Abstract
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.
Highlights
Introduction iationsTropospheric delay refers to the effect caused by the propagation of the radio signals among the neutral atmosphere, which can be divided into a hydrostatic part and a wet part [1]
ERA5 data retrieved from European Centre for Medium-range Weather Forecast (ECMWF) with the highest spatial-temporal resolution was applied to compute the tropospheric slant delays by the ray-tracing method
Traditional three order continued fraction mapping functions have been developed based on the assumption of atmospheric spherical symmetry, in which the azimuthal variation of tropospheric delays is neglected
Summary
Introduction iationsTropospheric delay refers to the effect caused by the propagation of the radio signals among the neutral atmosphere, which can be divided into a hydrostatic part and a wet part [1]. Many regional or global tropospheric delay models have been built to reduce the tropospheric delay error, which can be divided into two categories, depending on whether meteorological factors are needed or not [2]. Models of the first category use pressure, temperature, and humidity as their input parameters, such as Hopfield [3], Saastamoinen [4], Davis [5], Baby [6], Ifadis [7], Askne, Nordius [8], and MSAAS [9]. If in-situ meteorological observations are not available, the standard atmosphere [10,11,12] or empirical meteorological models [13,14,15] may be used in many GNSS data processing applications. The second category doesn’t rely on meteorological measurements, such as UNB [16], MOPS [17], TropGrid [18], ITG [19], IGGTrop [20], and SHAtropE [21].
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