Of the gradient accuracy in Full-Stokes ice flow model: basal slipperiness inference

Abstract. This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. We quantify the ability to identify the basal slipperiness for such methods with a non-linear friction law. The complete adjoint problem is solved and a comparison with the so called "self-adjoint" method, neglecting the viscosity dependency to the velocity, common in glaciology, is carried out. A lower bound of identifiable wavelengths of 10 ice thickness in the friction coefficient is established, when using the full adjoint method, while the "self-adjoint" method is limited to a maximum of 20 ice thickness wavelengths. In addition, the full adjoint method demonstrates a better robustness and reliability for the parameter identification process. The derivation of the adjoint model using algorithmic differentiation leads to formulate a generalization of the "self-adjoint" approximation towards an incomplete adjoint method, adjustable in precision and computational burden.