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Miller, Robert N.; Carter, Everett F.; Blue, Sally T. (2011)
Publisher: Co-Action Publishing
Journal: Tellus A
Languages: English
Types: Article
Subjects:
With very few exceptions, data assimilation methods which have been used or proposed foruse with ocean models have been based on some assumption of linearity or near-linearity. Thegreat majority of these schemes have at their root some least-squares assumption. While onecan always perform least-squares analysis on any problem, direct application of least squaresmay not yield satisfactory results in cases in which the underlying distributions are significantlynon-Gaussian. In many cases in which the behavior of the system is governed by intrinsicallynonlinear dynamics, distributions of solutions which are initially Gaussian will not remain soas the system evolves. The presence of noise is an additional and inevitable complicating factor.Besides the imperfections in our models which result from physical or computational simplifyingassumptions, there is uncertainty in forcing fields such as wind stress and heat flux which willremain with us for the foreseeable future. The real world is a noisy place, and the effects ofnoise upon highly nonlinear systems can be complex. We therefore consider the problem ofdata assimilation into systems modeled as nonlinear stochastic differential equations. When themodels are described in this way, the general assimilation problem becomes that of estimatingthe probability density function of the system conditioned on the observations. The quantitywe choose as the solution to the problem can be a mean, a median, a mode, or some otherstatistic. In the fully general formulation, no assumptions about moments or near-linearity arerequired. We present a series of simulation experiments in which we demonstrate assimilationof data into simple nonlinear models in which least-squares methods such as the (Extended)Kalman filter or the weak-constraint variational methods will not perform well. We illustratethe basic method with three examples: a simple one-dimensional nonlinear stochastic differentialequation, the well known three-dimensional Lorenz model and a nonlinear quasigeostrophicchannel model. Comparisons to the extended Kalman filter and an extension to the extendedKalman filter are presented.DOI: 10.1034/j.1600-0870.1999.t01-2-00002.x
  • The results below are discovered through our pilot algorithms. Let us know how we are doing!

    • Bennett, A. F. and Thorburn, M. A. 1992. The generalized inverse of a nonlinear quasigeostrophic ocean circulation model. J. Phys. Oceanogr. 22, 213-230.
    • Bennett, A. F., Leslie, L. M., Hagelberg, C. R. and Powers, P. E. 1993. Tropical cyclone prediction using a barotropic model initialized by a generalized inverse method. Mon. Wea. Rev. 121, 1714-1729.
    • Bergman, L. A., Wojtkiewicz, S. F., Johnson, E. A. and Spencer, B. F. 1996. A robust numerical solution of the Fokker-Planck equation for second order dynamical systems under parametric and external white noise excitation. Fields Inst. Comm. 9, 23-37.
    • Bergman, L. A. and Spencer, B. F. Jr. 1992. Robust numerical solution of the transient Fokker-Planck equation for nonlinear dynamical systems. IUTAM Symposium, Turin. N. Bellomo and F. Casciati, eds., Springer-Verlag, Berlin, Heidelberg, 49-59.
    • Bierman, G. J. 1977. Factorization methods for discrete sequential estimation. Academic Press, New York. 241 pp.
    • Bouttier, F. 1994. A dynamical estimation of forecast error covariances in an assimilation system. Mon. Wea. Rev. 122, 2376-2390.
    • Box, G. E. P and Muller, M. E. 1958. A note on the generation of random normal deviates. Annals Math. Stat. 29, 610-611.
    • Budgell, W. P. 1986. Nonlinear data assimilation for shallow water equations in branched channels. J. Geophys. Res. 91, 10633-10644.
    • Chang, J. S. and Cooper, G. 1970. A practical diVerence scheme for Fokker-Planck equations. J. Comput. Phys. 6, 1-16.
    • Charney, J. G. and Devore, J. G. 1979. Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci. 36, 1205-1216.
    • Courtier, P. 1997. Dual formulation of four-dimensional variational assimilation. Q. J. R. Meteorol. Soc. 123, 2449-2461.
    • Courtier, P., Derber, J., Errico, R., Louis, J.-F. and Vukicevic, T. 1993. Important literature on the use of adjoint, variational methods and the Kalman filter in meteorology. T ellus 45A, 342-357.
    • Courtier, P., The´paut, J.-N. and Hollingsworth, A. 1994. A strategy for operational implementation of 4D-Var, using an incremental approach. Q. J. R. Meteorol. Soc. 120, 1367-1387.
    • Evensen, G. 1992. Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model. J. Geophys. Res. 97, 17905-17924.
    • Evensen, G. 1994. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte-Carlo methods to forecast error statistics. J. Geophys. Res. 99, 10143-10162.
    • Evensen, G. and Fario, N. 1997. Solving for the generalized inverse of the Lorenz model. J. Meteor. Soc. Japan 75, 229-243.
    • Fletcher, C. A. J. 1988. Computational techniques for fluid dynamics, vol I. Springer Series in Computational Physics. Springer-Verlag, Berlin, Heidelberg. 409 pp.
    • Florchinger, P. and LeGland, F. 1990. Time-discretization of the Zakai equation for diVusion processes observed in correlated noise. 9th Conference on Analysis and optimization, A. Bensoussan and J. L. Lions, eds. Lecture Notes in Control and Information Sciences 144, Springer-Verlag.
    • Gardiner, C. W. 1983. Handbook of stochastic methods, for physics, chemistry, and the natural sciences. Springer-Verlag, Berlin, 442 pp.
    • Gauthier, P., Courtier, P. and Moll, P. 1993. Assimilation of simulated wind lidar data with a Kalman filter. Mon. Wea. Rev. 121, 1803-1820.
    • Geist, G. A, and Sunderam, V. S. 1991. T he PV M System: supercomputing level concurrent computations on a heterogeneous network of workstations. 6th Distributed Memory Computing Conference Proceedings, IEEE, Portland, OR, April/May 1991, 258-261.
    • Ghil, M. and Childress, S. 1987. T opics in geophysical fluid dynamics: atmospheric dynamics, dynamo theory and climate dynamics. Springer-Verlag, 485 pp.
    • Gravel, S. and Derome, J. 1993. A study of multiple equilibria in a b-plane and a hemispheric model of a barotropic atmosphere. T ellus 45A, 81-98.
    • It oˆ, K. 1951. On stochastic diVerential equations. American Mathematical Society Memoirs #4, 51 pp.
    • Jazwinski, A. H. 1970. Stochastic processes and filtering theory. Academic Press, New York, 376 pp.
    • Jin, F.-F. and Ghil, M. 1990. Intraseasonal oscillations in the extratropics: Hopf bifurcations and topographic instabilities. J. Atmos. Sci. 47, 3007-3022.
    • Kirkpatrick, S. and Stoll, E. 1981. A very fast ShiftRegister Sequence Random Number generator. J. Comput. Phys. 40, 517-526.
    • Kloeden, P. and Platen, E. 1992. Numerical solution of stochastic diVerential equations. Springer-Verlag, Berlin. 519 pp.
    • Kushner, H. J. 1962. On the diVerential equations satisfied by conditional probability densities of Markov processes, with applications. SIAM J. Control, Series A 2, 106-119.
    • Lacarra, J. F. and Talagrand, O. 1988. Short-range evolution of small perturbations in a barotropic model. T ellus 40A, 81-95.
    • Legras, B. and Ghil, M. 1985. Persistent anomalies, blocking and variations in atmospheric predictability. J. Atmos. Sci. 42, 433-471.
    • Lorenc, A. C. and Hammon, O. 1988. Objective quality control of observations using Bayesian methods - theory and a practical implementation. Q. J. R. Meteorol. Soc. 114, 515-543.
    • Lorenz, E. N. 1963. Deterministic nonperiodic flow. J. Atmos. Sci. 20, 448-464.
    • Miller, R. N. 1998. Introduction to the Kalman filter. In: Proceedings of the ECMW F Seminar on Data assimilation. European Centre for Medium Range Weather Forecasting, Shinfield Park, Reading, RG2 9AX UK, 9-11 September, 1996, pp. 47-59.
    • Miller, R. N., Ghil, M. and Gauthiez, P. 1994. Advanced data assimilation in strongly nonlinear dynamical systems. J. Atmos. Sci. 51, 1037-1056.
    • Milshtein, G. N. 1978. A method of second-order accuracy integration of stochastic diVerential equations. T heory Prob. Appl. 23, 396-401.
    • Palmer, T. N. 1993. Extended range atmospheric prediction and the Lorenz model. Bull. Amer. Met. Soc. 74, 49-65.
    • Pedlosky, J. 1981. Resonant topographic waves in barotropic and baroclinic flows. J. Atmos. Sci. 38, 2626-2641.
    • Press, W. H. and Teukolsky, S. A. 1989. Quasi- (that is, sub-) random numbers. Computers in Physics 3, 76-79.
    • Risken, H. 1984. T he Fokker-Planck equation. SpringerVerlag, New York, 454 pp.
    • Rozovskii, B. L. 1990. Stochastic evolution systems: linear theory and applications to nonlinear filtering. Kluwer Academic, 315 pp.
    • Silverman, B. W. 1986. Density estimation for statistics and data analysis. Chapman and Hall, London. 175 pp.
    • Spencer, B. F. Jr. and Bergman, L. A. 1993. On the numerical solution of the Fokker-Planck equation for nonlinear stochastic systems. Nonlinear Dynamics 4, 357-372.
    • Stratonovich, R. L. 1966. A new form of representing stochastic integrals and equations. SIAM J. Control 4, 362-371.
    • Strong, C., Jin, F.-F. and Ghil, M. 1995. Intraseasonal oscillations in a barotropic model with annual cycle, and their predictability. J. Atmos. Sci. 52, 2627-2642.
    • Wojtkiewicz, S. F., Bergman, L. A. and Spencer, B. F. 1995. Numerical solution of some three-state random vibration problems. DE-Vol 84-1, 1995 Design Engineering T echnical Conferences, Volume 3, Part A, ASME 1995, 939-947.
    • Zakai, M. 1969. On the optimal filtering of diVusion processes. Z. Wahrsch. verw. Gebiete 11, 230-243.
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