We developed a stochastic model that captures long term nonstationary oscillations (NSOs) within a given variable. The model employs a data-adaptive decomposition method named empirical mode decomposition (EMD). Irregular oscillatory processes in a given variable can be extracted into a finite number of intrinsic mode functions with the EMD approach. A unique data-adaptive algorithm is proposed in the present paper in order to study the future evolution of the NSO components extracted from EMD. To evaluate the model performance, the model is tested with the synthetic data set from Rossler attractor and with global surface temperature anomalies (GSTA) data. The results of the attractor show that the proposed approach provides a good characterization of the NSOs. For GSTA data, the last 30 observations are truncated and compared to the generated data. Then the model is used to predict the evolution of GSTA data over the next 50 years. The results of the case study confirm the power of the EMD approach and the proposed NSO resampling (NSOR) method as well as their potential for the study of climate variables.

Reproducing nonstationary oscillation (NSO) processes in a stochastic time series model is a difficult task because of the complexity of the nonstationary behaviors. In the current study, a novel stochastic simulation technique that reproduces the NSO processes embedded in hydroclimatic data series is presented. The proposed model reproduces NSO processes by utilizing empirical mode decomposition (EMD) and nonparametric simulation techniques (i.e., k-nearestneighbor resampling and block bootstrapping). The model was first tested with synthetic data sets from trigonometric functions and the Rossler system. The North Atlantic Oscillation (NAO) index was then examined as a real case study. This NAO index was then employed as an exogenous variable for the stochastic simulation of streamflows at the Romaine River in the province of Quebec, Canada. The results of the application to the synthetic data sets and the real-world case studies indicate that the proposed model preserves well the NSO processes along with the key statistical characteristics of the observations. It was concluded that the proposed model possesses a reasonable simulation capacity and a high potential as a stochastic model, especially for hydroclimatic data sets that embed NSO processes.

Climate indices generally contain nonstationary oscillations (NSO). Not much study has been done in the literature to reproduce the NSO processes through a stochastic time series model. Therefore, we proposed a model that reproduces the NSO of climate indices employing EMD- NSO resampling (NSOR) technique. The proposed simulation model was tested with three climate indices (i.e. AO, ENSO, and PDO) for the annual and winter (January, February, and March - JFM) datasets. The results of the proposed model are compared with the ones of the Contemporaneous Shifting Mean and Contemporaneous Autoregressive Moving Average (CSM-CARMA) model. One set of the 5000 year records is simulated from each model. The results (ex. Figure 1) indicated that the proposed model is superior to the CSM-CARMA model for reproducing the NSO process while the other basic statistics are comparatively well preserved in both models.