PyGeopack

A Python wrapper for Geopack-2008. This includes the T89, T96, T01 and TS05 magnetic field models for Earth's magnetosphere. See https://ccmc.gsfc.nasa.gov/modelweb/magnetos/tsygan.html and http://geo.phys.spbu.ru/~tsyganenko/modeling.html for more information.

1. Requirements

The following Python packages will be installed automatically:

• numpy
• PyFileIO
• RecarrayTools
• DateTimeTools

The following packages will also be required for running the PyGeopack.UpdateParameters() routine:

• kpindex
• pyomnidata

This package is primarily a Python 3 wrapper for a mixture of C/C++/FORTRAN code which is compiled during installation. For building to work, the following are needed:

• g++

• binutils

• make

• gfortran

2. Installation

2.1 Linux

Firstly a few environment variables need setting up: $KPDATA_PATH, $OMNIDATA_PATH and $GEOPACK_PATH, which will point to the Kp index data, the omni data and the Geopack data, respectively. This can be done by including the following in your ~/.bashrc file, or by running it in the terminal before starting Python:

export KPDATA_PATH=/path/to/kp
export OMNIDATA_PATH=/path/to/omni
export GEOPACK_PATH=/path/to/geopack/data

where both of those directories must be writable by the current user, unless the data already exist in them.

Then simply install using pip3:

pip3 install PyGeopack --user

or by downloading the latest release on GitHub and running:

pip3 install PyGeopack-1.2.2.tar.gz --user

NOTE: You should uninstall any previous versions before installing this. If you had a version installed before 0.0.12 - you will need to remove the old shared object files - they are likely to be contained somewhere like (depending on the Python version used):

~/.local/lib/python3.10/site-packages/PyGeopack/

It's best just to remove everything within that folder!

2.2 Windows

Install TDM-GCC (make sure to select g++ and gfortran), install anaconda and then install the package in an anaconda power shell session using pip3 as in the Linux instructions. The same environment variables will need to be set as those in the Linux instructions. This package has only briefly been tested in Windows 10 x64, mileage may vary with other versions of Windows. This code has also been successfully built using the Strawberry Perl compilers.

It appears that ctypes doesn't necessarily search the directories listed within the $PATH environment variable for the C++ dependencies on some versions of Python. To hack myself around this, I have added a function which with scan all of the directories within $PATH for libstdc++*.dll; if found then the paths which it is found in will be added using os.add_dll_directory(). If the directory of your compiler's libraries is not listed within $PATH, this may be the cause of any failures at build time or importing the library. If you have multiple compilers installed, then I am unsure what will happen! Feel free to post an issue if you encounter any errors, or if you have any suggestions for fixes.

2.3 Mac

This module should work on MacOS as it does on Linux, with the same requirements. I have tested it using MacOS Big Sur.

3 Post-install

After installation, the PyGeopack module will attempt to locate the OMNI data required for the models. If these data exist already in $GEOPACK_PATH then it will load into memory. If they don't exist, then the user will be shown a warning - the next section explains how to fix this.

4. Usage

There are three main uses for this Python package:

1. Calculating the model magnetic field at any given point in space.
2. Tracing along the magnetic field.
3. Coordinate conversions (usually for the purposes of 1 and 2).

Before doing any of the above, it's recommended that you grab the up to date omni parameters - the UpdateParameters routine will download and update the Kp index and OMNI parameters, then calculate the G and W parameters required for the models:

import PyGeopack as gp
gp.Params.UpdateParameters(SkipWParameters=True)

The SkipWParameters keyword (set to True by default) can be used to skip the lengthy process of calculating the six W parameters for the TS05 magnetic field model - if True then these will be filled with zeros. Apparently they aren't all that important anyway. The code included in this module can calculate them and is Tsyganenko's own code, but it produces different numbers to those given in the files on Tsyganenko's website! No idea why, so use them with caution!

If the above parameters are not loaded, a warning will appear when the module is imported. To suppress warnings, set:

export GEOPACK_NOWARN=1

4.1 Calculating the model field.

To calculate the model field, use the ModelField function:

Bx,By,Bz = gp.ModelField(x,y,z,Date,ut,Model='T96',CoordIn='GSM',CoordOut='GSM',**kwargs)

where the output field components Bx, By and Bz are in units of nT.

The ModelField function accepts the following arguments and keywords:

Name	Keyword/Argument	Description
x	argument	Scalar or array of x-coordinates
y	argument	Scalar or array of y-coordinates
z	argument	Scalar or array of z-coordinates
Date	argument	Date(s) in the format yyyymmdd - must be an integer and have either one element or the same number of elements as x
ut	argument	Time in hours since the start of the day.
Model	keyword	String denoting the model to use 'T89'|'T96'|'T01'|'TS05'
CoordIn	keyword	Input coordinate system string: 'GSE'|'GSM'|'SM'
CoordOut	keyword	Output coordinate system string: 'GSE'|'GSM'|'SM'
`WithinMPOnly	keyword	If True then return NaN's outside the magnetopause.
ReturnParams	keyword	If True then a dictionary containing the model parameters will be returned as a fourth output parameter.
**kwargs	keywords	Keyword arguments can be used to define some or all of the model parameters used. See model parameters section.

4.2 Tracing the magnetic field

The TraceField object will accept either one argument or 5 arguements, alongside a range of keyword arguments:

TraceField(*args,**kwargs)

Trace along the magnetic field from 1 or more starting positions in the magnetosphere x, y and z using the TraceField object, e.g.:

T = gp.TraceField(x,y,z,Date,ut)

where x, y, z, Date and ut are defined in the previous section.

Or loading from file:

T = gp.TraceField(filename)

where filename is the full path and file name of a file where a previous TraceField object was saved using TraceField.Save, e.g.:

T.Save(filename)

The keyword arguments accepted by the TraceField object include one discussed in the model parameters section and ones specific to this object:

Name	Description
Model	Model string: 'T89'|'T96'|'T01'|'TS05'`
CoordIn	Input coordinate system string: 'GSE'|'GSM'|'SM'
alt	Altitude (in km) to stop trace at.
MaxLen	Maximum trace steps
DSMax	Maximum step size (RE)
FlattenSingleTraces	Flattens all of the arrays if only a single field line is traced
Verbose	Output trace progress
TraceDir	Direction to trace in - normally 'both' is used to trace in both directions, 1 traces along the field (to the northern hemisphere)  and -1 traces in the opposite direction.
alpha	This can be an array or a scalar defining a polarization angle in degrees. This is typically used for ULF waves.

The TraceField object, T in the above code snippet, contains the following arrays:

xsm,ysm,zsm	x, y and z coordinates along the field trace(s) in the SM coordinate system
xgsm,ygsm,zgsm	x, y and z coordinates along the field trace(s) in the GSM coordinate system
xgse,ygse,zgse	x, y and z coordinates along the field trace(s) in the GSE coordinate system
Bxsm,Bysm,Bzsm	x, y and z components of the magnetic field along the trace(s) in the SM coordinate system
Bxgsm,Bygsm,Bzgsm	x, y and z components of the magnetic field along the trace(s) in the GSM coordinate system
Bxgse,Bygse,Bzgse	x, y and z components of the magnetic field along the trace(s) in the GSE coordinate system
nstep	number of steps along the trace(s)
GlatN	Geographic latitude of the northern footprint(s)
GlatS	Geographic latitude of the southern footprint(s)
MlatN	Magnetic latitude of the northern footprint(s)
MlatS	Magnetic latitude of the southern footprint(s)
GlonN	Geographic longitude of the northern footprint(s)
GlonS	Geographic longitude of the southern footprint(s)
MlonN	Magnetic longitude of the northern footprint(s)
MlonS	Magnetic longitude of the southern footprint(s)
GltN	Geographic local time of the northern footprint(s)
GltS	Geographic local time of the southern footprint(s)
MltN	Magnetic local time of the northern footprint(s)
MltS	Magnetic local time of the southern footprint(s)
Lshell	L-shell of the field line(s) at the equator
MltE	Magnetic local time of the equatorial footprint(s)
FlLen	Field line length in planetary radii
R	R = sqrt(x**2 + y**2 + z**2)
s	Distance along field line (in RE)
halpha	hα (see Singer et al., 1981) - this is an array with the shape (n,nalpha,MaxLen), where n is the number of traces, nalpha is the number of alpha values (polarizations) and  MaxLen is the maximum trace length.

4.3 Coordinate conversion

Coordinate conversion code is now within the PyGeopack.Coords submodule. A simple function exists to convert between the a bunch of Cartesian coordinate systems:

x1,y1,z1 = gp.Coords.ConvCoords(x0,y0,z0,Date,ut,CoordIn,CoordOut,V=V)

where x0, y0 and z0 are either scalars or arrays of positions to be transformed. Dateis an integer in the format yyyymmdd, ut is the time in hours (i.e. ut = hours + minutes/60.0) and V can be used to set a custom solar wind velocity. CoordIn and CoordOut are strings defining the input and output systems, which can be any of the following: 'GEI'|'GEO'|'GSE'|'GSM'|'MAG'|'SM'. x1, y1 and z1 are the transformed coordinates.

There are other Cartesian coordinate conversion routines:

x1,y1,z1 = gp.Coords.GEItoGEO(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GEItoGSE(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GEItoGSM(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GEItoMAG(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GEItoSM(x0,y0,z0,Date,ut)

x1,y1,z1 = gp.Coords.GEOtoGEI(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GEOtoGEO(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GEOtoGSE(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GEOtoGSM(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GEOtoMAG(x0,y0,z0,Date,ut)

x1,y1,z1 = gp.Coords.GSEtoGEI(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GSEtoGEO(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GSEtoGSE(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GSEtoGSM(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GSEtoMAG(x0,y0,z0,Date,ut)

x1,y1,z1 = gp.Coords.GSMtoGEI(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GSMtoGEO(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GSMtoGSE(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GSMtoGSM(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.GSMtoMAG(x0,y0,z0,Date,ut)

x1,y1,z1 = gp.Coords.MAGtoGEI(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.MAGtoGEO(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.MAGtoGSE(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.MAGtoGSM(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.MAGtoMAG(x0,y0,z0,Date,ut)

x1,y1,z1 = gp.Coords.SMtoGEI(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.SMtoGEO(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.SMtoGSE(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.SMtoGSM(x0,y0,z0,Date,ut)
x1,y1,z1 = gp.Coords.SMtoMAG(x0,y0,z0,Date,ut)

Also included are the following routines:

MLon,MLat = gp.Coords.GEOtoMAG(Lat,Lon,Date,ut)
Lon,Lat = gp.Coords.MAGtoGEO(MLat,MLon,Date,ut)

which convert between geographic (Lat and Lon) and magnetic (MLat and MLon) latitude and longitudes.

And for converting between magnetic longitude (MLon) and magnetic local time (MLT):

MLT = gp.Coords.MLONtoMLT(MLon,Date,ut)
MLon = gp.Coords.MLTtoMLON(MLT,Date,ut)

Descriptions of the coordinate systems:

Name	Description	x	y	z
GSE - Geocentric Solar Ecliptic	fixed	Towards the Sun	Opposite to Earth's orbit	Perpendicular to the ecliptic plane
GSM - Geocentric Solar Magnetospheric	fixed	Towards the Sun		Projection of the dipole axis in the Y-Z GSE plane
SM - Solar Magnetic	fixed	In the plane containing the Earth-Sum line and the dipole axis		Along the dipole axis
MAG - Geomagnetic	rotating		Through intersection of magnetic equator and geographic meridian 90 degrees east of the meridian containing the dipole axis	Along the dipole axis
GEO - Geographic	rotating	Through intersection of equator and Greenwich meridian		Along Earth's rotation axis
GEI - Geocentric Equatorial Inertial	fixed	Towards the first point of Ares		Along Earth's rotation axisbetical list

NOTE: By "fixed", I mean that they do not rotate with the Earth's spin, they are not really fixed.

4.4 Model Parameters

In this section, the parameters and relevant **kwargs are discussed for each model. If **kwargs aren't used, then the relevant parameters are found autmoatically for the date and time provided when using the models. Individual parameters amy be altered without affecting the others - if only a single parameter is changed, then the others are still automatically calculated. The **kwargs accepted by ModelField and TraceField are:

Keyword	Data Type	Description
iopt	scalar integer	iopt=Kp+1 (iopt=7 for Kp>=6)
parmod	10-element float array	Elements 0 - 3 are Pdyn, SymH, IMF By and IMF Bz, respectively. Elements 4 - 9 depend on the model
tilt	scalar float	The dipole tilt angle in radians
Vx	scalar float	x component of solar wind velocity
Vy	scalar float	y component of solar wind velocity
Vz	scalar float	z component of solar wind velocity
Kp	scalar integer	Kp index
Pdyn	scalar float	Dynamic pressure in nPa
SymH	scalar float	SymH in nT
By	scalar float	IMF y component in nT
Bz	scalar float	IMF z component in nT

A fucntion exists which will return a dict object containing the parameters for a given model, date and time:

params = gp.Params.GetModelParams(Date,ut,Model)

We can also return the dipole tilt:

tilt = gp.Params.GetDipoleDilt(Date,ut)

All models can be affected by the Vx, Vy, and Vz parameters as these are used to aberrate the coordinates into the GSW frame, where GSW is equivalent to GSM in the situation where Vy=0 and Vz=0. tilt is calculated automatically for all models based on the date, time and the IGRF magnetic field model.

T89

The only parameter used here is iopt which can be controlled with either setting iopt or Kp keywords to an integer. Valid values for iopt are integers in the range 1-7, if Kp is set, then iopt is set automatically equal to Kp+1. For Kp>=6 iopt=7.

T96

The first four elements of the parmod array are used for this model where parmod[0] is the dynamic pressure, parmod[1] is the SymH, parmod[2] is the y component of the interplanetary magnetic field (IMF) and parmod[3] is the z component of the IMF. All other elements of this array are ignored. The entire parmod array can be set using the parmod keyword, otherwise individual elements can be edited using the Pdyn, SymH, By and Bz keywords, where other unchanged parameters will be calculated automatically.

T01

This model uses the first six elements of the parmod array, where the first four are set in exactly the same way as in the T96 model. parmod[4] and parmod[5] correspond to the G1 and G2 parameters calculated in Tsyganenko, 2002b. These can, I believe, be set to 0.

TS05

This model uses all of the parmod array, where the first four are as in the T96 model. The last 6 elements are the W1-W6 parameters described in Tsyganenko and Sitnov, 2005.

References

1. N.A. Tsyganenko, A Magnetospheric Magnetic Field Model with a Warped Tail Current Sheet, Planet. Space Sci. 37, 5-20, 1989.
2. N.A. Tsyganenko, Modeling the Earth's Magnetospheric Magnetic Field Confined Within a Realistic Magnetopause, J.Geophys.Res., 100, 5599-5612, 1995.
3. N.A. Tsyganenko and D.P. Stern, Modeling the Global Magnetic Field of the Large-Scale Birkeland Current Systems, J. Geophys.Res., 101, 27187-27198, 1996.
4. N.A. Tsyganenko, A model of the near magnetosphere with a dawn-dusk asymmetry - 1. Mathematical Structure, J. Geophys.Res., 107, A8, 10.1029/2001JA000219, 2002.
5. N.A. Tsyganenko, A model of the near magnetosphere with a dawn-dusk asymmetry - 2. Parameterization and fitting to observations, J. Geophys.Res., 107, A7, 10.1029/2001JA000220, 2002.
6. N.A. Tsyganenko and M. I. Sitnov, Modeling the dynamics of the inner magnetosphere during strong geomagnetic storms, J. Geophys.Res., 110, A3, 10.1029/2004JA010798, 2005.
7. Singer, H. & Southwood, D. & Walker, Raymond & Kivelson, M.. (1981). Alfven wave resonances in a realistic magnetospheric magnetic field geometry. Journal of Geophysical Research. 86. 4589-4596. 10.1029/JA086iA06p04589.