Analysis of Geophysical Time Series Using Discrete Wavelet Transforms: An Overview

Percival, Donald B.

doi:10.1007/978-3-540-78938-3_4

Cited by 48 publications

(37 citation statements)

References 34 publications

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“…Thus, the application of standard power spectrum techniques (such as the Fast Fourier Transform) is not the most suitable method. The Maximal Overlap Discrete Wavelet Transform (MODWT) (Percival and Mojfeld, 1997) is the base of two possible additive decompositions of a given time-series: an analysis of variance over J time-scales and a multiresolution analysis (MRA) that consists in reexpressing the original time-series as a sum of sub-series corresponding to each time-scale (Percival, 2008). This decomposition results in J'1 sub-series: J wavelet coefficient (D j ) time-series corresponding to pass-band filtering scales s j of 2 j to 2 j'1 months (j 01, 2,. .…”

Section: Methodsmentioning

confidence: 99%

Discrete wavelet analysis of the influence of the North Atlantic Oscillation on Baltic Sea level

Bastos¹,

Trigo

Barbosa

2013

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C T Mean sea level (MSL) in the Baltic Sea is influenced by several factors and therefore presents a complex behaviour over a wide range of time-scales. This work performs a multi-scale analysis of MSL variability in the Baltic Sea using discrete wavelet analysis. The North Atlantic Oscillation (NAO) is well known for having a strong influence in MSL variability over the Baltic; however, the relationship between MSL and NAO at different time-scales is still little understood. In this work a comparison of MSL and NAO variability is performed for a wide range of temporal scales, uncovering distinct relationships in high-frequency and long-term temporal variability. The annual and sub-annual scales are found to account for more than 50% of the total MSL variability. The MSL annual cycle is analysed and a shift from low to high amplitude values is identified in the 1970s for most stations. MSL is found to be anti-correlated to NAO at short time-scales while on the long-term NAO and MSL appear to be positively correlated for most stations. The physical mechanisms behind these distinct relationships deserve deeper study.

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Section: Methodsmentioning

confidence: 99%

Discrete wavelet analysis of the influence of the North Atlantic Oscillation on Baltic Sea level

Bastos¹,

Trigo

Barbosa

2013

Tellus A: Dynamic Meteorology and Oceanography

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“…In order to avoid these redundancies the key features of the signal can be presented by only choosing sub samples of CWT, which is the DWT. It may be more acceptable to apply DWT over CWT in rainfall data analysis because CWT does not generate information in terms of time series (Percival 2008). In addition, process of transformation by DWT is simplified because it is based on the dyadic calculation of position and scale of a signal (Chou 2007).…”

Section: Wavelet Analysismentioning

confidence: 99%

Precipitation trend analysis using discrete wavelet transform at the Langat River Basin, Selangor, Malaysia

Palizdan

Falamarzi

Huang

et al. 2016

Stoch Environ Res Risk Assess

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The main purpose of this study was to determine the most dominant periodic components that affect the annual and seasonal precipitation trends in each homogenous rainfall region in the Langat River Basin, Malaysia for the period 1982-2011. Performing this research could be essential because in the previous studies on detection of trend in Malaysia, the details of variations of different time scales and the periodic responsible for the observed trends were not investigated. Using discrete wavelet transform (DWT) coupled with Mann-Kendall at the regional scale for the first time particularly in the context of Malaysia is the contribution of this study. In order to form the homogenous rainfall regions, first the total annual and seasonal precipitation in each year was spatialized into 5 km 9 5 km grids using the inverse distance weighting method. The obtained precipitation series for the grids were then grouped applying the Ward's clustering method based on the similarity of precipitation time series. After allocating a cluster number to each grid, the boundary of the regions was formed in ArcGIS software. Following which, in each homogenous region the areal precipitation series were computed by the Thiessen polygon method. The Mann-Kendall (MK) test was used to detect trend and the DWT coupled with the MK test and the sequential MK analysis were then utilized in order to find out the time scale which affected the observed trend in each homogenous region. On annual scale, it was found that D 1 (plus approximation) component in regions Annual Cluster1 (AC1) and AC2 was the periodic mode responsible for trends. On seasonal scale, in regions Northeast monsoon Cluster 1 (NC1), NC3, SC1 and Southwest monsoon Cluster 2 (SC2), D 1 (with approximation), in regions NC4, Inter monsoon 1 Cluster 1 (I1C1), I1C2, Inter monsoon 2 Cluster 1 I2C1 and I2C2, Detail 2 (D 2 ) (plus approximation) and in region NC2, Detail 3 (D 3 ) (with approximation added) component were the most influential periodicity for trends.

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“…Although some estimators were developed exactly in hydrology as well (see e.g. [25,26]) and they are generally considered very good [27], in our study, the technique making use of the socalled maximal overlap discrete wavelet transform (MODWT; [17,28,29]) was utilized because it should be insensitive to the presence of deterministic trends [12], which is beneficial in the cases when different components of time series may interact and mimic each other (deterministic and stochastic trends inclusive). The method builds on the estimation of wavelet variance at the so-called dyadic scales (i.e.…”

Section: Hurst Exponent Estimationmentioning

confidence: 99%

Freely available daily hydrometeorological data from Czechia: further insights

Ledvinka

Jedlicka

2018

E3S Web Conf.

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Abstract. Quite recently, freely available mean daily discharge series representing the territory of Czechia were complemented by ten daily series of nine climate variables, spanning usually from 1961 to the present. Their length thus allows the analyses similar to those conducted approximately a year ago in relation to the long series of discharge. Besides this possibility, the current paper goes further and shows how these long series (including discharge) can be used in order to assess the presence of the so-called Hurst phenomenon. Using a wavelet-based approach, several important differences in the wavelet spectra and values of the Hurst exponent (as well as the uncertainty in their estimation) were found when focusing on discharge, air temperature and precipitation. Furthermore, using the stationarity and unit root tests, it was revealed that, unlike precipitation, air temperature and discharge series may be characterized by long-memory processes in many cases. Finally, as the paper is devoted mainly to students, a short R script is presented in Appendix that makes it easier to work with the online files offered by Czech climatologists.

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Analysis of Geophysical Time Series Using Discrete Wavelet Transforms: An Overview

Cited by 48 publications

References 34 publications

Discrete wavelet analysis of the influence of the North Atlantic Oscillation on Baltic Sea level

Discrete wavelet analysis of the influence of the North Atlantic Oscillation on Baltic Sea level

Precipitation trend analysis using discrete wavelet transform at the Langat River Basin, Selangor, Malaysia

Freely available daily hydrometeorological data from Czechia: further insights

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