[1] We report Time History of Events and Macroscale Interactions during Substorms (THEMIS) and Geotail observations of prolonged magnetopause (MP) expansions during long-lasting intervals of quasi-radial interplanetary magnetic field (IMF) and nearly constant solar wind dynamic pressure. The expansions were global: The magnetopause was located more than 3 R E and ∼7 R E outside its nominal dayside and magnetotail locations, respectively. The expanded states persisted several hours, just as long as the quasi-radial IMF conditions, indicating steady state situations. For an observed solar wind pressure of ∼1.1-1.3 nPa, the new equilibrium subsolar MP position lay at ∼14.5 R E , far beyond its expected location. The equilibrium position was affected by geomagnetic activity. The magnetopause expansions result from significant decreases in the total pressure of the high-b magnetosheath, which we term the low-pressure magnetosheath (LPM) mode. A prominent LPM mode was observed for upstream conditions characterized by IMF cone angles less than 20°-25°, high Mach numbers and proton plasma b ≤ 1.3. The minimum value for the total pressure observed by THEMIS in the magnetosheath adjacent to the magnetopause was 0.16 nPa and the fraction of the solar wind pressure applied to the magnetopause was therefore 0.2, extremely small. The equilibrium location of the magnetopause was modulated by a nearly continuous wavy motion over a wide range of time and space scales.

The present empirical models describing a location and shape of the magnetopause and bow shock are based on a statistical evaluation of magnetopause and bow shock crossings. The crossings are usually identified by a visual inspection of the plots or by automatic methods which are less reliable. We present a new method of determination of the most probable boundary locations. The method is based on continuous plasma and magnetic field measurements in the regions visited by a sounding spacecraft (the solar wind, magnetosheath, and magnetosphere) and on the determination of ratios of these parameters to simultaneously monitored upstream parameters. The regions identified by this method are then used for development of simple models of the magnetopause and bow shock locations parameterized by the upstream pressure. The performance of the models is tested with corresponding boundary crossings based mainly on the THEMIS observations. Both developed models are in a good agreement with the results obtained from identification of crossings.

[1] We investigate the dependence of the magnetopause location on the interplanetary magnetic field (IMF) cone angle (the angle between the IMF and solar wind velocity vectors) in a statistical study based on ≈6500 magnetopause crossings observed by the five THEMIS spacecraft, both at the dayside and flanks. To remove other well-known effects, we analyze the difference between observed magnetopause radial distances and those predicted by an empirical magnetopause model (scalable by the solar wind dynamic pressure and IMF B Z component). The results demonstrate a systematic increase of the magnetopause distance for radial IMF directions, from ≈0.3 R E at 90°t o ≈1.7 R E at 0°or 180°cone angle. Moreover, a stronger dependence of the magnetopause location on the solar wind dynamic pressure than predicted by the current models was observed.

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[1] We present results from a new three-dimensional empirical magnetopause model based on 15,089 magnetopause crossings from 23 spacecraft. To construct the model, we introduce a Support Vector Regression Machine (SVRM) technique with a systematic approach that balances model smoothness with fitting accuracy to produce a model that reveals the manner in which the size and shape of the magnetopause depend upon various control parameters without any assumptions concerning the analytical shape of the magnetopause. The new model fits the data used in the modeling very accurately, and can guarantee a similar accuracy when predicting unseen observations within the applicable range of control parameters. We introduce a new error analysis technique based upon the SVRM that enables us to obtain model errors appropriate to different locations and control parameters. We find significant east-west elongations in the magnetopause shape for many combinations of control parameters. Variations in the Earth's dipole tilt can cause significant magnetopause north/south asymmetries and deviation of the magnetopause nose from the Sun-Earth line nonlinearly by as much as 5 Re. Subsolar magnetopause erosion effect under southward IMF is seen which is strongly affected by solar wind dynamic pressure. Further, we find significant shrinking of high-latitude magnetopause with decreased magnetopause flaring angle during northward IMF.