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 The paper presents clear evidence of zonally symmetric planetary waves with very large amplitudes present in the UK Met Office zonal wind data of the Northern Hemisphere stratosphere in the winter of 2003–2004. The spectral analysis reveals that three prevailing periods of ∼23, 17 and 11 days contribute to the observed zonally symmetric oscillations. These waves are extracted from the data and their amplitudes and phases are studied in detail depending on height and latitude. The wave amplitudes - particularly those of the 11- and the 17-day zonally symmetric waves - clearly indicate the presence of two latitudinal branches of amplifications centred at 50–60°N and 20–30°N. The phase analysis shows that these waves are vertically upward propagating waves and that the waves from the high-latitude and tropical branches are almost out of phase. A possible forcing mechanism is suggested. The zonally symmetric waves play an important role in coupling the dynamical regimes of the high- and low-latitude stratosphere particularly during the major stratwarm event in the Arctic winter of 2003–2004.
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 The dynamics of the middle atmosphere in winter are known to be dominated by the planetary waves of large amplitudes. The most important are quasi-stationary Rossby waves, which propagate upward from the troposphere and are very strong but quite variable during winter. Other planetary waves are the travelling normal modes, also known as free modes. These waves correspond to the natural mode of variability of the Earth's atmosphere. Usually a perturbation to the atmosphere excites a spectrum of waves including more than one normal mode and commonly observed modes are those with periods around 2, 5, 10 and 16 days. Their perturbations have wavelike form in the longitudinal and vertical directions and sometimes in the latitudinal direction as well. Usually their amplitudes grow with height due to the decrease in density. Normally these waves do not transport much momentum but they can interact with other waves such as quasi-stationary or travelling planetary waves, atmospheric tides and gravity waves. These interactions may play an important role in the dynamics of the middle atmosphere and certainly contribute significantly to the variability of the population of atmospheric waves at these heights.
 Classical studies showed that the zonal mean flow affects the planetary wave propagation by changing the refractive index [Charney and Drazin, 1961]. However, the planetary waves in the stratosphere strongly affect the zonal mean flow as well. They tend to reduce the wind speed or even changing its direction, to warm up the high-latitude stratosphere as it happens in sudden stratospheric warmings (SSW). The key mechanism for generating the SSW event, originally proposed by Matsuno  and now widely accepted, is the upward propagation of transient packet of planetary waves and their interaction with the mean flow, or the SSW is a result of a self-consistent, non-linear process [Liu and Roble, 2002]. Therefore, the time period preceding the onset of the SSW is usually characterized by more than one type of planetary waves present in the stratosphere.
 In the present paper we report global scale zonally symmetric planetary waves (5–30 days) which are present in the UK Met Office data during the winter period of time between 1 October 2003 and 30 April 2004. A major SSW took place in the Arctic winter of 2003–2004 which was particularly remarkable because of an extended period of nearly two months of polar vortex disruption and a reversed direction of the zonal mean flow observed in the middle and lower stratosphere [Manney et al., 2005]. It will be shown that the observed zonally symmetric planetary waves are related to this major SSW in 2003–2004 winter.
2. Data and Method of Analysis
 The UKMO (from the UK Meteorological Office) data set is used to examine the planetary waves present in the winter of 2003–2004 stratosphere of the Northern Hemisphere (NH). This data set is a result of assimilation of in situ and remotely sensed data into a numerical forecast model of the stratosphere and troposphere. The outputs of the assimilation are global fields of daily temperature, geopotential heights and wind components at pressure levels from the surface up to 0.1 hPa. The generated data fields have global coverage with 2.5° and 3.75° steps in latitude and longitude respectively. The UKMO data have been used by many researchers to study different dynamical events in the stratosphere including planetary waves [Fedulina et al., 2004] and SSWs [Cho et al., 2004]. All atmospheric parameters are investigated but only the result for the zonally symmetric planetary waves in the zonal wind of the NH stratosphere is shown in this paper.
 The mathematical expression for a zonally symmetric (with a zonal wavenumber s = 0) planetary wave is related to: cos (ωt − Φ), where ω is wave frequency, t is time and the quantity Φ is independent of longitude. This means that if there are global scale zonally symmetric planetary waves with large amplitudes which are present in the zonal wind they should be distinguished in the zonal mean zonal wind (the zonal wind averaged in the longitude). Figure 1 shows the latitude-time cross section of the zonal mean zonal winds at 1 hPa (∼45 km height) and 0.3 hPa (∼52 km height) pressure levels for the period of time from 1 October 2003 to 30 April 2004. Clearly outlined zonally symmetric planetary oscillations can be identified in both plots. These oscillations have a main maximum just before the onset of the major SSW at 10 hPa pressure level (2 January 2004) and a secondary one - in February–March 2004. Two branches of zonally symmetric waves can be discerned, one is situated in the high-latitudes and other – in tropical latitudes with relatively weak oscillations around 40°N. It seems that both branches of zonally symmetric waves are not in phase. We note that the zonally symmetric planetary oscillations are present in the lower and middle stratosphere (below 10 hPa geopotential height) as well but they are weaker than those in the upper stratosphere and predominantly the high latitude branch is developed at these heights. This is a reason only the results for the upper pressure levels, 1 hPa and 0.3 hPa, to be shown in this paper.
 To determine the prevailing periods of zonally symmetric waves we use a two-dimensional analogue of the Lomb-Scargle periodogram method based on a least-squares fitting procedure applied to the entire time series. The planetary waves with periods between 5 and 30 days are studied here. The main purpose of this study, however, is not only to define the predominant periods of the wave components which contribute to the observed zonally symmetric oscillations but to isolate and study them in detail. To extract the waves from the data or to determine their amplitudes and phases, we use again a least-squares fitting procedure, but this time it is applied to the time segment twice the length of the longest period under investigation. Then this segment is moved through the time series with steps of 1 day.
Figure 2 shows the latitudinal amplitude spectrum of the zonally symmetric waves (s = 0) present in the zonal wind at 1 hPa pressure level (Figure 2, left). The observations of planetary waves in the stratosphere are commonly viewed using the geopotential heights and that is why Figure 2 (right) shows the amplitude spectrum of the zonally symmetric waves present in the geopotential heights at 1 hPa. Both spectra are very similar and indicate 3 prevailing periods: ∼22–24, 17 and 11–12 days. There are two latitudinal amplifications of these periods in the zonal wind spectrum: the main amplification is centred around 50–60°N and the secondary one – around 20–30°N. Analogous to them there are two maxima in the geopotential height spectrum and they are centred at North Pole and at around 40°N respectively.
 It is well known that the strongest planetary waves in the winter stratosphere are the quasi-stationary planetary waves (SPW). To avoid the distortion of the zonally symmetric waves in isolating them from the data, we perform a linear two-dimensional (time-longitude) least-squares fitting including - besides the three above mentioned periods of the zonally symmetric waves - the first three modes of the stationary waves (it means the SPWs with zonal wavenumbers 1, 2 and 3 which are frequently noted as SPW1, SPW2 and SPW3) as well. Figure 3 shows the latitude-time cross sections of the amplitudes of the three investigated periods of the zonally symmetric waves at 1 and 0.3 hPa pressure levels. The upper two plots show the amplitude of the 23-day zonally symmetric oscillation present in the upper stratosphere. It amplifies particularly during the SSW (end of December–January) when the polar vortex was disrupted. There is another amplification visible in the second half of November–early December. Later it will be shown that at these moments the SPW1 and SPW2 are maximized. The latitude-time distributions of the amplitudes of the 17- and 11-day zonally symmetric waves are shown in the middle and bottom couple of plots. Both patterns are very similar and show first, that there are two branches of amplifications centred at 50–60°N and 20–30°N and second, that the main amplification is between day number 50 and 100 and the secondary one – between 130 and 150. The tropical amplification is particularly well visible in the amplitudes of the 17-day zonally symmetric wave.
Figure 4 shows the phases of the 17-day zonally symmetric wave observed in November–January at latitudes of 60°N (Figure 4, top) and 20°N (Figure 4, bottom) and at four pressure levels: 30, 10, 1 and 0.3 hPa. We chose the 17-day wave because the phases can be determined precisely only when the amplitudes are large enough at all latitudes and the tropical branch is quite strong mainly for this wave. Two lower than 1 hPa pressure levels are used in this case because we wanted to demonstrate more clearly the vertical direction of propagation. The two plots show that phases are quite variable (particularly those for the lower geopotential levels) but in spite of this they clearly indicate vertically upward direction of propagation. There is a well noticeable phase shift between the waves in the two branches; while the mean phase at high latitudes is between 0 and −20 degrees that at tropical latitudes is around 160 degrees. This means that the 17-day zonally symmetric waves are almost out of phase in the two branches. This result supports the observational evidence in Figure 1 that both branches of zonally symmetric waves are not in phase.
 This paper presents evidence for zonally symmetric planetary waves with large amplitudes observed in the UKMO zonal wind data of the NH stratosphere during the winter of 2003–2004. The spectral analysis indicates that three prevailing periods of 23, 17 and 11 days contribute to the observed zonally symmetric oscillations. The waves with the above periods are extracted from the data using a linear two-dimensional least-squares fitting method. The wave amplitudes and phases are studied in detail depending on the height and latitude. The wave amplitudes, particularly those of the 11- and the 17-day zonally symmetric waves, clearly demonstrate two latitudinal branches of amplifications centred at ∼50–60°N and ∼20–30°N - a feature that is well visible in the raw data of zonal mean zonal winds (Figure 1). The phase analysis shown in Figure 4 supports another feature of the zonally symmetric oscillations observed in the raw data of Figure 1, i.e. the high-latitude and the tropical branches of waves are not in phase. The phase result, particularly for the 17-day wave, reveals that the waves from the two branches are almost out of phase.
 The zonally symmetric waves found in the UKMO zonal wind data during the Arctic winter of 2003–2004 are of very large amplitudes. The detail analysis of this time period shows that after SPW1 and SPW2 the next most powerful waves are zonally symmetric waves. While the amplitude of the SPW1 is considerably larger than those of the zonally symmetric waves, the amplitude of the SPW2 is comparable to that of the 23- and the 17-day zonally symmetric waves in the upper stratosphere.
 The travelling planetary waves present in the UKMO zonal wind data have been studied as well. The latitudinal spectra of the eastward (Figure 5, left column) and westward (Figure 5, right column) propagating waves with zonal wavenumbers up to 3 are shown in Figure 5. These spectra reveal that besides the strong eastward propagating wave with period ∼29–30 days and zonal wave number 1 the next powerful westward and eastward propagating waves are those with periods similar to the periods of the zonally symmetric waves, or: ∼22–25, 15–18 and 10–12 days. All these propagating waves have large amplitudes, however, only the amplitudes of the 17- and the 24-day waves are approaching those of the zonally symmetric waves.
 It is known that there are no zonally symmetric normal modes with such long periods as those of the waves found in the UKMO zonal wind data [Longuet-Higgins, 1968]. The fact that we found zonally symmetric and zonally propagating waves with similar periods present simultaneously in the UKMO zonal wind data suggests that a possible forcing mechanism of the zonally symmetric waves could be a nonlinear interaction of the SPW1 and possibly of the SPW2 with the zonally propagating planetary waves with zonal wavenumber 1 or 2. In this way the zonally symmetric waves with the periods of the zonally propagating waves should be produced. To describe how this coupling process works we note the following: if a given oscillation composed of two primary travelling and stationary waves defined by their frequency –wave number pairs (ω, s1) and (0, s2) passes through a quadratic system, then the output from this system would yield the original primary waves plus four other secondary waves which have the following frequency-wave number pairs: (2 ω, 2 s1), (0, 2 s2), (ω, s1 + s2) and (ω, s1 − s2) [Pancheva et al., 2000; Angelats i Coll and Forbes, 2002]. In this case the last two types of secondary waves are of interest to us. They are known as “sum” and “difference” secondary waves. Through such a process the presence of zonally symmetric wave with frequency ω and wave number s = 0 could be due to the interactions of: (1) the SPW1 with eastward or with westward travelling planetary wave with frequency ω and zonal wave number 1; in the first case the zonally symmetric wave will be the “sum” secondary wave, while in the second one – the “difference” secondary wave, and (2) the SPW2 with eastward/westward travelling planetary wave with frequency ω and zonal wave number 2; similarly, in the first case the zonally symmetric wave would be the “sum”/“difference” secondary wave. Figure 5 clearly indicates the presence of eastward and westward propagating waves with zonal wave numbers 1 and 2 and with periods ∼23, 17 and 11 days, therefore the zonally symmetric waves could be produced by some of the above mentioned coupling processes.
 It is worth mentioning that when the SPW1 interacts with the eastward/westward travelling wave with zonal wave number 1, in addition to the zonally symmetric wave, the coupling also produces eastward/westward propagating wave with zonal wavenumber 2. Therefore, the interaction between the stationary and travelling planetary waves generates also travelling waves with the same period but with higher than the primary wave zonal wave number. Apparently, during the winter of 2003–2004 the wave-wave coupling processes must have been quite strong in order to produce travelling waves with similar periods having zonal wave numbers up to 3 (note that only wave numbers up to 3 have been studied in this paper; see Figure 5).
 If the above suggested forcing mechanism indeed takes place, then the zonally symmetric waves have to be modulated by the SPWs because they are disturbances with a longer duration and very large amplitudes. Figure 6 shows the latitude-time cross sections of: the zonal wind including only the three types of zonally symmetric waves with periods 23, 17 and 11 days (Figure 6a), the amplitudes of the SPW1 (Figure 6b), and the amplitudes of the SPW2 (Figure 6c). All results are calculated for the 0.3 hPa pressure level. First, there is some similarity between the plot of raw data (including mean flow and all types of waves) in Figure 1 and that including only the zonally symmetric waves shown in Figure 6a. This comparison indicates that the zonally symmetric waves are an important feature of the stratosphere dynamics in the Arctic winter of 2003–2004. There are some indications that the zonally symmetric waves are modulated mainly by the SPW1, but some effect by the SPW2 is evident as well. The amplification of the zonally symmetric waves in late November–early January is probably driven by the combined action of both SPW1 and SPW2, while the amplification in February–March is mainly forced by the SPW1.
 The zonally symmetric planetary waves with large amplitudes found in the UKMO zonal wind data during the Arctic winter of 2003–2004 are not only an important feature of the stratosphere dynamics but also play a significant role in the coupling of high- and low-latitude regions.
 We are grateful to the UKMO and BADC for access to the data (http://www.badc.rl.ac.uk/data/assim). One of the authors, DP, is grateful for enlightening discussions with A. Smith and E. Merzlyakov on the dynamics of middle atmosphere. We thank two anonymous reviewers for helpful comments.