Mechanisms and patterns of snow depth and land surface temperature interactions in arid mountains: coupling coordination and lagged responses across Xinjiang, China

Snow depth (SD) and land surface temperature (LST) interact through energy and mass exchanges that govern meltwater supply in arid mountain regions, yet the strength, quality, and timing of this interaction remain poorly quantified across topographically complex terrain. Here we develop a diagnostic framework that integrates coupling coordination analysis with time-lagged cross-correlation to simultaneously assess, between SD and LST, the intensity of their systemic association (coupling degree, CD), the harmony of their co-evolution (coupling coordination degree, CCD), and the spatiotemporal scales of their lagged response. Applied across the mountain-basin systems of Xinjiang, China, using long-term remote sensing and reanalysis data, the framework reveals three principal findings. First, SD-LST interactions are organized along a hierarchical environmental gradient: broad climatic setting shapes the north–south potential for coupling, while elevation modulates this pattern in southern ranges and local factors shape east–west variations in lagged responses. Second, a systematic decoupling emerges between interaction strength and system coordination – most notably in the southern Tianshan, where high CD coincides with low and declining CCD, suggesting that strong thermal forcing is no longer matched by sustainable snowpack evolution. Third, response lags exhibit distinct regional signatures: long and stable lags (14–22 d) in the snow-rich Altai reflect high thermal inertia; the Tianshan shows a north–south asymmetry with significant spring lag lengthening on the south slope; and the Kunlun displays elevation-threshold behavior, where coordination improves only above ∼3500 m. These lag patterns serve as empirical indicators of snowpack buffering capacity and its regional variation. As a diagnostic tool, the framework provides quantifiable, spatially explicit metrics for evaluating snow thermal schemes in land surface models and identifying climate-vulnerable zones in water-limited mountain regions.