Probabilistic Principal Component Analysis Guided Spatial Partitioning of Multivariate Ocean Biogeochemistry Data

Abstract

Farm-scale cultivation of macroalgae for the production of renewable biofuel depends on complex ocean hydrodynamics and also on the availability of different essential nutrients. To better understand such conditions that are conducive for the growth of macroalgae, scientists implement large-scale computational models, simulating several physical variables (essential nutrients, and other chemical compounds), relevant to study oceanic biogeochemistry (BGC). Visualizing and analysing the different physical variables and their inter-variable relationships across the spatial domain is crucial to form concrete understanding of the underlying physical phenomenon. To facilitate such multivariate analyses for large-scale simulation data, a popular and effective way is to decompose the spatial domain into smaller local regions based on the variable relationships. However, spatial decomposition of multivariate data is not trivial. In this paper, we propose a novel multivariate spatial data partitioning approach using probabilistic principal component analysis. We also perform detailed study of other prospective multivariate partitioning schemes and compare them with our proposed method. To demonstrate the efficacy of our approach, we studied nutrient relationships across different regions of the ocean using a high-resolution Ocean BCG simulation data set, which comprises of multiple physical variables essential for macroalgae cultivation. We further validate the results of our analyses by getting feedback from domain experts in the field of ocean sciences.