REDFIT: estimating red-noise spectra directly from unevenly spaced paleoclimatic time series

Paleoclimatic time series are often unevenly spaced in time, making it difficult to obtain an accurate estimate of their red-noise spectrum. A Fortran 90 program (REDFIT) is presented that overcomes this problem by fitting a first-order autoregressive (AR1) process, being characteristic for many climatic processes, directly to unevenly spaced time series. Hence, interpolation in the time domain and its inevitable bias can be avoided. The program can be used to test if peaks in the spectrum of a time series are significant against the red-noise background from an AR1 process. Generated and paleoclimatic time series are used to demonstrate the capability of the program.

[1]  K. Hasselmann Stochastic climate models Part I. Theory , 1976 .

[2]  Donald B. Percival,et al.  Spectral Analysis for Physical Applications , 1993 .

[3]  Jonathan M. Lees,et al.  Robust estimation of background noise and signal detection in climatic time series , 1996 .

[4]  Manfred Mudelsee,et al.  TAUEST: a computer program for estimating persistence in unevenly spaced weather/climate time series , 2002 .

[5]  P. Robinson,et al.  Estimation of a time series model from unequally spaced data , 1977 .

[6]  P. Imkeller,et al.  Stochastic climate models , 2001 .

[7]  David J. Thomson,et al.  Time series analysis of Holocene climate data , 1990, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[8]  M. Stuiver,et al.  Oxygen 18/16 variability in Greenland snow and ice with 10 -3- to 105-year time resolution , 1997 .

[9]  N. Lomb Least-squares frequency analysis of unequally spaced data , 1976 .

[10]  P. Welch The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms , 1967 .

[11]  J. M. Mitchell,et al.  On the Power Spectrum of “Red Noise” , 1963 .

[12]  J. Scargle Studies in astronomical time series analysis. III - Fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data , 1989 .

[13]  J. Scargle Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data , 1982 .

[14]  Michael Schulz,et al.  Spectrum: spectral analysis of unevenly spaced paleoclimatic time series , 1997 .

[15]  S. Baliunas,et al.  A Prescription for period analysis of unevenly sampled time series , 1986 .