Solving Richards Equation for snow improves snowpack meltwater runoff estimations in detailed multi-layer snowpack model

The runoff from a snow cover during spring snowmelt or rain-on-snow events is an important factor in the hydrological cycle. In this study, three water balance schemes for the 1 dimensional physically-based snowpack model SNOWPACK are compared to lysimeter measurements at two alpine sites with a seasonal snow cover, but with different climatological conditions: Weissfluhjoch (WFJ) and Col de Porte (CDP). The studied period consists of 14 and 17 yr, respectively. The schemes include a simple bucket-type approach, an approximation of Richards Equation (RE), and the full RE. The results show that daily sums of snowpack runoff are strongly related to a positive energy balance of the snow cover and therefore, all water balance schemes show very similar performance in terms of Nash-Sutcliffe efficiency (NSE) coefficients (around 0.63 and 0.72 for WFJ and CDP, respectively) and r(2) values (around 0.83 and 0.72 for WFJ and CDP, respectively). An analysis of the runoff dynamics over the season showed that the bucket-type and approximated RE scheme release meltwater slower than in the measurements, whereas RE provides a better agreement. Overall, solving RE for the snow cover yields the best agreement between modelled and measured snowpack runoff, but differences between the schemes are small. On sub-daily time scales, the water balance schemes behave very differently. In that case, solving RE provides the highest agreement between modelled and measured snowpack runoff in terms of NSE coefficient (around 0.48 at both sites). At WFJ, the other water balance schemes loose most predictive power, whereas at CDP, the bucket-type scheme has an NSE coefficient of 0.39. The shallower and less stratified snowpack at CDP likely reduces the differences between the water balance schemes. Accordingly, it can be concluded that solving RE for the snow cover improves several aspects of modelling snow cover runoff, especially for deep, sub-freezing snow covers and in particular on the sub-daily time scales. The additional computational cost was found to be in the order of a factor of 1.5-2