scholarly journals The Empirical Adaptive Wavelet Decomposition (EAWD): An adaptive decomposition for the variability analysis of observation time series in atmospheric science

2022 ◽  
Author(s):  
Olivier Delage ◽  
Thierry Portafaix ◽  
Hassan Bencherif ◽  
Alain Bourdier ◽  
Emma Lagracie
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Observation Time ◽  
Stationary Time Series ◽  
Original Time Series ◽  
Adaptive Wavelet ◽  
Time Frequency ◽  
Variability Analysis ◽  
Original Time ◽  
Different Time Scales

Abstract. Most observational data sequences in geophysics can be interpreted as resulting from the interaction of several physical processes at several time and space scales. As a consequence, measurements time series have often characteristics of non-linearity and non-stationarity and thereby exhibit strong fluctuations at different time-scales. The variability analysis of a time series consists in decomposing it into several mode of variability, each mode representing the fluctuations of the original time series at a specific time-scale. Such a decomposition enables to obtain a time-frequency representation of the original time series and turns out to be very useful to estimate the dimensionality of the underlying dynamics. Decomposition techniques very well suited to non-linear and non-stationary time series have recently been developed in the literature. Among the most widely used of these technics are the empirical mode decomposition (EMD) and the empirical wavelet transformation (EWT). The purpose of this paper is to present a new adaptive filtering method that combines the advantages of the EMD and EWT technics, while remaining close to the dynamics of the original signal made of atmospheric observations, which means reconstructing as close as possible to the original time series, while preserving its variability at different time scales.

scholarly journals Application of Discrete Wavelet Transform in Shapelet-Based Classification

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Lijuan Yan ◽  
Yanshen Liu ◽  
Yi Liu
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Weight Vector ◽  
Majority Voting ◽  
Discrete Wavelet ◽  
Time Series Classification ◽  
Original Time Series ◽  
Time Frequency ◽  
Original Time

Recently, several shapelet-based methods have been proposed for time series classification, which are accomplished by identifying the most discriminating subsequence. However, for time series datasets in some application domains, pattern recognition on the original time series cannot always obtain ideal results. To address this issue, we propose an ensemble algorithm by combining time frequency analysis and shape similarity recognition of time series. Discrete wavelet transform is used to decompose the time series into different components, and the shapelet features are identified for each component. According to the different correlations between each component and the original time series, an ensemble classifier is built by weighted majority voting, and the Monte Carlo method is used to search for optimal weight vector. The comparative experiments and sensitivity analysis are conducted on 25 datasets from UCR Time Series Classification Archive, which is an important open dataset resource in time series mining. The results show the proposed method has a better performance in terms of accuracy and stability than the compared classifiers.

scholarly journals Superiority of Hybrid Soft Computing Models in Daily Suspended Sediment Estimation in Highly Dynamic Rivers

2021 ◽  
Vol 13 (2) ◽  
pp. 542
Author(s):  
Tarate Suryakant Bajirao ◽  
Pravendra Kumar ◽  
Manish Kumar ◽  
Ahmed Elbeltagi ◽  
Alban Kuriqi
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Suspended Sediment ◽  
River Basin ◽  
Time Series Data ◽  
Series Data ◽  
Discrete Wavelet ◽  
Original Time Series ◽  
Inference System ◽  
Original Time

Estimating sediment flow rate from a drainage area plays an essential role in better watershed planning and management. In this study, the validity of simple and wavelet-coupled Artificial Intelligence (AI) models was analyzed for daily Suspended Sediment (SSC) estimation of highly dynamic Koyna River basin of India. Simple AI models such as the Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) were developed by supplying the original time series data as an input without pre-processing through a Wavelet (W) transform. The hybrid wavelet-coupled W-ANN and W-ANFIS models were developed by supplying the decomposed time series sub-signals using Discrete Wavelet Transform (DWT). In total, three mother wavelets, namely Haar, Daubechies, and Coiflets were employed to decompose original time series data into different multi-frequency sub-signals at an appropriate decomposition level. Quantitative and qualitative performance evaluation criteria were used to select the best model for daily SSC estimation. The reliability of the developed models was also assessed using uncertainty analysis. Finally, it was revealed that the data pre-processing using wavelet transform improves the model’s predictive efficiency and reliability significantly. In this study, it was observed that the performance of the Coiflet wavelet-coupled ANFIS model is superior to other models and can be applied for daily SSC estimation of the highly dynamic rivers. As per sensitivity analysis, previous one-day SSC (St-1) is the most crucial input variable for daily SSC estimation of the Koyna River basin.

scholarly journals The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 659
Author(s):  
Jue Lu ◽  
Ze Wang
Keyword(s):  
Time Series ◽  
Standard Deviation ◽  
Coarse Graining ◽  
Sample Entropy ◽  
Systematic Bias ◽  
Original Time Series ◽  
Multi Scale ◽  
Calculation Results ◽  
Surrogate Measure ◽  
Original Time

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.

HIGHER ORDER COMPLEXITY OF TIME SERIES

2004 ◽  
Vol 14 (08) ◽  
pp. 2979-2990 ◽  
Author(s):  
FANJI GU ◽  
ENHUA SHEN ◽  
XIN MENG ◽  
YANG CAO ◽  
ZHIJIE CAI
Keyword(s):  
Time Series ◽  
Mental Arithmetic ◽  
Higher Order ◽  
Second Order ◽  
Stationary Time Series ◽  
Eeg Signals ◽  
Eyes Closed ◽  
Logistic Mapping ◽  
Original Time ◽  
Different Order

A concept of higher order complexity is proposed in this letter. If a randomness-finding complexity [Rapp & Schmah, 2000] is taken as the complexity measure, the first-order complexity is suggested to be a measure of randomness of the original time series, while the second-order complexity is a measure of its degree of nonstationarity. A different order is associated with each different aspect of complexity. Using logistic mapping repeatedly, some quasi-stationary time series were constructed, the nonstationarity degree of which could be expected theoretically. The estimation of the second-order complexity of these time series shows that the second-order complexities do reflect the degree of nonstationarity and thus can be considered as its indicator. It is also shown that the second-order complexities of the EEG signals from subjects doing mental arithmetic are significantly higher than those from subjects in deep sleep or resting with eyes closed.

scholarly journals Technical Note: Long-term memory effect in the atmospheric CO<sub>2</sub> concentration at Mauna Loa

2006 ◽  
Vol 6 (6) ◽  
pp. 11957-11970 ◽  
Author(s):  
C. Varotsos ◽  
M.-N. Assimakopoulos ◽  
M. Efstathiou
Keyword(s):  
Carbon Dioxide ◽  
Time Series ◽  
Power Law ◽  
Carbon Dioxide Concentration ◽  
Global Climate Models ◽  
Fluctuation Analysis ◽  
Original Time Series ◽  
Mauna Loa ◽  
Carbon Dioxide Concentrations ◽  
Original Time

Abstract. The monthly mean values of the atmospheric carbon dioxide concentration derived from in-situ air samples collected at Mauna Loa Observatory, Hawaii, during 1958–2004 (the longest continuous record available in the world) are analyzed by employing the detrended fluctuation analysis to detect scaling behavior in this time series. The main result is that the fluctuations of carbon dioxide concentrations exhibit long-range power-law correlations (long memory) with lag times ranging from four months to eleven years, which correspond to 1/f noise. This result indicates that random perturbations in the carbon dioxide concentrations give rise to noise, characterized by a frequency spectrum following a power-law with exponent that approaches to one; the latter shows that the correlation times grow strongly. This feature is pointing out that a correctly rescaled subset of the original time series of the carbon dioxide concentrations resembles the original time series. Finally, the power-law relationship derived from the real measurements of the carbon dioxide concentrations could also serve as a tool to improve the confidence of the atmospheric chemistry-transport and global climate models.

scholarly journals Characterizing ecosystem-atmosphere interactions from short to interannual time scales

2007 ◽  
Vol 4 (3) ◽  
pp. 1405-1435
Author(s):  
M. D. Mahecha ◽  
M. Reichstein ◽  
H. Lange ◽  
N. Carvalhais ◽  
C. Bernhofer ◽  
...  
Keyword(s):  
Time Series ◽  
Time Scales ◽  
System Analysis ◽  
Singular System ◽  
Low Frequency ◽  
Data Adaptive ◽  
Effective Signal ◽  
Observation Space ◽  
Different Time Scales ◽  
Observation Period

Abstract. Characterizing ecosystem-atmosphere interactions in terms of carbon and water exchange on different time scales is considered a major challenge in terrestrial biogeochemical cycle research. The respective time series are now partly comprising an observation period of one decade. In this study, we explored whether the observation period is already sufficient to detect cross relationships of the variables beyond the annual cycle as they are expected from comparable studies in climatology. We explored the potential of Singular System Analysis (SSA) to extract arbitrary kinds of oscillatory patterns. The method is completely data adaptive and performs an effective signal to noise separation. We found that most observations (NEE, GPP, Reco, VPD, LE, H, u, P) were influenced significantly by low frequency components (interannual variability). Furthermore we extracted a set of nonlinear relationships and found clear annual hysteresis effects except for the NEE-Rg relationship which turned out to be the sole linear relationship in the observation space. SSA provides a new tool to investigate these phenomena explicitly on different time scales. Furthermore, we showed that SSA has great potential for eddy covariance data processing since it can be applied as novel gap filling approach relying on the temporal time series structure only.

Precipitation Forecast Based on WA-SVM Theory

2012 ◽  
Vol 518-523 ◽  
pp. 4039-4042
Author(s):  
Zhen Min Zhou
Keyword(s):  
Time Series ◽  
Support Vector Machine ◽  
Wavelet Analysis ◽  
Precipitation Forecast ◽  
Support Vector ◽  
Estimation Model ◽  
Original Time Series ◽  
Set Up ◽  
Original Time

In order to improve the precision of medium-long term rainfall forecast, the rainfall estimation model was set up based on wavelet analysis and support vector machine (WA-SVM). It decomposed the original rainfall series to different layers through wavelet analysis, forecasted each layer by means of SVM, and finally obtained the forecast results of the original time series by composition. The model was used to estimate the monthly rainfall sequence in the watershed. Comparing with other method which only uses support vector machine(SVM), it indicates that the estimated accuracy was improved obviously.

State Space Reconstruction of Nonstationary Time-Series

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Hong-Guang Ma ◽  
Chun-Liang Zhang ◽  
Fu Li
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
State Space ◽  
Phase Angle ◽  
Analytical Form ◽  
Nonstationary Time Series ◽  
Original Time Series ◽  
State Space Reconstruction ◽  
Original Time ◽  
The Hilbert Transform

In this paper, a new method of state space reconstruction is proposed for the nonstationary time-series. The nonstationary time-series is first converted into its analytical form via the Hilbert transform, which retains both the nonstationarity and the nonlinear dynamics of the original time-series. The instantaneous phase angle θ is then extracted from the time-series. The first- and second-order derivatives θ˙, θ¨ of phase angle θ are calculated. It is mathematically proved that the vector field [θ,θ˙,θ¨] is the state space of the original time-series. The proposed method does not rely on the stationarity of the time-series, and it is available for both the stationary and nonstationary time-series. The simulation tests have been conducted on the stationary and nonstationary chaotic time-series, and a powerful tool, i.e., the scale-dependent Lyapunov exponent (SDLE), is introduced for the identification of nonstationarity and chaotic motion embedded in the time-series. The effectiveness of the proposed method is validated.

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