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Volume 17 Issue 3

Sep.  2000

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Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 2000 >  17(3): 433-444

A Simple Method of Calculating the Optimal Step Size in 4DVAR Technique

  • 1.

    Laboratory of Meso-scale Severe Weather, Nanjing University, Nanjing, 210093,Laboratory of Meso-scale Severe Weather, Nanjing University, Nanjing, 210093,Laboratory of Meso-scale Severe Weather, Nanjing University, Nanjing, 210093,Laboratory of Meso-scale Severe Weather, Nanjing University, Nanjing, 210093


doi: 10.1007/s00376-000-0034-5

  • In four-dimensional variational data assimilation (4DVAR) technology, how to calculate the optimal step size is always a very important and indeed difficult task. It is directly related to the computational effi-ciency. In this research, a new method is proposed to calculate the optimal step size more effectively. Both nonlinear one-dimensional advection equation and two-dimensional inertial wave equation are used to test and compare the influence of different methods of the optimal step size calculations on the iteration steps, as well as the simulation results of 4DVAR processes. It is in evidence that the different methods have different influences. The calculating method is very important to determining whether the iteration is convergent or not and whether the convergence rate is large or small. If the calculating method of optimal step size is prop-erly determined as demonstrated in this paper, then it can greatly enlarge the convergence rate and further greatly decrease the iteration steps. This research is meaningful since it not only makes an important im-provement on 4DVAR theory, but also has useful practical application in improving the computational effi-ciency and saving the computational time.
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    • Manuscript History

    Manuscript received: 10 September 2000
    Manuscript revised: 10 September 2000
    通讯作者: 陈斌, bchen63@163.com
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      沈阳化工大学材料科学与工程学院 沈阳 110142

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    A Simple Method of Calculating the Optimal Step Size in 4DVAR Technique

    • 1. Laboratory of Meso-scale Severe Weather, Nanjing University, Nanjing, 210093,Laboratory of Meso-scale Severe Weather, Nanjing University, Nanjing, 210093,Laboratory of Meso-scale Severe Weather, Nanjing University, Nanjing, 210093,Laboratory of Meso-scale Severe Weather, Nanjing University, Nanjing, 210093
    • Manuscript received: 2000-09-10
    • Manuscript revised: 2000-09-10

    Abstract: In four-dimensional variational data assimilation (4DVAR) technology, how to calculate the optimal step size is always a very important and indeed difficult task. It is directly related to the computational effi-ciency. In this research, a new method is proposed to calculate the optimal step size more effectively. Both nonlinear one-dimensional advection equation and two-dimensional inertial wave equation are used to test and compare the influence of different methods of the optimal step size calculations on the iteration steps, as well as the simulation results of 4DVAR processes. It is in evidence that the different methods have different influences. The calculating method is very important to determining whether the iteration is convergent or not and whether the convergence rate is large or small. If the calculating method of optimal step size is prop-erly determined as demonstrated in this paper, then it can greatly enlarge the convergence rate and further greatly decrease the iteration steps. This research is meaningful since it not only makes an important im-provement on 4DVAR theory, but also has useful practical application in improving the computational effi-ciency and saving the computational time.

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