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.

Keywords

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