The GLE inversion software is intended to facilitate the study of Ground Level Events (GLEs) observed by the worldwide network of Neutron Monitor (NM) stations to understand the solar sources of GLEs and the conditions under which relativistic solar energetic particles propagate in interplanetary space, from the source to the Earth.

The software is written in Python, a widely used general-purpose, high-level programming language. Python is developed under an open source license, making it freely usable and available for installation on many operating systems. No license is required by the user.

The GLE inversion software solves an inversion problem to infer the characteristics of the solar source (injection profile and spectral index) and the interplanetary transport conditions of relativistic protons based on the comparison of the predicted measurements at each NM station with the actual measured ones by the NM stations of the worldwide network.

The main assumptions made in the GLE inversion software are the following:

Solar Source and Interplanetary Transport of Relativistic Protons

  • The solar source spectrum follows a power-law in rigidity, with spectral index γ.
  • The large scale interplanetary magnetic field can be described by an Archimedean spiral.
  • Relativistic protons propagate along the large scale magnetic field lines. Their transport can be described by the focused transport equation. Drifts and transport perpendicular to the average magnetic field are neglected.
  • The mean free path of relativistic protons increases with rigidity such that λr = λ0(R/R0)(2-q), where λ0 is a free parameter, R0 = 2 GV, q = 1 for R > R0 and q = 5/3 for R < R0.

Interplanetary Magnetic Field at the Earth's Bow Shock

  • The direction of the axis of symmetry of the directional relativistic proton distributions is related to the direction of the interplanetary magnetic field the Earth's bow shock nose. The OMNI database provides a well-documented dataset of time-shifted magnetic field observations, which describe the field evolution at the nose of the Earth’s bow shock as a function of time. The database is computed based on observations made by spacecrafts such as Wind and ACE. The field to which the proton distributions tend to become gyrotropic to is not the momentarily measured field but rather the average field the particles feel over their gyromotion. We used 5-min OMNI magnetic field data averaged over a 30-min time window to consider spatial averaging of the field over the size of the gyroradius of relativistic protons.

Asymptotic Directions of NM stations

  • The asymptotic directions are calculated using the software suite PLANETOCOSMICS. Due to computational constraints, the geomagnetic field is described by the IGRF model for the magnetic field contributions caused by sources in the Earth's interior and the Tsyganenko 1989 model describing the magnetic field caused by current systems within the geomagnetosphere. The asymptotic directions are calculated every 15 minutes for all neutron monitor stations.

Yield Function

  • The NM response function for primary protons is described by the 6-NM64 NM yield function determined by Flückiger et al. (2008) based on Monte Carlo calculations with Geant 4. It is a function of rigidity and the atmospheric depth, i.e. it is applicable for all altitudes and not only for sea level.
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