1. Difficulties of building crossing databases
2. Evolution of empirical models and contribution of physical parameters to components of magnetopause shape. Standoff distance estimation - parametrization. Flaring - parametrization in the X-Z and X-Y plane seperately.
3. Azimuth and north-south assymetries due to tilt and IMF clock angle. Graphs with the effects of each one. Parametrization of ξ (a) flaring in a general expression of .
4. Indentation Q of polar cups and comparison of models: Q=0, Lin, Liu
   • Cusps defined by two surfaces: cusp-magnetosphere and cusp-magnetopause current
   • Lin underestimates cusp-magnetopause surface (meaning we under underestimate it)

In-situ data of crossings

Boundary crossing detection is not a trivial task, although essential for the construction of empirical statistical models of the magnetopause and the bowshock. [[mdl1. A Gradient Boosting Based Automatic Detection of Near-Earth Regions.pdf]] attempts to breach the gap of the untreated and ever increasing accumulated data of satellite crossings by automating the event detection through a classification algorithm and building a multi-mission database. The established catalogs are available online at: https://doi.org/10.5281/zenodo.5668298.

A typical boundary crossing (event) from the data of THEMIS B satellite is shown in the following figure. The satellite starts from the magnetosphere crossing the magnetopause to go in the magnetosheath and finally crossing the bowshock to move into the interplanetary region (solar wind).

Models

Several models have used crossing events to construct analytical expressions of the magnetopause, parametrized by the solar wind and earth's magnetic field conditions:
Shue model : The crossings used to construct this model where taken from satellites of equatorial orbit, and thus assumes a rotational symmetry over the x axis.
Lin Model : Takes into account the dipole tilt, indentation in the near-cusp region and dawn-dusk assymetry. Dawn-dusk asymmetry proves to be a consequence of earth's rotation and is corrected from the data
Liu Model : Through MHD simulation, suggests the influence of IMF Bx and By components to the magnetopause

[[mdl2. Shape and Location.pdf]] evaluates the influence of pressure, IMF cone angle and clock angle to the subsolar distance as well as the flaring of the magnetopause.

Subsolar distance