Global atmospheric dynamics investigated by using Hilbert Frequency Analysis

El artículo pertenece al número especial: Applications of Information Theory in the GeosciencesThe Hilbert transform is a well-known tool of time series analysis that has been widely used to investigate oscillatory signals that resemble a noisy periodic oscillation, because it allows instantaneous phase and frequency to be estimated, which in turn uncovers interesting properties of the underlying process that generates the signal. Here we use this tool to analyze atmospheric data: we consider daily-averaged Surface Air Temperature (SAT) time series recorded over a regular grid of locations covering the Earth’s surface. From each SAT time series, we calculate the instantaneous frequency time series by considering the Hilbert analytic signal. The properties of the obtained frequency data set are investigated by plotting the map of the average frequency and the map of the standard deviation of the frequency fluctuations. The average frequency map reveals well-defined large-scale structures: in the extra-tropics, the average frequency in general corresponds to the expected one-year period of solar forcing, while in the tropics, a different behaviour is found, with particular regions having a faster average frequency. In the standard deviation map, large-scale structures are also found, which tend to be located over regions of strong annual precipitation. Our results demonstrate that Hilbert analysis of SAT time-series uncovers meaningful information, and is therefore a promising tool for the study of other climatological variables

Hilbert analysis of air temperature dynamics

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 Niño–Southern Oscillation and Rossby waves.La dinámica del sistema climático tiene un papel crucial en la sostenibilidad de la vida en la Tierra, y esto motiva la investigación para comprender y caracterizar nuestro clima y predecir su evolución. En esta tesis nos centramos en la dinámica de la temperatura atmosférica y analizamos series temporales de la temperatura superficial del aire utilizando la transformada de Hilbert. Esto nos permite caracterizar la dinámica de la temperatura con series temporales de amplitud, fase y frecuencia instantáneas. Utilizando estas series como base de nuestro análisis, extraemos información significativa sobre los patrones globales de la dinámica de la temperatura. En primer lugar, calculamos mapas de frecuencia promediada en el tiempo y de su desviación estándar y descubrimos patrones que corresponden a condiciones climáticas bien conocidas: diferentes amplitudes del ciclo anual de temperatura y regiones de alta precipitación. Además, estudiamos la dinámica de frecuencia y fase instantáneas en tres ubicaciones geográficas. Los resultados reflejan las características principales de los diferentes climas, en particular la diferencia entre el clima tropical y el extratropical. Luego, usamos las series temporales de Hilbert para cuantificar los cambios entre décadas en la dinámica de la temperatura (específicamente, en los últimos 35 años). Encontramos grandes cambios de amplitud en el Ártico y en la Amazonia, que se interpretan respectivamente como debidos a la fusión del hielo y a la disminución de precipitación. También descubrimos cambios de frecuencia en el océano Pacífico que sugieren un desplazamiento hacia el norte y un ensanchamiento del patrón de convección atmosférica conocido como zona de convergencia intertropical. En tercer lugar, descubrimos regularidades temporales en las dinámicas de fase. Suavizamos (haciendo un promedio temporal en una ventana móvil) la serie de temperatura, luego aplicamos el análisis de Hilbert y estudiamos cómo el periodo medio de rotación de la fase de Hilbert depende de la longitud de la ventana de promediado. De esta manera, descubrimos diferentes tipos de dinámica atmosférica y clasificamos las regiones geográficas según los resultados de nuestro análisis. Por último, buscamos correlaciones entre las dinámicas de fase, amplitud y frecuencia en diferentes regiones. Analizamos la sincronización de la fase en tres áreas: los extratrópicos del norte, los extratrópicos del sur y los trópicos. Luego, seleccionamos varias ubicaciones geográficas y estudiamos las correlaciones estadísticas con el resto del mundo, utilizando las series temporales de Hilbert. Encontramos que estas correlaciones capturan patrones climáticos a gran escala, como El Niño-Oscilación del Sur y las ondas de Rossby.Postprint (published version

Mapping atmospheric waves and unveiling phase coherent structures in a global surface air temperature reanalysis dataset

In the analysis of empirical signals, detecting correlations that capture genuine interactions between the elements of a complex system is a challenging task with applications across disciplines. Here, we analyze a global dataset of surface air temperature (SAT) with daily resolution. Hilbert analysis is used to obtain phase, instantaneous frequency, and amplitude information of SAT seasonal cycles in different geographical zones. The analysis of the phase dynamics reveals large regions with coherent seasonality. The analysis of the instantaneous frequencies uncovers clean wave patterns formed by alternating regions of negative and positive correlations. In contrast, the analysis of the amplitude dynamics uncovers wave patterns with additional large-scale structures. These structures are interpreted as due to the fact that the amplitude dynamics is affected by processes that act in long and short time scales, while the dynamics of the instantaneous frequency is mainly governed by fast processes. Therefore, Hilbert analysis allows us to disentangle climatic processes and to track planetary atmospheric waves. Our results are relevant for the analysis of complex oscillatory signals because they offer a general strategy for uncovering interactions that act at different time scales. In our “big data” times, extracting useful information from complex signals is an important challenge with applications across disciplines. Due to the presence of multiple time scales, climatological signals are particularly challenging to analyze. Here, we present a technique based on the Hilbert transform (HT) that, when applied to time series of surface air temperature (SAT) (with daily resolution, covering the last 30 years), unveils clear wave patterns that are interpreted as due to Rossby waves (these are atmospheric waves that propagate across our planet and have a major influence on weather). We also show that the patterns uncovered by analyzing anomaly times series include additional structures which likely appear due to climatic phenomena that have long time scales.Postprint (published version

The role of chemistry in the oscillating combustion of hydrocarbons : an experimental and theoretical study

The stable operation of low-temperature combustion processes is an open challenge, due to the presence of undesired deviations from steady-state conditions: among them, oscillatory behaviors have been raising significant interest. In this work, the establishment of limit cycles during the combustion of hydrocarbons in a wellstirred reactor was analyzed to investigate the role of chemistry in such phenomena. An experimental investigation of methane oxidation in dilute conditions was carried out, thus creating quasi-isothermal conditions and decoupling kinetic effects from thermal ones. The transient evolution of the mole fractions of the major species was obtained for different dilution levels (0.0025 <= X-CH4 <= 0.025), inlet temperatures (1080K <= T <= 1190K) and equivalence ratios (0.75 <= Phi <= 1). Rate of production analysis and sensitivity analysis on a fundamental kinetic model allowed to identify the role of the dominating recombination reactions, first driving ignition, then causing extinction. A bifurcation analysis provided further insight in the major role of these reactions for the reactor stability. One-parameter continuation allowed to identify a temperature range where a single, unstable solution exists, and where oscillations were actually observed. Multiple unstable states were identified below the upper branch, where the stable (cold) solution is preferred. The role of recombination reactions in determining the width of the unstable region could be captured, and bifurcation analysis showed that, by decreasing their strength, the unstable range was progressively reduced, up to the full disappearance of oscillations. This affected also the oxidation of heavier hydrocarbons, like ethylene. Finally, less dilute conditions were analyzed using propane as fuel: the coupling with heat exchange resulted in multiple Hopf Bifurcations, with the consequent formation of intermediate, stable regions within the instability range in agreement with the experimental observations

Uncovering temporal regularity in atmospheric dynamics through Hilbert phase analysis

Uncovering meaningful regularities in complex oscillatory signals is a challenging problem with applications across a wide range of disciplines.Here, we present a novel approach, based on the Hilbert transform (HT).We show that temporal periodicity can be uncovered by averagingthe signal in a moving window of appropriated length,t, before applying the HT. As a case study, we investigate global gridded surface airtemperature (SAT) datasets. By analyzing the variation of the mean rotation period,T, of the Hilbert phase as a function oft, we discoverwell-de ned plateaus. In many geographical regions, the plateau corresponds to the expected 1-yr solar cycle; however, in regions where SATdynamics is highly irregular, the plateaus reveal non-trivial periodicities, which can be interpreted in terms of climatic phenomena such asEl Niño. In these regions, we also nd that Fourier analysis is unable to detect the periodicity that emerges whentincreases and graduallywashes out SAT variability. The values ofTobtained for di erentts are then given to a standard machine learning algorithm. The resultsdemonstrate that these features are informative and constitute a new approach for SAT time series classi cation. To support these results, weanalyze the synthetic time series generated with a simple model and con rm that our method extracts information that is fully consistent withour knowledge of the model that generates the data. Remarkably, the variation ofTwithtin the synthetic data is similar to that observed in thereal SAT data. This suggests that our model contains the basic mechanisms underlying the unveiled periodicities. Our results demonstrate thatHilbert analysis combined with temporal averaging is a powerful new tool for discovering hidden temporal regularity in complex oscillatorysignals.Peer ReviewedPostprint (author's final draft