Refining Atmospheric Delay for Oblique Spaceborne LiDAR: A 3-D Ray-Tracing Perspective on Horizontal Inhomogeneity

Abstract

Atmospheric delay constitutes a primary source of ranging uncertainty in spaceborne laser altimetry, particularly for oceanic light detection and ranging (LiDAR) missions requiring large off-nadir incidence angles to mitigate saturation caused by specular reflection. Traditional correction models, typically limited to 2-D vertical profiles at the nadir point, may not adequately account for the substantial horizontal displacement—often reaching up to 100 km—that a laser pulse undergoes during oblique propagation. To address this methodological gap, we present a 3-D ray-tracing framework designed to evaluate the impact of horizontal atmospheric inhomogeneity on ranging precision. While existing 2-D models assume atmospheric uniformity relative to the nadir point, our 3-D approach permits an assessment of the atmospheric refractive index along the actual spatial trajectory. Analysis based on current meteorological data suggests that while horizontal variations currently contribute to discrepancies at the centimeter scale, this framework provides a necessary diagnostic tool for ensuring geodetic rigor in future spaceborne LiDAR missions with oblique incidence. Validation against ICESat-2 observational data, integrated with ERA5 reanalysis, demonstrates that the model maintains a mean absolute error (MAE) and root-mean-square error (RMSE) below 1.5 cm under near-zenith (<1.5°) conditions. Furthermore, we derive a parametric mapping function (MF) that offers a computationally efficient alternative to the 3-D model. Global assessment demonstrates that this function maintains subcentimeter precision (RMSE <0.94 cm) across incidence angles from 0° to 20°. These findings offer a supportive methodological foundation and a refined theoretical basis for future spaceborne altimetry systems.