### Direct comparison between Na density and CNA

Figure 1a shows a comparison between simultaneous Na density data at 105 km and CNA data, as an example. It seems that there was a large variability, and its correlation coefficient (CC) was very small (\(-0.065\)). This would be mainly due to large variations in the Na density, which may be due to seasonal, day-to-day, diurnal, and other variations. In addition, the narrow lidar beam, compared with the wide riometer beam, may contribute to the large variability to some extent. We may see a tendency that Na densities were lower (\(<1.5 \times 10^{8}\,\hbox {m}^{-3}\)) when CNA was larger (\(>1.5 \,\hbox {dB}\)), while the number of data for such larger CNA may not be enough.

Here, to see in more detail, we separated data into two groups based on CNA values. One is CNA of 0–0.25 dB, which corresponds to a quiet condition. The other is CNA of 0.25–2 dB, which corresponds to an active condition. The total number of data points for the quiet condition was 3148, and that for the active condition was 2847. We counted numbers of data points for each bin in the Na density for each group, and then normalized it with the total numbers of data points for each group. After that, we applied fittings with the lease-squares method assuming a log-normal distribution (\(f_{\left( x \right) }=\frac{A}{\sqrt{2\pi } \sigma x}{{\mathrm{exp}}}\left( -\frac{\left( {{\mathrm{ln}}}x-\mu \right) ^{2}}{2\sigma ^2}\right)\)). In this way, we obtained probability density functions (PDFs) for the two groups, as shown in Figs. 1b and c. The median (\(\mathrm{e}^{\mu }\)) of PDF for the quiet condition was \(1.8\times 10^{8} \pm 1.2\times 10^{7}\,\hbox {m}^{-3}\), and that for the active condition was \(1.4\times 10^{8} \pm 5.9 \times 10^{6}\, \hbox {m}^{-3}\). Thus, there was a significant difference between them, and the median Na density for the active condition was smaller. The mode (\(\mathrm{e}^{\mu - \sigma ^{2}}\)) for the quiet condition was \(4.0\times 10^{7}\pm 4.7\times 10^{6}\, \hbox {m}^{-3}\), and that for the active condition was \(4.8\times 10^{7}\pm 3.5\times 10^{6}\,\hbox {m}^{-3}\). Thus, the difference between them was not so clear. The standard deviation (\(\sqrt{{{\mathrm{e}}}^{2\mu + \sigma ^{2}}\left( {{\mathrm{e}}}^{\sigma ^{2}} -1 \right) }\)) for the quiet condition was \(6.7\times 10^{8}\pm 7.8\times 10^{7}\,\hbox {m}^{-3}\), and that for the active condition was \(3.2\times 10^{8}\pm 2.4\times 10^{7}\,\hbox {m}^{-3}\). Thus, there was a significant difference between them, and the standard deviation for the active condition was smaller.

We did same data processing for Na density data from 85 to 105 km, and then the obtained median values of PDFs are shown in Fig. 2a. Also, the deviation between the median values (\(\frac{{{\mathrm{Na}}}_{{{\mathrm{active}}}} - {{\mathrm{Na}}}_{{{\mathrm{quiet}}}}}{\mathrm{Na}_{{{\mathrm{quiet}}}}} \times 100\) (%)), where \({{\mathrm{Na}}}_{\mathrm{active}}\) is the median Na density during the active condition, and \({{\mathrm{Na}}}_{{{\mathrm{quiet}}}}\) is the median Na density during the quiet condition, are shown in Fig. 2b. The results at 95–105 km were basically similar to those at 105 km, which is mentioned in the previous paragraph (see Fig. 1), and thus, it is found that the median values above 95 km for the active condition were significantly smaller than those for the quiet condition. The deviations above 95 km correspond to 10–20% decreases (i.e., \(-10\) to \(-20\%\)) in the Na density.

### MLT characteristics

For investigation on the MLT characteristics, we used 3-h ap indices which indicate geomagnetical or auroral activity. In similar way as the CNA data, we selected ap indices during the 254 days and calculated 24-h averaged ap index from 09:00 MLT to 09:00 MLT, i.e., the center of time interval was set to the local midnight, 00:00 LT \(=\) 21:00 MLT \(=\) 21:00 UT. It should be noted that the calculated daily averaged ap index is different from the normal daily averaged ap index, Ap index, which is the averaged ap indices from 00:00 UT to 24:00 UT. We defined quiet days as days with the daily averaged ap index of \(<10\), and active days as days with that of \(\ge 10\). Thus, we categorized the Na density and CNA data into data of 153 quiet days and data of 101 active days.

To see statistical features, we calculated median values from the datasets at each time and height for each activity level. Figure 3 shows MLT-height variations in the median Na densities during the quiet and active days. It should be noted that the data coverages were limited during nighttime (14:00–30:00 MLT) because of the Na lidar observations during dark sky. In both the quiet and active days, Na layers were distributed at 80–105-km heights, and its density peaks were located at \(\sim 90 \,\hbox {km}\) height. Overall, it seems that there was no big difference between the median Na densities during the quiet and active days, but we can see some slight differences around the topside of Na layers (\(\sim 100 \,\hbox {km}\) height). At \(\sim 100 \,\hbox {km}\) height, the median Na densities during the active days were a bit smaller than those during the quiet days.

For more detailed inspection, Fig. 4 shows MLT variations of the Na densities at 97–103-km heights during the quiet and active days, together with the CNA variation. Variations of Na densities and CNA of each day were quite large, which may be due to seasonal, day-to-day, diurnal, and other variations. Here, we investigate statistical features utilizing median values during the quiet and active days. At 103-km height, median Na densities during the active days were \(\sim 300 \,\hbox {cm}^{-3}\) at \(\sim 15{:}00\) MLT and \(\sim 150 \,\hbox {cm}^{-3}\) at \(\sim 24{:}00\) MLT, and those during the quiet days were \(\sim 400\,\hbox {cm}^{-3}\) at \(\sim 15{:}00\) MLT and \(\sim 250\,\hbox {cm}^{-3}\) at \(\sim 24{:}00\) MLT. Thus, the median Na densities during the active days were mostly small compared with those during the quiet days, and those during both the quiet and active days were decreasing with MLT from dusk hours to dawn hours. Similar characteristics can be seen in those at 97–101-km heights.

On the other hand, median CNA values during the active days were \(\sim 0.2 \,\hbox {dB}\) at \(\sim 21{:}00\) MLT and \(\sim 0.5 \,\hbox {dB}\) at \(\sim 30{:}00\) MLT, and those during the quiet days were \(\sim 0.0 \,\hbox {dB}\) at \(\sim 21{:}00\) MLT and \(\sim 0.1 \,\hbox {dB}\) at \(\sim 30{:}00\) MLT. Thus, the median CNA values during the active days were mostly large compared with those during the quiet days, and that during the active days was decreasing with MLT from dusk hours to dawn hours.

To confirm significance in such differences between the median values during the quiet and active days, we did a statistical test which is the Mann–Whitney U test. Then, the median values with more than 98% probability were marked by red. It is found that most of such differences were significant in the cases of Na densities at 99–103-km heights, but most of those at 97-km height were not so significant. In the case of CNA, such differences were significant except for 13:00–20:00 MLT.

To make more detailed comparisons, we calculated Na deviations defined as \(\frac{{{\mathrm{Na}}}_{{{\mathrm{active}}}} - \mathrm{Na}_{{{\mathrm{quiet}}}}}{{{\mathrm{Na}}}_{{{\mathrm{quiet}}}}} \times 100\) (%), where \({{\mathrm{Na}}}_{{{\mathrm{active}}}}\) is the median Na density during the active days, and \({{\mathrm{Na}}}_{{{\mathrm{quiet}}}}\) is the median Na density during the quiet days. On the other hand, CNA deviations were also calculated as \({{\mathrm{CNA}}}_{{{\mathrm{active}}}} - {{\mathrm{CNA}}}_{{{\mathrm{quiet}}}}\) (dB), where \({{\mathrm{CNA}}}_{{{\mathrm{active}}}}\) is the median CNA during the active days, and \({{\mathrm{CNA}}}_{{{\mathrm{quiet}}}}\) is the median CNA during the quiet days. It should be noted that we did a normalization, i.e., \(\times \frac{100}{{{\mathrm{Na}}}_{{{\mathrm{quiet}}}}}\), for the Na deviation, and it would be useful to compare different Na densities at different heights. On the other hand, the CNA deviation corresponds to \(10\times \hbox {log}_{{10}}(\hbox {P}_{\mathrm{quiet}}{/}\hbox {P}_{{{\mathrm{active}}}}\)), because the definition of CNA is \(10\times \hbox {log}_{{10}}(\hbox {P}_{\mathrm{qdc}}/\hbox {P}_{{{\mathrm{abs}}}})\), where \(\hbox {P}_{{{\mathrm{qdc}}}}\), \(\hbox {P}_{{{\mathrm{abs}}}}\) are the received signal powers for the quiet day curve and the absorption, respectively. Then, \(\hbox {P}_{\mathrm{quiet}}\) is the received signal power for the absorption during the quiet days, and \(\hbox {P}_{{{\mathrm{active}}}}\) is that during the active days.

Figure 5 shows MLT-height variations in the Na and CNA deviations. Concerning to the Na densities around 95–105-km heights, significant negative Na responses (with \(>98\%\) probability), i.e., Na decreases, can be seen during most of the period, i.e., 15:00–30:00 MLT. The Na deviations were \(-20\%\) at \(\sim 15{:}00\) MLT, and \(-60\%\) at \(\sim 29{:}00\) MLT. Thus, amounts of the Na decreases were larger with MLT from dusk hours to dawn hours. On the other hand, most of the Na responses below 95-km height were insignificant (with \(\le 98\%\) probability). As for the CNA deviations, significant positive CNA responses, i.e., CNA increases, can be seen for 20:00–32:00 MLT. The CNA responses were opposite to the Na density responses, i.e., negative responses. The CNA deviations were \(\sim 0.1 \,\hbox {dB}\) at \(\sim 21{:}00\) MLT and \(\sim 0.4 \,\hbox {dB}\) at \(\sim 32{:}00\) MLT. Thus, amounts of the CNA increases were larger with MLT from dusk hours to dawn hours.

Scatter plots as well as CCs of the Na and CNA deviations are shown in Fig. 6. It should be noted that both the significant and insignificant data were included for CC calculations. It seems that the decreases in the Na deviations tended to be more severe with the increasing CNA deviations. For example, at 103-km height, the Na deviations were 0 to \(-40\%\) when the CNA deviations were \(\sim 0.0 \,\hbox {dB}\), and the Na deviations were \(-20\) to \(-60\%\) when the CNA deviations were 0.1–0.2 dB. The CCs at 103-km height have a negative peak around zero lag, and its value was about \(-0.6\). Similar characteristics can be seen also at 97–101-km heights. Thus, there were clear negative correlations between the Na and CNA deviations.