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 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.

scholarly journals Multi-scale investigation on streamflow temporal variability and its connection to global climate indices for unregulated rivers in India

2021 ◽  
Author(s):  
Pavan Kumar Yeditha ◽  
Tarun Pant ◽  
Maheswaran Rathinasamy ◽  
Ankit Agarwal
Keyword(s):  
Wavelet Transform ◽  
Temporal Variability ◽  
Global Climate ◽  
Phase Relationship ◽  
Wavelet Coherence ◽  
Climate Indices ◽  
Coherence Analysis ◽  
Cross Wavelet Transform ◽  
Wavelet Coherence Analysis ◽  
Cross Wavelet

Abstract With the increasing stress on water resources for a developing country like India, it is pertinent to understand the dominant streamflow patterns for effective planning and management activities. This study investigates the spatiotemporal characterization of streamflow of six unregulated catchments in India. Firstly, Mann Kendall (MK) and Changepoint analysis were carried out to detect the presence of trends and any abrupt changes in hydroclimatic variables in the chosen streamflows. To unravel the relationships between the temporal variability of streamflow and its association with precipitation and global climate indices, namely, Niño 3.4, IOD, PDO, and NAO, continuous wavelet transform is used. Cross-wavelet transform and wavelet coherence analysis was also used to capture the coherent and phase relationships between streamflow and climate indices. The continuous wavelet transforms of streamflow data revealed that intra-annual (0.5 years), annual (1 year), and inter-annual (2–4 year) oscillations are statistically significant. Furthermore, a better understanding of the in-phase relationship between the streamflow and precipitation at intra-annual and annual time scales were well-captured using wavelet coherence analysis compared to cross wavelet transform. Furthermore, our analysis also revealed that streamflow observed an in-phase relationship with IOD and NAO, whereas a lag correlation with Niño 3.4 and PDO indices at intra-annual, annual and interannual time scales.

scholarly journals Estudos de Variabilidades Interanuais e Interdecenais da Precipitação Pluvial das Regiões Hidrográficas Tocantins-Araguaia e São Francisco no Brasil

2021 ◽  
Vol 14 (2) ◽  
pp. 1116
Author(s):  
José Nildo da Nóbrega ◽  
Carlos Antonio Costa dos Santos ◽  
Francisco de Assis Salviano de Sousa ◽  
Bergson Guedes Bezerra ◽  
Geber Barbosa de Albuquerque Moura ◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Geographical Area ◽  
Monthly Data ◽  
The Pacific ◽  
Cross Wavelet Transform ◽  
Wavelet Transform Analysis ◽  
The Cross ◽  
Hydrographic Regions ◽  
Cross Wavelet ◽  
Phase Differences

O objetivo é investigar as fases temporais das variabilidades de precipitação pluvial das Regiões Hidrográficas do Tocantins-Araguaia e São Francisco, como, também, correlacioná-las com índices de anomalias de Temperatura da Superfície do Mar (TSM) do Pacífico, na região do Niño 3.4, utilizando a análise de transformada ondaleta. A área geográfica está localizada entre os paralelos 0,5º S a 20º S e meridianos 34,8º W a 55,4º W. Foram utilizados dados mensais de precipitação observados e de reanálise (1º x 1º), no período de 1945-2016, e de TSM de 1950-2016 provenientes de órgãos governamentais nacionais e internacionais. As Ondaletas Contínuas mostraram que as variabilidades dominantes, de precipitação total anual, nas Regiões Hidrográficas do Tocantins-Araguaia e do São Francisco são nas escalas de três a cinco anos, de 11 a 12 anos e em torno de 22 anos. Para ambas as Regiões essas frequências estão em fases, pela Transformada Ondaleta Cruzada e confirmada pela Ondaleta Coerente. Nas análises de Ondaletas Cruzada e Coerente das precipitações com os índices oceânicos se verificou que houve avanço (135º) na série do Niño 3.4 em relação as das precipitações das Regiões nas escalas de três a cinco anos, mas foram verificadas diferenças de fase nas escalas decenais da precipitação das Regiões com os índices oceânicos. Concluiu-se que as variabilidades da precipitação de ambas as Regiões estão em fase e que os eventos ENOS influenciam nas precipitações das Regiões Hidrográficas do Tocantins-Araguaia e São Francisco.  Studies of Interannual and Interdecennial Variabiliteis of Rainfall in the Tocantins-Araguaia and São Francisco Hydrographic Regions in Brazil ABSTRACTThe objective is to investigate the temporal phases of the variability of rainfall in the Hydrographic Regions of Tocantins-Araguaia and São Francisco, as well as to correlate them with anomalies indexes of the Sea Surface Temperature (SST) of the Pacific, in the Niño 3.4 region, using wavelet transform analysis. The geographical area is located between the parallels 0.5º S to 20º S and meridians 34.8º W to 55.4º W. We used monthly data of observed and reanalysis precipitation (1º x 1º), in the period from 1945 to 2016, and from 1950 to 2016 for SST. The data are from national and international government agencies. The continuous wavelet showed that the dominant variability of total annual precipitation, in the Hydrographic Regions of Tocantins-Araguaia and São Francisco, are in the frequencies of three to five years, 11 to 12 years and about 22 years. These frequencies are in phases by the cross wavelet transform and confirmed by the coherent wavelet. In the cross and coherent wavelet analysis of the precipitation with the oceanic indices, there was an advance (135º) in the Niño 3.4 series in relation to the precipitation of the Regions in the frequency of three to five years, but phase differences were observed in the decadal frequencies between the precipitation of the Regions and oceanic indices. We concluded that the variability of precipitation in both regions is in phase and that the ENOS events influence the rainfall in the Hydrographic Regions of Tocantins-Araguaia and São Francisco.Keywords: El Niño, hydrographic catchment, wavelet, climate variability.

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 Signature Matching For Seismic Signal Identification

2021 ◽  
Author(s):  
Pankaj Jadhav ◽  
Debabrata Datta ◽  
Siddhartha Mukhopadhyay
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Seismic Signal ◽  
Wavelet Coherence ◽  
Continuous Wavelet ◽  
Seismic Signals ◽  
Time Frequency ◽  
Maximum Covariance Analysis ◽  
Cross Wavelet Transform ◽  
Matching Techniques

Seismic signals can be classified as natural or manmade by matching signature of similar events that have occurred in the past. Waveform matching techniques can be effectively used for discrimination since the events with similar location and focal mechanism have similar waveform irrespective of magnitude. The seismic signals are inherently non-stationary in nature. The analysis of such signals can be best achieved in multiresolution framework by resolving the signal using continuous wavelet transform (CWT) in time-frequency plane. In this paper similarity testing and classification of nuclear explosion and earthquake are exploited with correlation, continuous wavelet transform, cross-wavelet transform and wavelet coherence (WC) of P phase of seismogram. Clustering of seismic signals continuous wavelet spectra is performed using maximum covariance analysis. The proposed classifier has an average classification accuracy of 94%.

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