**1. Introduction**

Snow is an important part of the land hydrological cycle and global climate system. Accurate real-time snow depth data are an important reference indicator for water resource management and climate disaster warning [1,2]. Among the existing snow depth detection

**Citation:** Tu, J.; Wei, H.; Zhang, R.; Yang, L.; Lv, J.; Li, X.; Nie, S.; Li, P.; Wang, Y.; Li, N. GNSS-IR Snow Depth Retrieval from Multi-GNSS and Multi-Frequency Data. *Remote Sens.* **2021**, *13*, 4311. https://doi.org/ 10.3390/rs13214311

Academic Editors: Serdjo Kos, José Fernández and Juan F. Prieto

Received: 3 October 2021 Accepted: 25 October 2021 Published: 26 October 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

methods, in situ snow sensor measurement lacks time resolution, and global navigation satellite system interferometric reflectometry (GNSS-IR), as a new microwave sensing technology, has proven to be able to realize snow depth detection [3]. GNSS-IR is a kind of satellite remote sensing technology that uses GNSS signals as the transmitting source to realize the retrieval of the physical parameters of surface targets by receiving and processing the interference effect of GNSS signals formed by direct and surface reflection [4–6]. At present, this technology is mainly employed to retrieve the soil moisture content (SMC), snow depth, and vegetation parameters [7–12].

In recent years, researchers have made remarkable achievements in GNSS-IR snow depth detection. Larson et al. first proposed to extend the application of signal-to-noise ratio (SNR) data observed by the traditional geodetic global positioning system (GPS) receiver in order to detect snow depth [3]. Larson et al. conducted snow depth retrieval using SNR data of a GPS L2C signal at multiple stations of the Plate Boundary Observatory (PBO) and further verified the feasibility of this technology [13]. Later, Larson et al. developed a snow depth retrieval algorithm based on GPS L1 SNR data, compared it with the snow depth results of L2C signal retrieval, and found that the accuracy was improved [14]. Tabibi et al. evaluated the value of GPS L5 SNR data in snow depth detection, compared the results with the L2C signal, and found that there was no detectable deviation in the L5 retrieval results [15]. Tabibi et al. proposed the global orbit navigation satellite system multipath reflectometry (GLONASS-MR) SNR retrieval model, which extended GPS-MR to multiple GNSS, and showed a strong correlation by comparing the retrieval results of GPS L2C and GLONASS R2-coarse acquisition (C/A) signals [16]. Later, Tabibi et al. used simulation and field measurements to evaluate the accuracy of GPS and GLONASS combined multi-GNSS-MR snow depth retrieval. At the same time, the variance factor was used to form the optimal multi-GNSS combined snow depth daily sequence retrieval. Compared with the single signal snow depth retrieval results, the accuracy was significantly improved [17]. Jin et al. used GPS L2P SNR data to retrieve the snow depth, and compared it with GPS L1 C/A code results, which showed a high correlation, indicating that using L2P SNR data can better estimate the snow depth [18]. Zhou et al. used GLONASS L1 SNR data for snow depth detection, and the accuracy reached centimeter-level and showed a strong correlation with the measured data [19]. Zhou et al. also studied the retrieval of different signal combinations and proposed using GPS L1, L2, and L5 signal multipath reflection and SNR combination for the retrieval of snow depth. The results showed that this method can be effectively used for snow depth detection [20].

The above scholars' research on snow depth retrieval is based on GPS and GLONASS observation data and has not been extended to other GNSS systems. To further analyze the potential of other GNSS systems in snow depth detection, Wang et al. used the SNR data of GPS L1 and BeiDou navigation satellite system (BDS) B1I signals to retrieve the snow depth, finally reaching an accuracy of 5 cm in a day [21]. Wang et al. used multi-GNSS system data to retrieve the snow depth and found that the trend of single signal retrieval results of multi-GNSS system constellations was in good agreement, except for the GPS precise code (P-code) signal. Then, the multi-GNSS system combination method based on robust regression was used to combine the signal retrieval between constellations. The results showed that the accuracy, availability, and time sampling of multi-GNSS system combination retrieval were improved [22].

From the current research status, snow depth retrieval is mainly concentrated in single or dual GNSS systems and single frequency SNR data, which is often found to be challenging when attempting to meet the accuracy and time resolution requirements of snow depth detection. Therefore, based on previous studies, this article conducts snow depth retrieval using multi-GNSS and multi-frequency SNR data. For the case that the antenna height of the GNSS receiver is unknown, the mean value of the multi-day Lomb-Scargle periodogram (LSP) spectrum analysis results in the snow-free surface is used as the initial reference reflector height of the multi-GNSS and multi-frequency GNSS-IR in the

article. Then, the snow depth retrieval capability of the Galileo satellite navigation system (Galileo) and BDS multi-frequency signal, which are rarely used to retrieve the snow depth, except the GPS and GLONASS signal, are evaluated. A mean fusion of multi-frequency retrieval results of different GNSS systems is proposed to improve the accuracy compared with different frequencies of multi-GNSS system retrieval results. Finally, the multi-GNSS system retrieval results are fused to further evaluate the accuracy of the GNSS combination retrieval of snow depth. In this article, through the above process, the feasibility and accuracy of multi-GNSS and multi-frequency GNSS-IR snow depth retrieval are evaluated.

#### **2. Materials and Methods**

#### *2.1. GNSS-IR Snow Depth Retrieval Principle*

The snow depth retrieval method used in the article is based on SNR data processing of traditional geodetic GNSS receivers. The SNR is an indicator used to measure the signal strength of global navigation satellites, which is mainly affected by antenna gain, satellite transmission power, and multipath [23–25]. The multipath effect of the SNR decreases with increasing satellite elevation angle. The direct and surface reflected signals will have obvious interference effects at the receiver antenna when the satellite is at low elevation angle. At the same time, the frequency of the reflected signal will also change with the change in antenna height. The snow depth parameter can be obtained by comparing the vertical distance difference between the reflection surface and the receiver antenna phase center under snow-free and snow conditions.

Figure 1 shows that direct signal and reflected signal generate corresponding interference effects at the receiver to form a composite interference signal, which can be expressed as [24]:

$$\text{SNR} = A\_{\text{d}}^2 + A\_{\text{r}}^2 + 2A\_{\text{d}}A\_{\text{r}}\cos\ \text{ }\text{ $\varphi$ }\tag{1}$$

where *A*<sup>d</sup> and *A*<sup>r</sup> are the amplitudes of the direct signal and the reflected signal, and *ϕ* is the difference between the phases of the direct signal and the phases of the reflected signal (the unit is rad), which can be expressed as [26]:

$$
\varphi = \frac{4\pi h}{\lambda} \text{sin } \theta\_{\prime} \tag{2}
$$

where *λ* is the wavelength of the signal; *θ* is the elevation angle of the satellite; *h* is the vertical distance from the reflector to the antenna phase center; and the full text is uniformly called the reflector height.

Because the change in snow depth parameters is only related to the reflected signal in the composite SNR data, it is necessary to eliminate the direct signal in the composite SNR to obtain the reflected signal part. In the article, the composite SNR data are fitted by a cubic low-order polynomial, and the composite SNR is linearized before fitting [27]:

$$\text{SNR}(\text{volts}/\text{volts}) = 10^{\frac{\text{SNR}(\text{dB} - \text{Hz})}{20}} \text{} \tag{3}$$

After the trend of the direct signal sequence is fitted, the SNR sequence of the reflected signal that removes the influence of the direct signal can be obtained, which can be expressed as SNRr [28]:

$$\text{SNR}\_{\text{I}} = A\_{\text{I}} \cos(\frac{4\pi h}{\lambda} \sin|\theta| + |\varphi|), \tag{4}$$

*f* is the signal frequency of the multipath effect part in the SNR. After simplification, the relationship reflector height and the satellite signal wavelength can be obtained as follows:

$$f = \frac{2h}{\lambda} \, h = \frac{\lambda \, f}{2},\tag{5}$$

**Figure 1.** Schematic diagram of GNSS-IR snow depth retrieval. After the satellite sends the signal, the right-handed circular polarized (RHCP) antenna receives the direct signal and the surface reflected signal, and produces interference effect at the receiver. The snow surface reflector height (*Hs*) and snow-free surface reflector height (*Hs f* ) are calculated, respectively, by analyzing the oscillation effect, and the snow depth (*hsd*) is calculated by comparing the differences between them. *θ* is the elevation angle of the satellite.

In the article, the LSP method is used to analyze SNRr, obtain *f* , and extract *h* [3,29,30]. As shown in Figure 1, the snow depth parameter is calculated by using the above method by comparing reflector height in the case of snow-free and snow surfaces:

$$h\_{sd} = H\_{sf} - H\_{s\star} \tag{6}$$

where *Hs f* and *Hs* are the snow-free and snow surface reflector height, and *hsd* is the snow depth.

Snow depth retrieval is mainly determined by snow and snow-free surface reflector height. Wang et al. mentioned that non-planar reflecting surface and atmospheric refraction in GNSS-IR techniques can lead to errors in reflector height. These two errors are mainly considered in the sea level height retrieval, but rarely in the snow depth, as the snow depth changes slowly, and the reflector height to snow depth is usually smaller than that to the sea level [22]. The purpose of the article is to evaluate the ability of multi-GNSS and multi-frequency GNSS-IR snow depth retrieval, without focusing on the actual error impact caused by these two factors.
