  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.
