Neutral atmosphere temperature trends and variability at 90 km , 70 ◦ N , 19 ◦ E , 2003 – 2014

Neutral temperatures at 90 km height above Tromsø, Norway, have been determined using ambipolar diffusion coefficients calculated from meteor echo fading times using the Nippon/Norway Tromsø Meteor Radar (NTMR). Daily temperature averages have been calculated from November 2003 to October 2014 and calibrated against temperature measurements from the Microwave Limb Sounder (MLS) on board Aura. Large-scale periodic oscillations ranging from ∼ 9 days to a year were found in the data using Lomb–Scargle periodogram analysis, and these components were used to seasonally detrend the daily temperature values before assessing trends. Harmonic oscillations found are associated with the large-scale circulation in the middle atmosphere together with planetary and gravity wave activity. The overall temperature change from 2003 to 2014 is −2.2 K± 1.0 K decade−1, while in summer (May–June– July) and winter (November–December–January) the change is −0.3 K± 3.1 K decade−1 and −11.6 K± 4.1 K decade−1, respectively. The temperature record is at this point too short for incorporating a response to solar variability in the trend. How well suited a meteor radar is for estimating neutral temperatures at 90 km using meteor trail echoes is discussed, and physical explanations behind a cooling trend are proposed.


Introduction
Temperature changes in the mesosphere and lower thermosphere (MLT) region due to both natural and anthropogenic variations cannot be assessed without understanding the dynamical, radiative and chemical couplings between the different atmospheric layers.Processes responsible for heating and cooling in the MLT region are many.Absorption of UV by O 3 and O 2 causes heating, while CO 2 causes strong radiative cooling.Planetary waves (PWs) and gravity waves (GWs) break and deposit heat and momentum into the middle atmosphere and influence the mesospheric residual circulation, which is the summer-to-winter circulation in the mesosphere.Also, heat is transported through advection and adiabatic processes.
For decades, it has been generally accepted that increased anthropogenic emissions of greenhouse gases are responsible for warming of the lower atmosphere (e.g.Manabe and Wetherald, 1975) and that these emissions are causing the mesosphere and thermosphere to cool (Akmaev and Fomichev, 2000;Roble and Dickinson, 1989).Akmaev and Fomichev (1998) report, using a middle atmospheric model, that if CO 2 concentrations are doubled, temperatures will decrease by about 14 K at the stratopause, by about 10 K in the upper mesosphere and by 40-50 K in the thermosphere.Newer and more sophisticated models include important radiative and dynamical processes as well as interactive chemistries.Some model results indicate a cooling rate near the mesopause lower than predicted by Akmaev and Fomichev (1998), while others maintain the negative signal (French and Klekociuk, 2011;Beig, 2011).The thermal response in this region is strongly influenced by changes in dynamics, and some dynamical processes contribute to a warming which counteracts the cooling expected from greenhouse gas emissions (Schmidt et al., 2006).
Even though the increasing concentration of greenhouse gases is generally accepted to be the main driver, other drivers of long-term changes and temperature trends also exist, namely stratospheric ozone depletion, long-term changes of solar and geomagnetic activity, secular changes of the Earth's magnetic field, long-term changes of atmospheric circulation and mesospheric water vapour concentration (Laštovička et al., 2012).Dynamics may influence temperatures in the MLT region on timescales of days to months, and investigations of the influence of this variability on averages used for temperature trend assessments are important.The complexity of temperature trends in the MLT region and their causes act as motivation for studying these matters further.
In this paper, we investigate trend and variability of temperatures obtained from the Nippon/Norway Tromsø Meteor Radar (NTMR), and we also look at summer and winter seasons separately.In Sect.2, specifications of the NTMR radar are given, and the theory behind the retrieval of temperatures using ambipolar diffusion coefficients from meteor trail echoes is explained.In Sect.3, the method behind the calibration of NTMR temperatures against Aura MLS temperatures is explained.Section 4 treats trend analysis and analysis of variability and long-period oscillations in temperatures.The theory and underlying assumptions for the method used for determining neutral temperatures from meteor trail echoes, thus how well suited a meteor radar is for estimating such temperatures is discussed in Sect. 5. Also, physical explanations behind changes in temperature and observed temperature variability are discussed, as well as comparison with other reports on trends.

Instrumentation and data
The NTMR is located at Ramfjordmoen near Tromsø, at 69.58 • N, 19.22 • E. It is operated 24 h per day, all year round.Measurements are available for more than 90 % of all days since the radar was first operative in November 2003.The meteor radar consists of one transmitter antenna and five receivers and is operating at 30.25 MHz.It detects echoes from ionised trails from meteors, which appear when meteors enter and interact with the Earth's neutral atmosphere in the MLT region.The ionised atoms from the meteors are thermalised, and the resulting trails expand in the radial direction mainly due to ambipolar diffusion, which is diffusion in plasma due to interaction with the electric field.Underdense meteors, which are the ones used in this study, have a plasma frequency that is lower than the frequency of the radar, which makes it possible for the radio wave from the radar to penetrate into the meteor trail and be scattered by each electron.Echoes are detected from a region within a radius of approximately 100 km (horizontal space).The radar typically detects around 10 000 echoes per day, of which around 200-600 echoes are detected per hour at the peak occurrence height of 90 km. Figure 1 shows the vertical distribution of meteor echoes as a function of height, averaged over the time period 2003-2014.The number of echoes detected per day allows for a 30 min resolution of temperature values.The intraday periodicity in meteor detections by the NTMR radar is less pronounced than that of lower-latitude stations and we do not anticipate tidally induced bias regarding echo rates at specific tidal phases for daily averages.The height resolution and the range resolution are both 1 km, when looking at altitudes around the peak occurrence height.From the decay time of the radar signal we can derive ambipolar diffusion coefficients, D a : where λ is the radar wavelength and τ is the radar echo decay time.It has been shown that this coefficient also can be expressed in terms of atmospheric temperature and pressure: where p is pressure, T is temperature and K 0 is the zerofield reduced mobility factor of the ions in the trail.In this study we used the value for K 0 of 2.4 × 10 −4 m 2 s −1 V −1 , in accordance e.g. with Holdsworth et al. (2006).Pressure values were derived from atmospheric densities obtained from falling sphere measurements appropriate for 70 • N, combining those of Lübken and von Zahn (1991) and Lübken (1999), previously used by e.g.Holdsworth (2006) and Dyrland et al. (2010).These densities do not take into account long-term solar cycle variations.
The NTMR radar is essentially identical to the Nippon/Norway Svalbard Meteor Radar (NSMR) located in Advent Valley on Spitsbergen at 78.33 • N, 16.00 • E. Further explanation of the radar and explanation of theories can be found in e.g.Hall et al. (2002), Hall et al. (2012), Cervera and Reid (2000) and McKinley (1961).
Calibration of temperatures derived from meteor echoes with an independent, coinciding temperature series is necessary, according to previous studies (e.g.Hocking, 1999).Temperatures from the NSMR radar have been derived most recently by Dyrland et al. (2010), employing a new calibration approach for the meteor radar temperatures, wherein temperature measurements from the Microwave Limb Sounder (MLS) on the Aura satellite were used instead of the previously used rotational hydroxyl and potassium lidar temperatures from ground-based optical instruments (Hall et al., 2006).Neither ground-based optical observations nor lidar soundings are available for the time period of interest or the location of the NTMR.In this study we therefore employ the same approach as Dyrland et al. (2010), using Aura MLS temperatures to calibrate the NTMR temperatures.
NASA's EOS Aura satellite was launched 15 July 2004 and gives daily global coverage (between 82 • S and 82 • N) with about 14.5 orbits per day.The MLS instrument is one of four instruments on Aura and samples viewing forward along the spacecraft's flight direction, scanning its view from the ground to ∼ 90 km every ∼ 25 s, making measurements of atmospheric temperature, among others (NASA Jet Propulsion Laboratory, 2015).
Because of a general cooling of most of the stratosphere and mesosphere the last decades due to e.g.altered concentrations of CO 2 and O 3 , the atmosphere has been shrinking, leading to a lowering of pressure surfaces at various altitudes.It is important to distinguish between trends on fixed pressure altitudes and fixed geometric altitudes, since trends on geometric altitudes include the effect of a shrinking atmosphere (Lübken et al., 2013).In this study, we have obtained Aura MLS temperature data (version 3.3) for latitude 69.7 • N ± 5.0 • and longitude 19.0 • E ± 10.0 • at 90 km geometric altitude.2), plotted together with Aura MLS temperatures.Standard error of the mean is omitted in the plot for better legibility, but typical standard error for daily temperatures is 0.2-0.6K, highest in winter.The Aura satellite overpasses Tromsø at 01:00-03:00 and 10:00-12:00 UTC, which means that the Aura daily averages are representative for these time windows.It was therefore necessary to investigate any bias arising from Aura not measuring throughout the whole day.A way to do this is to assume that Aura temperatures and NTMR temperatures follow the same diurnal variation and thus investigate the diurnal variation of NTMR temperatures.This was done by superposing all NTMR temperatures by time of day, obtaining 48 values for each day, since the radar allows for a 30 min resolution.

Calibration of NTMR temperatures
There is an ongoing investigation into the possibility that D a derived by NTMR can be affected by modified electron mobility during auroral particle precipitation.According to Rees et al. (1972), neutral temperatures in the auroral zone show a positive correlation with geomagnetic activity.It is therefore a possibility that apparent D a enhancements during strong auroral events do not necessarily depict neutral temperature increase.This matter requires further attention.
Plotting hourly D a values shows clear evening enhancements, especially during winter (not shown here).Investigation of possible unrealistic D a enhancements was carried out by calculating standard errors of estimated hourly D a values: where σ is standard deviation and ne is the number of echoes detected by the radar.By examining and testing different rejection criteria, we arrived at a threshold of 7 % in standard error of hourly D a values for identifying unrealistic enhancements.This rejection criterion led to that 5.4 % of the D a values were rejected.NTMR temperatures after application of the D a rejection procedure will hereafter be referred to as D a -rejected NTMR temperatures.
Figure 3 shows monthly averages of the superposed values of D a -rejected NTMR temperatures as a function of time of day for days coinciding with Aura measurements.It is evident from the figure that the lowest temperatures are in general achieved in the forenoon, which coincides with one of For clarity, time series are displaced by 5 K per month subsequent to January.The time of day corresponding to when Aura makes measurements over Tromsø (01:00-03:00 and 10:00-12:00 UTC) is highlighted.
the periods per day when Aura MLS makes measurements over Tromsø.
Subtracting monthly averages of the 00:00-24:00 UTC temperatures from the 01:00-03:00 and 10:00-12:00 UTC temperatures gave the estimated biases in Aura daily means due to only sampling during some hours of the day and are given in Table 1.By judging by the measurement windows, Aura underestimates the daily mean (00:00-24:00 UTC) more during winter than during spring and summer.Note the higher standard deviations in spring and summer compared with winter.
The initially obtained Aura temperatures were corrected by adding the biases from Table 1 in order to arrive at daily mean temperatures that were representative for the entire day.Also, the Aura temperatures were corrected for "cold bias".French and Mulligan (2010) report that Aura MLS temperatures exhibit a 10 K cold bias compared with OH * (6-2) nightly temperatures at Davis Station, Antarctica.A newer study by García-Comas et al. (2014) shows that Aura MLS exhibits a bias compared with several satellite instruments which varies with season.According to their findings, a 10 K correction for cold bias was applied to the Aura summer and winter temperatures (June-August, December-February), while a 5 K correction was applied to autumn and spring temperatures (September-November, March-May).The corrected Aura temperatures will hereafter be referred to as local time and cold bias-corrected Aura MLS temperatures.
Local time and cold bias-corrected Aura temperatures were plotted against D a -rejected NTMR temperatures, and the linear fit (R 2 = 0.83) is described by: where T NTMR is D a -rejected temperature obtained from NTMR, and T Aura is local time and cold bias-corrected temperature from Aura MLS.Inverting Eq. ( 4) enabled us to estimate NTMR temperatures calibrated with respect to Aura MLS temperatures.NTMR temperatures were now corrected for days of measurements coinciding with Aura measurements and are hereafter referred to as MLS-calibrated NTMR temperatures.For calibration of NTMR temperatures from November 2003 to August 2004 (before the beginning of the Aura MLS dataset), D a -rejected NTMR temperatures were used as input to the inverted equation to arrive at calibrated NTMR temperatures.
To estimate the calibration uncertainty, all local time and cold bias-corrected Aura temperatures were subtracted from the MLS-calibrated NTMR temperatures, and the differences were plotted in a histogram with 5 K bins (not shown here).A Gaussian was fitted to the distribution.The standard deviation of the Gaussian was 11.9 K, which is considered to be the overall uncertainty of the calibration.Finally, Fig. 4 shows the MLS-calibrated NTMR temperatures with uncertainties plotted together with Aura MLS temperatures, corrected for cold and time-of-day measurement bias.et al. (1998) discuss the effects of autocorrelation and variability on trend estimation and emphasise that changes in environmental variables are often modelled as being a linear change, even though there may be a high degree of periodic variation within the data in addition to the linear trend.A linear trend model assumes that measurements of the variable of interest at time t can be expressed as follows:

Weatherhead
where µ is a constant term, S t is a seasonal component, L t is the linear trend function, ω is the magnitude of the trend and N t is noise.N t may be autocorrelated and the result of various natural factors, which give rise to somewhat smoothly varying changes in N t over time.Such natural factors may not always be known or measurable.Taking this into account, variability of the data was explored before assessing the linear trend of the temperature data.In Sect.4.1, a Lomb-Scargle periodogram analysis is conducted, and periodic components in the data are identified before assessing the trend, while in Sect.4.2 solar cycle dependence is briefly explored, even though the temperature record is too short for this to be incorporated in the trend analysis.

Estimation of periodic variability and trend
To identify periodic variability, a Lomb-Scargle (LS) periodogram analysis was applied to the MLS-corrected NTMR temperatures (Press and Rybicki, 1989).LS analysis is a modified discrete Fourier transform algorithm suitable for unevenly spaced data.Figure 5 (upper panel) shows the LS periodogram, identifying a particularly strong annual (A) component, but also a semi-annual (A/2) and two sub-annual peaks (A/3 and A/4), significant at the 99 % level.Following the procedure of Niciejewski and Killeen (1995), the daily temperatures were fit to the following approximation: where T NTMR (t) is observed daily temperature, T 0 is the average temperature, i is the number of harmonic components found in the LS analysis, d i and e i are the amplitudes of the ith harmonic component, p i is the period of the ith harmonic component and t is the day number.L represents the trend.The average temperature over the 11-year period, T 0 , was found to be 189.4± 0.6 K.
It has been shown that the confidence levels in the periodogram are only strictly valid for the peak with the highest spectral power (Scargle, 1982).Thus, there may be peaks significant at the 95 % level even though they are not noticeable in the periodogram, due to their variance being overestimated by the presence of the larger peaks.Therefore, after fitting the primary periodic components with significance better than the 99 % level to the NTMR temperatures using Eq. ( 6), LS analysis was repeated on the temperature residuals to check for additional significant periodic components in the data.Horne and Baliunas (1986) point out that the periodogram power needs to be normalised by the total variance of the data in order to obtain spectral peaks with correct magnitude.The variance of the data was therefore adjusted to maintain the correct probability distribution of the periodogram.Figure 5 (lower panel) shows spectral power of harmonics found at better than 95 % significance level of residuals obtained after fitting the sinusoids of the four largest peaks.The apparently significant peaks located near 91, 121, 184 and 363 days, even though these harmonics have been filtered out at this stage, are due to spectral leakage, which means that for a sinusoidal signal at a given frequency, ω 0 , the power in the periodogram not only appears at ω 0 , but also leaks to other nearby frequencies (Scargle, 1982).All periodic components Table 2. Periodic components found in data using Lomb-Scargle periodogram analysis.All components were identified as better than the 99 % significance level, except for the 32-day harmonic, which was significant at the 95 % level.Amplitudes are given with 95 % confidence bounds.
The trend was estimated from the approximation in Eq. ( 6) to be −2.2K ± 1.0 K decade −1 .From Tiao et al. (1990), this trend can be considered significantly non-zero at the 5 % level, since the uncertainty (2σ = 2.0 K decade −1 ) is less than the trend itself.We estimated the number of years for which a trend can be detectable, following the formulation of Weatherhead et al. (1998): where n * is the number of years required, ω 0 is the magnitude of the trend per year, σ N is the standard deviation of noise N and ϕ is the autocorrelation function of the noise at lag 1.The value 3.3 corresponds to a 90 % probability that the trend is detectable after n * years.Solving Eq. ( 7) reveals that the minimum number of years required for detecting a decadal trend of −2.2 K is about 17 years.
The resulting composite of the least-squares fit is shown in Fig. 6, together with the MLS-corrected NTMR temperatures.We see that the smooth curve represents the periodicity in the data to a good extent, but there is still variability not accounted for.Temperature residuals obtained after subtracting the MLS-calibrated NTMR temperatures from the fit in Fig. 6 are henceforth referred to as fit residuals.
In addition to the harmonics listed in Table 2, we found a harmonic of ∼ 615 days (see Fig. 5, lower panel), which was not statistically significant.We also found a ∼ 17-day oscillation, significant at the 95 % level (see Fig. 5, lower panel), but the amplitude of this component was found to be close to 0 K.The 615-day and 17-day periodic components were therefore not incorporated in the composite fit.
In Fig. 7, all individual years are superposed by day of year.This was done to better visualise the variability of an average year.In addition to the broad maximum in temperatures during winter and the narrower minimum during summer, we see minor enhancements just after the spring equinox (day of year ∼ 100) and summer solstice (day of year ∼ 210) and also a local minimum in early winter.Explanations for the variability will be discussed in Sect.5.1.
In addition to the average temperature change, we also treated summer and winter seasons separately.First, monthly averages of the temperature residuals were calculated and  trends for each month were investigated.Figure 8 shows the result.Then, averages of November, December and January and of May, June and July were made.As opposed to the meteorological seasons as experienced in the troposphere, we have chosen to define "winter" and "summer" as the three months centred on the respective solstices.However, since the meteorological winter and summer are defined differently, we will refer to these trends as NDJ and MJJ trends.
The linear NDJ trend is −11.6 K ± 4.1 K decade −1 , and the MJJ trend is −0.3K ± 3.1 K decade −1 .Solving Eq. ( 7) for NDJ and MJJ trends reveals a minimum length for trend detection of 10.8 and 63 years, respectively.The trend analysis was also performed without carrying out the D a rejection procedure explained in Sect.3. Final results of the trend analysis, both when excluding and including rejection of D a values due to hypothetical anomalous electrodynamic processes, do not differ significantly.It is reasonable to believe that strong geomagnetic conditions can affect derived temperatures on a short timescale.However, due to the considerable quantity of data employed in this study, it is inconceivable that this effect will change the conclusions regarding trends, as our results also show.

Exploration of solar flux dependence
Our dataset covers 11 years of meteor radar temperatures and thus it is shorter than the corresponding solar cycle (which was somewhat longer than the average 11 years).Even though it is premature to apply solar cycle analysis to a time series this short, we will briefly explore and present our temperature data together with solar variability.In this study we use the F10.7 cm flux as a proxy for solar activity, which is the most commonly used index in middle/upper atmospheric temperature trend studies (e.g.Laštovicka et al., 2008;Hall et al., 2012).
Figure 9 shows yearly values of F10.7 cm plotted against yearly averaged fit residual temperatures.For clarity, black bullets corresponding to years are connected with lines, making it easier to see the progression from high solar flux to solar minimum and back to solar maximum.We see that, to some extent, there is a conjunction between low solar flux values and negative temperature fit residuals.For the years 2006-2010, which were years of solar minimum, fit residuals were on average negative.For the years 2005 and 2011, which were years in between solar maximum and minimum, fit residuals were close to zero.However, for years with higher F10.7 values the tendency of increasing fit residuals is less distinct.Ogawa et al. (2014) find a non-linear relationship between upper-atmospheric temperatures and solar activity using EISCAT UHF (ultra-high frequency) radar ob- servations from 200 to 450 km altitude over Tromsø, even though it must be noted that the altitude range they look at differs from ours.

Discussion
Statistically significant periodic components found in the temperature data are annual (A) and semi-annual (A/2) oscillations, and 121-(A/3), 91-(A/4), 69-(A/5), 52-(A/7), 46-(A/8), 32-and 9-day oscillations.Temperature change from 2003 to 2014 is −2.2K ± 1.0 K decade −1 , and MJJ and NDJ trends are −0.3K ± 3.1 and −11.6 K ± 4.1 K decade −1 , respectively.Explanations for the periodic variability will be proposed in Sect.5.1.In Sect.5.2, physical explanations for the temperature change will be explored, and our results will be compared with other reports on mesospheric trends at high and midlatitudes.Trends will be discussed in terms of the method used for deriving temperatures in Sect.5.3.

Mechanisms for the observed variability and harmonics
The A, A/2, A/3, A/4, A/5, A/7 and A/8 components are also found for OH * temperatures over other mid-and highlatitude sites (e.g.Espy and Stegman, 2002;Bittner et al., 2000;French and Burns, 2004).In addition to these components, A/6 and A/9 sub-annual harmonics, as well as other shorter-period components, have been identified in other datasets (e.g.Bittner et al., 2000;French and Burns, 2004).Espy and Stegman (2002) attribute the asymmetry with the broad winter maximum and the narrow summer minimum to the A/2 harmonic, and the temperature enhancements during the equinoxes to the A/3 and A/4 harmonics.French and Burns (2004) identify the visible variations of the 52-day (A/7) component in their data from Davis, Antarctica, and find this component's phase to be "locked" to the day of year, indicating a seasonal dependence.Espy and Stegman (2002) only find this component as a result of LS analysis of their superposed-epoch data, also indicat- ing that the phase is locked to the day of year.French and Burns (2002) and Bittner et al. (2000) find in general strong differences from year to year in the significant oscillations observed.We have not carried out analysis of the year-toyear variation in oscillations observed, but considering, e.g. the uneven occurrences of SSWs (sudden stratospheric warnings), we have no reason to conclude otherwise regarding our data.
The ∼ 9-day oscillation we find in our data can most likely be designated to travelling planetary waves, which have typical periods of 1-3 weeks, with 8-10 days as a prominent period (Salby, 1981a, b).
The ∼ 615 day periodic component (not statistically significant) may at first glance seem to be somehow related to the quasi-biennial oscillation (QBO), which is a system where zonal winds in the lower equatorial stratosphere alternate between westward (easterly) and eastward (westerly) with a mean period of 28-29 months.Also other studies find a ∼ 2 year periodic component in their temperature data, attributed to a QBO effect (Espy and Stegman, 2002;Bittner et al., 2000;French and Burns, 2004 -the two latter give statistically inconclusive results).However, our ∼ 615 day component is quite far from the mean period of the QBO.That, in addition to it not being significant, makes it difficult to interpret.
The higher temperature variability during winter comwith summer, visible in Fig. 7, is also found in other datasets at mid-and high latitudes (e.g.Espy and Stegman, 2002;Bittner et al., 2000).This feature and the observations of local temperature enhancement around day 200 as well as the reduction of the strong, negative seasonal gradient just after the spring equinox can be explained by the state of the background wind system in the middle atmosphere and the corresponding propagation of planetary and gravity waves.Enhanced GW and PW flux and momentum into the mesosphere lead to enhanced turbulent diffusion, which can result in increased temperatures.PWs can only propagate westward and against the zonal flow, so easterly winds in the middle atmosphere during summer are blocking vertical propagation of long-period PWs into the MLT region.In contrast, during winter stratospheric zonal winds are westerly, favouring PW propagation.The presence of upward-propagating PWs during winter is therefore an explanation for the higher variability during this season.
GWs can propagate both eastward and westward, but only against the zonal flow, implying the presence of eastwardpropagating GWs during summer and westward-propagating GWs during winter.The extratropical meso-and stratospheric zonal winds are very weak and change direction during the equinoxes, resulting in a damping of both westwardand eastward-propagating GWs during these periods (Hoffmann et al., 2010).Enhanced PW activity is observed at the same time (Stray et al., 2014).Temperature enhancements after the spring equinox are related to the final breakdown of the polar vortex or the last stratospheric warming event (Shepherd et al., 2002).Several studies have observed a "springtime tongue" of westward flow between 85 and 100 km, occurring approximately from day 95 to 120, reflecting the final warming (e.g.Hoffmann et al., 2010;Manson et al., 2002).The final warming is characterised by forced planetary Rossby waves that exert a strong westward wave drag from the stratosphere up to 100 km.
Enhanced PW activity has also been observed during midsummer, due to interhemispheric propagation of PWs into the summer mesopause (Stray et al., 2014;Hibbins et al., 2009).Also, enhanced short-period GW activity has been observed during summer (Hoffmann et al., 2010).Increased temperatures during midsummer may thus be a result of the combined effect of upward-propagating GWs and interhemispheric propagation of PWs.
Several studies have identified large temperature amplitude perturbations during the autumn equinox in particular (Taylor et al., 2001;Liu et al., 2001).The same signature is hard to find in our data.Hoffmann et al. (2010) find latitudinal differences in the amplitude of the semidiurnal meridional tide during the autumn equinox, observing stronger tidal amplitudes at Juliusruh (55 • N, 13 • E) compared with Andenes (69 • N, 16 • E).Manson et al. (2009) also find longitudinal differences in tides at high latitudes.Reasons for not observing increased temperatures around the autumn equinox are not clear, and further investigations are needed in order to make conclusions.
The local temperature minimum in early winter is also seen in other temperature data from mid-and high latitudes (e.g.French and Burns, 2004;Holmen et al., 2013;Shepherd et al., 2004).French and Burns (2004) find a decrease in large-scale wave activity during midwinter which they as-sociate with the observed temperature minimum, but identify this as a Southern Hemisphere phenomenon.Shepherd et al. (2004) attribute the decrease in temperature to early winter warming of the stratosphere, characterised by the growth of upward-propagating PWs from the troposphere which decelerate/reverses the eastward stratospheric jet, resulting in adiabatic heating of the stratosphere and adiabatic cooling of the mesosphere.However, Shepherd et al. used temperature data from 1991 to 1999, which is prior to the start of our temperature record, and timings of SSWs are different from year to year.We investigated the timing and occurrence of SSW events during the last decade using NASA reanalysis temperatures and zonal winds provided through the Modern-Era Retrospective analysis for Research and Applications (MERRA) project (NASA, 2016).Most SSWs occurring between 2003 and 2014 start in the beginning of January or mid-January.One exception is the major warming in 2003-2004, in which zonal winds started to decelerate in mid-December.There are signs of a minor warming in the transition between November and December 2012, but there is not enough evidence to conclude that the local minimum of NTMR temperatures starting in early November is associated with early winter warming of the stratosphere.It is more likely that the pronounced variability in temperatures we see in January and February (days ∼ 0-50) in Fig. 7 is a manifestation of the SSW effect.

Physical explanations for cooling and comparison with other studies
Other studies on long-term mesospheric temperature trends from mid and high latitudes yield mostly negative or nearzero trends.Few studies cover the same time period as ours, and few are from locations close to Tromsø.Hall et al. (2012) report a negative trend of −4 K ± 2 K decade −1 for temperatures derived from the meteor radar over Longyearbyen, Svalbard (78 indicates that the layer height at high latitudes is remarkably constant from 2003 to 2011.Beig (2011) report that most recent studies on mesopause region temperature trends show weak negative trends, which is in line with our results.According to the formulation by Weatherhead et al. (1998), our time series is not long enough for significant trend detection.We need another ∼ 6 years of data before a trend of magnitude −2.2 K ± 1.0 K decade −1 is significant.Response to solar variability has not been taken into account due to the length of the temperature record.Our slightly negative overall trend must therefore be considered tentative.The summer trend requires many more years of data before it can be considered significant, because is a near-zero trend.However, the winter trend can be considered detectable and also significantly different from zero, following the criteria from Weatherhead et al. (1998) and Tiao et al. (1990).
Our results indicate a cooling at 90 km altitude over Tromsø in winter.A general cooling of the middle atmosphere will cause a contraction of the atmospheric column, hence a lowering of upper-mesospheric pressure surfaces.The pressure model used as input to Eq. ( 2) is only seasonally dependent, so a possible trend in pressure at 90 km must be addressed.By looking at Eq. ( 2), it is evident that if pressure decreases, temperature will decrease even more.Incorporating a decreasing trend in the pressure model will then serve to further strengthen the negative temperature trend we observe.
It has been proposed that GWs may be a major cause of negative temperature trends in the mesosphere and thermosphere (Beig, 2011;Oliver et al., 2013).GWs effectively transport chemical species and heat in the region, and increased GW drag leads to a net effect of cooling above the turbopause (Yigit and Medvedev, 2009).GWs are shown to heat the atmosphere below about 110 km altitude, while they cool the atmosphere at higher altitudes by inducing a downward heat flux (Walterscheid, 1981).However, there are large regional differences regarding trends in GW activity.Hoffmann et al. (2011) find an increasing GW activity in the mesosphere in summer for selected locations, but Jacobi (2014) finds larger GW amplitudes during solar maximum and relates this to a stronger mesospheric jet during solar maximum, both for winter and summer.Since we have not conducted any gravity wave trend assessment in this study, we cannot conclude that GW activity is responsible for the negative temperature trend, but we cannot rule out its role either.
The stronger cooling trend for winter is also consistent with model studies.Schmidt et al. (2006) and Fomichev et al. (2007) show, using the HAMMONIA and CMAM models, respectively, that a doubling of the CO 2 concentration will lead to a general cooling of the middle atmosphere, but that the high-latitude summer mesopause will experience insignificant change or even slight warming.They propose that this is the result of both radiative and dynamical effects.In summer, the CO 2 radiative forcing is positive due to heat exchange between the cold polar mesopause and the warmer, underlying layers.Also, CO 2 doubling alters the mesospheric residual circulation.This change is caused by a warming in the tropical troposphere and cooling in the extratropical tropopause, leading to a stronger equator-to-pole temperature gradient and hence stronger midlatitude tropospheric westerlies.This causes the westerly gravity wave drag to weaken, resulting in decreased adiabatic cooling from a slower ascent of the upper-mesospheric circulation.However, it must be noted that our strong, negative NDJ trend may differ from a trend estimated for meteorological winter months.

Suitability of a meteor radar for estimation of neutral temperatures at 90 km height
As explained in Sect.2, neutral air temperatures derived from meteor trail echoes depend on pressure, p, the zero-field reduced mobility of the ions in the trail, K 0 , and ambipolar diffusion coefficients, D a .K 0 will depend on the ion composition in the meteor trail, as well as the chemical composition of the atmosphere.The chemical composition of the atmosphere is assumed to not change significantly with season (Hocking, 2004).Unfortunately, the exact content of a meteor trail is unknown.Usually, a value for K 0 between 1.9 × 10 −4 and 2.9 × 10 −4 m 2 s −1 V −1 is chosen, depending on what ion one assumes to be the main ion of the trail (Hocking et al., 1997).Even though we in this study have chosen a constant value for K 0 of 2.4 × 10 −4 m 2 s −1 V −1 , some variability in K 0 is expected.According to Hocking (2004), variability can occur due to fragmentation of the incoming meteoroid, anisotropy in the diffusion rate, plasma instabilities and variations in the composition of the meteor trail.Using computer simulations, they report a typical variability in K 0 from meteor to meteor of 27 % and that the variability is most dominant at higher temperatures.Based on this, we cannot rule out sources of error due to the choice of K 0 as a constant, but since we have no possibility to analyse the composition of all meteor trails detected by the radar, we have no other choice than to choose a constant value for K 0 .How well ambipolar diffusion coefficients obtained for 90 km altitude are suited for calculating neutral temperatures has previously been widely discussed, e.g. by Hall et al. (2012) for the trend analysis of Svalbard meteor radar data, but will be shortly repeated here.For calculations of temperatures using meteor radar, ambipolar diffusion alone is assumed to determine the decay of the underdense echoes.Diffusivities are expected to increase exponentially with height through the region from which meteor echoes are obtained (Ballinger et al., 2008;Chilson et al., 1996).Hall et al. (2005) find that this is only the case between ∼ 85 and ∼ 95 km altitude, using diffusion coefficients delivered by NTMR from 2004.They find diffusivities less than expected above ∼ 95 km and diffusivities higher than expected below ∼ 85 km.Ballinger et al. (2008) obtain a similar result using meteor observations over northern Sweden.It has been proposed that processes other than ambipolar diffusion influence meteor decay times.If this is the case it may have consequences for the estimation of temperatures, and therefore it is important to investigate this further.
Departures of the anticipated exponential increase with height of molecular diffusion above ∼ 95 km in previous studies are attributed to the gradient-drift Farley-Buneman instability.The Farley-Buneman instability occurs where the trail density gradient and electric field are largest.Due to frequent collisions with neutral particles, electrons are magnetised while ions are left unmagnetised, causing electrons and ions to differ in velocity.Electrons then create an electric field perpendicular to the meteor trail, leading to anomalous fading times that can be an order of magnitude higher than those expected from ambipolar diffusion.The minimum altitude at which this occurs depends on the trail altitude, density gradient and latitude, and at high latitudes this altitude is ∼ 95 km.Therefore, using ambipolar diffusion rates to calculate trail altitudes above this minimum altitude may lead to errors of several kilometres, since the diffusion coefficients derived from the measurements are underestimated (Ballinger et al., 2008;Dyrud et al., 2001;Kovalev et al., 2008).
Reasons for the higher-than-expected diffusivities below ∼ 85 km are not completely understood, according to theory.Hall (2002) proposes that neutral turbulence may be responsible for overestimates of molecular diffusivity in the region ∼ 70-85 km, but this hypothesis is rejected by Hall et al. (2005) due to a lacking correlation between neutral air turbulent intensity and diffusion coefficients delivered by the NTMR radar.Other mechanisms for overestimates of molecular diffusivity include incorrect determination of echo altitude and fading times due to limitations of the radar (Hall et al., 2005).
Since the peak echo occurrence height is 90 km and this is also the height at which a minimum of disturbing effects occur, 90 km height is therefore considered the optimal height for temperature measurements using meteor radar.Ballinger et al. (2008) report that meteor radars in general deliver reliable daily temperature estimates near the mesopause using the method outlined in this study, but emphasise that one should exercise caution when assuming that observed meteor echo fading times are primarily governed by ambipolar diffusion.They propose, after Havnes and Sigernes (2005), that electron-ion recombination can impact meteor echo decay times.This can especially affect the weaker echoes, hence this effect can lead to an underestimation of temperatures.
Determination of temperatures from meteor radar echo times is a non-trivial task, mainly because the calculation of ambipolar diffusion coefficients depends on the ambient atmospheric pressure.By using radar echo decay times to calculate ambipolar diffusion coefficients from Eq. (1), we can get an estimate for T 2 /p from Eq. (2).Input of pressure values into the equation will thus provide atmospheric temperatures.However, measurements of pressure are rare and difficult to achieve at 90 km height, and often one has to rely on model values.Traditionally, pressure values at 90 km have been calculated using the ideal gas law, taking total mass density from atmospheric models, e.g. the Mass Spectrometer and Incoherent Scatter Radar (MSIS) models, where the newest version is NRLMSISE-00.It is hard to verify the pressure values derived from the models because of lack of measurements to compare the model to; hence using the pressure values may result in uncertainties of estimated atmospheric temperatures.In this study, we obtained pressure values from measurements of mass densities obtained from falling spheres combined with sodium lidar from Andøya (69 • N, 15.5 • E) (Lübken, 1999;Lübken and von Zahn, 1991).All measurements have been combined to give a yearly climatology, that is, one pressure value for each day of the year.Since Andøya is located in close proximity to Tromsø (approximately 120 km), the pressure values are considered appropriate for our calculations of neutral temperatures.One disadvantage with using pressure values obtained from the falling sphere measurements is that no day-to-day variations are taken into account, only the average climatology.

Conclusions
A number of long-period oscillations ranging from ∼ 9 days to a year were found in the NTMR temperature data.Temperature variability observed may, to a large extent, be explained by the large-scale circulation of the middle atmosphere and the corresponding activity in waves propagating from below.Higher temperature variability in winter is due to the presence of upward-propagating PWs during this season, in contrast to summer, when easterly winds in the middle atmosphere are blocking vertical propagation of long-period PWs into the MLT region.The variability is particularly high in January and February, which are periods where SSW events occur frequently.In addition to the general maximum of temperatures in winter and minimum in summer, our data show a local temperature enhancement around day 210, a local minimum in early winter and reduction of the strong, negative seasonal gradient after the spring equinox.The reduction of the strong, negative seasonal gradient after the spring equinox is related to the final breakdown of the polar vortex (Shepherd et al., 2002), while the increase during summer is most likely associated with a combined effect of upwardpropagating GWs and interhemispheric propagation of PWs (Stray et al., 2014;Hoffmann et al., 2010).No evident reason can be found for the local temperature minimum in early winter or the fact that we do not see enhanced temperatures during the autumn equinox, as identified by others (e.g.Taylor et al., 2001;Liu et al., 2001).
The trend for NTMR temperatures at 90 km height over Tromsø was found to be −2.2K ± 1.0 K decade −1 .Summer (May, June, July) and winter (November, December, January) trends are −0.3K ± 3.1 and −11.6 K ± 4.1 K decade −1 , respectively.Following the criterion from Weatherhead et al. (1998), the temperature record is only long enough for the NDJ trend to be conwww.atmos-chem-phys.net/16/7853/2016/Atmos.Chem.Phys., 16, 7853-7866, 2016 sidered detectable.Response to solar variability was not incorporated in the trend, due to the time series being shorter than the corresponding solar cycle.However, when looking at the progression from high solar flux to solar minimum and back to solar maximum we see, to some extent, that there is a conjunction between low solar flux values and negative temperature fit residuals and vice versa.
A weak overall cooling trend is in line with other recent studies on mesopause region temperature trends.A cooling of the middle atmosphere will cause a lowering of uppermesospheric pressure surfaces.By implementing a negative trend in pressure at 90 km into the equation that we use for estimating temperatures, the negative temperature trend is enhanced, which reinforces our finding of a cooling trend.The most accepted theory behind a cooling of the middle atmosphere is increased greenhouse gas emissions, which may lead to a change in dynamics.Our results yield a more negative trend in winter compared with summer, which may be explained by radiative and dynamical effects.In summer, a larger heat exchange takes place from atmospheric layers below the cold, polar mesopause.Weakening of gravity wave drag leads to weakening of the mesospheric residual circulation, which counteracts cooling.These effects occur due to increased CO 2 concentrations in the atmosphere, according to model studies.

Data availability
Meteor echo fading times from the NTMR radar used to calculate ambipolar diffusion coefficients and neutral temperatures are available upon request from Chris Hall at Tromsø Geophysical Observatory (chris.hall@uit.no).The Aura MLS temperature data are publicly available from the NASA Jet Propulsion Laboratory at http://mls.jpl.nasa.gov/index-eos-mls.php.

Figure 1 .
Figure 1.Vertical distribution of the occurrence of meteor echoes over Tromsø, averaged over height between 2003 and 2014.The peak occurrence height is just over 90 km altitude.

Figure 2
Figure 2 shows daily NTMR temperatures from November 2003 to October 2014, derived from Eqs. (1) and (2), plotted together with Aura MLS temperatures.Standard error of the mean is omitted in the plot for better legibility, but typical standard error for daily temperatures is 0.2-0.6K, highest in winter.The Aura satellite overpasses Tromsø at 01:00-03:00 and 10:00-12:00 UTC, which means that the Aura daily averages are representative for these time windows.It was therefore necessary to investigate any bias arising from Aura not measuring throughout the whole day.A way to do this is to

Figure 2 .
Figure 2. Daily values of NTMR temperatures derived from Eqs. (1) and (2) before correction for high D a , plotted together with Aura MLS temperatures before applying any corrections.

Figure 3 .
Figure3.Monthly averages of diurnal temperature variation derived from NTMR after correction for high D a at 90 km altitude.For clarity, time series are displaced by 5 K per month subsequent to January.The time of day corresponding to when Aura makes measurements over Tromsø (01:00-03:00 and 10:00-12:00 UTC) is highlighted.

Figure 4 .
Figure 4. Daily values of MLS-calibrated NTMR temperatures plotted together with Aura MLS temperatures corrected for cold and timeof-day bias.The overall calibration uncertainty is indicated by the grey shading.

Figure 5 .
Figure 5. Upper panel: Lomb-Scargle periodogram for daily NTMR temperatures from 2003 to 2014.The y axis has been truncated for clarity.Lower panel: periodogram for residuals after fitting sinusoids for the four largest peaks from the upper panel.Peaks significant at better than 95 % are marked with numbers corresponding to period.

Figure 6 .Figure 7 .
Figure6.MLS-corrected NTMR daily temperatures (black dots) and the least-squares fit of the average, trend and periodic components (red curve).

Figure 8 .
Figure 8. Monthly temperature trends at 90 km altitude over Tromsø.Standard deviations are given as error bars.

F10Figure 9 .
Figure 9. Yearly values of F10.7 cm solar radio flux plotted against yearly averaged temperature fit residuals.Year 2003 is left out of the figure due to the data coverage (only data for November and December).

Table 2 .
Spring and autumn equinoxes and winter and summer solstice are marked SE, AE, WS and SS, respectively.
Savigny (2015)(2009)m height over the time period 2001 to 2011, while Holmen et al. (2014) find a near-zero trend for OH * airglow temperatures at ∼ 87 km height over Longyearbyen over the longer time period 1983 to 2013.Offermann et al. (2010) report a trend of −2.3 K ± 0.6 K decade −1 for ∼ 87 km height using OH * airglow measurements from Wuppertal (51 • N, 7 • E).It must be noted that the peak altitude of the OH * airglow layer can vary and thus affect the comparability of OH * airglow temperature trends and meteor radar temperature trends.Winick et al. (2009)report that the OH * airglow layer can range from 75 to > 90 km, while the newer study by vonSavigny (2015)