Joint Temperature-Precipitation Patterns in the U.S. South Central Region: Multivariate Functional Inference and Gaussian Mixture Modeling

Abstract

Joint variability in temperature and precipitation is central in characterizing seasonal climate structure and associated environmental processes, yet many regional analyses rely on marginal or univariate summaries. We analyze seasonal temperature-precipitation patterns across the Southern United States using two complementary multivariate statistical approaches. First, functional multivariate analysis of variance (FMANOVA) is employed to test the equality of state-level bivariate mean functions, with the permutation-based Wilks' lambda and Pillai's trace statistics. Second, Gaussian mixture models are applied to station-level seasonal summaries to identify latent climate regimes based on the joint distribution of temperature and precipitation. The FMANOVA results indicate statistically significant differences in bivariate mean trajectories between states in both winter and summer, with seasonal contrasts reflecting differing contributions of temperature and precipitation. Clustering analysis indicates more clearly defined and spatially coherent winter regimes than summer regimes, with summer regimes exhibiting greater variability and a stronger role for precipitation.