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A general theory for computing information transfers in nonlinear systems driven by deterministic forcings and additive and/or multiplicative noises, is presented. It extends the Liang-Kleeman framework of causality inference based on information transfer across system variables (Liang, 2016). An effective method of computing formulas of the rates of entropy transfers (RETs) is presented, the Causal Sensitivity Method (CSM), relying on the estimation from data of conditional expectations. Those expectations are approximated by nonlinear regressions, leading to a much easier and more robust way of computing RETs than the brute-force approach calling for numerical integrals over the phase space and the knowledge of the multivariate probability density function of the system. The CSM is furthermore fully adapted to the case where no model equations are available, starting with a nonlinear model fitting from data with the subsequent application of CSM to the fitted model. Moreover, the RETs are decomposed into sums of single one-to-one RETs plus synergetic terms, accounting for the joint causal effect of groups of variables. State-dependent RET formulas are also proposed, allowing for determining the dependencies of variables and synergies locally in phase space. A comparison of the RETs estimations is performed between the brute-force probability-density-based approach (AN), the CSM-based approach with and/or without model fitting, and the multivariate linear approach, in the context of two models: (i) a model derived from a potential and (ii) the classical chaotic Lorenz system, both forced by additive and/or multiplicative noises. The analysis demonstrates that the CSM estimations are robust and close to the AN-reference values in the different experiments, providing evidence of the possibilities offered by the method and opening new perspectives on real-world applications., Comment: 41 pages, 6 figures. Submitted to Physica D

Workshop: Multi-annual to Decadal Climate Predictability in the North Atlantic-Arctic Sector

This work evaluates the statistical predictabilityof the Arctic sea ice volume (SIV) anomaly – here definedas the detrended and deseasonalized SIV – on the interan-nual timescale. To do so, we made use of six datasets, fromthree different atmosphere–ocean general circulation models,with two different horizontal grid resolutions each. Basedon these datasets, we have developed a statistical empiricalmodel which in turn was used to test the performance of dif-ferent predictor variables, as well as to identify optimal lo-cations from where the SIV anomaly could be better recon-structed and/or predicted. We tested the hypothesis that anideal sampling strategy characterized by only a few optimalsampling locations can provide in situ data for statisticallyreproducing and/or predicting the SIV interannual variabil-ity. The results showed that, apart from the SIV itself, thesea ice thickness is the best predictor variable, although totalsea ice area, sea ice concentration, sea surface temperature,and sea ice drift can also contribute to improving the pre-diction skill. The prediction skill can be enhanced furtherby combining several predictors into the statistical model.Applying the statistical model with predictor data from fourwell-placed locations is sufficient for reconstructing about70 % of the SIV anomaly variance. As suggested by theresults, the four first best locations are placed at the tran-sition Chukchi Sea–central Arctic–Beaufort Sea (79.5◦N,158.0◦W), near the North Pole (88.5◦N, 40.0◦E), at the tran-sition central Arctic–Laptev Sea (81.5◦N, 107.0◦E), and off-shore the Canadian Archipelago (82.5◦N, 109.0◦W), in thisrespective order. Adding further to six well-placed locations,which explain about 80 % of the SIV anomaly variance, thestatistical predictability does not substantially improve tak-ing into account that 10 locations explain about 84 % of thatvariance. An improved model horizontal resolution allows abetter trained statistical model so that the reconstructed val-ues better approach the original SIV anomaly. On the otherhand, if we inspect the interannual variability, the predictorsprovided by numerical models with lower horizontal reso-lution perform better when reconstructing the original SIVvariability. We believe that this study provides recommenda-tions for the ongoing and upcoming observational initiatives,in terms of an Arctic optimal observing design, for studyingand predicting not only the SIV values but also its interannualvariability.

Since the mid-20th century, global average temperatures have dramatically risen mostly due to the increasing amount of greenhouse gas emissions in the atmosphere. The effects of this recent global warming are already evident and could be exacerbated in the near future if no real action is taken. Recent ice loss in West Antarctica, monitored by satellite measurements and other techniques, gives cause for concern in such a warming world. A major part of this loss has been driven by warm water masses penetrating underneath the ice shelves in this region. This has led to a flow acceleration of the inland outlet glaciers and a greater discharge of ice to the ocean. The actual resulting contribution of West Antarctica to sea-level rise is estimated to be around 0.2 mm per year between 1992 and 2011, i.e. about one third of the ice-sheet contribution (Antarctica and Greenland), and is expected to increase in the near future. In this thesis, we first clearly demonstrate that modeling grounding-line (the boundary between grounded and floating ice) migration depends on both the numerical approach and the physical approximation of the ice-sheet model used. Ice-sheet models prescribing the ice flux at the grounding line and using appropriate physical level and numerical approach converge to the same steady-state grounding-line position irrespective of the grid size used. However, the transient behavior of those models is less accurate than other models and leads to an overestimated grounding-line discharge. Therefore, they need to be used with particular attention on short time scales. Furthermore, the non-inclusion of vertical shear stress in those models increases the effective viscosity and gives steady-state grounding-line positions further downstream when compared to full-Stokes models. The second major finding of this thesis is the high control of geometry (glacier width and bedrock topography) on Thwaites Glacier, one of the fastest-flowing outlet glaciers in West Antarctica. A flowline finite-difference Shallow-Shelf Approximation (SSA) model is applied to the glacier and shows that ice-flow convergence (through width parameterization) slows down the grounding-line retreat when compared to simulations where the width is constant. A new buttressing parameterization is also tested on the glacier and permits a better understanding of this effect. Finally, the three-dimensional version of the model above is applied to Thwaites Glacier and highlights the strong control of lateral variations in bedrock topography on grounding-line migration./Depuis le milieu du 20e siècle, les températures moyennes globales ont fortement augmenté principalement à cause de l'augmentation des émissions de gaz à effet de serre d'origine humaine. Les effets de ce réchauffement global récent sont déjà détectables et pourraient s'accentuer dans un futur proche si aucune mesure réelle n'est prise. La perte récente de glace en Antarctique de l'Ouest, enregistrée par mesures satellites et d'autres techniques, est préoccupante dans un monde qui se réchauffe. Une grande partie de cette perte de glace est due à la pénétration de masses d'eau chaude sous les plateformes de glace flottante dans cette région. Cela engendre une accélération de l'écoulement des glaciers émissaires et une plus grande décharge de glace vers l'océan. Ainsi, la contribution récente à la hausse du niveau de la mer de l'Antarctique de l'Ouest s'élève à environ 0.2 mm par an entre 1992 et 2011, c'est-à-dire près du tiers de la contribution des calottes glaciaires (Antarctique et Groenland). On estime que cette contribution va continuer à augmenter dans le futur proche. Dans cette thèse, nous démontrons clairement que la modélisation de la migration de la ligne d'ancrage (frontière entre glaces posée et flottante) dépend de l'approche numérique et de l'approximation physique du modèle cryosphérique utilisé. Les modèles cryosphériques qui prescrivent le flux glaciaire à la ligne d'ancrage et qui utilisent un niveau de physique et une approche numérique appropriés convergent vers la même position d'équilibre de la ligne d'ancrage quelle que soit la taille de maille utilisée. Cependant, le comportement transitoire de ces modèles est moins précis que d'autres modèles et mène à une surestimation du flux à la ligne d'ancrage. Dès lors, ces modèles doivent être utilisés avec précaution sur de courtes périodes de temps. De plus, la non inclusion des contraintes verticales de cisaillement dans ces modèles augmente la viscosité effective et donne des positions d'équilibre de la ligne d'ancrage plus en aval en comparaison avec les modèles « full-Stokes ». La seconde découverte majeure de cette thèse est le contrôle important exercé par la géométrie (largeur du glacier et topographie du lit rocheux) sur Thwaites Glacier, l'un des glaciers émissaires les plus rapides en Antarctique de l'Ouest. Un modèle « Shallow-Shelf Approximation » (SSA) résolvant les différences finies le long d'une ligne d'écoulement est appliqué au glacier et montre que la convergence de l'écoulement glaciaire (au travers de la paramétrisation de la largeur) ralentit le retrait de la ligne d'ancrage comparé aux simulations où la largeur est constante. Une nouvelle paramétrisation de l'effet arc-boutant est testée sur le glacier et permet de mieux comprendre cet effet. Finalement, la version en trois dimensions du modèle ci-dessus est appliquée à Thwaites Glacier et met en évidence le contrôle important des variations latérales de l'altitude du lit rocheux sur la migration de la ligne d'ancrage., Doctorat en Sciences, info:eu-repo/semantics/published