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.

Fine-crack segmentation in high-resolution UAV images of bridges is hindered by weak crack signals, complex backgrounds, and substantial computational demands. This study proposes a dual-stage framework combining lightweight grid-wise screening with graph-enhanced segmentation. CrackClsNet identifies candidate regions, and CrackSegNet processes contextual patches comprising each candidate and its eight neighbors. Multiscale and deformable convolutions, attention, and cross-patch graph reasoning support feature extraction, while overlapping predictions are fused during reconstruction. In experiments using 1000 pixel-annotated crack-containing images collected from 13 highway bridges and 500 crack-free images, neighborhood retention increased candidate region crack-pixel coverage from 91.97% to 95.65% on the classification test set. The end-to-end framework achieved an F1-score of 0.5826, Crack IoU of 0.4110, and mIoU of 0.7052, exceeding six baseline methods in these metrics. The results of ablation experiments further support the benefits of neighboring context and cross-patch feature exchange, with 3 × 3 neighborhoods balancing segmentation quality and computational cost. With approximately 4.41 million parameters, the framework achieved 4.10 FPS with a reported memory consumption of 6.94 GB at 4096 × 5632 pixels, providing the highest throughput and lowest reported memory consumption among the evaluated methods at this resolution. These results indicate a promising balance between segmentation performance and computational cost on the evaluated bridge image dataset.