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 Dq 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.

Multifractal analysis of validated wind speed time series.

Multifractal properties of 30 min wind data series recorded at six locations in Cadiz (Southern Spain) have been studied in this work with the aim of obtaining detailed information for a range of time scales. Wind speed records have been validated, applying various quality control tests as a pre-requisite before their use, improving the reliability of the results due to the identification of incorrect values which have been discarded in the analysis. The scaling of the wind speed moments has been analysed and empirical moments scaling exponent functions K(q) have been obtained. Although the same critical moment (qcrit) has been obtained for all the places, some differences appear in other multifractal parameters like γmax and the value of K(0). These differences have been related to the presence of extreme events and zero data values in the data series analysed, respectively.