The troposphere is the low altitude portion of the 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.

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. Delays are computed 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.

**Note**: If a facility is configured to use DSN
Media Calibration Data for troposphere modeling and a requested
time (during a tracking interval) is not covered by the data
specified in the scenario properties, ODTK will stop
processing.

The SCF model is an implementation of the 'RC [pronounced "tick R C"] model, where RC means 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/or 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*:

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.

A priori hydrostatic delay is predicted using the formula due to Saastamoinen which depends on the pressure at the antenna phase center. The hydrostatic zenith delay is mapped 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.

The Mendes-Pavlis model is designed to be used at optical wavelengths used in Satellite Laser Ranging (SLR). It is tuned for a wavelength of 0.532 μm. Hydrostatic and non-hydrostatic zenith delays are computed using the formulation given in V.B. Mendes, E.C. Pavlis, "High accuracy zenith delay prediction at optical wavelengths," Geophysical Research Letters, Vol31, 2004. The sum of these two delays are then mapped 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 non-hydrostatic 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, the mapping function is selected via the property:

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

The "IERS2010Radio" model is designed to be used at 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 (http://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 which is a function of azimuth. Note that 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. Currently, only the GMF model is implemented in ODTK.

ODTK 6.5