scholarly journals Multiscale analysis of a non-periodic epidemic time series using wavelet transform

2019 ◽  
Author(s):  
Jean Gaudart ◽  
Stanislas Rebaudet ◽  
Gaetan Texier ◽  
Robert Barrais ◽  
Renaud Piarroux ◽  
...  
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Multiscale Analysis ◽  
Haar Wavelet ◽  
Rainfall Time Series ◽  
Cholera Case ◽  
Cross Wavelet Analysis ◽  
The Relationship ◽  
Cross Wavelet ◽  
Wavelet Spectra

SummaryThe aim of the present study was to develop a method for multiscale analysis of non-stationary and non-periodic epidemic time series. Indeed, the epidemiologists may need to know the features, at different resolutions, of short duration outbreaks that did not exhibit periodic cycles. Among of the large number of wavelets, we have developed a continuous wavelet that shows an analogous shape to the Haar wavelet, and leads to precise time localization. We applied the wavelet transform to the cholera epidemic, which began in October 2010 in Haiti. We determined the wavelet spectra of both the cholera case toll and rainfall time series, from September 01, 2010, to November 20, 2012 (812 days). The relationship between case toll and rainfall was analyzed using cross-wavelet spectra at different lags. Cholera case toll scalogram highlighted four epidemic bursts. Cross-wavelet analysis highlighted an absence of relationship between the first epidemic burst and rainfall, but a clear relationship between the following epidemic bursts and rainfall after a 3 to 8 day lag.

SLICES OF MULTIFRACTAL MEASURES AND APPLICATIONS TO RAINFALL DISTRIBUTIONS

Fractals ◽  
2000 ◽  
Vol 08 (04) ◽  
pp. 337-348 ◽  
Author(s):  
BIRGER LAMMERING
Keyword(s):  
Time Series ◽  
Field Data ◽  
Rainfall Data ◽  
Rainfall Time Series ◽  
Mathematical Ideas ◽  
Radar Images ◽  
The Usa ◽  
Self Similar ◽  
The Relationship ◽  
Plane Measure

We discuss the relationship between the multifractal functions of a plane measure and those of slices or sections of the measure with a line. Motivated by recent mathematical ideas about the relationship between measures and their slices, we formulate the "slice hypothesis," and consider the theoretical limitations of this hypothesis. We compute the multifractal functions of several standard self-similar and self-affine measures and their slices to examine the validity of the slice hypothesis. We are particularly interested in using the slice hypothesis to estimate multifractal properties of spatial rainfall fields by analyzing rainfall data representing slices of rainfall fields. We consider how rainfall time series at a fixed site and slices of composite radar images can be used for this purpose, testing this on field data from a radar composite in the USA and on appropriate time series.

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 the magnetotail response to solar wind fluctuations during HILDCAA events

2019 ◽  
Vol 37 (5) ◽  
pp. 919-929
Author(s):  
Adriane Marques de Souza Franco ◽  
Ezequiel Echer ◽  
Mauricio José Alves Bolzan
Keyword(s):  
Solar Wind ◽  
Wavelet Transform ◽  
Wavelet Analysis ◽  
Geomagnetic Field ◽  
Field Component ◽  
Long Duration ◽  
Analysis Technique ◽  
Spacecraft Mission ◽  
Cross Wavelet Analysis ◽  
Cross Wavelet

Abstract. In this work a study of the effects of the high-intensity long-duration continuous AE activity (HILDCAAs) events in the magnetotail was conducted. The aim of this study was to search the main frequencies during HILDCAAs in the Bx component of the geomagnetic field in the magnetotail, as well as the main frequencies, at which the magnetotail responds to the solar wind during these events. In order to conduct this analysis the wavelet transform was employed during nine HILDCAA events that coincided with Cluster spacecraft mission crossing through the tail of the magnetosphere from 2003 to 2007. The most energetic periods for each event were identified. It was found that 76 % of them have periods ≤4 h. With the aim to search the periods that have the highest correlation between the IMF Bz (OMNI) component and the Cluster Bx geomagnetic field component, the cross wavelet analysis technique was also used in this study. The majority of correlation periods between the Bz (IMF) and Bx component of the geomagnetic field observed also were ≤4 h, with 62.9 % of the periods. Thus the magnetotail responds stronger to IMF fluctuations during HILDCCAS at 2–4 h scales, which are typical substorm periods. The results obtained in this work show that these scales are the ones on which the coupling of energy is stronger, as well as the modulation of the magnetotail by the solar wind during HILDCAA events.

scholarly journals Enhanced accuracy of rainfall–runoff modeling with wavelet transform

2012 ◽  
Vol 15 (2) ◽  
pp. 392-404 ◽  
Author(s):  
Chien-ming Chou
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Response Function ◽  
Time Series Data ◽  
Series Data ◽  
Rainfall Time Series ◽  
Calibration Data ◽  
Validation Data ◽  
Original Scale ◽  
Using Data

Wavelet transform (WT) is typically used to decompose time series data for only one hydrological feature at a time. This study applied WT for simultaneous decomposition of rainfall and runoff time series data. For the calibration data, the decomposed rainfall and runoff time series calibrate the subsystem response function using the least squares (LS) method at each scale. For the validation data, the decomposed rainfall time series are convoluted with the estimated subsystem response function to obtain the estimated runoff at each scale. The estimated runoff at the original scale can be obtained by wavelet reconstruction. The efficacy of the proposed method is evaluated in two case studies of the Feng-Hua Bridge and Wu-Tu watershed. The analytic results confirm that the proposed wavelet-based method slightly outperforms the conventional method of using data only at the original scale. The results also show that the runoff hydrograph estimated by using the proposed method is smoother than that obtained using a single scale.

Multiscale analysis from turbulent time series with wavelet transform

2001 ◽  
Vol 295 (1-2) ◽  
pp. 215-218 ◽  
Author(s):  
C Rodrigues Neto ◽  
A Zanandrea ◽  
F.M Ramos ◽  
R.R Rosa ◽  
M.J.A Bolzan ◽  
...  
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Multiscale Analysis

scholarly journals An investigation on the relationship between the Hurst exponent and the predictability of a rainfall time series

2019 ◽  
Author(s):  
Sivapragasam Chandrasekaran ◽  
Saravanan Poomalai ◽  
Balamurali Saminathan ◽  
Sumila Suthanthiravel ◽  
Keerthi Sundaram ◽  
...  
Keyword(s):  
Time Series ◽  
Hurst Exponent ◽  
Rainfall Time Series ◽  
The Relationship

scholarly journals Long-term trend analysis of rainfall using hybrid Discrete Wavelet Transform (DWT) based Mann-Kendall tests in central Gujarat region, India

MAUSAM ◽  
2021 ◽  
Vol 71 (2) ◽  
pp. 209-224
Author(s):  
RAJANI NIRAV V ◽  
TIWARI MUKESH K ◽  
CHINCHORKAR S S
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Trend Analysis ◽  
Time Scales ◽  
Series Data ◽  
Trend Test ◽  
Discrete Wavelet ◽  
Rainfall Time Series

Trend analysis has become one of the most important issues in hydro-meteorological variables study due to climate change and the focus given to it in the recent past from the scientific community. In this study, long-term trends of rainfall are analyzed in eight stations located in semi-arid central Gujarat region, India by considering time series data of 116 years (1901-2016). Discrete wavelet transform (DWT) as a dyadic arrangement of continuous wavelet transformation combined with the widely applied and acknowledged Mann-Kendall (MK) trend analysis method were applied for analysis of trend and dominant periodicities in rainfall time series at monthly, annual and monsoonal time scales. Initially, rainfall time series applied in this study were decomposed using DWT to generate sub-time series at high and low frequencies, before applying the MK trend test. Further, the Sequential Mann-Kendall (SQMK) test was also applied to find out the trend changing points. The result showed that at the monthly annual and monsoon time scales, the trends in rainfall were significantly decreasing in most of the station. The 4-month and 8-month components were found as dominant at the monthly time series and the 2-year and 4-year component were found as dominant at the monsoon time series, whereas the 2-year components were observed as dominant in the annual time scale.

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.

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