scholarly journals Recognizing relationship between groundwater level and hydrological time series (Case study: Ardabil plain)

2021 ◽  
Author(s):  
Farnaz Daneshvar Vousoughi
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Groundwater Level ◽  
Entropy Measure ◽  
Main Role ◽  
Rainfall Runoff ◽  
Frequency Space ◽  
Time Frequency ◽  
Common Time

Abstract Two approaches to identify the relation between hydrological time series (rainfall and runoff) and groundwater level (GWL) were used in the Ardabil plain. In this way, Wavelet-entropy measure (WEM) and wavelet transform coherence (WTC) as two approaches of wavelet transform (WT) were used. WEM have been considered as a criterion for the degree of time series fluctuations and WTC present common time-frequency space. In WEM calculation, monthly rainfall, runoff and GWL time series were divided into three different time periods and decomposed to multiple frequent time series and then, the energies of wavelet were calculated for each sub-series. The result showed WEM reduction in rainfall, runoff and GWL. The reduction of WEM presents the natural fluctuations decrease of time series. The reduction of entropy for runoff, rainfall and GWL time series were about 1.58, 1.36 and 29% respectively, it is concluded that fluctuation reduction of hydrological time series has relatively not more effect on the oscillation patterns of GWL signal. In this regard, it could be concluded that the human activities such as water driving from wells can be played main role in the reduction of GWL in Ardabil plain. WTC findings showed that runoff had most coherence (0.9-1) among the hydrological variables with GWL time series in the frequency bands of 4-8 and 8-16 months.

scholarly journals Wavelet analysis of land subsidence time-series: Madrid Tertiary aquifer case study

2020 ◽  
Vol 382 ◽  
pp. 353-359
Author(s):  
Roberto Tomás ◽  
José Luis Pastor ◽  
Marta Béjar-Pizarro ◽  
Roberta Bonì ◽  
Pablo Ezquerro ◽  
...  
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Land Subsidence ◽  
Wavelet Coherence ◽  
Interferometric Synthetic Aperture Radar ◽  
Frequency Space ◽  
Time Frequency ◽  
Cross Wavelet Transform ◽  
Cross Wavelet

Abstract. Interpretation of land subsidence time-series to understand the evolution of the phenomenon and the existing relationships between triggers and measured displacements is a great challenge. Continuous wavelet transform (CWT) is a powerful signal processing method mainly suitable for the analysis of individual nonstationary time-series. CWT expands time-series into the time-frequency space allowing identification of localized nonstationary periodicities. Complementarily, Cross Wavelet Transform (XWT) and Wavelet Coherence (WTC) methods allow the comparison of two time-series that may be expected to be related in order to identify regions in the time-frequency domain that exhibit large common cross-power and wavelet coherence, respectively, and therefore are evocative of causality. In this work we use CWT, XWT and WTC to analyze piezometric and InSAR (interferometric synthetic aperture radar) time-series from the Tertiary aquifer of Madrid (Spain) to illustrate their capabilities for interpreting land subsidence and piezometric time-series information.

Dynamic correlation of Eastern and Western markets and forecasting: Scale-by-scale wavelet-based approach

2017 ◽  
Vol 04 (04) ◽  
pp. 1750040 ◽  
Author(s):  
Emrah Oral ◽  
Gazanfer Unal
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Moving Average ◽  
Wavelet Coherence ◽  
Vector Autoregressive ◽  
Frequency Space ◽  
Time Frequency ◽  
Dynamic Correlation ◽  
Frequency Scale ◽  
Highly Correlated

In this paper, dynamic four-dimensional (4D) correlation of eastern and western markets is analyzed. A wavelet-based scale-by-scale analysis method has been introduced to model and forecast stock market data for strongly correlated time intervals. The daily data of stock markets of SP500, FTSE and DAX (western markets) and NIKKEI, TAIEX and KOSPI (eastern markets) are obtained from 2009 to the end of 2016 and their co-movement dependencies on time–frequency space using 4D multiple wavelet coherence (MWC) are determined. Once the data is detached into levels of different frequencies using scale-by-scale continuous wavelet transform, all of the time series possessing the same frequency scale are selected, inversed and forecasted using multivariate model, vector autoregressive moving average (VARMA). It is concluded that the efficiency of forecasting is increased substantially using the same-frequency highly correlated time series obtained by scale-by-scale wavelet transform. Moreover, the increasing or decreasing trend of prospected price shift is foreseen fairly well.

scholarly journals Discrete and Dual Tree Wavelet Features for Real-Time Speech/Music Discrimination

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Timur Düzenli ◽  
Nalan Özkurt
Keyword(s):  
Wavelet Transform ◽  
Real Time ◽  
Wavelet Transforms ◽  
Principal Component ◽  
Discrete Wavelet ◽  
Vanishing Moments ◽  
Zero Crossings ◽  
Time Frequency ◽  
Common Time ◽  
Classification Tool

The performance of wavelet transform-based features for the speech/music discrimination task has been investigated. In order to extract wavelet domain features, discrete and complex orthogonal wavelet transforms have been used. The performance of the proposed feature set has been compared with a feature set constructed from the most common time, frequency and cepstral domain features such as number of zero crossings, spectral centroid, spectral flux, and Mel cepstral coefficients. The artificial neural networks have been used as classification tool. The principal component analysis has been applied to eliminate the correlated features before the classification stage. For discrete wavelet transform, considering the number of vanishing moments and orthogonality, the best performance is obtained with Daubechies8 wavelet among the other members of the Daubechies family. The dual tree wavelet transform has also demonstrated a successful performance both in terms of accuracy and time consumption. Finally, a real-time discrimination system has been implemented using the Daubhecies8 wavelet which has the best accuracy.

scholarly journals Application of the cross wavelet transform and wavelet coherence to geophysical time series

2004 ◽  
Vol 11 (5/6) ◽  
pp. 561-566 ◽  
Author(s):  
A. Grinsted ◽  
J. C. Moore ◽  
S. Jevrejeva
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Statistical Significance ◽  
Wavelet Coherence ◽  
The Arctic ◽  
Arctic Oscillation Index ◽  
Time Frequency ◽  
Cross Wavelet Transform ◽  
The Cross ◽  
Cross Wavelet

Abstract. Many scientists have made use of the wavelet method in analyzing time series, often using popular free software. However, at present there are no similar easy to use wavelet packages for analyzing two time series together. We discuss the cross wavelet transform and wavelet coherence for examining relationships in time frequency space between two time series. We demonstrate how phase angle statistics can be used to gain confidence in causal relationships and test mechanistic models of physical relationships between the time series. As an example of typical data where such analyses have proven useful, we apply the methods to the Arctic Oscillation index and the Baltic maximum sea ice extent record. Monte Carlo methods are used to assess the statistical significance against red noise backgrounds. A software package has been developed that allows users to perform the cross wavelet transform and wavelet coherence (www.pol.ac.uk/home/research/waveletcoherence/).

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.

Time-frequency analysis of fetal heartbeat fluctuation using wavelet transform

1998 ◽  
Vol 275 (6) ◽  
pp. H1993-H1999 ◽  
Author(s):  
Yoshitaka Kimura ◽  
Kunihiro Okamura ◽  
Takanori Watanabe ◽  
Nobuo Yaegashi ◽  
Shigeki Uehara ◽  
...  
Keyword(s):  
Heart Rate ◽  
Time Series ◽  
Wavelet Transform ◽  
Gamma Distribution ◽  
Frequency Analysis ◽  
Fetal Heart Rate ◽  
Fetal Heart ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Rate Fluctuation

We examined whether the nonlinear control mechanism of the fetal autonomic nervous system would change in various fetal states. Eight thousand or more fetal heartbeats were detected from normal, hypoxemic, and acidemic fetuses. Fetal heart Doppler-signal intervals were determined in a high-precision autocorrelation method, and a time series of fetal heart rate fluctuation was obtained. The distribution of the amplitude of temporal fluctuation in the low-frequency component of fetal heart rate frequency was studied using a method of time-frequency analysis called wavelet transform. Spline 4 was used as the mother wavelet function. A gamma distribution was observed from 17 wk of gestation onward. The value of the parameter ν of this gamma distribution was ∼1.6 and remained constant regardless of the gestational age or the time of day. The value of ν decreased significantly to 0.77 when the fetus developed acidemia and was 1.51 in hypoxemia and 1.54 in a normal condition. This study elucidates a nonlinear structure of the time series of heart rate fluctuation of the gamma distribution in the human fetus. This technique may provide a new quantitative index of fetal monitoring to diagnose fetal acidemia.

scholarly journals A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 2: Extension to time–frequency analysis

2018 ◽  
Vol 25 (1) ◽  
pp. 175-200 ◽  
Author(s):  
Guillaume Lenoir ◽  
Michel Crucifix
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Background Noise ◽  
Noise Model ◽  
Analysis Tool ◽  
Continuous Wavelet ◽  
Time Frequency Analysis ◽  
Time Frequency

Abstract. Geophysical time series are sometimes sampled irregularly along the time axis. The situation is particularly frequent in palaeoclimatology. Yet, there is so far no general framework for handling the continuous wavelet transform when the time sampling is irregular. Here we provide such a framework. To this end, we define the scalogram as the continuous-wavelet-transform equivalent of the extended Lomb–Scargle periodogram defined in Part 1 of this study (Lenoir and Crucifix, 2018). The signal being analysed is modelled as the sum of a locally periodic component in the time–frequency plane, a polynomial trend, and a background noise. The mother wavelet adopted here is the Morlet wavelet classically used in geophysical applications. The background noise model is a stationary Gaussian continuous autoregressive-moving-average (CARMA) process, which is more general than the traditional Gaussian white and red noise processes. The scalogram is smoothed by averaging over neighbouring times in order to reduce its variance. The Shannon–Nyquist exclusion zone is however defined as the area corrupted by local aliasing issues. The local amplitude in the time–frequency plane is then estimated with least-squares methods. We also derive an approximate formula linking the squared amplitude and the scalogram. Based on this property, we define a new analysis tool: the weighted smoothed scalogram, which we recommend for most analyses. The estimated signal amplitude also gives access to band and ridge filtering. Finally, we design a test of significance for the weighted smoothed scalogram against the stationary Gaussian CARMA background noise, and provide algorithms for computing confidence levels, either analytically or with Monte Carlo Markov chain methods. All the analysis tools presented in this article are available to the reader in the Python package WAVEPAL.

Wavelet Transform with Application in Roadside Landscape Design

2015 ◽  
Vol 744-746 ◽  
pp. 2032-2042 ◽  
Author(s):  
Tong Yang Zhang ◽  
Zhong Hua Wei ◽  
Li Wang ◽  
Xia Zhao ◽  
Ting Wang
Keyword(s):  
Heart Rate ◽  
Wavelet Transform ◽  
Mental Workload ◽  
Landscape Design ◽  
Landscape Patterns ◽  
Small Scale ◽  
Time Frequency ◽  
Rate Measure ◽  
Positive Effect

This paper aims to apply the wavelet transform to the study of driver’s heart rate in different roadside landscape patterns. In the methodology, we describe the procedure in detail that implementing wavelet transform to denoise heart rate signal. The result shows the algorithm presented with the best performance is suitable to process heart rate signal. In the case study, taking advantage of the superiority of wavelet transform in time-frequency domain, it is apparent that heart rate is in a state of fluctuation continuously. That confirms that sensitivity of heart rate measure the mental workload. We also observe that landscape transition enhance driver’s heart rate on a small scale, which makes a positive effect on driver and can be adopted as a countermeasure against the fatigue of driver in the further road landscape design.

scholarly journals Possible Linkages of Hydrological Variables to Ocean–Atmosphere Signals and Sunspot Activity in the Upstream Yangtze River Basin

Atmosphere ◽  
2021 ◽  
Vol 12 (10) ◽  
pp. 1361
Author(s):  
Ruting Yang ◽  
Bing Xing
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
River Basin ◽  
Yangtze River ◽  
Yangtze River Basin ◽  
Spatiotemporal Variability ◽  
Sunspot Activity ◽  
Monthly Precipitation ◽  
Time Frequency ◽  
Hydrological Variables

Profiling the hydrological response of watershed precipitation and streamflow to large-scale circulation patterns and astronomical factors provides novel information into the scientific management and prediction of regional water resources. Possible contacts of El Niño–Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO), sunspot activity to precipitation and streamflow in the upper Yangtze River basin (UYRB) were investigated in this work. Monthly precipitation and streamflow were utilized as well as contemporaneous same-scale teleconnections time series spanning a total of 70 years from 1951 to 2020 in precipitation and 121 years from 1900 to 2020 in streamflow. The principal component analysis (PCA) method was applied so as to characterize the dominant variability patterns over UYRB precipitation time series, with the temporal variability of first two modes explaining more than 80% of total variance. Long-term evolutionary pattern and periodic variation characteristics of precipitation and streamflow are explored by applying continuous wavelet transform (CWT), cross-wavelet transform (XWT) and wavelet coherence (WTC), analyzing multi-scale correlation between hydrological variables and teleconnections in the time-frequency domain. The results manifest that ENSO exhibits multiple interannual period resonance with precipitation and streamflow, while correlations are unstable in time and phase. PDO and sunspot effects on precipitation and streamflow at interannual scales vary with time-frequency domains, yet significant differences are exhibited in their effects at interdecadal scales. PDO exhibits a steady negative correlation with streamflow on interdecadal scales of approximately 10 years, while the effect of sunspot on streamflow exhibits extremely steady positive correlation on longer interdecadal scales of approximately 36 years. Analysis reveals that both PDO and sunspot have significantly stronger effects on streamflow variability than precipitation, which might be associated with the high spatiotemporal variability of precipitation.

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