Data Assimilation for a new generation of Sea Ice Models

Statement of Work:The PI will develop a new mathematical framework to incorporate data from non-stationary instrument with aLagrangian model of sea-ice dynamics.Objective:The key feature of the problem under study is the simultaneous presence of a Lagrangian model for sea-ice and observational suppliers of data from mobile instruments. Basic research is required to develop the appropriate mathematical framework and to explore novel Data Assimilation strategies for this class of problems. The fundamental driving idea in Data Assimilation for Sea Ice Models (DASIM) is the existence of a subspace of the system dynamics,and a subset of the observations, in which is embedded the largest informational content for the signal to be retrieved. Despite the intractable large size of the full problem, by monitoring and exploiting this subspace one can hope to achieve a satisfactory track of the unknown signal while reducing the computational load. DASIM~s ultimate, mid/longterm objective, is the application of advanced Lagrangian Data Assimilation (LaDA) methods to the new generation of state-of-the-art Lagrangian sea-ice models in a quasi-operational setting, setting up the basis for new sea-iceforecasting systems at the forefront in its domain. The necessary mathematical investigation envisaged in DASIM will put light on the feasibility of such a purpose and open the path toward its accomplishment. DASIM~s last deliverable will be the preparation of a scope document reporting pros and cons of a fully Lagrangian platform for sea-ice prediction that may serve as the basis for a larger proposal for an applied-oriented research initiative.Approach:The distinctive feature of the research methodology in DASIM stands on the extensive use of concepts and tools from dynamical system theory and nonlinear filtering. This will provide a critical view on the DA problem, guide new developments, and makes DASIM a naturally interdisciplinary project joining mathematical and environmental science expertise. Two specific aspects of sea-ice modelling, (1) the solid nature of the sea-ice and (2) Lagrangian DA methods for using data, will be the focus of the research activity. A central tool in DASIM is the dynamical/thermodynamical sea-ice model, neXtSIM, developed very recently at NERSC and based on: 1) A new elastic-brittle rheology to simulate the solid mechanical behavior of the ice cover (the relationship between internal stress and strain) that exhibits dynamical features with the correct spatio-temporal statistical characteristics. And 2) ALagrangian coordinate system, including an efficient algorithm for local mesh adaptation (dynamicalremeshing/remapping), that is able to maintain the spatial and temporal coherency of the aforementioned dynamical features. To address the second issue, i.e., to account for the fact that the dynamics of sea-ice in the ocean is Lagrangian (or at least pseudo-Lagrangian, in the sense that the sea ice affects the ocean because of its melting and freezing), DASIM proposes to assimilate observational data into sea-ice models using advanced Lagrangian data assimilation methods, that deal with this nonlinearity and the skew-product structure of the sea-ice dynamics. LaDA has so far dealt with the problem of assimilating Lagrangian measurements into Eulerian models. Models in Lagrangian coordinates have not been extensively used in conjunction with DA. The fact that both the observations and the model variables are Lagrangian is a potential advantage as it alleviates the need to recover the state variablesat the model grid based on the observed trajectory. However, it opens up new questions on how to adapt DAprocedures to this type of computational model:1) Lagrangian models do not offer any easy differentiation/automatic adjoint capabilities, thus preventing the use of variational techniques. And 2) Ensemble Kalman Filtering techniques rely on cross-covariances between observed and non-observed variables, which implies tha