GNSS-R snow depth retrieval algorithm based on PSO-LSTM

The global navigation satellite system (GNSS)-interferometric reflectometry technique has been applied to retrieve snow depth, which has a high potential for application. The GNSS reflectometry classical algorithm retrieves the snow depth by extracting the frequency of the multipath signal and substituting it into an empirical formula. However, the retrieval errors of high and low snow depths are large due to the influence of factors such as surface vegetation and terrain environment. In this paper, we propose a snow depth retrieval algorithm based on a particle swarm optimized long short-term memory (PSO-LSTM) neural network. The algorithm extracted three characteristic parameters (frequency, amplitude, and phase) from the signal-to-noise ratio (SNR) data as inputs, and optimized the LSTM hyperparameters by the PSO algorithm to improve the retrieval accuracy for low snow depths and snow depths close to the antenna. The snow depth retrieval results of global positioning system L1 band SNR data collected from the P351 station in 2022 and AB33 station in 2017 were evaluated in this paper. The snow depth retrieval results of the PSO-LSTM algorithm for P351 station were in high agreement with the snow depth data provided by the snowpack telemetry network; the coefficient of determination ( R 2 ) reached 0.986, and the root mean square error (RMSE) and mean absolute error (MAE) were 7.30 cm and 4.94 cm, respectively. Compared with the classical algorithm, the PSO-LSTM algorithm decreased the RMSE and MAE by 53.0% and 30.4% for the retrieval results of snow depths below 15 cm at the P351 station, and by 76.8% and 84.4% for the retrieval results of snow depths above 117 cm from the 1st day to the 137th day, respectively. Similarly, the RMSE, MAE, and R 2 for the 2017 retrieval results at AB33 station were 5.90 cm, 4.25 cm, and 0.965, respectively. Compared with the classical algorithm, the PSO-LSTM algorithm decreased the RMSE and MAE by 47.9% and 33.0% for the retrieval results of snow depths below 15 cm at the AB33 station, and by 75.4% and 82.3% for the retrieval results of snow depths above 56 cm from the day 46 to day 120. In addition, the snow depth retrieval algorithm was proposed in this paper does not require antenna height and empirical formulas to realize snow depth retrieval, and at the same time, the algorithm effectively improved the retrieval accuracy for both high and low snow depths with strong robustness.