Geometric Model of GNSS-MR Snow Depth Retrieval Under Terrain Slope and Undulation

Snow depth monitoring is of great significance for climate research and forecasting, natural resource management, ecological environmental protection, and disaster risk reduction and prevention. The existing in situ snow sensor network has limited spatial coverage and resolution. With the continuous development of Global Navigation Satellite Systems (GNSSs), a ground-based remote sensing technology, named GNSS-multipath reflectometry (GNSS-MR), based on GNSS geodetic receivers, has been proven to be capable of estimating snow depth. GNSS-MR infers the height of the reflecting surface beneath the antenna—referred to as reflector height (RH, $\text {RH}_{\text {cal}}$ )—by analyzing the frequency of multipath oscillations in the signal-to-noise ratio (SNR) data, thereby enabling snow depth estimation. However, since snow typically accumulates on uneven terrain, terrain undulation becomes the primary source of error in snow depth retrieval. Currently, the principles and methodologies for correcting such terrain effects remain underdeveloped. To address this, the present study derives the geometric relationships under sloping terrain conditions and establishes a geometric model, including a tilt-induced error model. Building on this geometric model, the study further derives terrain correction methods for snow depth retrieval under undulating terrain and proposes a multi-GNSS combination approach that incorporates terrain correction. The P351 GNSS station was selected for experiments, with data analyzed from four snow seasons between 2019 and 2023. Meanwhile, DEM data around the site were collected to calculate parameters such as slope and aspect for terrain correction. To assess the impact of DEM resolution on terrain correction effectiveness, DEM data with 1 and 12.5 m resolutions were used for comparison. The results indicate that using the 1-m resolution, DEM improved accuracy by 42%, while the 12.5-m resolution DEM led to a 34% improvement. Notably, even with globally available low-resolution DEMs, the correction method still performs satisfactorily, demonstrating strong adaptability and practical utility.