A wavelet analysis to compare environmental time series

The water erosion in semiarid region of northeastern Brazil is mainly influenced by the intense rainfalls, which can occur during long periods of drought, when a large amount of sediment yield can be observed during such events. Thus, this paper aims to study the rainfall frequencies in such region through the wavelet transform.

Scientific Reports, 2022

NO 2 and nitric oxide (NO) are the most reactive gases in the atmosphere. The interaction of NO x molecules with oxygen, water and other chemicals leads to the formation of acid rain. The presence of NO 2 in the air affects human health and forms a photochemical smog. In this study, we utilize wavelet analysis, namely, the Morlet wavelet, which is a type of continuous wavelet transform, to conduct a spectral analysis of the periodicity of nitrogen dioxide (NO 2). The study is conducted using data from 14 weather stations located in diverse geographic areas of the United Arab Emirates (UAE) over a period of two years (2019 and 2020). We explain and relate the significance of human activities to the concentration level of NO 2 , particularly considering the effect of the COVID-19 lockdown to the periodicity of NO 2. The results show that NO 2 concentrations in desert areas such as Liwa and Al Quaa were unaffected by the lockdown period (April-July 2020) resulting from the COVID-19 pandemic. The other stations in the urban areas of Abu Dhabi city, Al Dhafra and Al Ain, showed a reduction in NO 2 during the lockdown. NO 2 is more highly concentrated during winter seasons than during other seasons. The periodicity of NO 2 lasted from a few days up to 16 days in most regions. However, some stations located in the Al Dhafra region, such as Al Ruwais and the Gayathi School stations, exhibited a longer period of more than 32 days with a 0.05 significance test. In the Abu Dhabi region, NO 2 lasted between 64 and 128 days at the Al Mafraq station. The correlation between the NO 2 concentration across several ground stations was studied using wavelet coherence. Wavelet transform is a statistical method based on time series that is used in various fields, such as economics, climatology, astronomy, and medical image processing 1-4. Climate variability can be studied by using wavelet analysis to track patterns, cycles and periodicity 5. Climatic time series data are either stationary or nonstationary. The Fourier transform is usually used for stationary time series data. However, wavelet transform is used to track the periodicity and variability of nonstationary climatic and meteorological parameters, such as temperature and precipitation, and atmospheric composition, such as sodium, sulfate concentrations, carbon dioxide (CO2), and other greenhouse gases (GHGs) 1,6-9. Wavelet analyses are also used in other domains, such as studying the variability in phytoplankton seasonal and annual periodicity 10 and identifying the monsoon drought index period over India 11. Some GHGs, such as nitrogen dioxide (NO 2), sulfur dioxide (SO 2) and carbon monoxide (CO), were studied over China 12 and Poland 13 during the lockdown that resulted from the COVID-19 pandemic. Some researchers have focused on studying the variability of nitrogen dioxide (NO 2) and sulfur dioxide (SO 2) specifically more than other air pollution components because of their serious impacts on human health. Additionally, the emissions of these gases increase proportionally with the growth of human industrial activities 7,12-14. Recently, in 7 , the spatiotemporal fluctuation of the NO2 tropospheric column concentration from 1996 to 2017 in Italy was studied based on human activities in terms of gross domestic product (GDP). The study related GDP, an indicator of economic performance, to its effect on air quality and NO 2-induced pollution. In addition to human activities, the study considered the nature of NO 2 , as it is a reactive trace gas; its emissions are changeable during the daytime. The lifetime of NO 2 varies in different seasons from a few hours in summer to a day during winter. It also lasts for more days if it reaches the height of the boundary layer between the troposphere and stratosphere. The wavelet power spectrum classified NO 2 into three periods:

Slovak Journal of Civil Engineering, 2015

The paper presents an analysis of changes in the structure of the average annual discharges, average annual air temperature, and average annual precipitation time series in Slovakia. Three time series with lengths of observation from 1961 to 2006 were analyzed. An introduction to spectral analysis with Fourier analysis (FA) is given. This method is used to determine significant periods of a time series. Later in this article a description of a wavelet transform (WT) is reviewed. This method is able to work with non-stationary time series and detect when significant periods are presented. Subsequently, models for the detection of potential changes in the structure of the time series analyzed were created with the aim of capturing changes in the cyclical components and the multiannual variability of the time series selected for Slovakia. Finally, some of the comparisons of the time series analyzed are discussed. The aim of the paper is to show the advantages of time series analysis us...

World Environmental and Water Resources Congress 2017, 2017

The trend and shift in the seasonal temperature, precipitation and streamflow time series across the Midwest have been analyzed, for the period 1960-2013, using the statistical analyses (Mann-Kendall test with and without considering short term persistence (MK2 and MK1, respectively) and Pettitt test). The paper also utilizes a relatively new approach, wavelet analysis, for testing the existence of trend and shift in the time series. The method has the ability to decompose a time series in to lower (trend) and higher frequency components (noise). Discrete wavelet transform (DWT) has been employed in the present study with an aim to find which periodicities are mainly responsible for trend in the original data. The combination of MK1, MK2 and DWT along with Pettitt test hasn't been extensively used up to this time, especially in detecting trend and shift in the Midwest. The analysis of climate division temperature and precipitation data and USGS naturalized streamflow data revealed the presence of periodicity in the time series data. All the incorporated time series data were seasonal to analyze the trends and shifts for four seasons-winter, spring, summer and fall independently. D3 component of DWT were observed to be influential in detecting real trend in Temperature, precipitation and streamflow data, however unlike temperature, precipitation and streamflow showed decreasing trend as well. Shift was relatively observed more than trend in the region with dominance of D3 component in the data. The result indicate the significant warming trend which agrees with the "increasing temperature" observations in the past two decades, however a clear explanation for precipitation and streamflow is not obvious.

spatial-accuracy.org

In epidemiology, techniques which examine periodicity in times series data can be used to understand weekly, biannual or seasonal patterns of disease. However, a simple understanding of periodicity is not sufficient to examine the possible influence of variation in incubation period, distributed sources of infection, and infection due to environmental factors, especially if these influences affect the rate of disease on various spatio-temporal scales. Wavelet analysis provides the ability to consider influences on various spatio-temporal scales. In order to examine the feasibility of using wavelets to assess dependencies over different spatio-temporal scales in a time series of disease incidence, we abstracted 10 years of daily records of ambient temperature and precipitation in addition to daily disease incidence data for Massachusetts for two enterically transmitted diseases. We eliminated periodic fluctuation in both seasonal and weekly case reporting using various techniques (Fourier transformation and "loess" smoothing) on each time series of disease data. These different methods were employed in order to examine the possible effect of removed periodicities on the variance of the data. We then performed a wavelet decomposition to examine the residuals from these analyses on a variety of temporal scales and examined the resulting correlations to the environmental data.

Journal of Nonparametric Statistics, 1998

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The urban centers within northeastern Brazil are mainly influenced by the intense rainfalls, which can occur after long periods of drought, when flood events can be observed during such events. Thus, this paper aims to study the rainfall frequencies in such region through the wavelet transform. An application of wavelet analysis is done with long time series of the total monthly rainfall amount at the capital cities of northeastern Brazil. The main frequency components in the time series are studied by the global wavelet spectrum and the modulation in separated periodicity bands were done in order to extract additional information, e.g., the 8 and 16 months band was examined by an average of all scales, giving a measure of the average annual variance versus time, where the periods with low or high variance could be identified. The important increases were identified in the average variance for some periods, e.g. 1947 to 1952 at Teresina city, which can be considered as high wet periods. Although, the precipitation in those sites showed similar global wavelet spectra, the wavelet spectra revealed particular features. This study can be considered an important tool for time series analysis, which can help the studies concerning flood control, mainly when they are applied together with rainfall-runoff simulations.

2000

This thesis consists of two papers dealing with the methodology of wavelet and its application in time series. We give here a brief summary of the contents of the two papers in the thesis. The first paper describes an alternative approach for testing the existence of trend among time series. The test method has been constructed using wavelet analysis which have the ability to decompose a time series into low frequencies (trend) and high frequencies (noise) components. Under the normality assumption the test is distributed as F. However, the distribution of the test is unknown under other conditions, like non-normality. To investigate the properties of the test statistic under

Oecologia, 2008

Wavelet analysis is a powerful tool that is already in use throughout science and engineering. The versatility and attractiveness of the wavelet approach lie in its decomposition properties, principally its timescale localization. It is especially relevant to the analysis of nonstationary systems, i.e., systems with short-lived transient components, like those observed in ecological systems. Here, we review the basic properties of the wavelet approach for time-series analysis from an ecological perspective. Wavelet decomposition offers several advantages that are discussed in this paper and illustrated by appropriate synthetic and ecological examples. Wavelet analysis is notably free from the assumption of stationarity that makes most methods unsuitable for many ecological time series. Wavelet analysis also permits analysis of the relationships between two signals, and it is especially appropriate for following gradual change in forcing by exogenous variables. Keywords Ecological time series Á Transient dynamics Á Non-stationarity Á Discontinuities Á Wavelets Á Wavelet analysis Á Wavelet Power Spectrum Á Wavelet coherency Á Environmental forcing Communicated by Wolf Mooij.

In this paper, wavelet concepts are used to study a correlation between pairs of time series of meteorological param-11 eters such as pressure, temperature, rainfall, relative humidity and wind speed. The study utilized the daily average val-12 ues of meteorological parameters of nine meteorological stations of Saudi Arabia located at different strategic locations. 13 The data used in this study cover a period of 16 years between 1990 and 2005. Besides obtaining wavelet spectra, we also 14 computed the wavelet correlation coefficients between two same parameters from two different locations and show that 15 strong correlation or strong anti-correlation depends on scale. The cross-correlation coefficients of meteorological 16 parameters between two stations were also calculated using statistical function. For coastal to costal pair of stations,