Efficient Sensitivities for the Spin-Up Phase
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.
KeywordsReverse Mode Derivative Propagation Atmospheric Transport Forward Mode Methyl Chloroform
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