A combined GNSS-RR system is designed and installed on the Ekström ice shelf, Dronning Maud Land, Antarctica, providing data for the first-time development and evaluation of the combined GNSS-RR method based on reflected and refracted GNSS signals. Figure a shows the combined GNSS-RR system, which moves at ≈ 150 m a-1 with the ice shelf towards NNE (Fig. d). The setup is mounted on an already existing sensor mast from the Meteorological Observatory at the Neumayer Stations of the Alfred Wegener Institute (AWI), Helmholtz Center for Polar and Marine Research. The mast is located close to the AWI's air chemistry (Spuso) observatory (Fig. c), which is 1.5 km south of the German Antarctic research station Neumayer III .

The GNSS-RR setup consists of a high-end GNSS reference antenna and a high-end and low-cost GNSS rover antenna placed on the firn surface. The rover antennas are buried by the snow accumulating on top of the antennas (Fig. b). It is mandatory that the rover antennas are mechanically connected to the reference antenna when deployed on a moving surface. The physical connection enables the correct separation of the SWE-induced effects and station height changes due to the ice shelf movements in the GNSS parameter estimation, as both parameters are highly collinear with 99.7 % . The rover antennas are physically (mechanically) fixed to the sensor mast via another lateral boom. The buried lateral boom is rigid and initially placed on very dense, wind-packed snow. The bending of the arm is thus assumed to be negligible. All antennas are equally oriented towards north, and antenna calibration files are applied in the GNSS processing to minimize the antenna-phase center offset and variation effects on the results. Note that the data from a second GNSS reference antenna, mounted on a lateral boom to the sensor mast (Fig. a), are not used in the present study.

The specifications of the deployed GNSS-RR system are summarized in Table . A Raspberry Pi computer is used for remote control and data transfer of the low-cost receiver. The GNSS-RR system collects multifrequency and multisystem (GPS, GLONASS, and Galileo) GNSS signals. The GNSS antenna mounted on top of the sensor mast serves as a GNSS reference for differential processing and, additionally, tracks reflected GNSS signals (1 Hz sampling rate) from the surrounding snow surfaces. The buried GNSS antennas collect refracted GNSS signals (30 s sampling interval), influenced by the accumulated snow above the antennas, from all elevation angles. Power and Ethernet supply is provided by the Spuso which is connected to the Neumayer III station.

Ground truth data for snow deposition and erosion (snow accumulation) are provided with a 1 min sampling interval by a laser distance sensor (Jenoptik SHM30) from the same sensor mast . The laser observations are filtered by a moving median over 24 h to remove outliers and resampled to 15 min to match the temporal resolution of the GNSS-derived results. The nearby (distance ≈ 20 m) snow buoy observations , consisting of four sonic ranges (MaxBotix HRXL-MaxSonar-WR3), are furthermore used for reference. Additional ground truth data are provided weekly by 16 accumulation stakes from the nearby “Pegelfeld Spuso” (distance ≈ 200 m). Monthly manual snow accumulation, SWE, and snow density observations from the upper layer (first meter) are taken from the “density sample location” (distance ≈ 50 m) at the same test site (Fig. c). A relative uncertainty of 10 % is added as an error bar in all plots to indicate the general accuracy of such manual observations. Continuous snow accumulation data from the laser distance sensor are, additionally, converted to SWE by linearly interpolating the monthly density observations to enable an accuracy estimate for the GNSS-RR-derived SWE time series.

In situ snow accumulation (deposition and erosion) is estimated using ground-based GNSS reflectometry (e.g., ). Direct GNSS signals and GNSS signals reflected off a snow/firn surface are analyzed in order to measure the difference in height h between the GNSS reference antenna and the reflective surface. The influence of the reflected signals on the signal strength depends on the path extension, with respect to the direct signals. The overlay of the direct and reflected GNSS signals creates an interference pattern of the signal strengths when satellites move across the sky. The frequency f of these multipath oscillations is related to h (with λ being the GNSS wavelength of the observed satellite system from 18–26 cm) as follows: 1h=fλ2.

The snow accumulation b is given by the change in height (Δh) over time. Figure  shows that the area around the GNSS reference antenna, used to estimate snow accumulation, is determined by the first Fresnel reflection ellipses for the experimental setup. The size of these ellipses depends on the height of the reference antenna above the surface and the analyzed incident angles.

The 1 Hz GNSS reference data are post-processed by using the open-source gnssrefl package from . The best results are achieved by selecting GPS, GLONASS, and Galileo second frequencies within an elevation range of 5–30∘. The reflector height was set from 2–8 m to allow automated processing, which is independent of regular sensor mast extensions of approximately 3 m. Distracting low-elevation signals, bending around or reflecting off the nearby Spuso, are excluded based on their azimuthal range. The outliers in the snow accumulation results are removed using a statistical threshold based on the standard deviation (3σ). The resulting time series is filtered by a moving median over 24 h. The derived results are resampled to 15 min values to enable the combination with the SWE estimates from GNSS refractometry.

The GNSS refractometry method based on the biased “Up component” is applied to in situ SWE estimation. The signals received by an antenna buried underneath the snowpack are delayed while propagating in a snow/firn layer. These delays cause the estimated antenna position to be biased, especially the vertical up (height) component U. The resulting height deviation from a phase-based differential GNSS position estimation provides information on the change in SWE (i.e., snow mass change δm), as both parameters are highly collinear with 99.7 % : 2δm≈δU.

The δm above the buried rover antenna can, thus, be estimated based on the change in the estimated up component δU (Eq. ) of the rover coordinate. Equivalently, the up component of the derived GNSS baseline between both antennas could be used directly. In contrast to previous GNSS refractometry studies, the present setup is situated on a fast-moving surface. The correlation between the influence of snow on the GNSS signal delay and the ground movement is considered in the experimental setup (Sect. ) by physically connecting the rover to the base antenna. If the physical height difference between the two antennas were not known and fixed, the SWE parameter could not be separated from the station height due to the changes caused by the ground movement.

The GNSS refractometry data are post-processed using the open-source GNSS processing software, RTKLIB version 2.4.3 b34 . Although multisystem data are collected, the best results are achieved by only using multifrequency GPS data for the SWE estimation. For the processing, 7 to 13 GPS satellites are generally available on site. The additional use of Galileo and GLONASS observations increased the number of unusable solutions in the case of our experiment. This is assumed to be caused by the applied processing software, which was initially coded for GPS only and extended for multi-GNSS systems afterward, potentially leading to problems in nonstandard GNSS applications. Processing intervals of 15 min are applied to the differential GNSS processing with a very short baseline (3–6 m). All elevation observations are used to enhance the SWE estimation accuracy . The reference coordinate is not fixed due to the ground movement, but it is selected automatically from each day's navigation position (available in the resulting RINEX observation file header) to guarantee an adequate initial coordinate for the differential processing. Similar to the snow accumulation estimation, the outliers in the SWE results are removed using the 3σ statistical threshold. The 15 min SWE time series is filtered by a moving median over 24 h.

The in situ snow density ρs is derived by combining the individual results from GNSS reflectometry (snow accumulation b) and refractometry (SWE m): 3ρs=mb.

The resulting daily densities, that are lower than the density of new snow (50 kg m-3) or higher than the density of firn (830 kg m-3), are removed for plausibility. The SWE and snow density are determined as an average over an area of a few square meters around the antenna, depending on the height of the snow above the buried rover antennas, snow wetness, and signal incidence angles.

Figure a illustrates the results from GNSS reflectometry, using the open-source gnssrefl package, for the end of November 2021 to April 2023. All snow accumulation estimates (transparent steel blue area) are overlaid by the median-filtered snow accumulation estimates (steel blue line). The snow accumulation varies significantly (standard deviation of 23 cm) over the reflection area, which covers a radius of up to 80 m around the reference antenna (Fig. ). The variation is predominantly caused by strong winds, leading to spacial and temporal heterogeneity in snow deposition and erosion within the test site. The estimated snow accumulation is directly compared with the reference data of the laser distance sensor (dark blue) from the same mast. The GNSS-derived accumulation shows a very high level of agreement with the laser observations for the first weeks in November/December 2021, with differences around 2 cm (Fig. b). The storms in mid-December 2021 led to a strong increase in snow accumulation (up to 50 cm), as observed by the laser sensor. In contrast, the increase in accumulation derived by GNSS reflectometry is significantly less, with 32 cm for the same time period. This difference is in the order of the horizontal homogeneity of the snow surface and may be explained by the different footprints of the two methods. This rationale is supported by comparable extreme values of the GNSS estimate around this time. Note that the laser distance sensor broke down at the beginning of October 2022 and was replaced at the end of December 2023, leading to a lack of data for this time period.

Additional reference data (Sect. ) are available for comparison (Fig. c) from the nearby manual observations (dark blue dots), snow buoy (gray curves), and 16 stake observations (colored dotted lines). A strong variation in snow accumulation is observed among all the reference sensor's data, with similar magnitudes as the difference in accumulation between the GNSS-derived results and the laser observations.

The accumulation observations decrease significantly after the mid-December event and last until February 2022. The GNSS-derived accumulation closely follows the trend observed by the laser distance reference sensor for the rest of the observation period. The differences between the GNSS results and the laser vary around 35 cm. The overall results have a root mean square error (RMSE) of 8.5 cm (Table ), when compared with the laser observations.

The accumulation results are compared to the laser observations in Fig. d based on a linear regression. The snow accumulation estimated by GNSS reflectometry is highly correlated to the laser observations, with Pearson cross correlation coefficients (r) of 0.98. The offsets induced by the snow deposition and erosion heterogeneity are visible in the linear fit. Table  lists the regression coefficients.

The GNSS-refractometry-derived SWE is median filtered, and Fig. a shows the high-end (black) and low-cost (orange) system from the end of November 2021 to April 2023. The median SWE time series is overlaid by the noise (standard deviation per day, transparent black and orange) of the 30 s SWE estimation before filtering (3 kg m-2 a-1 for the high-end and 6 kg m-2 a-1 for the low-cost system). The standard deviation of the median-filtered SWE, resulting from the high-end and low-cost system, is 2 kg m-2 a-1. Both of the GNSS-derived SWE estimates strongly agree with each other until August 2022, with noisier results from the low-cost system. The differences between the high-end and low-cost system increase afterward, where the low-cost results start to underestimate the SWE up to 64 kg m-2 a-1 (Fig. b). All possible error sources related to the GNSS refractometry processing (antenna height, base coordinate, antenna calibration parameters, WGS84 reference ellipsoid, satellite availability, and signal strengths) were checked. As GNSS refractometry is a relative observation method between the base and rover antenna, the processing is consistent for all data epochs and receivers. There was no change in the satellite signatures; therefore, we could exclude all such error sources. Since the offset is sudden and affects the receiver height, we assume a change in the effective physical height of the low-cost antenna. The antenna is screwed on the submerged lateral boom via a small vertical balise bar. Due to the overlying pressure of the snowpack and the cold, it could be possible that the screw had become loose, and the antenna sank a few centimeters into the underlying snow.

The derived SWE is directly compared with the nearby manual reference observations (blue dots). A relative uncertainty of 10 % is added as an error bar to the manual observations. An additional reference, with a higher temporal resolution, is provided by the laser distance observations (dashed blue line). The observed snow accumulation data are, thereby, converted to SWE by linearly interpolating the available manual density measurements (Sect. ). Note that the laser distance sensor broke down at the beginning of October 2022 and was replaced at the end of December 2022, leading to a lack of data for this time period.

The GNSS-refractometry-derived SWE shows a very high level of agreement with the laser reference observations for the first weeks of the diminishing snow in November/December 2021, with differences around ±5 kg m-2 a-1 (Fig. b). As is already visible in the snow accumulation results (Sect. ), heavy snowfall increased the SWE up to 200 kg m-2 a-1 (observed by the laser sensor) or even 230 kg m-2 a-1 (observed manually) in mid-December 2021. The increase in SWE derived by GNSS refractometry is significantly less, with 105 kg m-2 a-1 for the same time period. The reason is similar to the reason for the difference observed in the snow accumulation results, and it is caused by the heterogeneity of the snow deposition and erosion within the test area. The GNSS-refractometry-derived SWE closely follows the trend of the laser observations after mid-December. The differences in the laser data vary within 193 kg m-2 a-1. The present deviations (up to 204 kg m-2 a-1) are higher, when compared with the manual observations. The results from the high-end system have an RMSE of 32 kg m-2 a-1 to the manual and 43 kg m-2 a-1 to the laser observations (Table ). The results from the low-cost system have an RMSE of 36 kg m-2 a-1 to the manual and 38 kg m-2 a-1 to the laser observations.

The SWE results are compared with the reference observations in Fig. c and d, using a linear regression. The SWE estimates derived from GNSS refractometry are highly correlated to the manual and laser observations, with r between 0.94 and 0.97 (Table ). The offsets induced by the snow deposition and erosion heterogeneity are visible in the linear fit. Table  lists the regression coefficients.

Combining the median-filtered, GNSS-derived results for snow accumulation and SWE leads to estimates of snow density (temporal resolution of 15 min) for the observed area. Figure a illustrates the SWE and accumulation results from GNSS reflectometry and refractometry, respectively. Snow accumulation decreases in November and December 2021, followed by snow deposition in mid-December 2021. Generally, snow deposition and erosion dominate the change in SWE. It seems, however, that the snow settles during August and September 2022, after an increase in accumulation, as the deposited snow decreases, while the SWE stays nearly constant.

Figure b shows the combined GNSS-RR-derived snow density from the high-end and low-cost system from the end of November 2021 to April 2023. Additionally, Fig. b shows the manual density observations and their accuracy, for reference. The GNSS-RR-derived densities are calibrated to the manual observation of 24 July 2022. Approximately 1 m of snow accumulated on top of the buried GNSS antennas on that day, which enables a correct match with the manual density observation of the upper 1 m layer (top 1 m), for better comparison. The results from the high-end and low-cost GNSS-RR method agree well with each other until August 2022. The low-cost system yields lower densities after August 2022 compared with the high-end results. Although the low-cost results seem to fit better with the manual density observations after August 2022, the lower density estimates are caused by the underestimated low-cost SWE results and error propagation, when calculating the density. The high-end GNSS-RR-derived estimates yield higher densities after August 2022 compared with the manual observations, with an increasing trend (Fig. c). The accumulation on top of the buried GNSS antennas exceeds 1 m after August 2022. The larger amount of snow above the buried antennas (b > 1 m) could lead to the illustrated increase in the density observations, when compared with the manual observation of the top 1 m of the snowpack.

Strong variations in the derived density time series are present until March 2022 for both systems, when compared with the manual reference observations. During this time interval, the snow accumulation above the buried antennas was quite shallow (below 20 cm), and, consequently, the estimated SWE values were very low. As the GNSS-derived SWE estimation uncertainties are independent of the magnitude of the SWE itself, large density variations can result from small SWE values. Once the snow above the antennas is thicker, the combined GNSS-RR method enables feasible density estimates, which agree well with the manual reference observations.

The high-end and low-cost density results are compared with the manual reference observations in Fig. d, using a linear regression. The GNSS-RR-derived density estimates show a low negative correlation to the manual observations, with r being -0.37 for the high-end and -0.42 for the low-cost system (Table ). These results are highly influenced by the strong variation in the first months due to the shallow snowpack above the buried GNSS antennas. Table  lists the regression coefficients.