In view of the fact that the atmospheric motion is an irreversible process, a memory function which can recall the observation data in the past is introduced, moreover, a special concept of self-memorization of the at...In view of the fact that the atmospheric motion is an irreversible process, a memory function which can recall the observation data in the past is introduced, moreover, a special concept of self-memorization of the atmospheric motion is proposed, and a so-called self-memorization equation of the atmospheric motion has been derived. Based on the self-memorization principle, a numerical model for decadal forecast is established by means of the thermodynamic equation and the precipitation equation. The verification scores of the hindcasts of the model in the period from 1 to 12 years are much higher than that of monthly weather forecasts at present.展开更多
The round-off error introduces uncertainty in the numerical solution. A computational uncertainty principle is explained and validated by using chaotic systems, such as the climatic model,the Rossler and super chaos s...The round-off error introduces uncertainty in the numerical solution. A computational uncertainty principle is explained and validated by using chaotic systems, such as the climatic model,the Rossler and super chaos system. Maximally effective computation time (MECT) and optimal stepsize (OS) are discussed and obtained via an optimal searching method. Under OS in solving nonlinear ordinary differential equations, the self-memorization equations of chaotic systems are set up, thus a new approach to numerical weather forecast is described.展开更多
To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of...To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme.展开更多
基金The study was supported by the National Natural Science Foundation of China under GrantNo.49875025 and National Key Program fo
文摘In view of the fact that the atmospheric motion is an irreversible process, a memory function which can recall the observation data in the past is introduced, moreover, a special concept of self-memorization of the atmospheric motion is proposed, and a so-called self-memorization equation of the atmospheric motion has been derived. Based on the self-memorization principle, a numerical model for decadal forecast is established by means of the thermodynamic equation and the precipitation equation. The verification scores of the hindcasts of the model in the period from 1 to 12 years are much higher than that of monthly weather forecasts at present.
文摘The round-off error introduces uncertainty in the numerical solution. A computational uncertainty principle is explained and validated by using chaotic systems, such as the climatic model,the Rossler and super chaos system. Maximally effective computation time (MECT) and optimal stepsize (OS) are discussed and obtained via an optimal searching method. Under OS in solving nonlinear ordinary differential equations, the self-memorization equations of chaotic systems are set up, thus a new approach to numerical weather forecast is described.
基金The project supported by the National Key Program for Developing Basic Sciences (G1999043408 and G1998040901-1)the National Natural Sciences Foundation of China (40175024 and 40035010)
文摘To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme.
