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, including deterministic trend, abrupt change, and a nontrivial power alternative. 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：本文研究了时变球面随机场在调和域中结构突变检验的渐近性质。特别地，在原假设为各向同性与平稳性的条件下，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结果；此外，在包括确定性趋势、突变以及非平凡功效备择假设在内的广泛备择假设下，我们证明了相应CUSUM检验的一致性。随后，我们将研究结果应用于NCEP全球温度数据：我们的估计表明，气候变化不仅影响全球平均温度，还会改变不同尺度下空间波动的本质特性。