Abstract. Over the last two decades, the Greenland ice sheet (GrIS) has been losing mass at an increasing rate, enhancing its contribution to sea-level rise (SLR). The recent increases in ice loss appear to be due to changes in both the surface mass balance of the ice sheet and ice discharge (ice flux to the ocean). Rapid ice flow directly affects the discharge, but also alters ice-sheet geometry and so affects climate and surface mass balance. Present-day ice-sheet models only represent rapid ice flow in an approximate fashion and, as a consequence, have never explicitly addressed the role of ice discharge on the total GrIS mass balance, especially at the scale of individual outlet glaciers. Here, we present a newgeneration prognostic ice-sheet model which reproduces the current patterns of rapid ice flow. This requires three essential developments: the complete solution of the full system of equations governing ice deformation; a variable resolution unstructured mesh to resolve outlet glaciers and the use of inverse methods to better constrain poorly known parameters using observations. The modelled ice discharge is in good agreement with observations on the continental scale and for individual outlets. From this initial state, we investigate possible bounds for the next century ice-sheet mass loss. We run sensitivity experiments of the GrIS dynamical response to perturbations in climate and basal lubrication, assuming a fixed position of the marine termini. We find that increasing ablation tends to reduce outflow and thus decreases the icesheet imbalance. In our experiments, the GrIS initial mass (im)balance is preserved throughout the whole century in the absence of reinforced forcing, allowing us to estimate a lower bound of 75 mm for the GrIS contribution to SLR by 2100. In one experiment, we show that the current increase in the rate of ice loss can be reproduced and maintained throughout the whole century. However, this requires a very unlikely perturbation of basal lubrication. From this result we are able to estimate an upper bound of 140 mm from dynamics only for the GrIS contribution to SLR by 2100.

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of the model). One of the statistical tools used to quantify the influence of each input variable on the output is the Sobol sensitivity index. We consider the statistical estimation of this index from a finite sample of model outputs: we present two estimators and state a central limit theorem for each. We show that one of these estimators has an optimal asymptotic variance. We also generalize our results to the case where the true output is not observable, and is replaced by a noisy version.Résumé. De nombreux modèles mathématiques font intervenir plusieurs paramètres qui ne sont pas tous connus précisément. L'analyse de sensibilité globale se propose de sélectionner les paramètres d'entrée dont l'incertitude a le plus d'impact sur la variabilité d'une quantité d'intérêt (sortie du modèle). Un des outils statistiques pour quantifier l'influence de chacune des entrées sur la sortie est l'indice de sensibilité de Sobol. Nous considérons l'estimation statistique de cet indice à l'aide d'un nombre fini d'échantillons de sorties du modèle: nous présentons deux estimateurs de cet indice et énonçons un théorème central limite pour chacun d'eux. Nous démontrons que l'un de ces deux estimateurs est optimal en terme de variance asymptotique. Nous généralisons également nos résultats au cas où la vraie sortie du modèle n'est pas observée, mais où seule une version dégradée (bruitée) de la sortie est disponible.1991 Mathematics Subject Classification. 62G05, 62G20.The dates will be set by the publisher.