Evaluating methods for reconstructing large gaps in historic snow depth time series

Abstract

Abstract. Historic measurements are often temporally incomplete and may contain longer periods of missing data, whereas climatological analyses require continuous measurement records. This is also valid for historic manual snow depth (HS) measurement time series, for which even whole winters can be missing in a station record, and suitable methods have to be found to reconstruct the missing data. Daily in situ HS data from 126 nivo-meteorological stations in Switzerland in an altitudinal range of 230 to 2536 m above sea level are used to compare six different methods for reconstructing long gaps in manual HS time series by performing a “leave-one-winter-out” cross-validation in 21 winters at 33 evaluation stations. Synthetic gaps of one winter length are filled with bias-corrected data from the best-correlated neighboring station (BSC), inverse distance-weighted (IDW) spatial interpolation, a weighted normal ratio (WNR) method, elastic net (ENET) regression, random forest (RF) regression and a temperature index snow model (SM). Methods that use neighboring station data are tested in two station networks with different density. The ENET, RF, SM and WNR methods are able to reconstruct missing data with a coefficient of determination (r2) above 0.8 regardless of the two station networks used. The median root mean square error (RMSE) in the filled winters is below 5 cm for all methods. The two annual climate indicators, average snow depth in a winter (HSavg) and maximum snow depth in a winter (HSmax), can be reproduced by ENET, RF, SM and WNR well, with r2 above 0.85 in both station networks. For the inter-station approaches, scores for the number of snow days with HS>1 cm (dHS1) are clearly weaker and, except for BCS, positively biased with RMSE of 18–33 d. SM reveals the best performance with r2 of 0.93 and RMSE of 15 d for dHS1. Snow depth seems to be a relatively good-natured parameter when it comes to gap filling of HS data with neighboring stations in a climatological use case. However, when station networks get sparse and if the focus is set on dHS1, temperature index snow models can serve as a suitable alternative to classic inter-station gap filling approaches.