For numerous hydrological applications, information on snow water equivalent (SWE) and snow liquid water content (LWC) are fundamental. In situ data are much needed for the validation of model and remote sensing products; however, they are often scarce, invasive, expensive, or labor‐intense. We developed a novel nondestructive approach based on Global Positioning System (GPS) signals to derive SWE, snow height (HS), and LWC simultaneously using one sensor setup only. We installed two low‐cost GPS sensors at the high‐alpine site Weissfluhjoch (Switzerland) and processed data for three entire winter seasons between October 2015 and July 2018. One antenna was mounted on a pole, being permanently snow‐free; the other one was placed on the ground and hence seasonally covered by snow. While SWE can be derived by exploiting GPS carrier phases for dry‐snow conditions, the GPS signals are increasingly delayed and attenuated under wet snow. Therefore, we combined carrier phase and signal strength information, dielectric models, and simple snow densification approaches to jointly derive SWE, HS, and LWC. The agreement with the validation measurements was very good, even for large values of SWE (>1,000 mm) and HS (> 3 m). Regarding SWE, the agreement (root‐mean‐square error (RMSE); coefficient of determination (R2)) for dry snow (41 mm; 0.99) was very high and slightly better than for wet snow (73 mm; 0.93). Regarding HS, the agreement was even better and almost equally good for dry (0.13 m; 0.98) and wet snow (0.14 m; 0.95). The approach presented is suited to establish sensor networks that may improve the spatial and temporal resolution of snow data in remote areas.

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.

This paper provides two methods to improve the reliability of carrier phase integer ambiguity resolution: The first one is a group of multi‐frequency linear combinations that include both code and carrier phase measurements, and allow an arbitrary scaling of the geometry, an arbitrary scaling of the ionospheric delay, and any preferred wavelength. The maximization of the ambiguity discrimination results in combinations with a wavelength of several meters and a noise level of a few centimeters. These combinations could be beneficial for both Real‐Time Kinematics (RTK) and Precise Point Positioning (PPP). The second method incorporates some statistical a priori knowledge of attitude into the actual fixing. The a priori knowledge includes the length and direction of the baseline between two receivers and is given either as a uniform or Gaussian distribution. It enables a substantial reduction of the search space volume but also ensures a large robustness over errors in the a priori information. Both methods improve the accuracy of the float solution, which motivates a simple rounding for ambiguity fixing. A method is described, which enables an efficient computation of its success rate with a few integral transformations. Copyright © 2012 Institute of Navigation.

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Carrier phase measurements of pseudoranges often allow for millimeter precision. The periodic nature of the carrier phase, however, leads to integer ambiguities. These ambiguities need to be resolved for accurate positioning. Blewitt and Teunissen provide two methods for the associated estimation process. The present paper complements their work with an improved real-valued diagonalization of the ambiguity covariance matrix, and a functional determination of an integer decorrelation transformation. The proposed method achieves a similar performance as Teunissen's LAMBDA method-in terms of the probability of wrong fixing, but with a reduced complexity. Furthermore, it shows a slightly different path towards ambiguity resolution.