arXiv subjects

Carlos Granero-Belinchon

Publications and source records attributed to Carlos Granero-Belinchon.

At least 19 recordsLinked to original sources

arXiv2026

Using analogues to investigate error growth and predictability in turbulence

In this study, we revisit Lorenz's pioneering concept of analogues to investigate error growth and predictability in fully developed turbulence using experimental data. By applying the method to a 1D turbulent velocity time series, we successfully identify the three error growth regimes intuited by Lorenz and later formalized by turbulence theory: the chaotic exponential regime, the algebraic regime of spontaneous stochasticity, and the saturation regime. Our analysis reveals that the Lyapunov exponent and the exponent of the algebraic regime depend on the initial error. We interpret this dependence as a statistical bias induced by the intermittency of turbulence, where rare events, characterized by lower Lyapunov exponents and more singular velocity increments, are preferentially sampled when considering larger initial errors. These findings not only validate Lorenz's qualitative intuition but also provide new quantitative insights into the predictability of turbulent flows, paving the way for potential applications in the prediction of extreme events.

physics.flu-dyn↗

arXiv2026

Structural and Lagrangian properties of analogue ensembles to characterize multifractality of stochastic processes

We present a framework for the scale-invariance characterization of stochastic processes in reconstructed finite-dimensional phase spaces. This framework analyses the structural and dynamical properties of the phase space and is based on a Takens embedding reconstruction followed by the definition of ensembles of analogue states. We define the analogues of a target state as its nearest neighbors. Then, we specify a collection of target states densely sampling the full phase space. For each target state, we search for the ensemble of its k-best analogues and we analyze its volume and dynamics. First, we study the probability distribution of the volumes and relate its mean and variance to the scale-invariance properties of the stochastic process. Second, we study the Lagrangian properties of the analogues by characterizing how they disperse in time. More particularly, we study the volume occupied by the analogue's successors in function of time and of their initial volume. We link these dynamical properties to the scale-invariance properties of the process. We analyze two types of stationary and dissipative 1-dimensional scale-invariant processes: regularized fractional Brownian motion and regularized multifractal random walk. For both processes, the structure and dynamics of the phase space are determined by their scale-invariant properties.

stat.AP↗

arXiv2026

Impact of geophysical fields on Deep Learning-based Lagrangian drift simulations

We assess the influence of different Eulerian geophysical input fields on Lagrangian drift simulations using DriftNet, a learning-based method designed to simulate Lagrangian drift on the sea surface. Two experiments are conducted: a fully numerical experiment (Benchmark B1) and a real-world drifters-based experiment (Benchmark B2). Both experiments are performed in two regions with different ocean dynamics: North East Pacific and Gulf Stream regions. The performance of DrifNet is evaluated with three different metrics: separation distance between simulated and ground-truth trajectories, the normalized cumulative Lagrangian separation and the autocorrelation of Lagrangian velocities. In both regions, results from B1 show that combining assimilated sea surface currents (SSC) with fully observed sea surface height (SSH) leads to greatest improvement in trajectory simulation. This configuration reduces separation distance by over 50\% and significantly decreases normalized cumulative Lagrangian separation and metrics related to velocities autocorrelation functions compared to the baseline using SSC alone. On the other hand, the inclusion of sea surface temperature (SST) either alone or in combination with SSC generally degrades performance. In B2, using satellite-derived SSH, Ekman and winds velocities improves surface drifters trajectories simulation, particularly in the North East Pacific. While the satellite-derived SST in combination with reanalysis-based SSC configuration leads to better trajectories simulation in the Gulf Stream. Overall, we highlight the added value of combining multiple geophysical fields to improve Lagrangian drift simulation on both numerical and real-world experiments.

physics.ao-ph↗

arXiv2026

Analog-based ensembles to characterize turbulent dynamics from observed data

We present a methodology for the study of the dispersion of trajectories of stochastic processes in reconstructed phase spaces from observed data. The methodology allows to find ensembles of analog states, i.e. states that are close in the phase space. Once these states are found, we focus on the characterisation of their dispersion in function of 1) the time and 2) their initial separation. We study an experimental turbulent velocity measurement and two scale-invariant stochastic processes: a regularized fractional Brownian motion and a regularized multifractal random walk. Both stochastic processes are synthesized to have the same covariance structure as the experimental turbulent velocity, but only the regularized multifractal random walk mimics the intermittency of turbulent velocity. We illustrate that while the covariance structure of the processes governs the time dependence of the dispersion of the analog states, the intermittency phenomenon is responsible for the impact of the initial separation of the analogs on their dispersion.

nlin.CD↗

arXiv2025

Relationship between unpredictability and intermittency in shell models of turbulence and experiments

We study the predictability of turbulent velocity signals using probabilistic analog-forecasting. Here, predictability is defined by the accuracy of forecasts and the associated uncertainties. We study the Gledzer--Ohkitani--Yamada (GOY) shell model of turbulence as well as experimental measurements from a fully developed turbulent flow. In both cases, we identify the extreme values of velocity at small scales as localized unpredictable events that lead to a loss of predictability: worse mean predictions and increase of their uncertainties. The GOY model, with its explicit scale separation, allows to evaluate the prediction performance at individual scales, and so to better relate the intensity of extreme events and the loss of forecast performance. Results show that predictability decreases systematically from large to small scales. These findings establish a statistical connection between predictability loss across scales and intermittency in turbulent flows.

physics.flu-dyn↗

arXiv2025

Structure functions and flatness of streamwise velocity in a turbulent channel flow

In this article, we present a multiscale characterization of the streamwise velocity of a turbulent channel flow. We study the 2nd and 4th order structure functions and the flatness for scales ranging from the dissipative to the integral domains and for a wide range of distances to the walls spanning four distinct regions of the channel. We characterize the impact of the shear stress induced by the walls on these statistics. Far from the walls, in the outer layer, the impact of the boundaries on the flow is negligible and the flow statistics follow the Kolmogorov-Obukhov theory. In the viscous, buffer and logarithmic regions, the inertial domain can be split in two subdomains of scales with two different statistical behaviors. In the logarithmic region, the scaling of the structure functions agrees with the model of Davidson et al. 2006 but the scaling of the flatness seems to better correspond to the characterization of intermittency proposed by Kolmogorov and Obukhov in 1962. The structure functions and flatness of the streamwise velocity in the buffer and viscous regions are studied for the first time. We show the strong non-Gaussianity of the velocity flow at any scale in the viscous layer with strong intermittent events that may correspond to high shear-induced dissipation.

physics.flu-dyn↗

arXiv2025

Simulation-informed deep learning for enhanced SWOT observations of fine-scale ocean dynamics

Oceanic processes at fine scales are crucial yet difficult to observe accurately due to limitations in satellite and in-situ measurements. The Surface Water and Ocean Topography (SWOT) mission provides high-resolution Sea Surface Height (SSH) data, though noise patterns often obscure fine scale structures. Current methods struggle with noisy data or require extensive supervised training, limiting their effectiveness on real-world observations. We introduce SIMPGEN (Simulation-Informed Metric and Prior for Generative Ensemble Networks), an unsupervised adversarial learning framework combining real SWOT observations with simulated reference data. SIMPGEN leverages wavelet-informed neural metrics to distinguish noisy from clean fields, guiding realistic SSH reconstructions. Applied to SWOT data, SIMPGEN effectively removes noise, preserving fine-scale features better than existing neural methods. This robust, unsupervised approach not only improves SWOT SSH data interpretation but also demonstrates strong potential for broader oceanographic applications, including data assimilation and super-resolution.

physics.ao-ph↗

arXiv2025

Land Surface Temperature Super-Resolution with a Scale-Invariance-Free Neural Approach: Application to MODIS

Due to the trade-off between the temporal and spatial resolution of thermal spaceborne sensors, super-resolution methods have been developed to provide fine-scale Land SurfaceTemperature (LST) maps. Most of them are trained at low resolution but applied at fine resolution, and so they require a scale-invariance hypothesis that is not always adapted. Themain contribution of this work is the introduction of a Scale-Invariance-Free approach for training Neural Network (NN) models, and the implementation of two NN models, calledScale-Invariance-Free Convolutional Neural Network for Super-Resolution (SIF-CNN-SR) for the super-resolution of MODIS LST products. The Scale-Invariance-Free approach consists ontraining the models in order to provide LST maps at high spatial resolution that recover the initial LST when they are degraded at low resolution and that contain fine-scale texturesinformed by the high resolution NDVI. The second contribution of this work is the release of a test database with ASTER LST images concomitant with MODIS ones that can be usedfor evaluation of super-resolution algorithms. We compare the two proposed models, SIF-CNN-SR1 and SIF-CNN-SR2, with four state-of-the-art methods, Bicubic, DMS, ATPRK, Tsharp,and a CNN sharing the same architecture as SIF-CNN-SR but trained under the scale-invariance hypothesis. We show that SIF-CNN-SR1 outperforms the state-of-the-art methods and the other two CNN models as evaluated with LPIPS and Fourier space metrics focusing on the analysis of textures. These results and the available ASTER-MODIS database for evaluation are promising for future studies on super-resolution of LST.

cs.LG↗

arXiv2024

Analog-Based Forecasting of Turbulent Velocity: Relationship between Unpredictability and Intermittency

This study evaluates the performance of analog-based methodologies to predict, in a statistical way, the longitudinal velocity in a turbulent flow. The data used comes from hot wire experimental measurements from the Modane wind tunnel. We compared different methods and explored the impact of varying the number of analogs and their sizes on prediction accuracy. We illustrate that the innovation, defined as the difference between the true velocity value and the prediction value, highlights particularly unpredictable events that we directly link with extreme events of the velocity gradients and so to intermittency. A statistical study of the innovation indicates that while the estimator effectively seizes linear correlations, it fails to fully capture higher-order dependencies. The innovation underscores the presence of intermittency, revealing the limitations of current predictive models and suggesting directions for future improvements in turbulence forecasting.This study evaluates the performance of analog-based methodologies to predict the longitudinal velocity in a turbulent flow. The data used comes from hot wire experimental measurements from the Modane wind tunnel. We compared different methods and explored the impact of varying the number of analogs and their sizes on prediction accuracy. We illustrate that the innovation, defined as the difference between the true velocity value and the prediction value, highlights particularly unpredictable events that we directly link with extreme events of the velocity gradients and so to intermittency. This result indicates that while the estimator effectively seizes linear correlations, it fails to fully capture higher-order dependencies. The innovation underscores the presence of intermittency, revealing the limitations of current predictive models and suggesting directions for future improvements in turbulence forecasting.

physics.data-an↗

arXiv2024

A multiscale and multicriteria Generative Adversarial Network to synthesize 1-dimensional turbulent fields

This article introduces a new Neural Network stochastic model to generate a 1-dimensional stochastic field with turbulent velocity statistics. Both the model architecture and training procedure ground on the Kolmogorov and Obukhov statistical theories of fully developed turbulence, so guaranteeing descriptions of 1) energy distribution, 2) energy cascade and 3) intermittency across scales in agreement with experimental observations. The model is a Generative Adversarial Network with multiple multiscale optimization criteria. First, we use three physics-based criteria: the variance, skewness and flatness of the increments of the generated field that retrieve respectively the turbulent energy distribution, energy cascade and intermittency across scales. Second, the Generative Adversarial Network criterion, based on reproducing statistical distributions, is used on segments of different length of the generated field. Furthermore, to mimic multiscale decompositions frequently used in turbulence's studies, the model architecture is fully convolutional with kernel sizes varying along the multiple layers of the model. To train our model we use turbulent velocity signals from grid turbulence at Modane wind tunnel.

cs.LG↗

arXiv2023

Neural network based generation of a 1-dimensional stochastic field with turbulent velocity statistics

We define and study a fully-convolutional neural network stochastic model, NN-Turb, which generates a 1-dimensional field with some turbulent velocity statistics. In particular, the generated process satisfies the Kolmogorov 2/3 law for second order structure function. It also presents negative skewness across scales (i.e. Kolmogorov 4/5 law) and exhibits intermittency as characterized by skewness and flatness. Furthermore, our model is never in contact with turbulent data and only needs the desired statistical behavior of the structure functions across scales for training.

eess.SP↗

arXiv2023

Multiscale and Anisotropic Characterization of Images Based on Complexity: an Application to Turbulence

This article presents a multiscale, non-linear and directional statistical characterization of images based on the estimation of the skewness, flatness, entropy and distance from Gaussianity of the spatial increments. These increments are characterized by their magnitude and direction; they allow us to characterize the multiscale properties directionally and to explore anisotropy. To describe the evolution of the probability density function of the increments with their magnitude and direction, we use the skewness to probe the symmetry, the entropy to measure the complexity, and both the flatness and distance from Gaussianity to describe the shape. These four quantities allow us to explore the anisotropy of the linear correlations and non-linear dependencies of the field across scales. First, we validate the methodology on two-dimensional synthetic scale-invariant fields with different multiscale properties and anisotropic characteristics. Then, we apply it on two synthetic turbulent velocity fields: a perfectly isotropic and homogeneous one, and a channel flow where boundaries induce inhomogeneity and anisotropy. Our characterization unambiguously detects the anisotropy in the second case, where our quantities report scaling properties that depend on the direction of analysis. Furthermore, we show in both cases that turbulent velocity fluctuations are always isotropic, when the mean velocity profile is adequately removed.

physics.flu-dyn↗

arXiv2022

Deep learning for Lagrangian drift simulation at the sea surface

We address Lagrangian drift simulation in geophysical dynamics and explore deep learning approaches to overcome known limitations of state-of-the-art model-based and Markovian approaches in terms of computational complexity and error propagation. We introduce a novel architecture, referred to as DriftNet, inspired from the Eulerian Fokker-Planck representation of Lagrangian dynamics. Numerical experiments for Lagrangian drift simulation at the sea surface demonstrates the relevance of DriftNet w.r.t. state-of-the-art schemes. Benefiting from the fully-convolutional nature of Drift-Net, we explore through a neural inversion how to diagnose modelderived velocities w.r.t. real drifter trajectories.

cs.LG↗

arXiv2022

Convolutional Neural Network Modelling for MODIS Land Surface Temperature Super-Resolution

Nowadays, thermal infrared satellite remote sensors enable to extract very interesting information at large scale, in particular Land Surface Temperature (LST). However such data are limited in spatial and/or temporal resolutions which prevents from an analysis at fine scales. For example, MODIS satellite provides daily acquisitions with 1Km spatial resolutions which is not sufficient to deal with highly heterogeneous environments as agricultural parcels. Therefore, image super-resolution is a crucial task to better exploit MODIS LSTs. This issue is tackled in this paper. We introduce a deep learning-based algorithm, named Multi-residual U-Net, for super-resolution of MODIS LST single-images. Our proposed network is a modified version of U-Net architecture, which aims at super-resolving the input LST image from 1Km to 250m per pixel. The results show that our Multi-residual U-Net outperforms other state-of-the-art methods.

cs.CV↗

arXiv2022

Two-dimensional structure functions to characterize convective rolls in the marine atmospheric boundary layer from Sentinel-1 SAR images

We study the shape of convective rolls in the Marine Atmospheric Boundary Layer from Synthetic Aperture Radar images of the ocean. We propose a multiscale analysis with structure functions which allow an easy generalization to analyse high-order statistics and so to finely describe the shape of the rolls. The two main results are : 1) second order structure function characterizes the size and direction of rolls just like correlation or power spectrum do, 2) high order statistics can be studied with skewness and Flatness which characterize the asymmetry and intermittency of rolls respectively. From the best of our knowledge, this is the first time that the asymmetry and intermittency of rolls is shown from radar images of the ocean surface.

cs.IT↗

arXiv2021

Quantifying Non-Stationarity with Information Theory

We introduce an index based on information theory to quantify the stationarity of a stochastic process.The index compares on the one hand the information contained in the increment at the time scale $τ$ of the process at time $t$ with, on the other hand, the extra information in the variable at time $t$ that is not present at time $t-τ$. By varying the scale $τ$, the index can explore a full range of scales. We thus obtain a multi-scale quantity that is not restricted to the first two moments of the density distribution, nor to the covariance, but that probes the complete dependences in the process. This index indeed provides a measure of the regularity of the process at a given scale.Not only is this index able to indicate whether a realization of the process is stationary, but its evolution across scales also indicates how rough and non-stationary it is.We show how the index behaves for various synthetic processes proposed to model fluid turbulence, as well as on experimental fluid turbulence measurements.

physics.data-an↗

arXiv2019

Information theory for non-stationary processes with stationary increments

We describe how to analyze the wide class of non stationary processes with stationary centered increments using Shannon information theory. To do so, we use a practical viewpoint and define ersatz quantities from time-averaged probability distributions. These ersatz versions of entropy, mutual information and entropy rate can be estimated when only a single realization of the process is available. We abundantly illustrate our approach by analyzing Gaussian and non-Gaussian self-similar signals, as well as multi-fractal signals. Using Gaussian signals allow us to check that our approach is robust in the sense that all quantities behave as expected from analytical derivations. Using the stationarity (independence on the integration time) of the ersatz entropy rate, we show that this quantity is not only able to fine probe the self-similarity of the process but also offers a new way to quantify the multi-fractality.

cs.IT↗

arXiv2017

Information Theory to probe Intrapartum Fetal Heart Rate Dynamics

Intrapartum fetal heart rate (FHR) monitoring constitutes a reference tool in clinical practice to assess the baby health status and to detect fetal acidosis. It is usually analyzed by visual inspection grounded on FIGO criteria. Characterization of Intrapartum fetal heart rate temporal dynamics remains a challenging task and continuously receives academic research efforts. Complexity measures, often implemented with tools referred to as \emph{Approximate Entropy} (ApEn) or \emph{Sample Entropy} (SampEn), have regularly been reported as significant features for intrapartum FHR analysis. We explore how Information Theory, and especially {\em auto mutual information} (AMI), is connected to ApEn and SampEn and can be used to probe FHR dynamics. Applied to a large (1404 subjects) and documented database of FHR data, collected in a French academic hospital, it is shown that i) auto mutual information outperforms ApEn and SampEn for acidosis detection in the first stage of labor and continues to yield the best performance in the second stage; ii) Shannon entropy increases as labor progresses, and is always much larger in the second stage;iii) babies suffering from fetal acidosis additionally show more structured temporal dynamics than healthy ones and that this progressive structuration can be used for early acidosis detection.

physics.med-ph↗