State Space Analysis of Ocean Surface Warming on Decadal Scale

Detection of small decadal-scale variation amidst larger variations on smaller timescales is carried out here by geometrical segregation rather than filtering. Sea surface temperature (SST) annual cycle is represented as a point in a 12-dimensional space and thermal history as a path connecting successive points. Drift of the domain of decadal variations in the state space is taken as a measure of change from one decade to another. Visualization of the path in the 12- dimensional space is achieved by projecting it on planes. A matrix transformation gives an orthogonal decomposition of the annual cycle resembling Fourier series. The specific problem investigated here is the response of the Northern, the Tropical and the Southern Oceanic Regions (NOR, 30°-90°N; TOR, 30°S-30°N; SOR, 90°-30°S) to global warming during 1951-2010. The results are based on the Extended Reconstructed Sea Surface Temperature version 4 (ERSSTv4) database. Several interesting findings are obtained. The decadal scale warming has a seasonal variation, the largest being in the NOR (~0.26°C to ~0.57°C), in 2001-10. The consequential change in the annual cycle is increase in the amplitude of the annual mode in addition to increase in the annual mean. Decade-on-decade SST increase has peaked first in the SOR in 1971-80, and last in the NOR in 2001-10.