Prévision d'ensembles | EPFL Graph Search

vignette|En haut: Modèle déterministe du WRF pour la prévision de trajectoire de l'ouragan Rita en 2005. En bas : Dispersion des différents modèles utilisés par le National Hurricane Center pour la même tempête. La prévision d'ensembles est une méthode de prévision numérique du temps utilisé pour tenter de générer un échantillon représentatif des états futurs possibles d'un système dynamique. En effet, ni les observations, ni l'analyse, ni le modèle de prévision ne sont parfaits et la dynamique atmosphérique est très sensible, dans certaines conditions, à la moindre fluctuation. C'est une forme de méthode de Monte Carlo : plusieurs prédictions numériques sont réalisées à l'aide de conditions initiales légèrement différentes mais plausibles étant donné les limites de résolution des observations et des équations. Dans chaque cas, l'analyse est délibérément rendue légèrement différente des autres membres de l'ensemble, à l'intérieur des incertitudes intrinsèques de mesure ou d'analyse. Les scénarios plus ou moins divergents des prévisions offertes par les membres de l'ensemble permettent de quantifier la prévisibilité de l'atmosphère et d'offrir une marge d'erreur statistique sur la prévision. Dans les premières décennies d'existence de la prévision numérique du temps, les services météorologiques nationaux ne pouvaient faire tourner qu'un seul modèle à la plus haute résolution permise par les contraintes informatiques, et adopter cette prévision telle quelle. Cette approche suppose implicitement que si les conditions initiales étaient connues parfaitement, et que le modèle lui-même était parfait, la prévision qui s'ensuivrait simulerait parfaitement le comportement futur de l'atmosphère. On qualifie cette approche de déterministe. Edward Lorenz démontra en 1963 que les prévisions déterministes à plus de deux semaines avec un quelconque degré de confiance sont impossibles. Ceci est dû à la nature chaotique des équations de la dynamique des fluides impliquées.

Calibration of ground surface albedo models

Christophe Ballif, Pierre-Jean Alet, Arttu Matias Tuomiranta

The emergence of bifacial photovoltaics as a serious option for large-scale power generation makes the accuracy of the in-situ estimation of ground surface albedo increasingly critical. Recent studies have evaluated the performance of different models but an investigation of how these models should be calibrated is missing. This paper proposes geographically generalised parametrisations for time-variant albedo models of vegetated and desert surfaces based on a worldwide database and reports their performance compared to site-specific, unbiased parametrisations. These geographically generalised formulations can be used as an alternative for lengthy calibration campaigns as their only parameters can be easily measured. The paper also presents a simple method for deriving white-sky albedo without the need for diffuse irradiance data. The method is founded both theoretically and empirically. If on-site measurements can be collected to calibrate a model, the duration of the campaign is usually a few weeks at the maximum. This paper first shows evidence of the strong impact of the timing on calibration performance and accordingly gives practical guidelines on the most suitable measurement seasons and weather conditions. In general, early-summer months appear to be the most appropriate time for calibrating most models. Atmospheric turbidity during the campaign period, however, should be either minimised or maximised depending on the site and the model. Finally, in case no flexibility exists in timing the calibration, simple models with few parameters should be deployed. Geometric mean shows the most robust performance at most sites.

PERGAMON-ELSEVIER SCIENCE LTD2022

Local Vulnerabilities and Global Robustness of Coupled Dynamical Systems on Complex Networks

Melvyn Sandy Tyloo

Coupled dynamical systems are omnipresent in everyday life. In general, interactions between individual elements composing the system are captured by complex networks. The latter greatly impact the way coupled systems are functioning and evolving in time. An important task in such a context, is to identify the most fragile components of a system in a fast and efficient manner. It is also highly desirable to have bounds on the amplitude and duration of perturbations that could potentially drive the system through a transition from one equi- librium to another. A paradigmatic model of coupled dynamical system is that of oscillatory networks. In these systems, a phenomenon known as synchronization where the individual elements start to behave coherently may occur if couplings are strong enough. We propose frameworks to assess vulnerabilities of such synchronous states to external perturbations. We consider transient excursions for both small-signal response and larger perturbations that can potentially drive the system out of its initial basin of attraction. In the first part of this thesis, we investigate the robustness of complex network-coupled oscillators. We consider transient excursions following external perturbations. For ensemble averaged perturbations, quite remarkably we find that robustness of a network is given by a family of network descriptors that we called generalized Kirchhoff indices and which are defined from extensions of the resistance distance to arbitrary powers of the Laplacian matrix of the system. These indices allow an efficient and accurate assessment of the overall vulnera- bility of an oscillatory network and can be used to compare robustness of different networks. Moreover, a network can be made more robust by minimizing its Kirchhoff indices. Then for specific local perturbations, we show that local vulnerabilities are captured by generalized resistance centralities also defined from extensions of the resistance distance. Most fragile nodes are therefore identified as the least central according to resistance centralities. Based on the latter, rankings of the nodes from most to least vulnerable can be established. In summary, we find that both local vulnerabilities and global robustness are accurately evaluated with resistance centralities and Kirchhoff indices. Moreover, the framework that we define is rather general and may be useful to analyze other coupled dynamical systems. In the second part, we focus on the effect of larger perturbations that eventually lead the sys- tem to an escape from its initial basin of attraction. We consider coupled oscillators subjected to noise with various amplitudes and correlation in time. To predict desynchronization and transitions between synchronous states, we propose a simple heuristic criterion based on the distance between the initial stable fixed point and the closest saddle point. Surprisingly, we find numerically that our criterion leads to rather accurate estimates for the survival probability and first escape time. Our criterion is general and may be applied to other dynamical systems.

EPFL2020

'Peak Oil' As Classical Economic Process

François Meynard

Forecasts about 'peak oil', the limits of oil production, are the subject of controversies. 'Peak oil' forecasts are based on extrapolations of a priori chosen mathematical models fitted to field data. Scientifically that is not very sound. To clarify this point, in this paper 'peak oil' is modelled in a generic reductionist, approach, in which the conflicting dynamic between economic forces and physical laws are well identified. This model finds a natural interpretation just supress in a classical economic analysis frame. The 'peak oil' controversy is thus brought into the field of economic thought as a debate between classical and mainstream economics, in particular between an objective and a faith based appraisal about this historical event. The goal is not to improve forecasts about 'peak oil', which is very likely not a predictable event, but to propose an objective framework for the analysis of its systemic effects on economic production.

Multi-Science Publ Co Ltd2014

Local Vulnerabilities and Global Robustness of Coupled Dynamical Systems on Complex Networks

Melvyn Sandy Tyloo

EPFL2020