sonAIR was developed for fixed-wing aircraft with jet propulsion. At the heart of sonAIR is a source model Zellmann et al. (2018) that calculates direction-dependent sound emissions as a function of flight conditions, providing one-third octave band spectra ranging from 20 Hz to 5 kHz. The partial sound source model provides separate information on engine noise, depending on engine speed (N1), speed, and the longitudinal and lateral emission angles (θ and φ), as well as on airframe noise, depending on speed, longitudinal emission angle (θ), and — if available — flap position, speedbrakes, landing gear, air density, and airspeed. The energetic sum of these two models provides direction-dependent sound power levels depending on the flight conditions.
The level of detail in the emission models depends on the quality of the input data:
(a) The directivity can be 2D or 3D.
(b) Ideally, the emission calculation takes into account not only the power setting, but also information on the flight configuration, such as the position of the flaps and landing gear.
(c) For reduced models, no information on the aircraft configuration is needed for simulation.
(d) If neither the power setting nor the configuration are known, procedural models are created which statical-ly represent the average conditions of certain flight phases.
In addition to jet-powered aeroplanes, emission models were also created for propeller-powered aeroplanes, military fighter jets, helicopters and drones, which use different input parameters depending on the character-istics of the source.

Determination of source data
Ideally, the source models are based on our own measurements, either of real air traffic, typically at Zurich Airport, or of specific test flights. As an alternative to measurement data, emission models from other sources can also be integrated, such as from the SANC-DB (Swiss Aircraft Noise Calculation DataBase) (Leitfaden Fluglärm).
Source models are created by calculating the measured spectra back to the source (known as back propagation) and linking them to the corresponding flight conditions. This takes into account the propagation times of sound, the Doppler effect (frequency shift and intensity), and all important propagation phenomena, including the ground effect and the respective vertical stratification of the atmosphere in terms of temperature, humidity, wind and air pressure.
With regard to model development, FDR data (flight deck recordings; ‘cockpit data’) provide an ideal basis for correlating the acoustic measurements with the respective aircraft condition. These were kindly made available to us by the airlines Swiss, Edelweiss and Helvetic for their aircraft types. 
If no cockpit data is available, the speed of the engine's primary shaft, N1, can be determined from the acoustic measurements using pure tone detection Ramseier et al. (2024).
A complete overview of the emission models available for sonAIR can be found in the sonAIR documentation.

Sound propagation model
In sonAIR, sound propagation is calculated using the sonX sound propagation model, which was developed and is maintained by the Laboratory for Acoustics/Noise Control at Empa. This model considers reflections on the ground ('ground effect'), the effects of obstacles, air attenuation, vegetation attenuation, and meteorological influences. It can also simulate reflections and shielding by artificial objects, such as buildings or noise barriers, as well as natural objects, such as forests and rocks. sonX is also used for other types of noise, such as shooting, road and railway noise.

Single flight simulation and superposition to yearly noise maps
The aircraft noise simulation uses a time-step method that simulates individual flights in the model. The position and orientation of the aircraft in space as well as the power setting and configuration are accounted in a fine temporal resolution of typically one second. This makes it possible to show the noise exposure at each receiver point in detail and to determine not only spectra but also level-time curves.
For the calculation of annual exposures and other complex scenarios, representative noise footprints of individual flights are calculated per aircraft type and route. If radar data of flight operations are available, this is done by simulating a larger number of individual flights (at least 100 per aircraft type and route; usually significantly more). In the case of idealized tracks and profiles, flights are simulated on main and side tracks and a weighted average is calculated. Based on a movement statistic, subdivided for different assessment periods, an energetic superposition of the footprints to an overall impact is then carried out.

Implementations
Empa develops sonAIR and operates a scientific implementation (sonAIR-WS), which serves as a development environment, research tool and reference implementation. Depending on the component, development is carried out in Matlab, Python and C++.
sonAIR was also implemented as an add-in for ArcGIS Pro from Esri by the company n-Sphere AG as a GIS-based software solution. sonAIR-DL (DL for services in German) is based on the D-noise product solution from n-Sphere and, depending on the license level, covers the entire process, from data import and noise calculation (simulation) to evaluation, analysis and provision of the results in the form of maps and reports, as well as for the simulation and assessment of targeted measures. sonAIR-DL can be obtained from n-Sphere in various license levels. Licenses for noise mapping in accordance with the Swiss Noise Abatement Ordinance and for research purposes are free of charge.

Results
In the single flight simulation, level-time curves are calculated as one-third octave band spectra from 20 Hz to 5 kHz with a temporal resolution of 1 s. The results are typically stored as A-weighted event levels LAE and/or maximum levels LASmax as raster files (so-called noise footprints). From this, A-weighted event levels LAE and/or maximum levels LASmax are typically saved as raster files (so-called noise footprints) as results. From the number of movements for a specific assessment period, average levels LAeq can be derived from the event levels, which in turn can be used to determine other variables such as rating levels in accordance with the Swiss Noise Abatement Ordinance.
sonAIR-WS offers additional evaluation options. For example, the number of people affected can be calculated from the annoyance during the day or the wake-up reactions at night (based on individual events or entire scenarios). Alternative metrics such as EPNL or loudness can also be calculated and displayed.

Comparison of measured versus simulated spectrograms; example of an A320 in approach with landing gears deployed after 28 s