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, The straight black lines mark the 0.025 and 0.975 quantiles of d and ? . The composite anomalies in SLP obtained by averaging the days beyond the quantiles can be associated with known weather regimes: A) Atlantic Ridge (maxima of ? ), B) NAO-(minima of ? ), C) Blocking, Scatterplot of the daily values of instantaneous dimension d and inverse persistence ? for the 20CRv2c ensemble-mean SLP (20CR-EM)

, The composite anomalies in SLP obtained by averaging the days beyond the quantiles can be associated with known weather regimes: A) Atlantic Ridge (maxima of ? ), B) NAO-(minima of ?

, Blocking (maxima of d), D) NAO+ (minima of d)

, CMCC-CMS (c,d) and IPSL-CM5A models (e,f). The color scales in (a,c,e) indicate the frequency of observations in number of days. The color scales in, FIG. 6. (d, ? ) bivariate histograms (a,c,e) and scatter-plots (b,d,f) for the 20CR-EM reanalysis (a,b)

, Comparison between the 56 20CR-ME median values of (d, ? ) (blue points whose average is denoted by 0), the 20CR-EM (in red and numbered by 1) and all the CMIP5 models (progressive numbers 2-27, see table 1 for details). The CMIP5 multi-model mean is marked by MM (black). The semiaxes of the two ellipses represent one standard deviation of d and ? for 20CR-EM (red) and 20CR-ME (blue), p.1851

, Comparison between R tot values (black) and Wasserstein distances W (blue) between the (d, ? ) of 20CR-EM (a) and 20CR-ME (b) and of the CMIP5 models

, Note that labels on the abscissa mark the last year in each 30-year averaging window. (a,b): local dimension d; (c,d): inverse persistence ? . Red: 20CR-EM; Blue: 20CR-ME; yellow: single 20CRv2c members; Black: CMIP5 multimodel mean

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. .. , Exemple d'une solution du système de Lorenz (1963), p.14

. Deux-trajectoires-de-l'attracteur-de-lorenz, prises aux conditions initiales suivantes : (5.16, ?0.87, 30.64) (courbe rouge) et (4.99, ?0.53, 30.02) (courbe bleue), et intégrées pendant 0.6 unité de temps. Les trajectoires ont été projetées dans le plan (y, z), 1963.

, Représentation d'un point fixe (en noir) d'un système dynamique. La courbe bleue représente sa direction stable, qui attire toutes les trajectoires. La courbe rouge représente sa direction instable, qui repousse toutes les trajectoires. Les courbes vertes sont les trajectoires des points x 0 et x 1, p.17

;. .. Attracteur-de-lorenz, La projection est choisie de manière à mettre en valeur que l'attracteur a une dimension proche de 2, p.19, 1963.

. Histogramme-de-la-coordonnée-x-d'une-trajectoire-du-modèle-de-lorenz, a) La condition initiale de la trajectoire est (1, 1, 1). b) La condition initiale de la trajectoire est (1, ?1, ?1), 1963.

. Deux and . Lorenz, Sur la Figure a), la condition initiale est (80, 50, 50), tandis que c'est (?50, ?50, ?50) sur la Figure b). Les deux orbites génèrent bien le même objet, 1963.

, Il faut 1 ? 2 = 16 carrés pour le recouvrir

. .. , Dimension locale de l'attracteur de Lorenz (1963), p.24

. Estimation-de-la-mesure-srb-du-système-de-lorenz, partir d'une orbite contenant 590000 points. 600000 points sont générés par pas de temps de 0.005 à l'aide de l'Équation (1.1). Les 10000 premiers sont ignorés pour ne conserver que des points sur l'attracteur. Chaque points de couleur est le centre d'un petit cube de taille 0.5 × 0.5 × 0.5. Il y a 14575 cubes sur cette figure, 1963.

. .. , Distribution des températures en Ile-de-France (France) pour les simulations CMIP5, modèle de l'IPSL. À gauche, une simulation de contrôle (préindustrielle). À droite, une simulation du scénario RCP85, p.30

L. Attracteurs-de, pour deux valeurs de F . a) F = 6 (été permanent, système non chaotique bloqué sur un cycle limite). b) F = 8 (hiver permanent, système chaotique), 1984.

. Lorenz, b) Rouge : Cycle saisonnier et forçage linéaire après 100 ans, 1984.

, La figure a) est l'état de toutes les conditions initiales au temps 0. La figure b) est l'état de toutes les conditions initiales au temps 0.05 .La figure c) est l'état de toutes les conditions initiales au temps 0.1. La figure d) est l, construit avec 1000 conditions initiales aléatoires, vol.35, 1963.

. Deux and . Lorenz, construis avec deux jeux de 1000 conditions initiales en bleu et rouge. La figure a) est l'état de toutes les conditions initiales au temps 0. La figure b) est l, 1963.

, En colonne : état des snapshots pendant le premier cycle saisonnier (année 0), puis le dixième cycle (année 10) et le cycle 180. Ce dernier est donc après que le forcing ait commencé à agir à l'année 0. En colonne : snapshots pendant l'automne, puis l'hiver, Snapshots de l'attracteur de Lorenz (1984) généré à partir de 1000 conditions initiales tirées uniformément dans le cube, vol.38

, Les mesures µ t sont des lois normales centrées en 2t, d'écart type égal à 1. a) Densités de µ t , notées ? t , aux temps 0, 2, 4, 6 et 8. b) Distance Euclidienne entre µ 0 et µ t

. Deux-exemples-du-problème-de-monge, Les points bleus x i sont les déblais, les rouges y j les remblais. Les segments noirs sont des déplacements possibles entre x i et y j

. .. , -2100. b) Idem mais entre les histogrammes centrés. c) Écarts types pour les mêmes périodes et variables. d) Idem que a) et b) mais pour des distributions centrées et réduites, Deux plans de transport entre les mesures empiriques µ (points bleus en x i ) et ? (points rouges en y j ), 2000.

, Scénario RCP des forcages radiatifs entre 1850 et 2100

. Dufresne, Gris : limite entre la partie historique et les scénarios RCP. Noir : simulation préindustrielle. Vert : scénario RCP26. Bleu : scénario RCP45. Violet : scénario RCP60. Rouge : scénario RCP85. a) Les fenêtres et la référence contiennent l'année complète. b) La référence est restreinte aux étés. c) La référence est restreinte aux hivers, Moyenne sur l'hémisphère nord des distances de Wasserstein entre une fenêtre glissante de 5 ans et une référence sur la période 1850-1855, 2013.

. Dufresne, Gris : limite entre la partie historique et les scénarios RCP. Noir : simulation pré-industrielle. Vert : scénario RCP26. Bleu : scénario RCP45. Violet : scénario RCP60. Rouge : scénario RCP85. a) Les fenêtres et la référence contiennent l'année complète. b) La référence est restreinte aux étés. c) La référence est restreinte aux hivers, Moyenne sur l'hémisphère nord des distances de Wasserstein entre une fenêtre glissante de 5 ans et une référence sur la période 1850-1855, 2013.

, Attracteur de (Rössler, 1976)