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Gap-filling snow-depth time-series with Kalman Filtering-Smoothing and Expectation Maximization: Proof of concept using spatially dense wireless-sensor-network data
Cold Regions Science and Technology ( IF 3.8 ) Pub Date : 2020-07-01 , DOI: 10.1016/j.coldregions.2020.103066
Francesco Avanzi , Zeshi Zheng , Adam Coogan , Robert Rice , Ram Akella , Martha H. Conklin

Abstract 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.

中文翻译:

使用卡尔曼滤波平滑和期望最大化的间隙填充雪深时间序列:使用空间密集无线传感器网络数据的概念证明

摘要 我们评估了卡尔曼滤波平滑和期望最大化 (EM-KF) 在间隙填充雪深传感器数据中的性能。为此,使用 EM-KF 随机删除和估算来自三个空间密集无线传感器网络的每小时雪深数据。最大间隙大小为 40 多个小时,并且在计算均方根误差和偏差之前删除了人工删除和大于 20 厘米的间隙填充数据之间的差异。这些差异是虚假的高估和低估,通常可以通过目视检查来识别,可能是由于间隙填充过程的不稳定性。在此初始受控概念验证中,EM-KF 的预期精度接近测量不确定度(超声波深度传感器为 1 至 2 厘米)。与针对附近传感器回归缺失数据相比,作为该领域常用的策略,EM-KF 往往在具有相对大量协同定位传感器(九个和八个,而不是第三个网络中的四个)的网络中产生较小的误差。在这些数据丰富的网络中,EM-KF 和回归之间的每日均方根误差的最大差异在每日时间尺度上高达 6 到 8 厘米,峰值出现在冬季,尤其是在降雪期间。EM-KF 尤其在降雪期间产生了出色的结果,这可能是因为它通过状态空间模型利用了数据中的时间结构和不确定性。在具有较少同位传感器的第三个网络中,EM-KF 和多元线性回归之间的准确性差异不一致。这意味着 EM-KF 的性能受益于增加可用信息量和增加跨节点数据的依赖性。在操作环境中越来越多地收集时间和空间上密集的雪深数据:EM-KF 可以支持这些数据中的空白的监督填充——特别是在降雪事件期间——从而为雪中的雪崩或水资源预测提供连续时间信息- 主导的地区。使用 EM-KF 自动、无监督地填补空白必然需要更多的研究来确定虚假高估和低估的原因。未来的工作还应该将这种概念验证升级到跨越大型水流域的可操作传感器网络,从而得出更接近现实世界应用的结论。在操作环境中越来越多地收集时间和空间上密集的雪深数据:EM-KF 可以支持这些数据中的空白的监督填充——特别是在降雪事件期间——从而为雪中的雪崩或水资源预测提供连续时间信息- 主导的地区。使用 EM-KF 自动、无监督地填补空白必然需要更多的研究来确定虚假高估和低估的原因。未来的工作还应该将这种概念验证升级到跨越大型水流域的可操作传感器网络,从而得出更接近现实世界应用的结论。在操作环境中越来越多地收集时间和空间上密集的雪深数据:EM-KF 可以支持这些数据中的空白的监督填充——特别是在降雪事件期间——从而为雪中的雪崩或水资源预测提供连续时间信息- 主导的地区。使用 EM-KF 自动、无监督地填补空白必然需要更多的研究来确定虚假高估和低估的原因。未来的工作还应该将这种概念验证升级到跨越大型水流域的可操作传感器网络,从而得出更接近现实世界应用的结论。EM-KF 可以支持对这些数据中的空白进行有监督的填充——尤其是在降雪事件期间——从而为以雪为主的地区的雪崩或水资源预测提供连续时间信息。使用 EM-KF 自动、无监督地填补空白必然需要更多的研究来确定虚假高估和低估的原因。未来的工作还应该将这种概念验证升级到跨越大型水流域的可操作传感器网络,从而得出更接近现实世界应用的结论。EM-KF 可以支持对这些数据中的空白进行有监督的填充——尤其是在降雪事件期间——从而为以雪为主的地区的雪崩或水资源预测提供连续时间信息。使用 EM-KF 自动、无监督地填补空白必然需要更多的研究来确定虚假高估和低估的原因。未来的工作还应该将这种概念验证升级到跨越大型水流域的可操作传感器网络,从而得出更接近现实世界应用的结论。
更新日期:2020-07-01
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