Snow Water Equivalent of Dry Snow Derived From GNSS Carrier Phases

Abstract

Snow water equivalent (SWE) is a key variable for various hydrological applications. It is defined as the depth of water that would result upon complete melting of a mass of snow. However, until now, continuous measurements of the SWE are either scarce, expensive, labor-intense, or lack temporal or spatial resolution especially in mountainous and remote regions. We derive the SWE for dry-snow conditions using carrier phase measurements from the Global Navigation Satellite System (GNSS) receivers. Two static GNSS receivers are used, whereby one antenna is placed below the snow and the other antenna is placed above the snow. The carrier phase measurements of both receivers are combined in double differences (DDs) to eliminate clock offsets and phase biases and to mitigate atmospheric errors. Each DD carrier phase measurement depends on the relative position between both antennas, an integer ambiguity due to the periodic nature of the carrier phase signal, and the SWE projected into the direction of incidence. The relative positions of the antennas are determined under snow-free conditions with millimeter accuracy using real-time kinematic positioning. Subsequently, the SWE and carrier phase integer ambiguities are jointly estimated with an integer least-squares estimator. We tested our method at an Alpine test site in Switzerland during the dry-snow season 2015-2016. The SWE derived solely by the GNSS shows very high correlation with conventionally measured snow pillow (root mean square error: 11 mm) and manual snow pit data. This method can be applied to dense low-cost GNSS receiver networks to improve the spatial and temporal information on snow.

Retrieval of Snow Water Equivalent, Liquid Water Content, and Snow Height of Dry and Wet Snow by Combining GPS Signal Attenuation and Time Delay

“…Figure b shows the approximately 5‐m high poles and racks, which were used at the test site Weissfluhjoch and the locations of GPS 1 and GPS 2 . During the snow‐covered season, GPS 2 was covered with snow such that the received GPS signals were influenced by travelling through the snowpack, whereas GPS 1 was permanently above the snow cover since the maximum HS at Weissfluhjoch did not exceed 5 m. This setup is similar to the ones previously described (Henkel et al, ; Koch et al, ). The GPS sensors were installed on 10 October 2015, and the data are still recorded.…”

“…This effect is mainly due to signal attenuation in wet snow (Koch et al, ). The values presented in the last column of Table result from an RMSE analysis between DD carrier phase residuals and the fitted arcs as described in Henkel et al (), which are also shown in S1 of the supporting information. Accuracy information on the carrier phase residuals is mainly representative for the SWE calculations.…”

“…The baseline vector was derived for snow‐free conditions using RTK positioning, which is, however, using both GPS carrier phase measurements and GPS pseudorange measurements . The baseline determination has to be very accurate, as, for example, an error of 2.5 cm would already cause an error in SWE of 50 mm (Henkel et al, ). Consequently, the anchoring to the ground of the mast for the upper antenna has to be stable to prevent tilting and sinking.…”

“…Thus, an RTK fixed solution is definitely required. Knowing from the snow‐free reference and considering the synchronization correction , it is possible to jointly estimate SWE and the carrier phase ambiguities (Henkel et al, ) with an integer least squares estimator (Teunissen, ). The errors of the phase multipath and the phase noise are unknown but in combination typically less than 2 cm.…”

“…theoretically and practically investigated the behavior of GPS signals of submerged antennas. By exploiting the GNSS carrier phases using low-cost sensors, Henkel et al (2018) derived SWE for 10.1029/2018WR024431…”