Bayesian spatiotemporal modelling: An application to glacier satellite imagery

Glaciers hold 1.7% of the Earth's total water supply, but they contain 68.7% of its freshwater. Given the global warming trend, accurate and recent inventory is necessary to assess glacial changes over time. However, frequent cloud and debris cover often make it difficult to determine the glacier's exact edge. Multispectral Landsat 8 imagery along with data from the Global Land Ice Velocity Extraction (GoLIVE) project are combined to to create a Bayesian multivariate general additive model of the glaciers surrounding Mount Rainier, with Autoregressive Moving Average (ARMA) and Gaussian processes used to model the temporal and spatial autocorrelations. Using root mean square error and Watanabe-Akaike information criterion, all 42 combinations of ARMA models up to 4 total parameters and exponential, Matérn 1/2 and spherical covariance kernels were compared. The ARMA(3,1) processes with the exponential Gaussian process kernel was determined to be the best fit model. Gaussian mixture models, hierarchical clustering, hard and soft K-means clustering, and support vector machines are used to classify the posterior distribution. The hard K-means algorithm was the best classifier, and it accurately predicted 85.1% of the glaciers, compared to 68.8% from a univariate classification on the Red/SWIR band ratio.