Wavelet based Hurst exponent and fractal dimensional analysis of Saudi climatic parameters

This paper utilizes wavelets technique to calculate the Hurst exponent, the fractal dimensions and finally the climate predictability indices of daily average time series of air temperature, surface pressure, precipitation, relative humidity and wind speed for nine meteorological stations (Dhahran, Gizan, Jeddah, Yanbu, Abha, Hail, Guryat, Turaif and Riyadh) spread over different parts of Saudi Arabia. The value of Hurst exponent dictates the degree of persistency of a time series on previous values while the fractal dimension provides the information about roughness of the series. The meteorological data (daily means of temperature, pressure, relative humidity and wind speed and daily totals for precipitation) used in this study covers a period of 16 years starting from 1990 till 2005. The Hurst exponents, calculated using wavelet method, were used to find the fractal dimensions for each of the meteorological parameters. Finally, the predictability indices of temperature, pressure, precipitation and wind speed were used to establish the climate predictability indices. The climate predictability indices of precipitation and wind speed time series were found to be independent of the temperature and pressure. The predictability indices of individual parameters were found to have persistence behaviour for the entire data set while anti-persistentence, in most of the cases, for winter and summer data sets.