Multifractal detrended moving average analysis of global temperature records

TL;DR

This study applies multifractal detrended moving average analysis to global temperature records from 1850 to 2012, revealing multifractal structures mainly due to long-range correlations and some influence from fat-tail distributions.

Contribution

It demonstrates the effectiveness of MFDMA in analyzing climate data and compares its results with multifractal detrended analysis, highlighting the role of long-range correlations in temperature anomalies.

Findings

Multifractal structure is confirmed in global temperature anomalies.

Long-range temporal correlations are the main source of multifractality.

Results depend on the detrending window location.

Abstract

Multifractal structure of global monthly mean temperature anomaly time series over the period of 1850-2012 are studied in terms of the multifractal detrended moving average (MFDMA) analysis. We try to address the possible source(s) and the nature of multifractality in the time series data by comparing the results derived from the actual series with those from a set of shuffled and surrogate series. It is seen that the MFDMA method predicts a multifractal structure of the temperature anomaly records that is more or less similar to what was obtained from the multifractal detrended analysis for the same set of data. In our analysis the major contribution of multifractality in the data is found to be due to the long-range temporal correlation among the measurements, however the contribution of a fat-tail distribution function of the variables is not negligible. The existence of long-range correlation is also confirmed by the constancy of the local slopes of the fluctuation function over a sufficient scale intervals. The results of the moving average analysis are found to depend upon the location of the detrending window and tend to the observations of the multifractal detrended analysis for a specific choice of the location of the detrending window.