siscoe, G. M. Erickson, Z. Kaymz, N. C. Maynard, K. D. Siebert, B. U. O. Sonnerup, and D. R. Weimer (1998), The magnetospheric sash and the cross-tail S, Geophys. Res. Lett., 25, Wiltberger, M., J. G. Lyon, and C. C. Goodrich (2003), Results from the Lyon-Fedder-Mobarry global magnetospheric model for the electrojet challenge, J. Atmos. Sol. Terr. Phys., 65, Wu, C. C., R. J. Walker, and J. M. Dawson (1981), A three dimensional MHD model of the Earth s magnetosphere, Geophys. Res. Lett., 8, H. Amo, Y. Hayashi, and K. Suehiro, 1st Computers Software Division, NEC Corporation, 5-7-1, Shiba, Minato-ku, Tokyo, , Japan. M. Den, Computer and Information Network Center, National Institute for Fusion Science, Oroshi-cho 322-6, Toki, Gifu , Japan. (den.mitsue@nifs.ac.jp) S. Fujita, Meteorological College, Asahi , Kashiwa, Chiba , Japan. E. Nakano, H. Takahara, and T. Takei, HPC Marketing Promotion Division, NEC Corporation, 5-7-1, Shiba, Minato-ku, Tokyo, , Japan. T. Obara and H. Shimazu, Simulator Group, Applied Research and Standards Department, National Institute of Information and Communications Technology, 4-2-1, Nukui-kita, Koganei, Tokyo, , Japan. Y. Seo, Internet Systems Research Laboratories, NEC Corporation, 5-7-1, Shiba, Minato-ku, Tokyo, , Japan. T. Tanaka, Department of Physics, Kyushu University, , Hakozaki, Higashi-ku, Fukuoka, , Japan. 10 of 10