Prediction of climate nonstationary oscillation processes with empirical mode decomposition

[1] Long-term nonstationary oscillations (NSOs) are commonly observed in climatological data series such as global surface temperature anomalies (GSTA) and low-frequency climate oscillation indices. In this work, we present a stochastic model that captures 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 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.

[1]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[2]  Keinosuke Fukunaga,et al.  Introduction to Statistical Pattern Recognition , 1972 .

[3]  H. Akaike.  A new look at the statistical model identification , 1974 .

[4]  O. Rössler.  An equation for continuous chaos , 1976 .

[5]  Jose D. Salas,et al.  Shifting level modelling of hydrologic series , 1980 .

[6]  H. Bozdogan.  Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions , 1987 .

[7]  M. Ghil,et al.  Interdecadal oscillations and the warming trend in global temperature time series , 1991, Nature.

[8]  William H. Press,et al.  Numerical Recipes in C, 2nd Edition , 1992 .

[9]  Robert Tibshirani,et al.  An Introduction to the Bootstrap , 1994 .

[10]  Low-frequency oscillation , 1994, Nature.

[11]  Michael E. Schlesinger,et al.  An oscillation in the global climate system of period 65–70 years , 1994, Nature.

[12]  M. Schlesinger,et al.  Low-frequency oscillation , 1994, Nature.

[13]  P. Hall,et al.  On blocking rules for the bootstrap with dependent data , 1995 .

[14]  Otto E. Rössler.  An introduction to chaos , 1995, Int. J. Intell. Syst..

[15]  R. Vogel,et al.  The moving blocks bootstrap versus parametric time series models , 1996 .

[16]  J. Elsner,et al.  Singular Spectrum Analysis: A New Tool in Time Series Analysis , 1996 .

[17]  Upmanu Lall,et al.  A Nearest Neighbor Bootstrap For Resampling Hydrologic Time Series , 1996 .

[18]  Darrell G. Fontane,et al.  INDEXED SEQUENTIAL HYDROLOGIC MODELING FOR HYDROPOWER CAPACITY ESTIMATION 1 , 1997 .

[19]  Daniel S. Wilks,et al.  Resampling Hypothesis Tests for Autocorrelated Fields , 1997 .

[20]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[21]  C. Torrence,et al.  A Practical Guide to Wavelet Analysis. , 1998 .

[22]  Nick Rayner,et al.  Adjusting for sampling density in grid box land and ocean surface temperature time series , 2001 .

[23]  Leonard J. Pietrafesa,et al.  Interannual and decadal variability of landfalling tropical cyclones in the southeast coastal states of the united states , 2002 .

[24]  J. Salas,et al.  Modeling the Dynamics of Long-Term Variability of Hydroclimatic Processes , 2003 .

[25]  T. Kuznetsova,et al.  Climate oscillations and abrupt changes in C14 data , 2004 .

[26]  N. Huang,et al.  A study of the characteristics of white noise using the empirical mode decomposition method , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[27]  Yonghong Li,et al.  Improved Methods for Analysis of Decadal Elevation-Change Time Series Over Antarctica , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[28]  M. Pagani,et al.  Quasi-periodic climate teleconnections between northern and southern Europe during the 17th–20th centuries , 2006 .

[29]  Zhaohua Wu,et al.  On the trend, detrending, and variability of nonlinear and nonstationary time series , 2007, Proceedings of the National Academy of Sciences.

[30]  Sun Xian,et al.  Multi-scale analysis of global temperature changes and trend of a drop in temperature in the next 20 years , 2007 .

[31]  Ahsan Kareem,et al.  Nonlinear Signal Analysis: Time-Frequency Perspectives , 2007 .

[32]  Murray C. Peel,et al.  A New Approach to Stochastically Generating Six-Monthly Rainfall Sequences Based on Empirical Mode Decomposition , 2008 .

[33]  Norden E. Huang,et al.  A review on Hilbert‐Huang transform: Method and its applications to geophysical studies , 2008 .

[34]  Taesam Lee.  Stochastic simulation of hydrologic data based on nonparametric approaches , 2008 .

[35]  G.G.S Pegram,et al.  Empirical mode decomposition using rational splines: an application to rainfall time series , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[36]  Murray C. Peel,et al.  Assessing the performance of rational spline-based empirical mode decomposition using a global annual precipitation dataset , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[37]  Norden E. Huang,et al.  Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method , 2009, Adv. Data Sci. Adapt. Anal..

[38]  Norden E. Huang,et al.  STATISTICAL SIGNIFICANCE TEST OF INTRINSIC MODE FUNCTIONS , 2010 .

[39]  Taha B. M. J. Ouarda,et al.  Long‐term prediction of precipitation and hydrologic extremes with nonstationary oscillation processes , 2010 .