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 Atomic oxygen [O] plays a fundamental role in the photochemistry and energy budget of the terrestrial mesopause region (80–100 km). [O] is difficult to measure directly and is typically inferred at night from measurements of hydroxyl [OH] or molecular oxygen [O2] emissions. During the day, measurements of ozone [O3] concentration are used to infer [O]. These inferences carry significant uncertainties [Mlynczak et al., 2013a]. Recently, Mlynczak et al. [2013b] have used energy balance principles to set an upper limit on the annual global mean [O] concentration in the mesopause region. In this paper, we use night measurements of OH emission to set a lower limit on the global annual mean atomic oxygen concentration. These independent, radiatively constrained values of the maximum and minimum atomic oxygen concentration also place constraints on the magnitude of dynamical processes in the annual global mean energy budget of the mesopause region.
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 Atomic oxygen [O] directly influences the heating and cooling of the terrestrial mesopause region between 80 and 100 km. Atomic oxygen participates in a series of exothermic chemical reactions that provide much of the direct heating of the mesopause region [Mlynczak and Solomon, 1993]. Collisions between atomic oxygen and infrared-active minor gases, such as carbon dioxide [CO2], water vapor [H2O], and ozone [O3], facilitate the radiative cooling of the mesopause region. Ironically, [O] is extremely difficult to measure directly from orbiting satellites. It has two fine structure lines in the far-infrared portion of the spectrum, one at 63 µm and the other at 145 µm. The 63 µm line is optically thick and not observable at the mesopause from space. The 145 µm line is not optically thick but would require complex instrumentation, and such measurements are not anticipated for the foreseeable future.
 Atomic oxygen in the mesopause region is then typically derived or inferred from related measurements. There are two approaches commonly used: the first is to derive [O] from measurements of the OH or O2 nightglow emissions [e.g., Good, 1976; Sheese et al., 2011; Mlynczak et al., 2013a, hereafter M13a] and the second is to derive [O] in the daytime from measurements of O3 as in M13a. All of these approaches depend on assumed photochemical balance relationships and numerous parameters, such as radiative lifetimes and rates of physical quenching of vibrationally excited [OH], electronically excited [O2], or vibrationally excited [O3]. Because of the different approaches and the many parameters used in the models, as well as the difficulty of validation, there is no direct way to test the validity of the inferred atomic oxygen concentration.
 Recently, Mlynczak et al. [2013b, hereafter M13b] have presented a technique for constraining the upper limit on the atomic oxygen concentration profile in the mesopause region. From an energy balance perspective, on annual time scales and on global spatial scales, the energy deposited by solar radiation and exothermic chemical reactions in the mesopause region must be less than or equal to that lost from the region by radiative cooling. Otherwise, the mesopause would heat perpetually in the absence of some other mechanism to remove the excess heat. Specifically,
 This expression includes only radiative and chemical energy terms. If dynamical heating is important, another term is required on the left-hand side of equation ((1)). M13b showed that the sum of the chemical heating and the solar heating in [O3] terms in equation ((1)) could be expressed as a function of atomic oxygen and that a “radiatively constrained” atomic oxygen concentration consistent with the global mean energy balance in equation ((1)) is obtained in the form of a simple quadratic equation in [O]. The radiatively constrained atomic oxygen profile represents an upper limit on the atomic oxygen concentration in the sense that larger concentrations would necessarily imply more heat deposition through exothermic reactions than could be accounted for in the long term from the observed radiative cooling due to CO2. The results are based on observations and calculations of solar heating rates and radiative cooling rates made by the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) instrument [Russell et al., 1999] on the NASA Thermosphere, Ionosphere, Mesosphere Energetics and Dynamics (TIMED) satellite. M13b also showed that SABER-derived day (from O3) and night atomic oxygen (from OH) were consistent with the independently derived radiatively constrained atomic oxygen.
 The mesopause region energy budget is quite complex, and it is likely that other processes such as energy deposition from gravity waves influence the heating and cooling. The extent to which these processes occur then necessarily alters the computed atomic oxygen concentration that is consistent with the overall energy balance of the region, as implied by equation ((1)) above. If, for example, gravity waves are a significant source of heating in the global annual mean, then the atomic oxygen concentration must be smaller than that derived by M13b for long-term energy balance to hold. It is therefore instructive to ask if a lower limit on atomic oxygen exists by which the amount of heating due to gravity waves or other dynamics can be constrained in the global mean.
 In this paper, we present vertical profiles of atomic oxygen that represent the minimum global annual mean values that are consistent with observed OH emission intensities and OH radiative lifetimes. These results, coupled with the results of M13b, effectively bracket the maximum and minimum radiatively allowed global annual mean atomic oxygen concentrations in the mesopause region. As will be shown, the maximum values near the peak in the [O] profile are 60%–70% larger than the minimum values. These results can then be used to test upper atmosphere general circulation models to evaluate their consistency with the range of radiative and energetically allowed atomic oxygen values. The results can also be used to guide parameterizations of additional heating mechanisms, such as gravity wave breaking, so that modeled thermal structure and chemical composition are consistent with observed energy balance and radiatively allowed chemical composition.
 The SABER instrument is a 10 channel radiometer that scans the Earth's limb, recording profiles of infrared emission intensity as a function of tangent altitude. One SABER channel observes emission near 2.0 µm and records emission with very high precision (signal-to-noise-ratio between 100 and 1000 at the peak) from the OH(9-7) and OH(8-6) bands (see M13a for full details). These measurements are used at night to derive atomic oxygen based on the assumption that reaction of [O3] with atomic hydrogen [H] is balanced by recombination of [O] and [O2]. The expression used to derive the SABER night [O] is given by
 In equation ((2)), V is the measured volume emission rate of OH 2.0 µm emission; P is the rate of recombination of [O] and [O2]; and f9 and f8 are the quasi-nascent pumping fractions of the υ = 9 and υ = 8 levels, respectively, of OH subsequent to reaction of [H] and [O3]; the A terms are Einstein coefficients for spontaneous emission of radiation of the OH molecule, and the C terms represent collisional loss or reaction of vibrationally excited [OH] with [N2], [O2], and [O]. Note that the P, C, and V terms are all altitude dependent. The term P is specifically given by the product k2[O][O2], where k2 is the rate coefficient for recombination of [O] and [O2]. (See M13a for information on the derivation of the SABER volume emission rate V and Table 1 of M13a for values of the f, A, and C terms.)
 From equation ((2)), it can be seen that the effect of collisional processes is to necessitate larger derived atomic oxygen for a given measured V. This is physically plausible since the effect of collisions is to remove vibrational excitation and thus decrease the overall emission intensity. In order for the atmosphere to attain an observed rate of emission, more H and O3, and thus more O, are required in the presence of collisional quenching. If collisions are minimized, less atomic oxygen is required to maintain the observed emission rate.
 Therefore, in the limit of no collisions, that is, in the limit in which it is assumed that the highly excited OH states observed by SABER relax solely by spontaneous emission of radiation, the minimum possible [O] concentration consistent with the SABER radiometric observations may be derived. The expression for this is obtained by setting all of the C terms in equation ((2)) to zero. The remaining terms in the bracket of equation ((2)) form a constant, and the equation for minimal radiative constrained atomic oxygen ([O]min) reduces to
 In equation ((3)), V is the SABER OH 2.0 µm volume emission rate; T and p are the temperature and the pressure, respectively, simultaneously measured by SABER; and 395 is a constant composed of the terms in the bracket in equation ((2)) and the rate constant (6 × 10−34) for the rate coefficient (6 × 10−34 (300/T)2.4) for recombination of [O] and [O2]. We use equation ((3)) and SABER measurements of OH 2.0 µm volume emission rates between 55°N and 55°S latitudes (approximately 82% of atmospheric area) over an entire year (approximately 500,000 profiles of OH volume emission rates) to derive minima atomic oxygen. The derived [O]min profiles are area weighted and averaged to provide a near global mean value of the radiatively allowed minimum atomic oxygen profile in the mesopause region. The effect of neglecting results poleward of 55° should be minimal. Even if the means were 25% smaller than those between ± 55°, the global means would change by less than 5%. Finally, although the values shown here are derived from night observations, M13a showed that daytime global mean [O] is nearly identical to the night [O], implying that [O]min is valid for day as well.
 Shown in Figure 1 are the global annual mean [O]min values for 2004 and 2008 derived from equation ((3)) (blue curves) as well as the radiatively constrained atomic oxygen for the same years derived from M13b (red curves). The year 2004 is chosen because it is the first year M13b obtained a complete annual mean assessment of the solar heating and radiative cooling. The year 2008 is chosen as it is near solar minimum. Each pair of curves in Figure 1 is representative of the variability of the maximum and minimum radiatively constrained values of atomic oxygen due to solar variability from 2004 to 2008. Although not shown, the 2012 maximum and minimum constrained [O] values are almost identical to those in 2004, implying a recovery from 2008 due to increasing solar activity. Finally, following M13a, the uncertainty in [O]min is assessed to be about 20%, comparable to that for the derived [O]. The value of the rate coefficient for recombination of O and O2 is, again, the largest source of uncertainty.
 The difference between the maximum and minimum radiatively constrained atomic oxygen profiles shown in Figure 1 is relatively small. Peak values (near 95 km) range from 3.0 × 1011 cm−3 for the minimum value to about 5.2 × 1011 cm−3 for the maximum value, a 60%–70% difference relative to the minimum value. Figure 2 shows the difference (for the year 2004) in the maximum and minimum radiatively constrained atomic oxygen. There is a relatively small range of radiatively/energetically allowed atomic oxygen in the mesopause region. Figure 3 shows a comparison between the minimum and maximum constrained atomic oxygen and that from the MSISE 2000 model [Picone et al., 2002] for the year 2004, with conditions matched to the time and location of each SABER measurement. The Mass Spectrometer Incoherent Scatter (MSIS) values are close to the maximum radiative constrained values and imply, on a global annual mean basis, relatively small heating by dynamical processes. Comparisons against general circulation models are planned for the future.
4 Discussion and Summary
 We begin this discussion by emphasizing that this letter is not suggesting that the highly excited OH molecule relaxes solely by spontaneous emission of radiation or that the corresponding minimum atomic oxygen profile represents a geophysical reality. Rather, the radiative constraint concept of M13b, coupled with the minimum atomic oxygen concept presented here, represents the range of global average atomic oxygen that is radiatively and energetically allowed in the mesopause region based on observations of the energy balance of the atmosphere and on the observed radiative properties of the OH molecule. These results are independent of the techniques commonly used to derive the atomic oxygen profile. The true global mean atomic oxygen profile must fall somewhere between the maximum and minimum profiles presented here. Because we know the OH molecule is collisionally quenched [e.g., Kalogerakis et al., 2011], the range of allowed [O] is actually smaller than that shown in Figures 1 and 2. Furthermore, because of the length of the SABER data set, we have information on the solar cycle variability and the allowed variability in the atomic oxygen concentration.
 These results provide observation-based guidance on the range of allowed global annual average atomic oxygen concentrations, largely constrained by the radiometric quality of the SABER instrument. The results will be of particular use in assessing photochemical model computations of [O]. Such models have historically run a deficit of odd oxygen in the mesosphere, largely reflected in smaller than observed ozone abundances, which imply smaller than actual [O] concentrations. In addition, energy deposition by gravity waves is not well parameterized in models but is thought to exert a significant influence on the thermal structure of the mesopause region. If gravity wave heating is significant in the global annual mean, then the radiatively constrained values of atomic oxygen that are consistent with global annual energy balance will be smaller than that shown in the red curves in Figure 1, via the relationship expressed in equation ((1)).
 The radiatively constrained maximum and minimum atomic oxygen can be used to estimate the range of allowed global mean heating due to dynamics. Referring to equation ((1)), we can write
where HC is chemical heating, HD is dynamical heating, C is radiative cooling, and HS is solar heating. In the limit HD = 0, the maximum atomic oxygen consistent with long-term energy balance is obtained, as in M13b. At the other limit, using the minimum atomic oxygen derived in this paper, HC will also be a minimum, called HCmin. An estimate of the range of allowed gravity wave heating is then given by
 To estimate the range of gravity wave heating, we use equation ((5)) and consider, at present, heating only due to the recombination of O with itself and to the recombination of O and O2. These results are shown in Figure 4. The blue curve labeled “RC Min” is the exothermic heating for these two recombinations for the minimum allowed [O] shown in Figure 1, while the “RC Max” is the exothermic heating for these two recombinations for the maximum allowed [O] shown in Figure 1. An estimate of the maximum global mean heating due to gravity waves and consistent with global mean energy balance is rendered by the difference between these two, indicated by the black curve labeled “GW.” Near 95 km, the effect of gravity waves could be as large as 4 K/d in the global mean according to this estimate. More detailed estimates of radiatively allowed heating due to gravity waves can be made by including additional reactions, such as that of [H] and [O3], with different levels of collisional quenching of OH(υ). This approach will narrow the gap between the minimum and maximum allowed concentrations of [O] and, hence, reduce the allowed range and value of global mean heating due to gravity waves in the mesopause region. This approach will be explored in more detail in a future paper.
 The authors gratefully acknowledge support from the NASA TIMED project and the NASA Living with a Star program.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.