Magnetism Models

Earth magnetic field models and computations.

Magnetism models module.

This module provides implementations of geomagnetic field models including the World Magnetic Model (WMM), International Geomagnetic Reference Field (IGRF), and high-resolution models (EMM, WMMHR).

Examples

>>> from pytcl.magnetism import wmm, magnetic_declination
>>> import numpy as np

>>> # Magnetic field at a location
>>> result = wmm(np.radians(40), np.radians(-105), 1.0, 2023.0)
>>> print(f"Declination: {np.degrees(result.D):.2f}°")
>>> print(f"Total intensity: {result.F:.0f} nT")

>>> # Just the declination
>>> D = magnetic_declination(np.radians(40), np.radians(-105))
>>> print(f"Declination: {np.degrees(D):.2f}°")

>>> # High-resolution models (require external coefficient files)
>>> from pytcl.magnetism import emm, wmmhr, create_emm_test_coefficients
>>> # Create test coefficients for demonstration
>>> coef = create_emm_test_coefficients(n_max=36)

class pytcl.magnetism.MagneticResult(X, Y, Z, H, F, I, D)

Bases: NamedTuple

Result of magnetic field computation.

X

Northward component (nT).

Type:

float

Y

Eastward component (nT).

Type:

float

Z

Downward component (nT).

Type:

float

H

Horizontal intensity (nT).

Type:

float

F

Total intensity (nT).

Type:

float

I

Inclination (dip angle) in radians.

Type:

float

D

Declination in radians.

Type:

float

X: float

Alias for field number 0

Y: float

Alias for field number 1

Z: float

Alias for field number 2

H: float

Alias for field number 3

F: float

Alias for field number 4

I: float

Alias for field number 5

D: float

Alias for field number 6

class pytcl.magnetism.MagneticCoefficients(g, h, g_dot, h_dot, epoch, n_max)

Bases: NamedTuple

Spherical harmonic coefficients for magnetic model.

g

Main field cosine coefficients (nT).

Type:

ndarray

h

Main field sine coefficients (nT).

Type:

ndarray

g_dot

Secular variation of g (nT/year).

Type:

ndarray

h_dot

Secular variation of h (nT/year).

Type:

ndarray

epoch

Reference epoch (decimal year).

Type:

float

n_max

Maximum degree.

Type:

int

g: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 0

h: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 1

g_dot: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 2

h_dot: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 3

epoch: float

Alias for field number 4

n_max: int

Alias for field number 5

class pytcl.magnetism.IGRFModel(epoch, coeffs, valid_from, valid_to)

Bases: NamedTuple

IGRF model for a specific epoch.

epoch

Reference epoch year.

Type:

float

coeffs

Spherical harmonic coefficients.

Type:

MagneticCoefficients

valid_from

Start of validity period.

Type:

float

valid_to

End of validity period.

Type:

float

epoch: float

Alias for field number 0

coeffs: MagneticCoefficients

Alias for field number 1

valid_from: float

Alias for field number 2

valid_to: float

Alias for field number 3

pytcl.magnetism.create_wmm2020_coefficients()

Create WMM2020 model coefficients.

Returns:

coeffs – WMM2020 spherical harmonic coefficients.

Return type:

MagneticCoefficients

Examples

>>> coeffs = create_wmm2020_coefficients()
>>> coeffs.epoch
2020.0
>>> coeffs.n_max
12

Notes

These are the official WMM2020 coefficients valid from 2020.0 to 2025.0. For use beyond 2025, updated coefficients should be obtained from NOAA.

pytcl.magnetism.magnetic_field_spherical(lat, lon, r, year, coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94045e+04, -1.45070e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.50000e+03, 2.98200e+03, 1.67680e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36390e+03, -2.38100e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03100e+02, 8.09400e+02, 8.62000e+01, -3.09400e+02, 4.79000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34400e+02, 3.63100e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.56000e+01, 6.55000e+01, -1.91000e+01, 7.30000e+01, -6.27000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.06000e+01, -7.67000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.44000e+01, 6.00000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.09000e+01, -1.30000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.10000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6529e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3480e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2200e+01, 2.4180e+02, -5.4290e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8200e+02, -1.5840e+02, 1.9980e+02, -3.5010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6700e+01, 1.9690e+02, -1.1940e+02, 1.6000e+01, 1.0010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5900e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5500e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.8000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0400e+01, 1.3400e+01, 1.2100e+01, -6.4000e+00, -8.4000e+00, 8.6000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.8000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 5.7, -1., 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 12), use_cache=True)

Compute magnetic field in spherical coordinates.

Parameters:

• lat (float) – Geocentric latitude in radians.

• lon (float) – Longitude in radians.

• r (float) – Radial distance from Earth’s center in km.

• year (float) – Decimal year (e.g., 2023.5 for mid-2023).

• coeffs (MagneticCoefficients, optional) – Model coefficients. Default WMM2020.

• use_cache (bool, optional) – Whether to use LRU caching for repeated queries. Default True. Set to False for single-use queries or when memory is constrained.

Returns:

• B_r (float) – Radial component (positive outward) in nT.

• B_theta (float) – Colatitude component (positive southward) in nT.

• B_phi (float) – Longitude component (positive eastward) in nT.

Return type:

Tuple[float, float, float]

Notes

Results are cached by default using LRU caching. Inputs are quantized to a configurable precision before caching to improve hit rates for nearby queries. Use get_magnetic_cache_info() to check cache statistics and clear_magnetic_cache() to free memory.

Examples

>>> import numpy as np
>>> from pytcl.magnetism import magnetic_field_spherical
>>> # Compute at Earth's surface (40°N, 105°W, sea level)
>>> lat = np.radians(40)
>>> lon = np.radians(-105)
>>> r = 6371.2  # Earth mean radius in km
>>> B_r, B_theta, B_phi = magnetic_field_spherical(lat, lon, r, 2023.0)
>>> # All components should be on order of tens to tens of thousands of nT
>>> 20000 < (B_r**2 + B_theta**2 + B_phi**2)**0.5 < 70000
True

pytcl.magnetism.wmm(lat, lon, h=0.0, year=2023.0, coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94045e+04, -1.45070e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.50000e+03, 2.98200e+03, 1.67680e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36390e+03, -2.38100e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03100e+02, 8.09400e+02, 8.62000e+01, -3.09400e+02, 4.79000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34400e+02, 3.63100e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.56000e+01, 6.55000e+01, -1.91000e+01, 7.30000e+01, -6.27000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.06000e+01, -7.67000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.44000e+01, 6.00000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.09000e+01, -1.30000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.10000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6529e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3480e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2200e+01, 2.4180e+02, -5.4290e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8200e+02, -1.5840e+02, 1.9980e+02, -3.5010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6700e+01, 1.9690e+02, -1.1940e+02, 1.6000e+01, 1.0010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5900e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5500e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.8000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0400e+01, 1.3400e+01, 1.2100e+01, -6.4000e+00, -8.4000e+00, 8.6000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.8000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 5.7, -1., 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 12))

Compute magnetic field using World Magnetic Model.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above WGS84 ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

• coeffs (MagneticCoefficients, optional) – Model coefficients. Default WMM2020.

Returns:

result – Magnetic field components and derived quantities.

Return type:

MagneticResult

Examples

>>> import numpy as np
>>> result = wmm(np.radians(40), np.radians(-105), 1.0, 2023.0)
>>> print(f"Declination: {np.degrees(result.D):.2f}°")
>>> print(f"Inclination: {np.degrees(result.I):.2f}°")
>>> print(f"Total intensity: {result.F:.0f} nT")

pytcl.magnetism.magnetic_declination(lat, lon, h=0.0, year=2023.0, coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94045e+04, -1.45070e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.50000e+03, 2.98200e+03, 1.67680e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36390e+03, -2.38100e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03100e+02, 8.09400e+02, 8.62000e+01, -3.09400e+02, 4.79000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34400e+02, 3.63100e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.56000e+01, 6.55000e+01, -1.91000e+01, 7.30000e+01, -6.27000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.06000e+01, -7.67000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.44000e+01, 6.00000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.09000e+01, -1.30000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.10000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6529e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3480e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2200e+01, 2.4180e+02, -5.4290e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8200e+02, -1.5840e+02, 1.9980e+02, -3.5010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6700e+01, 1.9690e+02, -1.1940e+02, 1.6000e+01, 1.0010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5900e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5500e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.8000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0400e+01, 1.3400e+01, 1.2100e+01, -6.4000e+00, -8.4000e+00, 8.6000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.8000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 5.7, -1., 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 12))

Compute magnetic declination (variation).

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

• coeffs (MagneticCoefficients, optional) – Model coefficients.

Returns:

D – Magnetic declination in radians. Positive = east of true north. Negative = west of true north.

Return type:

float

Examples

>>> import numpy as np
>>> # Declination in Denver, CO
>>> D = magnetic_declination(np.radians(39.7), np.radians(-105.0))
>>> print(f"Declination: {np.degrees(D):.1f}°")

pytcl.magnetism.magnetic_inclination(lat, lon, h=0.0, year=2023.0, coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94045e+04, -1.45070e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.50000e+03, 2.98200e+03, 1.67680e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36390e+03, -2.38100e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03100e+02, 8.09400e+02, 8.62000e+01, -3.09400e+02, 4.79000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34400e+02, 3.63100e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.56000e+01, 6.55000e+01, -1.91000e+01, 7.30000e+01, -6.27000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.06000e+01, -7.67000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.44000e+01, 6.00000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.09000e+01, -1.30000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.10000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6529e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3480e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2200e+01, 2.4180e+02, -5.4290e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8200e+02, -1.5840e+02, 1.9980e+02, -3.5010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6700e+01, 1.9690e+02, -1.1940e+02, 1.6000e+01, 1.0010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5900e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5500e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.8000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0400e+01, 1.3400e+01, 1.2100e+01, -6.4000e+00, -8.4000e+00, 8.6000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.8000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 5.7, -1., 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 12))

Compute magnetic inclination (dip angle).

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

• coeffs (MagneticCoefficients, optional) – Model coefficients.

Returns:

I – Magnetic inclination in radians. Positive = field points into Earth (Northern hemisphere). Negative = field points out of Earth (Southern hemisphere).

Return type:

float

Examples

>>> import numpy as np
>>> from pytcl.magnetism import magnetic_inclination
>>> # Inclination at 40°N, 105°W (Denver)
>>> lat = np.radians(40)
>>> lon = np.radians(-105)
>>> I = magnetic_inclination(lat, lon, 1.6, 2023.0)
>>> # Northern hemisphere: inclination should be positive
>>> I > 0
True
>>> # Typical values in US are 50-70 degrees
>>> 0.8 < I < 1.3  # ~46-74 degrees
True

pytcl.magnetism.magnetic_field_intensity(lat, lon, h=0.0, year=2023.0, coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94045e+04, -1.45070e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.50000e+03, 2.98200e+03, 1.67680e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36390e+03, -2.38100e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03100e+02, 8.09400e+02, 8.62000e+01, -3.09400e+02, 4.79000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34400e+02, 3.63100e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.56000e+01, 6.55000e+01, -1.91000e+01, 7.30000e+01, -6.27000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.06000e+01, -7.67000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.44000e+01, 6.00000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.09000e+01, -1.30000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.10000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6529e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3480e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2200e+01, 2.4180e+02, -5.4290e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8200e+02, -1.5840e+02, 1.9980e+02, -3.5010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6700e+01, 1.9690e+02, -1.1940e+02, 1.6000e+01, 1.0010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5900e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5500e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.8000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0400e+01, 1.3400e+01, 1.2100e+01, -6.4000e+00, -8.4000e+00, 8.6000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.8000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 5.7, -1., 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 12))

Compute total magnetic field intensity.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

• coeffs (MagneticCoefficients, optional) – Model coefficients.

Returns:

F – Total magnetic field intensity in nT.

Return type:

float

Examples

>>> import numpy as np
>>> from pytcl.magnetism import magnetic_field_intensity
>>> # Field intensity at magnetic equator vs pole
>>> F_eq = magnetic_field_intensity(0, 0, 0, 2023.0)  # Equator
>>> F_pole = magnetic_field_intensity(np.radians(80), 0, 0, 2023.0)  # Near pole
>>> # Field is stronger at poles
>>> F_pole > F_eq
True
>>> # Typical Earth field is 25,000 to 65,000 nT
>>> 25000 < F_eq < 35000  # Equatorial field is weaker
True
>>> 55000 < F_pole < 65000  # Polar field is stronger
True

pytcl.magnetism.get_magnetic_cache_info()

Get information about the magnetic field computation cache.

Returns:

info – Dictionary containing cache statistics: - hits: Number of cache hits - misses: Number of cache misses - maxsize: Maximum cache size - currsize: Current number of cached entries - hit_rate: Ratio of hits to total calls (0-1)

Return type:

dict

Examples

>>> from pytcl.magnetism import get_magnetic_cache_info
>>> info = get_magnetic_cache_info()
>>> print(f"Cache hit rate: {info['hit_rate']:.1%}")

pytcl.magnetism.clear_magnetic_cache()

Clear the magnetic field computation cache.

This can be useful when memory is constrained or when switching between different coefficient sets.

Examples

>>> from pytcl.magnetism import clear_magnetic_cache
>>> clear_magnetic_cache()  # Free cached computations

pytcl.magnetism.configure_magnetic_cache(maxsize=None, precision=None)

Configure the magnetic field computation cache.

Parameters:

• maxsize (int, optional) – Maximum number of entries in the cache. If None, keeps current. Set to 0 to disable caching.

• precision (dict, optional) – Dictionary with keys ‘lat’, ‘lon’, ‘r’, ‘year’ specifying decimal places for rounding. Higher values = more precision but fewer cache hits.

Notes

Changing cache configuration clears the existing cache.

Examples

>>> from pytcl.magnetism import configure_magnetic_cache
>>> # Increase cache size for batch processing
>>> configure_magnetic_cache(maxsize=4096)
>>> # Reduce precision for more cache hits
>>> configure_magnetic_cache(precision={'lat': 4, 'lon': 4, 'r': 2, 'year': 1})

pytcl.magnetism.create_igrf13_coefficients()

Create IGRF-13 model coefficients for epoch 2020.

Returns:

coeffs – IGRF-13 spherical harmonic coefficients.

Return type:

MagneticCoefficients

Examples

>>> coeffs = create_igrf13_coefficients()
>>> coeffs.epoch
2020.0
>>> coeffs.n_max
13

Notes

IGRF-13 is valid from 1900.0 to 2025.0. This function returns the coefficients for the 2020.0 epoch. For other epochs, the coefficients should be interpolated.

pytcl.magnetism.igrf(lat, lon, h=0.0, year=2023.0, coeffs=None)

Compute magnetic field using IGRF model.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above WGS84 ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

• coeffs (MagneticCoefficients, optional) – Model coefficients. Default IGRF13.

Returns:

result – Magnetic field components and derived quantities.

Return type:

MagneticResult

Examples

>>> import numpy as np
>>> result = igrf(np.radians(45), np.radians(-75), 0, 2023.0)
>>> print(f"Total field: {result.F:.0f} nT")

pytcl.magnetism.igrf_declination(lat, lon, h=0.0, year=2023.0)

Compute magnetic declination using IGRF.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

Returns:

D – Declination in radians.

Return type:

float

Examples

>>> import numpy as np
>>> from pytcl.magnetism import igrf_declination
>>> # Declination at Denver (40°N, 105°W)
>>> lat = np.radians(40)
>>> lon = np.radians(-105)
>>> D = igrf_declination(lat, lon, 1.6, 2023.0)
>>> # Eastern US has westerly declination (~10-20° W)
>>> -0.35 < D < 0  # West is negative
True

pytcl.magnetism.igrf_inclination(lat, lon, h=0.0, year=2023.0)

Compute magnetic inclination using IGRF.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

Returns:

I – Inclination in radians.

Return type:

float

Examples

>>> import numpy as np
>>> from pytcl.magnetism import igrf_inclination
>>> # Inclination comparison: equator vs pole
>>> I_eq = igrf_inclination(0, 0, 0, 2023.0)  # Equator
>>> I_pole = igrf_inclination(np.radians(85), 0, 0, 2023.0)  # Near pole
>>> # At equator, inclination is ~0; at poles it's ~90 degrees
>>> abs(I_eq) < 0.2  # ~11 degrees
True
>>> abs(I_pole) > 1.4  # ~80 degrees
True

pytcl.magnetism.dipole_moment(coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94048e+04, -1.45090e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.49960e+03, 2.98200e+03, 1.67700e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36320e+03, -2.38120e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03000e+02, 8.09500e+02, 8.63000e+01, -3.09400e+02, 4.80000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34300e+02, 3.63200e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.60000e+01, 6.55000e+01, -1.91000e+01, 7.29000e+01, -6.26000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.04000e+01, -7.66000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.42000e+01, 5.80000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.10000e+01, -1.40000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.00000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01, 0.00000e+00], [-1.00000e-01, -2.00000e-01, 1.00000e-01, 1.00000e-01, 0.00000e+00, 0.00000e+00, 1.00000e-01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6525e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3460e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2100e+01, 2.4190e+02, -5.4340e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8190e+02, -1.5840e+02, 1.9970e+02, -3.4970e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6900e+01, 1.9690e+02, -1.1930e+02, 1.6000e+01, 1.0020e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5800e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5400e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.9000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0300e+01, 1.3400e+01, 1.2000e+01, -6.4000e+00, -8.5000e+00, 8.5000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.7000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 0.0000e+00, 0.0000e+00, 1.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 6., -1.1, 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 13))

Compute the centered dipole moment.

Parameters:

coeffs (MagneticCoefficients, optional) – Model coefficients. Default IGRF13.

Returns:

M – Dipole moment in nT * km^3.

Return type:

float

Notes

The dipole moment is computed from the n=1 Gauss coefficients: M = a^3 * sqrt(g10^2 + g11^2 + h11^2)

Examples

>>> from pytcl.magnetism import dipole_moment, IGRF13
>>> # Compute Earth's dipole moment from IGRF-13
>>> M = dipole_moment(IGRF13)
>>> # Earth's dipole moment is approximately 7.9 × 10^22 A·m²
>>> # In nT·km³ units, this is about 7.9 × 10^15
>>> 7e15 < M < 8.5e15
True

pytcl.magnetism.dipole_axis(coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94048e+04, -1.45090e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.49960e+03, 2.98200e+03, 1.67700e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36320e+03, -2.38120e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03000e+02, 8.09500e+02, 8.63000e+01, -3.09400e+02, 4.80000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34300e+02, 3.63200e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.60000e+01, 6.55000e+01, -1.91000e+01, 7.29000e+01, -6.26000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.04000e+01, -7.66000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.42000e+01, 5.80000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.10000e+01, -1.40000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.00000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01, 0.00000e+00], [-1.00000e-01, -2.00000e-01, 1.00000e-01, 1.00000e-01, 0.00000e+00, 0.00000e+00, 1.00000e-01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6525e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3460e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2100e+01, 2.4190e+02, -5.4340e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8190e+02, -1.5840e+02, 1.9970e+02, -3.4970e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6900e+01, 1.9690e+02, -1.1930e+02, 1.6000e+01, 1.0020e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5800e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5400e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.9000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0300e+01, 1.3400e+01, 1.2000e+01, -6.4000e+00, -8.5000e+00, 8.5000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.7000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 0.0000e+00, 0.0000e+00, 1.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 6., -1.1, 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 13))

Compute the geocentric dipole axis direction.

Parameters:

coeffs (MagneticCoefficients, optional) – Model coefficients. Default IGRF13.

Returns:

• lat (float) – Latitude of the north geomagnetic pole in radians.

• lon (float) – Longitude of the north geomagnetic pole in radians.

Return type:

tuple[float, float]

Notes

The geomagnetic pole is where the centered dipole axis intersects the Earth’s surface.

Examples

>>> import numpy as np
>>> from pytcl.magnetism import dipole_axis, IGRF13
>>> # Compute geomagnetic pole location
>>> lat, lon = dipole_axis(IGRF13)
>>> # Geomagnetic north pole is around 80°N, 72°W
>>> 70 < np.degrees(lat) < 85
True
>>> -100 < np.degrees(lon) < -60
True

pytcl.magnetism.magnetic_north_pole(year=2023.0, coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94048e+04, -1.45090e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.49960e+03, 2.98200e+03, 1.67700e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36320e+03, -2.38120e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03000e+02, 8.09500e+02, 8.63000e+01, -3.09400e+02, 4.80000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34300e+02, 3.63200e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.60000e+01, 6.55000e+01, -1.91000e+01, 7.29000e+01, -6.26000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.04000e+01, -7.66000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.42000e+01, 5.80000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.10000e+01, -1.40000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.00000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01, 0.00000e+00], [-1.00000e-01, -2.00000e-01, 1.00000e-01, 1.00000e-01, 0.00000e+00, 0.00000e+00, 1.00000e-01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6525e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3460e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2100e+01, 2.4190e+02, -5.4340e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8190e+02, -1.5840e+02, 1.9970e+02, -3.4970e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6900e+01, 1.9690e+02, -1.1930e+02, 1.6000e+01, 1.0020e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5800e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5400e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.9000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0300e+01, 1.3400e+01, 1.2000e+01, -6.4000e+00, -8.5000e+00, 8.5000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.7000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 0.0000e+00, 0.0000e+00, 1.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 6., -1.1, 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 13))

Compute the location of the magnetic north pole.

The magnetic north pole is where the field is vertical (inclination = 90°). This differs from the geomagnetic pole due to non-dipole field contributions.

Parameters:

• year (float, optional) – Decimal year. Default 2023.0.

• coeffs (MagneticCoefficients, optional) – Model coefficients. Default IGRF13.

Returns:

• lat (float) – Latitude of magnetic north pole in radians.

• lon (float) – Longitude of magnetic north pole in radians.

Return type:

tuple[float, float]

Notes

This uses an iterative search starting from the dipole pole. The magnetic pole moves over time.

Examples

>>> import numpy as np
>>> from pytcl.magnetism import magnetic_north_pole, dipole_axis
>>> # Magnetic north pole location (2023)
>>> lat, lon = magnetic_north_pole(2023.0)
>>> # Should be in Canadian Arctic, around 80-85°N
>>> 75 < np.degrees(lat) < 90
True
>>> -150 < np.degrees(lon) < -60
True
>>> # Compare with geomagnetic pole
>>> geo_lat, geo_lon = dipole_axis()
>>> # Magnetic pole differs from geomagnetic pole
>>> abs(lat - geo_lat) > 0.01  # Different locations
True

class pytcl.magnetism.HighResCoefficients(g, h, g_dot, h_dot, epoch, n_max, n_max_sv, model_name)

Bases: NamedTuple

High-resolution magnetic model coefficients.

Extends MagneticCoefficients with additional metadata for high-degree models like EMM and WMMHR.

g

Main field cosine coefficients (nT), shape (n_max+1, n_max+1).

Type:

ndarray

h

Main field sine coefficients (nT), shape (n_max+1, n_max+1).

Type:

ndarray

g_dot

Secular variation of g (nT/year), shape (n_max_sv+1, n_max_sv+1).

Type:

ndarray

h_dot

Secular variation of h (nT/year), shape (n_max_sv+1, n_max_sv+1).

Type:

ndarray

epoch

Reference epoch (decimal year).

Type:

float

n_max

Maximum degree for main field.

Type:

int

n_max_sv

Maximum degree for secular variation (may be < n_max).

Type:

int

model_name

Model identifier (“EMM2017” or “WMMHR2025”).

Type:

str

g: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 0

h: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 1

g_dot: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 2

h_dot: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 3

epoch: float

Alias for field number 4

n_max: int

Alias for field number 5

n_max_sv: int

Alias for field number 6

model_name: str

Alias for field number 7

pytcl.magnetism.get_emm_data_dir()

Get the pytcl data directory for external data files.

The data directory is located at ~/.pytcl/data/ by default. Can be overridden by setting the PYTCL_DATA_DIR environment variable.

Returns:

Path to the data directory.

Return type:

Path

pytcl.magnetism.load_emm_coefficients(model='EMM2017', n_max=None)

Load high-resolution magnetic model coefficients.

Parameters:

• model (str) – Model name, either “EMM2017” or “WMMHR2025”.

• n_max (int, optional) – Maximum degree to load. If None, loads the full model.

Returns:

Loaded coefficient structure.

Return type:

HighResCoefficients

Raises:

• FileNotFoundError – If the coefficient file is not found.

• ValueError – If an unknown model is specified.

Examples

>>> coef = load_emm_coefficients("WMMHR2025", n_max=50)
>>> coef.n_max
50

pytcl.magnetism.create_emm_test_coefficients(n_max=36)

Create test coefficients for low-degree testing.

Creates a simplified set of coefficients for testing purposes, using the same low-degree terms as WMM2020 extended with synthetic crustal field terms.

Parameters:

n_max (int) – Maximum degree (default 36).

Returns:

Test coefficient set.

Return type:

HighResCoefficients

pytcl.magnetism.emm(lat, lon, h=0.0, year=2020.0, model='EMM2017', n_max=None, coefficients=None)

Compute magnetic field using Enhanced Magnetic Model.

The EMM provides higher spatial resolution than WMM by including crustal magnetic field contributions up to degree 790.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above WGS84 ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2020.0.

• model (str, optional) – Model name (“EMM2017” or “WMMHR2025”). Default “EMM2017”.

• n_max (int, optional) – Maximum degree to evaluate. Default uses full model.

• coefficients (HighResCoefficients, optional) – Pre-loaded coefficients. If None, loads from file.

Returns:

result – Magnetic field components and derived quantities.

Return type:

MagneticResult

Examples

>>> import numpy as np
>>> # Use test coefficients for demonstration
>>> coef = create_test_coefficients(n_max=36)
>>> result = emm(np.radians(40), np.radians(-105), 1.0, 2020.0, coefficients=coef)
>>> print(f"Declination: {np.degrees(result.D):.2f}°")
>>> print(f"Total intensity: {result.F:.0f} nT")

pytcl.magnetism.wmmhr(lat, lon, h=0.0, year=2025.0, n_max=None, coefficients=None)

Compute magnetic field using World Magnetic Model High Resolution.

WMMHR2025 extends WMM to degree 133, providing higher spatial resolution for applications requiring more accurate local field values.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above WGS84 ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2025.0.

• n_max (int, optional) – Maximum degree to evaluate. Default uses full model (133).

• coefficients (HighResCoefficients, optional) – Pre-loaded coefficients. If None, loads from file.

Returns:

result – Magnetic field components and derived quantities.

Return type:

MagneticResult

Notes

WMMHR2025 is valid for 2025.0 - 2030.0. For dates outside this range, results may be less accurate.

Secular variation is only computed for degrees 1-15. Higher degree terms represent static crustal field.

pytcl.magnetism.emm_declination(lat, lon, h=0.0, year=2020.0, model='EMM2017', n_max=None, coefficients=None)

Compute magnetic declination using EMM/WMMHR.

Parameters:

• lat (float or ndarray) – Geodetic latitude in radians.

• lon (float or ndarray) – Longitude in radians.

• h (float or ndarray, optional) – Height above WGS84 ellipsoid in km.

• year (float, optional) – Decimal year.

• model (str, optional) – Model name.

• n_max (int, optional) – Maximum degree to evaluate.

• coefficients (HighResCoefficients, optional) – Pre-loaded coefficients.

Returns:

Magnetic declination in radians.

Return type:

float or ndarray

pytcl.magnetism.emm_inclination(lat, lon, h=0.0, year=2020.0, model='EMM2017', n_max=None, coefficients=None)

Compute magnetic inclination using EMM/WMMHR.

Parameters:

• lat (float or ndarray) – Geodetic latitude in radians.

• lon (float or ndarray) – Longitude in radians.

• h (float or ndarray, optional) – Height above WGS84 ellipsoid in km.

• year (float, optional) – Decimal year.

• model (str, optional) – Model name.

• n_max (int, optional) – Maximum degree to evaluate.

• coefficients (HighResCoefficients, optional) – Pre-loaded coefficients.

Returns:

Magnetic inclination (dip) in radians.

Return type:

float or ndarray

pytcl.magnetism.emm_intensity(lat, lon, h=0.0, year=2020.0, model='EMM2017', n_max=None, coefficients=None)

Compute total magnetic field intensity using EMM/WMMHR.

Parameters:

• lat (float or ndarray) – Geodetic latitude in radians.

• lon (float or ndarray) – Longitude in radians.

• h (float or ndarray, optional) – Height above WGS84 ellipsoid in km.

• year (float, optional) – Decimal year.

• model (str, optional) – Model name.

• n_max (int, optional) – Maximum degree to evaluate.

• coefficients (HighResCoefficients, optional) – Pre-loaded coefficients.

Returns:

Total magnetic field intensity in nT.

Return type:

float or ndarray

World Magnetic Model (WMM)

World Magnetic Model implementation (WMM2020 epoch, valid 2020-2025).

World Magnetic Model (WMM) implementation.

The WMM is the standard model used by the U.S. Department of Defense, the U.K. Ministry of Defence, NATO, and the International Hydrographic Organization for navigation, attitude, and heading referencing.

References

[1]

Chulliat et al., “The US/UK World Magnetic Model for 2020-2025,” NOAA Technical Report, 2020.

[2]

https://www.ngdc.noaa.gov/geomag/WMM/

class pytcl.magnetism.wmm.MagneticResult(X, Y, Z, H, F, I, D)

Bases: NamedTuple

Result of magnetic field computation.

X

Northward component (nT).

Type:

float

Y

Eastward component (nT).

Type:

float

Z

Downward component (nT).

Type:

float

H

Horizontal intensity (nT).

Type:

float

F

Total intensity (nT).

Type:

float

I

Inclination (dip angle) in radians.

Type:

float

D

Declination in radians.

Type:

float

X: float

Alias for field number 0

Y: float

Alias for field number 1

Z: float

Alias for field number 2

H: float

Alias for field number 3

F: float

Alias for field number 4

I: float

Alias for field number 5

D: float

Alias for field number 6

class pytcl.magnetism.wmm.MagneticCoefficients(g, h, g_dot, h_dot, epoch, n_max)

Bases: NamedTuple

Spherical harmonic coefficients for magnetic model.

g

Main field cosine coefficients (nT).

Type:

ndarray

h

Main field sine coefficients (nT).

Type:

ndarray

g_dot

Secular variation of g (nT/year).

Type:

ndarray

h_dot

Secular variation of h (nT/year).

Type:

ndarray

epoch

Reference epoch (decimal year).

Type:

float

n_max

Maximum degree.

Type:

int

g: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 0

h: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 1

g_dot: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 2

h_dot: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 3

epoch: float

Alias for field number 4

n_max: int

Alias for field number 5

pytcl.magnetism.wmm.create_wmm2020_coefficients()

Create WMM2020 model coefficients.

Returns:

coeffs – WMM2020 spherical harmonic coefficients.

Return type:

MagneticCoefficients

Examples

>>> coeffs = create_wmm2020_coefficients()
>>> coeffs.epoch
2020.0
>>> coeffs.n_max
12

Notes

These are the official WMM2020 coefficients valid from 2020.0 to 2025.0. For use beyond 2025, updated coefficients should be obtained from NOAA.

pytcl.magnetism.wmm.magnetic_field_spherical(lat, lon, r, year, coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94045e+04, -1.45070e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.50000e+03, 2.98200e+03, 1.67680e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36390e+03, -2.38100e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03100e+02, 8.09400e+02, 8.62000e+01, -3.09400e+02, 4.79000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34400e+02, 3.63100e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.56000e+01, 6.55000e+01, -1.91000e+01, 7.30000e+01, -6.27000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.06000e+01, -7.67000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.44000e+01, 6.00000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.09000e+01, -1.30000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.10000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6529e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3480e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2200e+01, 2.4180e+02, -5.4290e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8200e+02, -1.5840e+02, 1.9980e+02, -3.5010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6700e+01, 1.9690e+02, -1.1940e+02, 1.6000e+01, 1.0010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5900e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5500e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.8000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0400e+01, 1.3400e+01, 1.2100e+01, -6.4000e+00, -8.4000e+00, 8.6000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.8000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 5.7, -1., 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 12), use_cache=True)

Compute magnetic field in spherical coordinates.

Parameters:

• lat (float) – Geocentric latitude in radians.

• lon (float) – Longitude in radians.

• r (float) – Radial distance from Earth’s center in km.

• year (float) – Decimal year (e.g., 2023.5 for mid-2023).

• coeffs (MagneticCoefficients, optional) – Model coefficients. Default WMM2020.

• use_cache (bool, optional) – Whether to use LRU caching for repeated queries. Default True. Set to False for single-use queries or when memory is constrained.

Returns:

• B_r (float) – Radial component (positive outward) in nT.

• B_theta (float) – Colatitude component (positive southward) in nT.

• B_phi (float) – Longitude component (positive eastward) in nT.

Return type:

Tuple[float, float, float]

Notes

Results are cached by default using LRU caching. Inputs are quantized to a configurable precision before caching to improve hit rates for nearby queries. Use get_magnetic_cache_info() to check cache statistics and clear_magnetic_cache() to free memory.

Examples

>>> import numpy as np
>>> from pytcl.magnetism import magnetic_field_spherical
>>> # Compute at Earth's surface (40°N, 105°W, sea level)
>>> lat = np.radians(40)
>>> lon = np.radians(-105)
>>> r = 6371.2  # Earth mean radius in km
>>> B_r, B_theta, B_phi = magnetic_field_spherical(lat, lon, r, 2023.0)
>>> # All components should be on order of tens to tens of thousands of nT
>>> 20000 < (B_r**2 + B_theta**2 + B_phi**2)**0.5 < 70000
True

pytcl.magnetism.wmm.wmm(lat, lon, h=0.0, year=2023.0, coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94045e+04, -1.45070e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.50000e+03, 2.98200e+03, 1.67680e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36390e+03, -2.38100e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03100e+02, 8.09400e+02, 8.62000e+01, -3.09400e+02, 4.79000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34400e+02, 3.63100e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.56000e+01, 6.55000e+01, -1.91000e+01, 7.30000e+01, -6.27000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.06000e+01, -7.67000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.44000e+01, 6.00000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.09000e+01, -1.30000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.10000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6529e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3480e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2200e+01, 2.4180e+02, -5.4290e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8200e+02, -1.5840e+02, 1.9980e+02, -3.5010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6700e+01, 1.9690e+02, -1.1940e+02, 1.6000e+01, 1.0010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5900e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5500e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.8000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0400e+01, 1.3400e+01, 1.2100e+01, -6.4000e+00, -8.4000e+00, 8.6000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.8000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 5.7, -1., 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 12))

Compute magnetic field using World Magnetic Model.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above WGS84 ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

• coeffs (MagneticCoefficients, optional) – Model coefficients. Default WMM2020.

Returns:

result – Magnetic field components and derived quantities.

Return type:

MagneticResult

Examples

>>> import numpy as np
>>> result = wmm(np.radians(40), np.radians(-105), 1.0, 2023.0)
>>> print(f"Declination: {np.degrees(result.D):.2f}°")
>>> print(f"Inclination: {np.degrees(result.I):.2f}°")
>>> print(f"Total intensity: {result.F:.0f} nT")

pytcl.magnetism.wmm.magnetic_declination(lat, lon, h=0.0, year=2023.0, coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94045e+04, -1.45070e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.50000e+03, 2.98200e+03, 1.67680e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36390e+03, -2.38100e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03100e+02, 8.09400e+02, 8.62000e+01, -3.09400e+02, 4.79000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34400e+02, 3.63100e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.56000e+01, 6.55000e+01, -1.91000e+01, 7.30000e+01, -6.27000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.06000e+01, -7.67000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.44000e+01, 6.00000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.09000e+01, -1.30000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.10000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6529e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3480e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2200e+01, 2.4180e+02, -5.4290e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8200e+02, -1.5840e+02, 1.9980e+02, -3.5010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6700e+01, 1.9690e+02, -1.1940e+02, 1.6000e+01, 1.0010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5900e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5500e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.8000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0400e+01, 1.3400e+01, 1.2100e+01, -6.4000e+00, -8.4000e+00, 8.6000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.8000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 5.7, -1., 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 12))

Compute magnetic declination (variation).

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

• coeffs (MagneticCoefficients, optional) – Model coefficients.

Returns:

D – Magnetic declination in radians. Positive = east of true north. Negative = west of true north.

Return type:

float

Examples

>>> import numpy as np
>>> # Declination in Denver, CO
>>> D = magnetic_declination(np.radians(39.7), np.radians(-105.0))
>>> print(f"Declination: {np.degrees(D):.1f}°")

pytcl.magnetism.wmm.magnetic_inclination(lat, lon, h=0.0, year=2023.0, coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94045e+04, -1.45070e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.50000e+03, 2.98200e+03, 1.67680e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36390e+03, -2.38100e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03100e+02, 8.09400e+02, 8.62000e+01, -3.09400e+02, 4.79000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34400e+02, 3.63100e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.56000e+01, 6.55000e+01, -1.91000e+01, 7.30000e+01, -6.27000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.06000e+01, -7.67000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.44000e+01, 6.00000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.09000e+01, -1.30000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.10000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6529e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3480e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2200e+01, 2.4180e+02, -5.4290e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8200e+02, -1.5840e+02, 1.9980e+02, -3.5010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6700e+01, 1.9690e+02, -1.1940e+02, 1.6000e+01, 1.0010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5900e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5500e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.8000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0400e+01, 1.3400e+01, 1.2100e+01, -6.4000e+00, -8.4000e+00, 8.6000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.8000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 5.7, -1., 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 12))

Compute magnetic inclination (dip angle).

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

• coeffs (MagneticCoefficients, optional) – Model coefficients.

Returns:

I – Magnetic inclination in radians. Positive = field points into Earth (Northern hemisphere). Negative = field points out of Earth (Southern hemisphere).

Return type:

float

Examples

>>> import numpy as np
>>> from pytcl.magnetism import magnetic_inclination
>>> # Inclination at 40°N, 105°W (Denver)
>>> lat = np.radians(40)
>>> lon = np.radians(-105)
>>> I = magnetic_inclination(lat, lon, 1.6, 2023.0)
>>> # Northern hemisphere: inclination should be positive
>>> I > 0
True
>>> # Typical values in US are 50-70 degrees
>>> 0.8 < I < 1.3  # ~46-74 degrees
True

pytcl.magnetism.wmm.magnetic_field_intensity(lat, lon, h=0.0, year=2023.0, coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94045e+04, -1.45070e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.50000e+03, 2.98200e+03, 1.67680e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36390e+03, -2.38100e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03100e+02, 8.09400e+02, 8.62000e+01, -3.09400e+02, 4.79000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34400e+02, 3.63100e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.56000e+01, 6.55000e+01, -1.91000e+01, 7.30000e+01, -6.27000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.06000e+01, -7.67000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.44000e+01, 6.00000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.09000e+01, -1.30000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.10000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6529e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3480e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2200e+01, 2.4180e+02, -5.4290e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8200e+02, -1.5840e+02, 1.9980e+02, -3.5010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6700e+01, 1.9690e+02, -1.1940e+02, 1.6000e+01, 1.0010e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5900e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5500e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.8000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0400e+01, 1.3400e+01, 1.2100e+01, -6.4000e+00, -8.4000e+00, 8.6000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.8000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 5.7, -1., 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 12))

Compute total magnetic field intensity.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

• coeffs (MagneticCoefficients, optional) – Model coefficients.

Returns:

F – Total magnetic field intensity in nT.

Return type:

float

Examples

>>> import numpy as np
>>> from pytcl.magnetism import magnetic_field_intensity
>>> # Field intensity at magnetic equator vs pole
>>> F_eq = magnetic_field_intensity(0, 0, 0, 2023.0)  # Equator
>>> F_pole = magnetic_field_intensity(np.radians(80), 0, 0, 2023.0)  # Near pole
>>> # Field is stronger at poles
>>> F_pole > F_eq
True
>>> # Typical Earth field is 25,000 to 65,000 nT
>>> 25000 < F_eq < 35000  # Equatorial field is weaker
True
>>> 55000 < F_pole < 65000  # Polar field is stronger
True

pytcl.magnetism.wmm.get_magnetic_cache_info()

Get information about the magnetic field computation cache.

Returns:

info – Dictionary containing cache statistics: - hits: Number of cache hits - misses: Number of cache misses - maxsize: Maximum cache size - currsize: Current number of cached entries - hit_rate: Ratio of hits to total calls (0-1)

Return type:

dict

Examples

>>> from pytcl.magnetism import get_magnetic_cache_info
>>> info = get_magnetic_cache_info()
>>> print(f"Cache hit rate: {info['hit_rate']:.1%}")

pytcl.magnetism.wmm.clear_magnetic_cache()

Clear the magnetic field computation cache.

This can be useful when memory is constrained or when switching between different coefficient sets.

Examples

>>> from pytcl.magnetism import clear_magnetic_cache
>>> clear_magnetic_cache()  # Free cached computations

pytcl.magnetism.wmm.configure_magnetic_cache(maxsize=None, precision=None)

Configure the magnetic field computation cache.

Parameters:

• maxsize (int, optional) – Maximum number of entries in the cache. If None, keeps current. Set to 0 to disable caching.

• precision (dict, optional) – Dictionary with keys ‘lat’, ‘lon’, ‘r’, ‘year’ specifying decimal places for rounding. Higher values = more precision but fewer cache hits.

Notes

Changing cache configuration clears the existing cache.

Examples

>>> from pytcl.magnetism import configure_magnetic_cache
>>> # Increase cache size for batch processing
>>> configure_magnetic_cache(maxsize=4096)
>>> # Reduce precision for more cache hits
>>> configure_magnetic_cache(precision={'lat': 4, 'lon': 4, 'r': 2, 'year': 1})

IGRF Model

International Geomagnetic Reference Field (IGRF-13) implementation.

International Geomagnetic Reference Field (IGRF) implementation.

The IGRF is a standard mathematical description of the Earth’s main magnetic field, used widely in studies of the Earth’s interior, its ionosphere and magnetosphere, and in various applications.

References

[1]

Alken et al., “International Geomagnetic Reference Field: the thirteenth generation,” Earth, Planets and Space, 2021.

[2]

https://www.ngdc.noaa.gov/IAGA/vmod/igrf.html

class pytcl.magnetism.igrf.IGRFModel(epoch, coeffs, valid_from, valid_to)

Bases: NamedTuple

IGRF model for a specific epoch.

epoch

Reference epoch year.

Type:

float

coeffs

Spherical harmonic coefficients.

Type:

MagneticCoefficients

valid_from

Start of validity period.

Type:

float

valid_to

End of validity period.

Type:

float

epoch: float

Alias for field number 0

coeffs: MagneticCoefficients

Alias for field number 1

valid_from: float

Alias for field number 2

valid_to: float

Alias for field number 3

pytcl.magnetism.igrf.create_igrf13_coefficients()

Create IGRF-13 model coefficients for epoch 2020.

Returns:

coeffs – IGRF-13 spherical harmonic coefficients.

Return type:

MagneticCoefficients

Examples

>>> coeffs = create_igrf13_coefficients()
>>> coeffs.epoch
2020.0
>>> coeffs.n_max
13

Notes

IGRF-13 is valid from 1900.0 to 2025.0. This function returns the coefficients for the 2020.0 epoch. For other epochs, the coefficients should be interpolated.

pytcl.magnetism.igrf.igrf(lat, lon, h=0.0, year=2023.0, coeffs=None)

Compute magnetic field using IGRF model.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above WGS84 ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

• coeffs (MagneticCoefficients, optional) – Model coefficients. Default IGRF13.

Returns:

result – Magnetic field components and derived quantities.

Return type:

MagneticResult

Examples

>>> import numpy as np
>>> result = igrf(np.radians(45), np.radians(-75), 0, 2023.0)
>>> print(f"Total field: {result.F:.0f} nT")

pytcl.magnetism.igrf.igrf_declination(lat, lon, h=0.0, year=2023.0)

Compute magnetic declination using IGRF.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

Returns:

D – Declination in radians.

Return type:

float

Examples

>>> import numpy as np
>>> from pytcl.magnetism import igrf_declination
>>> # Declination at Denver (40°N, 105°W)
>>> lat = np.radians(40)
>>> lon = np.radians(-105)
>>> D = igrf_declination(lat, lon, 1.6, 2023.0)
>>> # Eastern US has westerly declination (~10-20° W)
>>> -0.35 < D < 0  # West is negative
True

pytcl.magnetism.igrf.igrf_inclination(lat, lon, h=0.0, year=2023.0)

Compute magnetic inclination using IGRF.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height in km. Default 0.

• year (float, optional) – Decimal year. Default 2023.0.

Returns:

I – Inclination in radians.

Return type:

float

Examples

>>> import numpy as np
>>> from pytcl.magnetism import igrf_inclination
>>> # Inclination comparison: equator vs pole
>>> I_eq = igrf_inclination(0, 0, 0, 2023.0)  # Equator
>>> I_pole = igrf_inclination(np.radians(85), 0, 0, 2023.0)  # Near pole
>>> # At equator, inclination is ~0; at poles it's ~90 degrees
>>> abs(I_eq) < 0.2  # ~11 degrees
True
>>> abs(I_pole) > 1.4  # ~80 degrees
True

pytcl.magnetism.igrf.dipole_moment(coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94048e+04, -1.45090e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.49960e+03, 2.98200e+03, 1.67700e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36320e+03, -2.38120e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03000e+02, 8.09500e+02, 8.63000e+01, -3.09400e+02, 4.80000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34300e+02, 3.63200e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.60000e+01, 6.55000e+01, -1.91000e+01, 7.29000e+01, -6.26000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.04000e+01, -7.66000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.42000e+01, 5.80000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.10000e+01, -1.40000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.00000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01, 0.00000e+00], [-1.00000e-01, -2.00000e-01, 1.00000e-01, 1.00000e-01, 0.00000e+00, 0.00000e+00, 1.00000e-01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6525e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3460e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2100e+01, 2.4190e+02, -5.4340e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8190e+02, -1.5840e+02, 1.9970e+02, -3.4970e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6900e+01, 1.9690e+02, -1.1930e+02, 1.6000e+01, 1.0020e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5800e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5400e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.9000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0300e+01, 1.3400e+01, 1.2000e+01, -6.4000e+00, -8.5000e+00, 8.5000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.7000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 0.0000e+00, 0.0000e+00, 1.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 6., -1.1, 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 13))

Compute the centered dipole moment.

Parameters:

coeffs (MagneticCoefficients, optional) – Model coefficients. Default IGRF13.

Returns:

M – Dipole moment in nT * km^3.

Return type:

float

Notes

The dipole moment is computed from the n=1 Gauss coefficients: M = a^3 * sqrt(g10^2 + g11^2 + h11^2)

Examples

>>> from pytcl.magnetism import dipole_moment, IGRF13
>>> # Compute Earth's dipole moment from IGRF-13
>>> M = dipole_moment(IGRF13)
>>> # Earth's dipole moment is approximately 7.9 × 10^22 A·m²
>>> # In nT·km³ units, this is about 7.9 × 10^15
>>> 7e15 < M < 8.5e15
True

pytcl.magnetism.igrf.dipole_axis(coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94048e+04, -1.45090e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.49960e+03, 2.98200e+03, 1.67700e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36320e+03, -2.38120e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03000e+02, 8.09500e+02, 8.63000e+01, -3.09400e+02, 4.80000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34300e+02, 3.63200e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.60000e+01, 6.55000e+01, -1.91000e+01, 7.29000e+01, -6.26000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.04000e+01, -7.66000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.42000e+01, 5.80000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.10000e+01, -1.40000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.00000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01, 0.00000e+00], [-1.00000e-01, -2.00000e-01, 1.00000e-01, 1.00000e-01, 0.00000e+00, 0.00000e+00, 1.00000e-01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6525e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3460e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2100e+01, 2.4190e+02, -5.4340e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8190e+02, -1.5840e+02, 1.9970e+02, -3.4970e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6900e+01, 1.9690e+02, -1.1930e+02, 1.6000e+01, 1.0020e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5800e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5400e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.9000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0300e+01, 1.3400e+01, 1.2000e+01, -6.4000e+00, -8.5000e+00, 8.5000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.7000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 0.0000e+00, 0.0000e+00, 1.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 6., -1.1, 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 13))

Compute the geocentric dipole axis direction.

Parameters:

coeffs (MagneticCoefficients, optional) – Model coefficients. Default IGRF13.

Returns:

• lat (float) – Latitude of the north geomagnetic pole in radians.

• lon (float) – Longitude of the north geomagnetic pole in radians.

Return type:

tuple[float, float]

Notes

The geomagnetic pole is where the centered dipole axis intersects the Earth’s surface.

Examples

>>> import numpy as np
>>> from pytcl.magnetism import dipole_axis, IGRF13
>>> # Compute geomagnetic pole location
>>> lat, lon = dipole_axis(IGRF13)
>>> # Geomagnetic north pole is around 80°N, 72°W
>>> 70 < np.degrees(lat) < 85
True
>>> -100 < np.degrees(lon) < -60
True

pytcl.magnetism.igrf.magnetic_north_pole(year=2023.0, coeffs=(array([[0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.94048e+04, -1.45090e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.49960e+03, 2.98200e+03, 1.67700e+03, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [1.36320e+03, -2.38120e+03, 1.23620e+03, 5.25700e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [9.03000e+02, 8.09500e+02, 8.63000e+01, -3.09400e+02, 4.80000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-2.34300e+02, 3.63200e+02, 4.77000e+01, 1.87800e+02, -1.40700e+02, -1.51200e+02, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [6.60000e+01, 6.55000e+01, -1.91000e+01, 7.29000e+01, -6.26000e+01, 6.00000e-01, -2.42000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [8.04000e+01, -7.66000e+01, -8.20000e+00, -2.66000e+01, 3.00000e+00, -1.49000e+01, 1.04000e+01, -1.83000e+01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [2.42000e+01, 5.80000e+00, -2.00000e+00, -5.80000e+00, 1.00000e-01, 1.10000e+01, -1.40000e+00, -6.50000e+00, -2.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [5.00000e+00, 8.40000e+00, 3.00000e+00, -1.50000e+00, 1.00000e-01, -3.80000e+00, 4.30000e+00, -1.40000e+00, -2.40000e+00, -6.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00], [-1.80000e+00, -7.00000e-01, 2.10000e+00, 2.10000e+00, -2.40000e+00, -1.80000e+00, -5.00000e-01, 6.00000e-01, 9.00000e-01, -8.00000e-01, -2.00000e-01, 0.00000e+00, 0.00000e+00, 0.00000e+00], [3.00000e+00, -1.50000e+00, -2.00000e-01, -3.00000e-01, 5.00000e-01, 1.30000e+00, -1.20000e+00, 7.00000e-01, 4.00000e-01, 0.00000e+00, 6.00000e-01, -5.00000e-01, 0.00000e+00, 0.00000e+00], [-2.00000e-01, -2.00000e-01, -1.00000e-01, 1.00000e-01, 5.00000e-01, 1.00000e+00, -3.00000e-01, -4.00000e-01, -3.00000e-01, 2.00000e-01, -5.00000e-01, 4.00000e-01, -2.00000e-01, 0.00000e+00], [-1.00000e-01, -2.00000e-01, 1.00000e-01, 1.00000e-01, 0.00000e+00, 0.00000e+00, 1.00000e-01, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00, 0.00000e+00]]), array([[0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6525e+03, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.9916e+03, -7.3460e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -8.2100e+01, 2.4190e+02, -5.4340e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.8190e+02, -1.5840e+02, 1.9970e+02, -3.4970e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 4.6900e+01, 1.9690e+02, -1.1930e+02, 1.6000e+01, 1.0020e+02, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -7.6700e+01, 2.5400e+01, -9.2000e+00, 5.5800e+01, -1.7000e+01, 8.4000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 2.0000e-01, -2.1500e+01, 1.5400e+01, 1.3800e+01, -1.3500e+01, -1.0000e-01, 8.9000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0300e+01, 1.3400e+01, 1.2000e+01, -6.4000e+00, -8.5000e+00, 8.5000e+00, 2.2000e+00, -7.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 9.0000e-01, -1.4000e+00, 3.7000e+00, -5.3000e+00, -3.0000e-01, 4.0000e-01, 1.7000e+00, -9.0000e-01, 4.6000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, 8.0000e-01, -4.0000e-01, -2.0000e-01, 7.0000e-01, 3.0000e-01, 2.2000e+00, -2.5000e+00, 5.0000e-01, 6.0000e-01, -4.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00], [0.0000e+00, -2.0000e-01, 4.0000e-01, 5.0000e-01, 4.0000e-01, -6.0000e-01, 3.0000e-01, 0.0000e+00, -4.0000e-01, 1.0000e-01, -3.0000e-01, -3.0000e-01, 0.0000e+00, 0.0000e+00], [0.0000e+00, 1.0000e-01, 5.0000e-01, 0.0000e+00, -2.0000e-01, 3.0000e-01, -4.0000e-01, 3.0000e-01, 3.0000e-01, -1.0000e-01, -1.0000e-01, -1.0000e-01, -2.0000e-01, 0.0000e+00], [0.0000e+00, 1.0000e-01, 0.0000e+00, 0.0000e+00, 1.0000e-01, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00, 0.0000e+00]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [6.7, 7.7, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-11.5, -7.1, -2.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [2.8, -6.2, 3.4, -12.2, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-1.1, -1.6, -6., 5.4, -5.5, 0., 0., 0., 0., 0., 0., 0., 0., 0.], [-0.3, 0.1, -0.6, 0.2, 0.3, 1., 0., 0., 0., 0., 0., 0., 0., 0.], [-0.6, -0.4, 0.5, 1.4, -1.4, 0., 0.8, 0., 0., 0., 0., 0., 0., 0.], [-0.1, -0.3, 0.3, 0.2, -0.5, 0.2, -0.2, 0.6, 0., 0., 0., 0., 0., 0.], [0., 0., 0.1, -0.2, 0.4, 0.3, 0., 0.1, -0.1, 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -25.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -30.2, -23.9, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 6., -1.1, 1.1, 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0.2, 6.4, 3.1, -12., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.4, 2.1, 3.4, -0.9, -1.2, 0., 0., 0., 0., 0., 0., 0., 0.], [0., -0.2, -0.9, 0.3, 0.1, -0.1, 0.4, 0., 0., 0., 0., 0., 0., 0.], [0., -0.5, 0.4, 0.1, 0.4, -0.2, 0.4, 0.3, 0., 0., 0., 0., 0., 0.], [0., 0.1, -0.1, 0.3, 0., 0.2, -0.1, -0.1, 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.], [0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]]), 2020.0, 13))

Compute the location of the magnetic north pole.

The magnetic north pole is where the field is vertical (inclination = 90°). This differs from the geomagnetic pole due to non-dipole field contributions.

Parameters:

• year (float, optional) – Decimal year. Default 2023.0.

• coeffs (MagneticCoefficients, optional) – Model coefficients. Default IGRF13.

Returns:

• lat (float) – Latitude of magnetic north pole in radians.

• lon (float) – Longitude of magnetic north pole in radians.

Return type:

tuple[float, float]

Notes

This uses an iterative search starting from the dipole pole. The magnetic pole moves over time.

Examples

>>> import numpy as np
>>> from pytcl.magnetism import magnetic_north_pole, dipole_axis
>>> # Magnetic north pole location (2023)
>>> lat, lon = magnetic_north_pole(2023.0)
>>> # Should be in Canadian Arctic, around 80-85°N
>>> 75 < np.degrees(lat) < 90
True
>>> -150 < np.degrees(lon) < -60
True
>>> # Compare with geomagnetic pole
>>> geo_lat, geo_lon = dipole_axis()
>>> # Magnetic pole differs from geomagnetic pole
>>> abs(lat - geo_lat) > 0.01  # Different locations
True

Enhanced Magnetic Model (EMM) and WMMHR2025

High-resolution magnetic field models: EMM2017 (degree 790) and WMMHR2025 (degree 133). Both support scalar and array inputs for lat/lon/height.

Enhanced Magnetic Model (EMM) and World Magnetic Model High Resolution (WMMHR).

This module provides support for high-degree magnetic field models: - EMM2017: Degree 790, resolves anomalies down to 51 km wavelength - WMMHR2025: Degree 133, resolves anomalies down to ~300 km wavelength

These models provide higher spatial resolution than the standard WMM (degree 12) by including crustal magnetic field contributions.

References

[1]

Maus, S., et al. “EMAG2: A 2-arc min resolution Earth Magnetic Anomaly Grid compiled from satellite, airborne, and marine magnetic measurements.” Geochemistry, Geophysics, Geosystems 10.8 (2009).

[2]

NOAA National Centers for Environmental Information, “Enhanced Magnetic Model (EMM).” https://www.ncei.noaa.gov/products/enhanced-magnetic-model

[3]

NOAA National Centers for Environmental Information, “World Magnetic Model High Resolution (WMMHR).” https://www.ncei.noaa.gov/products/world-magnetic-model-high-resolution

class pytcl.magnetism.emm.HighResCoefficients(g, h, g_dot, h_dot, epoch, n_max, n_max_sv, model_name)

Bases: NamedTuple

High-resolution magnetic model coefficients.

Extends MagneticCoefficients with additional metadata for high-degree models like EMM and WMMHR.

g

Main field cosine coefficients (nT), shape (n_max+1, n_max+1).

Type:

ndarray

h

Main field sine coefficients (nT), shape (n_max+1, n_max+1).

Type:

ndarray

g_dot

Secular variation of g (nT/year), shape (n_max_sv+1, n_max_sv+1).

Type:

ndarray

h_dot

Secular variation of h (nT/year), shape (n_max_sv+1, n_max_sv+1).

Type:

ndarray

epoch

Reference epoch (decimal year).

Type:

float

n_max

Maximum degree for main field.

Type:

int

n_max_sv

Maximum degree for secular variation (may be < n_max).

Type:

int

model_name

Model identifier (“EMM2017” or “WMMHR2025”).

Type:

str

g: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 0

h: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 1

g_dot: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 2

h_dot: ndarray[tuple[Any, ...], dtype[floating]]

Alias for field number 3

epoch: float

Alias for field number 4

n_max: int

Alias for field number 5

n_max_sv: int

Alias for field number 6

model_name: str

Alias for field number 7

pytcl.magnetism.emm.get_data_dir()

Get the pytcl data directory for external data files.

The data directory is located at ~/.pytcl/data/ by default. Can be overridden by setting the PYTCL_DATA_DIR environment variable.

Returns:

Path to the data directory.

Return type:

Path

pytcl.magnetism.emm.parse_emm_file(filepath, n_max=None)

Parse an EMM/WMMHR coefficient file.

The file format is similar to WMM but with more coefficients:

n m g_nm h_nm g_dot_nm h_dot_nm

Parameters:

• filepath (Path) – Path to the coefficient file.

• n_max (int, optional) – Maximum degree to load. If None, loads all coefficients.

Returns:

• g (ndarray) – Cosine coefficients.

• h (ndarray) – Sine coefficients.

• g_dot (ndarray) – Secular variation of g.

• h_dot (ndarray) – Secular variation of h.

• epoch (float) – Model epoch.

• actual_n_max (int) – Maximum degree loaded.

Return type:

tuple[ndarray[tuple[Any, …], dtype[floating]], ndarray[tuple[Any, …], dtype[floating]], ndarray[tuple[Any, …], dtype[floating]], ndarray[tuple[Any, …], dtype[floating]], float, int]

pytcl.magnetism.emm.create_test_coefficients(n_max=36)

Create test coefficients for low-degree testing.

Creates a simplified set of coefficients for testing purposes, using the same low-degree terms as WMM2020 extended with synthetic crustal field terms.

Parameters:

n_max (int) – Maximum degree (default 36).

Returns:

Test coefficient set.

Return type:

HighResCoefficients

pytcl.magnetism.emm.load_emm_coefficients(model='EMM2017', n_max=None)

Load high-resolution magnetic model coefficients.

Parameters:

• model (str) – Model name, either “EMM2017” or “WMMHR2025”.

• n_max (int, optional) – Maximum degree to load. If None, loads the full model.

Returns:

Loaded coefficient structure.

Return type:

HighResCoefficients

Raises:

• FileNotFoundError – If the coefficient file is not found.

• ValueError – If an unknown model is specified.

Examples

>>> coef = load_emm_coefficients("WMMHR2025", n_max=50)
>>> coef.n_max
50

pytcl.magnetism.emm.emm(lat, lon, h=0.0, year=2020.0, model='EMM2017', n_max=None, coefficients=None)

Compute magnetic field using Enhanced Magnetic Model.

The EMM provides higher spatial resolution than WMM by including crustal magnetic field contributions up to degree 790.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above WGS84 ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2020.0.

• model (str, optional) – Model name (“EMM2017” or “WMMHR2025”). Default “EMM2017”.

• n_max (int, optional) – Maximum degree to evaluate. Default uses full model.

• coefficients (HighResCoefficients, optional) – Pre-loaded coefficients. If None, loads from file.

Returns:

result – Magnetic field components and derived quantities.

Return type:

MagneticResult

Examples

>>> import numpy as np
>>> # Use test coefficients for demonstration
>>> coef = create_test_coefficients(n_max=36)
>>> result = emm(np.radians(40), np.radians(-105), 1.0, 2020.0, coefficients=coef)
>>> print(f"Declination: {np.degrees(result.D):.2f}°")
>>> print(f"Total intensity: {result.F:.0f} nT")

pytcl.magnetism.emm.wmmhr(lat, lon, h=0.0, year=2025.0, n_max=None, coefficients=None)

Compute magnetic field using World Magnetic Model High Resolution.

WMMHR2025 extends WMM to degree 133, providing higher spatial resolution for applications requiring more accurate local field values.

Parameters:

• lat (float) – Geodetic latitude in radians.

• lon (float) – Longitude in radians.

• h (float, optional) – Height above WGS84 ellipsoid in km. Default 0.

• year (float, optional) – Decimal year. Default 2025.0.

• n_max (int, optional) – Maximum degree to evaluate. Default uses full model (133).

• coefficients (HighResCoefficients, optional) – Pre-loaded coefficients. If None, loads from file.

Returns:

result – Magnetic field components and derived quantities.

Return type:

MagneticResult

Notes

WMMHR2025 is valid for 2025.0 - 2030.0. For dates outside this range, results may be less accurate.

Secular variation is only computed for degrees 1-15. Higher degree terms represent static crustal field.

pytcl.magnetism.emm.emm_declination(lat, lon, h=0.0, year=2020.0, model='EMM2017', n_max=None, coefficients=None)

Compute magnetic declination using EMM/WMMHR.

Parameters:

• lat (float or ndarray) – Geodetic latitude in radians.

• lon (float or ndarray) – Longitude in radians.

• h (float or ndarray, optional) – Height above WGS84 ellipsoid in km.

• year (float, optional) – Decimal year.

• model (str, optional) – Model name.

• n_max (int, optional) – Maximum degree to evaluate.

• coefficients (HighResCoefficients, optional) – Pre-loaded coefficients.

Returns:

Magnetic declination in radians.

Return type:

float or ndarray

pytcl.magnetism.emm.emm_inclination(lat, lon, h=0.0, year=2020.0, model='EMM2017', n_max=None, coefficients=None)

Compute magnetic inclination using EMM/WMMHR.

Parameters:

• lat (float or ndarray) – Geodetic latitude in radians.

• lon (float or ndarray) – Longitude in radians.

• h (float or ndarray, optional) – Height above WGS84 ellipsoid in km.

• year (float, optional) – Decimal year.

• model (str, optional) – Model name.

• n_max (int, optional) – Maximum degree to evaluate.

• coefficients (HighResCoefficients, optional) – Pre-loaded coefficients.

Returns:

Magnetic inclination (dip) in radians.

Return type:

float or ndarray

pytcl.magnetism.emm.emm_intensity(lat, lon, h=0.0, year=2020.0, model='EMM2017', n_max=None, coefficients=None)

Compute total magnetic field intensity using EMM/WMMHR.

Parameters:

• lat (float or ndarray) – Geodetic latitude in radians.

• lon (float or ndarray) – Longitude in radians.

• h (float or ndarray, optional) – Height above WGS84 ellipsoid in km.

• year (float, optional) – Decimal year.

• model (str, optional) – Model name.

• n_max (int, optional) – Maximum degree to evaluate.

• coefficients (HighResCoefficients, optional) – Pre-loaded coefficients.

Returns:

Total magnetic field intensity in nT.

Return type:

float or ndarray