Improving the methodology for spectral analysis of climatic time series

Abstract

The paper discusses a methodology able to estimate both the discrete and continuous spectra without any assumption on the shape of spectral densities. The approach to estimate the spectral density is based on a robust smoothing of the periodogram. Bandwidth, a quantity similar to the width of spectral windows traditionally used in spectral analysis, is estimated locally in contrast to intuitively chosen global window lengths. Detection and estimation of frequencies forming discrete spectra are also addressed. The procedure is applied to Central England temperature (CEt), North Atlantic Oscillation (NAO) index and Oxygen Isotope of North Greenland Ice Core Project (δ18O of NGRIP) data. Annual and half annual cycles were detected in CEt data, whilst 118.2- and 41.7-ky cycles were found in δ18O of NGRIP. This latter periodicity is almost as intense as the dominant longer cycle. Several local peaks of spectral densities were recognised in each time series that mostly cover earlier results. However, a few previous findings at low frequencies have not been reinforced by the present method. Identification of modest local peaks or discrete amplitudes at low frequencies is an extremely challenging task as climatic data generally have spectral densities rising to low frequencies.