NRLMSISE 00 Atmosphere — Robotics/Atmosphere

NRLMSISE-00 Atmosphere

Robotics / Atmosphere

The US Naval Research Laboratory's NRLMSISE-00 empirical model of the neutral atmosphere, from the ground to the lower exosphere: the temperature and the number densities of helium, atomic oxygen, nitrogen, oxygen, argon, hydrogen and atomic nitrogen, plus the total mass density, at a position and a time, driven by the solar flux F10.7 and the geomagnetic index Ap.

The thermosphere (above 72.5 km) is a Bates temperature profile joined to a cubic spline below 120 km, with each species' density a diffusive profile blended into a fully mixed one at the turbopause; below 72.5 km the temperature is two more splines through nodes that are themselves spherical harmonic expansions. The arithmetic is the reference implementation's, line for line.

Ports

• LLA – [3,1]: the geodetic latitude and longitude in degrees and the altitude in metres. A latitude past ±90° is folded back over the pole, which also turns the longitude by 180°, and a longitude past ±180° is wrapped once.
• year – [1,1]. Read by nothing: the reference uses the year only to warn about a day of year past the end of it.
• doy – [1,1]: the day of year, 1 to 366, truncated toward zero to a whole day.
• sec – [1,1]: seconds of the UT day. The local apparent solar time is sec/3600 + lon/15 hours.
• F107a – [1,1]: the 81-day average of F10.7, centred on the day of year (150 is a moderate Sun).
• F107 – [1,1]: the daily F10.7 of the previous day.
• aph – [7,1]: the magnetic indices – the daily Ap, then the 3-hour ap now, 3, 6 and 9 hours before, and the averages of the eight 3-hour values 12–33 and 36–57 hours before. Only the daily Ap is read unless flag 9 is −1.
• T – [2,1]: the exospheric temperature and the temperature at the altitude, in kelvin.
• rho – [9,1]: the number densities of He, O, N2, O2, Ar per cubic metre, the total mass density in kg/m³, then H, N and the anomalous oxygen per cubic metre.

Parameters

• Flags – the model's 23 switches, a row of 23 numbers (default all 1). Each turns one term of the model on (1), off (0) or keeps only its cross terms (2); flag 9 at −1 selects the 3-hour ap history in place of the daily Ap. In order: F10.7 effect on the mean, time independent, symmetrical annual, symmetrical semiannual, asymmetrical annual, asymmetrical semiannual, diurnal, semidiurnal, daily Ap, all UT/longitude effects, longitudinal, UT and mixed UT/longitude, mixed Ap/UT/longitude, terdiurnal, departures from diffusive equilibrium, all TINF variations, all TLB variations, all TN1 variations, all S variations, all TN2 variations, all NLB variations, all TN3 variations, and turbopause scale height variations. Each entry is truncated toward zero, as the reference does.
• Include Anomalous Oxygen – off (default) or on: whether the anomalous oxygen joins the total mass density. Its own density is output either way.
• Sampling Time (s) – zero or less inherits the solver's rate; a positive value runs the block at that period.

Code export

All ten targets: Python, MATLAB, Java, Rust, C, C++, VHDL, Verilog, SystemVerilog and PLC Structured Text. Each carries the whole model as straight-line code with the model's coefficients written in at 17 significant digits, so every target computes the same doubles as the block's own simulation. The switches are baked in at export time.

The three hardware targets are simulation-only: exponentials, powers and cubic splines have no Q16.16 form, so values convert at the port boundary and the arithmetic runs in floating point. A Q16.16 port cannot hold a number density (they run from about 10⁶ to 10²⁶ per cubic metre) nor an altitude above about 32.7 km, so a hardware export answers the temperatures and little else.

Simulink bridge

Import and export, mapped to Aerospace Blockset's aerolibatmos2/NRLMSISE-00 Atmosphere Model. Two configuration values cross: Flags → flags, and Include Anomalous Oxygen → oxygen_in, one for one.

Five Simulink parameters are always implied: flux_ap_input is on, which is what gives the Simulink block this block's seven inputs; lst_input is off, the local solar time being computed from sec and lon as here; flags_input is Internal, the switches being a parameter; units is Metric (MKS), this block being metric throughout; and action is None, that parameter only choosing whether Simulink warns for an out-of-range input. The Simulink block defines no SampleTime parameter, measured, so the rate stays on the ICore side.

Notes

• Algebraic and stateless: the outputs depend on this sample alone.
• Not linear, so the block carries no state space and model reduction correctly reports it as unmergeable.
• Below 72.5 km the O, H, N and anomalous O densities are zero, as in the reference; the model is specified up to 1000 km and answers beyond it without complaint.
• Metres become kilometres by a multiply by 0.001, the Simulink block's own unit conversion, measured.
• One deliberate difference: at exactly 32.5 km the reference reuses spline nodes computed for an earlier sample. They are multiplied by zero there, so the answer does not move, unless no earlier sample ever computed them, in which case the reference answers NaN. This block computes them, and answers the finite value.
• Verified bit for bit against the reference C over 6000 samples, and within 1.7×10⁻¹² relative of R2026a's Simulink block.