Amplitude-frequency fluctuations of the seasonal cycle, temperature anomalies, and long-range persistence of climate records

The presence of long-term persistence of climate records on scales from 2 to 15 yr has been reported in the literature, even if the universality of this result is controversial. In the present paper results from monthly temperature records measured for about 250 yr in Prague and Milan are reported. Because of the nonlinear and nonstationary character of temperature time series the seasonal contribution has been identified through the empirical mode decomposition. We find that the seasonal component of the climate records is characterized by some time scales showing both amplitude and phase fluctuations. By using a more suitable definition of temperature anomalies, and thus excluding persistence effects due to seasonal oscillations and trends, the occurrence of long-term persistence has been investigated through the detrended fluctuation analysis. Our results indicate persistence on scales from 3 to 10 yr with similar values for the detrended fluctuation analysis indices.

Figure 1

Time history of temperatures for the Milan data set (upper panel) and the Prague data set (lower panel). Temperatures are given in $°\text{C}$.

Figure 2

Time evolution of the IMFs ${\theta }_j$ for both data sets. Left column refers to the Milan data set, and right column refers to the Prague data set.

Figure 3

Upper panels report the Fourier power spectra of (a) Milan and (b) Prague temperature records. Middle panels report the Fourier spectra of seasonal oscillation given by (c) the EMD mode $j=1$ for Milan and (d) the sum of modes $j=1$ and $j=2$ for Prague. Lower panels represent the Fourier spectra of the temperature anomalies for both (e) Milan and (f) Prague. The numbers over the peaks indicate the corresponding periodicity in months.

Figure 4

Time history of the IMF (a) $j=1$ and (b) $j=2$, for a time period of about 25 yr around an irregular seasonal period for the Prague data set. In the lower panel we report the sum of both modes [(a) and (b), respectively].

Figure 5

Autocorrelation functions of temperature anomalies for Milan (white symbols) and Prague (black symbols) as a function of the lag time.

Figure 6

Autocorrelation functions of temperature anomalies for Milan (white symbols) and Prague (black symbols) as a function of the lag time. Temperature anomalies are defined by excluding subannual fluctuations.

Figure 7

The scaling function $F_2\left(n\right)$ [(a) and (b)] and logarithmic derivative $dy$ [(c) and (d)] as a function of the temporal scale $n$ for both the Milan and Prague data set. Straight lines correspond to linear fits (see the text for details).