Spectral Unmixing of Antarctic Snow Grain Size Distribution: A Data-Driven Perspective

The microstructure of snow grains is the result of both thermodynamic and mechanical processes that can produce a variety of grain size mixtures. Spectral unmixing methods applied to remote sensing imagery aim to decompose multispectral retrievals into spectral signatures from different endmembers that relate to surface microstructure and, in particular, optical grain size of surface snow crystals. Although ice-sheet surface grain size is typically modeled based on remote sensing imagery analysis as unimodal grain size ranging from 10 m up to 1 cm, the spatial scale of the observations (100s of m to 1s of kms) suggests such methods are inherently capturing a distribution of grain sizes. In this work we estimate a nonparametric probabilistic distribution of optical grain sizes of an ice-sheet surface from the MODIS Aqua/Terra multispectral imagery dataset using an endmember library of different grain size signatures. Our method can also resolve different sources of contamination, like clouds and shadows, and provides error estimates associated with our retrievals. To accomplish this task, we use optimization methods from the regreg software in Python, which offers flexibility for including various forms of regularization constraints. We take advantage of this to develop a sparse regression model that extracts a finite set of prominent grain sizes. In comparison with standard approaches, our method has the advantage of dealing with the more realistic and flexible assumption of multiple grain-size contributions. The use of Dask for parallel computing and xArray for data management offers scalability for the analysis of multidecadal, ice-sheet-wide datasets. These distributions of grain size can then be incorporated into surface microstructure studies to better understand surface mass balance processes, such as snow accumulation, wind redistribution, and firn densification.