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.

翻译：空间边界，如生态过渡带或气候状态界面，捕捉了陡峭的环境梯度，其结构变化可能预示着环境变化的出现。量化空间边界位置的不确定性并对其时间变化进行正式检验仍具挑战性，尤其是当边界源自含噪声的网格化环境数据时。本文提出一个统一框架，将异方差高斯过程回归与尺度化最大绝对差异全局包络检验相结合，用于估计空间边界曲线并评估其是否随时间演变。异方差高斯过程为边界线提供了灵活的概率重构，能够捕捉空间变化的均值结构和位置特异性变异，而该检验则为检测边界行为偏离预期提供了严格的假设检验工具。模拟研究表明，所提方法在零假设下具有正确的检验水平，并在检测局部边界变化时表现出较高的检验功效。将该框架应用于萨赫勒-撒哈拉过渡带，使用1960年至1989年的年度柯本-特雷瓦撒气候分类数据，我们发现干旱与半干旱或半干旱与非干旱界面在十年尺度上未出现统计显著的变化。然而，该方法成功识别出1983年和1984年极端干旱年份的局部边界偏移，这与记录该时期这些界面区域异常的气候研究结果一致。