Assessing Vegetation–Hydrothermal Trend Regimes Across Elevation Gradients in Semiarid Mountains via Gaussian Mixture Models in Saudi Arabia

Vegetation–hydrothermal trend patterns in semiarid mountains are inherently multidimensional across altitudinal gradients, requiring probabilistic frameworks to characterize overlapping vegetation–hydrothermal trend patterns. We develop a Gaussian mixture model (GMM)-based framework to classify vegetation trend regimes from multidimensional trend variables and to characterize their climate–regime associations across elevation gradients in the semiarid Al Baha region, Saudi Arabia. Landsat time-series data (2014–2025) were used to derive trends in the Normalized Difference Vegetation Index (NDVI), normalized difference water index (NDWI), and land surface temperature (LST) using the Mann–Kendall test. These standardized trend variables were integrated within a probabilistic GMM framework, with candidate models evaluated using Bayesian information criterion (BIC), Integrated Completed Likelihood (ICL), classification entropy, resampling-based partition stability, and held-out predictive performance. Although BIC favored the eight-component VVV model, the six-component solution was retained as a balanced intermediate-complexity representation based on partition reproducibility, near-optimal predictive performance, classification ambiguity, and parsimony. The results reveal a pronounced elevation-dependent reorganization of vegetation–hydrothermal trends, characterized by High Relative LST Trend dominance at low elevations (~44%), Mixed Trend State at mid elevations (~40.8%), and Low Relative NDWI Trend at higher elevations (>48%), with High Relative LST Trend becoming negligible at the highest altitudes. This spatial organization showed a moderate association with elevation (Cramér’s V = 0.299; χ2 = 74,265.54, p < 0.001), with statistical significance interpreted cautiously given the large, spatially autocorrelated sample. Climate–regime analysis further reveals that precipitation variability exhibits the strongest association at mid elevations, whereas temperature shows stronger associations at both low- and high-elevation extremes. Cross-sensor comparison with VIIRS showed substantial classification consistency after class-label alignment (overall agreement ≈ 0.76; κ ≈ 0.64). These findings demonstrate systematic variation in vegetation–hydrothermal trend regimes and their climate associations along elevation gradients. The proposed GMM-based framework provides a scalable and uncertainty-aware approach for assessing climate–vegetation associations in semiarid mountain systems and other data-scarce dryland environments.