Feasibility demonstration of using the signal-to-noise ratio observations from geodetic GNSS receivers to retrieve dry snow density

The geodetic Global Navigation Satellite System (GNSS) receiver has been proven to retrieve snow depth using the phase change rate of the signal-to-noise ratio (SNR) observations. Snow density can be related to the permittivity of snow and is theoretically sensitive to the amplitude of the GNSS reflected signal. However, retrieving snow density using the SNR observations is challenging due to the difficulty in extracting the reflected amplitude since it hides in the interference waveform and changes with the satellite elevation angle. Overcoming this issue by taking an indirect path, this study proposes a novel GNSS Signal Amplitude Ratio Model (GSARM) that relates the corrected amplitude ratio (α) to the snow permittivity and the resulting snow density. First, the model extracts the instantaneous amplitude from SNR observations to derive an initial amplitude ratio (α0). Then, it uses a step-wise strategy to correct systematic errors from antenna gain and random errors from soil moisture in α0 to achieve the finalized corrected α. The GSARM-derived dry snow density is compared with three other data sources, i.e., the PBO-H2O, the ERA5-Land, and the in-situ measurements over two GNSS sites for six consecutive years. The overall mean RMSD (RMSPD) values of snow density for GSARM compared to PBO-H2O, ERA5-Land, and in-situ measurements are 0.036 g/cm³ (22.08%), 0.040 g/cm³ (21.43%), and 0.032 g/cm³ (23.05%), respectively. The corresponding MAD (MAPD) values are 0.029 g/cm³ (21.90%), 0.035 g/cm³ (18.46%), and 0.025 g/cm³ (22.87%), respectively. The findings of this study first prove the feasibility of using geodetic GNSS receivers for snow density retrieval. It also provides supportive information for extending the added-value applications of traditional geodetic GNSS sites and for developing new observation patterns.

大地测量型全球导航卫星系统（Global Navigation Satellite System, GNSS）接收机已被证实可通过信噪比（signal-to-noise ratio, SNR）观测值的相位变化率反演雪深。雪密度与积雪介电常数密切相关，且理论上对GNSS反射信号的振幅具有敏感性。然而，由于反射振幅隐藏于干涉波形中且随卫星仰角动态变化，提取反射振幅存在较大难度，因此利用SNR观测值反演雪密度颇具挑战。本研究采用间接路径攻克该难题，提出一种新型GNSS信号振幅比模型（GNSS Signal Amplitude Ratio Model, GSARM），将校正后振幅比（α）与积雪介电常数及由此推导得到的雪密度建立关联。首先，该模型从SNR观测值中提取瞬时振幅以计算初始振幅比（α₀）；随后，通过逐步策略校正α₀中的天线增益系统误差与土壤湿度引发的随机误差，得到最终校正后的振幅比α。将基于GSARM反演得到的干雪密度与三类数据源进行对比分析，即PBO-H2O、ERA5-Land以及两个GNSS站点连续6年的原位测量数据。GSARM反演的雪密度与PBO-H2O、ERA5-Land及原位测量数据相比，整体平均均方根偏差（均方根百分比偏差）分别为0.036 g/cm³（22.08%）、0.040 g/cm³（21.43%）和0.032 g/cm³（23.05%）；对应的平均绝对偏差（平均绝对百分比偏差）分别为0.029 g/cm³（21.90%）、0.035 g/cm³（18.46%）和0.025 g/cm³（22.87%）。本研究结果首次证实了利用大地测量型GNSS接收机反演雪密度的可行性，同时为拓展传统大地测量型GNSS站点的增值应用场景以及开发新型观测模式提供了有力的支撑依据。