REDFIT-X: Cross-spectral analysis of unevenly spaced paleoclimate time series

• Cross-spectral analysis of unevenly spaced paleoclimate time series.
• Data properties like uneven spacing and persistence in the data taken into account.
• Introduce a Monte Carlo approach to estimate the uncertainty of phase and coherency.
• Present Fortran 90 program, REDFIT-X where the cross-spectral analysis have been implemented.

Cross-spectral analysis is commonly used in climate research to identify joint variability between two variables and to assess the phase (lead/lag) between them. Here we present a Fortran 90 program (REDFIT-X) that is specially developed to perform cross-spectral analysis of unevenly spaced paleoclimate time series. The data properties of climate time series that are necessary to take into account are for example data spacing (unequal time scales and/or uneven spacing between time points) and the persistence in the data. Lomb–Scargle Fourier transform is used for the cross-spectral analyses between two time series with unequal and/or uneven time scale and the persistence in the data is taken into account when estimating the uncertainty associated with cross-spectral estimates. We use a Monte Carlo approach to estimate the uncertainty associated with coherency and phase. False-alarm level is estimated from empirical distribution of coherency estimates and confidence intervals for the phase angle are formed from the empirical distribution of the phase estimates. The method is validated by comparing the Monte Carlo uncertainty estimates with the traditionally used measures. Examples are given where the method is applied to paleoceanographic time series.