A Bayesian spatial assimilation scheme for snow coverage observations in a gridded snow model

A spatial probability distribution of the variables in a parametric snow depletion curve (SDC) is tailored to the assimilation of satellite snow cover data into a gridded hydrological model. The assimilation is based on Bayes’ theorem, in which the proposed distribution represents the a priori information about the SDC variables. From the prior 5 gridded maps of snow storage and accumulated melt depth, the elevation gradients and the degree-day factor are separated out, creating elevation-normalised surfaces of snow storage and degree-day sum. Because the small-scale variability linked to elevation is removed, these surfaces can be described by prior distribution models with a strong spatial dependency structure. This reduction of spatial uniqueness in the 10 prior distribution greatly increases the informational value of the remotely sensed snow coverage data. The assimilation is evaluated in a 2400 km mountainous region in central Norway (61◦N, 9◦ E), based on two Landsat 7 ETM+ images evaluated at 1 km scale. An image acquired on 11 May, a week before the peak flood, removes 78% of the variance 15 in the remaining snow storage. Even an image from 4 May, less than a week after the melt onset, reduces this variance by 53%. Including observed discharge in the updating information improves the 4 May results, but has weak effect on 11 May. Estimated elevation gradients are shown to be sensitive to informational deficits occurring at high altitude, where snowmelt has not yet started. Caution is therefore required when using 20 early images.