Since first identified the strong OH airglow emission originating from vibrational rotation transitions of OH vibrationally excited molecules (OH* or simply OH hereafter), its measurements have been extensively used to study the mesopause region temperature and OH emission layer from the ground. These studies have focused on varied topics: analysis of the impact of atmospheric waves on regional and global scales, the detection of geo-hazards, the effect of sudden stratospheric warmings (SSWs), seasonal and interannual variations, external forcing response, long-term trends, cross-validation for satellite measurements, the detection of satellite drifts and the determination of OH radiative properties e.g.,to mention just a few..

Ground-based OH airglow intensity and temperatures are often assumed to be representative of an emission layer centered at a fixed altitude, generally around 87 km ± 2 km e.g.,. Nevertheless, the OH layer altitude varies on multiple timescales. Its variation is partially driven by changes in transport (advection), primarily by those in atomic oxygen (the main source of nighttime ozone and thus of excited OH), temperature and density (through their effect on chemical reactions) . On a short timescale, measured daily variations are due to internal gravity waves and tides. reported vertical displacements of the order of ±3 km at the Equator. Day-to-day changes are mainly due to the varying effect of planetary waves and tides. In addition, sudden stratospheric warmings alter the OH altitude, producing up to 10 km vertical shifts during the descent phase . On a medium timescale, the seasonal variation in the emission altitudes exhibits semiannual, annual and quasi-biennial oscillations with up to 1.0, 1.5 and 0.5 km amplitudes, respectively . and reported a year-to-year monthly mean OH altitude variation of 2–3 km and attributed it to the effect of the El Niño–Southern Oscillation (ENSO). Some authors e.g have found no obvious long-term trend or solar cycle signatures in the OH emission altitude, in contrast to other studies that found a slow altitude decrease with time . Furthermore, the magnitude of all these variations depends on the vibrational level .

A ground-based OH airglow instrument does not provide direct information on the altitudes at which the OH emission emanates. The measured intensities and temperatures are vertically weighted means. Knowledge of the altitude of the emitting layer is necessary for a comprehensive interpretation of variations of the OH layer. As mentioned above, this is because the three variables are interconnected. The view from the ground complements global geospace measurements on a regional scale, particularly for short-lived events and short period and wavelength oscillations. Moreover, omitting information on altitude biases comparisons with models and satellite measurements because changes in altitude produce or are produced by intensity and temperature variations . Nevertheless, the issues caused by the assumption of a fixed altitude have very often been neglected in past studies.

There are few reports on methods to estimate the OH layer altitude from ground-based measurements. One possibility is to use observations with more than one instrument and determine whether to triangulate OH observations at separated locations or to correlate them with simultaneous ground-based wind measurements . Another possibility is to employ the OH intensities measured from the ground to infer the OH emission altitude, relying on the fact that the latter depends quasi-linearly on the former . In this context, proposed a method to predict the altitude of the OH layer from ground-based instrument measurements of intensities by using an empirical function derived from space-based instrument measurements. Three main steps are then needed: (1) to set and fit an expression from the satellite instrument that reproduces the altitude as a function of the independent variable (the OH intensity in their case), (2) to derive the independent variable transfer function from measurements of the ground- to the space-based instrument and (3) to apply both functions to estimate the altitude from the ground-based instrument measurements alone. The empirical function used by included a term proportional to the OH intensity plus five more terms accounting for annual and semiannual oscillations, diurnal and semidiurnal variations and the solar cycle. further added a term proportional to the OH intensity squared and slightly reduced the residual.

In this work, we aim to provide a mathematical expression to estimate OH altitude from airglow intensity and temperature ground-based measurements and to report the short-term nocturnal variability in the three variables at northern midlatitudes. We use measurements of a SATI spectrometer, which observes OH intensity and temperature over the Sierra Nevada Observatory in Granada, Spain (37∘ N, 3∘ W). In order to derive the altitude of the OH layer, we adopt a similar methodology to except that we use a new empirical function, including not only OH airglow intensity but also temperature as independent variables. We only needed two additional terms: a semiannual oscillation and a linear local time term. We selected SABER data (onboard the TIMED satellite and that simultaneously measures OH volume emission rate and temperature profiles) for estimating the coefficients of the empirical function connecting OH altitude with intensity and temperature. Moreover, we study the seasonal variability, the solar impact and the trends in airglow altitudes, intensities and temperatures observed by SABER.

The structure of this article is as follows. We briefly describe the SATI and SABER measurements in Sects.  and , respectively. The rationale for the selection of the empirical function and the results from the fit to SABER data are given in Sect. . In that section, we also discuss SABER OH layer seasonal and decadal variations. The evaluation of the SATI-to-SABER OH intensity and temperature transfer functions, including estimations of instrument relative drifts, and the subsequent application to SATI measurements to determine OH altitude are presented in Sect. . We also report two case studies and discuss day-to-day changes in the nocturnal variability for the complete SATI dataset. We conclude this report with a summary in Sect. .

Spectral Airglow Temperature Imagers (SATIs) are Fabry–Pérot spectrometers in which the etalon is an ultra-narrow band (2Å) interference filter . In addition to O2 emissions in the atmospheric band, SATIs measure OH emissions from the Δv=4 transition of the v=6 vibrational level. The OH layer temperature, i.e., the temperature weighted with the OH relative intensity at the OH layer altitudes, is retrieved from the rotational structure of single measurements considering the relative emission of three pairs of Q-branch lines (K1, K2 and K3 transitions) under the assumption of rotational local thermodynamic equilibrium (LTE, which holds for low rotational levels) and assuming the Einstein coefficients. Background emission is simultaneously determined and subtracted, and the total OH(6–2) band emission, SATI OH intensity hereafter, is derived after simulation assuming the rotational LTE of a scaled spectrum at the derived temperature. The relative contribution from the three pairs of Q-branch lines to the total band emission is roughly 25 % .

One of the currently operating SATIs around the world is located at 37∘ N and 3∘ W in the Observatorio de Sierra Nevada (OSN), in Granada (Spain). It belongs to the Instituto de Astrofísica de Andalucía (CSIC) and is a part of the Network for the Detection of Mesopause Change (NDMC). An OH spectrum is measured every 4 min during nighttime under clear-sky and no-moon conditions. SATI-OSN has been routinely operating since 1998. Its observations have not been continuous due to instrumental problems. We use measurements from the beginning of 2002, when SABER started measuring, until the end of 2015, available by request at the NDMC site (http://wdc.dlr.de/ndmc). There are three main gaps in this period: January 2005–October 2005, January 2008–September 2009 and January 2010–January 2012. Measurements were intermittent from the end of 2012 until 2015 (see Fig. 1 in ). Since temperatures are retrieved considering relative line intensities, offsets between separated (in time) measurement periods are not significant.

The Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) is a broadband radiometer onboard the TIMED satellite developed by NASA. It has provided profiles of atmospheric infrared and near-infrared emission in 10 channels since 2002 in a nearly global manner . Latitudes from 52∘ S to 52∘ N are observed continuously. Higher latitudes (up to 82∘) are covered alternately at each hemisphere after the satellite yaws every 2 months. SABER measures each day at two almost fixed local solar times (LSTs) at each latitude, but its slow precession allows for a complete LST coverage in 120 days.

Among other atmospheric variables, SABER provides measurements of temperature from 15 µm CO2 emissions and OH volume emission rates (VERs) from Abel inversions of the limb radiance measured at 1.64 and 2.06 µm, sensitive to Δv=2 transitions of v=4,5 and v=8,9 vibrational levels, respectively . We use version 2.0 data, publicly available at http://saber.gats-inc.com. OH VERs used here are unfiltered, so the band contribution outside the channel bandpass is taken into account . Errors in temperature around the OH layer at low latitudes to midlatitudes are estimated to be 3.5 K (systematic) and 3.3 K (random) . Systematic errors in OH VER are less than 5 % . Pointing altitude is inferred from the satellite position with an error smaller than 200 m.

Since SABER data are to be expressed as a function of ground-based instrument OH measurements in this work, we use vertically integrated quantities throughout this paper. We define SABER OH intensity as the vertically integrated SABER OH VER voh: Ioh=∫vohdz‾. SABER OH altitudes used here are vertically weighted with SABER OH VER, zoh=∫vohzdz/∫vohdz‾. The SABER OH equivalent temperatures are obtained in the same fashion as the rotational temperatures are retrieved from the ground-based instrument . The ratio rJ′ of the intensity IJ′ and the Einstein coefficient AJ′ for each rotational line J′ is estimated with rJ′=∫vohe-EJ′/kTkdz‾, where EJ′ is the energy of the rotational transition, k is the Boltzmann constant and Tk the SABER temperature retrieved from its measurements at 15 µm. Then, the negative inverse of the slope of the linear fit between ln⁡rJ′ and EJ′/k is the equivalent rotational temperature. These differ from OH VER vertically weighted temperatures at SATI latitudes by less than 1 K on average but avoid potentially larger differences when temperature vertical gradients are steep . We note that equivalent temperatures calculated this way are independent of the Einstein coefficients used.

SATI measurements are not sensitive to the same OH vibrational bands as SABER. Models and measurements show that the altitude of the band peak emission depends on its upper vibrational level, mainly due to deactivation by atomic oxygen . The work of showed that the peak altitude difference increases by 0.6 km per increasing vibrational level, assuming linear dependence. reported shifts of 0.4 km for adjacent levels. Therefore, there should be offsets of roughly +1 and -1.5 km between the peak altitude in SATI and in SABER 1.6 and 2.0 µm channels, respectively. The peak altitude of the vibrational levels depends on atomic oxygen abundance, which suffers temporal variations, and so should the altitude offsets between SATI and SABER 1.6 and 2.0 µm measurements. In order to minimize the impact of the offset variations on the estimation of SATI peak altitudes (sensitive to v=6), we used the mean of SABER 1.6 and 2.0 µm intensities (sensitive to v=4,5 and v=8,9, respectively) and the corresponding OH temperature and altitudes means.

expressed the altitude of the OH layer as a linear function of the OH intensity that was corrected with annual, semiannual, diurnal and semidiurnal sinusoidal oscillations and a linear solar term. added OH intensity squared in the expression. Thus, they needed 10 and 11 coefficients, respectively, those related to the intensity plus two for each oscillation (eight in total) and one for the solar term. Our aim here is to select an empirical function that better reproduces the layer altitude as a function of the measured variables with a reduced number of coefficients. In addition to OH intensity, temperature embeds additional information on the atmospheric dynamics and chemistry affecting the OH layer altitude, suggesting the inclusion of simultaneously measured temperatures as a predictor.

Figure  shows time series of SABER nighttime OH intensity, temperature and altitude. The data are first binned in 1 h, ±7∘ longitude and ±5∘ latitude around the SATI location. This leaves data in one or two local time bins per day. The layer altitude and intensity exhibit a semiannual oscillation (minima in solstice and equinoxes), which is somewhat more marked on the intensity (see also Fig. ). The altitude has an additional annual variation, with minima in the winter solstice. Temperature presents a marked annual oscillation in antiphase with that of the altitude.

The semiannual variation in OH intensities has been measured in the past. It is not fully understood but it is believed that it is affected by Kelvin and gravity waves and from a semiannual variation in the diurnal tide amplitude . mention that the OH airglow emission rate is not correlated with temperature in the same manner at all altitudes. They discuss that, at the Equator, these variables are positively correlated below 94 km (where O vertical transport dominates) and negatively correlated above (where the temperature dependence of photochemical reactions and atmospheric density dominate). The different seasonal variations in SABER OH intensity and equivalent temperature shown in Figs.  and  might be reflecting different responses due to a seasonally varying layer altitude.

In order to determine the relationships between trends and responses to solar variation, we have calculated the 12-month moving averages for OH intensity, equivalent temperature and VER-weighted altitude (red lines in Fig. ). Since these are 12-month means (on average 700 measurements), the errors in the data are then reduced to ±0.2 %, ±0.1 K and ±7 m, respectively. We then fitted trend and solar flux (F10.7; GSFC Space Physics Data Facility; omniweb.gsfc.nasa.gov) linear components. The fit coefficients are shown in Table . Both OH temperature and intensity exhibit correlations with the solar flux. The effect (3.9 K per 100 s.f.u. and 7.8 % per 100 s.f.u.) is smaller than the seasonal and daily variations. The OH equivalent temperature solar response is in agreement with that derived by and (4.89 K per 100 s.f.u. and 4.2 K per 100 s.f.u., respectively) but larger than that of (1.2 K per 100 s.f.u. for SLOAN and 2.7 K per 100 s.f.u. for MLS). In contrast, the OH layer altitude is not significantly affected by the solar cycle. also found a clear dependence of the OH peak intensities on the solar cycle but not an obvious one for the layer altitude. The correlation coefficients for trends are small, showing that the dependence is not necessarily linear. Nevertheless, the slopes show a long-term tendency of decreasing altitude and temperature, -40 m decade-1 and -0.6 K decade-1, respectively. The altitude decrease is slightly faster than that derived by (-20 m decade-1). The decadal OH equivalent temperature decrease derived here is 0.1 K decade-1 stronger than that of kinetic temperature at 88 km previously reported for SABER at midlatitudes. The OH intensity increases 0.7 % decade-1, opposite to the negative trend derived by but in agreement with the expected increase in intensity with decreasing altitude.

Figure  shows the dependence among SABER OH intensity, equivalent temperature and altitude. The OH altitude generally changes quasi-linearly with OH intensity, but there seems to be an offset in the winter measurements with respect to the rest of the year. Indeed, the altitude displays a semiannual oscillation (see Fig. b) that is asymmetric, whereas that of the intensity is not (see Fig. a). We note that this asymmetry is in antiphase with the temperature annual variation. This suggests that temperature provides additional information for the altitude prediction. Furthermore, as mentioned above, the correlation between airglow emission and temperature is altitude dependent , meaning that the relative information content of these variables depends on the altitude of the OH layer. Indeed, the seasonal change in the intensity–temperature relationship (Fig. b, d) is most likely related to the seasonal change in the relative importance of the chemistry over dynamics. As discuss, higher OH altitudes are dominated by chemistry, larger temperatures implying lower intensities, whereas lower altitudes are dominated by dynamics, with larger temperatures implying larger intensities. From March to June when the altitude of the layer is high, chemistry is relatively more important and the intensity–temperature dependence has a small (even negative) slope. Also, SABER intensity, temperature and altitude variations with LST reveal the effect of semidiurnal and diurnal tides (lower row in Fig. ) that change in amplitude over the year, although not in the same way for the three variables (compare, for example, the relatively larger intensity variations with LST in March and April with the smaller variations in temperature and altitude during the same period). This points to the consideration of oscillation amplitudes varying with time.

The facts described here support the inclusion of the measured temperature as a predictor. The same conclusion follows from a theoretical perspective. There are two chemical sources of vibrationally excited OH in the mesopause: H + O3→ OH(v=1-9) + O2 and O + HO2→ OH(v=1-6) + O2 . The first one dominates. The excited OH losses are governed by collisions with molecular and atomic oxygen and spontaneous emission . Removal in collisions with molecular nitrogen and in chemical reactions with atomic oxygen also occur but do not significantly affect the OH(v) population . Assuming photochemical equilibrium (both for OH and O3), approximated the OH number density for the v level, [OH(v)]. Using the ideal gas law in his Eq. (20) and solving for the pressure, we obtain: p≈A[OH(v)]1/2T2.2(BVMRO-1+C)-1/2, where VMRO is the volume mixing ratio (VMR) of atomic oxygen, T is temperature, p is pressure and A, B and C are constants. Assuming hydrostatic equilibrium, z=-∫kbTmgd(ln⁡p) and using p as defined by Eq. (), we suggest the use of an empirical function for the peak altitude depending on z=f(Tln⁡([OH(v)]),Tln⁡T,fO), where fO is a function of the atomic oxygen VMR, but simultaneous ground-based O measurements are not generally available. Thus, we do not use the last term. Nevertheless, the dynamical processes that trigger daily and seasonal variation in the nighttime atomic oxygen also affect the temperature and should somehow be embedded in the temperature. Another caveat of this approach is that we have assumed an isothermal atmosphere in the vicinity of the OH layer.

We also note that, instead of [OH(v)], the OH vertically integrated emission rate or intensity, Ioh, is the available measurement from the ground. We note that OH VER is proportional to the OH(v) concentration and, as showed, Ioh is directly proportional to the peak VER. Furthermore, we also used OH-VER-weighted altitude (zoh) and equivalent temperature (Toh), or simply OH altitude and temperature, similar to what the ground-based instruments observe.

SABER OH altitude linear correlation with Toh×ln⁡Ioh is better than with Ioh (-0.85 compared to -0.77; compare top row panels in Fig. ). Its correlation is further improved (0.88) with the sun-corrected intensity when the F10.7 linear component (see Table ) is subtracted. This is because the OH altitude is not strongly correlated with the solar cycle. We also found after thorough testing that we improved the fit of SABER nighttime measurements when adding a sinusoidal semiannual correction weighted with temperature. This time-dependent amplitude might be representative of a time-dependent source of the semiannual oscillation (either Kelvin waves, gravity waves or tides). Considering additional seasonal and daily oscillations did not significantly improve the goodness of the fit. We only further decreased the residuals when taking into account a linear local solar time term (compared to the diurnal and semidiurnal oscillations used by ). The multiple linear correlation coefficient is then 0.93 (see Table ).

Putting all the above together, we adopted the following empirical formula: zoh=sITTohln⁡Ioh+sTTohln⁡Toh+ssao1Tohsin⁡(2π182.5d)+ssao2Tohcos⁡(2π182.5d)+sLSTLST+c, where d is the day of the year, sIT, sT, ssao1, ssao2 and sLST are the slopes of the regression and c is a constant.

Figure  shows the change in the residual OH layer altitude as the terms in Eq. () are fitted. When fitting only the first two terms in the equation (top row), seasonal and local time components still remain and the standard deviation of the residual is still rather significant (400 m). These components mainly disappear when also fitting the temperature-weighted semiannual oscillation and the linear local time terms (bottom row). Then, the standard deviation of the residual is reduced to 250 m (see also Fig. d).

Table  shows the coefficients that result from the fit of SABER OH temperatures (K), sun-corrected OH intensity (in erg cm-2 s-1) and LST in hours from midnight to SABER OH altitude (in meters) by using Eq. (). The multiple linear correlation and the residual standard deviation are similar to what we obtain by using the function. Nevertheless, we only need five parameters and a constant term. This relationship applies for midlatitudes. Since low and high latitudes are affected by dynamics and chemistry to a different extent, the expression should be revised and further terms might need to be considered in those cases.

We recall that the use of Eq. () requires using sun-corrected OH intensities. This mainly improves the fit (it reduces the standard deviation of the residual). However, it is not always possible to correct the measured ground-based signal from the sun contribution (for example, if a dataset is not long enough or has gaps). In that case, the solar slope in Table  shall be used.

Equation  and the corresponding coefficients derived from SABER in Table  predict OH altitude from OH intensities and temperatures simultaneously measured from the ground at northern midlatitudes. We apply these to SATI measurements from the Sierra Nevada Observatory (Spain) for a subsequent exploration of nocturnal variability in the three variables simultaneously. Before applying the equation and in order to avoid potential errors due to disagreements between SATI and SABER, it is required to determine the transfer functions between SATI OH intensities, Ig, and temperatures, Tg, and between SABER vertically integrated OH volume emission rates, Ioh, and OH equivalent temperatures, Toh. For this purpose, we use SABER and SATI colocated measurements. We selected SATI and SABER measurements with SZA > 100∘ and taken within ±1 h, ±5∘ latitude and ±7∘ longitude. The natural variability within these ranges at midlatitudes is mainly caused by waves. According to the results shown in , the expected maximum intensity and temperature differences due to that space–time mismatch are smaller than 15 % and 6 K, respectively. Nevertheless, we find on average around 20 SATI measurements colocated with each SABER measurement, reducing the average time–space mismatch and the associated differences to 3 % and 1 K, respectively. Relaxing the colocation criteria reduces the correlation between SATI and SABER measurements, and constraining them does not significantly change the results but reduces the number of coincidences.

We found 14 113 SABER–SATI pairs from 2002 to 2015. We averaged SATI colocations around each SABER measurement, leading to 852 coincidences. Comparisons between measurements are shown in Fig. . We use a linear SATI-to-SABER transfer function. We also allow for linear drifts between instruments that may include, for example, those due to aging: Xoh=m(Xg+dt)+n, where X is either OH intensity or temperature, t is time, d is the relative drift, m is the slope, n is a constant and the oh and g subindices correspond to the satellite and the ground-based instrument variables, respectively.

Table  shows the retrieved values for slopes, drifts and constants after performing the regressions. There is a 1.3 % per year relative drift between SATI and SABER intensities, the SATI signal being relatively smaller with time, probably due to faster aging. The mean SABER and SATI temperature difference is 5.6 K, which is in agreement with previous results from . Temperature differences do not strongly depend on temperature, so the slope is close to unity. This indicates that the errors in the Einstein coefficients used in SATI retrievals are not significant, as concluded using a similar approach. The relative temperature drift is -0.8 K yr-1, with SATI measuring higher temperatures with time relative to SABER. A reason for this drift might be nonlinear aging of SATI, resulting in a response depending on wavelength and consequently affecting the derived rotational temperature. In principle, this fact suggests using SATI data for trend analysis with caution, except for measurements taken at early stages when an accurate calibration was performed. Nevertheless, we do not rule out a SABER contribution to this drift. We note that found a 0.7 K yr-1 bias trend in SABER version 1.07 temperatures (we use version 2.0) by comparing them with ground-based OH and the Aura Microwave Limb Sounder data at Davis, Antarctica, with SABER getting warmer with time. Either way, SATI measurements are still valid for temperature wave analyses because these deal with relative changes and, as shown above, temperature differences do not depend on absolute temperature (the slope in Eq.  is close to 1).

We used Eq. () with the coefficients in Table  to transfer SATI-to-SABER intensities and temperatures and then used Eq. () with the coefficients in Table  to predict the OH layer altitude at high temporal sampling (2 min) from SATI measurements. We present the wave decomposition of the three variables for two typical cases, showing the potential and abilities of the method (Fig. ).

The first case (Fig. a) shows a typical example (October 2009) in which tidal variation in SATI OH intensity, temperature and predicted altitude are superimposed to a quasi-2-day planetary wave. Comparisons with SABER colocated measurements transferred to SATI scale using Eq. () (also plotted) show reasonable agreement with SATI data for the three variables. After determining the significant components in SATI data from the Lomb–Scargle periodogram, we fitted the data to a composite of diurnal, semidiurnal, terdiurnal and 1.7-day oscillations (shown in orange in the figure). That yielded amplitudes of 0.6, 1.2, 0.25 and 0.6 km (with errors around ±0.1 km) in altitude associated with 15, 45, 15 and 15 % (with errors around ±2 %) intensity amplitudes and 7, 9, 4 and 5 K temperature amplitudes, respectively (with errors around ±1 K). Their combinations produced overall peak-to-peak variations along this period of 4.5 km in altitude, a factor of 3 in intensity (with respect to the lowest value) and 40 K in temperature. Waves do not contribute in equal proportion to the three variables. Whereas the terdiurnal component is similar to the diurnal for intensity, altitude and temperature present amplitudes half as strong. Additionally, altitude variations are in antiphase with temperature and intensity variations. Tidal altitude amplitudes are on the order of previously measured values e.g.,. We recall that the displacements of the OH layer cause SATI OH temperature variations not to coincide with kinetic temperature variations occurring at a fixed altitude. Indeed, an examination of the colocated SABER temperature gradients shows that temperature decreases around 3–4 K km-1 at 80–90 km. Thus, around 15 K of the overall OH temperature change is due to OH altitude. Slight night-to-night changes in the tidal amplitudes are also detected by SATI.

In the second case, nighttime SATI OH intensity, temperature and predicted altitude from 2 August 2013 to 14 August 2013 (Fig. b) presented a wealth of superposed oscillations. SABER colocated measurements (also plotted) agree well with SATI data. The high temporal sampling in SATI data allowed for the extraction of significant (98 % significance in the power spectrum) semidiurnal, terdiurnal, 1.8-day and 2.3-day wave contributions to the signal. The fit to the combination of those oscillations yielded amplitudes of 0.5, 0.3, 0.7 and 0.8 km, respectively, in altitude associated with intensity amplitudes of 10 % for the first three modes and 20 % for the latter and temperature amplitudes of 5, 8 and 7 K for the latter two modes.

We have also studied SATI OH altitude, intensity and temperature nocturnal variability for all nights from 2002 to 2015. In order to reduce artifacts related to a varying time sampling over the year (seasonal variation in the length of the night), we use variabilities only within 6 h of measurements. We have estimated the peak-to-peak nocturnal variability for each night (nocturnal variability hereafter) as 2 times the maximum standard deviation of the 6 h running bins (2-σ). Since we do not strictly use peak-to-peak differences, these estimations are conservative. We also note that the semidiurnal tide dominates SATI nighttime variability .

The black dots in Fig.  shows the nocturnal variability (2-σ) versus the day of the year (DOI) for altitude, intensity and temperature. These deviations from the nighttime mean values are caused by waves (tides, planetary waves and, plausibly, large-scale gravity waves). The scattering of the dots around each DOI is striking. Instruments providing measurements at low temporal resolution mask this day-to-day variability. We calculated 60-day running means to mimic a 2-month temporal resolution (see Fig. ). The OH altitude peak-to-peak nocturnal variability bimonthly mean exhibits mainly annual variation (0.5 km smaller in midsummer than at the beginning of January), with a slight increase in May (following a more significant rise in intensity but not in temperature). This seasonal variation is related to and in phase with those corresponding to the intensity and the temperature, which exhibit semiannual (maximum values in early winter and late spring) and annual (minimum values in late spring) oscillations, respectively.

The standard deviations of these nocturnal variability bimonthly means for each calendar month are also shown in Fig. . In these standard deviations, the contribution of instrumental random errors (precision) is superposed on that of wave variability. The standard deviation of the layer altitude nocturnal variability in autumn (±0.9 km standard deviation) is significantly larger than from late spring to summer (±0.3 km standard deviation). As an upper limit of our estimation, these deviations are assigned completely to wave variability. To estimate the lower limit, we assign the minimum standard deviation to precision (±0.3 km) and assume a constant precision through the year. Then, considering the root square sum of deviations, the change from minimum to maximum standard deviations leads to wave variations of at least ±0.8 km within each 60-day period during autumn. The intensity and the temperature nocturnal variabilities have standard deviations changing from ±175 A.U. (±55 %) in December to ±110 A.U. (±40 %) in spring, and from ±7 K in January to ±4 K from late spring to August. Analogous to the reasoning for altitude, these become the upper limits for intensity and temperature wave variability within 60 days for those seasons. The lower limit is then ±45 % variability for intensity waves in December and ±6 K for temperature waves in January.

An understanding of the variations in the OH layer from ground-based measurements on multiple timescales relies on simultaneous knowledge of the intensities, temperatures and altitudes of the emitting layer. A ground-based OH airglow instrument cannot directly observe the OH altitude of the layer from which the measured emission emanates. Similar to the approaches of and , we provide in this work an empirical formula to predict the altitude of the OH layer from airglow intensities and temperatures at midlatitudes. The expression was determined by fitting vertically integrated OH volume emission rates and OH equivalent temperatures measured by SABER (version 2.0) from 2002 to 2015.

The empirical formula derived in this work takes into account not only OH intensity, as and did, but also dependence on OH temperature. Additional information on altitude variations embedded in temperature (for example, processes not altering OH intensity or doing it in a different manner) is also taken into account by this method. By including both variables and only two more terms, namely, a temperature-weighted semiannual oscillation and a local time linear term, we fitted the SABER OH layer altitude at midlatitudes with a similar accuracy (250 m) to that by the earlier studies. That is, we obtain a similar residual standard deviation by using only six parameters (compared to 10 and 11 coefficients that the abovementioned authors needed, respectively). Since lower and higher latitudes are affected by dynamics and chemistry to a different extent, the expression should be revised and further terms might need to be considered under those conditions.

In the course of the analysis of SABER data spanning more than a solar cycle, we inferred a descent of 40 m decade-1 in OH altitude, an increase of 0.7 % decade-1 in OH intensity and a decrease of 0.6 K decade-1 in OH temperature. As previously reported, we found a significant correlation between intensity and temperature with the solar cycle (7.8 % per 100 s.f.u. and 3.9 K per 100 s.f.u.) but not for altitude.

We applied the altitude empirical formula derived from SABER to 2002–2015 SATI airglow spectrometer measurements taken over the Sierra Nevada Observatory (Spain) in order to examine OH intensity, temperature and altitude nocturnal variabilities simultaneously. SATI OH temperature and intensity measurements were previously transferred to the SABER reference system. The transfer functions relating both instrument measurements, which were derived using colocated measurements from 2002–2015, included a constant-with-time linear term allowing for biases between instruments and a time variable term allowing for relative drifts. The relative drift between SATI and SABER intensities is -1.3 % yr-1, plausibly due to faster SATI aging. The derived slope for temperature is close to unity, which suggests that the Einstein coefficients assumed in SATI retrievals are adequate. We found an average 5.6 K SATI–SABER temperature difference. SATI temperature drift is positive relative to SABER (0.8 K yr-1). Nonlinear aging of SATI, depending on wavelength and affecting the derived rotational temperature, might explain this bias drift. Nevertheless, we cannot rule out a contribution from SABER. This result evidences the need for accurate traceability of the intensity responsivity of ground-based spectrometers. Even so, we note that SATI data are still valid for wave analyses in which only relative changes are used.

We examined SATI typical cases showing the convenience of using this approach when inspecting the OH layer nocturnal variability from ground-based measurements. In both cases, predicted altitudes from SATI temperatures and intensities agree well with SABER colocated observations. SATI measurements allowed us to decompose the overlapping wave components with a high temporal resolution. We measured vertical variations of more than 4 km between two consecutive nights due to the combined effect of tides and planetary waves that accompanied 100 % and 40 K changes in intensity and temperature, respectively. The SABER colocated temperature gradients suggest that, in this case, the 4 km vertical displacement is responsible for around 15 K of temperature change.

An additional advantage of using SATI measurements is that the temporal resolution permits the evaluation of day-to-day wave variability. Our estimations suggest that peak-to-peak OH nocturnal variability, mainly caused by wave variability, changes within 60 days at least 0.8 km for altitude in autumn, 45 % for intensity in early winter and 6 K for temperature in midwinter. Plausible upper limit ranges of those variabilities are 0.3–0.9 km, 40–55 % and 4–7 K depending on season. This short-term variability should be accounted for when studying waves and their impact using circulation models at high temporal resolution. A comprehensive analysis of (planetary and tidal) wave decomposition on predicted altitudes for the complete SATI dataset will be the focus of a future study.