Multivariate analysis of Kelvin wave seasonal variability in ECMWF L91 analyses

Abstract. 1 The paper performs multivariate analysis of the linear Kelvin waves (KWs) represented by the operational 91-level ECMWF 2 analyses in 2007-2013 period, with focus on seasonal variability. The applied method simultaneously filters Kelvin wave 3 wind and temperature perturbations in the continuously stratified atmosphere on the sphere. The spatial filtering of the three4 dimensional Kelvin wave structure in the upper troposphere and lower stratosphere is based on the Hough harmonics using 5 several tens of linearized shallow-water equation systems on the sphere with equivalent depths ranging from 10 km to a few 6 meters. 7 Results provide the global Kelvin wave energy spectrum. It shows a clear seasonal cycle with the Kelvin wave activity 8 predominantly in zonal wavenumbers 1−2 where up to 50% more energy is observed during the solstice seasons in comparison 9 with boreal spring and autumn. 10 Seasonal variability of Kelvin waves in the upper troposphere and lower stratosphere is examined in relation to the back11 ground wind and stability. A spectral bandpass filtering is used to decompose variability into three period ranges: seasonal, 12 intraseasonal and intramonthly variability component. Results reveal a slow seasonal KW component with a robust dipole 13 structure in the upper troposphere with its position determined by the location of the dominant convective outflow throughout 14 the seasons. Its maximal strength occurs during boreal summer when easterlies in the Eastern hemisphere are strongest. Other 15 two components represent vertically propagating Kelvin waves and are observed throughout the year with seasonal variability 16 mostly found in the wave amplitudes being dependent on the seasonality of the background easterly winds and static stability. 17


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The KW temperature perturbation, T kw can be derived from the h kw fields on σ levels using the hydrostatic relation in σ 142 coordinates: (3) 144 The orthogonality of the normal-mode basis functions provides KW energy as a function of the zonal wavenumber and 145 vertical mode. After the forward projection, the energy spectrum of total (potential and kinetic) energy for each Kelvin wave 146 can be computed using the energy product for the kth and mth normal modes (Žagar et al., 2015) as:  Figure 2 also shows that below 300 hPa the KW activity decreases and we shall not discuss levels under 300 hPa in 177 the paper.

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KW temperature perturbation is proportional to the negative vertical gradient in geopotential (and vice versa), as well as in the 180 zonal wind since the zonal wind and geopotential are in phase. Horizontally, the cold anomaly is always located between the 181 westerly and the easterly phase of the zonal wind component. and to the Doppler-shifted phase speed as ∝ (c − U ) −1/2 , such that N is expected to play a primary role above 120 hPa where 224 its value starts increasing rapidly (see Fig. 3). 225 Alexander and Ortland (2010)  We start with a discussion of the KW energy distribution among zonal wavenumbers as given by (5), followed by seasonal 239 differences.

Energy distribution of Kelvin wave 241
The seasonal cycle in the energy-zonal wavenumber spectra is shown in Fig. 4 after summing up over all vertical modes. On 242 average, energy decreases as the zonal wavenumber increases as typical for atmospheric energy spectra. As we deal with the in response to ongoing tropical convection. Therefore, the zonal distribution of tropical convection may likely play a crucial 254 role in explaining DJF and JJA season differences of KW energy, which will be explored in next section.  284 The year to year differences can be explained by many coupled factors. In general, one expects the vertically-integrated KW  namely: (i) the (semi)annual cycle using a low-pass filter with cut-off period at 90 days, (ii) the intraseasonal period using 304 a bandpass filter over periods between 20-90 days, and finally (iii) the intramonthly period with bandpass filtered periods 305 between 3-20 days. The chosen periods, especially the intramonthly periods, are similar to those used in previous studies. In 306 each case, mean 6-year fields as well as seasonal means shall be presented.

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Note that our temporal filtering operates on time series of KW signals at every grid point. This is different from the commonly 308 applied space-time filtering following Hayashi (1982) that applies KW dispersion relations. Our filtered KWs can appear 309 stationary or even westward shifted due to westward-moving sources of the KW amplification (e.g. easterly winds, high static 310 stability in the TTL). Most previous studies define KW activity as square amplitude rather than absolute amplitude. In our high resolution dataset we observe highly localized patterns of the KW activity in the Eastern hemisphere due to ongoing wave amplification. By using absolute amplitudes we better visualize the longitudinal structure of the KW activity in comparison to its local maxima.
the solution in Fig. 7a illustrates, in addition to a low-frequency KW variability in westerly winds, also a considerable low-  The largest amplitudes are found during the JJA months. A strong dipole "wave-1" pattern is evident in the TTL. The

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During DJF, the dipole pattern has shifted more eastward and upward compared to JJA and has a more slanted structure.  The average background winds maximize at 150 hPa as shown in Fig. 3(a). In Fig. 8  The seasonality of intraseasonal Kelvin wave variability is shown in Fig. 11    here. We showed that large-scale KWs readily persist in the data despite analyzing selected processing times independently.

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The KW is a normal mode of the global atmosphere and our 3D-orthogonal decomposition allows quantification of its