Scientific- Research Quarterly of Geographical Data (SEPEHR)

Scientific- Research Quarterly of Geographical Data (SEPEHR)

Evaluation of different mapping functions using 3-D Ray tracing

Document Type : Research Paper

Authors
Hamid Akbari 1
Vahab Nafisi 2
Jamal Asgari 3
1 M.Sc. in Geodesy
2 Department of Geomatics Engineering- Faculty of Civil engineering and Transportation- University of Isfahan
3 Associate professor- Department of geomatics engineering- Faculty of civil engineering and transportation- University of Isfahan
10.22131/sepehr.2019.34612
Abstract
 
Extended Abstract
The troposphere is a layer of atmosphere that consists of dry gases and water vapor, which causes a time delay in the emission of electromagnetic waves resulting in an error in determining the precise position. In space geodesy, normally, the travelling time of the wave between an emission source in space (a satellite for GNSS or a quasar in VLBI) and a receiver located in a geodetic station on the surface of the Earth is measured. This time is then converted to distance by the speed of light in vacuum. There are two ways to manage the atmospheric delays in space geodetic data analysis; either, external measurements of the atmospheric delays are used to correct the measurements or, the atmospheric delays are estimated in a least square adjustment as the unknowns. To model this error using the first strategy, several methods have been proposed, among which, the most prominent ones are the three dimensional (3-D) ray tracing and the use of mapping functions. 3D ray tracing is considered to be a direct method for this estimation and the actual path of the wave which is curved, is estimated by using Eikonal equation and is compared with the theoretical straight path. It means we can find the amount of correction which should be considered. Contrary to this method, the use of mapping functions is considered as indirect method and by using proper functions, the amount of delay (hydrostatic and non-hydrostatic) in the vertical direction is plotted in the desired direction. The basic assumption in this method is to take the azimuth symmetry for the troposphere into considerations and therefore, the amount of delay will depend only on the elevation angle. In this paper, comparisons have been made between this method and the method of using mapping functions that are commonly used.
Based on this research, it is determined which method to be used in different conditions to achieve the desired accuracy for space geodesy techniques such as GNSS and VLBI, and which method is the priority. In this comparison, VMF (Vienna Mapping Function) and GMF (Global Mapping Function) which are used widely in space geodetic techniques were used. Coefficients in these mapping functions are obtained based on Numerical Weather Models (NWMs) and specially ECMWF. VMF is called Isobaric Mapping Function (IMF) based on the older mapping function, and GMF function has been created with changes in VMF, so that it can be used offline in some software including VieVs software. To this end, data from two observation campaigns managed by IVS (International VLBI Service) namedCONT08 and CONT11 have been used in the years 2008 and 2011 for VLBI stations. These two campaigns involve 15 days continuous observations. The results of this study show that the station with the highest humidity (KOKEE) requires ray tracing at all intervals of accuracy and mapping functions cannot be used to produce reasonable accuracy. Also, in order to achieve the accuracy of less than 10 mm in the station's elevation, it is necessary to use ray tracing at almost all angles of elevation, or in order to achieve the accuracy of less than 20 mm, it should be used at the angles of elevation of approximately 0 to 35 degrees, and mapping functions can be used for the rest of the angles of elevation.
Based on the diagrams and tables presented in this paper, the following results can also be extracted:
-Use ray tracing method at the station with the highest humidity (KOKEE)
-Use ray tracing to achieve an accuracy of better than 10 mm for the stations’ elevation at all angles of elevation 
- Use ray tracing to achieve an accuracy of better than 20 mm for station’s elevation of approximately 0º to 35 º of the angles of elevation. Mapping functions can be used for the rest of the angles of elevation.
-Use ray tracing to achieve an accuracy of better than 30 mm for the station’s elevation of 0 to 26 degrees of the angles of elevation. Mapping functions can be used for the rest of elevation angles.
-At angles of elevation which do not require ray tracing, mapping functions are used. It can be said that in 2008, finally, GMF mapping function achieved a better accuracy than the VMF, while in 2011, the performance of VMF mapping function was better than that of GMF.
Keywords
Ray tracing
Refractivity
Numerical weather models
Mapping functions
Atmospheric modeling
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