Snow water equivalents exclusively from snow depths and their temporal changes: the Δsnow model

Reliable historical manual measurements of snow depths are available for many years, sometimes decades, across the globe, and increasingly snow depth data are also available from automatic stations and remote sensing platforms. In contrast, records of snow water equivalent (SWE) are sparse, which is significant as SWE is commonly the most important snowpack feature for hydrology, climatology, agriculture, natural hazards, and other fields. Existing methods of modeling SWE either rely on detailed meteorological forcing being available or are not intended to simulate individual SWE values, such as seasonal “peak SWE”. Here we present a new semiempirical multilayer model, Δsnow, for simulating SWE and bulk snow density solely from a regular time series of snow depths. The model, which is freely available as an R package, treats snow compaction following the rules of Newtonian viscosity, considers errors in measured snow depth, and treats overburden loads due to new snow as additional unsteady compaction; if snow is melted, the water mass is stepwise distributed from top to bottom in the snowpack. Seven model parameters are subject to calibration. Snow observations of 67 winters from 14 stations, well-distributed over different altitudes and climatic regions of the Alps, are used to find an optimal parameter setting. Data from another 71 independent winters from 15 stations are used for validation. Results are very promising: median bias and root mean square error for SWE are only −3.0 and 30.8 kg m−2, and +0.3 and 36.3 kg m−2 for peak SWE, respectively. This is a major advance compared to snow models relying on empirical regressions, and even sophisticated thermodynamic snow models do not necessarily perform better. As such, the new model offers a means to derive robust SWE estimates from historical snow depth data and, with some modification, to generate distributed SWE from remotely sensed estimates of spatial snow depth distribution