Troposphere Modeling

The troposphere is the low-altitude portion of Earth's atmosphere. Each radio wave front is refracted by the troposphere according to textbook physics. Tropospheric range refraction is proportional to the distance the radio wave front travels through the troposphere. From a ground station attached to the Earth's surface, this distance is long at low antenna elevations and short at high antenna elevations. That is, the greatest tropospheric range is experienced at low antenna elevation. The effect of troposphere on range decreases significantly above 10 degrees in elevation. It is significantly magnified below five degrees in elevation.

DSNMedia model

DSNMedia models troposphere zenith delays using the JPL DSN media correction data files and as described in 820-013 Deep Space Network External Interface Specification JPL D-16765 TRK-2-23 Media Calibration Interface. It computes delays based on power or trigonometric series representations of dry and wet delay corrections. Series representations are input via files as specified in the Scenario.EarthDefinition.DSNMediaCalibration file list. Computed dry delays due to the troposphere represent corrections to a baseline seasonal correction model from C.C. Chao. This baseline model is described in JPL Publication 94-24, “A Comparative Survey of Current and Proposed Tropospheric Refraction-Delay Models for DSN Radio Metric Data Calibration”, 1994 by Estefan and Sovers. Computed values of wet delays represent the total wet delay in the zenith direction. Zenith delays are mapped to the current elevation of the satellite using the Niell (NMF) mapping functions.

If you configure a facility to use DSN Media Calibration Data for troposphere modeling and request a time during a tracking interval that is not covered by the data specified in the scenario properties, ODTK will stop processing.

SCF model

The SCF model is an implementation of the 'RC [pronounced "tick R C"] model, where RC stands for "refraction correction." This model was developed by the System Development Corporation and is defined in the controlled document TM-(L)-5048/492/01. This model takes as input the surface refractivity at each facility location, which is based on local temperature, pressure, and humidity, and corrects elevation and range from apparent to true.

The equation used in ODTK for tropospheric range, R, is:

where R is in km, η = elevation angle, and = mean surface refractivity. Refractivity N is a function of the index of refraction, n:

Marini-Murray model

The Marini-Murray atmospheric correction model is designed for use with Satellite Laser Ranging data, correcting for the frequency-dependent, meteorological data-dependent, altitude-dependent effects of the atmosphere on the laser ranging signal. The Marini-Murray model is documented in the IERS Conventions. Required meteorological data (temperature, atmospheric pressure, and relative humidity) and wavelength are determined based on the facility settings.

Saastamoinen model

The model predicts apriori hydrostatic delay using the formula credited to Saastamoinen. The formula depends on the pressure at the antenna phase center. The model maps the hydrostatic zenith delay to the current elevation angle using the Niell NMF model, which is independent of meteorological conditions. Required meteorological data (atmospheric pressure) is determined based on the facility settings.

Mendes-Pavlis model

The Mendes-Pavlis model applies to optical wavelengths used in Satellite Laser Ranging (SLR). It is tuned for a wavelength of 0.532 μm. It computes hydrostatic and nonhydrostatic zenith delays using the formulation given in the article by V.B. Mendes and E.C. Pavlis called "High accuracy zenith delay prediction at optical wavelengths," Geophysical Research Letters, Vol31, 2004. The model maps the sum of these two delays into the current elevation angle using one of the two mapping functions given in Mendes et al., "Improved mapping functions for atmospheric refraction in SLR," Geophysical Research Letters, 29(10), 2002.

The zenith model uses metrological data (pressure, relative humidity, temperature), where the temperature and relative humidity are only used in the computation of the relatively small nonhydrostatic zenith delay.

Both mapping functions are as its basis the truncated form of the continued fraction in terms of 1/sin(elevation) similar to the Neill NMF model. The difference is the calculation of three model parameters input to this algorithm. The first mapping function (called FCULs in Mendes' paper) computes the parameters as a function of site location and surface temperature. The second mapping function (called FCULb in Mendes' paper) computes the parameters as a function of site location and day of year.

In ODTK, you select the mapping function via the property:

MappingFunction = "MP Surface Temperature" | "MP Day of Year"

IERS2010 model for radio frequencies

The "IERS2010Radio" model applies to radio frequencies (e.g., GPS). It is similar to the Saastamoinen model but includes the IERS 2010 propagation model updates for radio frequencies, reference section 9.2 in the IERS conventions on propagation delay (https://iers-conventions.obspm.fr/chapter9.php).

Differences from the Saastamoinen model include an updated wet/dry elevation mapping function and the addition of a horizontal gradient mapping term that is a function of azimuth. The IERS model identifies two possible wet/dry mapping functions: a Global Mapping Function (GMF) similar in structure to the Saastomonien Niels mapping function, and a Vienna Mapping Function (VMF), which is based on ray traces through refractivity profiles. ODTK only implements the GMF model.