Atmosphere

Overview

Atmospheric modeling is essential for aerospace engineering, satellite operations, meteorology, and environmental science. These functions provide computational tools to characterize the Earth’s atmosphere at different altitudes and conditions. At its core, atmospheric modeling addresses how temperature, pressure, density, and composition vary with altitude, latitude, time, and solar activity.

The atmosphere is a complex, dynamic system influenced by gravitational compression, solar radiation, geomagnetic activity, and seasonal variations. Accurate atmospheric models are critical for aircraft performance calculations, rocket trajectory analysis, satellite drag estimation, and atmospheric reentry simulations.

Figure 1: US Standard Atmosphere 1976 properties up to 20 km: (Left) Temperature lapse rates in the troposphere and stratosphere; (Center) Exponential pressure decay; (Right) Exponential density decay.

Standard Atmosphere Models

Standard atmosphere models provide idealized, deterministic representations of atmospheric properties as a function of altitude. These models are widely used in engineering design and performance calculations when real-time atmospheric data is unavailable or when standardized conditions are required for comparison.

The U.S. Standard Atmosphere 1976 is the most commonly used standard model in aerospace engineering. It defines atmospheric properties from sea level to 1000 km altitude, assuming mid-latitude conditions and moderate solar activity. The model divides the atmosphere into layers with defined temperature lapse rates and uses the hydrostatic equation and ideal gas law to compute pressure and density. The ATMOSPHERE_1976 function implements this model, providing temperature, pressure, density, speed of sound, and other properties at any specified altitude.

Empirical Atmospheric Models

While standard atmosphere models provide useful baselines, empirical models incorporate real observational data to capture variations due to solar activity, geomagnetic conditions, time of day, and geographic location. These models are essential for high-fidelity applications such as satellite orbit prediction and space weather analysis.

The NRLMSISE-00 (Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Radar Extended Model) is a widely adopted empirical model of the Earth’s atmosphere from ground to space. It extends to altitudes above 500 km and provides temperature, total mass density, and species-specific densities (N₂, O₂, O, He, H, Ar, N) as functions of: - Altitude - Geographic latitude and longitude - Day of year - Universal time - F10.7 solar radio flux (a proxy for solar activity) - Ap geomagnetic index (a measure of geomagnetic disturbance)

The ATMOS_NRLMSISE00 function implements this model, enabling users to compute atmospheric conditions for specific dates and locations. This is particularly valuable for satellite drag calculations, where atmospheric density directly affects orbital decay rates.

Atmospheric Mass and Optical Depth

Beyond basic atmospheric properties, specialized calculations address how the atmosphere affects radiation and light transmission. Air mass is a concept from astronomy and solar energy applications that quantifies the relative path length of radiation through the atmosphere.

When sunlight or starlight travels through the atmosphere at an angle (such as near sunrise or sunset), it traverses more atmospheric mass than when arriving from directly overhead. The air mass coefficient AM is defined as:

AM = \frac{\text{path length through atmosphere}}{\text{vertical path length}}

For a plane-parallel atmosphere, AM \approx \sec(\theta), where \theta is the zenith angle. More sophisticated models account for atmospheric curvature and density profiles. The AIRMASS function calculates the total atmospheric mass along a specified path angle using a realistic density profile, which is crucial for: - Solar energy calculations (solar panels produce less power at higher air mass due to increased atmospheric absorption) - Astronomical observations (atmospheric extinction corrections) - Radiative transfer modeling

Native Excel capabilities

Excel does not include built-in functions for atmospheric modeling. Users typically rely on lookup tables or simplified formulas for basic atmospheric properties. For example: - Manual lookup tables: Engineers often create tables of standard atmosphere values and use VLOOKUP or INTERPOLATE for intermediate altitudes. - Custom formulas: Simple exponential approximations for pressure decay (e.g., barometric formula) can be implemented with basic Excel functions.

These approaches lack the precision, flexibility, and efficiency of dedicated atmospheric models like NRLMSISE-00 or the full U.S. Standard Atmosphere 1976. They also cannot account for solar activity or geographic variations.

Third-party Excel add-ins

There are no widely recognized third-party Excel add-ins specifically for atmospheric modeling. Engineers typically turn to: - MATLAB Aerospace Toolbox: Includes implementations of standard atmosphere models and space environment tools. - Systems Tool Kit (STK) by Ansys: Professional satellite analysis software with comprehensive atmospheric models, though not Excel-integrated. - Standalone atmospheric model code: The original NRLMSISE-00 Fortran code is available from the Naval Research Laboratory, and various Python/MATLAB implementations exist.

The Python functions provided here bring industrial-grade atmospheric modeling directly into Excel, eliminating the need for external software or custom VBA implementations.

Tools

Tool	Description
AIRMASS	Calculate the mass of air per square meter in the atmosphere along a given angle using a density profile.
ATMOS_NRLMSISE00	Compute temperature, density, and pressure using the NRLMSISE-00 atmospheric model.
ATMOSPHERE_1976	Calculate standard atmospheric properties at a given altitude using the US Standard Atmosphere 1976 model.