Snow depth retrieval using GPS signal-to-noise ratio data based on improved complete ensemble empirical mode decomposition

Snow is essential to the Earth's water source and plays a significant role in studying the climate system and hydrological cycle. Snow depth monitoring has recently become an application of Global Navigation Satellite System (GNSS) instruments. The traditional snow depth retrieval algorithm for GNSS Interferometric Reflectometry (GNSS-IR) extracts the reflected signal from the signal-to-noise ratio (SNR) data by polynomial fitting, in which high- or low-frequency noise affects the accuracy of the results. This study introduces an improved complete ensemble empirical mode decomposition (ICEEMDAN) method for use in GNSS-IR. The reflected signal is reconstructed using the correlation coefficient method, which could effectively reduce noise interference. The accuracy of the proposed algorithm is evaluated using snow depth measurements collected on GNSS footprints at 14 sites that are GNSS stations of the EarthScope Plate Boundary Observatory (PBO). The root-mean-square error (RMSE) and mean absolute error (MAE) are 10.1 cm and 8.3 cm, respectively, 21.1% and 24.5% better than the traditional algorithm's RMSE of 12.8 cm and MAE of 11.0 cm. The accuracy of the proposed algorithm in the uncertainty range is comparable to the standard algorithm. The results of the proposed algorithm for snow depth retrieval over a 262-day time series at site P351, which belongs to the PBO in the western United States, correspond well with that of the traditional algorithm and the reference snow depth. The ICEEMDAN-based algorithm for snow depth retrieval reduces the background noise of signals and increases the number of tracks with significant spectral peak amplitudes, which makes the algorithm applicable for more accurate snow depth retrieval with complex environments. Its derived Hilbert spectrum can help to visualize the variation of reflected height with elevation angle and has the potential to identify azimuth/elevation angles without reflection features.