It has been known for a long time that the night sky, even in moonless nights, is not completely dark. In 1868, Anders Ångström, who is the namesake of the Ångström unit, noticed that the color of the nighttime illumination was the same as the color of aurora, although the highly structured features were clearly missing . About 50 years later, in the 1920s, John McLennan and Gordon Merritt Shrum found the green emission line of oxygen which could explain the two apparently related phenomena in the night sky . Less than a decade later, Vesto Melvin Slipher found that in addition to the oxygen green line, the night sky emissions contained features at wavelengths corresponding to the sodium doublet. Therefore, he concluded that there has to be a layer of sodium atoms in the upper atmosphere . Today, we know that the sodium layer is located in the mesosphere and lower thermosphere (MLT) region, which is found at altitudes between 70 and 110 km. In that layer peak sodium concentrations range between ca. 500 and ca. 5000 atoms cm-3 depending on altitude, location, and both the time of the day and the time of the year. An often discussed feature of the sodium layer emission is its semiannual cycle in the tropics with peaks around the spring and fall equinoxes . This has also been observed in other atmospheric parameters, e.g., OH rotational temperature, OH emission rate, oxygen green line emission rate and atomic oxygen concentration . The reason is thought to be connected to the semi-annual variation of the amplitude of the diurnal tide which has its maxima around the equinox .

The chemical reactions that lead to the emission of electromagnetic radiation by excited sodium atoms at night were first proposed by Sydney Chapman in 1939 and thus are called the “Chapman mechanism” (see Eqs. –). 1Na+O3⟶k1NaO(A3Σ+)+O22NaO(A3Σ+)+O⟶fA⋅k2Na(2PJ)+O2⟶(1-fA)⋅k2Na(2S1/2)+O23Na(2PJ)⟶ANa(2S1/2)+hν(589.0/589.6nm) These reactions yield excited sodium that emits electromagnetic radiation with a wavelength of either 589.0 nm (D2) or 589.6 nm (D1) , depending on the exact quantum state of excitation. This state is given by the total angular momentum quantum number J=1/2 or J=3/2. Later, empirical studies found that the D2 / D1 line ratio is highly variable with values between 1.2 and 2.0, which could not be explained by the Chapman mechanism. Laboratory studies carried out by showed that this variability could be a result of a dependence on the O2/O ratio. That led them to the suggestion that the original mechanism needs to be expanded by additional quenching reactions () and (). 4NaO(A3Σ+)+O2⟶k4NaO(X2Π)+O25NaO(X2Π)+O⟶fX⋅k5Na(2PJ)+O2⟶(1-fX)⋅k5Na(2S1/2)+O2 Although, the mechanism of the sodium D-line excitation is now much better understood, there are still uncertainties. These include the values of the branching ratios fA and fX that determine the ratio of excited sodium to sodium in the ground state. There has been a lot of research focusing on ways to derive sodium concentration profiles from sodium D-line nightglow measurements. showed that using only the reactions of the original Chapman mechanism together with one additional sodium loss reaction and an “effective branching ratio f” yields sodium concentrations with uncertainties less than 1 %. Many studies have investigated the “effective branching ratio” and found values between 0.05 and 0.6 (e.g., ). The sodium retrieval of this study is based on the results of . By using lidar measurements to validate the sodium profiles retrieved from Na D-line nightglow measurements with OSIRIS on Odin and changing the branching ratio f until the profiles match, they found a branching ratio of 0.064±0.024.

A key motivation to find the exact value of the branching ratio is to gain a deeper understanding of the sodium concentrations and their variations in the MLT region. proposed a method to retrieve sodium concentration profiles from nighttime satellite limb measurements. They show sodium profiles for monthly averaged data for the 30∘ S to 30∘ N latitude range obtained from the limb measurements with the SCIAMACHY instrument. In the current study, we use the MLT Na profiles retrieved from SCIAMACHY Na nightglow measurements to validate sodium profiles retrieved from OSIRIS nighttime limb measurements. This paper is structured as follows. In Sect. 2 we give an overview of all the sets of data and the corresponding instruments used in this study. Section 3 describes the method used to analyze the data. Section 4 shows the results, and the main conclusions are presented at the end.

The instruments OSIRIS on Odin and SCIAMACHY on Envisat provide the sodium nightglow measurements, which are the key measurements to obtain sodium profiles. Additionally, we use ozone profiles from the SABER instrument on TIMED and the model NRL-MSIS 00 provides information on the background atmosphere. Lastly, Na vertical column densities (VCDs) determined from GOMOS/Envisat stellar occultation measurements were used to validate the results obtained from OSIRIS and SCIAMACHY.

The SCIAMACHY nightglow measurements have a low signal-to-noise ratio, so showed that averaging over a great number of measurements is needed to obtain a sufficient signal. Because the measurements only cover the 30∘ S to 30∘ N latitude range sufficiently and are only available in the years 2003 to 2011, we selected all the other data in a way that they fit in this geographical and temporal range.

To retrieve sodium concentration profiles from volume emission rate (VER) profiles of the Na D-line nightglow at 589 nm, we used the approach first proposed by . They showed that the Na chemistry is dominated by only three reactions. Those are Reactions () and () of the Chapman mechanism and the following additional Na loss reaction: 6Na+O2+M⟶k3NaO2+M. The steady-state assumption leads to the following equation: 7[Na]ret=VER/fk1[O3]+k3[O2][M]. demonstrated that neglecting all other chemical reactions leads to Na retrieval errors of less than 1 %. Here, f is the effective branching ratio (f=0.064±0.024, taken from ), and k1 and k3 are reaction rate constants. For k1 we use 1.1×10-9exp⁡(-116/T)cm3s-1 and for k3 (5.0×10-30)(T/200)-1.22cm6s-1. Both values are taken from . For more detailed information see and .

This study aims to compare LER, VER and sodium profiles that we have obtained from measurements with two independent (OSIRIS/Odin and SCIAMACHY/Envisat) satellite measurements. Additionally, we want to show the comparison of SCIAMACHY and OSIRIS sodium VCDs to those obtained from fitting a sodium density model to GOMOS data . The comparison of the LER profiles shown in Fig.  of the time interval 2006 to 2011 shows that they are in good overall agreement. Here we show contour plots of SCIAMACHY (upper panel) and OSIRIS (lower panel) monthly LERs for the tangent heights between 80 and 103 km and one profile for each month. The white region in the upper panel is a result of measurements with a SNR below a certain threshold (see Sect. ). The LER peaks lie between 83 and 87 km. and showed that, at low latitudes, there is a semi-annual cycle in the LERs, with peaks in the spring and fall months. Here, we see the same cycle. Looking at the VER contour plots in Fig.  we also see a very good agreement between the SCIAMACHY and OSIRIS VERs. The VERs are shown for altitudes between 80 and 103 km. Although there are more fluctuations than in the LERs, the VER peak is identifiable at around 91 km. Again the semi-annual cycle is clearly visible. To visualize this cycle even better we show the LERs, VERs and also sodium concentration profiles for two tangent heights/altitudes in Fig. . This figure shows the LERs (panels a and b) and VERs (panels c and d) at 83 and 93 km tangent height and altitude, respectively. For the sodium concentration we chose to show the altitudes of 93 and 95 km. In panels (a) and (b) the semi-annual cycle of the LERs can be seen very clearly. The panels also show that the SCIAMACHY LER peaks are slightly larger with peak magnitudes of about 2.5×109 photons cm-2 s-1 than the LER peaks of OSIRIS that are only 2×109 photons cm-2 s-1, i.e., 20 % lower. In Fig. c and d, which show the VER, we find the same semi-annual cycle as in the LERs and again SCIAMACHY shows slightly higher values than OSIRIS. While the OSIRIS peak emissions are between 20 and 30 photons cm-3 s-1, the SCIAMACHY peak emissions lie between 35 and 40 cm-3 s-1, i.e., around 25 % higher than those of OSIRIS. Both instruments show especially high values in the year 2011. Looking at panels (e) and (f), which show the sodium concentrations at one altitude, the semi-annual cycle is not as clearly visible. Although the reason is not fully understood we attribute it to the fact that the semi-annual oscillation of the LERs and VERs has its origin in the semi-annual oscillation of the ozone concentration. Other studies that dealt with the sodium layer in the tropics also show that seasonal variations are weaker in the tropics and stronger at high latitudes . Since we can only retrieve OSIRIS sodium concentration profiles for every second month, we interpolated the values in between. Hereby, the green diamonds correspond to the retrieved values.

Figure  shows the comparison of the sodium concentration profiles (panel b – SCIAMACHY and c – OSIRIS) as well as the VCDs (panel a). It is obvious that although the shape of the profiles can be slightly different, the values of the sodium concentrations detected by the two instruments agree well with each other. The exact reasons for the high variability, especially of the SCIAMACHY sodium profiles, are currently not fully understood. In panels (c) and (b) the sodium concentrations for the altitudes between 80 and 103 km are shown. The sodium peaks are located between 93 and 98 km and vary strongly from month to month and between the instruments. The white months in panel (c) are a result of missing co-located measurements between the SABER (ozone concentration profiles) and OSIRIS measurements. In panel (a) we show the VCDs of OSIRIS measurements (green squares), SCIAMACHY measurements (red triangles) and those obtained when fitting a sodium density model to the GOMOS data (pink circles). The latter show a very regular seasonal evolution, which is not as clearly present in the OSIRIS and SCIAMACHY VCDs. Moreover, the SCIAMACHY measurements in most months lead to higher sodium VCDs than the OSIRIS measurements. That becomes even clearer when looking at the mean values of the sodium VCDs: OSIRIS VCD =3.37×109±1.07×109atomscm-2; SCIAMACHY VCD =4.25×109±1.52×109atomscm-2; GOMOS VCD =3.30×109±3.54×108atomscm-2. In Fig.  we then show the comparison of sodium profiles retrieved from OSIRIS and SCIAMACHY measurements in four different months of the year 2008 with uncertainties corresponding to each altitude. It can be seen in panels (a) and (c) that SCIAMACHY yields higher values than OSIRIS and in panel (b) the opposite is the case. Only in panel (d) the values of the sodium concentration profiles agree well with each other. We assumed the errors of N2 and O2 are 5 % of their concentration,; for the mesospheric temperatures we assumed an error of 10 K and for the ozone concentration we used the standard error of the mean. That we determined by dividing the standard deviation of the ozone concentrations at a certain altitude by the square root of the number of measurements which we averaged over to determine the ozone profile. For the error of the sodium nightglow emission we took the highest available tangent height and calculated the standard deviation of a part of the spectrum that has no sodium emission and the same number of pixels as the part of the spectrum with emission. We then determined the overall sodium concentration uncertainty by propagation of uncertainty. At an altitude of 95 km it lies between 2 % and 15 %. But in some months the uncertainties can go up to 25 % and above 98 km the sodium uncertainties become very large with values over 200 %. The absolute calibration uncertainty of the two instruments could also influence the retrieved sodium profiles. For OSIRIS it is estimated to lie between 5 % and 10 % while for SCIAMACHY it is between 2 % and 4 %. We tested how this could affect the sodium profiles by changing the LER profiles by ±10%. This changes the resulting sodium profiles by around 15 %.

The differences between SCIAMACHY and OSIRIS become even more obvious when looking at the mean profile of all the available profiles (Fig. ). Here, we summed up the values of the LERs, VERs and sodium profiles at each tangent height/altitude of every available month and then divided the value by the number of months for that we could retrieve sodium concentration profiles. The mean LER, VER and sodium profiles retrieved from SCIAMACHY (red) are slightly larger than the mean profiles of OSIRIS (green). The dashed lines show the standard deviations for every corresponding tangent height/altitude. For the mean LER profiles the standard deviation is small at high tangent heights and becomes larger between 90 and 95 km. Below 90 km it stays large. This is a difference to the standard deviation of the mean VER and sodium profiles. Here the standard deviation is low above and below the peak height and only relatively high in the peak regions at around 90 and 95 km, respectively.

The reasons for the larger overall values of the SCIAMACHY measurements could be that OSIRIS conducts measurements with a different latitudinal and longitudinal coverage than SCIAMACHY. The first usually only conducts measurements in one hemisphere each month; the latter covers the whole -30 to 30∘ latitude band. Although we select the profiles of the other parameters accordingly, this difference could still be the reason for the difference in the obtained sodium concentration profiles. We found out that the parameters with the largest influence are the mesospheric ozone concentration and temperature. In Fig.  we show how variations of the ozone concentration and mesospheric temperature influence the corresponding sodium profiles. In the left panel we increased (dashed line) and decreased (dotted line) the temperature and show how the sodium concentration changes in relation to the sodium profile obtained when using the original temperature. Here we see that changing the temperature by 10 K changes the sodium concentration by about 5 %. In the right panel we show a similar plot for the ozone concentration. Here we changed the ozone concentration by 30 %, which corresponds to 1 standard deviation, and this leads to an increase in the sodium concentration by up to 100 %. Figure  shows ozone concentration profiles that are used to retrieve sodium concentration profiles from SCIAMACHY (panel a) and OSIRIS (panel b) mesospheric limb nighttime measurements. The months with no data in panel (b) are a result of the differences in latitudinal and longitudinal coverage between OSIRIS and SCIAMACHY. Ozone concentrations range between 1 and 7×108 cm-3 with a peak at 90 km. Also there is a seasonal variation with peaks in the spring and fall months and low concentrations in the northern hemispheric summer and winter. We found out that low ozone concentrations, as stated by Eq. (), are related to high retrieved sodium concentrations, especially regarding the SCIAMACHY measurements. All ozone measurements are taken from the SABER/TIMED database. Ozone is photolyzed when the sun is present but recovers very quickly after sunset and is expected to be almost constant during the night . The differences seen in Fig.  are probably mainly a result of the different latitudinal and temporal coverage of OSIRIS and SCIAMACHY. SCIAMACHY covers the whole 30∘ S to 30∘ N latitude band, while OSIRIS usually covers only one hemisphere and the SABER measurements are selected accordingly.

Also the local time of the measurements could influence the sodium profiles. As OSIRIS conducts measurements around 18:50 and SCIAMACHY at 22:00, we select the ozone profiles obtained at those local times to until 30 min later and average over all profiles that fall into this time period. Although we see in Fig.  that the variation of ozone between the two local times is not very big, we have seen in Fig.  that small variations of ozone can lead to huge differences of the sodium concentration. Additionally, we tested how that non-linearity of the sodium sensitivity to variations of the ozone concentration is affected by using monthly averaged ozone profiles. To do this we retrieved sodium concentration profiles with each individual ozone profile that would be used for averaging. Then we averaged over all the resulting sodium profiles and compared this profile to the profile obtained when using one monthly averaged ozone profile. The result is, in most months, a difference of the peak sodium concentrations of around 5 %. However, in a few months the difference can be up to 20 %. In conclusion, the different latitudinal and longitudinal coverage as well as the difference of the local time of the SCIAMACHY and OSIRIS measurements together with the high variability in the mesospheric temperature and ozone profiles can have a big effect on the resulting sodium concentration profiles. And lastly, as already reported in , sodium concentrations themselves are highly variable during one night. Using lidar measurements to detect the sodium layer over São José dos Campos (23∘ S, 46∘ W) they found variations between 2500 and 5000 atoms cm-3.

In this study, we compared sodium concentration profiles retrieved from Na D-line nightglow measurements from two different instruments, the Optical Spectrograph and Infrared Imager System (OSIRIS) and the Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY). We were able to retrieve sodium concentration profiles with uncertainties between 2 % and 15 %, and over the period 2006 to 2011 we found 34 months that were suitable for comparison. We found out that, while SCIAMACHY detects slightly larger LERs and VERs, the overall seasonal variation of the three parameters agrees very well. To retrieve the sodium concentration we used a branching ratio of 0.064±0.024 which was determined by . A very similar value was calculated by using ozone concentrations profiles from the SABER instrument, which is close to the value found by . We were able to show that, as was expected, the LERs and VERs undergo a semi-annual cycle in the tropics. It was then concluded that the higher concentrations detected by SCIAMACHY could be primarily a consequence of the differences in the spatial and temporal coverage. While SCIAMACHY usually covers both hemispheres in the -30 to 30∘ latitude band at 22:00 local time, the OSIRIS measurements only cover one of the hemispheres each month at around 18:50 local time. Additionally, the SCIAMACHY mesospheric nighttime limb measurements, as a result of SCIAMACHY's photodiode array, have a lower SNR than the OSIRIS measurements. We then analyzed how changing the parameters used to obtain sodium concentration profiles would affect those. We found out that the ozone concentrations have a huge influence on the value of the retrieved sodium. Changing the ozone concentration by 30 %, which corresponds to one standard deviation, changes the sodium concentration by up to 100 %. And lastly, we stated that differences in the sodium concentration could be a result of the local time difference between the measurements. While SCIAMACHY measures at a local time of 22:00, OSIRIS measurements are carried out at a local time around 18:50.