Monte-Carlo SSA Analysis of the NAO Index

Resumen

Singular Spectral Analysis (SSA) is a tool for time series analysis whose purpose is to identify temporal patterns that explain a high proportion of the total variance of the series. The test Monte Carlo-SSA is used in two different situations: (i) in a simple hypothetical noise model, where the data consist of white or red noise; and (ii) in a composite hypothetical noise model, assuming some deterministic components, such as trends or annual cycles, already found in the data. In this case, it is necessary to examine whether or not the remainder components can be attributed to noise. Following this strategy, we have applied different SSA algorithms to two annual series of winter annual NAO index, proposed by Jones et al. (1997) and Hurrell (1995). We also have compared these two indices with a shorter third NAO index proposed by Barnston and Livezey (1987), obtained by a PCA of SLP data. SSA does not provide any estimation in the frequency domain, thus we have carried out a Fourier analysis to accurately determine oscillations present in the series. Then, we have computed the significance levels using a Monte Carlo method, and we have reconstructed the set of the significant components, RCs. The statistically significant results found for both series are very similar: a non-linear trend and periodicities around 7.8, 2.4, 2.2 and 5.8 years. For the Gibraltar series the periodicities of 2.9 and 4.5 years are also found. The RCs series fit quite well the both series, particularly the last part of the records.