A Statistical Framework for Spatial Boundary Estimation and Change Detection: Application to the Sahel Sahara Climate Transition

TL;DR

This paper introduces a statistical framework combining heteroskedastic Gaussian process regression with a global envelope test to estimate and detect changes in spatial environmental boundaries, demonstrated on the Sahel Sahara climate transition.

Contribution

The framework provides a unified, probabilistic approach for boundary estimation and change detection, addressing uncertainty and noise in environmental data.

Findings

No significant decade-scale boundary changes detected in Sahel Sahara.

Localized boundary shifts identified during 1983-1984 drought years.

Method shows high power in detecting local boundary shifts.

Abstract

Spatial boundaries, such as ecological transitions or climatic regime interfaces, capture steep environmental gradients, and shifts in their structure can signal emerging environmental changes. Quantifying uncertainty in spatial boundary locations and formally testing for temporal shifts remains challenging, especially when boundaries are derived from noisy, gridded environmental data. We present a unified framework that combines heteroskedastic Gaussian process (GP) regression with a scaled Maximum Absolute Difference (MAD) Global Envelope Test (GET) to estimate spatial boundary curves and assess whether they evolve over time. The heteroskedastic GP provides a flexible probabilistic reconstruction of boundary lines, capturing spatially varying mean structure and location specific variability, while the test offers a rigorous hypothesis testing tool for detecting departures from expected boundary behaviors. Simulation studies show that the proposed method achieves the correct size under the null and high power for detecting local boundary shifts. Applying our framework to the Sahel Sahara transition zone, using annual Koppen Trewartha climate classifications from 1960 to 1989, we find no statistically significant decade scale changes in the arid and semi arid or semi arid and non arid interfaces. However, the method successfully identifies localized boundary shifts during the extreme drought years of 1983 and 1984, consistent with climate studies documenting regional anomalies in these interfaces during that period.