DiscontinuityPy

A python package for identifying and analyzing discontinuities for time series data.

All statistics are wrong, but some may be useful:)

User Guide

This package is designed to identify and analyze discontinuities in time series data.

1. Finding the discontinuities, see this notebook
   • Corresponding to limited feature extraction / anomaly detection
2. Calculating the properties of the discontinuities, see this notebook
   • One can use higher time resolution data

For how to use this project as a python library, please see this page.

See accompanying package Discontinuity.jl for Julia about data processing and visualization.

Installation

pip install discontinuitypy

Getting started

Import the package

from discontinuitypy.utils.basic import *
from discontinuitypy.core import *

Related projects and publications

• Solar wind discontinuities spatial evolution in the outer heliosphere
• Evolution of solar wind discontinuities in the inner heliosphere: PSP and Earth conjunctions and alignments

Properties of Discontinuities

Notations:

• \(\vec{B}\) : Magnetic field in ANY coordinate system
• \(B\) : Magnetic field magnitude
• \(V\) : Ion velocity in ANY coordinate system, in units of \(km/s\)
• \(n\) : Plasma density, in units of \(1/cm^3\)

For the unit, by default we use

• length : \(km\)
• time : \(s\)
• magnetic field : \(nT\)
• current : \(nA/m^2\)

Outputs

For more derivable outputs, please see Discontinuity.jl

• t_{us,ds} : moments of time corresponding to upstream and downstream boundaries of the current sheet

• b_mag : mean of magnetic field magnitude across the discontinuity

• \(|Δ B|/B\) : Change in magnetic field magnitude over magnetic field magnitude (mean) db_over_b

  • see Fig.14 in Tsurutani and Smith (1979)

• bn_over_b : \(\bar{B}_N/\bar{B}\) : Normal component of magnetic field over magnetic field magnitude (mean)

• \(\vec{e}_l, \vec{e}_m, \vec{e}_n\) : unit vector in the direction of the maxium, medium, minium variance magnetic field in ANY coordinate system e_{max/med/min}{x,y,z}

• \(\vec{n}\) : normal of the discontinuity plane

• \(\vec{n}_{\text{MVA}}\) : normal from minimum variance analysis (unit vector in the minium variance direction) n_mva = e_min

• \(\vec{n}_{\text{cross}}\) : cross product of the magnetic field vector \(B_u\) upstream and the field vector \(B_d\) downstream of the transition n_cross

• \(V\) : Velocity vector in ANY coordinate system V

• \(V_l\) : Velocity component along the maximum variance direction V_l

• \(V_{n,MVA}\) : Velocity component along the normal direction from minimum variance analysis V_n_mva

• \(V_{n,cross}\) : Velocity component along the normal direction from cross product of upstream and downstream magnetic field V_n_cross

• j0{_norm}: current density, in units of \(nA/m^2\)

References

Tsurutani, Bruce T., and Edward J. Smith. 1979. “Interplanetary Discontinuities: Temporal Variations and the Radial Gradient from 1 to 8.5 AU.” Journal of Geophysical Research: Space Physics 84 (A6): 2773–87. https://doi.org/10.1029/JA084iA06p02773.