Latitudinal- and Height- Dependent Long-Term Climatology of Propagating Quasi-16-day in the Troposphere and Stratosphere


 The global amplitude of the westward propagating quasi-16-day wave (16DW) with wavenumber 1 (Q16W1), the strongest component of 16DW, is derived from European Centre for Medium-Range Weather Forecasts ERA-Interim reanalysis temperature data set from February 1979 to January 2018. The strong climatological mean amplitudes of the Q16W1 appear in winter in the upper stratosphere at high latitudes in both hemispheres, and the wave amplitude is stronger in the Northern Hemisphere (NH) than in the Southern Hemisphere (SH). Multivariate linear regression is applied to calculate responses of the Q16W1 amplitude to QBO (quasi-biennial oscillation), ENSO (El Niño-Southern Oscillation), solar activity and the linear trend of the Q16W1 amplitude. The QBO signatures of the Q16W1 amplitude are mainly located in the stratosphere. In addition to the significant QBO response in the low latitude and low stratosphere, the largest QBO response occurs in the region with the strongest Q16W1 climatology amplitude. There no significant responses to ENSO and solar activity are observed. The linear trend of the monthly mean Q16W1 amplitude is generally positive, especially in the mid-high latitudes of the stratosphere. The trend is asymmetric about the equator and significantly stronger in the NH than in the SH. The trend shows obvious seasonal changes, that is, stronger in winter, weaker in spring and autumn. Further investigation suggests that the background and local instability trends contribute most of the increasing trend of the Q16W1 amplitude. In winter in both hemispheres, the weakening trend of eastward zonal wind provide more favourable background wind for Q16W1 upward propagation, in autumn and winter in the NH and in spring, autumn and winter in the SH, the increasing trend of local instability may enhance the wave excitation.


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The quasi 16-day wave (16DW) is one of the PWs and was identified as the second 57 symmetric westward propagating Rossby mode with zonal wavenumber 1 (Salby 1981a, b). 58 In the realistic atmosphere, due to Doppler shifting by the non-zero background flow, the 59 period of 16DWs is from 12 to 20 days (Amitava et al. 2016). The 16DWs have been 60 extensively reported over the past decades from ground-based measurements (Mitchell et al. April. However, the exploration of 16DWs is relatively insufficient in the lower atmosphere, 66 most likely due to the lack of high-quality data sets, i.e., data with a long duration, good 67 continuity, and high resolution. Since local observations cannot provide a global distribution, 68 and satellite observations with long-term duration usually are rare. Hence, global data with a 69 long duration are necessary for a further study. suggested that the trend for stratospheric wave intensity from 200 hPa to 10 hPa at NH 80 mid-high latitudes was strengthening during 1979-2000 and weakening during 2001-2015. 81 However, most of the studies are related to PW, research on travelling PW activity trends, 82 especially the Q16W1, is rare. Hence, the global trend in Q16W1 amplitude is far from being 83 fully understood.

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The background wind can significantly affect the excitation, propagation and 85 dissipation of PWs. On the other hand, PWs will impact the background wind by depositing 86 energy and momentum into the background atmosphere through various dissipation processes. were examined. In addition, we attempt to find a possible link between the wave and 99 background wind and instability at the climate time scale. To this end, the rest of paper is 100 organized as follows. In the following section, we introduce the adopted data, the dominant 101 modes of the 16DW and the calculation method. Subsequently, the global climatology of 102 wave amplitude is presented. In sections 4 and 5, we present the latitude-and 103 height-dependent responses of the 16DW to the QBO and the linear trend of the strongest 104 wave mode of 16DW, respectively. In the last section, we provide a brief summary of our 105 analyses. averaged to determine the temporal averaged spectra. Finally, a mean spectrum was obtained 127 by averaging the temporal averaged spectra at all pressure levels. The mean 128 frequency-wavenumber spectrum averaged from 38,475,745 spectra is shown in Figure 1, 129 which shows that the most prominent spectral peak has a period of 15 days and a wavenumber 130 of W1, with the largest amplitude of 0.46 K. The secondary wave mode with a period of 20 131 days and a wavenumber of E1 can also be recognized. Here, we focus only on the strongest 132 PW , i.e., 16DW with wavenumber W1, which is named as Q16W1 for simplicity.

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To extract the monthly averaged amplitudes of Q16W1, in each sliding 60-day 134 window to determine the amplitude at the centre day of the window (Wu et al. 1995 PWs. There are also seasonal changes in PWs, which are mainly reflected in annual, 153 semi-annual, tri-annual and quarter-annual oscillations. Therefore, when performing MLR 154 analysis on the amplitude of the Q16W1, the influences from all these factors should be 155 considered. So, we chose a particular set of indices for the regression.

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Before implementing MLR, some inflection point analysis based on the piecewise 157 fittings of the Q16W1 amplitude had been performed during the 39-year period, so 158 confirming that the linear trend fit over entire time range is appropriate. In this study, MLR 159 analysis was performed on the time series of the monthly mean amplitude of the Q16W1, i.e., 160 ( ). The fitting equation is written as: where t is time in months (478 months over 39 years), = 2 12 ℎ ⁄ , and B is the 166 coefficient of the linear trend. The third to the fourteenth terms on the right side of Equation

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(2) are the linear correlations between the ( ) and the SC, ENSO, two QBO components,    Where overbar, prime and subscript denote respectively zonal average and derivative； , ,

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, Ω, ∅, and represent the zonal wind, background density, Earth radius, angular velocity 326 of the Earth, latitude and Coriolis parameter, respectively; is the altitude above the Earth's 327 surface; is the buoyancy frequency, which is specified by calculating from The long-term trend of the monthly mean Q16W1 amplitude is generally positive and 376 mainly concentrated in the stratosphere. The trend is asymmetric around the equator at 30-1 377 hPa and significantly stronger in the NH than in the SH. Weak negative trend is mainly 378 located below 300 hPa at high latitudes in the NH.

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The trend of the monthly mean Q16W1 amplitude has evident seasonal variation. The

Availability of data and materials 391
The ERA-Interim data set were freely downloaded from the European Centre for Medium-Range 392 Weather Forecasts (https://apps.ecmwf.int/datasets/data/interim-full-daily/levtype=pl/), The F 10.7 393 solar flux data and multivariate ENSO index data were downloaded from 394 http://www.esrl.noaa.gov/psd/, and the QBO data series were from 395 http://www.geo.fu-berlin.de/en/met/ag/strat/produkte/qbo/index.html. pressure of the monthly-mean Q16W1 amplitude from the 39 years ERA-interim temperature data set. 570 The solid and dashed contours denote the positive and negative trends, respectively. The black 571 contours denote the trend with confident level at/above 95%. The colors represents the climatological 572 distributions of the monthly mean Q16W1 amplitude in four seasons. 573  Mean frequency-wavenumber spectrum of temperature (in K) from February 1979 to January 2018 (39 years in total) at 37 pressure levels from 1000 hPa to 1 hPa. W (E) represents westward (eastward) propagation.

Figure 2
The time series of (a) SC index (F10.7cm ux), (b) multivariate ENSO index (MEI), and (c) the QBO indices on the monthly basis from February 1979 to January 2018, respectively.

Figure 3
The latitude-pressure distribution of the monthly mean Q16W1 amplitude averaged over 39 years from the ERA-interim temperature data set. Month-latitude sections of the monthly and zonal-mean Q16W1 amplitude at high, middle, and low latitudes in the NH (three upper rows) and SH (three lower rows), respectively. Latitude-pressure sections of the responses of the monthly-mean Q16W1 amplitude to (a) QBO1 and (b) QBO2, respectively. Only the results with the con dence level at/above 95% are plotted in contours. The solid and dashed contours denote the positive and negative responses, respectively. Long-term trend (in K per decade) as a function of pressure and latitude of the monthly mean Q16W1 amplitude obtained from the 39 years ERA-interim temperature data set. Only the results with the con dence level at/above 95% are plotted in contours. The solid and dashed contours denote the positive and negative trends, respectively.

Figure 7
Seasonal variation of the Long-term trend (in K per decade) as a function of latitude and pressure of the monthly-mean Q16W1 amplitude from the 39 years ERA-interim temperature data set. The solid and dashed contours denote the positive and negative trends, respectively. The black contours denote the trend with con dent level at/above 95%. The colors represents the climatological distributions of the monthly mean Q16W1 amplitude in four seasons.

Figure 8
Trend (contours, units: m/s/decade) of the monthly mean zonal wind in four seasons derived from the 39 years ERA-interim zonal wind set. The solid and dashed contours denote the positive and negative trends, respectively. The thick black contour represents the 0 value. The stippled regions represent the trends at/above 95% con dent level. The colors present the climatological distributions of the monthly mean zonal wind in four seasons.

Figure 9
Trend (contours, units: 10-5 m-1 s-1/decade) of the monthly mean qΦ in four seasons. The dashed contours denote the negative trend. The stippled regions represent the trends at/above 95% con dent level. The colors present the climatological distributions of the monthly mean zonal qΦ in four seasons.

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