Efficient Sensitivities for the Spin-Up Phase

Abstract

In geosciences, it is common to spin up models by integrating with annually repeated boundary conditions. AD-generated code for evaluating sensitivities of the final cyclo-stationary state with respect to model parameters or boundary conditions usually includes a similar iteration for the derivative statements, possibly with a reduced number of iterations. We evaluate an alternative strategy that first carries out the spin-up, then evaluates the full Jacobian for the final iteration and then applies the implicit function theorem to solve for the sensitivities of the cyclo-stationary state. We demonstrate the benefit of the strategy for the spin-up of a simple box-model of the atmospheric transport. We derive a heuristic inequality for this benefit, which increases with the number of iterations and decreases with the size of the state space.