1. Geophysical Concept
1.1. Origins
Images of the far ultraviolet (FUV) dayglow observed in the direction of the Earth's disk have been made for more than 40 years, for example by the Apollo 16 Lunar Camera (Carruthers & Page, 1976a, 1976b), the Dynamics Explorer (Frank and Craven, 1988) and the POLAR missions (Germany et al., 1994; Frank et al., 1995; Torr et al., 1995). Often these observations were used to provide context for in situ measurements without requirement for quantitative assessment. Despite the application of forward models to assess magnitudes and morphologies of the imaged emission rates (e.g., Drob et al., 1998; Germany et al., 1994; Meier et al., 1995) and empirical models to assess variability (Immel et al., 2000), the extraction of quantitative atmospheric composition information from the data proved challenging because the FUV disk images depict column emission rates (CER) without revealing the altitudes where the signal originates. In contrast, observations of the ultraviolet emission from Earth's limb do contain quantitative information (e.g., Meier & Anderson, 1983; Meier & Picone, 1994; Meier et al., 2015) because their altitude variations above the horizon allow extraction of composition profiles.
Strickland et al. (1995) overcame the disk problem, for the first time, by demonstrating a functional relationship between the ratios of observed far ultraviolet airglow emission intensities and the ratios of the column densities of O and N2. The latter quantity is designated herein as ΣO/N2 to distinguish the ratio of column densities from the volume density ratio, O/N2. Strickland et al. found minimal ambiguity in the relationship when the vertical column densities are calculated above an altitude, z17, corresponding to an N2 column (from infinity down to z17) of 1017 cm−2 (= NN2 in Equation 1; NO is the O column density above z17). Thus, ΣO/N2 is defined as: equation
At NN2 = 1017 cm−2, Strickland et al. found little dependence of the relationship between ΣO/N2 and the 135.6 nm/LBH emission ratio on the details of the model atmosphere, although they did find a dependence on solar zenith angle and viewing angle from nadir (Evans et al., 1995). The main point of their discovery is that the column density ratio can be found from the ratio of disk radiances without knowing how O and N2 are distributed throughout the atmosphere.
Further, they were able to quantify the solar extreme ultraviolet (EUV) energy flux required to produce the observed airglow by using the absolute magnitude of either the O or the N2 CERs. Strickland et al. designated this solar variable as Qeuv the integral over wavelength of the model solar spectral irradiance from 1 to 45 nm, in units of W m−2, a quantity directly comparable to independent measurements of solar EUV spectral irradiance (e.g., Woods et al., 2008). This allows for determination of the internal consistency of the FUV airglow observations and extracted geophysical quantities.
Subsequent studies arising from the pioneering work of Strickland et al. (1995) leave no doubt about the geophysical importance of ΣO/N2 and the value of its close relationship to O and N2 FUV emission rates. Embodied in Equation 1 is the prescription for comparison of observed ΣO/N2 to atmospheric model predictions: simply integrate the model N2 density vertically downward until the altitude (z17) is found where the column density is 1017 cm−2. Next, the O column density is computed above that altitude and divided by 1017 to obtain the model ΣO/N2 for comparison with observations. This definition of altitude is only needed for comparison with models. It does not violate the Strickland et al. finding that the ΣO/N2 retrieved from observed OI 135.6/N2 LBH has little dependence on the altitudinal distribution of composition.
For an atmosphere in pure diffusive equilibrium, ΣO/N2 is independent of temperature. A simple example of this independence is an isothermal atmosphere: temperature cancels in the ratio of O to N2 scale heights. The independence is also true for the Bates-Walker (Walker, 1965) and Jacchia (1977) diffusive equilibrium models. But in realistic atmospheres, column density ratio and temperature can be related. For example, high latitude joule heating causes upwelling that results in increased molecular concentrations relative to atomic oxygen. This lower ΣO/N2, hotter air is redistributed globally by equatorward winds, especially at night, that can result in dramatic changes in the column density ratio (Meier et al., 2005). I have even noticed high latitude decreases in GUVI observations of ΣO/N2 for very weak geomagnetic activity increases in Ap from 2 to 4. As well, Crowley et al. (2008) have related 7- and 9-days oscillations in the solar wind to modulation of ΣO/N2 by vertical winds at high latitudes and by inference, thermal expansion at low latitudes.
In summary, it is now established that observed "two-color" disk images of FUV dayglow emissions (i.e., measured at oxygen and nitrogen wavelengths) are readily convertible into a geophysically meaningful quantity, ΣO/N2 which, in turn, can be analyzed with simulations by atmospheric models. Research incorporating and comparing observed and modeled ΣO/N2 has established the dramatic responsivity of this ratio to thermospheric dynamical processes that change the abundance of O relative to N2 (e.g., Crowley et al., 2008; Meier et al., 2005; Zhang et al., 2004). A connection between ΣO/N2 and both F-region peak electron density and total electron content is also apparent (e.g., Lean, Meier, et al., 2011; Strickland et al., 2001), surmised to be the result of ionospheric F-region photochemistry that relates the volume densities of electrons to O/N2 in photochemical equilibrium.
So far, this paper has categorically referred to the N2 emission rate in the denominator of the Strickland et al. algorithm as "LBH." Specifically, it means emission from the a1Πg electronic state of the molecule to the X 1Σg+ ground state. Details of the LBH spectrum used by Strickland et al. (1995) and in this paper are taken from Conway (1982). Conway's spectral synthesis includes bands ranging from 127.3 to 360 nm. So, it is important to define what is meant by "LBH." The definition depends on the type of measurement; so a unique Strickland et al. algorithm must be derived for each instrument. For the ICON FUV instrument, the LBH channel covers the wavelength range, 152–162 nm, with peak responsivity at 158 nm (Mende et al., 2017). Convolution of the instrument responsivity with the LBH emission spectrum results in a measurement of 6.8% of the total band emission. FUV remote sensing missions should always report the fraction of the total LBH band that is observed.
1.2. Conceptual Confusion
Much of the current confusion about the thermospheric column O/N2 ratio and its geophysical interpretation concerns the reference altitude, z17, for which the N2 column reaches 1017 cm−2. Some researchers have attempted to assign geophysical significance to this altitude, by postulating that it is a fundamental variable (Yu et al., 2020; Zhang & Paxton, 2011, 2012). Strickland et al. (2012) objected to this interpretation, asserting that "the proper and necessary way to understand O concentration changes from satellite observations of OI 135.6 nm and N2 LBH dayglow from the Earth's disk is not in terms of altitude but in terms of column densities, including total column density."
The present study aims to resolve this argument by demonstrating with explicit examples in Sections 2 and 3, that ΣO/N2 must follow the Strickland et al. interpretation in terms of thermospheric column density (or equivalently optical depth). Strickland et al. found that the relationship between ΣO/N2 and the 135.6 nm/LBH ratio becomes less accurate for column densities less than or greater than NN2 = 1017 cm−2. The way to understand this is to recognize that the emission rates are sensitive to the atmospheric column where the solar EUV radiation is deposited. At column base less than NN2 = 1017 cm−2, the lower accuracy is likely a consequence of not including in the algorithm, the production of airglow by solar EUV photons that have passed through to greater column depths. Similarly, for a column density base in excess of NN2 = 1017 cm−2, there is little or no airglow production, so the numerator and denominator of Equation 1 needlessly include large non-contributing values that reduce the accuracy of the relationship between the column density ratio and the emission rate ratio. An N2 column density base of 1017 cm−2 defines a region that contains most of the photon production and therefore results in the optimal algorithmic relationship for sunlight incident on a terrestrial atmosphere.
1.3. Other Complexities
As aforementioned, the simple relationship between column density ratio and emission rate ratio does depend on the solar zenith angle and the viewing angle from nadir. Consequently, when viewing the disk away from nadir, the azimuth angle relative to the solar azimuth angle also becomes an essential parameter—viewing toward the sun leads to a different result than viewing away from the sun. Figure 1 illustrates the geometric concepts. The azimuth of the instrument line of sight (LOS) is of minimal importance near the subsolar location but becomes critically important for observations approaching twilight.
Later investigations have revealed additional effects that influence the dependence of the column density ratio on the emission rate ratio. For example, variations in the spectral distribution of the solar EUV irradiance can affect the relationship, both over a solar cycle and during solar flares. This is a consequence of wavelength dependence of the atmospheric absorption cross sections that effectively move the energy deposition to different column depths (Strickland et al., 2007). And, as this paper describes, there is actually a slight dependence on atmospheric composition (less than ~2%) of the relationship of the 135.6/LBH ratio to ΣO/N2 when evaluated over a larger range of atmospheres than used by Strickland et al. (1995). As explained later, this is undoubtedly due to the inclusion of physical effects traceable to O2 or to instrumental configuration.
In the most general case, accurate retrieval of ΣO/N2 from measurements of the 135.6/LBH ratio therefore requires knowledge of 1) the solar zenith angle, 2) the view angle from nadir and 3) its azimuth relative to the sun's azimuth (Figure 1), 4) the solar EUV spectral irradiance, and 5) atmospheric concentrations. The solar spectrum and the minimal atmospheric effects are readily accommodated in the algorithm by including a priori information from empirical models that are dependent on solar activity. For nadir viewing, there is no azimuthal effect; even up to 20° from nadir the error from using a fixed azimuth is less than a few per cent. Nonetheless, an accurate algorithm suitable for any atmospheric observation must include all five parameters. Alternatively, this paper proposes a generalized approach for the extraction of ΣO/N2 from radiance ratios.
Section 2 discusses the basic principles that relate the observed airglow ratios to thermosphere ΣO/N2 and Section 3 establishes the irrelevance of the reference altitude. Section 4 assesses effects of neglecting the various parameters in a table lookup algorithm. Section 5 describes the new approach for retrieving column O/N2 from OI 135.6 nm to N2 LBH emissions, a methodology that abolishes the need for a five-parameter table.
2. Why is the Airglow Intensity Ratio Proportional to the Column O/N2 Ratio?
The production of FUV emission is initiated by solar EUV radiation incident on and absorbed by the atmosphere. Following absorption by atmosphere gases, photons with wavelengths shorter than about 45 nm have enough energy to photoionize O and N2, releasing photoelectrons with energy sufficient to excite the FUV dayglow (45 nm corresponds to 15.4 eV photoionization energy of N2 plus 12 eV photoelectron energy). Such photoelectrons can then inelastically collide with O and N2, exciting them to the 5S and a1Πg electronic states, respectively. The relaxation of excited species to their ground states produces OI 135.6 nm and N2 LBH photons. Using altitude for the benefit of visualization, the profiles of the volume emission rates of these species peak between 150 and 200 km, depending on solar activity, atmospheric conditions and solar zenith angle. The topside profiles (at altitudes above the emission peak) mostly follow the O and N2 scale heights with some modification due to the photoelectron flux profile. The bottom sides of the emitting layers (at altitudes below the emission peak) decrease rapidly with decreasing altitude due to extinction of the solar EUV radiation. Meier (1991), and Strickland et al. (1999) provide examples of such profiles.