ATMOS_NRLMSISE00

This function computes atmospheric temperature, mass density, and pressure using the NRLMSISE-00 empirical atmosphere model. The model supports conditions from near ground level to the upper atmosphere and accounts for geophysical inputs including location, day-of-year, and solar flux.

The pressure value reported by this model interface is derived from ideal-gas relationships applied to modeled species densities and temperature:

P = \rho R T

Inputs include altitude, latitude, longitude, time-of-year, and solar activity proxies (f107 and f107_{avg}). Results are returned as a single-row 2D array for spreadsheet compatibility.

Excel Usage

=ATMOS_NRLMSISE00(z, latitude, longitude, day, seconds, daily_flux, avg_flux)

• z (float, required): Elevation above sea level in meters.
• latitude (float, optional, default: 0): Latitude in degrees (-90 to 90).
• longitude (float, optional, default: 0): Longitude in degrees (-180 to 180).
• day (int, optional, default: 0): Day of year (0-366).
• seconds (float, optional, default: 0): Seconds since start of day (UT1 time).
• daily_flux (float, optional, default: 150): Daily average 10.7 cm solar flux.
• avg_flux (float, optional, default: 150): 81-day average solar flux.

Returns (list[list]): 2D list [[Temperature, Density, Pressure]], or error string.

Example 1: Standard Atmosphere at 1 km

Inputs:

z	latitude	longitude	day	seconds	daily_flux	avg_flux
1000	0	0	0	0	150	150

Excel formula:

=ATMOS_NRLMSISE00(1000, 0, 0, 0, 0, 150, 150)

Expected output:

Result
293.656	1.05754	89219.1

Example 2: Mid-latitude Summer Day at 5 km

Inputs:

z	latitude	longitude	day	seconds	daily_flux	avg_flux
5000	45	45	180	0	150	150

Excel formula:

=ATMOS_NRLMSISE00(5000, 45, 45, 180, 0, 150, 150)

Expected output:

Result
263.506	0.733251	55509.5

Example 3: High Altitude at Equator (20 km)

Inputs:

z	latitude	longitude	day	seconds	daily_flux	avg_flux
20000	0	0	100	0	150	150

Excel formula:

=ATMOS_NRLMSISE00(20000, 0, 0, 100, 0, 150, 150)

Expected output:

Result
206.28	0.0955605	5663.17

Example 4: Custom Solar Flux at 10 km

Inputs:

z	latitude	longitude	day	seconds	daily_flux	avg_flux
10000	30	-90	50	36000	200	180

Excel formula:

=ATMOS_NRLMSISE00(10000, 30, -90, 50, 36000, 200, 180)

Expected output:

Result
227.886	0.424547	27795

Python Code

Show Code

from fluids.atmosphere import ATMOSPHERE_NRLMSISE00 as fluids_ATMOSPHERE_NRLMSISE00

def atmos_nrlmsise00(z, latitude=0, longitude=0, day=0, seconds=0, daily_flux=150, avg_flux=150):
    """
    Compute temperature, density, and pressure using the NRLMSISE-00 atmospheric model.

    See: https://fluids.readthedocs.io/fluids.atmosphere.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        z (float): Elevation above sea level in meters.
        latitude (float, optional): Latitude in degrees (-90 to 90). Default is 0.
        longitude (float, optional): Longitude in degrees (-180 to 180). Default is 0.
        day (int, optional): Day of year (0-366). Default is 0.
        seconds (float, optional): Seconds since start of day (UT1 time). Default is 0.
        daily_flux (float, optional): Daily average 10.7 cm solar flux. Default is 150.
        avg_flux (float, optional): 81-day average solar flux. Default is 150.

    Returns:
        list[list]: 2D list [[Temperature, Density, Pressure]], or error string.
    """
    try:
      # Validate input types and ranges
      z = float(z)
      latitude = float(latitude)
      longitude = float(longitude)
      day = int(day)
      seconds = float(seconds)
      daily_flux = float(daily_flux)
      avg_flux = float(avg_flux)
    except Exception:
      return "Error: Invalid input types."

    try:
      if not (-90 <= latitude <= 90):
        return "Error: latitude must be between -90 and 90 degrees."
      if not ((-180 <= longitude <= 180) or (0 <= longitude <= 360)):
        return "Error: longitude must be between -180 and 180 degrees or 0 and 360 degrees."
      if not (0 <= day <= 366):
        return "Error: day must be between 0 and 366."

      result = fluids_ATMOSPHERE_NRLMSISE00(z, latitude, longitude, day, seconds, daily_flux, avg_flux)
      T = float(result.T)
      rho = float(result.rho)
      P = float(result.P)
      return [[T, rho, P]]
    except Exception as e:
      return f"Error: {str(e)}"

Online Calculator

z *

Elevation above sea level in meters.

latitude

Latitude in degrees (-90 to 90).

longitude

Longitude in degrees (-180 to 180).

day

Day of year (0-366).

seconds

Seconds since start of day (UT1 time).

daily_flux

Daily average 10.7 cm solar flux.

avg_flux

81-day average solar flux.