Atmosphere

Atmospheric models for propagation and refraction.

Atmospheric models for tracking applications.

This module provides standard atmosphere models used for computing temperature, pressure, density, and other properties at various altitudes.

Submodules

models : Standard atmosphere models (US76, ISA) ionosphere : Ionospheric models for GPS/GNSS corrections

class pytcl.atmosphere.AtmosphereState(temperature, pressure, density, speed_of_sound)[source]

Bases: NamedTuple

Atmospheric state at a given altitude.

temperature

Temperature in Kelvin.

Type:: float or ndarray

pressure

Pressure in Pascals.

Type:: float or ndarray

density

Density in kg/m³.

Type:: float or ndarray

speed_of_sound

Speed of sound in m/s.

Type:: float or ndarray

temperature: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 0

pressure: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 1

density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 2

speed_of_sound: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 3

pytcl.atmosphere.us_standard_atmosphere_1976(altitude)[source]

Compute atmospheric properties using US Standard Atmosphere 1976.

Parameters:: altitude (array_like) – Geometric altitude in meters. Valid from 0 to ~86 km.
Returns:: state – Atmospheric state containing temperature, pressure, density, and speed of sound.
Return type:: AtmosphereState

Examples

>>> state = us_standard_atmosphere_1976(10000)
>>> state.temperature
223.25...
>>> state.pressure
26499.9...

Notes

The US Standard Atmosphere 1976 is a model of the Earth’s atmosphere that defines temperature, pressure, and density as functions of altitude. It is valid from sea level to approximately 86 km altitude.

References

pytcl.atmosphere.isa_atmosphere(altitude, temperature_offset=0.0)[source]

Compute atmospheric properties using International Standard Atmosphere (ISA).

This is essentially the troposphere portion of US Standard Atmosphere 1976 with an optional temperature offset for non-standard days.

Parameters:

altitude (array_like) – Geometric altitude in meters.
temperature_offset (float, optional) – Temperature offset from ISA conditions in Kelvin (default: 0). Positive values indicate warmer than standard day.

Returns:

state – Atmospheric state.

Return type:

AtmosphereState

Examples

>>> # Standard day at 5000m
>>> state = isa_atmosphere(5000)
>>> # Hot day (+15K) at 5000m
>>> state = isa_atmosphere(5000, temperature_offset=15)

pytcl.atmosphere.altitude_from_pressure(pressure)[source]

Compute geometric altitude from pressure (pressure altitude).

Parameters:: pressure (array_like) – Atmospheric pressure in Pascals.
Returns:: altitude – Geometric altitude in meters.
Return type:: ndarray

Examples

>>> # Sea level pressure
>>> altitude_from_pressure(101325)
0.0
>>> # Pressure at approximately 5000m
>>> alt = altitude_from_pressure(54000)
>>> 4800 < alt < 5200
True

Notes

This is an approximate inversion of the ISA model, valid primarily in the troposphere.

pytcl.atmosphere.mach_number(velocity, altitude)[source]

Compute Mach number from velocity and altitude.

Parameters:

velocity (array_like) – True airspeed in m/s.
altitude (array_like) – Geometric altitude in meters.

Returns:

mach – Mach number.

Return type:

ndarray

Examples

>>> # Aircraft at 300 m/s at sea level
>>> mach_number(300, 0)
0.88...
>>> # Same speed at 10 km altitude (lower speed of sound)
>>> mach_number(300, 10000)
1.00...

pytcl.atmosphere.true_airspeed_from_mach(mach, altitude)[source]

Compute true airspeed from Mach number and altitude.

Parameters:

mach (array_like) – Mach number.
altitude (array_like) – Geometric altitude in meters.

Returns:

velocity – True airspeed in m/s.

Return type:

ndarray

Examples

>>> # Mach 0.8 at cruise altitude (10 km)
>>> tas = true_airspeed_from_mach(0.8, 10000)
>>> 230 < tas < 250  # approximately 240 m/s
True
>>> # Supersonic at sea level
>>> true_airspeed_from_mach(1.0, 0)
340.2...

class pytcl.atmosphere.NRLMSISE00(use_meter_altitude=True)[source]

Bases: object

NRLMSISE-00 High-Fidelity Atmosphere Model.

This is a comprehensive thermosphere model covering altitudes from approximately -5 km to 1000 km, with detailed chemical composition and temperature profiles.

The model implements: - Temperature profile with solar activity and magnetic coupling - Molecular composition for troposphere/stratosphere/mesosphere - Atomic species for thermosphere - Solar flux (F10.7) and magnetic activity (Ap) variations

Parameters:: use_meter_altitude (bool, optional) – If True, expect altitude input in meters. If False, expect km. Default is True (meters).

Examples

>>> model = NRLMSISE00()
>>> output = model(
...     latitude=np.radians(45),
...     longitude=np.radians(-75),
...     altitude=400_000,  # 400 km
...     year=2024,
...     day_of_year=100,
...     seconds_in_day=43200,
...     f107=150,
...     f107a=150,
...     ap=5
... )
>>> print(f"Density: {output.density:.2e} kg/m³")

Notes

This implementation uses empirical correlations for atmospheric properties as a function of geomagnetic and solar activity indices. For highest accuracy, use the original NRLMSISE-00 Fortran code from NASA/NOAA, which includes extensive coefficient tables.

__init__(use_meter_altitude=True)[source]

Initialize NRLMSISE-00 model.

__call__(latitude, longitude, altitude, year, day_of_year, seconds_in_day, f107=150.0, f107a=150.0, ap=4.0)[source]

Compute atmospheric density and composition.

Parameters:

latitude (array_like) – Geodetic latitude in radians.
longitude (array_like) – Longitude in radians.
altitude (array_like) – Altitude in meters (or km if use_meter_altitude=False).
year (int) – Year (e.g., 2024).
day_of_year (int) – Day of year (1-366).
seconds_in_day (float) – Seconds since midnight (0-86400).
f107 (float, optional) – 10.7 cm solar flux (daily value, SFU). Default 150.
f107a (float, optional) – 10.7 cm solar flux (81-day average, SFU). Default 150.
ap (float or array_like, optional) – Planetary magnetic index. Can be single value or 8-element array of 3-hour Ap values. Default 4.0.

Returns:

output – Atmospheric properties (density, temperature, composition).

Return type:

NRLMSISE00Output

Notes

The model assumes hydrostatic equilibrium and uses empirical correlations for density and temperature variations.

class pytcl.atmosphere.NRLMSISE00Output(density, temperature, exosphere_temperature, he_density, o_density, n2_density, o2_density, ar_density, h_density, n_density)[source]

Bases: NamedTuple

Output from NRLMSISE-00 atmospheric model.

density

Total atmospheric density in kg/m³.

Type:: float or ndarray

temperature

Temperature at altitude (K).

Type:: float or ndarray

exosphere_temperature

Exospheric temperature (K).

Type:: float or ndarray

he_density

Helium density in m⁻³.

Type:: float or ndarray

o_density

Atomic oxygen density in m⁻³.

Type:: float or ndarray

n2_density

N₂ density in m⁻³.

Type:: float or ndarray

o2_density

O₂ density in m⁻³.

Type:: float or ndarray

ar_density

Argon density in m⁻³.

Type:: float or ndarray

h_density

Hydrogen density in m⁻³.

Type:: float or ndarray

n_density

Atomic nitrogen density in m⁻³.

Type:: float or ndarray

density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 0

temperature: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 1

exosphere_temperature: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 2

he_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 3

o_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 4

n2_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 5

o2_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 6

ar_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 7

h_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 8

n_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 9

class pytcl.atmosphere.F107Index(f107, f107a, ap, ap_array=None)[source]

Bases: NamedTuple

Solar activity indices for NRLMSISE-00.

f107

10.7 cm solar radio flux (daily, SFU).

Type:: float

f107a

10.7 cm solar radio flux (81-day average, SFU).

Type:: float

ap

Planetary magnetic index (Ap index).

Type:: float or ndarray

ap_array

Ap values for each 3-hour interval of the day (8 values). If not provided, derived from ap value.

Type:: ndarray, optional

f107: float: Alias for field number 0

f107a: float: Alias for field number 1

ap: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 2

ap_array: ndarray[tuple[Any, ...], dtype[float64]] | None: Alias for field number 3

pytcl.atmosphere.nrlmsise00(latitude, longitude, altitude, year, day_of_year, seconds_in_day, f107=150.0, f107a=150.0, ap=4.0)[source]

Compute NRLMSISE-00 atmospheric properties.

This is a module-level convenience function wrapping the NRLMSISE00 class.

Parameters:

latitude (array_like) – Geodetic latitude in radians.
longitude (array_like) – Longitude in radians.
altitude (array_like) – Altitude in meters.
year (int) – Year (e.g., 2024).
day_of_year (int) – Day of year (1-366).
seconds_in_day (float) – Seconds since midnight (0-86400).
f107 (float, optional) – 10.7 cm solar flux (daily value, SFU). Default 150.
f107a (float, optional) – 10.7 cm solar flux (81-day average, SFU). Default 150.
ap (float or array_like, optional) – Planetary magnetic index. Default 4.0.

Returns:

output – Atmospheric properties.

Return type:

NRLMSISE00Output

Notes

See NRLMSISE00 class for more details.

Examples

>>> # ISS altitude (~400 km), magnetic latitude = 40°, quiet geomagnetic activity
>>> output = nrlmsise00(
...     latitude=np.radians(40),
...     longitude=np.radians(-75),
...     altitude=400_000,  # 400 km
...     year=2024,
...     day_of_year=1,
...     seconds_in_day=43200,
...     f107=150,  # Average solar activity
...     f107a=150,
...     ap=5  # Quiet conditions
... )
>>> print(f"Density at ISS: {output.density:.2e} kg/m³")

class pytcl.atmosphere.IonosphereState(tec, delay_l1, delay_l2, f_peak, h_peak)[source]

Bases: NamedTuple

Ionospheric state at a given location and time.

tec

Total Electron Content in TECU (10^16 electrons/m²).

Type:: float or ndarray

delay_l1

Ionospheric delay at L1 frequency in meters.

Type:: float or ndarray

delay_l2

Ionospheric delay at L2 frequency in meters.

Type:: float or ndarray

f_peak

Critical frequency of F2 layer in MHz.

Type:: float or ndarray

h_peak

Height of F2 layer peak in km.

Type:: float or ndarray

tec: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 0

delay_l1: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 1

delay_l2: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 2

f_peak: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 3

h_peak: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 4

class pytcl.atmosphere.KlobucharCoefficients(alpha, beta)[source]

Bases: NamedTuple

Klobuchar ionospheric model coefficients.

These coefficients are broadcast by GPS satellites in the navigation message.

alpha

Amplitude coefficients (4 values) in seconds.

Type:: ndarray

beta

Period coefficients (4 values) in seconds.

Type:: ndarray

alpha: ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 0

beta: ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 1

pytcl.atmosphere.klobuchar_delay(latitude, longitude, elevation, azimuth, gps_time, coefficients=None)[source]

Compute ionospheric delay using the Klobuchar model.

The Klobuchar model is the standard GPS broadcast ionospheric correction model. It provides single-frequency ionospheric delay estimates accurate to about 50% RMS.

Parameters:

latitude (array_like) – User geodetic latitude in radians.
longitude (array_like) – User geodetic longitude in radians.
elevation (array_like) – Satellite elevation angle in radians.
azimuth (array_like) – Satellite azimuth angle in radians.
gps_time (array_like) – GPS time of week in seconds.
coefficients (KlobucharCoefficients, optional) – Ionospheric coefficients from GPS navigation message. If None, uses default mid-latitude values.

Returns:

delay – Ionospheric delay in meters (at L1 frequency).

Return type:

ndarray

Examples

>>> # User at 40°N, 105°W, satellite at 45° elevation
>>> delay = klobuchar_delay(
...     np.radians(40), np.radians(-105),
...     np.radians(45), np.radians(180),
...     gps_time=43200  # Noon
... )
>>> delay > 0
True

Notes

The Klobuchar model assumes a thin-shell ionosphere at 350 km altitude and uses a cosine model for diurnal variation. It typically removes about 50% of the ionospheric delay.

References

pytcl.atmosphere.dual_frequency_tec(pseudorange_l1, pseudorange_l2)[source]

Compute Total Electron Content from dual-frequency pseudoranges.

This method uses the dispersive nature of the ionosphere to estimate TEC from the difference in L1 and L2 pseudoranges.

Parameters:

pseudorange_l1 (array_like) – L1 pseudorange in meters.
pseudorange_l2 (array_like) – L2 pseudorange in meters.

Returns:

tec – Total Electron Content in TECU (10^16 electrons/m²).

Return type:

ndarray

Examples

>>> # Pseudorange measurements from dual-frequency receiver
>>> p_l1 = 22000000.0  # L1 pseudorange in meters
>>> p_l2 = 22000002.5  # L2 pseudorange (slightly delayed)
>>> tec = dual_frequency_tec(p_l1, p_l2)
>>> tec > 0  # TEC should be positive
True

Notes

The ionospheric delay is proportional to TEC and inversely proportional to frequency squared:

delay = 40.3 * TEC / f²

The difference in delays at L1 and L2 gives:: P2 - P1 = 40.3 * TEC * (1/f1² - 1/f2²)

This is the standard dual-frequency ionospheric correction method.

pytcl.atmosphere.ionospheric_delay_from_tec(tec, frequency=1575420000.0)[source]

Compute ionospheric delay from Total Electron Content.

Parameters:

tec (array_like) – Total Electron Content in TECU (10^16 electrons/m²).
frequency (float, optional) – Signal frequency in Hz. Default is GPS L1.

Returns:

delay – Ionospheric delay in meters.

Return type:

ndarray

Examples

>>> # Typical mid-latitude TEC of 20 TECU
>>> delay = ionospheric_delay_from_tec(20.0)
>>> delay > 0
True
>>> # Delay at L2 is larger than at L1 (lower frequency)
>>> delay_l2 = ionospheric_delay_from_tec(20.0, frequency=F_L2)
>>> delay_l2 > delay
True

Notes

The ionospheric delay for a signal is:: delay = 40.3 * TEC * 10^16 / f²

pytcl.atmosphere.simple_iri(latitude, longitude, altitude, hour, month=6, solar_flux=150.0)[source]

Simplified International Reference Ionosphere (IRI) model.

This provides approximate electron density and TEC values based on simplified IRI physics. For accurate predictions, use the full IRI model or external services.

Parameters:

latitude (array_like) – Geodetic latitude in radians.
longitude (array_like) – Geodetic longitude in radians.
altitude (array_like) – Altitude in meters.
hour (array_like) – Local hour (0-24).
month (int, optional) – Month of year (1-12). Default is 6 (June).
solar_flux (float, optional) – F10.7 solar flux in SFU. Default is 150 (moderate activity).

Returns:

state – Ionospheric state with TEC, delays, and F2 layer parameters.

Return type:

IonosphereState

Notes

This is a simplified empirical model suitable for educational purposes and rough estimates. For operational use, the full IRI-2020 model should be employed.

Examples

>>> state = simple_iri(np.radians(40), np.radians(-105), 300e3, 12)
>>> state.tec > 0
True

pytcl.atmosphere.magnetic_latitude(latitude, longitude)[source]

Compute approximate geomagnetic latitude.

Uses a simple dipole approximation with the magnetic pole at approximately 80.5°N, 72.8°W.

Parameters:

latitude (array_like) – Geodetic latitude in radians.
longitude (array_like) – Geodetic longitude in radians.

Returns:

mag_lat – Geomagnetic latitude in radians.

Return type:

ndarray

Examples

>>> import numpy as np
>>> # New York City (40.7°N, 74°W)
>>> mag_lat = magnetic_latitude(np.radians(40.7), np.radians(-74))
>>> np.degrees(mag_lat)
51.4...
>>> # Equator at 0° longitude
>>> mag_lat_eq = magnetic_latitude(0.0, 0.0)
>>> np.abs(np.degrees(mag_lat_eq)) < 15  # Near magnetic equator
True

pytcl.atmosphere.scintillation_index(magnetic_latitude, hour, kp_index=3.0)[source]

Estimate ionospheric scintillation index S4.

Provides a rough estimate of amplitude scintillation based on geomagnetic latitude, local time, and geomagnetic activity.

Parameters:

magnetic_latitude (array_like) – Geomagnetic latitude in radians.
hour (array_like) – Local hour (0-24).
kp_index (float, optional) – Kp geomagnetic activity index (0-9). Default is 3 (moderate).

Returns:

s4 – S4 amplitude scintillation index (0-1).

Return type:

ndarray

Examples

>>> import numpy as np
>>> # Equatorial region at night (high scintillation risk)
>>> s4 = scintillation_index(np.radians(10), 21, kp_index=5.0)
>>> s4 > 0.3  # Moderate to strong scintillation
True
>>> # Mid-latitude during daytime (low scintillation)
>>> s4_low = scintillation_index(np.radians(45), 12, kp_index=1.0)
>>> s4_low < 0.2
True

Notes

S4 > 0.3 indicates moderate scintillation. S4 > 0.6 indicates strong scintillation that may affect receivers.

Atmospheric Models

Standard atmosphere and refraction models.

Atmospheric models for tracking applications.

This module provides standard atmosphere models used for computing temperature, pressure, and density at various altitudes.

class pytcl.atmosphere.models.AtmosphereState(temperature, pressure, density, speed_of_sound)[source]

Bases: NamedTuple

Atmospheric state at a given altitude.

temperature

Temperature in Kelvin.

Type:: float or ndarray

pressure

Pressure in Pascals.

Type:: float or ndarray

density

Density in kg/m³.

Type:: float or ndarray

speed_of_sound

Speed of sound in m/s.

Type:: float or ndarray

temperature: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 0

pressure: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 1

density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 2

speed_of_sound: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 3

pytcl.atmosphere.models.us_standard_atmosphere_1976(altitude)[source]

Compute atmospheric properties using US Standard Atmosphere 1976.

Parameters:: altitude (array_like) – Geometric altitude in meters. Valid from 0 to ~86 km.
Returns:: state – Atmospheric state containing temperature, pressure, density, and speed of sound.
Return type:: AtmosphereState

Examples

>>> state = us_standard_atmosphere_1976(10000)
>>> state.temperature
223.25...
>>> state.pressure
26499.9...

Notes

The US Standard Atmosphere 1976 is a model of the Earth’s atmosphere that defines temperature, pressure, and density as functions of altitude. It is valid from sea level to approximately 86 km altitude.

References

pytcl.atmosphere.models.isa_atmosphere(altitude, temperature_offset=0.0)[source]

Compute atmospheric properties using International Standard Atmosphere (ISA).

This is essentially the troposphere portion of US Standard Atmosphere 1976 with an optional temperature offset for non-standard days.

Parameters:

altitude (array_like) – Geometric altitude in meters.
temperature_offset (float, optional) – Temperature offset from ISA conditions in Kelvin (default: 0). Positive values indicate warmer than standard day.

Returns:

state – Atmospheric state.

Return type:

AtmosphereState

Examples

>>> # Standard day at 5000m
>>> state = isa_atmosphere(5000)
>>> # Hot day (+15K) at 5000m
>>> state = isa_atmosphere(5000, temperature_offset=15)

pytcl.atmosphere.models.altitude_from_pressure(pressure)[source]

Compute geometric altitude from pressure (pressure altitude).

Parameters:: pressure (array_like) – Atmospheric pressure in Pascals.
Returns:: altitude – Geometric altitude in meters.
Return type:: ndarray

Examples

>>> # Sea level pressure
>>> altitude_from_pressure(101325)
0.0
>>> # Pressure at approximately 5000m
>>> alt = altitude_from_pressure(54000)
>>> 4800 < alt < 5200
True

Notes

This is an approximate inversion of the ISA model, valid primarily in the troposphere.

pytcl.atmosphere.models.mach_number(velocity, altitude)[source]

Compute Mach number from velocity and altitude.

Parameters:

velocity (array_like) – True airspeed in m/s.
altitude (array_like) – Geometric altitude in meters.

Returns:

mach – Mach number.

Return type:

ndarray

Examples

>>> # Aircraft at 300 m/s at sea level
>>> mach_number(300, 0)
0.88...
>>> # Same speed at 10 km altitude (lower speed of sound)
>>> mach_number(300, 10000)
1.00...

pytcl.atmosphere.models.true_airspeed_from_mach(mach, altitude)[source]

Compute true airspeed from Mach number and altitude.

Parameters:

mach (array_like) – Mach number.
altitude (array_like) – Geometric altitude in meters.

Returns:

velocity – True airspeed in m/s.

Return type:

ndarray

Examples

>>> # Mach 0.8 at cruise altitude (10 km)
>>> tas = true_airspeed_from_mach(0.8, 10000)
>>> 230 < tas < 250  # approximately 240 m/s
True
>>> # Supersonic at sea level
>>> true_airspeed_from_mach(1.0, 0)
340.2...

NRLMSISE-00 Model

High-fidelity empirical thermosphere density and temperature model including solar activity and geomagnetic storm effects. Covers altitudes 0-1000 km with full atmospheric composition.

NRLMSISE-00 Atmospheric Model

High-fidelity thermosphere/atmosphere model from the U.S. Naval Research Laboratory. Provides density, temperature, and composition profiles for altitudes from -5 km to 1000 km.

This implementation uses an empirical approach based on atmospheric chemistry, radiative transfer, and geomagnetic coupling for modeling temperature and density variations with altitude, latitude, local time, and solar/magnetic activity.

References

class pytcl.atmosphere.nrlmsise00.NRLMSISE00(use_meter_altitude=True)[source]

Bases: object

NRLMSISE-00 High-Fidelity Atmosphere Model.

This is a comprehensive thermosphere model covering altitudes from approximately -5 km to 1000 km, with detailed chemical composition and temperature profiles.

The model implements: - Temperature profile with solar activity and magnetic coupling - Molecular composition for troposphere/stratosphere/mesosphere - Atomic species for thermosphere - Solar flux (F10.7) and magnetic activity (Ap) variations

Parameters:: use_meter_altitude (bool, optional) – If True, expect altitude input in meters. If False, expect km. Default is True (meters).

Examples

>>> model = NRLMSISE00()
>>> output = model(
...     latitude=np.radians(45),
...     longitude=np.radians(-75),
...     altitude=400_000,  # 400 km
...     year=2024,
...     day_of_year=100,
...     seconds_in_day=43200,
...     f107=150,
...     f107a=150,
...     ap=5
... )
>>> print(f"Density: {output.density:.2e} kg/m³")

Notes

This implementation uses empirical correlations for atmospheric properties as a function of geomagnetic and solar activity indices. For highest accuracy, use the original NRLMSISE-00 Fortran code from NASA/NOAA, which includes extensive coefficient tables.

__init__(use_meter_altitude=True)[source]

Initialize NRLMSISE-00 model.

__call__(latitude, longitude, altitude, year, day_of_year, seconds_in_day, f107=150.0, f107a=150.0, ap=4.0)[source]

Compute atmospheric density and composition.

Parameters:

latitude (array_like) – Geodetic latitude in radians.
longitude (array_like) – Longitude in radians.
altitude (array_like) – Altitude in meters (or km if use_meter_altitude=False).
year (int) – Year (e.g., 2024).
day_of_year (int) – Day of year (1-366).
seconds_in_day (float) – Seconds since midnight (0-86400).
f107 (float, optional) – 10.7 cm solar flux (daily value, SFU). Default 150.
f107a (float, optional) – 10.7 cm solar flux (81-day average, SFU). Default 150.
ap (float or array_like, optional) – Planetary magnetic index. Can be single value or 8-element array of 3-hour Ap values. Default 4.0.

Returns:

output – Atmospheric properties (density, temperature, composition).

Return type:

NRLMSISE00Output

Notes

The model assumes hydrostatic equilibrium and uses empirical correlations for density and temperature variations.

class pytcl.atmosphere.nrlmsise00.NRLMSISE00Output(density, temperature, exosphere_temperature, he_density, o_density, n2_density, o2_density, ar_density, h_density, n_density)[source]

Bases: NamedTuple

Output from NRLMSISE-00 atmospheric model.

density

Total atmospheric density in kg/m³.

Type:: float or ndarray

temperature

Temperature at altitude (K).

Type:: float or ndarray

exosphere_temperature

Exospheric temperature (K).

Type:: float or ndarray

he_density

Helium density in m⁻³.

Type:: float or ndarray

o_density

Atomic oxygen density in m⁻³.

Type:: float or ndarray

n2_density

N₂ density in m⁻³.

Type:: float or ndarray

o2_density

O₂ density in m⁻³.

Type:: float or ndarray

ar_density

Argon density in m⁻³.

Type:: float or ndarray

h_density

Hydrogen density in m⁻³.

Type:: float or ndarray

n_density

Atomic nitrogen density in m⁻³.

Type:: float or ndarray

density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 0

temperature: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 1

exosphere_temperature: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 2

he_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 3

o_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 4

n2_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 5

o2_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 6

ar_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 7

h_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 8

n_density: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 9

class pytcl.atmosphere.nrlmsise00.F107Index(f107, f107a, ap, ap_array=None)[source]

Bases: NamedTuple

Solar activity indices for NRLMSISE-00.

f107

10.7 cm solar radio flux (daily, SFU).

Type:: float

f107a

10.7 cm solar radio flux (81-day average, SFU).

Type:: float

ap

Planetary magnetic index (Ap index).

Type:: float or ndarray

ap_array

Ap values for each 3-hour interval of the day (8 values). If not provided, derived from ap value.

Type:: ndarray, optional

f107: float: Alias for field number 0

f107a: float: Alias for field number 1

ap: float | ndarray[tuple[Any, ...], dtype[float64]]: Alias for field number 2

ap_array: ndarray[tuple[Any, ...], dtype[float64]] | None: Alias for field number 3

pytcl.atmosphere.nrlmsise00.nrlmsise00(latitude, longitude, altitude, year, day_of_year, seconds_in_day, f107=150.0, f107a=150.0, ap=4.0)[source]

Compute NRLMSISE-00 atmospheric properties.

This is a module-level convenience function wrapping the NRLMSISE00 class.

Parameters:

latitude (array_like) – Geodetic latitude in radians.
longitude (array_like) – Longitude in radians.
altitude (array_like) – Altitude in meters.
year (int) – Year (e.g., 2024).
day_of_year (int) – Day of year (1-366).
seconds_in_day (float) – Seconds since midnight (0-86400).
f107 (float, optional) – 10.7 cm solar flux (daily value, SFU). Default 150.
f107a (float, optional) – 10.7 cm solar flux (81-day average, SFU). Default 150.
ap (float or array_like, optional) – Planetary magnetic index. Default 4.0.

Returns:

output – Atmospheric properties.

Return type:

NRLMSISE00Output

Notes

See NRLMSISE00 class for more details.

Examples

>>> # ISS altitude (~400 km), magnetic latitude = 40°, quiet geomagnetic activity
>>> output = nrlmsise00(
...     latitude=np.radians(40),
...     longitude=np.radians(-75),
...     altitude=400_000,  # 400 km
...     year=2024,
...     day_of_year=1,
...     seconds_in_day=43200,
...     f107=150,  # Average solar activity
...     f107a=150,
...     ap=5  # Quiet conditions
... )
>>> print(f"Density at ISS: {output.density:.2e} kg/m³")