Simultaneous model spin-up and parameter identification with the one-shot method in a climate model example

Simultaneous model spin-up and parameter identification with the one-shot method in a climate model example

We investigate the One-shot Optimization strategy introduced in this form by Hamdi andGriewank for the applicability and efficiency to identify parameters in models of the earth's climatesystem. Parameters of a box model of the North Atlantic Thermohaline Circulation are optimizedwith respect to the Şt 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 necessaryto avoid extensive recomputations or storing when using gradient-based local optimization algorithms.The One-shot approach simultaneously updates state, adjoint and parameter values. For the requiredpartial derivatives, the algorithmic/automatic differentiation tool TAF was used. Numerical resultsare compared to results obtained by the BFGS and L-BFGS quasi-Newton method.

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  • [1] Griewank, A., Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. SIAM, Philadelphia, PA (2000).
  • [2] Christianson, B., Reverse accumulation and implicit functions. Optimization Methods and Software, 9(4), 307-322 (1998).
  • [3] Kaminski, T., Giering, R., and Voßbeck, M., Efficient sensitivities for the spin-up phase. Automatic Differentiation: Applications, Theory, and Implementations, Lecture Notes in Computational Science and Engineering, Springer, New York, 50, 283-291 (2005).
  • [4] Hamdi, A. and Griewank, A., Reduced Quasi-Newton Method for Simultaneous Design and Optimization. Comput. Optim. Appl. online, Available at www. springerlink.com (2009).
  • [5] Hamdi, A. and Griewank, A., Properties of an Augmented Lagrangian for Design Optimization. Optimization Methods and Software, 25(4), 645-664 (2010).
  • [6] Ozkaya, E. and Gauger, N., Single-Step One- ¨ Shot Aerodynamic Shape Optimization. International Series of Numerical Mathematics, 158, 191-204 (2009).
  • [7] Ta'asn, S., Pseudo-Time Methods for Constrained Optimization Problems Governed by PDE. ICASE Report No. 95-32 (1995).
  • [8] Hazra, S. B. and Schulz, V., Simultaneous Pseudo-Timestepping for PDE-Model Based Optimization Problems. BIT Numerical Mathematics, 44, 457-472 (2004).
  • [9] Pham, D. and Karaboga, D., Intelligent Optimisation Techniques: Genetic Algorithms, Tabu Search, Simulated Annealing and Neural Networks. Springer London, Limited (2012).
  • [10] Ciric, L. B., A Generalization of Banach's Contraction Principle. Proceedings of the American Mathematical Society, 45(2), 267- 273 (1974).
  • [11] Griewank, A. and Kressner, D., "Time-lag in Derivative Convergence for Fixed Point Iterations. ARIMA Num´ero sp´ecial CARI'04, 87-102 (2005).
  • [12] Giering, R., Kaminski, T., and Slawig, T., Generating Efficient Derivative Code with TAF: Adjoint and Tangent Linear Euler Flow Around an Airfoil. Future Generation Computer Systems, 21(8), 1345-1355 (2005).
  • [13] Bischof, C. H., Lang, B., and Vehreschild, A., Automatic Differentiation for MATLAB Programs. Proceedings in Applied Mathematics and Mechanics, 2(1), 50-53 (2003).
  • [14] Griewank, A., Juedes, D., and Utke, J., Algorithm 755: ADOL-C: A Package for the Automatic Differentiation of Algorithms Written in C/C++. ACM Transactions on Mathematical Software, 22(2), 131- 167 (1996).
  • [15] Zickfeld, K., Slawig, T., and Rahmstorf, S., A low-order model for the response of the Atlantic thermohaline circulation to climate change. Ocean Dynamics, 54, 8-26 (2004).
  • [16] Titz, S., Kuhlbrodt, T., Rahmstorf, S., and Feudel, U., On freshwater-dependent bifurcations in box models of the interhemispheric thermohaline circulation. Tellus A, 54, 89 - 98 (2002).
  • [17] Rahmstorf, S., Brovkin, V., Claussen, M., and Kubatzki, C., CLIMBER-2: A climate system model of intermediate complexity. Part II: Model sensitivity. Clim. Dyn., 17, 735-751 (2001).
  • [18] Zhu, C., Byrd, R. H., and Nocedal, J., LBFGS-B: Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization. ACM Transactions on Mathematical Software, 23(4), 550-560 (1997).