Abstract
We investigate the Oneshot Optimization strategy introduced by Hamdi and Griewank for the applicability and efficiency to identify parameters in models of the earth's climate system. Parameters of a box model of the North Atlantic Thermohaline Circulation are optimized with respect to the fit of model output to data given by another model of intermediate complexity. Since the model is run into a steady state by a pseudo time-stepping, efficient techniques are necessary to avoid extensive recomputations or storing when using gradient-based local optimization algorithms. The Oneshot approach simultaneously updates state, adjoint and parameter values. For the required partial derivatives, the algorithmic/automatic differentiation tool TAF was used. Numerical results are compared to results obtained by the BFGS-quasi-Newton method.
Highlights
Parameter optimization is an important task in all kinds of climate models or models that simulate parts of the climate system, as for example ocean or atmospheric models
As mentioned in the introduction, in climate modeling an optimization is at first performed for steady states, which means in this example for temperatures and salinities which do not change in time anymore
We compare results to values obtained by the Limited-memory BFGS (L-BFGS) algorithm implemented by Zhu, Byrd, Nocedal and Morales, see [18], version 3.0 from 2011, without and with box constraints on the control parameters (L-BFGS-B) because we find that computed optimal parameter values of the BFGS and limited-memory BFGS (L-BFGS) method are far away from actual real world values
Summary
Parameter optimization is an important task in all kinds of climate models or models that simulate parts of the climate system, as for example ocean or atmospheric models. (and this is the second point where engineering and geophysical flow problems are similar), the computation of steady states is often performed by running a transient model into the steady state This strategy is called pseudo time-stepping, since the time variable may be regarded as a kind of iteration counter. In the One-shot approach used here, the idea is that for fixed parameters there is a given (not necessarily (pseudo-) time-stepping) strategy to solve the state equations. We apply the One-shot approach to a box model of the North Atlantic This problem is different from the application in [6] in that the parameters enter in a nonlinear fashion resulting in so-called non-separable adjoints where the adjoint is no longer only the sum of a term on the state and a term on design.
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