## Section: New Results

### Glaciology

Participants : Maëlle Nodet, Éric Blayo, Bénédicte Lemieux-Dudon.

#### Adjoint methods for glaciology modelling

In collaboration with C. Ritz (CNRS, Laboratoire de Glaciologie et Geophysique de l'Environnement, Grenoble), we aim to develop adjoint methods for ice cap models.

In the framework of global warming, the evolution of sea level is a major but ill-known impact. It is difficult to validate the models which are used to predict the sea level elevation, because observations are heterogeneous and sparse.

Data acquisition in polar glaciology is difficult and expensive. Satellite data have a good spatial coverage, but they allow only indirect observation of the interesting data. We wish to make the most of all available data and evaluate where/when/what we have to add new observations. Sensitivity analysis, and in particular the adjoint method, allows to identify the most influential parameters and variables and can help to design the observation network.

The objective of this work is to develop the adjoint code of the polar ice cap model (with code differentiation and transposition methods), in order to evaluate the sensitivity of the model to various parameters, such as the boundary conditions, ice rheology... This work has just been funded by the ANR-ADAGe project.

#### Dating ice matrix and gas bubbles

Dating ice matrix and gas bubbles of ice-cores is essential to study paleoclimates. The conjunction of information brought by observations and flow models is now a commonly used approach to build the chronology of ice cores. Till now this technique has been applied: 1) to one core at a time, 2) to estimate the age of the ice but not of the gas (which is younger), 3) under the assumption of perfect glaciological models after the optimization of their parameters. This currently used methodology faces three problems: 1) for distinct cores the chronologies calculated separately usually show discrepancies, 2) chronologies sometimes fail to respect relevant data constraints precisely because models are imperfect (not well understood physical processes are omitted), at last 3) the gas and ice ages are not independent entities and some valuable observations contain information on both. To go beyond these restrictions B. Lemieux-Dudon has proposed in her PhD a new inverse approach which takes into account the modelling errors. It aims at identifying the accumulation rate, the total thinning function and the close-off depth of ice equivalent (i.e. depth below the surface where the gas is trapped) which are in best agreement with some prior guesses and with independent observations. This method operates on several cores simultaneously by the mean of stratigraphic links relating the gas or ice phase of two cores. The Bayesian framework of this method also enables to associate confidence intervals to the solution. This approach is applied to derive simultaneously a common age scale for the North Grip core and for the two EPICA cores (DML and DC). [13]