Antonio Turiel

Numerical methods for the estimation of multifractal singularity spectra on sampled data

Physical variables in scale invariant systems often show chaotic, turbulent-like behavior, commonly associated to the existence of an underlying fractal or multifractal structure. However, the assessment of multifractality over experimental, discretized data requires of appropriate methods and to establish criteria to measure the confidence degree on the estimates. In this paper we have evaluated the quality of different techniques used for multifractal analysis. We have tested four different techniques: the moment (M) method, the wavelet transform modulus maxima (WTMM) method, the gradient modulus wavelet projection (GMWP) method and the gradient histogram (GH) method, which are used to estimate the singularity spectra of multifractal signals. The test consists in analyzing synthetic multifractal 1D signals with given multifractal spectrum. We have compared the results, studying the sensibility of each method to the length of the series, size of the ensemble and type of spectrum. Our results show that GMWP method is the one attaining the best performance, providing reliable estimates which can be improved when the statistics is increased. All the other methods are affected by problems such as the linearization of the right tail of the spectrum, and some of them are very demanding in data.

SMOS first data analysis for sea surface salinity determination

Soil Moisture and Ocean Salinity (SMOS), launched on 2 November 2009, is the first satellite mission addressing sea surface salinity (SSS) measurement from space. Its unique payload is the Microwave Imaging Radiometer using Aperture Synthesis (MIRAS), a new two-dimensional interferometer designed by the European Space Agency (ESA) and operating at the L-band frequency. This article presents a summary of SSS retrieval from SMOS observations and shows initial results obtained one year after launch. These results are encouraging, but also indicate that further improvements at various data processing levels are needed and hence are currently under investigation.

Self-Similarity Properties of Natural Images Resemble Those of Turbulent Flows

We show that the statistics of an edge type variable in natural images exhibits self-similarity properties which resemble those of local energy dissipation in turbulent flows. Our results show that selfsimilarity and extended self-similarity hold remarkably for the statistics of the local edge variance, and that the very same models can be used to predict all of the associated exponents. These results suggest using natural images as a laboratory for testing more elaborate scaling models of interest for the statistical description of turbulent flows. The properties we have exhibited are relevant for the modeling of the early visual system: They should be included in models designed for the prediction of receptive fields. [S0031-9007(97)05190-9]

Microcanonical multifractal formalism—a geometrical approach to multifractal systems: Part I. Singularity analysis

Multifractal formalism in the microcanonical framework has proved to be a valuable approach to understand and analyze complex signals, typically associated with natural phenomena in scale invariant systems. In this paper, we discuss the multifractal microcanonical formalism in a comprehensive, unified way, including new theoretical proofs and validation tests on real signals, so completing some known gaps in the foundations of this theory. We also review the latest advances and describe the present perspectives in this field. Some technical details on the implementation of involved algorithms and relevant open issues are also discussed.

How reliable are finite-size Lyapunov exponents for the assessment of ocean dynamics?

Abstract Much of atmospheric and oceanic transport is associated with coherent structures. Lagrangian methods are emerging as optimal tools for their identification and analysis. An important Lagrangian technique which is starting to be widely used in oceanography is that of finite-size Lyapunov exponents (FSLEs). Despite this growing relevance there are still many open questions concerning the reliability of the FSLEs in order to analyse the ocean dynamics. In particular, it is still unclear how robust they are when confronted with real data. In this paper we analyze the effect on this Lagrangian technique of the two most important effects when facing real data, namely noise and dynamics of unsolved scales. Our results, using as a benchmark data from a primitive numerical model of the Mediterranean Sea, show that even when some dynamics is missed the FSLEs results still give an accurate picture of the oceanic transport properties.

Multifractal geometry in stock market time series

It has been recently noticed that time series of returns in stock markets are of multifractal (multiscaling) character. In that context, multifractality has been always evidenced by its statistical signature (i.e., the scaling exponents associated to a related variable). However, a direct geometrical framework, much more revealing about the underlying dynamics, is possible. In this paper, we present the techniques allowing the multifractal decomposition. We will show that there exists a particular fractal component, the most singular manifold (MSM), which contains the relevant information about the dynamics of the series: it is possible to reconstruct the series (at a given precision) from the MSM. We analyze the dynamics of the MSM, which shows revealing features about the evolution of this type of series.

Microcanonical multifractal formalism: Application to the estimation of ocean surface velocities

In this paper we investigate the validity of the multifractal formalism to study sea surface temperature (SST). It is shown that SST patterns observed in moderate resolution SST images have anomalous scaling properties characteristic of a multifractal structure. The most probable origin of the observed structures is the turbulent character of the oceanic flow as they evolve slowly and are very persistent in times compatible with ocean mesoscale dynamics (several days). The spectrum of singularity exponents indicates that the dynamics of the processes leading to the geometrical arrangement of the SST patterns is quite general over the available range of scales. As a consequence, multifractal techniques can be used to extract properties of the underlying flow. In particular, the geometry of the SST multifractal components is closely linked with the ocean flow, which allows to build a reasonable guess of the streamfunction (defined as the maximum singular streamfunction (MSS)) from a single SST image. Thus the ocean surface velocity field can be easily inferred, with some limitations. As multifractal analysis is in essence a geometrical approach, the method is able to retrieve a high resolution velocity field, well localized in space, but with some indetermination on the modulus and sense of velocity vectors. To solve this, a general framework for the integration of extra information is proposed, what is illustrated with an example merging MSS with altimetric data.

Rain Effects on ASCAT-Retrieved Winds: Toward an Improved Quality Control

The quality of the Ku-band scatterometer-derived winds is known to be degraded by the presence of rain. Little work has been done in characterizing the impact of rain on C-band scatterometer winds, such as those from the Advanced Scatterometer (ASCAT) onboard Metop-A. In this paper, the rain impact on the ASCAT operational level 2 quality control (QC) and retrieved winds is investigated using the European Centre for Medium-range Weather Forecasts (ECMWF) model winds, the Tropical Rainfall Measuring Missions (TRMM) Microwave Imager (TMI) rain data, and tropical buoy wind and precipitation data as reference. In contrast to Ku-band, it is shown that C-band is much less affected by direct rain effects, such as ocean splash, but effects of increased wind variability appear to dominate ASCAT wind retrieval. ECMWF winds do not well resolve the airflow under rainy conditions. ASCAT winds do but also show artifacts in both the wind speed and wind direction distributions for high rain rates (RRs). The operational QC proves to be effective in screening these artifacts but at the expense of many valuable winds. An image-processing method, known as singularity analysis, is proposed in this paper to complement the current QC, and its potential is illustrated. QC at higher resolution is also expected to result in improved screening of high RRs.

SMOS Semi-Empirical Ocean Forward Model Adjustment

A prerequisite for the successful retrieval of geophysical parameters from remote sensing measurements is the development of an accurate forward model. The European Space Agency Soil Moisture and Ocean Salinity (SMOS), carrying onboard an L-band interferometric radiometer (Microwave Interferometric Radiometer using Aperture Synthesis), was launched on November 2009. Due to the lack of L-band passive ocean measurements from space, several prelaunch forward models were developed and initially used in the SMOS ocean salinity operational processor. In this paper, an update of the prelaunch semi-empirical forward model is presented, using for the first time, real SMOS data. In particular, the ocean surface emissivity modulation at L-band due to rough sea surface is reviewed and reanalyzed. A new model definition is provided with the help of a simple neural network. The improvement is quantified in terms of retrieved salinity accuracy compared with the climatology and concerns essentially the range of wind speeds higher than 12 m·s-1.

Coherent Stranski-Krastanov growth in 1¿1 dimensions with anharmonic interactions: An equilibrium study

The formation of coherently strained three-dimensional islands on top of the wetting layer in Stranski-Krastanov mode of growth is considered in a model in 1+1 dimensions accounting for the anharmonicity and non-convexity of the real interatomic forces. It is shown that coherent 3D islands can be expected to form in compressed rather than in expanded overlayers beyond a critical lattice misfit. In the latter case the classical Stranski-Krastanov growth is expected to occur because the misfit dislocations can become energetically favored at smaller island sizes. The thermodynamic reason for coherent 3D islanding is the incomplete wetting owing to the weaker adhesion of the edge atoms. Monolayer height islands with a critical size appear as necessary precursors of the 3D islands. The latter explains the experimentally observed narrow size distribution of the 3D islands. The 2D-3D transformation takes place by consecutive rearrangements of mono- to bilayer, bi- to trilayer islands, etc., after exceeding the corresponding critical sizes. The rearrangements are initiated by nucleation events each next one requiring to overcome a lower energetic barrier. The model is in good qualitative agreement with available experimental observations.