Multifractal analysis to study break points in temperature data sets

Since the last century, the air surface temperature has increased at a global scale, showing trends and inhomogeneities that vary from place to place. Many statistical methods can be used to analyze whether or not an inhomogeneity or break point exists in a meteorological data series, and even to detect the time of the break. Sometimes, there is no agreement in the year at which the inhomogeneity occurs detected by different tests. The scale invariance of a process can be studied through its multifractal properties that can be related to the existence of break points in it. In this work, the multifractal properties of monthly temperature data series are used to test what is the right break point year in those situations at which different dates are found by two different tests: the Pettitt and the Standard Normal Homogeneity tests. The comparison of the fractal dimension function D_q and the multifractal spectrum obtained by the box counting method for both the original data sets and for those obtained by splitting the original into two considering the break point years was made. When different multifractal functions and parameters were obtained, a break point was confirmed. Whereas, if equal values appeared, the break point year was discarded. These results let to select the most suitable test to be applied to detect inhomogeneities in a certain data set that will be very useful for climate change studies.