apexpy.apex

Classes that make up the core of apexpy.

Exceptions

ApexHeightError

Specialized ValueError definition, to be used when apex height is wrong.

Classes

Apex	Calculates coordinate conversions, field-line mapping, and base vectors.

Module Contents

exception apexpy.apex.ApexHeightError

Bases: ValueError

Specialized ValueError definition, to be used when apex height is wrong.

class apexpy.apex.Apex(date=None, refh=0, datafile=None, fortranlib=None)

Bases: object

Calculates coordinate conversions, field-line mapping, and base vectors.

Parameters:

• date (NoneType, float, dt.date, or dt.datetime, optional) – Determines which IGRF coefficients are used in conversions. Uses current date as default. If float, use decimal year. If None, uses current UTC. (default=None)

• refh (float, optional) – Reference height in km for apex coordinates, the field lines are mapped to this height. (default=0)

• datafile (str or NoneType, optional) – Path to custom coefficient file, if None uses apexsh.dat file (default=None)

• fortranlib (str or NoneType, optional) – Path to Fortran Apex CPython library, if None uses linked library file (default=None)

Variables:

• year (float) – Decimal year used for the IGRF model

• RE (float) – Earth radius in km, defaults to mean Earth radius

• refh (float) – Reference height in km for apex coordinates

• datafile (str) – Path to coefficient file

• fortranlib (str) – Path to Fortran Apex CPython library

• igrf_fn (str) – IGRF coefficient filename

Notes

The calculations use IGRF-13 with coefficients from 1900 to 2025 [1].

The geodetic reference ellipsoid is WGS84.

References

[1]

Thébault, E. et al. (2015), International Geomagnetic Reference Field: the 12th generation, Earth, Planets and Space, 67(1), 79, doi:10.1186/s40623-015-0228-9.

RE = 6371.009

datafile

fortranlib

igrf_fn

_geo2qd

_geo2apex

_geo2apexall

_qd2geo

_basevec

_apex2qd

_qd2apex

_get_babs

__repr__()

Produce an evaluatable representation of the Apex class.

__str__()

Produce a user-friendly representation of the Apex class.

__eq__(comp_obj)

Performs equivalency evaluation.

Parameters:

comp_obj – Object of any time to be compared to the class object

Returns:

bool or NotImplemented – True if self and comp_obj are identical, False if they are not, and NotImplemented if the classes are not the same

_apex2qd_nonvectorized(alat, alon, height)

Convert from apex to quasi-dipole (not-vectorised)

Parameters:

• alat ((float)) – Apex latitude in degrees

• alon ((float)) – Apex longitude in degrees

• height ((float)) – Height in km

Returns:

• qlat ((float)) – Quasi-dipole latitude in degrees

• qlon ((float)) – Quasi-diplole longitude in degrees

_qd2apex_nonvectorized(qlat, qlon, height)

Converts quasi-dipole to modified apex coordinates.

Parameters:

• qlat (float) – Quasi-dipole latitude

• qlon (float) – Quasi-dipole longitude

• height (float) – Altitude in km

Returns:

• alat (float) – Modified apex latitude

• alon (float) – Modified apex longitude

Raises:

ApexHeightError – if apex height < reference height

_map_EV_to_height(alat, alon, height, newheight, data, ev_flag)

Maps electric field related values to a desired height

Parameters:

• alat (array-like) – Apex latitude in degrees.

• alon (array-like) – Apex longitude in degrees.

• height (array-like) – Current altitude in km.

• new_height (array-like) – Desired altitude to which EV values will be mapped in km.

• data (array-like) – 3D value(s) for the electric field or electric drift

• ev_flag (str) – Specify if value is an electric field (‘E’) or electric drift (‘V’)

Returns:

data_mapped (array-like) – Data mapped along the magnetic field from the old height to the new height.

Raises:

ValueError – If an unknown ev_flag or badly shaped data input is supplied.

_get_babs_nonvectorized(glat, glon, height)

Get the absolute value of the B-field in Tesla

Parameters:

• glat (float) – Geodetic latitude in degrees

• glon (float) – Geodetic longitude in degrees

• height (float) – Altitude in km

Returns:

babs (float) – Absolute value of the magnetic field in Tesla

convert(lat, lon, source, dest, height=0, datetime=None, precision=1e-10, ssheight=50 * 6371)

Converts between geodetic, modified apex, quasi-dipole and MLT.

Parameters:

• lat (array_like) – Latitude in degrees

• lon (array_like) – Longitude in degrees or MLT in hours

• source (str) – Input coordinate system, accepts ‘geo’, ‘apex’, ‘qd’, or ‘mlt’

• dest (str) – Output coordinate system, accepts ‘geo’, ‘apex’, ‘qd’, or ‘mlt’

• height (array_like, optional) – Altitude in km

• datetime (datetime.datetime) – Date and time for MLT conversions (required for MLT conversions)

• precision (float, optional) – Precision of output (degrees) when converting to geo. A negative value of this argument produces a low-precision calculation of geodetic lat/lon based only on their spherical harmonic representation. A positive value causes the underlying Fortran routine to iterate until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to within the specified precision (all coordinates being converted to geo are converted to QD first and passed through APXG2Q).

• ssheight (float, optional) – Altitude in km to use for converting the subsolar point from geographic to magnetic coordinates. A high altitude is used to ensure the subsolar point is mapped to high latitudes, which prevents the South-Atlantic Anomaly (SAA) from influencing the MLT.

Returns:

• lat (ndarray or float) – Converted latitude (if converting to MLT, output latitude is apex)

• lon (ndarray or float) – Converted longitude or MLT

Raises:

ValueError – For unknown source or destination coordinate system or a missing or badly formed latitude or datetime input

geo2apex(glat, glon, height)

Converts geodetic to modified apex coordinates.

Parameters:

• glat (array_like) – Geodetic latitude

• glon (array_like) – Geodetic longitude

• height (array_like) – Altitude in km

Returns:

• alat (ndarray or float) – Modified apex latitude

• alon (ndarray or float) – Modified apex longitude

apex2geo(alat, alon, height, precision=1e-10)

Converts modified apex to geodetic coordinates.

Parameters:

• alat (array_like) – Modified apex latitude

• alon (array_like) – Modified apex longitude

• height (array_like) – Altitude in km

• precision (float, optional) – Precision of output (degrees). A negative value of this argument produces a low-precision calculation of geodetic lat/lon based only on their spherical harmonic representation. A positive value causes the underlying Fortran routine to iterate until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to within the specified precision.

Returns:

• glat (ndarray or float) – Geodetic latitude

• glon (ndarray or float) – Geodetic longitude

• error (ndarray or float) – The angular difference (degrees) between the input QD coordinates and the qlat/qlon produced by feeding the output glat and glon into geo2qd (APXG2Q)

geo2qd(glat, glon, height)

Converts geodetic to quasi-dipole coordinates.

Parameters:

• glat (array_like) – Geodetic latitude

• glon (array_like) – Geodetic longitude

• height (array_like) – Altitude in km

Returns:

• qlat (ndarray or float) – Quasi-dipole latitude

• qlon (ndarray or float) – Quasi-dipole longitude

qd2geo(qlat, qlon, height, precision=1e-10)

Converts quasi-dipole to geodetic coordinates.

Parameters:

• qlat (array_like) – Quasi-dipole latitude

• qlon (array_like) – Quasi-dipole longitude

• height (array_like) – Altitude in km

• precision (float, optional) – Precision of output (degrees). A negative value of this argument produces a low-precision calculation of geodetic lat/lon based only on their spherical harmonic representation. A positive value causes the underlying Fortran routine to iterate until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to within the specified precision.

Returns:

• glat (ndarray or float) – Geodetic latitude

• glon (ndarray or float) – Geodetic longitude

• error (ndarray or float) – The angular difference (degrees) between the input QD coordinates and the qlat/qlon produced by feeding the output glat and glon into geo2qd (APXG2Q)

apex2qd(alat, alon, height)

Converts modified apex to quasi-dipole coordinates.

Parameters:

• alat (array_like) – Modified apex latitude

• alon (array_like) – Modified apex longitude

• height (array_like) – Altitude in km

Returns:

• qlat (ndarray or float) – Quasi-dipole latitude

• qlon (ndarray or float) – Quasi-dipole longitude

Raises:

ApexHeightError – if height > apex height

qd2apex(qlat, qlon, height)

Converts quasi-dipole to modified apex coordinates.

Parameters:

• qlat (array_like) – Quasi-dipole latitude

• qlon (array_like) – Quasi-dipole longitude

• height (array_like) – Altitude in km

Returns:

• alat (ndarray or float) – Modified apex latitude

• alon (ndarray or float) – Modified apex longitude

Raises:

ApexHeightError – if apex height < reference height

mlon2mlt(mlon, dtime, ssheight=318550)

Computes the magnetic local time at the specified magnetic longitude and UT.

Parameters:

• mlon (array_like) – Magnetic longitude (apex and quasi-dipole longitude are always equal)

• dtime (datetime.datetime) – Date and time

• ssheight (float, optional) – Altitude in km to use for converting the subsolar point from geographic to magnetic coordinates. A high altitude is used to ensure the subsolar point is mapped to high latitudes, which prevents the South-Atlantic Anomaly (SAA) from influencing the MLT. The current default is 50 * 6371, roughly 50 RE. (default=318550)

Returns:

mlt (ndarray or float) – Magnetic local time in hours [0, 24)

Notes

To compute the MLT, we find the apex longitude of the subsolar point at the given time. Then the MLT of the given point will be computed from the separation in magnetic longitude from this point (1 hour = 15 degrees).

mlt2mlon(mlt, dtime, ssheight=318550)

Computes the magnetic longitude at the specified MLT and UT.

Parameters:

• mlt (array_like) – Magnetic local time

• dtime (datetime.datetime) – Date and time

• ssheight (float, optional) – Altitude in km to use for converting the subsolar point from geographic to magnetic coordinates. A high altitude is used to ensure the subsolar point is mapped to high latitudes, which prevents the South-Atlantic Anomaly (SAA) from influencing the MLT. The current default is 50 * 6371, roughly 50 RE. (default=318550)

Returns:

mlon (ndarray or float) – Magnetic longitude [0, 360) (apex and quasi-dipole longitude are always equal)

Notes

To compute the magnetic longitude, we find the apex longitude of the subsolar point at the given time. Then the magnetic longitude of the given point will be computed from the separation in magnetic local time from this point (1 hour = 15 degrees).

map_to_height(glat, glon, height, newheight, conjugate=False, precision=1e-10)

Performs mapping of points along the magnetic field to the closest or conjugate hemisphere.

Parameters:

• glat (array_like) – Geodetic latitude

• glon (array_like) – Geodetic longitude

• height (array_like) – Source altitude in km

• newheight (array_like) – Destination altitude in km

• conjugate (bool, optional) – Map to newheight in the conjugate hemisphere instead of the closest hemisphere

• precision (float, optional) – Precision of output (degrees). A negative value of this argument produces a low-precision calculation of geodetic lat/lon based only on their spherical harmonic representation. A positive value causes the underlying Fortran routine to iterate until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to within the specified precision.

Returns:

• newglat (ndarray or float) – Geodetic latitude of mapped point

• newglon (ndarray or float) – Geodetic longitude of mapped point

• error (ndarray or float) – The angular difference (degrees) between the input QD coordinates and the qlat/qlon produced by feeding the output glat and glon into geo2qd (APXG2Q)

Notes

The mapping is done by converting glat/glon/height to modified apex lat/lon, and converting back to geographic using newheight (if conjugate, use negative apex latitude when converting back)

map_E_to_height(alat, alon, height, newheight, edata)

Performs mapping of electric field along the magnetic field.

It is assumed that the electric field is perpendicular to B.

Parameters:

• alat ((N,) array_like or float) – Modified apex latitude

• alon ((N,) array_like or float) – Modified apex longitude

• height ((N,) array_like or float) – Source altitude in km

• newheight ((N,) array_like or float) – Destination altitude in km

• edata ((3,) or (3, N) array_like) – Electric field (at alat, alon, height) in geodetic east, north, and up components

Returns:

out ((3, N) or (3,) ndarray) – The electric field at newheight (geodetic east, north, and up components)

map_V_to_height(alat, alon, height, newheight, vdata)

Performs mapping of electric drift velocity along the magnetic field.

It is assumed that the electric field is perpendicular to B.

Parameters:

• alat ((N,) array_like or float) – Modified apex latitude

• alon ((N,) array_like or float) – Modified apex longitude

• height ((N,) array_like or float) – Source altitude in km

• newheight ((N,) array_like or float) – Destination altitude in km

• vdata ((3,) or (3, N) array_like) – Electric drift velocity (at alat, alon, height) in geodetic east, north, and up components

Returns:

out ((3, N) or (3,) ndarray) – The electric drift velocity at newheight (geodetic east, north, and up components)

basevectors_qd(lat, lon, height, coords='geo', precision=1e-10)

Get quasi-dipole base vectors f1 and f2 at the specified coordinates.

Parameters:

• lat ((N,) array_like or float) – Latitude

• lon ((N,) array_like or float) – Longitude

• height ((N,) array_like or float) – Altitude in km

• coords ({‘geo’, ‘apex’, ‘qd’}, optional) – Input coordinate system

• precision (float, optional) – Precision of output (degrees) when converting to geo. A negative value of this argument produces a low-precision calculation of geodetic lat/lon based only on their spherical harmonic representation. A positive value causes the underlying Fortran routine to iterate until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to within the specified precision (all coordinates being converted to geo are converted to QD first and passed through APXG2Q).

Returns:

• f1 ((2, N) or (2,) ndarray)

• f2 ((2, N) or (2,) ndarray)

Notes

The vectors are described by Richmond [1995] [2] and Emmert et al. [2010] [3]. The vector components are geodetic east and north.

References

[2]

Richmond, A. D. (1995), Ionospheric Electrodynamics Using Magnetic Apex Coordinates, Journal of geomagnetism and geoelectricity, 47(2), 191–212, doi:10.5636/jgg.47.191.

[3]

Emmert, J. T., A. D. Richmond, and D. P. Drob (2010), A computationally compact representation of Magnetic-Apex and Quasi-Dipole coordinates with smooth base vectors, J. Geophys. Res., 115(A8), A08322, doi:10.1029/2010JA015326.

basevectors_apex(lat, lon, height, coords='geo', precision=1e-10)

Returns base vectors in quasi-dipole and apex coordinates.

Parameters:

• lat (array_like or float) – Latitude in degrees; input must be broadcastable with lon and height.

• lon (array_like or float) – Longitude in degrees; input must be broadcastable with lat and height.

• height (array_like or float) – Altitude in km; input must be broadcastable with lon and lat.

• coords (str, optional) – Input coordinate system, expects one of ‘geo’, ‘apex’, or ‘qd’ (default=’geo’)

• precision (float, optional) – Precision of output (degrees) when converting to geo. A negative value of this argument produces a low-precision calculation of geodetic lat/lon based only on their spherical harmonic representation. A positive value causes the underlying Fortran routine to iterate until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to within the specified precision (all coordinates being converted to geo are converted to QD first and passed through APXG2Q).

Returns:

• f1 ((3, N) or (3,) ndarray) – Quasi-dipole base vector equivalent to e1, tangent to contours of constant lambdaA

• f2 ((3, N) or (3,) ndarray) – Quasi-dipole base vector equivalent to e2

• f3 ((3, N) or (3,) ndarray) – Quasi-dipole base vector equivalent to e3, tangent to contours of PhiA

• g1 ((3, N) or (3,) ndarray) – Quasi-dipole base vector equivalent to d1

• g2 ((3, N) or (3,) ndarray) – Quasi-dipole base vector equivalent to d2

• g3 ((3, N) or (3,) ndarray) – Quasi-dipole base vector equivalent to d3

• d1 ((3, N) or (3,) ndarray) – Apex base vector normal to contours of constant PhiA

• d2 ((3, N) or (3,) ndarray) – Apex base vector that completes the right-handed system

• d3 ((3, N) or (3,) ndarray) – Apex base vector normal to contours of constant lambdaA

• e1 ((3, N) or (3,) ndarray) – Apex base vector tangent to contours of constant V0

• e2 ((3, N) or (3,) ndarray) – Apex base vector that completes the right-handed system

• e3 ((3, N) or (3,) ndarray) – Apex base vector tangent to contours of constant PhiA

Notes

The vectors are described by Richmond [1995] [4] and Emmert et al. [2010] [5]. The vector components are geodetic east, north, and up (only east and north for f1 and f2).

f3, g1, g2, and g3 are not part of the Fortran code by Emmert et al. [2010] [5]. They are calculated by this Python library according to the following equations in Richmond [1995] [4]:

• g1: Eqn. 6.3

• g2: Eqn. 6.4

• g3: Eqn. 6.5

• f3: Eqn. 6.8

References

[4] (1,2,3,4,5)

Richmond, A. D. (1995), Ionospheric Electrodynamics Using Magnetic Apex Coordinates, Journal of geomagnetism and geoelectricity, 47(2), 191–212, doi:10.5636/jgg.47.191.

[5] (1,2,3,4)

Emmert, J. T., A. D. Richmond, and D. P. Drob (2010), A computationally compact representation of Magnetic-Apex and Quasi-Dipole coordinates with smooth base vectors, J. Geophys. Res., 115(A8), A08322, doi:10.1029/2010JA015326.

get_apex(lat, height=None)

Calculate apex height

Parameters:

• lat (float) – Apex latitude in degrees

• height (float or NoneType) – Height above the surface of the Earth in km or NoneType to use reference height (default=None)

Returns:

apex_height (float) – Height of the field line apex in km

get_height(lat, apex_height)

Calculate the height given an apex latitude and apex height.

Parameters:

• lat (float) – Apex latitude in degrees

• apex_height (float) – Maximum height of the apex field line above the surface of the Earth in km

Returns:

height (float) – Height above the surface of the Earth in km

set_epoch(year)

Updates the epoch for all subsequent conversions.

Parameters:

year (float) – Decimal year

set_refh(refh)

Updates the apex reference height for all subsequent conversions.

Parameters:

refh (float) – Apex reference height in km

Notes

The reference height is the height to which field lines will be mapped, and is only relevant for conversions involving apex (not quasi-dipole).

get_babs(glat, glon, height)

Returns the magnitude of the IGRF magnetic field in tesla.

Parameters:

• glat (array_like) – Geodetic latitude in degrees

• glon (array_like) – Geodetic longitude in degrees

• height (array_like) – Altitude in km

Returns:

babs (ndarray or float) – Magnitude of the IGRF magnetic field in Tesla

bvectors_apex(lat, lon, height, coords='geo', precision=1e-10)

Returns the magnetic field vectors in apex coordinates.

Parameters:

• lat ((N,) array_like or float) – Latitude

• lon ((N,) array_like or float) – Longitude

• height ((N,) array_like or float) – Altitude in km

• coords ({‘geo’, ‘apex’, ‘qd’}, optional) – Input coordinate system

• precision (float, optional) – Precision of output (degrees) when converting to geo. A negative value of this argument produces a low-precision calculation of geodetic lat/lon based only on their spherical harmonic representation. A positive value causes the underlying Fortran routine to iterate until feeding the output geo lat/lon into geo2qd (APXG2Q) reproduces the input QD lat/lon to within the specified precision (all coordinates being converted to geo are converted to QD first and passed through APXG2Q).

Returns:

• main_mag_e3 ((1, N) or (1,) ndarray) – IGRF magnitude divided by a scaling factor, D (d_scale) to give the main B field magnitude along the e3 base vector

• e3 ((3, N) or (3,) ndarray) – Base vector tangent to the contours of constant V_0 and Phi_A

• main_mag_d3 ((1, N) or (1,) ndarray) – IGRF magnitude multiplied by a scaling factor, D (d_scale) to give the main B field magnitudee along the d3 base vector

• d3 ((3, N) or (3,) ndarray) – Base vector equivalent to the scaled main field unit vector

Notes

See Richmond, A. D. (1995) [4] equations 3.8-3.14

The apex magnetic field vectors described by Richmond [1995] [4] and Emmert et al. [2010] [5], specfically the Be3 (main_mag_e3) and Bd3 (main_mag_d3) components. The vector components are geodetic east, north, and up.

References

Richmond, A. D. (1995) [4] Emmert, J. T. et al. (2010) [5]