TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere
Tropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, te...
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| Format: | Article |
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MDPI AG
2021-06-01
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| Series: | Remote Sensing |
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| Online Access: | https://www.mdpi.com/2072-4292/13/13/2568 |
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| author | Di Zhang Jiming Guo Tianye Fang Na Wei Wensheng Mei Lv Zhou Fei Yang Yinzhi Zhao |
| author_facet | Di Zhang Jiming Guo Tianye Fang Na Wei Wensheng Mei Lv Zhou Fei Yang Yinzhi Zhao |
| author_sort | Di Zhang |
| collection | DOAJ |
| description | Tropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, temperature, and humidity fields of ERA5 data with the highest spatio-temporal resolution available from the European Centre for Medium-range Weather Forecast (ECMWF) were utilized to compute ray-traced delays by the software WHURT. Results reveal the universal asymmetry of the hydrostatic and wet tropospheric delays. To accurately represent these highly variable delays, a new mapping function that depends on elevation and azimuth angles—Tilting Mapping Function (TMF)—was applied. The basic idea is to assume an angle between the tropospheric zenith direction and the geometric zenith direction. Ray-traced delays served as the reference values. TMF coefficients were fitted by Levenberg–Marquardt nonlinear least-squares method. Comparisons demonstrate that the TMF can improve the MF-derived slant delay’s accuracy by 73%, 54% and 29% at the 5° elevation angle, against mapping functions based on the VMF3 concept, without, with a total and separate estimation of gradients, respectively. If all coefficients of a symmetric mapping function are determined together with gradients by a least-square fit at sufficient elevation angles, the accuracy is only 6% lower than TMF. By adopting the b and c coefficients of VMF3, TMF can keep its high accuracy with less computational cost, which could be meaningful for large-scale computing. |
| first_indexed | 2024-03-10T09:53:24Z |
| format | Article |
| id | doaj.art-036daf2603d042d189805cb5891d3b13 |
| institution | Directory Open Access Journal |
| issn | 2072-4292 |
| language | English |
| last_indexed | 2024-03-10T09:53:24Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Remote Sensing |
| spelling | doaj.art-036daf2603d042d189805cb5891d3b132023-11-22T02:31:04ZengMDPI AGRemote Sensing2072-42922021-06-011313256810.3390/rs13132568TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral AtmosphereDi Zhang0Jiming Guo1Tianye Fang2Na Wei3Wensheng Mei4Lv Zhou5Fei Yang6Yinzhi Zhao7School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, ChinaSchool of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, ChinaSchool of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, ChinaGNSS Research Center, Wuhan University, 129 Luoyu Road, Wuhan 430079, ChinaSchool of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, ChinaCollege of Geomatics and Geoinformation, Guilin University of Technology, Guilin 541004, ChinaCollege of Geoscience and Surveying Engineering, China University of Mining and Technology-Beijing, Beijing 100083, ChinaSchool of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan 430079, ChinaTropospheric mapping function plays a vital role in the high precision Global Navigation Satellites Systems (GNSS) data processing for positioning. However, most mapping functions are derived under the assumption that atmospheric refractivity is spherically symmetric. In this paper, the pressure, temperature, and humidity fields of ERA5 data with the highest spatio-temporal resolution available from the European Centre for Medium-range Weather Forecast (ECMWF) were utilized to compute ray-traced delays by the software WHURT. Results reveal the universal asymmetry of the hydrostatic and wet tropospheric delays. To accurately represent these highly variable delays, a new mapping function that depends on elevation and azimuth angles—Tilting Mapping Function (TMF)—was applied. The basic idea is to assume an angle between the tropospheric zenith direction and the geometric zenith direction. Ray-traced delays served as the reference values. TMF coefficients were fitted by Levenberg–Marquardt nonlinear least-squares method. Comparisons demonstrate that the TMF can improve the MF-derived slant delay’s accuracy by 73%, 54% and 29% at the 5° elevation angle, against mapping functions based on the VMF3 concept, without, with a total and separate estimation of gradients, respectively. If all coefficients of a symmetric mapping function are determined together with gradients by a least-square fit at sufficient elevation angles, the accuracy is only 6% lower than TMF. By adopting the b and c coefficients of VMF3, TMF can keep its high accuracy with less computational cost, which could be meaningful for large-scale computing.https://www.mdpi.com/2072-4292/13/13/2568tropospheric delayray-tracemapping functiontilting tropospheregradient |
| spellingShingle | Di Zhang Jiming Guo Tianye Fang Na Wei Wensheng Mei Lv Zhou Fei Yang Yinzhi Zhao TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere Remote Sensing tropospheric delay ray-trace mapping function tilting troposphere gradient |
| title | TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere |
| title_full | TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere |
| title_fullStr | TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere |
| title_full_unstemmed | TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere |
| title_short | TMF: A GNSS Tropospheric Mapping Function for the Asymmetrical Neutral Atmosphere |
| title_sort | tmf a gnss tropospheric mapping function for the asymmetrical neutral atmosphere |
| topic | tropospheric delay ray-trace mapping function tilting troposphere gradient |
| url | https://www.mdpi.com/2072-4292/13/13/2568 |
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