The understanding of the response of atmospheric ozone and temperature to the solar cycle of ∼11 years is important for both scientific and practical reasons. Global responses in the stratosphere, mesosphere, and lower thermosphere have been investigated over decades based on a variety of satellite data.

There is evidence that the magnitude of responses to decadal solar cycles depends on the local times at which the measurements are made. For example, Beig et al. (2012), in analyzing data from the Halogen Occultation Experiment (HALOE), found that derived responses are different at sunrise (6 LST) and sunset (18 LST).

However, with a few exceptions, the instruments on satellites only measure at one or two local times, which are fixed for the entire mission.

Generally, previous studies do not address the issue of diurnal variations of the responses in detail, and there have been no studies describing the variations of the responses over the 24 h local time period. In the following, we provide estimates of the diurnal variations of the responses over a 24 h period, which was previously not available.

As noted in Huang et al. (2016b), previous global responses to the 11-year solar cycle based on measurements have been largely based on data from the NOAA operational satellites, including the Stratosphere Sounding Unit (SSU), the Microwave Sounding Unit (MSU), and the Solar Backscatter Ultraviolet (SBUV) instruments; from the Stratospheric Aerosol and Gas Experiment (SAGE I, II) on the Explorer and Earth Radiation Budget (ERB) satellites; from the Halogen Occultation Experiment (HALOE) on the Upper Atmosphere Research Satellite (UARS); and from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument on the Thermosphere-Ionosphere-Mesosphere-Energetics and Dynamics (TIMED) satellite, among others. The advantage of the operational satellites is that they can provide global measurements covering decades, and can be replaced as needed. However, issues regarding instrument offsets, stability, and continuity over many years and decades can be problematic.

Except for SABER (and UARS), instruments on these satellites only make measurements at one or two local times, which are fixed for the mission duration. The NOAA operational satellites are sun-synchronous, in which case the measurements are made at two fixed local times: one for the ascending orbital mode and one for the descending mode. HALOE and SAGE only make solar occultation measurements at instrument sunrise and sunset. Consequently, used as is, responses based on zonal means of the above measurements reflect long-term variations at the fixed local times, and could be a source of differences among the various studies.

They could also be a source of differences with 3-D models, in which ozone amounts and temperature vary with local time around a latitude circle, and zonal means are averages over both longitude and a 24 h local time period. When comparing the results of responses based on zonal means from measurements with models, Austin et al. (2008) pointed out that “The model results are strictly zonal average values, which is an average over local time, whereas the observations are typically made at fixed local times. Therefore, in the mesosphere, where the diurnal variation of ozone is large, some of the differences between model results and observations may have arisen from a diurnal variation in the actual solar response”. See also Beig et al. (2012).

In addition, the orbits of some operational satellites have drifted, so that the local times at which the measurements are made have also drifted over several hours or more (see McPeters et al., 2013; Frith et al., 2014; Remsberg, 2008; Randel et al., 2009; Tummon et al., 2015; Hood et al., 2015). Tummon et al. (2015) summarizes some of the data processing methods used by various groups. Generally, they report that diurnal variations are either neglected, or are assumed to be negligible below ∼45–50 km (see also Davis et al., 2016).

Previous results have not generally agreed so well with one another with respect to their details. A major reason for these differences may be the conditions and constraints under which the various measurements were made (for details, see Austin et al., 2008; Crooks and Gray 2005, Gray et al., 2005, and Huang et al., 2016b).

In addition, previous studies have generally not described how they treat diurnal variations, so that comparisons related to responses as a function of local times are problematic. We are also not aware of studies based on orbital drift.

In contrast to most other measurements, SABER provides additional information which allows us to estimate daily ozone and temperature diurnal variations, and, in turn, the dependence of their responses to the decadal solar cycle on local time. In the following, we focus on zonal means of ozone and temperature, either at various specific local times, or averaged over local times (as in a 3-D model), and the effects of their diurnal variations on their responses to solar variability over a solar cycle of ∼11 years (2002–2014), from 20 to 100 km.

In this study, we find that not only do the values of the responses depend on the local times at which the measurements are made, but they can be significant even at altitudes as low as 30 km.

In Sect. 2, we review our previous analysis and derivation of diurnal variations and zonal means that are averages of both longitude and local time around a latitude circle, based on SABER measurements. We also describe how we can estimate new results of zonal means corresponding to specific local times, and new results estimating the effects of orbital drift on diurnal variations. In Sect. 3 we describe our new results of responses to the solar cycle at the specific local times of sunrise (6 LST) and sunset (18 LST), and compare them with results from HALOE. This gives an indication of the quality and reality of both sets of results. In Sect. 4 we describe our new results for responses to the solar cycle over a diurnal cycle of 24 h. In Sect. 5 we describe our estimates of responses in situations where the local times have “drifted” due to satellite orbital drifts. We also describe some previous studies. In Sect. 6 we discuss the issue of data length.

The SABER/TIMED instrument (Russell et al., 1999) was launched in December 2001 with an orbital inclination of ∼74∘. SABER views the Earth's limb to the side of the orbital plane, and vertical profiles, corresponding to the line-of-sight tangent point, are retrieved from measurements of the CO2 15 and 4.3 µm emissions for kinetic temperature, and from the 9.6 µm channel for ozone. About every 60 d, TIMED is yawed by 180∘, so that the SABER measurement footprint spans the latitudes from ∼83∘ N to 52∘ S or ∼83∘ S to 52∘ N on alternate yaw periods. Over a given day and for a given latitude circle, measurements are made as the satellite travels northward (ascending mode) and again as the satellite travels southward (descending mode). Data at different longitudes are sampled over 1 d as the Earth rotates relative to the orbital plane.

SABER scans altitude (∼10–105 km for temperature, 15–100 km for ozone) every 58 s with an altitude resolution of ∼2 km, ∼96 scans per orbit, and ∼14 longitudes per day.

The orbital characteristics of the satellite are such that, over a given day, a given latitude circle, and a given orbital mode (ascending or descending), the local time at which the data are measured is essentially the same, independent of longitude and time of day. For a given day, latitude, and altitude, we work with data averaged over longitude: one for the ascending orbital mode and one for the descending mode, each corresponding to a different local solar time, resulting in two data points for each day. Each can be biased by the local time variations and is therefore not a true zonal mean. True zonal means are averages made at a specific time over longitude around a latitude circle, with the local solar time varying by 24 h over 360∘ of longitude. The local times of the SABER measurements decrease by about 12 min from day to day, and it takes ∼60 d to sample over the 24 h of local time.

In this section, we extend our results to other local times. Although the figures only show responses at 6, 12, 18, and 24 LST, we have generated hourly responses, and can do so at any local time. We do not believe that plots at additional local times would add important information for the purpose of this paper, and would only make other details less discernible.

Generally, previous studies based on other satellite measurements do not describe how they treat data with respect to local times, and we cannot make comparisons as with HALOE. Some studies use different data from various instruments, which mix data measured at different local times. See Sect. 5.2 and the discussion in reference to Fig. 9, for details.

Figure 6 shows our ozone (Fig. 6a) and temperature (Fig. 6b) responses from 50 to 100 km, at 16∘ N over a diurnal cycle (6, 12, 18, and 24 LST). The black line denotes our responses based on SABER data, where the zonal means are averages over both longitude and a 24 h local time period. The green asterisks denote responses for 6 LST, blue diamonds represent 12 LST, red plusses represent 18 LST, and magenta triangles represent 24 LST.

Up until this point, ozone values are responses at solar max minus responses at solar min (%/100 sfu). In the following, note that unlike the situation above at 6 and 18 LST for ozone, the normalizing values used to obtain responses in percent are now averaged over local time, to be consistent with responses based on zonal means that are averages over both longitude and local time (black line in Fig. 6).

Figure 7 shows the ozone (Fig. 7a) and temperature (Fig. 7b) responses to solar activity versus altitude at the Equator; from 20 to 60 km, at 6 LST (green asterisks), 12 LST (blue diamonds), 18 LST (red plusses), and 24 LST (magenta triangles); and based on zonal means that are averages over local times (black asterisks). For ozone, below about 40 km, diurnal variations have relatively little effect on responses. For temperature, the effects can be larger, even at altitudes as low as 30 km.

Figures A1 and A2 in the Appendix present plots corresponding to Fig. 7, but for 32 and 44∘.

In the stratosphere and lower mesosphere, previous global results of responses to the decadal solar cycle have been largely based on data from the NOAA operational satellites, including the Stratosphere Sounding Unit (SSU), the Microwave Sounding Unit (MSU), and the Solar Backscatter Ultraviolet (SBUV) instruments. An advantage of the operational satellites is that they can provide global measurements covering decades, and can be replaced as the instruments degrade. However, issues of calibration, instrument offsets, stability, and continuity, can be problematic. The satellites are generally polar orbiters and sun-synchronous, and make measurements at two fixed local times, one for the satellite ascending mode, and one for the descending mode.

As noted above, in merging data from different satellites, consistency in local times needs to be considered. Tummon et al. (2015), in reviewing some of the data processing methods used by various groups, report that diurnal variations are generally either neglected or are assumed to be negligible below ∼45–50 km (see also Davis et al., 2016).

In Sect. 2.2.2, we noted that in the application of Eq. (1), possible aliasing among the different terms is not definitively addressed. In addition, it has been argued that more than one solar cycle of data is more advantageous. Following our analysis given in Huang et al. (2016b), we address these issues in this section.

Figure 11 is a scatterplot of monthly values versus the 10.7 cm flux. Figure 11a and b show ozone at 47.5 km at the Equator, whereas Fig. 11c and d show temperature at 45 km at the Equator. Figure 11a and c represent the monthly zonal means that are averaged over both longitude and local time, and Fig. 11b and d use zonal means where the local times simulate orbital drift as discussed in reference to Fig. 8. The red lines in Fig. 11 represent linear fits between the monthly values and the 10.7 cm flux, which corresponds to using only the solar term (F107) of the multiple regression (Eq. 1). For ozone (Fig. 11a, b), the values 0.28 %/100 sfu (Fig. 11a, top-left label) and 3.24 %/100 sfu at 47.5 km (Fig. 11b, top-left label) compare well with the regression results which use all of the terms of Eq. (1), seen in Fig. 8a. For temperature (Fig. 11c, d), the values 1.23 K/100 sfu and 0.32 K/100 sfu at 45 km also compare well with Fig. 8b. Consequently, aliasing from other terms in Eq. (1) is not significant.

As for issues of data length, unlike time series data, where time increases monotonically with data length, the 10.7 cm flux values remain within a fixed interval between solar minimum and solar maximum (∼70 and 200 sfu). In Fig. 11, the values span about one solar cycle. However, even over more solar cycles, the 10.7 cm flux values would only repeat and backfill in with values in the same general area in Fig. 11, effectively providing a more average result but not necessarily reducing the uncertainty much otherwise.

It can be argued that even with more than one solar cycle of data available, analysis over individual cycles should be carried out to analyze differences among solar cycles.

Using SABER data, we investigated the effects of ozone and temperature diurnal variations on their responses to the solar cycle, from 2002 to 2014 and 20 to 100 km.

We find that for ozone, above ∼40 km, zonal means reflecting specific local times (e.g., 6, 12, 18, and 24 LST) lead to different values of responses compared to each other, and compared to responses based on zonal means that are averaged over the 24 h local time period (Figs. 6, 7). For temperature, effects of diurnal variations are not negligible at ∼30 km and above.

We also considered the variations of local times themselves due to orbital drifts of certain operational satellites, and their effects on responses to the solar cycle (Fig. 8). The differences can be significant above ∼35 km.

The quality and validity of our analysis are shown in comparisons with responses found by Beig et al. (2012) and Fadnavis and Beig (2006), based on HALOE data, which made measurements only at sunrise and sunset. Comparisons with our corresponding results, based on SABER measurements, are favorable, both at sunrise and sunset separately, and combined. Our analysis is robust in that the average of responses at specific local times over a diurnal period of 24 h is the same as responses based on zonal means that are averages over longitude and local time together.

Previous studies based on other satellite data generally do not describe the treatment, if any, of local times, so we cannot compare our data with their studies as we have with HALOE data. Some studies also analyzed data merged from different sources, with measurements made at different local times. As discussed in Sect. 5.2 in reference to Fig. 9, the results of these studies do not generally agree very well among themselves.

We do not believe that diurnal variations are the major reason for the discrepancies, as there are likely other data-related issues. Other reasons for differences may be the conditions and constraints under which the various measurements were made. Details can be found in Austin et al. (2008), Crooks and Gray (2005), Gray et al. (2005), and Huang et al. (2016b). However, diurnal variations should be included as part of the analysis of the differences among various results.

The effects due to satellite orbital drift (discussion in reference to Fig. 8) may explain some unexpected variations in the responses, especially above 40 km.