“Application of seeding and automatic differentiation in a large scale ocean circulation model”

Authors: Frode Martinsen and Dag Slagstad,
Affiliation: SINTEF and NTNU, Department of Engineering Cybernetics
Reference: 2005, Vol 26, No 3, pp. 121-134.

Keywords: Jacobian, automatic differentiation, seeding

Abstract: Computation of the Jacobian in a 3-dimensional general ocean circulation model is considered in this paper. The Jacobian matrix considered in this paper is square, large and sparse. When a large and sparse Jacobian is being computed, proper seeding is essential to reduce computational times. This paper presents a manually designed seeding motivated by the Arakawa-C staggered grid, and gives results for the manually designed seeding as compated to identity seeding and optimal seeding. Finite differences are computed for reference.

PDF PDF (1770 Kb)        DOI: 10.4173/mic.2005.3.1

References:
[1] BISCHOF, C., CARLE, A., KADHEMI, P. MAUER, A. (1996). ADIFOR2,0: Automatic differentiation of Fortran 77 programs, IEEE Computational Science and Engineering .3, pp. 18-32 doi:10.1109/99.537089
[2] BISCHOF, C., CARL, A., HOVLAND, P., KHADEMI, P. MAUER, A. (1998). ADIFOR 2,0 UsersĀ“ guide, Tech rep., Argonne National Laboratory, Argonne, IL., aNL/MCS-TM-192.
[3] COLEMAN, T. F. MORE, J. J. (1983). Estimation of sparse Jaeobian matrices and graph coloring problems, SIAM J. Numer. Anal. 2.1, pp. 187-209 doi:10.1137/0720013
[4] COLEMAN, T. F. GARBOW, B. S. MORE J.J. (1984). Software for estimating sparse Jacobian matrices, ACM Trans. Math. Software 1.3 pp. 329-345 doi:10.1145/1271.1610
[5] CURTIS, A. R., POWELL, M.J D. REID, J. K. (1974). On the estimation of sparse Jacobian matrices, J. Inst. Math. Appl. 13, pp. I 17-119.
[6] Dickey, T. D. (2003). Emerging ocean observations for interdisciplinary data assimilation systems, J. Mar. Syst. 40-41 pp. 5-48 doi:10.1016/S0924-7963(03)00011-3
[7] ELIZONDO, D., CAPPELAERE, B. FAURE, C. (2002). Automatic versus manual model differentiation to compute sensitivities and solve non-linear inverse problems, Computers and Geoscience 28, pp. 309-326 doi:10.1016/S0098-3004(01)00048-6
[8] ERRICO, R.M. (1997). What is an adjoint model?, Bull. Amer. Met. Soc. 78, pp. 2577-2591.
[9] EVENSEN, G. (1994). Sequential data assimilation with a nonlinear quasi-geostrophic model using monte carlo methods to forecast error statistics, J. Geophys. Res. 99, pp. 10143-10162 doi:10.1029/94JC00572
[10] GIERING, R. KAMINSKI, T. (1998). Recipes for adjoint code construction, ACM Trans. Math. Software 24, pp. 437-474 doi:10.1145/293686.293695
[11] GIERING, R. (2000). Tangent linear and adjoint hiogeochemical models, In: P. KASIBHATLA, M. HEIMANN, P. RAYNER, N. MAHOWAD, R. PRINN and a HARTLEY.Eds., Inverse methods in global biogeochemical cycles, American Geophysical Union, pp. 33-48.
[12] GRIEWANK, A. (2000). Evaluating derivatives, Vol. 19 of Frontiers in Applied Mathematics, Society for Industrial and Applied Mathematics.SIAM, Philadelphia, PA, principles and techniques of algorithmic differentiation.
[13] HOMESCU, C. NAVON, I.M. (2003). Numerical and theoretical considerations for sensitivity calculation of discontinuous flow, Systems and Control Letters 48, pp. 253-260 doi:10.1016/S0167-6911(02)00270-0
[14] HOSSAIN, S. STEIHAUG, T. (2002). Sparsity issues in the computation of Jacobian matrices, Tech. rep., Department of Informatics, University of Bergen, report 223.
[15] HOVLAND, P.. MOHAMMADI. B. Bischof, C. (1998). Automatic differentiation and Navier-Stokes computations, In: Computational methods for optimal design and control.Arlington, VA, 1997, Vol. 24 of Progr. Systems Control Theory, Birkhauser Boston, Boston, MA, pp. 265-284.
[16] MARTINSEN, F., BIEGLER, L. T. Foss, B. A. (2004). A new optimization algorithm with application to nonlinear MPC, J. Proc. Cont. 1.8, pp. 853-865 doi:10.1016/j.jprocont.2004.02.007
[17] NAVON, I.M. (1997). Practical and theoretical aspects of adjoint parameter estimation and identifiahility in meteorology and oceanography, Dyn. Atmos. Oceans 27, 55-79 doi:10.1016/S0377-0265(97)00032-8
[18] NOCEDAL, J. WRIGHT, S.J. (1999). Numerical optimization, Springer-Verlag, New York doi:10.1007/b98874
[19] PARK, S. K., DROEGEMEIER, K. K. BISCHOF, C. H. (1996). Automatic differentiation as a tool for sensitivity analysis of a convective storm in a 3-D cloud model, In: M. BERZ, C. BISCHOF, G. CORLISS and A. GRIEWANK (Eds.), Computational differentiation: Proceedings of the 2nd International Workshop held in Santa Fe. NM. February 12-14,1996. Society for industrial and Applied Mathematics (SIAM), Philadelphia, PA, pp. 205-214, techniques, applications, and tools.
[20] ROBINSON, A. R., LERMUSIAUX, P. F. J. SLOAN HI, N. Q. (1998). Data assimilation, In: K. H. BRINK and A. R. ROBINSON.Fds., The sea, Wiley, NY., pp. 541-594.
[21] SLAGSTAD, D. McCLIMANS, T. (2005). Modelling the ecosystem dynamics of the Barents Sea including the marginal ice zone, I. Physical and chemical oceanography., J. Mar. Syst. Submitted doi:10.1016/j.jmarsys.2005.05.005
[22] THUBURN, J. HAINE, T. W. N. (2001). Adjoints of nonoscillatory advection schemes, J. Comp. Phys. 171, pp. 616-63 doi:10.1006/jcph.2001.6799


BibTeX:
@article{MIC-2005-3-1,
  title={{Application of seeding and automatic differentiation in a large scale ocean circulation model}},
  author={Martinsen, Frode and Slagstad, Dag},
  journal={Modeling, Identification and Control},
  volume={26},
  number={3},
  pages={121--134},
  year={2005},
  doi={10.4173/mic.2005.3.1},
  publisher={Norwegian Society of Automatic Control}
};