混沌时间序列可预报时间长度分析

摘要：以经典混沌序列——Henon映射序列为例，对不同长度、不同噪声水平的序列进行了预报试验．结果表明：(a)纯净序列，序列越长，预报精度越高，同时预报精度衰减速度随之减慢，并且，当序列足够长时，即使较长预报步长的多步预报，仍可取得相当高的预报精度；(b)含噪声序列，其预报精度随步长的增加迅速地呈指数衰减，并且，序列长度基本上不会对预报时间长度产生影响，但噪声水平对可预报时间长度有一定影响，噪声水平越高，可预报时间长度越短．因此，不明确可预报的标准、不考虑序列长度、噪声水平等因素的影响而简单地以最大Lyapunov指数的倒数定义最大可预报时间长度，是不可取的．同样，根据最大Lyapunov指数推断水文过程的可预报时间长度也是不合适的．

Analysis of length of predictable time of chaotic time series

Prediction experiments were performed on a classic chaotic time series, the Henon mapping series, with different lengths and noise levels. It is shown that: (a) for the noise-free series, the accuracy increases with the size of the series, and the longer the series, the slower the accuracy of prediction decays, besides, the accuracy of multi-step prediction is fairly high if the series is long enough; (b) for the noisy series, the accuracy decays exponentially with the increase of the step length, and the size of the series almost has no influence on the length of the predictable time, while the noise level is of certain influence on the length of the predictable time: the higher the noise level, the shorter the length of predictable time. Therefore it is unreasonable to take the reciprocal of the maximum Lyapunov exponent as the maximum length of predictable time without clear definition of the criterion of prediction and without consideration of the influences of the size and noise level of the series, and it is meaningless to deduce the length of predictable time of hydrological processes according to the maximum Lyapunov exponent.