"Hilbert analysis of air temperature dynamics de Dario Zappalà el dia 4/4/2019

The dynamics of the climate system plays a crucial role in the sustainability of life on Earth, and this motivates research to understand and characterise our climate and predict its evolution. In this thesis we focus on the dynamics of atmospheric temperature and analyse time series of surface air temperature using the Hilbert transform. This allows us to characterise the dynamics of temperature with time series of instantaneous amplitude, phase and frequency. Using these series as the basis of our analysis, we extract meaningful information about global patterns of temperature dynamics. Firstly, we calculate maps of time-averaged frequency and of its standard deviation and uncover patterns that correspond to well-known climatic conditions: different amplitudes of the annual temperature cycle and regions of high precipitation. In addition, we study the dynamics of instantaneous frequency and phase in three geographical sites. The results reflect the main features of different climates, in particular the difference between the tropical and the extratropical climate. Then, we use the Hilbert time series to quantify inter-decadal changes in temperature dynamics (specifically, in the last 35 years). We find high changes of amplitude in the Arctic and in Amazonia, which are interpreted respectively as due to ice melting and precipitation decrease. We also uncover frequency changes in the Pacific Ocean that suggest a shift towards north and a widening of the atmospheric convection pattern known as the intertropical convergence zone. Thirdly, we uncover temporal regularities in phase dynamics. We smooth (by doing a temporal average on a moving window) the temperature series, then we apply the Hilbert analysis and study how the mean rotation period of the Hilbert phase depends on the length of the averaging window. In this way, we discover different types of atmospheric dynamics and classify geographical regions according to the results of our analysis. Finally, we analyse correlations between the phase, amplitude and frequency dynamics in different regions. We analyse phase synchronisation in three areas: the northern extratropics, the southern extratropics and the tropics. Then, we select several geographical sites and study the statistical correlations with the rest of the world, using the different Hilbert time series. We find that these correlations capture large-scale climatic patterns, such as El NinoSouthern Oscillation and Rossby waves.