References of "Deliège, Adrien"
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See detailApplication of wavelet transforms to geosciences: Extraction of functional and frequential information
Deliège, Adrien ULg

Doctoral thesis (2017)

It is now well-known that there exist functions that are continuous but nowhere differentiable. Still, it appears that some of them are less “irregular” than others. The pointwise regularity of a function ... [more ▼]

It is now well-known that there exist functions that are continuous but nowhere differentiable. Still, it appears that some of them are less “irregular” than others. The pointwise regularity of a function can be characterized by its Hölder exponent at each point. For the sake of practicability, it is more appropriate to determine the “size” of the sets of points sharing a same exponent, through their Hausdorff measure. By doing so, one gets the multifractal spectrum of a function, which characterizes in particular its monofractal or multifractal nature. The first part of this work is based on the so-called “wavelet leaders method” (WLM), recently developed in the context of multifractal analysis, and aims at its application to concrete situations in geosciences. First, we present the WLM and we insist particularly on the major differences between theory and practice in its use and in the interpretation of the results. Then, we show that the WLM turns out to be an efficient tool for the analysis of Mars topography from a unidimensional and bidimensional point of view; the first approach allowing to recover information consistent with previous works, the second being new and highlighting some areas of interest on Mars. Then, we study the regularity of temperature signals related to various climate stations spread across Europe. In a first phase, we show that the WLM allows to detect a strong correlation with pressure anomalies. Then we show that the Hölder exponents obtained are directly linked to the underlying climate and we establish criteria that compare them with their climate characteristics as defined by the Köppen-Geiger classification. On the other hand, the continuous version of the wavelet transform (CWT), developed in the context of time-frequency analysis, is also studied in this work. The objective here is the determination of dominant periods and the extraction of the associated oscillating components that constitute a given signal. The CWT allows, unlike the Fourier transform, to obtain a representation in time and in frequency of the considered signal, which thus opens new research perspectives. Moreover, with a Morlet-like wavelet, a simple reconstruction formula can be used to extract components. Therefore, the second part of the manuscript presents the CWT and focuses mainly on the border effects inherent to this technique. We illustrate the advantages of the zero-padding and introduce an iterative method allowing to alleviate significantly reconstruction errors at the borders of the signals. Then, we study in detail the El Niño Southern Oscillation (ENSO) signal related to temperature anomalies in the Pacific Ocean and responsible for extreme climate events called El Niño (EN) and La Niña (LN). Through the CWT, we distinguish its main periods and we extract its dominant components, which reflect well-known geophysical mechanisms. A meticulous study of these components allows us to elaborate a forecasting algorithm for EN and LN events with lead times larger than one year, which is a much better performance than current models. After, we generalize the method used to extract components by developing a procedure that detects ridges in the CWT. The algorithm, called WIME (Wavelet-Induced Mode Extraction), is illustrated on several highly non-stationary examples. Its ability to recover target components from a given signal is tested and compared with the Empirical Mode Decomposition. It appears that WIME has a better adaptability in various situations. Finally, we show that WIME can be used in real-life cases such as an electrocardiogram and the ENSO signal. [less ▲]

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See detailBelgian speleothem records Holocene cold events?
Allan, Mohammed ULg; Deliège, Adrien ULg; Nicolay, Samuel ULg et al

Poster (2017, May 12)

Speleothem is now regarded as valuable archive of climatic conditions on the continents, offering a number of advantages relative to other continental climate proxy recorders such as lake sediments and ... [more ▼]

Speleothem is now regarded as valuable archive of climatic conditions on the continents, offering a number of advantages relative to other continental climate proxy recorders such as lake sediments and peat cores. High spatial resolution measurements of Mg, Al, Sr, Ba were realized by using laser-ablation inductively coupled plasma mass spectrometry in the Belgian Pere Noel cave. A stalagmite from the Pere Noel (PN) cave representing 12000 years dated by U/Th method. Trace element variations in speleothem are a reflection of hydrochemical conditions. These changes were interpreted as indications of changes in climate in the Han-sur-Lesse region. The similar patterns found in δ 18O, δ 13C and chemical composition along the Pere Noel stalagmite suggests that trace elements in speleothems have the potential to provide high resolution insights into palaeoclimatic variability during the Holocene. A deeper analysis reveals several periods of significant rapid climate change during the Holocene (at 10.7-9.2 ka, 8.2-7.9 ka, 7.2-6.2 ka, 4.8-4.5 ka, and 3-2.4 ka BP), which are similar to the cold events detected from different natural paleoclimate archivers. A comparison between the geochemical analysis of Père Noël speleothem and solar activity (sunspot number) reveals a significant correlation. Spectral analysis methods reveal common solar periodicities (Gleissberg cycle, de Vries cycle, unnamed 500 year, Eddy cycles, and Hallstatt cycle). The geochemical analyses have the potential to prove that PN speleothem is sensitive to changes in solar activity on centennial and millennial timescales during the Holocene. [less ▲]

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See detailHow to extract the oscillating components of a signal? A wavelet-based approach compared to the Empirical Mode Decomposition
Deliège, Adrien ULg

Scientific conference (2017, February 07)

Researchers are often confronted with time series that display pseudo-periodic tendencies with time-varying amplitudes and frequencies. In that framework, a classic Fourier analysis of the data may be of ... [more ▼]

Researchers are often confronted with time series that display pseudo-periodic tendencies with time-varying amplitudes and frequencies. In that framework, a classic Fourier analysis of the data may be of limited interest, especially if the objective is to derive components from the signal that capture the non-stationary behaviour of the oscillating factors. In this talk, we present two powerful tools designed to extract amplitude modulated-frequency modulated (AM-FM) components from a given signal. The first one is the renowned Empirical Mode Decomposition (EMD); we explain the technique, its main benefits, limitations and major practical uses. Then, we introduce the continuous wavelet transform and the equations that justify its relevance in the present context. We propose an algorithm based on the wavelet-induced time-frequency representation of a signal to extract its main components. The performances of this method are compared with the EMD on various AM-FM signals exhibiting different particularities. After briefly broaching the problem of edge effects, we investigate whether the wavelet-based procedure can be used in the domain of time series forecasting. For that purpose, we study the El Nino Southern Oscillation index and develop a model aimed at predicting the long-term trends of the signal. Its predictive skills are tested in several ways and exposed in the final part of the talk. [less ▲]

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See detailAnalysis and indications on long-term forecasting of the Oceanic Niño Index with wavelet-induced components
Deliège, Adrien ULg; Nicolay, Samuel ULg

in Pure and Applied Geophysics (2017), 174(4), 1815-1826

The present paper provides an analysis and a long-term forecasting scheme of the Oceanic Niño Index (ONI) using the continuous wavelet transform. First, it appears that oscillatory components with main ... [more ▼]

The present paper provides an analysis and a long-term forecasting scheme of the Oceanic Niño Index (ONI) using the continuous wavelet transform. First, it appears that oscillatory components with main periods of about 17, 31, 43, 61 and 140 months govern most of the variability of the signal, which is consistent with previous works. Then, this information enables us to derive a simple algorithm to model and forecast ONI. The model is based on the observation that the modes extracted from the signal are generally phased with positive or negative anomalies of ONI (El Niño and La Niña events). Such a feature is exploited to generate locally stationary curves that mimic this behavior and which can be easily extrapolated to form a basic forecast. The wavelet transform is then used again to smooth out the process and finalize the predictions. The skills of the technique described in this paper are assessed through retroactive forecasts of past El Niño and La Niña events and via classic indicators computed as functions of the lead time. The main asset of the proposed model resides in its long-lead prediction skills. Consequently, this approach should prove helpful as a complement to other models for estimating the long-term trends of ONI. [less ▲]

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See detailExtracting oscillating components from nonstationary time series: A wavelet-induced method
Deliège, Adrien ULg

E-print/Working paper (2017)

This paper consists in the description and application of a new method named Wavelet-Induced Mode Extraction (WIME) in the context of time-frequency analysis. WIME aims to extract the oscillating ... [more ▼]

This paper consists in the description and application of a new method named Wavelet-Induced Mode Extraction (WIME) in the context of time-frequency analysis. WIME aims to extract the oscillating components that build amplitude modulated-frequency modulated signals. The essence of this technique relies on the successive extractions of the dominant ridges of wavelet-based timefrequency representations of the signal under consideration. Our tests on simulated examples indicate strong decomposition and reconstruction skills, trouble-free handling of crossing trajectories in the time-frequency plane, sharp performances in frequency detection in the case of mode-mixing problems and a natural tolerance to noise. These results are compared with those obtained with the Empirical Mode Decomposition. We also show that WIME still gives meaningful results with real-life data, namely the Oceanic Niño Index. [less ▲]

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See detailMars Topography Investigated Through the Wavelet Leaders Method: a Multidimensional Study of its Fractal Structure
Deliège, Adrien ULg; Kleyntssens, Thomas ULg; Nicolay, Samuel ULg

in Planetary and Space Science (2017), 136C

This work examines the scaling properties of Mars topography through a wavelet-based formalism. We conduct exhaustive one-dimensional (both longitudinal and latitudinal) and two-dimensional studies based ... [more ▼]

This work examines the scaling properties of Mars topography through a wavelet-based formalism. We conduct exhaustive one-dimensional (both longitudinal and latitudinal) and two-dimensional studies based on Mars Orbiter Laser Altimeter (MOLA) data using the multifractal formalism called Wavelet Leaders Method (WLM). This approach shows that a scale break occurs at approximately 15 km, giving two scaling regimes in both 1D and 2D cases. At small scales, these topographic profiles mostly display a monofractal behavior while a switch to multifractality is observed in several areas at larger scales. The scaling exponents extracted from this framework tend to be greater at small scales. In the 1D context, these observations are in agreement with previous works and thus suggest that the WLM is well-suited for examining scaling properties of topographic fields. Moreover, the 2D analysis is the first such complete study to our knowledge. It gives both a local and global insight on the scaling regimes of the surface of Mars and allows to exhibit the link between the scaling exponents and several famous features of the Martian topography. These results may be used as a solid basis for further investigations of the scaling laws of the Red planet and show that the WLM could be used to perform systematic analyses of the surface roughness of other celestial bodies. [less ▲]

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See detailPoster EGU 2016: Mars Topography Investigated Through the Wavelet Leaders Method
Deliège, Adrien ULg; Kleyntssens, Thomas ULg; Nicolay, Samuel ULg

Poster (2016, April)

This work examines the scaling properties of Mars topography through a wavelet-based formalism. We conduct exhaustive one-dimensional (both longitudinal and latitudinal) and two-dimensional studies based ... [more ▼]

This work examines the scaling properties of Mars topography through a wavelet-based formalism. We conduct exhaustive one-dimensional (both longitudinal and latitudinal) and two-dimensional studies based on Mars Orbiter Laser Altimeter (MOLA) data using the multifractal formalism called Wavelet Leaders Method (WLM). This approach shows that a scale break occurs at approximately 15 km, giving two scaling regimes in both 1D and 2D cases. At small scales, these topographic profiles mostly display a monofractal behavior while a switch to multifractality is observed in several areas at larger scales. The scaling exponents extracted from this framework tend to be greater at small scales. In the 1D context, these observations are in agreement with previous works and thus suggest that the WLM is well-suited for examining scaling properties of topographic fields. Moreover, the 2D analysis is the first such complete study to our knowledge. It gives both a local and global insight on the scaling regimes of the surface of Mars and allows to exhibit the link between the scaling exponents and several famous features of the Martian topography. These results may be used as a solid basis for further investigations of the scaling laws of the Red planet and show that the WLM could be used to perform systematic analyses of the surface roughness of other celestial bodies. [less ▲]

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See detail[Beamer] A New Wavelet-Based Mode Decomposition for Oscillating Signals and Comparison with the Empirical Mode Decomposition
Deliège, Adrien ULg; Nicolay, Samuel ULg

Conference (2016, April)

We introduce a new method based on wavelets (EWMD) for decomposing a signal into quasi-periodic oscillating components with smooth time-varying amplitudes. This method is inspired by both the “classic” ... [more ▼]

We introduce a new method based on wavelets (EWMD) for decomposing a signal into quasi-periodic oscillating components with smooth time-varying amplitudes. This method is inspired by both the “classic” wavelet-based decomposition and the empirical mode decomposition (EMD). We compare the reconstruction skills and the period detection ability of the method with the well-established EMD on toys examples and the ENSO climate index. It appears that the EWMD accurately decomposes and reconstructs a given signal (with the same efficiency as the EMD), it is better at detecting prescribed periods and is less sensitive to noise. This work provides the first version of the EWMD. Even though there is still room for improvement, it turns out that preliminary results are highly promising. [less ▲]

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See detailA New Wavelet-Based Mode Decomposition for Oscillating Signals and Comparison with the Empirical Mode Decomposition
Deliège, Adrien ULg; Nicolay, Samuel ULg

in Information Technology: New Generations (2016, April)

We introduce a new method based on wavelets (EWMD) for decomposing a signal into quasi-periodic oscillating components with smooth time-varying amplitudes. This method is inspired by both the “classic” ... [more ▼]

We introduce a new method based on wavelets (EWMD) for decomposing a signal into quasi-periodic oscillating components with smooth time-varying amplitudes. This method is inspired by both the “classic” wavelet-based decomposition and the empirical mode decomposition (EMD). We compare the reconstruction skills and the period detection ability of the method with the well-established EMD on toys examples and the ENSO climate index. It appears that the EWMD accurately decomposes and reconstructs a given signal (with the same efficiency as the EMD), it is better at detecting prescribed periods and is less sensitive to noise. This work provides the first version of the EWMD. Even though there is still room for improvement, it turns out that preliminary results are highly promising. [less ▲]

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See detailThe Fractal Nature of Mars Topography Analyzed via the Wavelet Leaders Method
Kleyntssens, Thomas ULg; Deliège, Adrien ULg; Nicolay, Samuel ULg

in Information Technology: New Generations (2016, April)

This paper studies the scaling properties of Mars topography based on Mars Orbiter Laser Altimeter (MOLA) data through the wavelet leaders method (WLM). This approach shows a scale break at 15 km. At ... [more ▼]

This paper studies the scaling properties of Mars topography based on Mars Orbiter Laser Altimeter (MOLA) data through the wavelet leaders method (WLM). This approach shows a scale break at 15 km. At small scales, these topographic profiles display a monofractal behavior while a multifractal nature is observed at large scales. The scaling exponents are greater at small scales. They also seem to be influenced by latitude and may indicate a slight anisotropy in topography. [less ▲]

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See detailKöppen–Geiger Climate Classification for Europe Recaptured via the Hölder Regularity of Air Temperature Data
Deliège, Adrien ULg; Nicolay, Samuel ULg

in Pure and Applied Geophysics (2016), 173

In this paper, we make use of the monoHölder nature of surface air temperature data to recapture the Köppen–Geiger climate classification in Europe. Using data from the European climate Assessment and ... [more ▼]

In this paper, we make use of the monoHölder nature of surface air temperature data to recapture the Köppen–Geiger climate classification in Europe. Using data from the European climate Assessment and Dataset (ECA&D), we first show that the Ho ̈lder exponents of surface air temperature data are statistically related to pressure anomalies. Then, we establish a climate classification based on these Hölder exponents in such a way that it allows to recover the Ko ̈ppen–Geiger climate classification. We show that the two classifications match for a vast majority of stations, and we corroborate these observations with a confirmation test. We compare these results with those obtained with another dataset (NCEP-NCAR Reanalysis Project) to show that the new classification is still well-adapted, before eventually discussing these findings. [less ▲]

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See detailThe Fractal Nature of Mars Topography Analyzed via the Wavelet Leaders Method
Kleyntssens, Thomas ULg; Deliège, Adrien ULg; Nicolay, Samuel ULg

Poster (2016)

This work studies the scaling properties of Mars topography based on Mars Orbiter Laser Altimeter (MOLA) data through the wavelet leaders method (WLM). This approach shows a scale break at 15 km. At small ... [more ▼]

This work studies the scaling properties of Mars topography based on Mars Orbiter Laser Altimeter (MOLA) data through the wavelet leaders method (WLM). This approach shows a scale break at 15 km. At small scales, these topographic profiles display a monofractal behavior while a multifractal nature is observed at large scales. The scaling exponents are greater at small scales. They also seem to be influenced by latitude and may indicate a slight anisotropy in topography. [less ▲]

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See detailMa thèse en 180 secondes
Deliège, Adrien ULg

Conference given outside the academic context (2015)

Concours de vulgarisation scientifique "Ma thèse en 180 secondes"

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See detailA wavelet-based mode decomposition compared to the EMD
Deliège, Adrien ULg; Nicolay, Samuel ULg

Poster (2015, September 08)

We introduce a new method based on wavelets for decomposing a signal into quasi-periodic oscillating components with smooth time-varying amplitudes. This method is inspired by both the "classic" wavelet ... [more ▼]

We introduce a new method based on wavelets for decomposing a signal into quasi-periodic oscillating components with smooth time-varying amplitudes. This method is inspired by both the "classic" wavelet-based decomposition and the empirical mode decomposition (EMD). We compare the efficiency of the method with the well-established EMD on toys examples and the ENSO climate index. [less ▲]

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See detailA forecasting method using a wavelet-based mode decomposition and application to the ENSO index
Deliège, Adrien ULg; Nicolay, Samuel ULg; Fettweis, Xavier ULg

Conference (2015, June)

This work consists of a presentation and applications of a forecasting methodology based on a mode decomposition performed through a continuous wavelet transform. The idea is comparable to the Fourier ... [more ▼]

This work consists of a presentation and applications of a forecasting methodology based on a mode decomposition performed through a continuous wavelet transform. The idea is comparable to the Fourier series decomposition but where the amplitudes of the components are not constant anymore: the signal is written as a sum of periodic components with smooth time-varying amplitudes. This leads to a drastic decrease in the number of terms needed to decompose and rebuild the original signal without loss of precision. Once the decomposition is performed, the components are separately extrapolated, which leads to an extrapolation of the reconstructed signal that stands for a forecast of the original one. The quality of the forecast is assessed through a hindcast procedure (running retroactive probing forecasts) and Pearson correlations and root mean square errors are computed as functions of the lead time. This technique is first illustrated in details with a toy example, then with the El Niño Southern Oscillation (ENSO) time series. This signal consists of monthly-sampled sea surface temperature (SST) anomalies in the Eastern Pacific Ocean and is well-known to be one of the most influential climate patterns on the planet, inducing many consequences worldwide (hurricanes, droughts, flooding,…) and affecting human activities. Therefore, short-term predictions are of first importance in order to plan actions before the occurrence of these phenomena. As far as the ENSO time series is concerned, the wavelet-based mode decomposition leads to four components corresponding to periods of about 20, 31, 43 and 61 months respectively and the reconstruction recovers 97% of the El Niño/La Niña events (anomalous warming/cooling of the SST) of the last 65 years. Also, it turns out that more than 78% of these extreme events can be retrieved up to three years in advance. Finally, a forecast of the ENSO index is issued: the next La Niña event should start early in 2018 and should be followed soon after by a strong El Niño event in the second semester of 2019. [less ▲]

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See detailEGU2015 - ENSO forecast using a wavelet-based mode decomposition
Deliège, Adrien ULg; Nicolay, Samuel ULg; Fettweis, Xavier ULg

Conference (2015, April 13)

The aim of this work is to introduce a new method for forecasting major El Niño/ La Niña events with the use of a wavelet-based mode decomposition. These major events are related to sea surface ... [more ▼]

The aim of this work is to introduce a new method for forecasting major El Niño/ La Niña events with the use of a wavelet-based mode decomposition. These major events are related to sea surface temperature anomalies in the tropical Pacific Ocean: anomalous warmings are known as El Niño events, while excessive coolings are referred as La Niña episodes. These climatological phenomena are of primary importance since they are involved in many teleconnections ; predicting them long before they occur is therefore a crucial concern. First, we perform a wavelet transform (WT) of the monthly sampled El Niño Southern Oscillation 3.4 index (from 1950 to present) and compute the associated scale spectrum, which can be seen as the energy carried in the WT as a function of the scale. It can be observed that the spectrum reaches five peaks, corresponding to time scales of about 7, 20, 31, 43 and 61 months respectively. Therefore, the Niño 3.4 signal can be decomposed into five dominant oscillating components with time-varying amplitudes, these latter being given by the modulus of the WT at the associated pseudo-periods. The reconstruction of the index based on these five components is accurate since more than 93% of the El Niño/ La Niña events of the last 60 years are recovered and no major event is erroneously predicted. Then, the components are smoothly extrapolated using polynomials and added together, giving so several years forecasts of the Niño 3.4 index. In order to increase the reliability of the forecasts, we perform several months hindcasts (i.e. retroactive probing forecasts) which can be validated with the existing data. It turns out that most of the major events can be accurately predicted up to three years in advance, which makes our methodology competitive for such forecasts. Finally, we discuss the El Niño conditions currently undergone and give indications about the next La Niña event. [less ▲]

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See detailPar A plus B
Deliège, Adrien ULg; Nicolay, Samuel ULg

Conference given outside the academic context (2015)

Exposé de vulgarisation sur l'état de l'art concernant les ondelettes et ses applications, en particulier l'étude du phénomène El Niño.

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See detailENSO forecast using a wavelet-based mode decomposition
Deliège, Adrien ULg; Nicolay, Samuel ULg; Fettweis, Xavier ULg

Poster (2014, December)

We introduce a new method for forecasting major El Niño/ La Niña events based on a wavelet mode decomposition. This methodology allows us to approximate the ENSO time series with a superposition of three ... [more ▼]

We introduce a new method for forecasting major El Niño/ La Niña events based on a wavelet mode decomposition. This methodology allows us to approximate the ENSO time series with a superposition of three periodic signals corresponding to periods of about 31, 43 and 61 months respectively with time-varying amplitudes. This pseudo-periodic approximation is then extrapolated to give forecasts. While this last one only resolves the large variations in the ENSO time series, three years hindcast as retroactive prediction allows to recover most of the El Niño/ La Niña events of the last 60 years. [less ▲]

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See detailA multifractal analysis of air temperature signals based on the wavelet leaders method
Deliège, Adrien ULg; Nicolay, Samuel ULg

Conference (2014, August 20)

We present the wavelet leaders method (introduced by S. Jaffard) as a tool to study the Hölder regularity of signals, which is closely related to some functional spaces. We use the associated multifractal ... [more ▼]

We present the wavelet leaders method (introduced by S. Jaffard) as a tool to study the Hölder regularity of signals, which is closely related to some functional spaces. We use the associated multifractal formalism to show that surface air temperature signals are monofractal, i.e. these are regularly irregular. Then we use this result to establish a climate classification of weather stations in Europe which matches the Köppen-Geiger climate classification. This result could give rise to new criteria to determine the effectiveness of current climatic models. [less ▲]

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