Multifractal analysis of oceanic chlorophyll maps remotely sensed from space

International audiencePhytoplankton patchiness has been investigated with multifractal analysis techniques. We analyzed oceanic chlorophyll maps, measured by the SeaWiFS orbiting sensor, which are considered to be good proxies for phytoplankton. Multifractal properties are observed, from the sub-mesoscale up to the mesoscale, and are found to be consistent with the Corssin-Obukhov scale law of passive scalars. This result indicates that, within this scale range, turbulent mixing would be the dominant effect leading to the observed variability of phytoplankton fields. Finally, it is shown that multifractal patchiness can be responsible for significant biases in the nonlinear source and sink terms involved in biogeochemical numerical models

Nanocellulose/bioactive glass cryogels as scaffolds for bone regeneration

A major challenge exists in the preparation of scaffolds for bone regeneration, namely, achieving simultaneously bioactivity, biocompatibility, mechanical performance and simple manufacturing. Here, cellulose nanofibrils (CNF) are introduced for the preparation of scaffolds taking advantage of their biocompatibility and ability to form strong 3D porous networks from aqueous suspensions. CNF are made bioactive for bone formation through a simple and scalable strategy that achieves highly interconnected 3D networks. The resultant materials optimally combine morphological and mechanical features and facilitate hydroxyapatite formation while releasing essential ions for in vivo bone repair. The porosity and roughness of the scaffolds favor several cell functions while the ions act in the expression of genes associated with cell differentiation. Ion release is found critical to enhance the production of the bone morphogenetic protein 2 (BMP-2) from cells within the fractured area, thus accelerating the in vivo bone repair. Systemic biocompatibility indicates no negative effects on vital organs such as the liver and kidneys. The results pave the way towards a facile preparation of advanced, high performance CNF-based scaffolds for bone tissue engineering

Multifractal and multiscale entropy scaling of in-situ soil moisture time series: Study of SMOSMANIA network data, southwestern France

Soil moisture processes exhibit a strong variability in space and time due to the variability of the meteorological forcing and the spatial heterogeneity of soil properties. This study aims at providing a statistical description of soil moisture variability by analyzing data from nine in situ stations located over an West-East gradient in southwestern France (SMOSMANIA stations, distributed over an area of about 300 x 200 km). For each station, four time series of soil moisture observed at four different depths ranging from 5 cm to 30 cm are analyzed. First, possible scaling properties are investigated within the Fourier domain with the help of spectral analysis tools. Red noise-like (1/f(2)) scaling properties could be noticed over a fairly wide scale range (1000 h-1 h) with relatively homogeneous scaling parameters for 5 cm depth soil moistures regardless of the station. These properties are confirmed at other depths with slightly steeper spectra and more heterogeneity across stations. In a second step, multifractal analysis has been carried out on the same data. Multifractal scaling is observed over a narrower scaling range (128 h-1 h). Moment scaling functions can be parameterized within the framework of Universal Multifractals: typical parameters are C-1 approximate to 0.25 and alpha approximate to 1.6-1.8 for surface data while both parameters are subject to strong changes (C-1 increases and a decreases) as the depth increases. In a third step, Multiscale Entropy (MSE) analysis has been applied in order to analyze the dataset from an information theory point of view and to infer whether multifractal properties could have a signature on MSE estimates. The MSE function has been found to follow a power law of the aggregation time with a scaling exponent close to 0.3-0.4 for surface data. These exponents were generally close to the Hurst exponent H estimated by first-order structure functions. While it is already known that MSE should follow scaling properties in the case of monofractal signals, the results suggest that the latter property holds for natural multifractal processes. Finally, complementary numerical tests based on synthetic multifractal time series are done in order to assess the relationship between the MSE scaling exponent H' and multifractal parameters C-1, alpha and H. A dependency on the three multifractal parameters has been observed, yet in practice the approximation H' approximate to H seems somewhat acceptable for processes with relatively large Hurst exponents and/or low multifractal intermittency (C-1). On a more broad perspective, the existence of relationships between multifractal scaling and MSE properties could help to refine the physical interpretation of observed scaling properties in many geophysical processes

Modélisation de la variabilité spatiale et temporelle des précipitations à la sub-mésoéchelle par une approche multifractale

Rainfall is characterized by an extreme variability over a wide range of space- and timescales. Underlying nonlinear phenomena produce strong and localized extremes that are poorly represented in current meteorological models. There is a need of stochastic representations that could reproduce rainfall statistics whatever the scale. Multifractal cascades, initially introduced in statistical physics of turbulence, are possible candidates. In this work, the "Universal Multifractal" model (Schertzer & Lovejoy, 1987) is considered. This model enables multiscale statistical characterization of a field by the means of three fundamental ("universal") parameters. Multifractal analysis tools have been applied to rainfall datasets representative of submesoscale variability, especially to weather radar measurements and to high-resolution disrometer time series. "Scaling ranges", i.e. ranges of scales dominated by multifractal symmetries are identified and associated with specific estimated universal parameters. It is shown that analysis algorithms applied conditionnally in the interior of the rain events provide results that differ significantly from those reported in scientific literature. By the means of theoretical calculations and of simulations, it is demonstrated that classical multifractal analysis algorithms are very sensitive to the proportion of zeros, which is obviously problematic in the case of rainfall. A new methodology of analysis has been proposed, based on the computation of weighted statistics that overweight nonzero values. Consistent parameters that are not affected by zeros are estimated and the obtained values suggest that rainfall and passive scalars share some statistical scaling symmetries at scales sufficiently large so that turbulent advection dominates inertial effects. Finally, it is shown how the existence of multifractal properties may impact applications. In particular, a universal multifractal downscaling algorithm has been defined. This algorithm exploits scaling symmetries associated with universal parameters in order to simulate a statistically consistent and realistic variability at scales inaccessible to observation or simulation. For instance, this algorithm could be used to build hourly rainfall time series from daily ones, or even to increase the resolution of observed precipitation maps, leading to possible hydrological applications.Les précipitations sont caractérisées par une variabilité extrême sur une large gamme d'échelles spatiales et temporelles. Elles résultent de phénomènes non linéaires qui produisent des extrêmes violents et localisés difficiles à représenter dans les modèles météorologiques. Il est alors souhaitable de pouvoir disposer de représentations stochastiques susceptibles de reproduire les propriétés statistiques des précipitations aux différentes échelles. Une famille de candidats possibles est constituée par les cascades multifractales, initialement introduites en mécanique statistique de la turbulence. Dans ce travail, nous considérons le modèle des " multifractales universelles " (Schertzer & Lovejoy, 1987), qui permet de caractériser les propriétés statistiques d'un champ d'un point de vue multi-échelle au moyen de trois paramètres fondamentaux (" universels "). Nous avons appliqué des outils d'analyse multifractale à des jeux de données de précipitations représentatifs de la variabilité à la sub-mésoéchelle, notamment à des cartes radar de pluie et à des séries chronologiques à très haute résolution temporelle. Cette étude a permis d'identifier les gammes d' " invariance d'échelle " dans lesquelles des symétries multifractales prédominent, et d'estimer les trois paramètres universels. Nous montrons aussi que l'application des algorithmes d'analyse à l'intérieur des événements de pluie fournit des résultats sensiblement différents de ceux généralement publiés. On a pu démontrer, par des calculs théoriques et au moyen de simulations, que les algorithmes classiques d'analyse multifractale sont très sensibles à la proportion de zéros dans les champs, ce qui est évidemment problématique pour la pluie. Une méthode d'analyse pondérée par le support d'occurrence de pluie des données a été proposée pour corriger les biais. Les valeurs des paramètres universels corrigés semblent indiquer que la pluie et les scalaires passifs présentent certaines symétries d'échelles communes aux échelles suffisamment grandes pour que l'advection turbulente domine les effets inertiels. Enfin, on montre que l'existence de propriétés multifractales présente un grand intérêt au niveau des applications. Notamment, un algorithme de downscaling multifractal universel a été défini. Cet algorithme exploite les symétries caractérisées par les paramètres universels pour générer une variabilité statistiquement réaliste à des échelles plus fines qu'une échelle d'observation donnée. Potentiellement, cet algorithme pourrait être utilisé pour générer des séries de précipitations de résolution horaire à partir de données journalières, ou pour augmenter la résolution de cartes de précipitations, ce qui peut donner lieu à des applications en hydrologie

Relation d’échelle de la loi Z-R : quelle conséquence pour l’observation radar ?

International audienceL'estimation de l'intensité des précipitations à partir des mesures radar repose en grande partie surla relation Z-R (Z = aRb) reliant la réflectivité radar Z à l’intensité de pluie R. Les paramètres a et b decette relation sont dépendants de la distribution de taille de gouttes de pluie (DSD Drop SizeDistribution). En pratique, le volume sondé à l’intérieur d’une porte radar est rarement homogène,cela est d’autant plus vrai que la porte considérée est éloignée du radar, c’est-à-dire lorsqu’onobserve avec une échelle de plus en plus grossière. La non linéarité de la relation Z-R implique unproblème concernant la stabilité des paramètres a et b en fonction de l’échelle d’observation. Laprésentation se focalisera sur l’étude du comportement statistique de la relation Z-R en fonction del’échelle d’observation d’un point de vue théoriques et empiriques.Compte tenu des propriétés multifractales des précipitations on montre que la pré-facteur « a » de larelation Z-R dépend de l’échelle d’observation alors que l’exposant b n’en dépend pas. L’étudeprésentée s’appuie sur des observations de granulométrie obtenues par un disdromètre pour deséchelles de temps comprises entre 15 s et 64 minutes. Ces observations permettent d’estimer à lafois la réflectivité radar et l’intensité de pluie à différentes échelles et ainsi étudier la dépendancedes paramètres a et b à diverses échelles d’observation. On montre de façon empirique qu’il apparaitclairement une relation d’échelle du pré-facteur a qui croit suivant une loi puissance en fonction del’échelle d’observation alors que l’exposant b reste relativement stable. Ce comportement estcorroboré par la théorie.Cette dépendance à l’échelle pourrait dans certain cas être la cause de surestimation de l’intensitéde pluie, notamment dans le cas de pluies convectives. Des corrections possibles sont suggérées etdiscutées

Theoretical and empirical scale dependency of Z-R relationships: Evidence, impacts, and correction

International audienceEstimation of rainfall intensities from radar measurements relies to a large extent on power-laws relationships between rain rates R and radar reflectivities Z, i.e., Z = a*R^b. These relationships are generally applied unawarely of the scale, which is questionable since the nonlinearity of these relations could lead to undesirable discrepancies when combined with scale aggregation. Since the parameters (a,b) are expectedly related with drop size distribution (DSD) properties, they are often derived at disdrometer scale, not at radar scale, which could lead to errors at the latter. We propose to investigate the statistical behavior of Z-R relationships across scales both on theoretical and empirical sides. Theoretically, it is shown that claimed multifractal properties of rainfall processes could constrain the parameters (a,b) such that the exponent b would be scale independent but the prefactor a would be growing as a (slow) power law of time or space scale. In the empirical part (which may be read independently of theoretical considerations), high-resolution disdrometer (Dual-Beam Spectropluviometer) data of rain rates and reflectivity factors are considered at various integration times comprised in the range 15 s - 64 min. A variety of regression techniques is applied on Z-R scatterplots at all these time scales, establishing empirical evidence of a behavior coherent with theoretical considerations: a grows as a 0.1 power law of scale while b decreases more slightly. The properties of a are suggested to be closely linked to inhomogeneities in the DSDs since extensions of Z-R relationships involving (here, strongly nonconstant) normalization parameters of the DSDs seem to be more robust across scales. The scale dependence of simple Z = a*R^b relationships is advocated to be a possible source of overestimation of rainfall intensities or accumulations. Several ways for correcting such scaling biases (which can reach >15-20% in terms of relative error) are suggested. Such corrections could be useful in some practical cases where Z-R scale biases are significant, which is especially expected for convective rainfall

Scaling and stochastic cascade properties of NEMO oceanic simulations and their potential value for GCM evaluation and downscaling

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Multiscale description of Sentinel-2/MAJA products: a spectral and structure function approach

International audienceSentinel-2 surface reflectances exhibit a strong spatial variability that is due to both natural variability and strong anthropogenic effects. From an image processing view point, Sentinel-2 products maybe seen as images that embed a hierarchy of spatial structures of different sizes and of different energy levels. Many remote-sensing images of natural variables show a fractal structure that can be evidenced by various geometrical and statistical tools. Thus, it is tempting to check if Sentinel-2 images exhibit such scaling features.The objective of this study is to test the existence of scaling properties in Sentinel-2/MAJA products based on two main tools: 2D Fourier power spectra and first order structure functions