[1] Peredo et al. (1995) derived a frequently used three-dimensional bow shock model parameterized by the upstream Alfvénic Mach number from the set of approximately 550 bow shock crossings provided by 17 distinct spacecraft over the period of 1963-1980. However, several studies reported some systematic biases in the bow shock model predictions. Therefore we have attempted to improve upon the bow shock model of Peredo et al. (1995) using their original data set and methodology in an effort to better understand these effects. We have performed three-dimensional best fits to the bow shock crossings binned by the upstream Mach numbers M A , M S , and M MS and found that the best fitting surfaces were best ordered with the M A . In agreement with predictions from the magnetohydrodynamic theory, the results show that the bow shock surface expands when the M A decreases. The found dawn-dusk asymmetry in the bow wave is consistent with previous studies only in the Geocentric Plasma Ecliptic System (GPE) coordinates but not in the Geocentric Interplanetary Medium (GIPM) coordinates which suggests that the employed data set is not comprehensive enough for resolving this asymmetry. Nor is the Mach cone asymmetry resolved in our data set (not even in the GIPM frame). We have derived two models predicting the statistical position and shape of the bow shock in the GPE or GIPM coordinates. Error analysis shows that the GPE-based model is more accurate and applicable for M A = 3-20 except the nose region where the model underestimates the bow shock position for M A < 5. A direct comparison of the model predictions with 5870 IMP 8 bow shock crossings demonstrated high accuracy of predictions and, for the GPEbased model, an exceptional stability of predictions even under extreme upstream conditions. Indeed, the new GPE-based bow shock model is more accurate and equally or more stable than the Formisano (1979), Němeček and Š afránková (1991), Farris and Russell (1994)
[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.
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