Roble and Dickinson (1989) estimated the effects of hypothetical future increases in greenhouse gas concentrations on the global mean structure and predicted considerable cooling in the mesosphere and thermosphere. About this time, a number of long-term temperature observations in the mesopause region (80–110 km) were initiated or reinitiated at locations in the Northern Hemisphere with passive OH emissions and/or active probes, such as Na lidar and falling spheres. These observations and those in the Southern Hemisphere via OH emission, as well as the long series of Russian rocket measurements and OH emissions between about 1960 and 1995 over a wide range of latitudes, measured cooling trends in the mesopause region ranging from 0 to ∼ 10 K decade-1, suggesting that after 2 decades, the observed trend remains uncertain (Beig, 2006). These observational temperature trend results were referenced in Table I of She et al. (2009).

Based on the nocturnal lidar temperatures acquired between March 1990 and December 2007 (data set (90-07)), the same paper reported a linear long-term trend, starting from an insignificant cooling trend of 0.28 ± 1.32 K decade-1 at 87 km, reaching a maximum value of 1.55 ± 1.15 K decade-1 at 91 km, and turning into a warming trend above 102 km. The magnitude and altitude dependences are consistent with the prediction of the Spectral Mesosphere/Lower Thermosphere Model (SMLTM) (Akmaev et al., 2006) and of the Hamburg Model of the Neutral and Ionized Atmosphere (HAMMONIA) (Schmidt et al., 2006). Subsequent substantial reviews on thermospheric trends, Lašttovička et al. (2012) and Cnossen (2012), included some studies on the mesopause region neutral temperatures. Recent observational reports on mesopause region temperature trends at specific altitudes include Offermann et al. (2010) and Hall et al. (2012), based on ∼ 10-year data sets. The former utilized the annual mean OH imager temperatures between 1988 and 2008 over Wippertal (51∘ N, 7∘ E) and reported a long-term trend at 87 km of -2.3 ± 0.6 K decade-1 in temperatures; the latter utilized meteor wind radar between October 2001 and October 2012 at Svalbard (78∘ N, 16∘ E) calibrated by satellite measurements and reported a temperature trend at 90 km of -4 ± 2 K decade-1.

The Colorado State University (CSU) Na lidar performed nocturnal mesopause region temperature observations between March 1990 and March 2010 at Fort Collins, CO (41∘ N, 105∘ W). It employed a vertical beam between 1990 and 2001. Since 2002, the lidar has operated in 2- or 3-beam geometry for simultaneous temperature and wind measurements, leading to two or three mean temperatures at a given altitude each night. The lidar was relocated to Utah State University (USU) and has continued its regular observation at Logan, Utah (42∘ N, 112∘ W) since September 2010. Because of similar geographical coordinates, we combine the data from both locations to form a data set from March 1990 to December 2014, denoted as (90-14_Avg). The extension _Avg indicates that, unlike the data set employed in previous publications such as (90-07), which utilized temperatures from the beam with the largest signal at 3.7 km vertical resolution, here we use the average of temperatures acquired from two or three beams at 2.0 km vertical resolution.

As an overview, we plot the 25 years of nightly mean temperatures at 86 km, which shows large annual and semiannual variation, and at 99 km, an altitude with minimal annual and small semiannual variation (She and von Zahn, 1998), respectively, in Fig. 1a and b. The data acquired at CSU (March 1990–March 2010) is in black and that acquired at USU (September 2010–December 2014) is in blue; apart from a small data gap in 2010, the two sets of data blend nicely. From Fig. 1a summer is about 60–80 K cooler than winter at 86 km. At 99 km one can see long-term temperature variation. The 81-day averaged daily F10.7 solar flux also plotted in the figure, in the red curve, shows that the nightly mean temperatures track the variation in solar flux after 1993. Note that there exists a warming episode after the Mt Pinatubo Eruption (MPE), tMPE = 1.45 years, which peaked in 1993 and mostly died away near the beginning of 1999 for altitudes between 88 and 102 km (Fig. 3a). Since the warming episode is in our data, we must account for it in the analysis, whether its causes are fully understood or not. As a result, a nonlinear least-square regression analysis is required for long-term study.

Following She et al. (2009), who performed regression analysis on a shorter data set (90-07), a time series with 894 points, we express the nocturnal temperature at each altitude, T(z,t), of (90-14_Avg), a time series of 1200 points, as T(z,t)=Tfit(z,t)+TRes(z,t), where, Tfit(z,t)=α(z)+A1(z)cos⁡(2πt)+B1(z)sin⁡(2πt)+A2(z)cos⁡(4πt)+B2(z)sin⁡(4πt)+β(z)t+γ(z)P(z,t)+δ(z)Q81(t);Pz,t=2/exp⁡t0-t/t1+exp⁡t-t0/t2, where t is time in years from 1 January 1990, α(z) is independent of time, and the 4 A–B terms represent annual and semiannual variations. The three long-term effects have the amplitudes β(z), γ(z), and δ(z), in this model. The strong warming episode in our data, initially attributed to the Mt Pinatubo eruption in June 1991 (She et al., 1998), is represented by an amplitude γ(z) times P(z,t)=2/exp⁡(t0-t)/t1+exp⁡(t-t0)/t2, with parameters t0(z),t1(z), and t2(z), for the delay, rise, and decay time, respectively. The delay time here is relative to 1 January 1990, with the Mt Pinatubo eruption at 1.45 years (see Fig. 1b). Other long-term responses include δ(z), the solar response in K/SFU with Q81(t) being the 81-day averaged F10.7 solar flux, and β(z), the linear trend in K years-1. The residual from the best fit is TRes(z,t).

Since all effects of comparable strengths must be included in the time series for the nonlinear regression analysis (Akmaev, 2012) and the warming episode, solar activity and linear trend are not independent, the best fit of one term will affect that of the other and they will depend upon the length of the data set.

The long-term linear trend of the 11-parameter fit to the long data set, F-11P(90-14_Avg), is shown in Fig. 2 along with F-7P(90-14_Avg), deduced from the 7-parameter fit by setting γ(z)=0. Also shown are the published results from F-11P(90-07) and F-7P(90-07) from the shorter data set from March 1990 to 2007. As expected, the uncertainty from the 25-year data set is smaller than that from the 18-year data set. The cooling trend in F-11P(90-14_Avg) starts from an insignificant value of 0.64 ± 0.99 K decade-1 at 85 km, increases to a maximum of 2.8 ± 0.58 K decade-1 between 91 and 93 km, and then gradually decreases to a warming trend above 103 km. Turning from a cooling to a warming trend above 100 to 120 km in geographic altitudes is the result of the cooling and contraction of underlying atmosphere, the lower thermosphere, the mesosphere, and the stratosphere; it is predicted by models (Akmaev, 2012; Qian et al., 2013). This does not occur in the seven-parameter analysis (see F-7P(90-14_Avg) in Fig. 2). A similar difference between F-11P(90-07) and F-7P(90-07) is also evident. To our knowledge, metal resonance lidar is the only ground-based instrument that covers the entire mesopause region, and ours is the only Na lidar with a long enough data set to see this trend reversal.

Compared to the trends deduced from the shorter data set, (90-07), we note that the difference between F-7P(90-07) and F-11P(90-07) is bigger than the difference between F-7P(90-14_Avg) and F-11P(90-14_Avg) because the influence of the warming episode on the temperature trend is reduced in a longer data set. Statistically, the results from the longer data set are more accurate; the mean uncertainty between 88 and 102 km is 0.6 and 1.3 K decade-1, respectively, for F-11P(90-14_Avg) and the previously published F-11P(90-07). However, below we investigate the discrepancy between the two 11-parameter analyses, i.e., the 25-year data set has a larger cooling trend by ∼ 1 K decade-1.

Since the three long-term effects with magnitudes β(z),γ(z), and δ(z) are not independent in our analysis, we can understand their mutual influences by realizing that, in addition to the annual and semiannual variations, the observed temperature at a given time is the sum of three contributions β(z)t, γ(z)P(z,t), and δ(z)Q81(t). Because the solar flux, Q81(t), is a quasi-periodic function with a period of ∼ 11 years, for data sets longer than 11 years, the dominating competition is between the warming episode and trend. There is then a trade-off between the two best-fit values, which depend upon the observed values in the entire time series, i.e., data length. To see how this interdependence or correlation affects the ∼ 1 K decade-1 discrepancy more explicitly, we recall that the proxy of the warming episode is the function γ(z)P(z,t), which is shown in Fig. 3a for selected altitudes. This function rises to a peak temperature (max temperature), Tp, at the time tp=t0+ℓn(t2/t1)/[(1/t1)+(1/t2)]. Comparing tp and Tp in the 25- and 18-year-long data sets reveals the difference of their warming episode affecting the temperature trend. We plot these quantities as a function of altitude in Fig. 3b for F-11P(90-14_Avg) and for F-11P(90-07). Note that the altitude dependences for the two data sets are similar. Between 88 and 102 km, where the lidar signal is strong, we see little difference in tp but a systematic difference in Tp between the two data sets. Above 93 km, tp is about constant, but Tp increases continuously. Note that the peak warming (or maximum temperature response), Tp, from the shorter data set is consistently higher by 0.5 to 2.5 K, depending on altitude, implying that a larger share of observed temperatures in the 1990s are attributed to the warming episode; this leads to a lower share for the trend assessment and thus a smaller cooling trend. With the longer data set, the reverse is true. Since the longer data set assesses the lingering warming episode more fully, it can render better judgment on the sharing between the two competitors; of course, more data leads to statistical accuracy and thus to a smaller uncertainty than the corresponding trend deduced from the shorter data set as shown in Fig. 2. We thus accept F-11P(90-14_Avg) from 25 years of Na lidar observations, marked in solid black circles, as the deduced midlatitude mesopause region temperature trend.

The warming episode in our data plays a critical role in the temperature trend analysis based on our data sets. Furthermore, we assume a single temperature trend over 25 years in analysis. We thus shall discuss these issues before the final conclusion.

We have performed a regression analysis for the deduction of the mesopause region temperature trend based on an unprecedented Na lidar data set between March 1990 and December 2014. The 81-day averaged F10.7 solar is used as a proxy for solar activity, and a linear trend is assumed. Owing to a strong warming episode in the 1990s, the quarter century data set (90-14_Avg) is least-square fitted to an 11-parameter nonlinear model. The temperature trend shown in Fig. 2 starts from an insignificant value of 0.64 ± 0.99 K decade-1 at 85 km, increases to a maximum of 2.8 ± 0.58 K decade-1 between 91 and 93 km, and then gradually decreases to a warming trend above 103 km. Compared to the trend from the shorter data set, (90-07), which has a marginally significant cooling maximum of 1.55 ± 1.15 K decade-1 at 91 km (She et al., 2009), the quarter century data set gives a statistically quite significant cooling trend, larger by ∼ 1 K decade-1. The discrepancy is due to the competition between warming episode and temperature trend. Since the longer data set assesses the long-lasting warming episode more fully, it leads to more significant results. The mean uncertainty between 88 and 102 km are 0.6 and 1.3 K decade-1, respectively, for the long and shorter data sets. The altitude dependence from the two data sets is quite similar, and their magnitudes are in the general range predicted by models. The trends reported here are -1.0 ± 1.0 K decade-1 at 87 km and -2.5 ± 0.5 K decade-1 at 90 km; they are consistent with the recently reported trends: respectively, -2.3 ± 0.6 K decade-1 (Offermann et al., 2010) and -4 ± 2 K decade-1 (Hall et al., 2012).

With regard to an interesting connection, we analyzed the surface temperature response after the Mt Pinatubo eruption reported by Thompson et al. (2009) with the same functional dependence as that used for the observed warming episode in the mesopause region. We determined the respective peak delay time, tpd, and mean age, tMA, to be, respectively, 1.43 and 2.51 years for surface temperature and 1.82 and 2.92 years for mesopause region warming. These similarities between the global surface temperature anomaly and the mesopause warming episode should hopefully spur community scientists and modelers to figure out the causal effects of these interesting phenomena.