Spatial Clustering of Curves with Functional Covariates: A Bayesian Partitioning Model with Application to Spectra Radiance in Climate Study

Abstract: In climate change study, the infrared spectral signatures of climate change have recently been conceptually adopted, and widely applied to identifying and attributing atmospheric composition change. We propose a Bayesian hierarchical model for spatial clustering of the high-dimensional functional data based on the effects of functional covariates and local features. We couple the functional mixed-effects model with a generalized spatial partitioning method for: (1) producing spatially contiguous clusters for the high-dimensional spatio-functional data; (2) improving the computational efficiency via parallel computing over subregions or multi-level partitions; and (3) capturing the near-boundary ambiguity and uncertainty for data-driven partitions. We propose a generalized partitioning method which puts less constraints on the shape of spatial clusters. Dimension reduction in the parameter space is also achieved via Bayesian wavelets to alleviate the increasing model complexity introduced by clusters. The model well captures the regional effects of the atmospheric and cloud properties on the spectral radiance measurements. The results elaborate the importance of exploiting spatially contiguous partitions for identifying regional effects and small-scale variability.