A novel method for tropospheric delay mapping function vertical modeling

In high-precision space geodetic techniques data processing, the mapping function (MF) is a key factor in mapping the radio waves from the zenith direction down to the signal incoming direction. Existing MF products, either site-wise Vienna Mapping Function (VMF1 and VMF3) or grid-wise VMF1 and VMF3, are only available at the Earth surface. For overhead areas, height correction is always required, which is becoming increasingly important with growing airborne aircraft activity. In this contribution, we introduce a novel method aimed at providing a large number of MFs to the user in a simple and efficient manner, while minimizing the loss of precision. The approach effectively represents the vertical profile of the MFs from the Earth's surface up to altitudes of 14 km. In addition, the new model corrects for height in the assessment using the fifth generation of the European Centre for Medium-Range Weather Forecasts ReAnalysis (ERA5) ray tracing calculations for a global 5° × 5° grid with 54 layers in the vertical direction, a total of 8 azimuths in the plane, and 7 elevation angles, for each day in 2021. Specifically, for both polynomial and exponential model of order 2 and 3, the relative residuals are < 0.3% for the hydrostatic delay MF coefficient \(a_{{\text{h}}}\), and < 1% for the wet delay MF coefficient \(a_{{\text{w}}}\). The precision of the new model on the Earth’s surface is evaluated using site-wise VMF1 and VMF3 GNSS (Global Navigation Satellite System) products from Technische Universität Wien. The root mean square error of slant hydrostatic delay and slant wet delay at a 3° elevation angle is approximately 4–5 cm and 2–5 cm, respectively.