Multi-scale analysis of teleconnection indices: climate noise and nonlinear trend analysis

Abstract. The multi-scale nature and climate noise properties of teleconnection indices are examined by using the Empirical Mode Decomposition (EMD) procedure. The EMD procedure allows for the analysis of non-stationary time series to extract physically meaningful intrinsic mode functions (IMF) and nonlinear trends. The climatologically relevant monthly mean teleconnection indices of the North Atlantic Oscillation (NAO), the North Pacific index (NP) and the Southern Annular Mode (SAM) are analyzed. The significance of IMFs and trends are tested against the null hypothesis of climate noise. The analysis of surrogate monthly mean time series from a red noise process shows that the EMD procedure is effectively a dyadic filter bank and the IMFs (except the first IMF) are nearly Gaussian distributed. The distribution of the variance contained in IMFs of an ensemble of AR(1) simulations is nearly χ2 distributed. To test the statistical significance of the IMFs of the teleconnection indices and their nonlinear trends we utilize an ensemble of corresponding monthly averaged AR(1) processes, which we refer to as climate noise. Our results indicate that most of the interannual and decadal variability of the analysed teleconnection indices cannot be distinguished from climate noise. The NP and SAM indices have significant nonlinear trends, while the NAO has no significant trend when tested against a climate noise hypothesis.

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Prediction of Sea Level Nonlinear Trends around Shandong Peninsula from Satellite Altimetry

Sensors ◽

10.3390/s19214770 ◽

2019 ◽

Vol 19 (21) ◽

pp. 4770

Author(s):

Jian Zhao ◽

Ruiyang Cai ◽

Yanguo Fan

Keyword(s):

Sea Level ◽

Satellite Altimetry ◽

Prediction Models ◽

Stationary Time Series ◽

Intrinsic Mode Functions ◽

Shandong Peninsula ◽

Rbf Network ◽

Multi Scale ◽

Nonlinear Trends ◽

Prediction Approach

Sea level change is a key indicator of climate change, and the prediction of sea level rise is one of most important scientific issues. In this paper, the gridded sea level anomaly (SLA) data from satellite altimetry are used to analyze the sea level variations around Shandong Peninsula from 1993 to 2016. Based on the Complete Ensemble Empirical Mode Decomposition (CEEMD) method and Radial Basis Function (RBF) network, the paper proposes an improved sea level multi-scale prediction approach, namely, CEEMD-RBF combined model. Firstly, the multi-scale frequency oscillatory modes (intrinsic mode functions (IMFs)) representing different oceanic processes are extracted by CEEMD from the highest frequency to the lowest frequency oscillating mode. Secondly, RBF network is used to establish prediction models for various IMF components to predict their future trends, and each IMF is used as an input factor of the RBF network separately. Finally, the prediction results of each IMF component with RBF network are reconstructed to obtain the final predictions of sea level anomalies. The results shows that CEEMD is particularly suitable for analyzing nonlinear and non-stationary time series and RBF network is applicable for regional sea level prediction at different scales.

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Search for the 531 day-period wobble signal in the polar motion based on EEMD

Nonlinear Processes in Geophysics Discussions ◽

10.5194/npgd-2-647-2015 ◽

2015 ◽

Vol 2 (2) ◽

pp. 647-673 ◽

Cited By ~ 1

Author(s):

H. Ding ◽

W. B. Shen

Keyword(s):

Time Series ◽

Polar Motion ◽

Superconducting Gravimeter ◽

Ensemble Empirical Mode Decomposition ◽

Stationary Time Series ◽

Analysis Method ◽

Intrinsic Mode Functions ◽

Conventional Analysis ◽

Mode Decomposition ◽

Empirical Mode Decomposition Method

Abstract. In this study, we use a nonlinear and non-stationary time series analysis method, the ensemble empirical mode decomposition method (EEMD), to analyze the polar motion (PM) time series (EOP C04 series from 1962 to 2013) to find a 531 day-period wobble (531 dW) signal. The 531 dW signal has been found in the early PM seires (1962–1977) while cannot be found in the recent PM seires (1978–2013) using conventional analysis approaches. By the virtue of the demodulation feature of EEMD, the 531 dW can be confirmed to be present in PM based on the differences of the amplitudes and phases between different intrinsic mode functions. Results from three sub-series divided from the EOP C04 series show that the period of the 531 dW is subject to variations, in the range of 530.9–524 d, and its amplitude is also time-dependent (about 2–11 mas). Synthetic tests are carried out to explain why the 531 dW can only be observed in recent 30-years PM time series after using EEMD. The 531 dW is also detected in two longest available superconducting gravimeter (SG) records, which further confirms the presence of the 531 dW. The confirmation of 531 dW existence could be significant in establishing a more reasonable Earth rotation model and may effectively contribute to the prediction of the PM and its mechanism interpretation.

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Search for the 531-day-period wobble signal in the polar motion based on EEMD

Nonlinear Processes in Geophysics ◽

10.5194/npg-22-473-2015 ◽

2015 ◽

Vol 22 (4) ◽

pp. 473-484 ◽

Cited By ~ 1

Author(s):

H. Ding ◽

W. Shen

Keyword(s):

Time Series ◽

Polar Motion ◽

Superconducting Gravimeter ◽

Ensemble Empirical Mode Decomposition ◽

Stationary Time Series ◽

Analysis Method ◽

Intrinsic Mode Functions ◽

Conventional Analysis ◽

Mode Decomposition ◽

Empirical Mode Decomposition Method

Abstract. In this study, we use a nonlinear and non-stationary time series analysis method, the ensemble empirical mode decomposition method (EEMD), to analyze the polar motion (PM) time series (EOP C04 series from 1962 to 2013) to find a 531-day-period wobble (531 dW) signal. The 531 dW signal has been found in the early PM series (1962–1977), but cannot be found in the recent PM series (1978–2013) using conventional analysis approaches. By virtue of the demodulation feature of EEMD, the 531 dW can be confirmed to be present in PM based on the differences of the amplitudes and phases between different intrinsic mode functions. Results from three sub-series divided from the EOP C04 series show that the period of the 531 dW is subject to variations, in the range of 530.9–524 days, and its amplitude is also time-dependent (about 2–11 mas). Synthetic tests are carried out to explain why the 531 dW can only be observed in recent 30-year PM time series after using EEMD. The 531 dW is also detected in the two longest available superconducting gravimeter (SG) records, which further confirms the presence of the 531 dW. The confirmation of the 531 dW existence could be significant in establishing a more reasonable Earth rotation model and may effectively contribute to the prediction of the PM and its mechanism interpretation.

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Nonlinear Trends, Long-Range Dependence, and Climate Noise Properties of Surface Temperature

Journal of Climate ◽

10.1175/jcli-d-11-00293.1 ◽

2012 ◽

Vol 25 (12) ◽

pp. 4172-4183 ◽

Cited By ~ 104

Author(s):

Christian Franzke

Keyword(s):

Time Series ◽

Climate Variability ◽

Null Model ◽

Warming Trend ◽

Temperature Time Series ◽

Trend Detection ◽

Detection Methods ◽

Nonlinear Trends ◽

Temperature Time ◽

Climate Noise

Abstract This study investigates the significance of trends of four temperature time series—Central England Temperature (CET), Stockholm, Faraday-Vernadsky, and Alert. First the robustness and accuracy of various trend detection methods are examined: ordinary least squares, robust and generalized linear model regression, Ensemble Empirical Mode Decomposition (EEMD), and wavelets. It is found in tests with surrogate data that these trend detection methods are robust for nonlinear trends, superposed autocorrelated fluctuations, and non-Gaussian fluctuations. An analysis of the four temperature time series reveals evidence of long-range dependence (LRD) and nonlinear warming trends. The significance of these trends is tested against climate noise. Three different methods are used to generate climate noise: (i) a short-range-dependent autoregressive process of first order [AR(1)], (ii) an LRD model, and (iii) phase scrambling. It is found that the ability to distinguish the observed warming trend from stochastic trends depends on the model representing the background climate variability. Strong evidence is found of a significant warming trend at Faraday-Vernadsky that cannot be explained by any of the three null models. The authors find moderate evidence of warming trends for the Stockholm and CET time series that are significant against AR(1) and phase scrambling but not the LRD model. This suggests that the degree of significance of climate trends depends on the null model used to represent intrinsic climate variability. This study highlights that in statistical trend tests, more than just one simple null model of intrinsic climate variability should be used. This allows one to better gauge the degree of confidence to have in the significance of trends.

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Monthly Streamflow Forecasting Using EEMD-Lasso-DBN Method Based on Multi-Scale Predictors Selection

Water ◽

10.3390/w10101486 ◽

2018 ◽

Vol 10 (10) ◽

pp. 1486 ◽

Cited By ~ 7

Author(s):

Haibo Chu ◽

Jiahua Wei ◽

Jun Qiu

Keyword(s):

Time Series ◽

Ensemble Empirical Mode Decomposition ◽

Intrinsic Mode Functions ◽

Streamflow Forecasting ◽

Multi Scale ◽

Mode Decomposition ◽

Monthly Streamflow ◽

Residual Series ◽

The Usa ◽

Monthly Streamflow Forecasting

For the inherent characteristics of a raw streamflow times series and the complicated relationship between multi-scale predictors and streamflow, monthly streamflow forecasting is very difficult. In this paper, an method was proposed integrating the ensemble empirical mode decomposition (EEMD), least absolute shrinkage and selection operator (Lasso) with deep belief networks (DBN) for forecasting monthly streamflow time series, which is EEMD-Lasso-DBN (ELD) method. To develop the ELD model, the raw streamflow time series was resolved into different elements, including intrinsic mode functions (IMFs) and residue series, using the EEMD technique. The predictors of each IMF element and residue were screened using the Lasso technique from a large number of candidate predictors, respectively. Then, the DBN models were built to simulate the complex relationship between the resolved elements and the selected predictors, respectively. The predicted results of the IMFs and residual series were assembled as an ensemble forecast for the raw streamflow time series and were compared with the other models. The monthly streamflow series from Tennessee, in the USA, were investigated using the ELD method. It was found that each IMF has different characteristics and physical meaning, corresponding to different predictors. The proposed ELD model can significantly improve the accuracy of monthly streamflow forecasting.

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Long-Range Dependence and Climate Noise Characteristics of Antarctic Temperature Data

Journal of Climate ◽

10.1175/2010jcli3654.1 ◽

2010 ◽

Vol 23 (22) ◽

pp. 6074-6081 ◽

Cited By ~ 69

Author(s):

Christian Franzke

Keyword(s):

Time Series ◽

Long Range ◽

Short Range ◽

Null Model ◽

Null Models ◽

Environmental Research ◽

Noise Characteristics ◽

Dependent Process ◽

Nonlinear Trends ◽

Climate Noise

Abstract This study examines the long-range dependency, climate noise characteristics, and nonlinear temperature trends of eight Antarctic stations from the Reference Antarctic Data for Environmental Research (READER) dataset. Evidence is shown that Antarctic temperatures are long-range dependent. To identify possible nonlinear trends, the ensemble empirical mode decomposition (EEMD) method is used, and then the question of whether the observed trends can arise from internal atmospheric fluctuations is examined. To answer this question, surrogate data are generated from two paradigmatic null models: a standard first-order autoregressive process representing a short-range dependent process and a fractional integrated process representing a long-range dependent process. It is found that three of the eight stations show statistically significant trends when tested against the short-range dependent process while only the Faraday–Vernadsky station temperature time series shows a significant trend when tested against the long-range dependent null model. All other considered stations show no trends that are statistically significant against the two null models, and thus they can be explained by internal atmospheric variability. These results imply that more attention should be given to assessing the correlation structure of climate time series.

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