We assessed the performance of Kalman Filtering-Smoothing and Expectation Maximization (EM-KF) in gap filling snow-depth sensor data. To this end, hourly snow-depth data from three spatially dense wireless-sensor networks were randomly removed and imputed using EM-KF. Maximum gap size was 40+ hours and differences between artificially removed and gap-filled data larger than 20 cm were removed before computing Root Mean Square Error and Bias. These differences are spurious over- and underestimations that can generally be identified through visual inspection, likely due to instability in the gap-filling process. The expected accuracy of EM-KF in this initial, controlled proof of concept is close to measurement uncertainty (1 to 2 cm for ultrasonic depth sensors). Compared to regressing missing data against nearby sensors, a frequently used strategy in the field, EM-KF tends to yield smaller errors in networks with a comparatively large number of co-located sensors (nine and eight as opposed to four in a third network). In these data-rich networks, maximum differences in daily Root Mean Square Errors between EM-KF and a regression are up to 6 to 8 cm at a daily time scale, with peaks in winter and in particular during snowfalls. EM-KF yields superior results particularly during snowfalls, likely because it exploits the temporal structure and uncertainty in the data through a state-space model. In the third network with fewer co-located sensors, differences in accuracy between EM-KF and a multilinear regression were inconsistent. This implies that the performance of EM-KF benefits from increasing the amount of available information and with increasing dependency of data across nodes. Temporally and spatially dense snow-depth data are being increasingly collected in operational contexts: EM-KF may support supervised filling of gaps in these data – particularly during snowfall events – and thus provide continuous-time information for avalanche or water-resources forecasting in snow-dominated regions. Automatic, unsupervised gap-filling using EM-KF will necessarily need more research to identify reasons of spurious over- and underestimations. Future work should also upscale this proof of concept to operational sensor networks spanning large water basins to bring conclusions closer to real-world applications.
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