[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.

[1] We report the first in situ observation of high-latitude magnetopause (near the northern duskward cusp) Kelvin-Helmholtz waves (KHW) by Cluster on January 12, 2003, under strongly dawnward interplanetary magnetic field (IMF) conditions. The fluctuations unstable to Kelvin-Helmholtz instability (KHI) are found to propagate mostly tailward, i.e., along the direction almost 90 to both the magnetosheath and geomagnetic fields, which lowers the threshold of the KHI. The magnetic configuration across the boundary layer near the northern duskward cusp region during dawnward IMF is similar to that in the low-latitude boundary layer under northward IMF, in that (1) both magnetosheath and magnetospheric fields across the local boundary layer constitute the lowest magnetic shear and (2) the tailward propagation of the KHW is perpendicular to both fields. Approximately 3-hour-long periods of the KHW during dawnward IMF are followed by the rapid expansion of the dayside magnetosphere associated with the passage of an IMF discontinuity that characterizes an abrupt change in IMF cone angle, f = acos B x B j j , from $90 to $10 . Cluster, which was on its outbound trajectory, continued observing the boundary waves at the northern evening-side magnetopause during sunward IMF conditions following the passage of the IMF discontinuity. By comparing the signatures of boundary fluctuations before and after the IMF discontinuity, we report that the frequencies of the most unstable KH modes increased after the discontinuity passed. This result demonstrates that differences in IMF orientations (especially in f) are associated with the properties of KHW at the high-latitude magnetopause due to variations in thickness of the boundary layer, and/or width of the KH-unstable band on the surface of the dayside magnetopause.