The exothermic reaction of H and O3 in the atmosphere was identified by as the major source of vibrationally excited hydroxyl radicals (OH*) near the mesopause region. R1H+O3→OH*(v≤9)+O2 Metastable excited OH* can be de-excited via radiative, chemical, and collisional relaxation processes. OH(v≤8) is not only initially populated by the reaction of H+O3 but is also produced by the deactivation of higher vibrational states of OH* via radiative relaxation and quenching. The number density of OH(v) can be obtained from its emission line measurements by dividing by the corresponding Einstein coefficients. The volume emission rate Vv-v′(i) of an arbitrary ro-vibrational line within a vibrational band OH(v-v′) can be calculated as 1Vv-v′(i)=nv⋅gv(i)⋅e-Ev(i)/(k⋅T)Qv(T)⋅Av-v′(i). nv is the total number density of the corresponding upper vibrational state v, and Av-v′(i) is the Einstein coefficient of the specific state-to-state transition from vibrational level v to v′. Ev(i) and gv(i) are the rotational energy and degeneracy of the upper rotational state of the ith line considered. k is the Boltzmann constant and T is the temperature. Qv(T) is the rotational partition sum of OH(v). This formula is only valid under rotational local thermodynamic equilibrium (LTE) conditions and deviations are discussed later.

SCIAMACHY measured integrated OH spectra along the line of sight in the tangent altitude range from approx. 73 km to approx. 149 km. The SCIAMACHY OH limb measurements can be expressed as 2y=F(x,b)+ϵ. y corresponds to the measured SCIAMACHY OH limb spectra. F is the functional formula of the forward model involving Eq. (). x represents the number densities (nv) of the corresponding upper vibrational state of the emission lines. b is the parameter vector of the forward model, e.g., Einstein coefficients. ϵ represents stochastic measurement errors. The retrieval can be regarded as an approach to solving an inversion problem in the presence of indirect measurements of the properties of interest. In our setup we assume that each atmospheric layer emits OH airglow homogeneously, and we set the retrieval grid to be identical to the tangent altitude grid of the averaged OH limb measurements. To improve the efficiency of the retrieval, to suppress noise in the solution, and to achieve a smooth transition of the retrieved quantities into model data at the upper boundary, a regularization term is added to the minimization : xi+1=xa+(KiTSϵ-1Ki+Sa-1)-1KiTSϵ-13×[y-F(xi,b)+Ki(xi-xa)]. xi reaches the optimal estimate solution when the retrieval converged. Ki corresponds to the first derivative matrix of the forward model, named the Jacobian matrix. xa represents the a priori knowledge of the total number densities of OH(v), and Sa-1 is the regularization matrix. Sϵ is a diagonal error covariance matrix of y.

The confidence level of simulated volume emission rates (VERs) can be assessed by considering three main aspects: the uncertainty of the auxiliary atmospheric quantities, i.e., temperature; the uncertainty of rate constants, i.e., Einstein coefficients; and the potential uncertainty introduced by overpopulated high rotational states due to nonlocal thermodynamic equilibrium (non-LTE) effects. The temperature uncertainty in the SABER measurements includes random and systematic errors; summarized SABER temperature uncertainties. We consider only systematic errors in SABER temperatures, because monthly mean data are used. The SABER systematic temperature uncertainty is approx. 1.5 K at 70–80 km, 4 K at 90 km, and 5 K at 100 km. Accordingly, VERs are affected by temperature uncertainties by less than 1 % between 80 and 96 km on average, as obtained by in their investigation of the temperature dependence of the band Einstein coefficients as well.

Many OH Einstein coefficient datasets can be found in the OH research community (see, e.g., ). We consider the values given in the latest HITRAN molecular spectroscopic database and the OH Einstein A values calculated by and . The uncertainty of the Einstein coefficient affects simulated VERs in two ways. In the retrieval of vibrationally excited OH from SCIAMACHY data and in the simulation of the SABER measurements. Figure a shows simulated SABER unfiltered OH 1.6 and 2.0 µm VER profiles obtained from SCIAMACHY measurements using these three Einstein coefficient datasets. Corresponding OH number density profiles as derived using Einstein coefficients from the HITRAN database at vibrational states 9, 8, 5, and 4 are also given. The highest VERs are obtained by using the Einstein coefficients calculated by and the lowest are obtained by using the HITRAN database. The differences between them are approx. 26 % for the simulation of SABER 2.0 µm VERs and approx. 19 % for the simulation of SABER 1.6 µm VERs. Similar values were also obtained if we used data for other latitude bins or time periods. The same procedure was also applied to the simulation of SABER 2.0 and 1.6 µm in-band data, giving similar results. Therefore, we used these results as a proxy to estimate related uncertainties of the Einstein coefficients.

, , and reported that middle and higher excited rotational states (N≥4) of OH do not meet the LTE hypothesis and that these levels are overpopulated. An estimation of the non-LTE contribution was performed by based on cross-dispersed cryogenic spectrometer measurements in the spectral range of 0.97 to 2.4 µm. A combination of two Boltzmann distribution equations with cold and hot OH rotational temperatures was used to predict the observed intensities of OH emission lines. re-analyzed the data used by to estimate the OH rotational temperatures following the approach taken by and . They found that the thermalization of every OH vibrational level is incomplete.

The low spectral resolution of SCIAMACHY spectra does not allow us to estimate this effect from the measured data. Therefore, we performed model simulations using the same approach and parameter sets as to quantify the effect of incomplete thermalization on the spectral ranges used in this study. We calculated OH 1.6 and 2.0 µm VERs by considering only the cold rotational temperature and then obtained them using cold and hot temperatures together as and did. It was found that differences between them are less than 2 % for both SABER channels. The SABER 1.6 and 2.0 µm channels also observe emission lines from OH(3-1) and OH(7-5), respectively. We estimated their influence on spectrally integrated radiances by the derivation of the corresponding emissions using SCIAMACHY OH(3-1) and OH(7-4) nightglow measurements. These simulations show that the contributions of OH(7-5) and OH(3-1) to the two channels are about 3 % and 1 % on average, respectively.

In summary, the uncertainty of the Einstein coefficient dominates the error budget for the in-band and unfiltered data, which is on the order of 20 % and 26 % for the SABER 1.6 and 2.0 µm VER simulations, respectively.

An intercomparison between 1.6 and 2.0 µm in-band and unfiltered VERs as measured by SABER and corresponding simulations using SCIAMACHY data and HITRAN OH Einstein coefficients is given in Fig.  for two different latitudes in September 2005. Error bars shown in Fig.  represent the root-mean-square value of all uncertainties discussed in the Sect. . Panels (a) and (b) show a comparison of the unfiltered data, and panels (c) and (d) show the in-band data. SABER measurements are always larger than the simulations using SCIAMACHY data. For the unfiltered data, deviations of SABER OH 1.6 µm measurements with respect to the corresponding simulations increase with altitude from 30 % to 45 % at 83 km to 55 %–80 % at 96 km, depending on latitudes. The difference of SABER OH 2.0 µm measurements with respect to the corresponding simulations is 16 % at 86 km. At 96 km, it reaches 70 % in latitude bins 0–20∘ N and approx. 90 % in 20–40∘ N.

Surprisingly, for the in-band data, the differences for the 1.6 and 2.0 µm channels are significantly smaller at most altitudes. They vary in a range of 8 %–28 % (21 %–50 %) and 8 %–60 % (28 %–100 %) from 83 to 96 km at 0–20∘ N (20–40∘ N). It should be noted that SCIAMACHY and SABER have a resolution of about 3.3 and 2 km, respectively. A linear interpolation has been applied to SABER data to make a comparison with SCIAMACHY data. This may underestimate the SABER data at peak altitudes and overestimate the SABER data at two wings besides the peak altitudes.

Figure  shows the global spatial distributions of SABER OH 2.0 µm VERs (panel b) and the corresponding simulations (panel a) using SCIAMACHY data for the year 2007. A strong annual variation with a maximum in April and a semiannual oscillation are visible in the radiance data over the Equator region, as was also found by in a study of SCIAMACHY OH(3-1) and OH(6-2) volume emission rates. It is obvious that SABER VERs are significantly larger than corresponding simulated values based on SCIAMACHY observations, as already stated. Comparing the SABER OH 1.6 µm VERs and the corresponding simulations leads to the same conclusion (not shown).

Figure  shows two pairs of scatter plots which elucidate the consistency of SABER unfiltered 1.6 µm (Fig. a, c) and 2.0 µm (Fig. b, d) VERs and corresponding simulated values based on SCIAMACHY observations. Again, SABER data are systematically larger than the SCIAMACHY simulations. The SABER 1.6 µm channel data (Fig. a, c) are 44 % larger for the unfiltered data and 23 % larger for the in-band data, if all altitudes and latitudes are considered simultaneously in one fit. For the 2.0 µm data (Fig. b, d), the differences are 23 % and 35 % on average.

To illustrate whether this difference changes on long timescales, Fig.  shows the ratio of SABER unfiltered and in-band data to the corresponding simulations based on SCIAMACHY data from 2003 to 2011. For the OH 1.6 µm unfiltered (in-band) data, the ratio value varies roughly between 1.2 (1.0) and 1.3 (1.2) for 2003–2009, reaching 1.1 for 2010 and 1.36 for 2011. The ratio varies between 1.0 (1.1) and 1.1 (1.2) for the OH 2.0 µm unfiltered (in-band) data. The data indicate that there are no significant variations in the slope of SABER data vs. SCIAMACHY simulations from 2003 to 2011 and that there is a systematic bias between them in general.