Response of middle atmospheric temperature to the solar 27-day cycle: an analysis of 13 years of MLS data

Abstract. This work focuses on studying the presence and characteristics of solar 27-day signatures in middle atmospheric temperature observed by the Microwave Limb Sounder (MLS) on NASA’s Aura spacecraft. The 27-day signatures in temperature are extracted using the superposed epoch analysis (SEA) technique. We use time-lagged linear regression (sensitivity analysis) and a Monte-Carlo test method (significance test) to explore the dependence of the results on latitude and altitude, on solar activity and season, as well as on different parameters (e.g., smoothing filter, window width and epoch centers). Using different parameters does impact the results to a certain degree, but it does not affect the overall results. Analyzing the 13-year data set shows that highly significant solar 27-day signatures in middle atmospheric temperature are present at many altitudes and latitudes. A tendency to higher temperature sensitivity to solar forcing in the winter hemisphere is found. In addition, the sensitivity of temperature to solar 27-day forcing tends to be larger at high latitudes than at low latitudes. For solar 11-year minimum conditions no statistically significant identification of a solar 27-day signature is possible at most altitudes and latitudes. Several results we obtained suggest that processes other than solar variability drive atmospheric temperature variability at periods around 27-days. Comparisons of the obtained sensitivity values with earlier experimental and model studies show good overall agreement.



MLS on Aura
The National Aeronautics and Space Administration (NASA) Earth Observation Satellite Aura has been in a near-polar 705 km altitude orbit since 2004. The Microwave Limb Sounder (MLS) on Aura consists of seven radiometers observing emission in the 118 GHz,190 GHz,240 GHz,640 GHz and 2.5 THz regions. The MLS measurements provide vertical profiles of temperature, geopotential height, several atmospheric trace species and ice water content of clouds with near-global coverage 5 on a daily basis (Waters et al., 2006;Livesey et al., 2018).
MLS temperature is retrieved primarily from MLS measurements of the thermal emission of O 2 near 118 GHz and 240 GHz (Schwartz et al., 2008). The isotopic 240 GHz line is the primary source of temperature information in the troposphere (extending the profile down to about 9 km), while the 118 GHz line is the primary source of temperature information in the stratosphere and above (from 90 km down to about 16 km) (Livesey et al., 2018). 10 In this work, we use the MLS Level 2 temperature product version 4.2. MLS version 4.2 temperature is available from 2 August 2004 to present. The precision and accuracy of the MLS temperature data product are shown in Table 3.22.1 of Livesey et al. (2018). The precision is 1 K or better in the troposphere and lower stratosphere (from 261 hPa to 3.16 hPa), degrading to 3.6 K in the upper mesosphere (at 0.001 hPa). The observed biases based upon comparisons with analyses and other previously validated satellite-based measurements range from −2.5 K to +1 K in the troposphere and lower stratosphere, increasing to −9 15 K at the highest altitude. The recommended useful vertical range for scientific studies is between 261 hPa (10 km) and 0.001 hPa (96 km), and the vertical resolution varies between 3.6 km (at 31.6 hPa) and 13 -14 km (at 0.001 hPa). The horizontal resolution is ∼165 km between 261 hPa and 0.1 hPa and degrades to 280 km at 0.001 hPa. To investigate the presence of a 27-day solar cycle signature in the temperature data set and to keep the annual data complete, the period from January 1, 2005 to December 31, 2017 was selected as shown in the bottom panel of Figure 1. In the following analysis, we first employ the 20 day and night averaged MLS temperature data. In section 4.1.1 and 4.2.1 we investigate how the results change if daytime (or nighttime) measurements only are employed for the analysis.

Methodology
The approach employed to analyze the 27-day solar cycle signal in temperature is illustrated in Figure 2. First, temperature and Mg II index anomalies are calculated (see section 3.1). Next, the SEA method is applied to the temperature and Mg II 25 index anomalies to obtain the epoch-averaged temperature and Mg II index anomalies (section 3.2). Then, the epoch-averaged temperature and Mg II index anomalies are used to perform the sensitivity analysis (section 3.3) and the significance test (section 3.4). The individual steps are described in detail in the corresponding subsections.
In the process, different input observational and statistical parameters may affect the results. For example, the results may depend on whether daytime, nighttime or daily averaged MLS temperature data is used for the analysis. Other parameters that 30 may affect the results are latitude and altitude, the width of the window used in the data pre-processing, the choice of the epoch centers (maxima or minima of Mg II index anomalies) applied for the SEA, the smoothing filter used to choose the maxima or 4 https://doi.org/10.5194/acp-2019-765 Preprint. Discussion started: 9 September 2019 c Author(s) 2019. CC BY 4.0 License. minima as epoch centers. In addition, the dependence of the results on solar activity and season also needs to be discussed. To check how these parameters affect the results, different tests are performed and described in section 4.

Data pre-processing
We defined a standard altitude grid with 36 levels from 20 to 90 km with a step size of 2 km and a standard latitude grid with 18 bins from 90 • S to 90 • N with a step size of 10 • . MLS geopotential height was converted to geometric height using the 5 height and latitude dependent formula provided by Roedel and Wagner (2011). The temperature data were averaged daily and zonally for each altitude and latitude bin between 1 January 2005 and 31 December 2017.
The bottom panel of Figure 1 shows the daily averaged temperature data for an altitude of 88 km and a latitude of 5 • N (averaged zonally and over the 0 -10 • N latitude range). There are 5 data gaps and 6 abnormal peaks. The data gaps occur  Figure 3). The white lines in Figure 3 indicate that temperature data is missing. The outliers/abnormal peaks visible in the bottom panel of Figure 1 occur on days 341,417,452,1532,1759,3717. Note that the outliers appear on different days for different altitudes and latitudes. In order to investigate the presence of a 27-day solar cycle signature in the temperature data set, it is necessary to avoid the invalid points 15 (temperature gaps and outliers) in the SEA. This can be easily implemented in the SEA by ignoring the data gaps and outliers in the averaging procedure (see below).
Next, we apply a 35-day running mean and then calculate the anomalies as the deviation from the running mean for MLS temperature and the Mg II index time series. The resulting temperature anomalies for an altitude of 88 km and a latitude of 5 • N are shown in the top panel of Figure 4. We define outliers as data points for which the absolute of the temperature anomaly 20 exceeds 4 times the standard deviation of the anomaly time series. The bottom panel of Figure 4 shows the temperature anomaly with removed outliers. The width of the smoothing window is chosen as 35 days to remove the seasonal modulation of the temperature signal while leaving the variation at shorter time scales unaltered. In sections 4.1.1 and 4.2.1 we investigate how the results change if different window widths (e.g., 27 days and 50 days) are employed for the analysis. Those steps above are a preparation for the following SEA, the significance testing and sensitivity analysis.

Superposed epoch analysis (SEA)
To identify weak solar 27-day signatures in temperature time series affected by variability from various sources, the superposed epoch analysis method (SEA) (e.g., Howard, 1833;Chree, 1912) is an effective choice. The SEA is applied to the time series covering the period from January 2005 to December 2017.
An overview of the SEA is shown in Figure 5. First, the epoch centers need to be chosen. The local maxima in the Mg II 30 index time series -reflecting maxima in solar spectral irradiance -can be used as the epoch centers (represented as Max 1 to Max N in Figure 5). The Mg II index maxima are identified in the un-smoothed (0-day) or 7-day or 13-day smoothed Mg II index anomalies as shown in Figure 6. The yellow, blue and red points represent the local maxima identified for the 0-day, 7-day and 13-day smoothed Mg II index anomalies, respectively. We discuss the impact of the smoothing filter on the results in sections 4.  (1).
Here, x represents an integer between -30 and 30. Similarly, the epoch-averaged Mg II anomaly is determined this way.
However, as shown in Figure 7 (a), there is a time lag or shift (l) between solar maximum and temperature maximum. If the times of the maxima do not coincide, then an ellipse is fitted instead of a straight line. To remove the phase shift between the two anomalies, we need to shift the temperature curve by l days to obtain the time-lagged epoch-averaged temperature anomalies T anomaly [x + l]. Then the sensitivity parameter (k) is derived from Equation (3).
The phase lag (l) can be determined by time-lagged cross correlation as shown in Figure 7

Significance testing
We Comparing the amplitude of the fitted sinusoidal function of the 1000 random cases to the amplitude of the actual case, the statistical significance of the SEA results can be evaluated. The amplitude and phase of fitted sinusoidal functions, as well as 15 the fraction of random realizations with amplitudes larger than actual data are the results of the significance test. If the fraction of random realizations with amplitudes larger than the amplitude of the actual SEA is close to zero, then the 27-day signature in MLS temperature data is likely not a spurious signature. Figure 8 shows the results of the Monte-Carlo significance test at 88 km and 5 • N. The local solar maxima used here are determined based on the 7-day smoothed Mg II index anomalies, which were obtained by subtracting a 35-day running mean from the daily Mg II index data.

Results and discussion
The main purpose of the present work is to investigate the presence and characteristics of solar 27-day signatures in the middle atmosphere temperature observed by MLS. In order to investigate how robust the results are, different tests were performed, i.e., a significance test, a sensitivity test, and an investigation of the dependence of the results on real geophysical parameters (i.e., solar activity, season, latitude and altitude) and on statistical/numerical parameters (i.e., window width, epoch centers, 25 and smoothing filter).

Significance test results
The significance testing method was described in section 3.4. To investigate the dependence of the significance results on altitude and latitude, on the width of the window, on epoch centers and on the temperature observations, these tests were performed at each altitude and latitude, for different window widths of 27 days, 35 days and 50 days, as well as different local The dependence of the results on the different parameters is carried out based upon temperature data in the tropical (5 • N) mesopause region (88 km). Table 1 lists the results for the different statistical parameters considered and for the different 5 observational temperature (daytime, nighttime and daily averaged temperature) data sets. The maximum and minimum of the fraction of random realizations with amplitudes larger than actual data are underlined. The max-to-min variation of the fraction for the daytime temperature case is larger than the one for the nighttime and daily averaged temperature cases. In terms of daily averaged temperature, the maximum and minimum fractions are about 1.0 % and 0.0 %, respectively. That is, the variation of the fraction is about 1.0 % for different input parameters. For nighttime temperature, the maximum and minimum fractions are 10 about 1.9 % and 0.0 %, respectively. The max-to-min variation of the fraction is about 1.9 %, but for the daytime temperature, the maximum and minimum fractions are about 28.6 % and 1.5 %, respectively. The max-to-min variation of the fraction increases to about 27.1 %. The exact origin of this different behaviour of the daytime temperature data is currently unknown.
More discussion on the dependence of the results on statistical parameters at different latitudes and altitudes will be given in subsection 4.1.2.

Dependence of the results on latitude
We performed the significance test for the daily averaged temperature from 2005 to 2017 for the latitude range from 85 • S to 85 • N and the altitude range from 20 to 90 km. The resulting fraction of random realizations with amplitudes larger than the actual SEA is displayed in Figure 9 as a function of latitude and altitude. For the results shown in Figure  In addition, Figure 10 provides two examples of high and low significance cases. Figure 10 (a) shows the epoch-averaged Mg II index and temperature anomalies and the sinusoidal fit to the 3-day smoothed epoch averaged temperature anomalies for the actual SEA and for 1000 randomly chosen epoch ensembles at 88 km for a latitude of 5 • N. There is no random sinusoidal fit amplitude larger than the actual one, that is, the fraction of the significance test is 0.0 %. Figure 10  In order to check the influence of the input parameters on the results at different latitudes, we show in Figure 9 the significance results for some of the combinations of input parameters yielding the largest fractions of random realizations with amplitudes larger than the actual SEA (see Table 1). The results obtained using a 27-day window width and 0-day smoothing filter are shown in Figure 9 (b). The results obtained using a 27-day window width, a 0-day smoothing filter, and daytime temperature data are shown in Figure 9 (c). The results obtained using a 50-day window width, a 0-day smoothing filter, nighttime 5 temperature data, and minima of Mg II index anomaly are shown in Figure 9 (d). The low fraction regions obviously become smaller in 9 (b-d), but the locations of these regions have not changed. That means, different input parameters have an impact on the results, but will not affect the overall characteristics.

Dependence of the results on season
To determine whether the solar 27-day cycle signal in middle atmospheric temperature depends on season, the SEA and the 10 subsequent significance tests were performed for winter and summer separately. We assume that "winter" includes the six months of October, November, December, January, February and March, and "summer" includes the other six months for the northern hemisphere. For the southern hemisphere, it is the opposite. More than three months for each season are considered here in order to increase the number of epochs available for analysis.
The significance testing results depending on season are shown in Figure 11 (a -b). The input parameters used in this analysis 15 are the same as in the Figure 9 (a). In the southern hemisphere, the solar 27-day cycle signal in daily averaged temperature is more obvious in winter than in summer. In the northern hemisphere, the 27-day signature in temperature at low latitudes (below 50 • ) for the altitude of 35 -60 km is more significant in summer than in winter, but for the altitude of 20 -30 km the signature is more significant in winter. At high latitudes (70 -85 • N), the 27-day signature more significant in winter than in summer, especially for the middle stratosphere (30 -40 km). In total, the low fraction (less than 10 %) region is larger for 20 "summer" months (October -March) than "winter" months (April -September) for the global region.
An important finding is that large differences exist between northern hemisphere winter and summer. For northern summer (see panel (b) of Figure 11), the latitude-altitude ranges with fractions less than 10% -indicative of a likely solar origin of the identified signatures -are significantly larger than for northern winter (see panel (a) of Figure 11). These differences could be related to enhanced planetary wave activity during northern hemisphere winter, leading to enhanced overall atmospheric 25 variability and consequently making the identification of a solar 27-day signature in atmospheric temperature more difficult.

Dependence of the results on solar activity
In addition, we investigated the dependence of the results on solar activity. The comparison of the strong solar activity years (2011 -2014) with the weak solar activity years (2007 -2009) is shown in Figure 12 (a -b). The input parameters used here are identical with the ones for Figure 9 (a). The low fraction (less than 10 %) region is larger for strong solar activity years 30 than for weak solar activity years. For weak solar activity years, the low fraction region mainly concentrates in the equatorial mesopause region as shown in Figure 12 (b). For strong solar activity years, the low fraction region is more distributed over high latitudes, mainly at 70 -85 • N and 40 -60 • S at around 40 km, and at 70 -85 • S at around 80 -80 km.
The results demonstrate that the overall significance of the potential solar 27-day signatures in temperature is generally much lower for solar minimum conditions (see panel (b) of Figure 12) than for solar maximum conditions (see panel (a) of Figure   12). An exception is the tropical mesopause region, where the fraction of random realizations with amplitudes exceeding the amplitude of the actual SEA is smaller for low solar activity than for enhanced solar activity. The reasons for this behaviour are currently not understood. The general decrease of the significance with decreasing solar activity is, however, as expected. It 5 is also worth pointing out that the overall significance of the results (as quantified by the latitude-altitude ranges with fractions less than 10%) is smaller for enhanced solar activity compared to analyzing the entire data set (compare panel (a) of Figure 12 and panel (a) of Figure 9). This can be explained by the reduced number of epochs available if only parts of the time series are analyzed and highlights the importance of the length of the time series for obtaining statistically significant results.

Sensitivity analysis 10
The temperature sensitivity to solar forcing was calculated with the method described in section 3.3. Similar to the significance testing, we also investigated the dependence of the sensitivity results on different input and observational parameters.

Dependence of the results on statistical parameters
The sensitivity analysis was performed first with the temperature data at the mesopause (88 km) and in the tropics (5 • N). Table   2 lists the sensitivity values (i.e., the slope of fitted linear regression line) and the uncertainties depending on the different input 15 parameters. The underlined values in the table represent the maximum and minimum sensitivity values for different cases. The uncertainties are below 0.6 K (100 sfu) −1 . The maximum of the sensitivity is 2.74 (± 0.28) K (100 sfu) −1 for daily averaged temperature, 3.18 (± 0.40) K (100 sfu) −1 for daytime temperature, and 2.95 (± 0.45) K (100 sfu) −1 for nighttime temperature.
The minimum of the sensitivity is 1.82 (± 0.27) K (100 sfu) −1 for daily averaged temperature, 1.33 (± 0.34) K (100 sfu) −1 for daytime temperature, and 1.81 (± 0.38) K (100 sfu) −1 for nighttime temperature. The max-to-min variation of the sensitivity 20 value due to different input parameters is 0.92 K (100 sfu) −1 for daily averaged temperature, 1.85 K (100 sfu) −1 for daytime temperature, and 1.14 K (100 sfu) −1 for nighttime temperature. Thus, the influence of the input parameters on the sensitivity result is relatively smaller in daily averaged temperature. This feature is in line with the results derived from the significance test which was discussed in section 4.1.1.
Overall, there is a tendency to larger sensitivity values if a wider window width is used for determining the anomalies. The 25 effect is particularly pronounced for the cases with a 0-day and 7-day smoothing of the anomalies. This dependence of the sensitivities on window width may be expected, because, for narrower window widths, parts of the 27-day signatures present may be removed. The same window width is, however, also used for determining the MgII index anomalies so that part of this effect is compensated, reducing the effect of window width on the sensitivity value. It is also worth pointing out that, for most cases, the sensitivity values for the different window widths agree within combined uncertainties. When comparing the graph with the significance test results shown in Figure 9 (a), it is apparent that the larger sensitivity 10 values appear in regions with lower fraction, i.e., higher significance. The bottom panel of Figure 13 shows the determined time lag between local solar maximum (at the 27-day scale) and the temperature maximum. Comparing the two panels of Figure 13 shows that large time lags tend to occur in latitude-altitude regions with small sensitivity.
In Figure 14  In order to study the sensitivity features for regions with high significance of the identified 27-day signatures, we choose the region that meets the condition that the significance test fraction is less than 10 %. The white parts in the panels of Figure   15 represent the regions for significance test fractions exceeding 10 %. Figure 15

Dependence of the results on season
Next, the temperature sensitivity to solar forcing was analyzed for different seasons. Figure 11 (c -f) show the sensitivity and shift for the latitude range from 85 • S to 85 • N and the altitude range from 20 to 90 km for different seasons. As shown in Figure 11 (c -d), the sensitivity in winter is obviously larger than in summer. In the northern hemisphere, the maximum sensitivity, i.e., 12.41 K (100 sfu) −1 , occurs in winter at 85 • N for altitudes of about 40 km. In the southern hemisphere, the 5 maximum sensitivity is 5.16 K (100 sfu) −1 and occurs at around 70 • S for about 75 km altitude winter. In other words, the sensitivity increases in general with increasing latitude in the winter hemisphere. In summer, the sensitivity shows a tendency to increase with altitude in general. Figure 11 (e -f) shows the determined lag. The shifts do not exhibit the same obvious characteristics as sensitivity, which is not further investigated here.
The graphs indicate larger sensitivity of atmospheric temperature to solar forcing at the 27-day scale in the winter hemisphere 10 (see panels (c) and (d) in Figure 11) -although one has to keep in mind that the results are not significant at all latitudes and altitudes. The identified interhemispheric difference in temperature sensitivity is in agreement with the model results of Gruzdev et al. (2009), who reported that the temperature response to the 27-day solar cycle at extra-tropical latitudes is seasonally dependent with frequently higher sensitivities in winter than in summer. This has also been reported, e.g., by Ruzmaikin (2007), who analyzed MLS ozone and temperature observations in the stratosphere. The origin of the enhanced 15 sensitivity in the winter hemisphere -particularly at high latitudes -is not well understood.
In Figure 14  Overall, the results show a tendency to enhanced temperature sensitivity to solar forcing during periods of low solar activity.         Table 1. Significance testing results for different input parameters used in the analysis. The temperature data at latitude of 5°N and altitude of 88 km are used here. There are two parameters shown in the table. The first one is absolute amplitude in K of the fitted sinusoidal function.
The second one is the fraction (%) of random realizations with amplitudes larger than actual data. The underlined values correspond to the maximum and minimum of the fraction of random realizations with amplitudes larger than the actual data for the daily averaged, the daytime and the nighttime measurements.