A fast, physically based point snowmelt model for use in distributed applications

A new mathematical solution to the problem of water flow through snow is presented and its implementation in a snowmelt model, SNAP, is discussed. An analytical solution for vertical water flow through homogeneous snow is developed and formulae that allow the solution to accommodate time-varying surface input from rain or snowmelt are derived. This facilitates use of the technique in a computer snowmelt model. Because the new technique requires no matrix computation, it is sufficiently computationally efficient to be a candidate for use in watershed-scale, distributed forecasting systems. Because it is a physically based model that takes into account the effect of the snow itself on the timing and magnitude of outflow, the model allows more accurate prediction of the magnitude and timing of snowmelt than in currently employed operational models. Results of the new model agree well with previous theoretical solutions and with field measurements of melt and rain-on-snow events in a seasonal snow pack.