Probabilistic estimation of glacier surface elevation changes from DEM differentiation: a Bayesian method for outlier filtering, gap filling and uncertainty estimation with examples from High Mountain Asia

Various interdisciplinary studies have shown substantial discrepancies between modeled and remotely sensed glacier surface elevation change.It is therefore crucial to better understand and quantify uncertainties associated to both methods. We design a probabilistic framework with the aim to filter outliers, fill data voids and estimate uncertainties in glacier surface elevation changes computed from Digital Elevation Model (DEM) differentiation. The technique is based on a Bayesian formulation of the DEM difference problem and specifically targets surging and debris-covered glaciers, both at glacier and regional scales. We first define a set of physically admissible surface elevation changes as an elevation-dependent probability density function.

In a second step, terrain roughness is defined as the main descriptor for DEM uncertainty. Each surface elevation change pixel is a probability distribution. We present validation experiments in High Mountain Asia and show that the model produces results consistent with conventional DEM differencing, while avoiding the caveats of already existing methods. We further demonstrate that accounting for unstable glacier dynamics is crucial for accurate outlier filtering and robust uncertainty estimation. The technique can be applied to other types of remotely sensed glacier quantities (surface velocity etc.) and would provide more reliable characterization of uncertainty associated with changes in glacier mass and dynamics.