This paper investigates the asymptotic behavior of structural break tests in the harmonic domain for time-dependent spherical random fields. In particular, we prove a Functional Central Limit Theorem result for the fluctuations over time of the sample spherical harmonic coefficients, under the null of isotropy and stationarity; furthermore, we prove consistency of the corresponding CUSUM test, under a broad range of alternatives. Our results are then applied to NCEP data on global temperature: our estimates suggest that Climate Change does not simply affect global average temperatures, but also the nature of spatial fluctuations at different scales.

翻译：本文研究了时间相关球面随机场在调和域中结构断点检验的渐近行为。具体而言，在各向同性与平稳性的原假设下，我们证明了样本球谐系数随时间波动的泛函中心极限定理；进一步，我们在广泛的备择假设下证明了相应CUSUM检验的一致性。随后，我们将结果应用于NCEP全球温度数据：估计结果表明，气候变化不仅影响全球平均温度，还改变了不同尺度空间波动的性质。