Modelling the spatial distribution of snow water equivalent at the catchment scale taking into account changes in snow covered area

Abstract. A successful modelling of the snow reservoir is necessary for water resources assessments and the mitigation of spring flood hazards. A good estimate of the spatial probability density function (PDF) of snow water equivalent (SWE) is important for obtaining estimates of the snow reservoir, but also for modelling the changes in snow covered area (SCA), which is crucial for the runoff dynamics in spring. In a previous paper the PDF of SWE was modelled as a sum of temporally correlated gamma distributed variables. This methodology was constrained to estimate the PDF of SWE for snow covered areas only. In order to model the PDF of SWE for a catchment, we need to take into account the change in snow coverage and provide the spatial moments of SWE for both snow covered areas and for the catchment as a whole. The spatial PDF of accumulated SWE is, also in this study, modelled as a sum of correlated gamma distributed variables. After accumulation and melting events the changes in the spatial moments are weighted by changes in SCA. The spatial variance of accumulated SWE is, after both accumulation- and melting events, evaluated by use of the covariance matrix. 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. The negative contributions become dominant only after some time into the melting season so at the onset of the melting season, the spatial variance thus continues to increase, for later to decrease. This behaviour is consistent with observations and called the "hysteretic" effect by some authors. The parameters for the snow distribution model can be estimated from observed historical precipitation data which reduces by one the number of parameters to be calibrated in a hydrological model. 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 HBV model, the hydrological model used for flood forecasting in Norway. When implemented in the HBV model, simulations show that the precision in predicting runoff is maintained although there is one parameter less to calibrate.