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

Claudia Kratzenstein, Thomas Slawig


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.


Algorithmic differentiation; bounded retardation; climate model; fixed point iteration; parameter identification

Full Text:

Full Text [PDF]


Griewank, A., Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation. SIAM, Philadelphia, PA (2000).

Christianson, B., Reverse accumulation and implicit functions. Optimization Methods and Software, 9(4), 307–322 (1998). Crossref

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).

Hamdi, A. and Griewank, A., Reduced Quasi-Newton Method for Simultaneous Design and Optimization. Comput. Optim. Appl. online, Available at (2009).

Hamdi, A. and Griewank, A., Properties of an Augmented Lagrangian for Design Optimization. Optimization Methods and Software, 25(4), 645–664 (2010). Crossref

Ozkaya, E. and Gauger, N., Single-Step One-Shot Aerodynamic Shape Optimization. International Series of Numerical Mathematics, 158, 191–204 (2009).

Ta’asn, S., Pseudo-Time Methods for Constrained Optimization Problems Governed by PDE. ICASE Report No. 95-32 (1995).

Hazra, S. B. and Schulz, V., Simultaneous Pseudo-Timestepping for PDE-Model Based Optimization Problems. BIT Numerical Mathematics, 44, 457–472 (2004). Crossref

Pham, D. and Karaboga, D., Intelligent Optimisation Techniques: Genetic Algorithms, Tabu Search, Simulated Annealing and Neural Networks. Springer London, Limited (2012).

Ciric, L. B., A Generalization of Banach’s Contraction Principle. Proceedings of the American Mathematical Society, 45(2), 267–273 (1974). Crossref

Griewank, A. and Kressner, D., â€Time-lag in Derivative Convergence for Fixed Point Iterations. ARIMA Numero special CARI’04, 87–102 (2005).

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). Crossref

Bischof, C. H., Lang, B., and Vehreschild, A., Automatic Differentiation for MATLAB Programs. Proceedings in Applied Mathematics and Mechanics, 2(1), 50–53 (2003). Crossref

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). Crossref

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). Crossref

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). Crossref

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). Crossref

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). Crossref



  • There are currently no refbacks.

Copyright (c) 2013 Claudia Kratzenstein, Thomas Slawig

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


   ithe_170     crossref_284         ind_131_43_x_117_117  Scopus  EBSCO_Host    ULAKBIM     ZBMATH more...