Machine-learned mapping functions for the asymmetric troposphere

Abstract

Accurate empirical tropospheric mapping functions (MFs) are essential for high-precision geodetic applications such as GNSS and VLBI. However, traditional MFs assume azimuthal symmetry or explicitly model gradients on regular grids, limiting their ability to represent real atmospheric conditions. To address the limitation, this study designs a novel physics-constrained machine learning-based framework implemented with a multilayer perceptron and develops global empirical asymmetric MFs on five years of ERA5-based ray-tracing data. Compared to the widely used GPT3 model, our models reduce global RMSE by up to 12.0% for hydrostatic and 2.8% for wet components. Relative to GPT3 with gradient corrections, they remain globally competitive, with locally improved performance, especially at low elevations, high altitudes, and over many continental regions. The improvements are particularly evident at low elevation angles, high-altitude sites, and over continental regions. To our knowledge, this work marks the first global machine learning-based empirical MF models that directly capture atmospheric asymmetry, offering a flexible and physically consistent alternative to traditional models in space geodesy. The first global machine-learning-based empirical mapping functions for the asymmetric troposphere are developed. A physics-constrained machine-learning framework enables robust and physically consistent mapping function modeling. The models outperform symmetric GPT3, remain competitive with GPT3 with gradients, and support flexible updating and extension. The first global machine-learning-based empirical mapping functions for the asymmetric troposphere are developed. A physics-constrained machine-learning framework enables robust and physically consistent mapping function modeling. The models outperform symmetric GPT3, remain competitive with GPT3 with gradients, and support flexible updating and extension.