Application of wavelet transform in the study of coastal trapped waves off the west coast of South America

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 33, L22601, doi: /2006gl026395, 2006 Application of wavelet transform in the study of coastal trapped waves off the west coast of South America Rosio Camayo 1 and Edmo J. D. Campos 1 Received 23 March 2006; revised 27 September 2006; accepted 18 October 2006; published 18 November [1] Wavelet transform and cross wavelet transform were applied for analyzing long time series of sea level and alongshore wind stress to identify intraseasonal variability off western South America and the relations with remote and local forcings. Hydrographic data were used to estimate properties of coastal trapped waves with a theoretical model. For El Niño years, we found the existence of intraseasonal oscillations with periods days, between 2S and 27S. At the peak of and EL Niños, we found perturbations in the northern region, probably associated with remotely forced internal Kelvin waves, with periods 6 11 days and phase velocities km/day. Between 12S and 15S, during two El Niño events, our calculations show perturbations which appear to be barotropic shelf waves propagating southward with velocities between 110 and 150 km/day and periods between 30 and 50 days. Citation: Camayo, R., and E. J. D. Campos (2006), Application of wavelet transform in the study of coastal trapped waves off the west coast of South America, Geophys. Res. Lett., 33, L22601, doi: /2006gl strongly contribute to the observed variance to the north of 5 S. Clarke [1983], suggests that waves with periods of one to two weeks are forced by equatorial Rossby-Gravity waves traveling to east. Enfield [1987] found a significant intraseasonal variability off the coast of Peru with days period. These oscillations are more pronounced during the southern hemisphere spring-summer time, at the onset of El Niño, and derive from baroclinic equatorial waves. According to Shaffer et al. [1997], as these waves can strongly modify the source of upwelled waters, they might have a significant influence on the pelagic ecosystem along Chilean and Peruvian coast at least during El Niño. [3] In the present work, we use wavelet transform to identify statistically significant oscillations during the occurrence of some of the recent El Niño events ( , and ) off Peruvian and northern Chilean coast. Also, properties of remotely forced perturbations are compared with simple theoretical models of coastal trapped waves. 1. Introduction [2] The ocean along the west coast of South America is well known by its very high primary productivity and due to its direct exposure to the El Niño phenomenon, which impacts profoundly all the physical-biological ecosystem. Besides upwelling and the presence of poleward currents at deeper layers, the Peru-Chile Current system shares a number of attributes with other boundary currents, including the presence of coastal trapped waves (CTWs) [Strub et al., 1998]. Several studies have detected low frequency oscillations, which propagate poleward. Smith [1978], using sea surface temperature and current data along the Peruvian coast during the period, observed fluctuations propagating along the coast with speed in the order of 200 km/day and time-scale ranging from daily to weekly. These perturbations showed poor correlation with local winds but were well correlated with winds hundreds of kilometers offshore. For the same period, Romea and Smith [1983] found low-frequency fluctuations in the sea level (periods larger than four days) with poleward phase speed of baroclinic Kelvin waves ( km/day). In another study, Brink [1982] compared observations from the Peruvian coast (sea level and alongshore velocity) with coastal trapped wave theory. He concluded that fluctuations in the band 5 10 days are due to free Equatorial Waves, which 1 Instituto Oceanografico da Universidade de Sao Paulo, Sao Paulo, Brazil. Copyright 2006 by the American Geophysical Union /06/2006GL Data and Methodology [4] For the wavelet analysis we used historical time series from the Sea Level Center of NODC, covering the period , and satellite wind stress data from IFREMER, for , with temporal resolutions of one day and seven days, respectively. For the local hydrographic data, we used information from the stations listed in Table 1. Grinsted et al. [2004] show that time-series far from normally distributed produces rather unreliable results. Because of that, we applied the Smirnov-Kolmogorov test to the cumulative distribution functions of the time series and found that the data obey a normal distribution at 95% confidence level. Then, we computed the anomalies with respect to the sample mean. For the sea level, oscillations associated with the Nyquist frequency (period of 2 days in this case) and the annual cycle variability were removed. The wind stress was linearly interpolated to obtain daily data. This is certainly a weakness of our cross wavelet analysis of wind stress and sea level. It is not easy to extract daily features from the interpolated weekly wind fields and, for this reason, results for oscillations with periods shorter than 14 days should, in principle, not be considered. However, we would like to point out that in a recent work Ayina et al. [2006] compared results of a model run forced with daily ECMWF wind-stress ( true daily data) with another forced with daily data obtained by interpolating weekly averaged ECMWF wind stress ( simulated daily data). They found that the results of the true and simulated daily data experiments do not show significant difference over the inter-tropical area. Thus, in our analysis L of5

2 Table 1. Locations of the Hydrographic Stations Station Latitude S Longitude W La Libertad Lobos de Afuera Paita Santa Cruz Callao Pisco San Juan Matarani Arica Antofagasta Caldera we keep these higher frequency oscillations, but advise that their results should be considered with precaution. [5] As a complementary data source, we used data from a cruise along Peruvian coast conducted by IMARPE (Instituto del Mar de Peru) in Temperature and salinity data were used to compute density, Brunt-Vaisala frequency and coastal trapped waves properties. Bathymetry was taken from the NODC ETOPO-5 data set. For classification of El Niño years we used the analysis produced by the NCEP Climate Prediction Center Wavelet Transform [6] Fourier transform (FT) gives a limited amount of information on the characteristics of a time varying signal. As FT reveals frequencies present in the whole time series, information about an individual event would be lost [Kantha and Clayson, 2000]. On the contrary, Wavelet transform (WT) expands time series into time-frequency space and can therefore find localized intermittent periodicities [Grinsted et. al., 2004]. However, it must kept in mind that WT loses frequency information in the high-frequency band and time information in the low-frequency band. [7] Wavelet analysis is based on the convolution of a function f(t) with a set of functions g(t) derived from translations and stretching of a mother wavelet [Meyers et al., 1993]. The Continuous Wavelet Transform (CWT) of a time series x n with uniform time steps dt is defined as the convolution of x n with the scaled and normalized wavelet [Grinsted et al., 2004]. In the present study, wavelet analysis was applied to sea level and alongshore wind stress component data using the methodology proposed by Torrence and Compo [1998]. First we computed the Fourier Transform of the time series, applying padding. Following this, a mother wavelet and the scales to analyze were Figure 1. Results of XWT to sea level and wind stress time series, on two stations (top), and to time series of sea level from two pairs of different stations (bottom). 2of5

3 Table 2. Theoretical Phase Speed c for Barotropic Continental Shelf Waves (n = 1, 2, 3) and for the First Mode of Baroclinic Kelvin Waves a Internal Kelvin Barotropic Shelf Wave Wave (n = 1) Section n=1 n=2 n=3 Rd i c i Paita Lobos Callao San Juan Matarani a Theoretical phase speed c is given in km/day. Also shown are the internal Rossby radius of deformation (Rd) in some of the locations listed in Table 1. chosen. The choice of wavelet must be such that has attributes resembling the signal, such as asymmetry and slow or fast variation with time. In the present case we opted for the Morlet function. For each scale we constructed a normalized wavelet function using padding to reduce spectral leakage. After finding the WT for all scales, we removed the paddings and used a chi-squared distribution to calculate the significance levels at 95%. Here we used the value 0.9 for the auto-correlation parameter (alfa) at lag-1, assuming small errors and low degree of randomness for the data The Cross Wavelet Transform (XWT) [8] The XWT finds regions in time-frequency space where the time series show high common power. The XWT of two time series X n and X n is defined as W XY = W X W Y *, where W X is the continuous wavelet transform of the time series X n and * denotes the complex conjugate. The cross wavelet power is defined as jw XY j [Grinsted et al., 2004]. [9] In this study we calculated the XWT of pairs of sea level and alongshore velocity in the same location for an analysis of local forcing and to pairs of sea level time series in different locations to investigate the effects of remote forcing. Results of these computations for some of the stations listed in Table 1 are shown in Figure Theoretical Characteristics of Coastal Trapped Waves 3.1. Continental Shelf Waves (CSW) [10] According to Leblond and Mysak [1978], CSW are highly rotational planetary topographic waves. They consist of a series of horizontal eddies with alternate sign and propagate with the coast to the left in the southern hemisphere. They are generated by weather systems with movements along or across the coast; present long wavelengths compared with the continental shelf and slope; have frequencies much smaller than f and very small amplitudes (usually of a few centimeters), and are predominantly barotropic. There exist a challenge to find analytic solutions for CSW in a region with arbitrary depth profile. However, for the simple case of a continental shelf with exponential profile H(x) = dexp(2bx) there exist infinite discrete solutions given by the dispersion relation s = 2bfk/(m 2 + k 2 + b 2 ), where L is the cross-shore scale, m is the cross-shore wave number and tan(ml) = m/(b + k). For n integer, (n 1/2)p < ml < np. Applying this theory for the study area, we calculated the phase speed for long wavelengths (n =1,n = 2 and n = 3) as shown in Table Baroclinic Kelvin waves [11] A Kelvin wave in a two-layers ocean with constant depth has phase speed given by c ¼ Dr r g H 1=2 1H 2 ð1þ H 1 þ H 2 and the internal Rossby radius of deformation is Rd = c/f. Values of c and Rd for the first baroclinic mode, calculated with the observed vertical profiles of density and Brunt- Vaisala frequency (N 2 (z)) for Callao, San Juan and Matarani stations are also shown in Table Results 4.1. Dominant Periods During El Niño Years [12] From the wavelet spectra of sea level data for coastal stations we list in Table 3 the periods in which significant peaks occurred for El Niño years. The presence of intraseasonal oscillations with periods ranging from about 20 to 90 days, is evident in practically the entire region Local Forcing [13] The XWT was applied to pairs of sea level data and alongshore wind stress to detect oscillations of local origin. All along the coastal region we found good correlations in periodicities ranging from 10 to 50 days. Off the northern Peruvian coast, these oscillations occurred mainly during June 1992, which correspond to an El Niño event. In the south, these oscillations were observed every year, but they were more intense during El Niño. Fluctuations with periods of 10 days could be associated with coastal lows, which are atmospheric trapped waves, as proposed by Shaffer et al. [1997], who found perturbations with periods 6-10 days in the Chilean coast. It is likely that these atmospheric coastal lows could be the response to tropical convection related with El Niño Remote Forcing [14] Applying the XWT to sea level data on different pairs of stations we computed phase speed of propagating Table 3. Significant Periods in the Wavelet Spectra for Sea Level Time Series in Some Locations off Peruvian Northern Chilean Coast a Stations Jan 83 Jan 87 Jan 92 Jan 93 Jan 97 Jun 97 Jan 88 La Libertad < < Paita < < L. Afuera < <30 40 < Callao <60 < < < San Juan < < Arica Antofagasta <30 <30 <60 < a Significant periods are in days. 3of5

4 Table 4. Significant Periods for the Cross Wavelet Spectra (left) and Calculated Phase Speed for Sea Level Time Series for Two Pairs of Different Stations a Jan92 Mar92 Apr97 May97 Oct97 Stations T c T c T c T c T c 6 S 12 S S-15 S a Significant periods are in days, and calculated phase speed is in km/day. signals of remote origin. In Table 4 we list the dominant period T, in days, and the phase speed c for two pairs of stations (6 S 12 S and 12 S 15 S). For instance, for March of 1992 our results show oscillations with period 6 11 days, propagating to the south with phase speed of km/day Evidence of Coastal Trapped Waves: Comparison Between Theoretical and Observational Data [15] Previous studies have shown the presence of coastal trapped waves with typical periods of 5 20 days. Brink et al. [1983] associated these waves with remote wind forcing. Strub et al. [1998], mentioned that, at periods of days to weeks, one of the major findings off Peru is that neither local winds nor those located closer to the equator are well correlated with sea level or alongshore currents below the shallow Ekman layer. It was also observed by several researchers [Smith, 1978; Brink, 1982; Romea and Smith, 1983], that the sea level and the alongshore current were strongly lag-correlated with phase speeds of 180 and 260 km/day, characteristic of the first baroclinic mode of coastal trapped waves. Shaffer et al. [1997], observed strong fluctuations with periods around 50 days (associated with equatorial Kelvin Waves), and between 5 and 10 days, probably associated with Mixed Rossby-Gravity waves and Inertio-Gravity waves trapped at the Equator, during El Niño [16] With CWT we determined the dominant modes of sea level data on each station between 6 S and 15 S and then used XWT to determine the occurrence of significant common peaks at given periods. With the time shift of the occurrence of these peaks, we determined the phase speed of these oscillations. Finally we looked for the correspondence between the observational and theoretical values. A comparison of phase speed obtained with sea level crossspectra and the theoretical values shown in Table 2 are summarized in Table 5. [17] At the beginning of 1992, southward traveling disturbances that resemble internal Kelvin waves occurred between 6 S 15 S, with periods in bands of 6 11 days and days, and with phase speeds between 160 and 260 km/day. These agree quite well with several works [Brink, 1982; Brink et al., 1983; Smith, 1978; Romea and Smith, 1983]. In the region comprised between 12 S and 15 S, disturbances probably associated with barotropic shelf waves (n = 1) were found propagating poleward with phase speed in the range km/day and periods days. In contrast, Shaffer et al. [1997] found oscillations of around 50 days but with velocities of 266 km/day. Further studies should be done with these particular oscillations (50 days). [18] For May 1997, as a first approximation, we used the theoretical phase speeds obtained for the 1992 cruise. In the region comprised between 6 S and 12 S, probably occurred baroclinic Kelvin waves of days and days, with phase speed around of km/day and 340 km/day, respectively. More to the south (12 S 15 S), the results show what seems to be baroclinic Kelvin waves with periods in the band of days with velocities of 200 km/day, and barotropic shelf waves of 30 to 40 days with velocities between 100 and 150 km/day. 5. Summary and Conclusions [19] Wavelet transform and cross wavelet transform were applied to sea level and alongshore wind stress time series off the South American west coast. Temperature and salinity profiles from oceanographic cruises were used to compute properties of coastal trapped waves using a simple theoretical model. The raw wind stress have period of seven days and was interpolated to one day for the cross wavelet analysis with sea level. For this reason, the results for oscillations with periods shorter than 14 days should be taken with caution. [20] For El Niño events we found the presence of intraseasonal oscillations with periods between 20 and 90 days along the coastal region from 2 S to27 S. Specifically, during the months when the extraordinary El Niño reached its maximum extension and strongest intensity (beginning of 98), in the region around 2 S we found Table 5. Summary of the Remotely Forced Oscillations Indicating the Significant Periods and Phase Speed a Jan 92 Apr May 97 Oct 97 Stations T c T c T c 6 S 12 S 6 11 IKW IKW IKW IKW IKW S 15 S 6 8 IKW IKW IKW CSW CSW a Significant periods are in days, and phase speed is in km/day. Also shown are indications of the possible type of the trapped waves: IKW, Internal Kelvin Wave; CSW, barotropic Continental Shelf Wave. 4of5

5 coastal oscillations in a broad band of periods shorter than 70 days. In the central Peruvian coast, the region between 6 S and 15 S, our computations show oscillations shorter than 50 days. Along almost all the coast we observed strong correlation between sea level and local alongshore wind stress in the periods around of 10 and 50 days, with larger intensity during El Niño and to the south. These oscillations can be associated with Coastal Lows, that are one type of atmospheric waves trapped at the western side of the Andes. [21] The deformation radius we calculated is larger than the topographic scale (shelf and slope) off the coast of Peru and northern Chile. This could be an indication that the perturbations are likely to be Kelvin waves. But small values obtained for the stratification parameter (S) also suggest they could be barotropic shelf waves. Because of this controversy we used a simple theoretical model to compute the phase speeds and compared them with velocities calculated from the wavelet spectra. [22] We found that in the more intense periods of the and Nios (onset of 1992 and 1998), between 6 S and 12 S, there were oscillations probably associated with remotely forced internal Kelvin waves, with periods in the bands of 6 11 days (only for El Niño 91 92) and days (only for El Niño 97 98), with phase speeds between 160 and 340 km/day. For these two El Niño events, in the region between 12 S and 15 S, southward barotropic shelf waves probably occurred with velocities between km/day, and with periods in the band of days. Shaffer et al. [1997] observed oscillations with periods of nearly 50 days, but with velocities of 260 km/day. For 1997, our calculations also suggest that baroclinic Kelvin waves occurred for the same region, with periods of 6 30 days and velocities around of 200 km/day. [23] Our final conclusion is that the cross wavelet analysis allowed us to identify oscillations strongly correlated with the local wind stress, what is an indicative that these waves are being forced locally. The analysis with sea level data from different pairs of stations produced information that could be indicative of waves propagating along the coast. Because with the CWT it is possible to extract the period and phase speed of these signals, we were able to sort out these waves either as baroclinic Kelvin waves or barotropic shelf waves, with the aid of the simple theoretical model. As a final remark, we would like to say that in a continuation to this work we plan to repeat our analysis using the NODC buoys data and daily wind stress (0.5deg in longitude and latitude) available at IFREMER from 1999 to present. [24] Acknowledgments. This work was funded by The Sao Paulo State Science Foundation-FAPESP (grant 2004/ ); by the Inter- American Institute for Global Change Research (IAI), through project SACC CRN-061; and by the Brazilian Council for Scientific and Technological Development-CNPq (Processos / and / Conv. Prosul). The first author is supported by a CAPES student fellowship. We especially thank Enver Ramrez Gutiérrez and the anonymous reviewers, for their most valuable comments. References Ayina, L.-H., A. Bentamy, A. M. Mestas-Nuez, and G. Madec (2006), The impact of satellite winds and latent heat fluxes in a numerical simulation of the tropical Pacific Ocean, J. Clim., in press. Brink, H. K. (1982), A comparison of long coastal-trapped wave theory with observations off Peru, J. Phys. Oceanogr., 12, Brink, H. K., D. Halpern, A. Huyer, and R. L. Smith (1983), The physical environment of the Peruvian Upwelling system, Progr. Oceanogr., 13, Clarke, A. J. 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Salinas, and J. Rutllant (1997), Circulation and low-frequency variability near the Chile Coast: Remotely-forced fluctuations during the El Niño, J. Phys. Oceanogr., 27, Smith, R. L. (1978), Poleward propagating perturbations in currents and sea levels along the Peru coast, J. Geophys. Res., 83, Strub, P. T., J. Mesas, V. Montecino, J. Rullant, and S. Salinas (1998), Coastal ocean circulation off western South America, The Sea, vol. 11, pp , John Wiley, Hoboken, N. J. Torrence, C., and G. P. Compo (1998), A practical guide to wavelet analysis, Bull. Am. Meteorol. Soc., 79, R. Camayo and E. J. D. Campos, LABMON/IOUSP, Pca. do Oceanografico 191, Cid. Universitaria, Sao Paulo, SP, Brazil. (edmo@io.usp.br) 5of5