Reconstrução e procura de periodicidades nos dados de ozonio região sul do Brasil (29ºS, 53ºW)
Nivaor Rodolfo Rigozo^{I}; Marcelo Barcellos da Rosa^{II}; Pabulo Henrique Rampelotto^{III}; Mariza Pereira de Souza Echer^{IV}; Ezequiel Echer^{IV}; Daniel Jean Roger Nordemann^{IV}; Damaris Kirsch Pinheiro^{II}; Nelson Jorge Schuch^{I}
^{I}Instituto Nacional de Pesquisas Espaciais, Centro Regional Sul de Pesquisas Espaciais (INPE/CRS), Santa Maria, RS, Brasil. nivaor.rigozo@crs.inpe.br, njschuch@lacesm.ufsm.br
^{II}Universidade Federal de Santa Maria (UFSM), Departamento de Química, Santa Maria, RS, Brasil. marcelobdarosa@gmail.com, damariskp@gmail.com
^{III}UFSM, Departamento de Biologia, Santa Maria, RS, Brasil. pabulobio@gmail.com
^{IV}INPE, Divisão de Geofísica Espacial, São José dos Campos, SP, Brasil. mariza@dge.inpe.br, eecher@dge.inpe.br, nordeman@dge.inpe.br
ABSTRACT
Ozone plays a very important role in the nature due its characteristics as a natural filter of ultraviolet solar radiation. Thus, it is pertinent for the scientific community to understand all natural influence factors involving ozone along with a large time series. In this work, a reconstruction of ozone time series obtained by Brewer spectrophotometer from 1994 to 2008 at the Southern Space Observatory (SSO)  29ºS, 53ºW  Southern Brazil is presented. TOMSOMI data were used to follow the days without data, where a coefficient of correlation between TOMSOMI and Brewer is acceptable around r = 0.89. Besides, wavelet analysis to determine the temporal evolution of the frequencies and the amplitudes was applied. Moreover, wavelet analysis aiming to determine the temporal evolution of the frequencies and the amplitudes was performed. The results pointed a period of 365 days (1 yr) for the seasonal variation of ozone, of 600 days attributed for a possible QBO influence and two periods of 2000 and other 4000 days regarding possibly to the second harmonic of the 11year solar cycle.
Keywords: Ozone, Brewer, QuasiBiennial Oscillation, solar activity, wavelet analysis
RESUMO
O ozônio tem um papel muito importante na natureza devido as suas características como um filtro natural da radiação solar ultravioleta. Portanto, é pertinente para a comunidade científica compreender todos os fatores de influência natural envolvendo ozônio ao longo das séries temporais de grande porte. Neste trabalho, uma reconstrução da série temporal do ozônio obtido pelo espectrofotômetro Brewer 19942008 no Observatório Espacial do Sul (29 º S, 53 º W)  Sul do Brasil é apresentado. Os dados do TOMSOMI foram usados para completar os dias sem dados, onde um coeficiente de correlação entre TOMSOMI e Brewer é aceitável, em torno de r=0,89. Além disso, foi aplicada a análise de ondeletas para determinar a evolução temporal das frequências e das amplitudes. Os resultados apontam um período de 365 dias (ou 1 ano) para a variação sazonal do ozônio, um período de 600 dias para uma possível influência QBO e dois períodos, um de 2000 e outro de 4.000 dias referentes ao segundo harmônico do ciclo solar de 11 anos e 11 Ciclo de ano solar.
PalavrasChaves: Ozônio, Brewer, Oscilação QuaseBienal, Atividade solar, Análise de Ondeletas
]]> 1. INTRODUCTION
The monitoring of ozone by different ground instruments and spaceborn systems results in a collection of diverse data sets that have been used to investigate ozone changes caused by natural atmospheric processes and/or chemical emissions. Estimations of ozone trends and the beginning of the recovery of the ozone layer are the highpriory research tasks that require assessment of the relation between longterm data records of different origins. Many details of the expected ozone recovery are unclear so are the possible interactions with climate change and the consequences of increasing bromine (Salby and Callaghan, 2002; Ramaswamy et al., 2001). In order to actually "see" a recovery, high quality measurements are needed for many years to come. For the early detection of signs of a recovery or of a possible worsening, a good quantitative understanding is necessary for the various natural processes, which contribute to the variation of ozone levels from year to year.
The ozone distribution itself is driven by atmospheric circulation and atmospheric temperature distribution. It is influenced by its variability, and hence potentially affected by climate change [World Meteorological Organization (WMO), 2006].
In order to identify the key processes in the atmospheric ozone budget, satellite soundings of the atmospheric abundance of the relevant trace gases have been routinely performed since the 1970s. These satellite observations allow us to determine the total ozone column and vertical profiles of ozone in the atmosphere, from the stratosphere down into the troposphere. Thus, groundbased observations have been widely used as a validation tool for satellite data or in terms of complementation of satellite data by means of extending the tropospheric observations down to the surface, where most satellite instruments have a reduced sensitivity. This is especially important to understand the role of local and regional sources and sinks of tropospheric ozone and its precursors.
Satellite remote sensing observations are currently commonly used for the daily monitoring of the state of the globalozone layer from regional to continental spatial scales, as well as for the investigation of the chemical and dynamical causes of ozone decline. Also, such observations are likely to be used for the monitoring of the expected future globalozone recovery. Satellites provide a global view of the Earth's atmospheric system over extended periods of time, with an appreciable spatial resolution allowing the detection of regional to globalscale ozone trends. Recently, several spacebased instruments have been designed for retrieving the total ozone column (TOC) from observations of backscattered solar irradiance emerging at the top of the atmosphere.
Several studies using ground based and satellite measurements have demonstrated that since the late 1970s until the early 1990s, there have been significant negative trends in total ozone in the middle and highlatitude regions of the two hemispheres (Harris et al., 1997, Staehelin et al., 2001). The implementation of the Montreal Protocol Ozone Layer depletors and their later amendments have created high expectations about the recovery of the total ozone toward pre 1980s concentrations as a result of the declining halogen loading in the stratosphere. Thus, Newchurch et al. (2003) reported signs of an ozone turnaround after 1996 from a statistical analysis of observations in the upper stratosphere, where ozone is mainly controlled by gas phase catalytic cycles.
Satellite instruments provide daily images of the global ozone distribution with good spatial resolution that is an important advantage over the local measurements of groundbased ozone from a sparse network. TOMS global observations have proven to be crucial to the understanding of the geographical and temporal distribution and variability of TOC (Hudson et al., 2006; Antón et al., 2008). These observations are being continued by the Ozone Monitoring Instrument aboard the NASA EOS Aura platform (Levelt et al., 2006) since October 2004.
In terms of data validation, Balis et al. (2007) showed a small negative bias of −1% and a seasonal behavior with amplitude of ±0.5% for EPTOMS–Brewer comparisons with the corrected satellite data set, while McPeters and Labow (1996) analyzed the satellite–ground based differences as a function of satellite solar zenith angle (SZA) for Northern Hemisphere stations (25◦ N to 55◦ N) for OMI TOC data and for empirically corrected EPTOMS TOC data. While the EPTOMS SZAdependent error increases to almost −3% at 70◦ SZA, OMI TOC shows no significant dependence on SZA. Therefore, many studies have investigated variations of ozone and as consequence temperature on interannual time scales has been observed. This includes trends (Bojkov et al., 1990; Staehelin et al., 2001), influences from the QBO (Baldwin et al., 2001), from the 11year solar cycle (Labitzke and van Loon, 2000; Lee and Smith, 2003), from El Ninõ/Southern Oscillation (ENSO) (Reid, 1994) or from meteorological factors (Appenzeller et al., 2000; Steinbrecht et al., 2001).
Tropical and subtropical scenarios including anomalies can be explained by a residual circulation with descending/ascending motion in the tropics and ascending/descending motion in the subtropics (Andrews et al., 1987; Baldwin et al., 2001). According to the thermal wind relation, these vertical motions are induced by the westerly/easterly vertical wind shear associated with the QBO. For the case of westerly wind shear, e.g., when maximum westerly winds are found at or above 30 hPa, descending motion occurs below 30 hPa. This brings ozone rich air down in the tropical lower stratosphere, thereby increasing tropical total ozone and adiabatically warming the tropical lower stratosphere.
Speciously addressing the atmospheric characteristics from the South of Brazil, aspects as the South Atlantic Geomagnetic Anomaly as well as the secondary ozone effects, which are lower levels of ozone from Antarctica coming yearly and normally in Spring, we proposed to reconstruct ozone time series considering the data over our region, South of South America, aiming to search periodicity signals on ozone time series. In other words, this work aimed to collaborate in the comprehension of the mechanisms driving the ozone variability in Southern Brazil.
]]>2. DATA AND METODOLOGY
2.1 Satellite measurements
TOMSOMI from NASA/Goddard Space Flight Center was used as our data source. The NASA TOMS series of four satellite instruments has been successfully designed and launched for measuring global TOCs since November 1978. The last TOMS instrument of this series was launched in July 1996 aboard the EP satellite. The EPTOMS instrument measures solar irradiance and the radiance backscattered by the Earth's atmosphere in six selected wavelength bands in the ultraviolet (UV) spectral region (between 308 and 360 nm)
2.2 GroundBased data
The Brewer spectrophotometer works with principles similar to the Dobson instrument but has an improved optical design and is fully automated. TOC values are obtained taking the ratio of sunlight intensities at four wavelengths between 306 and 320 nm with a resolution of 0.6 nm overcoming the spectral interference of sulfur dioxide with ozone (Kerr, 2002).
A Brewer Spectrophotometer 167 installed at Southern Space Observatory – Sao Martinho da Serra – Southern Brazil, is an MKIII model with double monochromator and resolution of 0.6 nm and has been used in the monitoring of the total atmospheric ozone (O_{3}), sulfur dioxide (SO_{2}) columns and UVB solar irradiance.
The days considered in our analysis were selected according to the following criteria: (i) because of Brewers data, the individual DS ozone observations are performed five times in 3 min. The ozone standard deviations are computed on a group of five individual DS measurements for each wavelength. Data are accepted if the standard deviation is lower than 2.5 DU; (ii) to obtain a better statistics analysis, the number of the individual DS data must be at least 35 (seven sequences of five observations); (iii) only typical clear sky days at solar zenith angles below 65 were considered in the calculation of ozone.
The interval of ozone Brewer data was between 1994  2008, while for TOMSOMI the period was 1979  2008. Figure 1 presents a generic profile with gaps of Brewer and TOMS data.
2.3 Methodology
]]> 2.3.1 Definition of errorA linear regression analysis was performed using the Brewer x TOMSOMI data considering 19942008. Regression coefficients, coefficients of correlation (R^{2}) and the root mean square errors (RMSE) were calculated and the mean bias error (MBE) comparing Brewer x TOMSOMI measurements was calculated. These parameters are obtained by the following expression:
where N is the number of data pairs Brewer TOMS.
2.3.2 SavitzkyGolay smoothing
One way of smoothing data and suppressing disturbances is to use a filter, and replace each data value I_{i}, i =1,..., N by a linear combination of nearby values in a window:
In the simplest case, referred to as a moving average, the weights are c_{j}=1/(2n+1) and the data value Ii is replaced by the average of the values in the window. The moving average method preserves the area and mean position of a seasonal peak, but alters both the width and height. The latter properties can be preserved by approximating the underlying data value, not by the average in the window, but with the value obtained from a leastsquares fit to a polynomial. For each data value Ii; We fit a we fit a polynomial of fifth order:
to all 2n+1 points in the moving window and replace the value Ii with the value of the polynomial at position ti : The procedure above is commonly referred to as an Savitzky–Golay filter (Press et al., 1995, Jönsson and Eklundh, 2004).
]]> The SavitzkyGolay filter method essentially performs a local polynomial regression to determine the smoothed value for each data point. This method is superior to adjacent averaging because it tends to preserve features of the data such as peak height and width, which are usually 'washed out' by adjacent averaging (Press et al., 1995).2.3.3 Wavelet analysis
In terms of mathematical tool, we drive our study using wavelet transform, which is a powerful tool for non stationary signal analysis and permits to identify the main periodicities in a time series and their evolution (Kumar and FoufoulaGeorgiou, 1997; Torrence and Compo, 1998; Percival and Walden, 2000). The wavelet transform of a series of discrete data is defined as the convolution between the series and a scaled and translated version of the wavelet function chosen. By varying the wavelet time scale and translating the scaled versions of the wavelet, it is possible to build a graph showing the amplitudes versus frequency (or scale) and how they vary with time.
Herein, we used the complex Morlet wavelet function, which consists of a plane wave modulated by a Gaussian function: , where ω_{o} is the nondimensional frequency and η a nondimensional "time" parameter. Let us assume that the time series, x_{n}, has equal time spacing Δt, with n =0,..., N1 . To be "admissible" as a wavelet, this function must have zero mean and be localized in both time and frequency space (Farge, 1992). Therefore, the continuous wavelet transform of x_{n} is defined as the convolution of x_{n} with a scaled and translated version of ψ_{0 }(η):
where (*) indicates the complex conjugate and S the wavelet scale. The technique allows to construct a picture showing the variation of amplitude in time and scale (Torrence and Compo, 1998).
If a vertical slice through a wavelet plot is a measure of the local spectrum, then the timeaveraged wavelet spectrum over a certain period is when the average is over all the local wavelet spectra, which gives the global wavelet spectrum (Torrence and Compo, 1998):
Percival (1995) shows that the global wavelet spectrum provides an unbiased and consistent estimation of the true power spectrum of a time series. Finally, it has been suggested that the global wavelet spectrum could provide a useful measure of the background spectrum, against which peaks in the local wavelet spectra could be tested (Kestin et al. 1998).
In addition, the crosswavelet analysis indicates whether exists or not a correspondence between detected cycles from independent time series, obtained for the same time base. If two time series X and Y are given, with respective wavelet transforms W_{n}^{X} (s) and W_{n}^{Y} (s), one can define the crosswavelet spectrum as W_{n}^{X} (s) = W_{n}^{X} (s)[W_{n}^{Y*} (s)], where W_{n}^{Y*} (s)is the complex conjugate of W_{n}^{Y} (s). The crosswavelet spectrum is complex, and hence one can define the crosswavelet power as W_{n}^{X} (s)^{2} (Torrence and Compo, 1998).
]]>3. RESULTS AND DISCUSSION
Before the reconstruction of the ozone Brewer data, a mathematical difference between TOMSOMI and Brewer was performed (Figure 2), where the data with a statistical difference greater than 1s is discarded. The correlation between the TOMSOMI and Brewer data was from r = 0.89 (Figure 3) to r = 0.93, when we used this criterion. Indeed, only after these data adjust we started the reconstruction of the ozone Brewer data in two ways, each subdivided in two supplementary steps:
]]>

First way: 1 We obtained a linear regression between the TOMSOMI and Brewer data, where the coefficient of correlation is r = 0.93; 2 The gaps that could not be obtained by the linear regression were interpolated using the SavitzkyGolay filter method (Press et al., 1995, Jönsson and Eklundh, 2004).

Second way: 1 As a high correlation between the TOMSOMI and Brewer data was observed, we completed the missing Brewer data with TOMS data; 2 The gaps that could not be obtained by the TOMSOMI data were interpolated using the SavitzkyGolay filter method (Press et al., 1995, Jönsson and Eklundh, 2004).
The ozone Brewer reconstructed "first way" is presented in Figure 4a and "second way" in Figure 4b. The first way reconstructed shows a mean of 274.7±19.6 for Brewer and 273.9±20.1 in terms of ozone fro TOMS. To investigate the proportionality and similarity of the groundbased and satellitebased observations, the Brewer and OMI total ozone column data are fitted using a linear regression. Statistical parameters obtained are shown in Table 1. The correlation between TOMS ozone observations and Brewer measurements is significantly high. The R^{2} values higher than 0.78 are indicative of the groundbased and satellitebased data sets showing a similar behavior. The statistical analysis renders slopes very close to unity. The scatterplot presented in Figure 3 between satellite and groundbased data for the Southern Brazil (29ºS, 53ºW) data set reveal a high degree of proportionality. It can be seen that the RMSE values and uncertainty of MBE parameters are significantly lower. These reveal a high degree of proportionality with a notably small spread (RMSE smaller than 4%). This reveals the presence of a bias with a small statistical spread. The uncertainty of MAB parameters is lower than 1%, indicating the statistical significance of the reported values. Bhartia and Wellemeyer (2002) reported that the relative uncertainty of OMITOMS ozone data is around 2% for solar zenith angles lower than 70 degrees. Therefore, apparently a significant difference between the reconstructed ozone data is considered insignificant.
The wavelet spectra show negligible differences between the two reconstructed time series. This situation is most clearly observed when we consider the crosswavelet spectrum between the two way ozone reconstruction data (Figure 5), where the same period variation in time is observed as in wavelet spectra for ozone Brewer reconstructed time series (Figure 4).
This signal indicates a possible seasonal variation of the ozone. Also, the existence of other periods was observed between 530900 days being more persistent in two time series, as well as approximately between 54807758 and 885810958 days. In this case, the periodicities come from a possible QBO influence on ozone in Southern Brazil.
It is observed that a period variation exists with the time of ~2000 days, which is more persistent to time interval of 54808858 days in terms of long trends. In this case, we assign these frequencies as a possible influence of the second harmonic of the 11year solar cycle regarding ozone in Southern Brazil.
]]> The wavelet spectrum of reconstructed ozone from time series indicates the strongest feature and a persistent signal near 365days (Figure 5). This signal indicates a possible seasonal variation of the ozone. Also, the existence of other periods was observed between 530900 days being more persistent in two time series, as well as approximately between 54807758 and 885810958 days. In this case, the periodicities come from a possible QBO influence on ozone in Southern Brazil. Hood and McCornack (1992) reported have found the QBO signal in their studies about components of interannual ozone change based on NIMBUS 7 TOMS data to 65ºN65ºS. Sych et al. (2005), also, reported this signal of 2.5 years of QBO influence on ozone to 10º S latitude, in yours studying about the periodic spatial–temporal characteristics variations of the total ozone content. It is observed that a period variation exists with the time of ~2000 days, which is more persistent to time interval of 54808858 days in terms of long trends. In this case, we assign these frequencies as a possible influence of the second harmonic of the 11year solar cycle regarding ozone in Southern Brazil.The wavelet spectra show negligible differences between the two reconstructed time series. This situation is most clearly observed when we consider the crosswavelet spectrum between the two ways ozone reconstruction data (Figure 6), where the same period variation in time is observed as in wavelet spectra in both ozone Brewer reconstructed time series (Figure 5).
The data of the ozone from TOMSOMI presents a long time series in comparison with our Brewer data. Therefore, we used the first one in the reconstruction of ozone Brewer data considering the very good correlation factor obtained from the linear regression between the two time series. The reconstructed ozone Brewer data for our region, 29ºS, 53ºW, is presented in Figure 7a. The wavelet spectrum of new ozone Brewer reconstructed time series in Southern Brazil (Figure 7b) shows that the periodicities (seasonal, QBO and second harmonic of the 11yr solar cycle variations) found in Figures 5a and 5b remain in the past 15400 days. Thus, increasing the time series it is possible to observe a representative periodicity of the second harmonic of the 11yr solar activity (~2000 days) as a strong feature. Furthermore, a persistent time for the 15008258 days (Figure 7b) has also been observed, in which it is also possible to show a periodicity of ~4000 days (Figure 7b) and that is related with a possible influence of the 11yr solar cycle in ozone in Southern Brazil. This results in agreement with Hood and McCornack (1992) that reported to have found the of solar cycle (1011 years) influence on ozone change based on NIMBUS 7 TOMS data to 65ºN65ºS. So who, Sych et al. (2005), also, reported this signal of 11.0 years of solar cycle influence on ozone to 10º S latitude, and Soukharev and Hood (2006) have found a response of the solar cycle variation of stratospheric ozone in the two hemispheres.
4. CONCLUSION
In this work ozone Brewer time series for Southern Brazil were reconstructed and wavelet analysis was applied. We have found the following periodicities that influence the ozone: (i) A seasonal variation with periodicity of ~365 days; (ii) The QBO phenomenon with periodicity of ~530900 days; (iii) The second harmonic of the 11yr solar cycle with periodicity of ~2000 days; and (iv) The 11yr solar cycle with periodicity of ~4000 days.
Therefore, we contributed with an overview and profile of ozone data on our region (29ºS, 53ºW) and presented some aspects involving the ozone periodicities in the South of Brazil. We understand further studies are necessary to obtain more precise information on the current weather conditions in South America as a whole. Thus, we also intended with this work to collaborate as source for mathematical models that address global climate changes and their direct or indirect effects on the ozone behavior and global dynamic.
5. ACKNOWLEDGMENTS
Authors would like to thanks for support granted to this research: N. R. Rigozo  CNPq (APQ 470252/20090, 470455/20101 and research productivity, 301033/20099) and FAPERGS (APQ 1013273); M.P Souza Echer  CNPq (151609/20098); CNPQ/PQ (300211/20082) e FAPESP (2007/525331); A. Prestes FAPESP  (2009/029078).
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Received October 2010
Accepted November 2011