The adjoint approach has become quite popular in constraining glacial ice flow models to observations by gradient-based optimization. For the most part, however, the adjoint model is only generated for the stress balance of the ice model, and "snapshots" of velocities must be inverted with assumptions of perfect knowledge of ice geometry. As remote sensing data becomes more frequent and more complete, it is fair to expect that time-dependent models of ice dynamics, with physical process implementations, might be constrained to time-dependent data. This would provide better capture of transient states - which can then be perturbed to study various processes - and potentially a better representation of unknown properties, such as bed topography or submarine ice shelf melt.

A prerequisite to such approaches, however, is the adjoint of such a model. Typically adjoints of the stress balance take advantage of the structure of the stress balance equations to generate the adjoint model analytically. This becomes more difficult, though, with additional physics (such as mass advection and calving front movement) and multiple time steps. Algorithmic differentiation (AD) presents an alternative. I will present the generation of the adjoint of a time-dependent higher-order (L1L2) flow model of a marine ice sheet. The model has been developed as a part of the MITgcm framework, and so many of the AD practices coded into MITgcm are taken advantage of. I will discuss the additional considerations that needed to (and still need to) be made, and progress with the AD tools Transformations of Algorithms in Fortran (TAF) and the open-source OpenAD. Lastly, I will show the results of a number of numerical experiments, using both real and synthetic data, that illustrate both the utility of the ice adjoint model, and the possibilities (and limitations) of time-dependent assimilation of ice sheet data.