Modeling the spatial distribution of snow water equivalent, taking into account changes in snow-covered area

Abstract

A good estimate of the spatial probability density function (PDF) of snow water equivalent (SWE) provides the mean of the snow reservoir, but also enables modelling of the changes in snow-covered area (SCA), which is crucial for the runoff dynamics in spring. The spatial PDF of accumulated SWE is here modelled as a sum of correlated gamma-distributed variables, called units. The spatial variance of accumulated SWE is evaluated by the covariance matrix of the units. For accumulation events, there are only positive elements in the covariance matrix, whereas for melting events there are both positive and negative elements. The negative elements dictate that the correlation between melt and SWE is negative. After accumulation and melting events, the changes in the spatial moments are weighted by changes in SCA. Results from the model are in good agreement with observed spatial moments of SWE and SCA and found to provide better estimates of the spatial variability than the current model for snow distribution used in the Norwegian version of the Swedish rainfall–runoff model HBV. The parameters in the distribution model are estimated from observed historical precipitation, so no calibration parameters are introduced.