| A method for assimilating remotely sensed snow covered area (SCA) into the
snow subroutine of a grid distributed precipitation-runoff model (PRM) is
presented. The PRM is assumed to simulate the snow state in each grid cell
by a snow depletion curve (SDC), which relates that cell's SCA to its snow
cover mass balance. The assimilation is based on Bayes' theorem, which
requires a joint prior distribution of the SDC variables in all the grid
cells. In this paper we propose a spatial model for this prior distribution,
and include similarities and dependencies among the grid cells. Used to
represent the PRM simulated snow cover state, our joint prior model regards
two elevation gradients and a degree-day factor as global variables, rather
than describing their effect separately for each cell. This transformation
results in smooth normalised surfaces for the two related mass balance
variables, supporting a strong inter-cell dependency in their joint prior
model. The global features and spatial interdependency in the prior model
cause each SCA observation to provide information for many grid cells. The
spatial approach similarly facilitates the utilisation of observed
discharge.
Assimilation of SCA data using the proposed spatial model is evaluated in a
2400 km2 mountainous region in central Norway (61° N, 9° E),
based on two Landsat 7 ETM+ images generalized to 1 km2 resolution. An
image acquired on 11 May, a week before the peak flood, removes
78% of the variance in the remaining snow storage. Even an image from 4 May,
less than a week after the melt onset, reduces this variance by
53%. These results are largely improved compared to a cell-by-cell
independent assimilation routine previously reported. 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 started and the snow coverage is close to unity. Caution is
therefore required when using early images. |