Inverse hydrological modeling to infer historical snow mass based on streamflow records

Mapping the dynamics of snow water equivalent (SWE) is critical for understanding the hydrology of mountain regions. While methods to reconstruct SWE exist, they usually rely on either remote sensing data or the presence of in-situ observations. Streamflow observations can be considered an indirect and delayed observation of catchment-wide SWE, but despite their broad spatial and temporal availability, their potential for SWE reconstructions has not been explored so far. In this study, we investigate how much SWE information can be extracted from the streamflow record, both in terms of its total mass as well as its spatial distribution. To this end, we set up an inverse streamflow-based SWE reconstruction framework that can operate without remote sensing data or in-situ snow observations. As a basis, we use a distributed hydrological model with a temperature-index snow model at 1km resolution, which generates SWE reconstructions from a set of prior snow and climate parameters and translates them into streamflow. By using the streamflow observations to optimize these parameters, we obtain SWE reconstructions that better match the streamflow. However, there is likely a multitude of SWE reconstructions that all lead to the same streamflow, which is defined as an ill-posed inverse problem. In order to find out by how much the streamflow can constrain the prior SWE reconstructions, we perform an experiment with synthetic observations. Using synthetic observations instead of real observations eliminates both model and observation errors, allowing us to focus solely on the nature of this ill-posed problem. Firstly, we select a set of soil, snow and climate parameters to generate synthetic SWE observations and their corresponding streamflow. All parameters are kept constant over the entire period except the parameter controlling the snowfall bias correction, which is set to fluctuate on a yearly basis and consequently also needs to be optimized for each year separately. Then, we run a single calibration to attempt to rederive these parameters and reconstruct the synthetic observations. Finally, we analyze our posterior ensemble of parameter sets and SWE reconstructions and quantify the resemblance to the synthetic streamflow and SWE observations. We expect to find a near-perfect match with the synthetic streamflow observations, a strong constraint of the total catchment-wide SWE but a weak constraint of the spatial distribution of this SWE.