Eliciting core spatial association from spatial time series: a random matrix approach

Spatial time series (STS) data are fundamental to climate science, yet conventional approaches often conflate temporal co-evolution with genuine spatial dependence, obscuring subtle but critical climatic anomalies. We introduce a Random Matrix Theory (RMT)-based framework to isolate "core spatial association" by suitably trimming out strong but routine temporal signals while preserving spatial signals. Our pipeline introduces Hilbert space filling curve technique and Bergsma's correlation measure of statistical dependence, to climate modelling. Applied to the diurnal temperature range (DTR) data of India (1951-2022), the method reveals distinct spatial anomalies shaped by topography, mesoclimate, and urbanization. The approach uncovers temporal evolution in spatial dependence and demonstrates how regional climate variability is structured by both physical geography and anthropogenic influences. Beyond the Indian application, the framework is broadly applicable to diverse spatio-temporal datasets, offering a robust statistical foundation for predictive modelling, resilience planning, and policy design in the context of accelerating climate change.