On the formulation of sea-ice models. Part 2: Lessons from multi-year adjoint sea-ice export sensitivities through the Canadian Arctic Archipelago

The adjoint of an ocean general circulation model is at the heart of the ocean state estimation system of the Estimating the Circulation and Climate of the Ocean (ECCO) project. As part of an ongoing effort to extend ECCO to a coupled ocean/sea-ice estimation system, a dynamic and thermodynamic sea-ice model has been developed for the Massachusetts Institute of Technology general circulation model (MITgcm). One key requirement is the ability to generate, by means of automatic differentiation (AD), tangent linear (TLM) and adjoint (ADM) model code for the coupled MITgcm ocean/sea-ice system. This second part of a two-part paper describes aspects of the adjoint model. The adjoint ocean and sea-ice model is used to calculate transient sensitivities of solid (ice and snow) freshwater export through Lancaster Sound in the Canadian Arctic Archipelago (CM). The adjoint state provides a complementary view of the dynamics. In particular, the transient, multi-year sensitivity patterns reflect dominant pathways and propagation timescales through the CAA as resolved by the model, thus shedding light on causal relationships, in the model, across the Archipelago. The computational cost of inferring such causal relationships from forward model diagnostics alone would be prohibitive. The role of the exact model trajectory around which the adjoint is calculated (and therefore of the exactness of the adjoint) is exposed through calculations using free-slip vs no-slip lateral boundary conditions. Effective ice thickness, sea surface temperature, and precipitation sensitivities, are discussed in detail as examples of the coupled sea-ice/ocean and atmospheric forcing control space. To test the reliability of the adjoint, finite-difference perturbation experiments were performed for each of these elements and the cost perturbations were compared to those predicted by the adjoint. Overall, remarkable qualitative and quantitative agreement is found. In particular, the adjoint correctly predicts a seasonal sign change in precipitation sensitivities. A physical mechanism for this sign change is presented. The availability of the coupled adjoint opens up the prospect for adjoint-based coupled ocean/sea-ice state estimation. (C) 2010 Elsevier Ltd. All rights reserved.