Abstract
Conditional nonlinear optimal perturbation (CNOP) is the initial perturbation that has the largest nonlinear evolution at prediction time for initial perturbations satisfying certain physical constraint condition. It does not only represent the optimal precursor of certain weather or climate event, but also stand for the initial error which has largest effect on the prediction uncertainties at the prediction time. In sensitivity and stability analyses of fluid motion, CNOP also describes the most unstable (or most sensitive) mode. CNOP has been used to estimate the upper bound of the prediction error. These physical characteristics of CNOP are examined by applying respectively them to ENSO predictability studies and ocean’s thermohaline circulation (THC) sensitivity analysis. In ENSO predictability studies, CNOP, rather than linear singular vector (LSV), represents the initial patterns that evolve into ENSO events most potentially, i.e. the optimal precursors for ENSO events. When initial perturbation is considered to be the initial error of ENSO, CNOP plays the role of the initial error that has largest effect on the prediction of ENSO. CNOP also derives the upper bound of prediction error of ENSO events. In the THC sensitivity and stability studies, by calculating the CNOP (most unstable perturbation) of THC, it is found that there is an asymmetric nonlinear response of ocean’s THC to the finite amplitude perturbations. Finally, attention is paid to the feasibility of CNOP in more complicated model. It is shown that in a model with higher dimensions, CNOP can be computed successfully. The corresponding optimization algorithm is also shown to be efficient.
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References
Lorenz, E. N., A study of the predictability of a 28-variable atmospheric model, Tellus, 1965, 17: 321–333.
Thompson, C. J., Initial conditions for optimal growth in a coupled ocean-atmosphere model of ENSO, J. Atmos. Sci., 1998, 55: 537–557.
Samelson, R. G., Tziperman E., Instability of the chaotic ENSO: The growth-phase predictability barrier, J. Atmos.Sci., 2001, 58: 3613–3625.
Tziperman, E., Ioannou P. J., Transient growth and optimal excitation of thermohaline variability, J. Phys.Oceanogr., 2002, 32: 3427–3435.
Barkmeijer, J., Constructing fast-growing perturbations for the nonlinear regime, J. Atmos. Sci., 1996, 53: 2838–2851.
Oortwijin, J., Barkmeijer J., Perturbations that optimally trigger weather regimes, J. Atmos. Sci., 1995, 52: 3932–3944.
Mu Mu, Nonlinear singualr vectors and nonlinear singular values, Science in China, Ser.D, 2000, 43(4), 375–385.
Mu Mu, Wang Jiacheng, Nonlinear fastest growing perturbation and the first kind of predictability, Science in China, Ser. D, 2001, 44(12): 1128–1139.
Mu Mu, Duan Wansuo, Wang, B., Conditional nonlinear optimal perturbation and its applications, Nonlinear Processes in Geophysics, 2003, 10: 493–501.
Mu Mu, Duan Wansuo, A new approach to studying ENSO predictability: conditional nonlinear optimal perturbation, Chinese Sci. Bull., 2003, 48(10): 1045–1047.
Duan Wansuo, Mu Mu, Wang, B., Conditional nonlinear optimal perturbation as the optimal precursors for El Nino-Southern oscillation events, J.Geophy. Res., 2004, 109: D23105, doi:10.1029/2004JD004756.
Mu Mu, Sun Liang, Henk, D. A., The sensitivity and stability of the ocean’s thermocline circulation to finite amplitude freshwater perturbations, J. Phys. Oceanogr., 2004, 34: 2305–2315.
Powell, M. J. D., VMCWD: A FORTRAN subroutine for constrained optimization, DAMTP Report 1982/NA4, University of Cambridge, England, 1982.
Gill, P. E., Murray, W., Saunders M. A., SNOPT: An SQP algorithm for large-scale constrained optimization, Numerical Analysis Report 97-1, Department of Mathematics, University of California, San Diego, La Jolla, CA, 1997.
Mu Mu, Duan Wansuo, Wang Jiacheng, The predictability problems in numerical weather and climate prediction, Adv. Atmos. Sci., 2002, 19(2): 191–204.
Xue, Y., Cane M. A., Zebiak S. E., Predictability of a coupled model of ENSO using singular vector analysis. Part I: optimal growth in seasonal background and ENSO cycles, Mon. Wea. Rev., 1997, 125: 2043–2056.
Xue, Y., Cane M. A., Zebiak S. E. et al., Predictability of a coupled model of ENSO using singular vector analysis. Part II: optimal growth and forecast skill, Mon. Wea. Rev., 1997, 125: 2057–2073.
Chen, D., Cane M. A., Kaplan, A. et al., Predictability of El Niño over the past 148 years, Nature, 2004, 128: 733–736.
Moore, A. M., Kleeman R., The dynamics of error growth and predictability in a coupled model of ENSO, Q. J. R. Meteorol. Soc., 1996, 122: 1405–1446.
Wang, B., Fang Z., Chaotic oscillation of tropical climate: A dynamic system theory for ENSO, J. Atmos. Sci., 1996, 53: 2786–2802.
Webster P. J., Yang S., Monsoon and ENSO: Selectively interactive systems. Q.J.R. Meterorol. Soc., 1992, 118: 877–926.
Knutti, R. Stocker T. F., Limited predictability of future thermohaline circulation to an instability threshold, J. Climate, 2002, 15: 179–186.
Stommel, H., Thermohaline convection with two stable regimes of flow, Tellus, 1961, 2: 230–244.
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Mu, M., Duan, W. Conditional nonlinear optimal perturbation and its applications to the studies of weather and climate predictability. Chin. Sci. Bull. 50, 2401–2407 (2005). https://doi.org/10.1007/BF03183626
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DOI: https://doi.org/10.1007/BF03183626