Les recherches en milieu lacustre ont généralement porté sur les grands lacs naturels et les barrages. Or les défis scientifiques que présentent les lacs urbains sont nombreux du fait de leur faible profondeur et de leur extension .Le travail que nous présentons ici s'inscrit dans le cadre du projet Petits Lacs Urbains Mesures Modèles Multi-Echelles (PLUMMME), projet financé par la région Île-de-France (programme DIM R2DS).Ce projet a permis l'équipement du lac de Créteil en mesures à haute résolution. Ce sont ces mesures physiques et biologiques qui sont essentiellement exploitées dans cette thèse, parfois en comparaison avec celles du lac du Bourget. La première étape de cette thèse a été ainsi d'enrichir la base de données déjà disponible. Pour cela, nous avons mis en place une station de mesure en continu (capteurs de température, chlorophylle et luminosité, données météorologique telles que vitesse du vent et température atmosphérique), ainsi que deux chaînes de mesures comportant différents capteurs. Des campagnes de mesures spécifiques ont également été réalisées pour l'étude de hydrodynamique à l'aide d'un courantomètre de type Acoustic Doppler Velocimeter (ADV), ainsi qu'un profileur de type Acoustic Doppler Current Profilers (ADCP) à deux points différents du lac (point central et point du rejet d'eaux pluviales). L'analyse des différents champs montre que le lac présente des stratifications avec une période d'une semaine. Nous avons également identifié les modes d'oscillations des ondes internes lorsque ces dernières se produisent sous l'effet du vent. L'analyse spectrale a permis de mettre en évidence une première propriété d'invariance d'échelle des différents champs mesurés. Les différents processus physique (turbulence, stratification, écoulement proche de la paroi) opérant le long de la colonne d'eau ont également été caractérisés. L'analyse spectrale ne permet pas de mettre en évidence le caractère intermittent des fluctuations des champs mesurés, ces dernières peuvent par contre être analysées à l'aide des techniques multifractales. Dans cette thèse nous avons montré que lorsqu'il existe une dépendance entre deux champs, celle ci est multi-échelle. L'utilisation du modèle multifractal universel (UM) a permis de quantifier le degré de cette dépendance. La qualité de l'estimation des paramètres UM dépend fortement de celle de l'invariance d'échelle observée: des séries temporelles présentant des tendances ne respectent pas cette invariance. Les effets de ces dernières sur l'estimation des paramètres UM peuvent être éliminés en utilisant la méthode de décomposition empirique modale dans l'espace physique. L'utilisation des données du champ de vitesse mesuré à l'aide de l'ADCP montre que, les pentes des spectres suivent un profil logarithmique selon la verticale, cela met en évidence que différents processus physiques opèrent le long de la colonne d'eau. Nous montrons également que l'hydrodynamique du lac est fortement perturbée à petite échelle au point du rejet d'eau pluviale. La dernière partie de la thèse examine ce que notre analyse à petites échelles apporte aux modèles numériques. Nous montrons que si les modèles déterministes arrivent à reproduire certains phénomènes à grande échelle, ils sont dans l'incapacité de représenter correctement les fluctuations à petites échelles, donc les processus physiques correspondants. L'analyse multifractale montre que la variabilité des champs physiques présente une forte intermittence. Le fait que la majorité des interactions biologiques/chimiques se produisent à petites échelles souligne la nécessité d'améliorer qualitativement les modèles de fermeture des équations de Navier-Stokes. Enfin, nous montrons que les fonctions de structures, observables statistiques de base en turbulence, ne permettent pas de caractériser de façon unique les champs non conservatifs et donc correspondent à des simulations multifractales non identiques / Research in limnology has generally focused on natural lakes and dams. Moreover, the scientific challenges posed by urban lakes are numerous because of their large width and shallow depth resulting in complex problems that involve. This work is part of the project Petits Lacs Urbains Mesures Modèles Multi-Echelles (PLUMMME), founded by Région Île-de-France (DIM R2DS program). The project provides the high-resolution equipment measuring equipment used at Lake Créteil. Physical and biological measurements are the primary scope of this thesis, with some comparisons of measurements done between Lake Creteil and Lake Bourget. With this in mind, the first step of the thesis was to enhance currently available data. In order to do this we installed a station for the continuous measurement of: temperature, chlorophyll and light, also meteorological quantities such as wind speed, and air temperature were measured. The quantities were measured using two measuring chains comprising different sensors. Measurements were conducted in order to characterise hydrodynamics, using a current meter of type Acoustic Doppler Velocimeter (ADV) and a profiler of type Acoustic Doppler Current Profilers (ADCP) positioned at different points in the lake (centrally, and at the point of stormwater discharge). The analysis of the various measured fields shows that the lake is periodically stratified with a period of one week. We also identify the different modes of the internal waves that occur due to the effects of the wind. Spectral analysis was used to highlight the first scale invariant propriety of the different measured fields. Various physical processes (turbulence, stratification, near-wall flow) operating along the water column were also characterised using this method. The spectral analysis, however, does not provide information about the intermittency of the fluctuations of the measured fields, this can only be done using multifractal techniques. In this thesis, we have shown that when there is a dependence between two fields, the dependence is multiscale. The use of the Universal Multifractal (UM) model, allows one to quantify the degree of this dependence. The quality of the estimation of the UM parameters depends strongly on that of the observed scale: time-series with trends are not scaling. The effects of the latter on the estimation of UM parameters can be improved by the application of the Empirical Modal Decomposition method. The measured velocity data from the ADCP shows that the slope of the power spectra density follow a logarithmic profile along the depth of the lake, it shows that different physical processes operate along the water column. We also show that the hydrodynamics of the lake at small scale are strongly perturbed at the point of waterstorm discharge. The last part of the thesis is focused on what our analysis at small-scales brings to numerical models. We show that, if the deterministic models are able to reproduce some phenomena at large scale, they fail to describe the small-scale variability. the small scale variability and the physical processes involved. A multifractal analysis showed that the small-scale variability of the physical fields displays a strong intermittency, an extremely important feature for biological or chemical reactions and therefore for biological scenarios. Knowing that the majority of biological/chemical interactions occur at smaller scales, this result underlines the necessity to greatly improve the closure of the Navier-Stokes equations. Finally, we show that the structure function, a frequently used statistical tool in turbulence, do not uniquely characterize non-conservative fields, i.e., they do not correspond to identical simulations

Since electric power is one the most important necessities for today’s life and industry, its service reliability must be maintained in an extremely high level. Thunderstorms often reduce this quality of service. Since cloud-to-ground lightning strokes are among the most frequent yet least understood causes of service interruption, predicting the geographical and temporal distribution of the lightning strokes can help power system planners and designers improve the protection of new and existing transmission lines. Such a prediction needs a model that is based on physical properties of the phenomenon and acquired data. This approach requires several stages including modelling, simulation, and characterization. Characterization provides metrics for comparison between the physical and simulated data. The distributions of the lightning stroke densities (aka lightning stroke maps (LSMs)) have patterns that are highly nonlinear, nonstationary, and stochastic. Ordinary analyzes and metrics are insufficient to characterize such patterns. Multiscale analysis of these patterns indicates their self-affinity over multiple scales, which is an indication of their multifractality. Consequently, multifractal analysis methods such as the Rényi fractal dimension spectrum are appropriate candidates for characterization of these density maps. This work uses the lightning stroke data collected by Canadian lightning detection network for Manitoba from 1998 to 2006, employs a multifractal analysis of the lightning stroke maps, and investigates the consistency of such a characterization over time. The results indicate that the LSMs of Manitoba have multifractal distributions, both locally and globally. The results also indicate a convergence in statistical distribution for the LSMs and strong sensitivity of the Rényi spectra to the data variations. For modelling such data, multifractal approaches such as diffusion limited aggregation, percolation, or cellular automata are appropriate candidates. This work provides diffusion limited aggregate modelling and simulation for the maps and compares the physical and simulated lightning stroke maps through Rényi spectra, where the results indicate a high similarity, both visually and analytically. Since lightning strokes are global phenomena, the same methods and techniques can be used for LSMs anywhere in the world. In addition, the utilized methods and approaches for analysis and modelling can be used for similarly complicated phenomena.

Since electric power is one the most important necessities for today’s life and industry, its service reliability must be maintained in an extremely high level. Thunderstorms often reduce this quality of service. Since cloud-to-ground lightning strokes are among the most frequent yet least understood causes of service interruption, predicting the geographical and temporal distribution of the lightning strokes can help power system planners and designers improve the protection of new and existing transmission lines. Such a prediction needs a model that is based on physical properties of the phenomenon and acquired data. This approach requires several stages including modelling, simulation, and characterization. Characterization provides metrics for comparison between the physical and simulated data. The distributions of the lightning stroke densities (aka lightning stroke maps (LSMs)) have patterns that are highly nonlinear, nonstationary, and stochastic. Ordinary analyzes and metrics are insufficient to characterize such patterns. Multiscale analysis of these patterns indicates their self-affinity over multiple scales, which is an indication of their multifractality. Consequently, multifractal analysis methods such as the Rényi fractal dimension spectrum are appropriate candidates for characterization of these density maps. This work uses the lightning stroke data collected by Canadian lightning detection network for Manitoba from 1998 to 2006, employs a multifractal analysis of the lightning stroke maps, and investigates the consistency of such a characterization over time. The results indicate that the LSMs of Manitoba have multifractal distributions, both locally and globally. The results also indicate a convergence in statistical distribution for the LSMs and strong sensitivity of the Rényi spectra to the data variations. For modelling such data, multifractal approaches such as diffusion limited aggregation, percolation, or cellular automata are appropriate candidates. This work provides diffusion limited aggregate modelling and simulation for the maps and compares the physical and simulated lightning stroke maps through Rényi spectra, where the results indicate a high similarity, both visually and analytically. Since lightning strokes are global phenomena, the same methods and techniques can be used for LSMs anywhere in the world. In addition, the utilized methods and approaches for analysis and modelling can be used for similarly complicated phenomena.

The purpose of this dissertation is to introduce a natural and unifying multifractal formalism which contains the above mentioned multifractal parameters, and gives interesting results for a large class of natural measures. In Part 2 we introduce the proposed multifractal formalism and study it properties. We also show that this multifractal formalism gives natural and interesting results when applied to (nonrandom) graph directed self-similar measures in Rd and "cookie-cutter" measures in R. In Part 3 we use the multifractal formalism introduced in Part 2 to give a detailed discussion of the multifractal structure of random (and hence, as a special case, non-random) graph directed self-similar measures in R^d.

In this thesis we propose an automated process for the removal of non-precipitation echoes present in weather radar signals and accurate detection of rainfall. The process employs multifractal analysis using directional Gabor wavelets for accurate detection of the rain events. An optoelectronic joint transform correlator is proposed to provide ultra fast processing and wavelet analysis. Computer simulations of the proposed system show that the proposed algorithm is successful in the detecting rainfall accurately in radar images. The accuracy of the algorithms proposed are compared to accurate results that were generated under expert supervision. Results of the proposed system are also compared to results of QC algorithm for the ground validation software (GVS) used by TRMM ground validity Project and a previous QC algorithm. Several statistical measures computed for different reflectivity ranges show that the proposed algorithm gives accuracy as high as 98.95%, which exceed the 97.46% maximum accuracy for the GVS results. Also, the minimum error rate obtained by the proposed algorithm for different dB ranges decreases to 1.09% whereas the GVS results show a minimum error rate of 1.80%. The rain rate accumulation confirms the success of the proposed algorithm in the accurate removal of nonprecipitation echoes and a higher precision in rain accumulation estimates.

Multifractals have during the past 20 − 25 years been the focus of enormous attention in the mathematical literature. Loosely speaking there are two main ingredients in multifractal analysis: the multifractal spectra and the Renyi dimensions. One of the main goals in multifractal analysis is to understand these two ingredients and their relationship with each other. Motivated by the powerful techniques provided by the use of the Artin-Mazur zeta-functions in number theory and the use of the Ruelle zeta-functions in dynamical systems, Lapidus and collaborators (see books by Lapidus & van Frankenhuysen [32, 33] and the references therein) have introduced and pioneered use of zeta-functions in fractal geometry. Inspired by this development, within the past 7−8 years several authors have paralleled this development by introducing zeta-functions into multifractal geometry. Our result inspired by this work will be given in section 2.2.2. There we introduce geometric multifractal zeta-functions providing precise information of very general classes of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic Birkhoff averages of continuous functions. Results in that section are based on paper [37]. Dynamical zeta-functions have been introduced and developed by Ruelle [63, 64] and others, (see, for example, the surveys and books [3, 54, 55] and the references therein). It has been a major challenge to introduce and develop a natural and meaningful theory of dynamical multifractal zeta-functions paralleling existing theory of dynamical zeta functions. In particular, in the setting of self-conformal constructions, Olsen [49] introduced a family of dynamical multifractal zeta-functions designed to provide precise information of very general classes of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic Birkhoff averages of continuous functions. However, recently it has been recognised that while self-conformal constructions provide a useful and important framework for studying fractal and multifractal geometry, the more general notion of graph-directed self-conformal constructions provide a substantially more flexible and useful framework, see, for example, [36] for an elaboration of this. In recognition of this viewpoint, in section 2.3.11 we provide main definitions of the multifractal pressure and the multifractal dynamical zeta-functions and we state our main results. This section is based on paper [38]. Setting we are working unifies various different multifractal spectra including fine multifractal spectra of self-conformal measures or Birkhoff averages of continuous function. It was introduced by Olsen in [43]. In section 2.1 we propose answer to problem of defining Renyi spectra in more general settings and provide slight improvement of result regrading multifractal spectra in the case of Subshift of finite type.

The usefulness of watershed hydrological process models is considerably increased when they can be extrapolated across spatial and temporal scales. This scale transfer problem, meaning the description and prediction of characteristics and processes at a scale different from the one at which observations and measurements are made, and has become the subject of much current research in hydrology and other areas. Quantitative description of fractal scaling behavior of runoff and stream network morphometry in agricultural watersheds has not been previously reported. In the present study, fractal and multifractal scaling of daily runoff rate in four experimental agricultural watersheds and their associated sub-watersheds (32 in total) were investigated. The time series of daily runoff rate were obtained from the database (comprising about 16,600 station years of rainfall and runoff data for small agricultural watersheds across the U.S.) developed by the Hydrological and Remote Sensing Laboratory, Agricultural Research Service, US Department of Agriculture (HRSL/ARS/USDA). Fractal scaling patterns of the Digital Elevation Model (DEM)-extracted stream network morphometry for these four watersheds were also examined. The morphometry of stream networks of four watersheds were obtained by Geographic Information System (GIS) manipulation of digital elevation data downloaded from the most recent (July 2004) U.S. Geological Survey (USGS) National Elevation Dataset (NED). Several threshold values of contribution area for stream initiation were used to extract stream networks for each of the four watersheds. The principal measures of fractal scaling determined for the runoff series were the Hurst exponent obtained by rescaled range (R/S) analysis, the fractal dimension estimated by the shifted box-counting method, and the multifractal scaling function parameters (a and C1) of the Universal Multifractal Model (UMM). Corresponding measures for the DEM-extracted stream networks at each threshold value were the fractal dimension estimated using the box-counting technique and the Horton ratios of the network. Daily runoff rate exhibited strong long-term dependence and scale invariance over certain time scales. The same fractal dimensions and Hurst exponents were obtained for the sub-watersheds within each watershed. Runoff exhibited multifractal behavior that was well described by UMM. The multifractal parameters a (quantifies how far the process is from monofractality) and C1 (characterizes the sparseness or inhomogeneity of the mean of the process) were reasonably close to each other for sub-watersheds within a watershed and were generally similar among four watersheds. For the DEM-extracted networks, the morphometric attributes and Horton ratios as well as their fractal dimensions were dependent on the threshold values of contribution area used in the extraction process. The fractal dimensions were almost identical for DEM-extracted stream networks of the four watersheds. The DEM-extracted stream network displayed a single scaling pattern, rather than multifractal behavior. Explanation of the physical significance of fractal characteristics of the stream network in relation to runoff time series would require more data than were available in this study. / Ph. D.

Este trabalho apresenta uma nova abordagem para fusão de vídeo e som diretamente no espaço de atributos visando otimizar a identificação do comportamento de insetos. Foi utilizado o detector de Harris para rastreamento dos insetos, assim como a técnica inovadora Wavelet-Multifractal para análise de som. No caso da Wavelet-Multifractal, foram testadas várias Wavelet-mães, sendo a Morlet a melhor escolha para sons de insetos. Foi proposto a Wavelet Módulo Máximo para extrair atributos multifractais dos sons para serem utilizados no reconhecimento de padrões de comportamento de insetos. A abordagem Wrapper de mineração de dados foi usada para selecionar os atributos relevantes. Foi constatado que a abordagem Wavelet-multifractal identifica melhor os sons, particularmente no caso de distorções provocadas por ruídos. As imagens foram responsáveis pela identificação de acasalamento e os sons pelos outros comportamentos. Foi também proposto um novo método do triângulo como representação simplificada do espectro multifractal visando simplificação do processamento. / This work presents an innovative video and sound fusion approach by feature subset selection under the space of attributes to optimally identify insects behavior. Harris detector was used for insect movement tracking and an innovative technique of Multifractal-Wavelet was used to analyze the insect sounds. In the case of Multifractal-Wavelet, more than one mother-wavelet was tested, being the Morlet wavelet the best choice of mother-wavelet for insect sounds. The wavelet modulus maxima was proposed to extract multifractal sound attributes to be used in pattern recognition of an insect behavior. The wrapper data mining approach was used to select relevant attributes. It has been found that, in general, wavelet-multifractal based schemes perform better for sound, particularly in terms of minimizing noise distortion influence. The image features only determine the mating and the sound other behaviors. A new triangle representation of multifractal spectrum was proposed as a processing simplification.

Este trabalho apresenta uma nova abordagem para fusão de vídeo e som diretamente no espaço de atributos visando otimizar a identificação do comportamento de insetos. Foi utilizado o detector de Harris para rastreamento dos insetos, assim como a técnica inovadora Wavelet-Multifractal para análise de som. No caso da Wavelet-Multifractal, foram testadas várias Wavelet-mães, sendo a Morlet a melhor escolha para sons de insetos. Foi proposto a Wavelet Módulo Máximo para extrair atributos multifractais dos sons para serem utilizados no reconhecimento de padrões de comportamento de insetos. A abordagem Wrapper de mineração de dados foi usada para selecionar os atributos relevantes. Foi constatado que a abordagem Wavelet-multifractal identifica melhor os sons, particularmente no caso de distorções provocadas por ruídos. As imagens foram responsáveis pela identificação de acasalamento e os sons pelos outros comportamentos. Foi também proposto um novo método do triângulo como representação simplificada do espectro multifractal visando simplificação do processamento. / This work presents an innovative video and sound fusion approach by feature subset selection under the space of attributes to optimally identify insects behavior. Harris detector was used for insect movement tracking and an innovative technique of Multifractal-Wavelet was used to analyze the insect sounds. In the case of Multifractal-Wavelet, more than one mother-wavelet was tested, being the Morlet wavelet the best choice of mother-wavelet for insect sounds. The wavelet modulus maxima was proposed to extract multifractal sound attributes to be used in pattern recognition of an insect behavior. The wrapper data mining approach was used to select relevant attributes. It has been found that, in general, wavelet-multifractal based schemes perform better for sound, particularly in terms of minimizing noise distortion influence. The image features only determine the mating and the sound other behaviors. A new triangle representation of multifractal spectrum was proposed as a processing simplification.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2014-11-06T17:22:37Z No. of bitstreams: 2 Dissertacao - Bruno Henrique Pereira Gonçalves - 2013.pdf: 2765842 bytes, checksum: 73031d592b28fd2dc03d6bbdfa04cc34 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Erika Demachki (erikademachki@gmail.com) on 2014-11-06T17:22:46Z (GMT) No. of bitstreams: 2 Dissertacao - Bruno Henrique Pereira Gonçalves - 2013.pdf: 2765842 bytes, checksum: 73031d592b28fd2dc03d6bbdfa04cc34 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2014-11-06T17:22:46Z (GMT). No. of bitstreams: 2 Dissertacao - Bruno Henrique Pereira Gonçalves - 2013.pdf: 2765842 bytes, checksum: 73031d592b28fd2dc03d6bbdfa04cc34 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2013-12-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This paper proposes adaptive resource allocation in multiuser wireless networks based on OFDM. Two allocation schemes are proposed: for TDMA networks and LTE networks. The resource allocation schemes that provide QoS are developed from the union of OFDM wireless networks, the proposal of adaptive modeling of traffic flows and the proposal of adaptive estimation of effective bandwidth. The performances of the proposed schemes are verified through simulation. Concepts and studies on traffic modeling, multifractal traffic modeling, theory of effective bandwidth, OFDM, are addressed in order to support the understanding and development of the proposed schemes. An algorithm for adaptive parameter estimation of the multifractal model bMWM is proposed, and studies to estimate the effective bandwidth are presented. Some methods of estimating effective bandwidth are proposed using traffic flow models. / Este trabalho propõe esquemas de alocação adaptativa de recursos em redes sem fio multiusuário OFDM. Dois esquemas de alocação são propostos: para redes TDMA e para redes LTE. Os esquemas de alocação de recursos foram elaborados a partir da união de tecnologia de redes sem fio OFDM, proposta de modelagem adaptativa de fluxos de tráfego e proposta de estimação adaptativa de banda efetiva, de maneira a garantir requisitos de QoS em redesmultiusuário. Simulações são realizadas para validar o desempenho dos esquemas de alocação propostos. Conceitos e estudos sobre modelagem de tráfego, modelagem de tráfego multifractal, teoria de banda efetiva e OFDM são tratados de maneira a subsidiar o entendimento e a elaboração dos esquemas propostos. É proposto um algoritmo para estimação adaptativa de parâmetros do modelo multifractal bMWM, e são apresentados estudos realizados para estimação de banda efetiva. Alguns métodos de estimação de banda efetiva são propostos utilizando modelos de fluxo de tráfego.