Abstract
The uncertainties caused by the errors of the initial states and the parameters in the numerical model are investigated. Three problems of predictability in numerical weather and climate prediction are proposed, which are related to the maximum predictable time, the maximum prediction error, and the maximum admissible errors of the initial values and the parameters in the model respectively. The three problems are then formulated into nonlinear optimization problems. Effective approaches to deal with these nonlinear optimization problems are provided. The Lorenz’ model is employed to demonstrate how to use these ideas in dealing with these three problems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Lacarra, J. F., and O. Talagrand, 1988: Short-range evolution of small perturbation in a barotropic model. Tellus, 40A, 81–95.
Li Jianping, Zeng Qingcun, and Chou Jifan, 2000: Computational uncertainty principle in nonlinear ordinary differential equations (I). Science in China, 43, 449–460.
Liu Dong C, and Jorge Nocedal, 1989: On the memory BFGS method for large scale optimization. Mathematical Programming, 45, 503.
Lorenz, E. N., 1965a: Deterministic nonperiodic flow. J. Atmos. Sci., 20, 78–89.
Lorenz, E. N., 1965b: A study of the predictability of a 28-variable atmospheric model. Tellus, 17, 321–333.
Mu Mu, Guo Huan, Wang Jiafeng, and Li Yong, 2000: The impact of nonlinear stability and instability on the validity of the tangent linear model. Advances in Atmospheric Sciences, 17, 375–390.
Mu Mu, 2000:Nonlinear singular vectors and nonlinear singular values. Science in China, 43(D), 375–385.
Mu Mu, and Wang Jiacheng, 2001: Nonlinear fastest growing perturbation and the first kind of predictability. Science in China, 44(D), 1128–1139.
Talagrand, O., 1997: Assimilation of observations, an introduction. J. Meteor. Soc. Japan. 1B, 191–209.
Tanguay, M., P. Bartello, and P. Gauthier, 1995: Four-dimensional data assimilation with a wide range of scales. Tellus, 47A, 974.
Thompson, C. J., 1998: Initial Conditions for optimal growth in a coupled ocean-atmosphere model of ENSO. J. Atmos. Sci., 35, 537–557.
Xue, Y., M. A. Cane, and S. E. Zebika, 1997: Predictability of a coupled model of ENSO using singular vector analysis. Part I: Optimal growth in seasonal background and ENSO cycles. Mon. Wea. Rev., 125, 2043–2073.
Yuan Fan, M. R. Allen, D. L. T. Anderson, and M. A. Balmaseda, 2000: How predictability depends on the nature of uncertainty in initial conditions in a coupled model of ENSO. J. Climate, 13, 3298–3313.
Yuan Y., 1990: On a subproblem of trust region algorithms for constrained optimization. Mathematical Programming, 47, 53–63.
Author information
Authors and Affiliations
Additional information
This work was supported by the National Key Basic Research Project “Research on the Formation Mechanism and Prediction Theory of Severe Synoptic Disasters in China” (No.G1998040910), the National Natural Science Foundation of China (No.40023001 and 40075015), and KZCX2-208 of the Chinese Academy of Sciences.
Rights and permissions
About this article
Cite this article
Mu, M., Wansuo, D. & Jiacheng, W. The predictability problems in numerical weather and climate prediction. Adv. Atmos. Sci. 19, 191–204 (2002). https://doi.org/10.1007/s00376-002-0016-x
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s00376-002-0016-x