Understanding the dynamical mechanism of year-to-year incremental prediction by nonlinear time series prediction theory

Abstract

Previous studies have shown that year-to-year incremental prediction (YIP) can obtain considerable skill in seasonal forecasts. This study analyzes the mathematical definition of YIP and derives its formula in the nonlinear time series prediction (NP) method. It is shown that the two methods are equivalent when the prediction time series is embedded in one-dimensional phase space. Compared to previous NP models, the new one introduces multiple external forcings in the form of year-to-year increments. The year-to-year increments have physical meaning, which is better than the NP model with empirically chosen parameters. The summer rainfall over the middle to lower reaches of the Yangtze River is analyzed to examine the prediction skill of the NP models. Results show that the NP model with year-to-year increments can reach a similar skill as the YIP model. When the embedded number of dimensions is increased to two, more accurate prediction can be obtained. Besides similar results, the NP method has more dynamical meaning, as it is based on the classical reconstruction theory. Moreover, by choosing different embedded dimensions, the NP model can reconstruct the dynamical curve into phase space with more than one dimension, which is an advantage of the NP model. The present study suggests that YIP has a robust dynamical foundation, besides its physical mechanism, and the modified NP model has the potential to increase the operational skill in short-term climate prediction.

摘要

基于年际增量预测（YIP）方法的数学原理，推导得出新的非线性时间序列预测(NP)方法，并从理论上证明了两种预测方法在一定条件下的等效性。以长江中下游地区的夏季降水为例，新的NP方法在使用年际增量作为强迫项时，可以取得与YIP相当的预测效果。而且，通过调整重构维数等参数，能够将预测模型重构于高于一维的相空间中，进而可获得更好的预测效果。研究发现YIP方法除了有物理基础外，还有隐含的动力基础，新NP模型有助于提高短期气候预测的水平。

Keywords:

• Year-to-year incremental prediction
• nonlinear time series prediction
• precipitation
• Yangtze River
• seasonal prediction

关键词:

• 年际增量
• 非线性时间序列
• 降水
• 季节预测

Acknowledgments

Pengfei WANG acknowledges Prof. Geli WANG for providing the FORTRAN code of the nonlinear time series prediction.