The Radiative Transfer Characteristics of the O2 Infrared Atmospheric Band in Limb-Viewing Geometry

remote sensing

Letter The Radiative Transfer Characteristics of the O2 Infrared Atmospheric Band in Limb-Viewing Geometry

Weiwei He 1, Kuijun Wu 2,* , Yutao Feng 3, Di Fu 3, Zhenwei Chen 2 and Faquan Li 2

1 City College, Wuhan University of Science and Technology, Wuhan 430083, China; [email protected] 2 State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan National Laboratory for Optoelectronics, Wuhan 430071, China; [email protected] (Z.C.); [email protected] (F.L.) 3 Key Laboratory of Spectral Imaging Technology of Chinese Academy of Sciences, Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, China; [email protected] (Y.F.); [email protected] (D.F.) * Correspondence: [email protected]; Tel.: +86-027-8719-8037

Received: 29 September 2019; Accepted: 15 November 2019; Published: 18 November 2019

1 Abstract: The O2(a ∆g) emission near 1.27 µm provides an important means to remotely sense the thermal characteristics, dynamical features, and compositional structures of the upper atmosphere because of its photochemistry and spectroscopic properties. In this work, an emission–absorption transfer model for limb measurements was developed to calculate the radiation and scattering spectral brightness by means of a line-by-line approach. The nonlocal thermal equilibrium (non-LTE) 1 model was taken into account for accurate calculation of the O2(a ∆g) emission by incorporating the latest rate constants and spectral parameters. The spherical adding and doubling methods were used in the multiple scattering model. Representative emission and absorption line shapes of the 1 3 O (a ∆g, υ = 0) O (X Σ , υ00 = 0) band and their spectral behavior varying with altitude were 2 0 → 2 g examined. The eﬀects of solar zenith angle, surface albedo, and aerosol loading on the line shapes were also studied. This paper emphasizes the advantage of using infrared atmospheric band for remote sensing of the atmosphere from 20 up to 120 km, a signiﬁcant region where the strongest coupling between the lower and upper atmosphere occurs.

Keywords: radiative transfer; limb-viewing; infrared atmospheric band; nonlocal thermal equilibrium; multiple scattering

1. Introduction Measurements of radiation of electronically excited molecular oxygen in the atmospheric 1 3 band O2 (b Σg, υ0 = 0 X Σg, υ00 = 0) at 762 nm and in the infrared atmospheric band O2 1 3 → (a ∆ , υ = 0 X Σ , υ00 = 0) at 1.27 µm provide fundamental probes into energy transfer, g 0 → g compositional structures, and thermodynamic and dynamic features of the upper stratosphere, mesosphere, and lower thermosphere. Compared with the atmospheric band, the infrared atmospheric band has a greater advantage in bright signal (the strongest radiative signal in the visible and 1 near-infrared region of the spectrum) and extended altitude (from 20 to 120 km). Therefore, the O2(a ∆g) airglow is selected as the target source by many space-based instruments aboard rockets and satellites. Mesosphere-Thermosphere Emissions for Ozone Remote Sensing (METEORS) [1], Optical Spectrograph and Infrared Imager System (OSIRIS) [2], and Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) [3] prove that the O3 altitude distribution can be extracted by incorporating

Remote Sens. 2019, 11, 2702; doi:10.3390/rs11222702 www.mdpi.com/journal/remotesensing Remote Sens. 2019, 11, 2702 2 of 18

1 O2(a ∆g) dayglow observations. The remarkable success of Spectroscopy for the Investigation of the Characteristics of the Atmosphere of Mars (SPICAM) instrument onboard the Mars Express orbiter 1 has stimulated interest in taking measurements of O2(a ∆g) dayglow emission and their comparison with photochemical models to yield the Martian water cycle [4]. The Mesospheric Imaging Michelson Interferometer (MIMI) supported by Canada’s StaSci program and the Waves Michelson Interferometer (WAMI) funded by NASA’s MIDEX program use a Michelson interferometer to observe the strong and weak groups of emission lines in the O2 infrared atmospheric band to achieve simultaneous measurements of the Earth temperature and wind [5]. More recently, the the Near-space Wind and Temperature Sensing Interferometer (NWTSI) instrument, which closely follows the WAMI and MIMI concepts, was designed ingeniously to improve the accuracies of wind and temperature 1 measurements in the near space [6]. Last year, Wu et al. reported the application of O2(a ∆g) dayglow for wind observation with a Doppler Asymmetric Spatial Heterodyne (DASH) type instrument from a limb-viewing satellite by measuring Doppler shifts of the emission line O19P18, which were detectable due to their weak self-absorption, bright radiation intensity, and large spectral separation range [7]. High-resolution spectra of the reflected and scattered sunlight near the O2 infrared atmospheric band also play a key role in atmospheric remote sensing, especially for the determination of CO2 mixing ratio columns from space. Several infrared CO2 absorption bands (e.g., 15, 4.3, 2.7, 2.0, and 1.6 µm) can be used for CO2 mixing ratio retrievals by the use of atmospheric pressure and temperature, which can be retrieved from the O2 absorption bands (e.g., 0.76 or 1.27 µm) [8]. The O2 absorption band around 1.27 µm is much weaker than the 0.76 µm band, so the radiative transfer modeling will be more accurate. In addition, the 1.27 µm band is much closer in wavelength to the CO2 absorption bands (1.6 and 2.0 µm), which reduces uncertainties caused by spectral variations in the atmospheric path. 1 Sun et al. evaluated the use of O2(a ∆g) band in spaceborne remote sensing of greenhouse gas with modern spaceborne spectrometers [9]. Dobler et al. discussed the feasibility of determining surface pressure by measuring atmospheric O2 near the 1.27 µm band for determination of CO2 mixing ratio columns with a laser absorption spectrometer [10]. 1 Depending on the atmospheric region, the O2(a ∆g) band can be observed both in emission and absorption, with the latter dominating below about 30 km. The absorption and emission spectral features also interact with each other in atmospheric remote sensing. Sharp et al. reported the impact 1 of ambient O2(a ∆g) on O2 column remote sensing with satellite-based laser using absorption lines in 1 the 1.27 µm band [11]. Bertaux et al. evaluated the contribution of O2(a ∆g) airglow to the retrieval accuracy of CO2 mixing ratio columns in the MicroCarb optical concept [12]. Wu et al. analyzed the 1 spectral interference of scattered sunlight on the O2(a ∆g) dayglow observations and evaluated wind precision with and without the effect of spectral interference [7]. In this paper, we report the radiative transfer characteristics of the O2 infrared atmospheric band in limb-viewing geometry. Section2 describes the photochemical reaction mechanism of the O 2 1 1 infrared atmospheric band, the O2(a ∆g, v’ = 0) emission rates, and the O2(a ∆g, v’ = 0, J) rotational distribution. Section3 presents the results of the limb spectral radiance and the line shape simulations 1 of the O2(a ∆g) emission spectrum and multiple scattering spectrum as well as the total spectral radiance. The effects of solar zenith angle (SZA), surface albedo, and aerosol loading on the line shapes are also discussed in this Section. A concluding summary in Section4 completes this paper.

2. The O2 Infrared Atmospheric Band Molecular oxygen absorbs radiation in its two lowest-lying electronic transitions: O (a1∆ ) O (X3Σ ) at 1.27 µm (the infrared atmospheric band) and O (b1Σ ) O (X3Σ ) 2 g ← 2 g 2 g ← 2 g with bands at 762, 688, and 629 nm, which are referred to as the A, B, and γ atmospheric bands. The absorption line strength and spectral distribution of the four bands are shown in Figure1. The B 1 3 1 3 (b Σ , υ = 1 X Σ , υ00 = 0) and γ (b Σ , υ = 1 X Σ , υ00 = 0) bands do not produce airglow g 0 → g g 0 → g because the excited vibrational states are quenched into the v’ = 0 state before the electronic transition takes place. Compared with the A atmospheric band, the infrared atmospheric band provides a Remote Sens. 2019, 11, 2702 3 of 18 Remote Sens. 2019, 11, x FOR PEER REVIEW 3 of 18 strongerradiative radiative signal, covers signal, a covers much a more much extended more extended altitude altitude region region (between (between ~20 and ~20 120and km120 kmin the in dayglow), and suffers less from the self-absorption of O2 molecules in the ground state. the dayglow), and suﬀers less from the self-absorption of O2 molecules in the ground state.

Figure 1. The absorption line strength and spectral distribution of the O2 infrared atmospheric band Figure 1. The absorption line strength and spectral distribution of the O2 infrared atmospheric band and the O2 atmospheric band (from HITRAN [13]). and the O2 atmospheric band (from HITRAN [13]). 1 2.1. The O2(a ∆g) Photochemistry 2.1. The O2(a1Δg) Photochemistry The key to accurate calculation of the limb spectral radiance of the O2 infrared atmospheric band dependsThe notkey onlyto accurate on an accuratecalculation knowledge of the limb of spectral the atmospheric radiance of and the spectroscopic O2 infrared atmospheric parameters band but depends not only on an accurate knowledge of the1 atmospheric and spectroscopic parameters but also on a detailed accounting of all sources of O2(a ∆g)[14]. Remote sensing of airglow emissions 1 hasalso contributed on a detailed significantly accounting toof theall sources current of understanding O2(a Δg) [14]. Remote of the production sensing of andairglow loss emissions mechanisms has contributed significantly to the1 current understanding of the production1 and loss mechanisms of of electronically excited O2(a ∆g). The metastable molecule O2(a ∆g) is formed in the processes of electronically excited O2(a1Δg). The metastable molecule O2(a1Δg) is formed in the processes of photodissociation of O3 and O2 by absorption of ultraviolet radiation of the sun. The first commonly photodissociation of O3 and O2 by absorption of ultraviolet radiation of the sun. The first commonly accepted model of O3 and O2 photolysis was developed by Thomas (1984) [15] and Harris and Adams (1983)accepted [16 ].model M.G. of Mlynczak, O3 and O S.2 photolysis Solomon, andwas D.S.developed Zaras significantlyby Thomas (1984) improved [15] and this Harris model and in 1993 Adams (for the(1983) sake [16 of]. brevity,M.G. Mlynczak, this model S. Solomon, is called MSZ)and D.S. [14 Zaras]. In 2011, significantly Yankovsky improved et al. developed this model ain complete 1993 (for the sake of brevity, this model is called MSZ) [14]. In 2011, Yankovsky et al. developed a complete model of electronic vibrational kinetics of O2 and O3 photolysis products (YM2011) [17,18]. In 2017, Martyshenkomodel of electronic and Yankovsky vibrational solved kinetics the of problemO2 and O of3 photolysis systematic products overestimation (YM2011) in [ the17,1 retrieve8]. In 2017, of ozoneMartysh concentrationsenko and Yankovsky by taking thesolved electronic the problem vibrational of systematic kinetics of overestimation photolysis products in the of retrieveozone and of ozone concentrations by1 taking the electronic1 vibrational kinetics of photolysis products of ozone and molecular oxygen O2(b Σg, v) and O2(a ∆g, v) into the scheme of electronic vibrational kinetics of the molecular oxygen O (b1 ,v) and O (a1 ,v) into the scheme of electronic vibrational kinetics of products of O3 and O22 photolysisg [19].2 Figureg 2 shows the dayglow production mechanism of the O 2 infraredthe products atmospheric of O3 and band O2 photolysis [20]. [19]. Figure 2 shows the dayglow production mechanism of the O2 infraredWith the atmospheric values of theband rates [20]. of photodissociation and photoexcitation and the values of the 1 rate constantsWith the ofvalues the processesof the rates considered of photodissociation by Yankovsky and et photoexcitation al. [17,19], the Oand2(a the∆g )values number of density,the rate 1 nconstants1 , can of the be calculatedprocesses assumingconsidered photochemical by Yankovsky equilibrium. et al. [17,19] Figure, the O3 2shows(a Δg) number the amounts density, of O2(a ∆g) n 11 , can be calculated assuming photochemical equilibrium. Figure 3 shows the amounts of O2O()(a2 a ∆g g) attributable to each source of predominant mechanisms. The source corresponding to each curveO2(a1Δ isg) describedattributable and to markedeach source in the of figure predominant legend. mechanism It is apparents. The from source this figure corresponding that the primary to each 1 1 sourcecurve is for described O2(a ∆g )and is generated marked in directly the figure upon legend. photolysis It is ofapparent O3. The from coproduct this figure O( D) that through the primary energy transfersource for emerges O2(a1Δ asg) is the generated secondary, directly parallel upon contribution photolysis andof O dominates3. The coproduct the emission O(1D) through process energy above 1 100transfer km. Theemerges photoexcitation-induced as the secondary, parallel O2(b contributionΣg) becomes and a major dominates contributor the emission between process 65 and above 85 km. 100 1 km. The photoexcitation-induced O()2 b g becomes a major contributor between 65 and 85 km.

RemoteRemote Sens. Sens. 20192019,, 1111,, x 2702 FOR PEER REVIEW 44 of of 18 18 Remote Sens. 2019, 11, x FOR PEER REVIEW 4 of 18

Figure 2. Dayglow production mechanism of the O2 infrared atmospheric band [20]. Figure 2. Dayglow production mechanism of the O 2 infraredinfrared atmospheric atmospheric band band [ [20]]..

1 Figure 3. The modeled1 O (a ∆ ) concentration proﬁle and respective contributions of each Figure 3. The modeled O2(a Δg2) concentrationg profile and respective contributions of each production Figure 3. The modeled O2(a1Δg) concentration profile and respective contributions of each production mechanism.production mechanism. mechanism. 1 2.2. The O (a ∆g, v’ = 0) Emission Rates 2 1 2.2. The O2(a 1Δg, v’ = 0) Emission Rates 2.2. The O2(a Δg, v’ = 0) Emission Rates 1 The excited vibrational states O2(a 1∆g, ν0 1) are quenched into the ground vibrational state 1  The1 excited vibrational states O2 (a g ,  ≥ 1) are quenched into the ground vibrational state O2(aThe∆g, νexcited0 = 0) muchvibrational more rapidlystates thanO2 (a theg ,electronic 1) are transition. quenched Figure into 4the shows ground the modeledvibrational number state 1 O2 (a 1g , =0) much1 more rapidly than the electronic transition. Figure 4 shows the modeled densitiesO2 (a g , of =0) O2(a much∆g) molecules more rapidly at ν0 = than0, ν 0 the= 1 , electronic and ν0= 2 transition.as a function Fig ofure altitude. 4 shows As the can model be seen,ed number densities of O2(a1Δg) molecules at  =0 ,  =1 , and  =2 as a function of altitude. As can be number densities of O2(a1Δg) molecules at  =0 ,  =1 , and  =2 as a function of altitude. As can be 1 seen, the contributions from the excited vibrational states O2 (a 1g , 1) are negligible, and seen, the contributions from the excited vibrational states O2 (a g , 1) are negligible, and

Remote Sens. 2019, 11, 2702 5 of 18

Remote Sens. 2019, 11, x FOR PEER REVIEW 5 of 18 the contributions from the excited vibrational states O (a1∆ , ν 1) are negligible, and vibrational 2 g 0 1  vibrational distribution of the ground vibrational1 state O2 (a≥g , =0) dominates the infrared distribution of the ground vibrational state O2(a ∆g, ν0 = 0) dominates the infrared atmospheric band: atmospheric band:

n 1 n 1 O (ann∆ ,ν11=0) O (a ∆ ).. (1) 2 O22g (aa0gg , =0)≈ 2 O (g ) (1)

1 1 = = = FigureFigure 4. 4. TheThe calculatedcalculated relativerelative contributioncontribution of O2(a(a Δ∆gg) )molecules molecules at at ν0=00,, ν0 =11,, and andν0  2=2as as a functiona function of altitude.of altitude.

1 3 The local emission rate of the infrared atmospheric band O2(a ∆g,13υ0 = 0) O2(X Σg, υ00 = 0) , The local emission rate of the infrared atmospheric band O22 (aXgg ,  0)→  O (  ,   0) , i.e., η1.27µm, is obtained by multiplying its vibrational distribution n ( 1 = ) and the Einstein  On2 a ∆g,ν0 0 i.e., 1.27μm , is obtained by multiplying its vibrational distribution O (a 1  ,  =0) and the Einstein transition probability A1.27µm [3]: 2 g

transition probability A1.27μm [3]: η = A µ n 1 . (2) 1.27µm 1.27 m O2(a ∆g,ν0=0)  =An1.27μm 1 . 1.27μm O2 (a g ,  =0) (2) Figure5 shows the calculated volume emission rate (VER) profiles of the O infrared atmospheric Figure 5 shows the calculated volume emission rate (VER) profiles2 of the O2 infrared bandatmospheric under daytime band under condition daytime in the fourcondition seasons in inthe the four Northern seasons Hemisphere in the N (simulatedorthern Hemisphere by taking the(simulated mid-latitude by taking for example). the mid-latitude As is apparent, for example there). As are is onlyapparent minor, there diff erencesare only between minor differences different seasons.between Thedifferent VER seasons. for the summer The VER illuminated for the summer atmosphere illuminated (July) atmos is slightlyphere larger(July) is at slightly low altitude. larger Theat low major altitude reason. The for major this behavior reason for is the this consequence behavior is ofthe larger consequence solar illumination of larger solar at north illumination latitude in at summertime.north latitude The in summertime spring volume. The emission spring becomes volume emission the largest becomes over the the altitude largest region over the from altitude 30 to 50region km because from 30 the to 50 ozone km because content isthe the ozone most content abundant is the in spring.most abundant in spring.

Remote Sens. 2019, 11, x FOR PEER REVIEW 6 of 18 Remote Sens. 2019, 11, 2702 6 of 18

1 Figure 5. The calculated volume emission rate (VER) profiles of the O2(a ∆g) dayglow in the fourFigure seasons. 5. The calculated volume emission rate (VER) profiles of the O2(a1Δg) dayglow in the four seasons. 1 2.3. The O2(a ∆g, v’ = 0, J) Rotational Distribution 2.3. The O2(a1Δg, v’ = 0, J) Rotational Distribution1 3 The spectral distribution of the O (a ∆ , υ = 0) O (X Σ , υ00 = 0) vibrational transition band 2 g 0 → 2 g 13( 1 = ) dependsThe onspectral the rotational distribution distribution of the O of22 ( theaX Ogg ,2a ∆ 0)g, υ0 O (0 state  , and   0) their vibrational individual transition line shapes. band 1 The emission rate per O2(a ∆g, υ0 = 0) molecule1 ε(J0, J00 ) of a given rotational transition J0 J00 depends on the rotational distribution of the O2 (a g , 0) state and their individual line shapes.→ is obtained by multiplying the particular Einstein coefficient for the vibration–rotation transition AJ ,J The emission rate per O (a1 , 0) molecule  (,)JJ  of a given rotational transition0 00 with the relative population of the2 upperg level: JJ  is obtained by multiplying the particular Einstein coefficient for the vibration–rotation g ( hcE (J ) kT ) transition AJJ,  with the relative population ofJ 0theexp upper level:v 0 / R (J J00 ) = A · − ε 0, J0,J00 (3) Qtot(T) gJ exp( hcE v ( J ) / kT R ) (,)JJA   JJ,  (3) where J0 and J00 are initial and final values of the total angularQTtot momentum() of the transition, respectively; E (J ) is the upper state rotational term value; g is the statistical weights of the initial level; k is the wv here0 J  and J  are initial and final valuesJ 0 of the total angular momentum of the transition, Boltzmann constant; h is the Planck constant; c is the speed of light; TR is the rotational temperature respectively; EJv () is the upper state rotational term value; gJ  is the statistical weights of the assumed to be in thermal equilibrium with the ambient atmospheric temperature; and Qtot(T) is the initial level; k is the Boltzmann constant; h is the Planck constant; c is the speed of light; TR is the electronic–rotational partition function given as [21] rotational temperature assumed to be in thermal equilibrium with the ambient atmospheric temperature; and QT() is the electronicX–rotational partition function given as [21] tot Qtot(T) = gJ exp( hcEv(J0)/kTR). (4) 0 · − Q( T )J0 g  exp(  hcE ( J ) / kT ) tot J v R . (4) J Figure6a shows the emission spectrum as a function of the transition wavelength, which is Figure 6a shows the emission spectrum as a function of the transition wavelength, which is displayed on the right scale. For comparison, the absorption line intensity from the HITRAN displayed on the right scale. For comparison, the absorption line intensity from the HITRAN database database [13] can also be found in this figure (left scale). As can be seen, the emission lines and the [13] can also be found in this figure (left scale). As can be seen, the emission lines and the absorption absorption ones show different distributions in spectrum. By simply doing a division, we could find ones show different distributions in spectrum. By simply doing a division, we could find the ratio of the ratio of emission to absorption line strength for each line, which is shown in Figure6b. This ratio is emission to absorption line strength for each line, which is shown in Figure 6b. This ratio is a a temperature-dependent value, varying with the total angular momentum of the transition. temperature-dependent value, varying with the total angular momentum of the transition.

RemoteRemoteRemote Sens. Sens. Sens.2019 2019 2019, ,11 ,11 11,, 2702, xx FORFOR PEER REVIEWREVIEW 7 of 7187of of 1818

Figure 6. (a) The emission and absorption spectrum as a function of the transition wavelength. (b) Figure 6. (a) The emission and absorption spectrum as a function of the transition wavelength. (b) The The ratio of emission to absorption line strength for each line. ratioFigure of emission6. (a) The to emission absorption and line absorption strength forspectrum each line. as a function of the transition wavelength. (b) The ratio of emission to absorption line strength for each line. 3.3. Limb Limb Spectral Spectral RadianceRadiance

3. LimbFigure Spectral 7 illustrates Radiance the construction of the path model in limb-viewing geometry. For the O2 Figure7 illustrates the construction of the path model in limb-viewing geometry. For the O 2 infrared atmospheric band, a strong self-absorption appears because of the relatively large line infraredFigure atmospheric 7 illustrates band, the a strongconstruction self-absorption of the path appears model because in limb of the-viewing relatively geometry. large line For strength the O2 strength of ground state. Therefore, the limb spectral radiance is not simply a straightforward Abel- ofinfrared ground atmospheric state. Therefore, band, the a strong limb spectral self-absorption radiance appears is not simplybecause a straightforwardof the relatively Abel-type large line type integration of the VER profile along the path between the emitter and the observer. The integrationstrength of ofground the VER state. proﬁle Therefore, along thethe pathlimb between spectral theradiance emitter is andnot simply the observer. a straightforward The brightness Abel is- brightness is modified by the attenuation along the line-of-sight path. In addition, limb brightness modiﬁedtype integration by the attenuation of the VER along profile the line-of-sight along the path path. betwee In addition,n the emitter limb brightness and the measurements observer. The measurements unavoidably include Rayleigh scattering and Mie scattering, which will be subject to unavoidablybrightness is includemodified Rayleigh by the attenuation scattering and along Mie the scattering, line-of-sight which path. will In be addition, subject to limb the extinctionbrightness the extinction process in the O2 infrared atmospheric band spectral region. For accurate calculation processmeasurements in the O unavoidablyinfrared atmospheric include Rayleigh band spectral scattering region. and ForMie accuratescattering calculation, which will of be the subject spectral to of the spectral brightness2 of the O2 infrared atmospheric band, the absorption for both emission lines brightnesstheand extinction the scattered of the proces O sunlight2 infrareds in the continuum atmospheric O2 infrared background band, atmospheric the must absorption bandbe taken spectral for into both consid region. emissioneration, For lines accurate especially and the calculation at scattered low sunlightoftangent the spectralcontinuum heights brightness. background of the O must2 infrared be taken atmospheric into consideration, band, the especiallyabsorption at for low both tangent emission heights. lines and the scattered sunlight continuum background must be taken into consideration, especially at low tangent heights.

Figure 7. The construction of the path model in limb-viewing geometry. Figure 7. The construction of the path model in limb-viewing geometry.

Figure 7. The construction of the path model in limb-viewing geometry.

Remote Sens. 2019, 11, 2702 8 of 18

1 3.1. O2(a ∆g, v’ = 0) Emission Spectrum 1 As described above, O2(a ∆g, v’ = 0) distribution is in collisional and chemical balance. At lower 1 altitude, the quenching-related decay of O2(a ∆g, v’ = 0) is signiﬁcant because the probability of 1 quenching determines the lifetime of O2(a ∆g, v’ = 0), while at higher altitude, the local thermodynamic equilibrium (LTE) is broken because of the presence of constant sources of excited molecular oxygen 1 due to O2 and O3 photodissociation. O2(a ∆g) is formed mainly by photolysis of O3 in the Hartley band below about 100 km and by energy transfer from O(1D) above that altitude [20,22]. The collisional 1 1 quenching of O2(b Σg) with N2 and O2 also contributes to the production of O2(a ∆g), especially at 1 65–85 km. Thus, the distribution of O2(a ∆g, v’ = 0) is not strongly connected to the kinetic temperature and cannot be given by the Boltzmann distribution. This behavior is referred to as nonlocal thermal equilibrium (non-LTE). 1 3 In the non-LTE case, the source function of the O (a ∆ , υ = 0) O (X Σ , υ00 = 0) transition 2 g 0 → 2 g is given by [23] hc 1 1 J(ν) B(ν, T ) exp( ( )E 1 ) (5) K O2(a ∆ ,ν =0) ≈ − k T 1 − T g 0 O2(a ∆ g,ν0=0) K where B(ν, TK) is the value of the Planck function at wavenumber ν and temperature 1 1 T ,E 1 = 7882.42 cm is the vibrational energy of the O (a ∆ , υ = 0) state, T 1 K O2(a ∆g,ν0=0) − 2 g 0 O2(a ∆g,ν0=0) is the vibrational temperature and is expressed as

E 1 O2(a ∆ g,ν0=0) T 1 = . (6) O2(a ∆ ,ν =0) g ! g 0 nO (X3Σ ,ν =0) O (a1∆ ,ν =0) k ln 2 g 00 2 g 0 n ( 1 = ) g ( 3 = ) O2 a ∆ g,ν0 0 O2 X Σg,ν00 0

1 Here, g 1 and g 3 refer to the statistical weight of the O (a ∆ ) and the O2(a ∆g,ν0=0) O2(X Σg,ν00 =0) 2 g 1 O2(b Σg) states. It is important to note that the vibrational temperature, which, being substituted in Boltsmann distribution, gives the vibrational level population. Correspondingly, at the LTE conditions, the vibrational temperature becomes equal to a kinetic one. When the self-absorption process is considered, the limb spectral brightness of any given rotational line in the O2 infrared atmospheric band can be carried out numerically by [23]

Z zU IE(ν)l = IE(ν)l 1 exp( α(ν)lul) + J(ν)lα(ν)lnl τ(ν, z, zU)dz (7) − − zL where z is a certain position along the line of sight between the observation point zobs and the point zs at the furthest extent of the limb; zU and zL are the upper and lower boundaries of layer l, respectively; α(ν) is the molecular absorption coeﬃcient; n(z) is the number density of O2 molecules in the ground state; u = n (zU zL) is the layer absorber amount of layer l; and τ(ν, z, z ) is the atmospheric l l − obs transmission caused by self-absorption eﬀect between z and zobs, which can be given by

Z zobs ! τ(ν, z, zobs) = exp α(ν, z0)n(z0)dz0 . (8) − zs

It is obvious that the forward model for the spectral brightness has a strong dependence on the atmospheric temperature, which is concretely embodied in the self-absorption cross section, the line strength, and the Doppler width. In addition, the spectral brightness has a linear dependence on the VER proﬁle. Figure8 shows the calculated limb spectral brightness and the spectral radiance of the target layer at diﬀerent tangent heights using the non-LTE model. As illustrated, the spectral radiance of the target layer comes closer to the limb spectral brightness at relatively high tangent heights (up to ~60 km), while at low altitude, the target layer radiance is relatively small compared Remote Sens. 2019, 11, 2702 9 of 18

Remote Sens. 2019, 11, x FOR PEER REVIEW 9 of 18 with the limb brightness. Two factors explain this phenomenon: (1) O2 number density leads to a 1 strong self-absorption at low altitude and (2) the lower the altitude, the smaller the O2(a ∆g) VER.

FigureFigure 8. 8.The The calculated calculated limb limb spectral spectral brightness brightness and the and spectral the spectral radiance radiance of the target of the layer target at di layerﬀerent at tangentdifferent heights. tangent heights.

FigureFigure9 shows9 shows the the spectral spectral brightness brightness and and the the atmospheric atmospheric transmittance transmittance of a relativelyof a relatively strong strong line (R Q at 1264.06 nm) of O infrared atmospheric band at the tangent height of 50 km. For comparison, line9 10 (R9Q10 at 1264.06 nm)2 of O2 infrared atmospheric band at the tangent height of 50 km. For thecomparison, spectral line the brightness spectral neglecting line brightness self-absorption neglecting is alsoself- displayedabsorption in is the also same displayed figure. As in illustrated, the same the self-absorption of the R Q line is significant even at 50 km tangent height. As a type of Doppler figure. As illustrated, the self9 10-absorption of the R9Q10 line is significant even at 50 km tangent height. lineAs a shape, type theof Doppler value of line the absorptionshape, the crossvalue section of the isabsorption large at the cross line section center andis large decreases at the toward line center the twoand wings, decreases so the toward process the of self-absorptiontwo wings, so leads the process to a spectral of self line-absorption broadening leads for theto a emission spectral line. line Duebroadening to this broadening for the emission effect, the line. WAMI, Due MIMI, to this and broadening NWTSI instruments effect, the WAMI, cannot provide MIMI, and meaningful NWTSI Dopplerinstruments temperature, cannot provide and the meaningful rotational Doppler temperatures temperature need to, and be measuredthe rotational by observingtemperatures relative need radiationto be measured intensity by of observing three rotational relative lines. radiation intensity of three rotational lines.

Remote Sens. 2019, 11, 2702 10 of 18 Remote Sens. 2019, 11, x FOR PEER REVIEW 10 of 18 Remote Sens. 2019, 11, x FOR PEER REVIEW 10 of 18

Figure 9. The spectral brightness of line R9Q10 with and without self-absorption as well as its FigureFigure 9. 9.TheThe spectral spectral brightness brightness of of line line R9Q R109Q with10 with and and without without self self-absorption-absorption as as well well as as its its atmospheric transmission at 50 km tangent height. atmosphericatmospheric transmission transmission at at50 50km km tangent tangent height. height.

The integral radiance and limb-view weight work together to affect the retrieval accuracy in TheThe integral integral radiance radiance and and limb limb-view-view weight weight work work together together to toaffect aﬀect the the retrieval retrieval accuracy accuracy in in satellite remote sensing applications. The radiance values and weight profile of the R9Q10 line varying satellitesatellite remote remote sensing sensing applications. applications. The The radiance radiance values values and and weight weight profile proﬁle of of the the R9 RQ910Q 10lineline varying varying with the tangent altitude are shown in Figure 10. At lower heights, the contribution of the target layer withwith the the tangent tangent altitude altitude are are shown shown in inFigure Figure 10 10. At. Atlower lower heights, heights, the the contribution contribution of ofthe the target target layer layer is very small because of the small VER and strong self-absorption. As the tangent height increases, is isvery very small small because because of ofthe the small small VER VER and and strong strong self self-absorption.-absorption. As As the the tangent tangent height height increases increases,, the limb-view weight also increases, which leads to an increase in measurement precision. However, thethe limb limb-view-view weight weight also also increases, increases, which which leads leads to toan anincrease increase in inmeasurement measurement precision precision.. However, However, at higher altitudes, the integral radiance goes down exponentially with height, which is certain to at athigher higher altitudes, altitudes, the the integral integral radiance radiance goes goes down down exponentially exponentially with with height height,, which which is iscertain certain to to cause decrease in the signal-to-noise ratio. Therefore, if the R9Q10 line is used as the target source, the causecause decrease decrease in the in the signal signal-to-noise-to-noise ratio. ratio. Therefore, Therefore, if the if R the9Q10 R 9lineQ10 isline used is as used the astarget the targetsource, source, the atmospheric information of the tangent point can be obtained from 20 to 90 km, where both the atmosphericthe atmospheric information information of the of tangent the tangent point point can be can obtained be obtained from from 20 to 20 90 to km,90 km, where where both both the the integral radiance and the weight value are large enough. integralintegral radiance radiance and and the the weight weight va valuelue are are large large enough. enough.

Figure 10. The integral radiance (a) and limb-view weight (b) of the R Q line varying with the Figure 10. The integral radiance (a) and limb-view weight (b) of the R99Q10 line varying with the Figure 10. The integral radiance (a) and limb-view weight (b) of the R9Q10 line varying with the tangent altitude. tangent altitude.

Remote Sens. 2019, 11, 2702 11 of 18

3.2. Scattering Absorption Spectrum

The brightness spectrum of the O2 infrared atmospheric band scattered by the Earth’s atmosphere is strongly marked by rotational lines of molecular oxygen. Considering source terms reﬂected by clouds and the Earth’s surface, and scattered by molecules and particles, the limb brightness spectrum with absorption characteristics can be expressed as [24] Z " Z # ∞ ∞ I (υ, zt) = [ηs(υ, s) + η (υ, s)] exp n(s0)σa(s0)ds0 ds (9) S G − −∞ −∞ where ηs(υ, s) = Γ(υ, s)na(s)σs(υ) (10) " Z # ∞ n(s0)σ(s0)D(υ, s0)ds0 Γ(υ, s) = Γ (υ) exp . (11) ∞ · − Z(s) cos δ

Here, ηs(υ, s) is the Rayleigh or Mie scattering rate per unit volume, σs(υ) is the total Rayleigh or Mie scattering cross section, Γ(υ, s) is the attenuated solar flux, Γ (υ) is the top-of-atmosphere solar ∞ spectral irradiance, δ is the SZA, and ηG(υ, s) is the volume scattering rate at the scattering altitude due to ground reflected light. For our study, we adopted the expression of ηG(υ, s) provided by Hays, et al. [25]. Figure 11 shows the limb spectral radiance of the scattered sunlight at 1.27 µm and the absorbance of the target layer at tangent heights of 40, 60, and 80 km. The spherical adding and doubling methods developed by Abreu, et al. were adopted in this work [26]. As illustrated, the scattered sunlight radiance as well as the absorbance of the target layer goes down exponentially with tangent height. The O2 absorption spectrum is quite similar to limb emission spectrum in shape (shown in Figure8), while emission lines are much narrower than absorption lines because pressure broadening can be ignored at high altitude. They also have different distributions in spectrum because the emission rate and the absorption cross section are influenced differently by atmospheric temperature due to their different populations of rotational levels (as noted before). In order to better follow the spectral shape development as a function of tangent height, a close-up of one of these lines (red in Figure 11) is shown in Figure 12 after normalization to the maximum intensity (the asymptotic value). As can be seen, the absorption lines are very broad at tangent heights of 5 and 10 km because of the atmospheric scattering from low altitudes, where collision broadening dominates. At tangent heights higher than 20 km, the whole line shape becomes a superposition of two components: (1) a narrow one, which is sensitive to the atmospheric condition at the tangent point, and (2) a much broader component, which is contributed by the reflection and scattering taking place near the ground and the lower atmosphere. Remote Sens. 2019, 11, 2702 12 of 18 RemoteRemote Sens. Sens. 2019 2019, 11, 11, x, xFOR FOR PEER PEER REVIEW REVIEW 1212 of of 18 18

FigureFigureFigure 11. 11.11. TheThe The limb limblimb spectral spectralspectral radiance radianceradiance of ofof the thethe scattered scatteredscattered sunlight sunlightsunlight at atat 1.27 1.271.27 μmµ μmm and andand the thethe absorbance absorbanceabsorbance of ofof the thethe targettargettarget layer layer layer at at at different di differentﬀerent tangent tangent tangent heights. heights. heights.

FigureFigureFigure 12. 12. 12. Variation VariationVariation in inin thethe the absorption absorptionabsorption lineline line shape shape shape with with with tangent tangent tangent height heights. heights.s. TheThe The line lineline shape shapeshape is isis broad broadbroad at atat lower lowerlower tangenttangenttangent heights heightsheights of ofof 5 5 5and andand 10 1010 km kmkm and andand becomes becomesbecomes a a asuperposition superpositionsuperposition of ofof a a anarrow narrownarrow component componentcomponent and andand a a amuch muchmuch broaderbroaderbroader one one one above above above 20 20 20 km. km. km.

3.3. Total Spectral Radiance 3.3.3.3. Total Total Spectral Spectral Radiance Radiance The spectral brightness that would be observed either in absorption or in emission can be TheThe spectral spectral brightness brightness that that would would be be observed observed either either in in abs absorptionorption or or in in emission emission can can be be calculated using the above-described airglow emission or scattering absorption radiative transfer calculatedcalculated using using the the above above-described-described airglow airglow emission emission or or scattering scattering absorption absorption radiative radiative transfer transfer models, respectively. The scattering absorption spectrum IS is obtained separately using the line- models, respectively. The scattering absorption spectrum IS is obtained separately using the line-

Remote Sens. 2019, 11, 2702 13 of 18

Remote Sens. 2019, 11, x FOR PEER REVIEW 13 of 18 models, respectively. The scattering absorption spectrum IS is obtained separately using the line-by-line multiple scattering radiative transfer model. The emission brightness I is calculated under the by-line multiple scattering radiative transfer model. The emission brightnessE I is calculated under assumption that the attenuation along the line-of-sight path is caused by singleE scattering and the assumption that the attenuation along the line-of-sight path is caused by single scattering and self-absorption. Total spectral radiance ITotal in both emission and absorption can be obtained by I combiningself-absorption these. Total two componentsspectral radiance together Total simply in both because emission the scattering and absorption and emission can beprocesses obtained areby independentcombining these of each two othercomponents in both together physical andsimply mathematical because the models scattering [27]: and emission processes are independent of each other in both physical and mathematical models [27]: ITotal = IE + IS. (12) IIITotal E S . (12) The surface characteristics play a key role in determining the line shape of the total spectral brightness for limb observation. Figure 1133 shows the asymptotic value and line center intensity as a function of albedos at thethe tangenttangent heightheight ofof 1515 km.km. The asymptoticasymptotic value increases with increasingincreasing albedo, while the line center intensity remains the same.same.

Figure 13. The line shape of the total spectral brightness as a function of albedos at the tangent height of 15 km.

Figure 1414 showsshows thethe totaltotal spectralspectral brightnessbrightness ofof thethe RR99Q1010 lineline for for albedos albedos equal equal to to 0.2 0.2 at different diﬀerent tangent heights.heights. As As illustrated, the total spectral brightness can be observed both in absorption and emission, withwith thethe latter latter dominating dominating above above 20 km.20 km. The T Oh2e infraredO2 infrared atmospheric atmospheric band band line is line very is broad very atbroad low at altitudes low altitudes but observable but observable in narrow in narrow emission emission at higher at higher altitude altitude because because thermal thermal motion motion rather thanrather collision than collision dominates dominates the broadening the broadening process. Note process. that Note the wings that theof the wings line vary of the signiﬁcantly line vary withsignificantly tangent with height, tangent both inheight, width both and in magnitude. width and The magnitude. line center, The however, line center, develops however, a peak develops in the absorptiona peak in the valley. absorption At higher valley tangent. At higher heights tangent (>20 km), heights the asymptotic(>20 km), the value asymptotic goes down value exponentially, goes down butexponentially, the general but shape the ofgeneral the lines shape remains of the unchanged. lines remains unchanged.

Remote Sens. 2019, 11, 2702 14 of 18 Remote Sens. 2019, 11, x FOR PEER REVIEW 14 of 18

Figure 14. The total spectral brightness of the R 9QQ1010 lineline varying varying with with tangent tangent heights. heights.

TheThe SZA SZA and and atmospheric atmospheric aerosol aerosol have have significant significant influence influence on on both both the the asymptotic asymptotic value value and and lineline center center intensity. intensity. Figure Figure 1155 showsshows the the variations variations in in total total spectral spectral brightness brightness with with the the SZA SZA and and atmosphericatmospheric aerosol atat the the tangent tangent heights heights from from 0 to 0 100to 10 km.0 km. Wavelength Wavelength is the is abscissa, the abscissa, tangent tangent height heightis the ordinate,is the ordinate, and the and scale the of scale the spectralof the spectral brightness brightness is made is bymade the pseudoby the pseudo color intensity color inten in eachsity ingraph. each Several graph. features Several are features apparent are in apparent this figure. in this The asymptoticfigure. The intensity asymptotic increases intensity by approximately increases by approximatelytwo times when two the SZAtimes grows when from the SZA zero togrows 45◦. Thefrom impact zero to of this45°. eTheffect impact can be explainedof this effect by Mie canand be explainedRayleigh scatteringby Mie and phase Rayleigh functions: scattering scattering phase angle functions: becomes scattering smaller angle as the becomes SZA increases, smaller and as the the SZAdecreasing increases, scattering and the angle decreasing leads to an scattering increase angle in scattered leads signal.to an increase The variation in scattered in the line signal center. The is variationnot as large in the as it line is in center the asymptote. is not as large This as behavior it is in the is due asymptote. to the fact This that behavior the intensity is due in to the the line fact center that thedepends intensity not only in the on linethe amount center dependsof scattered not light only but on also the on amount absorption of scattered and emission. light The but variation also on absorptionin the SZA and changes emission. the path The length variation of the in solar the SZA radiation changes passing the path through, length which of the causes solar a changeradiation in passingthe solar through, energy beingwhich deposited causes a change at different in the heights. solar energy As the columnbeing deposite densitiesd at through different the heights O2 and. As O3 theincrease, column the densities optical through depth increases, the O2 and while O3 increase, the photolysis the optical rate depth decreases. increases, At tangent while the heights photolysis above 1 rate80 km, decreases. the SZA has At a tangent smaller heightseffect on above the O2 (a 80 ∆ km,g) concentration the SZA has because a smaller of the effect gradual on disappearance the O2(a1Δg) 1 1 concentrationof O3. The production because of of O( theD) grad becomesual disappearance the dominant source of O3. ofThe O2 (a production∆g), and this of O( production1D) becomes steadily the dominantdecreases withsource the of SZA. O2(a1 TheΔg), atmosphericand this production aerosol is steadily important decreases in determining with the theSZA asymptotic. The atmospheric intensity. aerosolSimilar is to important SZA, the centerin determining intensity the is not asymptotic a strong functionintensity. of Similar the atmospheric to SZA, the aerosol. center intensity The center is notintensity a strong variations function with of the Mie atmospheric scattering are aerosol. mostly The due center to changes intensity in extinctionvariations coe withffi cientMie scattering caused by arethe mostly existence due of to aerosol. changes Changes in extinction in the coefficient intensity of caused the absorption by the existence feature atof lowaerosol. tangent Changes height in lines the intensityof sight are of maskedthe absorption by the dominantfeature at emissionlow tangent feature height of thelines mesosphere. of sight are masked by the dominant emission feature of the mesosphere.

Remote Sens. 2019, 11, 2702 15 of 18 Remote Sens. 2019, 11, x FOR PEER REVIEW 15 of 18

Remote Sens. 2019, 11, x FOR PEER REVIEW 15 of 18

FigureFigure 15. 15. TheThe variations in in total total spectral spectral brightness brightness with withthe solar the zenithsolar angle zenith (SZA) angle and (SZA atmospheric) and atmosphericaerosolFigure at theaerosol 15. tangent The at variationsthe heights tangent from in heights total 0 to spectral 100 from km. 0 brightness to 100 km. with the solar zenith angle (SZA) and atmospheric aerosol at the tangent heights from 0 to 100 km. InIn order order to tovalidate validate the the emission emission–absorption–absorption transfer transfer algorithm, algorithm, we we compared compared our our model model results results withwith those those Inobtained obtained order to fromvalidate from MODTRAN4 the emission– [[absorption2828]] andand the the transfer TIMED–SABER TIMED algorithm,–SABER measurementswe measurements compared our [29 model [,3029,30] for results] for the samethe samelatitude latitudewith (48.9 those (◦48.9N), obtained° dateN), date (10 from July)(10 MODTRAN4 July) and and SZA SZA (35.5 [28 (35.5]◦ ).and Figure° the). Figure TIMED 16a shows16–SABERa shows the measurements comparisonthe comparison between [29,30 between] for our the model our modeland the sameand MODTRAN4 thelatitude MODTRAN4 (48.9 result°N), date atresult tangent (10 July) at tangent height and SZA of height 20(35.5 km° ).ofwith Figure 20 akm surface16 awith shows albedoa surfacethe comparison of 0.2 albedo and anbetween of aerosol 0.2 and our model an aerosolof stratosphericmodel model and of thestratospheric background, MODTRAN4 whichbackground result validates at tangent, which the height multiplevalid ofates 20 scattering kmthe withmultiple a algorithm. surface scattering albedo Due algorithm.of to 0.2 the and resolution an Due aerosol model of stratospheric background, which validates the multiple scattering1 algorithm. Due tolimitation the resolution of MODTRAN4, limitation of the MODTRAN4, MODTRAN the result MODTRAN was calculated result at was 1 cm calculated− . The spectral at 1 cm resolution−1. The to the resolution1 limitation of MODTRAN4, the MODTRAN result was calculated at 1 cm−1. The spectralcan reach resolution 0.001 cm can− withreach our 0.001 model, cm−1 in with which our the model multiple, in which scattering the multiple algorithm scattering is achieved algorithm by means spectral resolution can reach 0.001 cm−1 with our model1 , in which the multiple scattering algorithm is of achieved a line-by-line by means approach. of a line Figure-by- line16b shows approach. the OFigure2(a ∆ g16b) band shows brightness the O2(a calculated1Δg) band by brightness our model is achieved by means of a line-by-line approach. Figure 16b shows the O2(a1Δg) band brightness and that measured by the TIMED–SABER. The agreement between the observed band brightness and calculatedcalculated by our by modelour model and andthat that measured measured by by the the TIMED TIMED––SABER.SABER. The The agreement agreement between between the the observedmodelobserved prediction band bandbrightness is brightness remarkable, and and model which model prediction suggests prediction isthat is remarkable, remarkable, the emission which which algorithm, suggests suggests including that that the the emission the emission non-LTE algorithmsourcealgorithm function, including, in andcluding the self-absorption non the -nonLTE-LTE source source calculation, function function isand veryand self self sound.-absorption-absorption calculation, is is very very sound. sound.

FigureFigure 16. Comparisons 16. Comparisons between between the emission–absorption the emission–absorption transfer transfer model and model results and from results MODTRAN4 from

and theMODTRA TIMED–SABERN4 and the TIMEDmeasurements.–SABER measurements. (a) Calculated (a) C spectralalculated radiance spectral radiance using our using model our and Figure model 16. Comparisons and MODTRAN4 between at tangent the heightemission of 20–absorption km. (b) M easured transfer and model modeled1 and O 2(a results1Δg) band from MODTRAN4 at tangent height of 20 km. (b) Measured and modeled O2(a ∆g) band brightness as a MODTRAfunctionbrightnessN4 of tangent and as thea function height. TIMED of –tangentSABER height. measurements. (a) Calculated spectral radiance using our 1 model and MODTRAN4 at tangent height of 20 km. (b) Measured and modeled O2(a Δg) band brightness as a function of tangent height.

Remote Sens. 2019, 11, 2702 16 of 18

4. Conclusions

We have presented simulations of the radiative transfer characteristics of the O2 infrared atmospheric band in limb-viewing geometry. Both the non-LTE effect and multiple scattering were taken into account for developing the radiative transfer model. This model incorporates the most recent cross sections, spectroscopic parameters, rate constants, and solar fluxes. The limb spectral brightness observed in both absorption and emission was first calculated separately. The scattering absorption spectrum was carried out using the line-by-line multiple scattering radiative transfer model. The emission brightness was calculated based on the non-LTE theory, assuming that the attenuation along the line-of-sight path is caused by single scattering and self-absorption. Total spectral radiance was then obtained by combining these two components together. For the absorption spectrum simulation, the spherical adding and doubling methods were used. In the calculation of emission brightness, the source function under condition of non-LTE was used, which differed greatly from the Planck’s law. The emission rates for calculation of source function were carried out based on six 1 major O2(a ∆g) production mechanisms, and the vibrational temperature was obtained to describe the excitation degree of the excited vibrational state relative to the ground state. The variations in the limb spectral brightness with surface albedo, atmospheric aerosol, and SZA were simulated, and their basic characteristics were discussed. The surface characteristics, SZA, and atmospheric aerosol play key roles in determining the asymptotic value of the line shape, while the line center intensity is just sensitive to changes in atmospheric aerosol and SZA. It is expected that a better understanding of the radiative transfer characteristics of the O2 infrared atmospheric band will certainly improve the accuracy of near-infrared spaceborne instruments, such as WAMI, MIMI, and NWTSI, for which such new knowledge of non-LTE and multiple scattering could be used for an improved retrieval of atmospheric temperature and wind field.

Author Contributions: Conceptualization: W.H., K.W., and Y.F.; methodology: W.H. and K.W.; validation: D.F. and Z.C.; investigation: W.H. and Z.C.; formal analysis: K.W. and F.L.; writing—original draft preparation: W.H. and K.W.; writing—review and editing: Y.F. and F.L.; project administration: Y.F. and K.W.; supervision: F.L. and K.W.; funding acquisition: K.W. Funding: This research was funded by the National Natural Science Foundation of China (NSFC), grant number 61705253, 41975039. Acknowledgments: We gratefully acknowledge informative and helpful discussions with Wang Dingyi on theoretical details of this work. We also thank three anonymous reviewers for constructive comments on the initial manuscript. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

1. Mlynczak, M.G.; Morgan, F.; Yee, J.H.; Espy, P.; Murtagh, D.; Marshall, B.; Schmidlin, F. Simultaneous 1 1 measurements of the O2( ∆) and O2( Σ) airglows and ozone in the daytime mesosphere. Geophys. Res. Lett. 2001, 28, 999–1002. [CrossRef] 2. Khabibrakhmanov, I.K.; Degenstein, D.A.; Llewellyn, E.J. Mesospheric ozone: Determination from orbit with the OSIRIS instrument on Odin. Can. J. Phys. 2002, 80, 493–504. [CrossRef] 3. Mlynczak, M.G.; Marshall, B.T.; Martin-Torres, F.J.; Russell, J.M.; Thompson, R.E.; Remsberg, E.E.; Gordley,L.L. Sounding of the Atmosphere using Broadband Emission Radiometry observations of daytime mesospheric 1 O2( ∆) 1.27 µm emission and derivation of ozone, atomic oxygen, and solar and chemical energy deposition rates. J. Geophys. Res. Atmos. 2007, 112, D15. [CrossRef] 1 4. Guslyakova, S.; Fedorova, A.A.; Lefèvre, F.; Korablev, O.I.; Montmessin, F.; Bertaux, J.L. O2( ∆g) dayglow limb observations on Mars by SPICAM IR on Mars-Express and connection to water vapor distribution. Icarus 2014, 239, 131–140. [CrossRef] 5. Ward, W.E.; Gault, W.A.; Shepherd, G.G.; Rowlands, N. The Waves Michelson Interferometer: A visible/near-IR interferometer for observing middle atmosphere dynamics and constituents. Proc. SPIE 2001, 4540, 100–111. Remote Sens. 2019, 11, 2702 17 of 18

6. He, W.W.; Wu, K.J.; Feng, Y.T.; Fu, D.; Chen, Z.; Li, F.Q. The Near-Space Wind and Temperature Sensing Interferometer: Forward Model and Measurement Simulation. Remote Sens. 2019, 11, 914. [CrossRef]

7. Wu., K.J.; Fu, D.; Feng, Y.T.; Li, J.; Hao, X.B.; Li, F.Q. Simulation and application of the emission line O19P18 1 of O2( ∆g) dayglow near 1.27 µm for wind observations from limb-viewing satellites. Opt. Express 2018, 26, 16984–16999. [CrossRef]

8. Park, J.H. Atmospheric CO2 monitoring from space. Appl. Opt. 1997, 36, 2701–2712. [CrossRef] 1 9. Kang, S.; Gordon, I.E.; Sioris, C.E.; Xiong, L.; Chance, K.; Wofsy, S.C. Reevaluating the use of O2( ∆g) band in spaceborne remote sensing of greenhouse gases. Geophys. Res. Lett. 2018, 45, 5779–5787. 10. Dobler, J.T.; F Wallace, H.; Browell, E.V.; Bing, L.; Doug, M.G.; Susan, K.; Yonghoon, C.; Syed, I. Atmospheric

CO2 column measurements with an airborne intensity-modulated continuous wave 1.57 µm ﬁber laser lidar. Appl. Opt. 2013, 52, 2874–2892. [CrossRef] 1 11. Sharp, W.E.; Zaccheo, T.S.; Browell, E.V.; Ismail, S.; Dobler, J.T.; Llewellyn, E.J. Impact of Ambient O2( ∆g) on Satellite-Based Laser Remote Sensing of O2 Columns using Absorption Lines in the 1.27 µm region. J. Geophys. Res. Atmos. 2014, 119, 7757–7772. [CrossRef] 12. Bertaux, J.L.; Hauchecorne, A.; Lefèvre, F.; Bréon, F.M.; Blanot, L.; Jouglet, D.; Lafrique, P.; Akaev, P. The use

of O2 1.27 µm absorption band revisited for GHG monitoring from space and application to MicroCarb. Atmos. Meas. Tech. Discuss. 2019. in review. [CrossRef] 13. Gordon, I.E.; Rothman, L.S.; Hill, C.; Kochanov,R.V.; Tan, Y.; Bernath, P.F.; Birk, M.; Boudon, V.; Campargue, A.; Chance, K.V.; et al. The HITRAN2016 molecular spectroscopic database. J. Quant. Spectrosc. Radiat. Transf. 2017, 203, 3–69. [CrossRef] 1 14. Mlynczak, M.G.; Solomon, S.; Zaras, D.S. An updated model for O2( ∆g) concentrations in the mesosphere and lower thermosphere and implications for remote sensing of ozone at 1.27 µm. J. Geophys. Res. Atmos. 1993, 98, 18639–18648. [CrossRef] 15. Thomas, R.J.; Barth, C.A.; Rusch, D.W.; Rusch, D.W.; Sanders, R.W. Solar Mesosphere Explorer near-infrared spectrometer: Measurements of 1.27-µm radiances and the inference of mesospheric ozone. J. Geophys. Res. Atmos. 1984, 89, 9569–9580. [CrossRef] 16. Harris, R.D.; Adams, G.W. Where does the O(1D) energy go? J. Geophys. Res. Space 1983, 88, 4918–4928. [CrossRef]

17. Yankovsky, V.A.; Babaev, A.S. Photolysis of O3 at Hartley, Chappuis, Huggins, and Wulf bands in the middle 3 atmosphere: Vibrational kinetics of oxygen molecules O (X Σg , ν 35). Atmos. Ocean. Opt. 2011, 24, 6–16. 2 − ≤ [CrossRef] 18. Yankovsky, V.A.; Manuilova, R.; Babaev, A.; Feoﬁlov, A.; Kutepov, A. Model of electronic-vibrational kinetics

of the O3 and O2 photolysis products in the middle atmosphere: Applications to water vapour retrievals from SABER/TIMED 6.3 µm radiance measurements. Int. J. Remote Sens. 2011, 32, 3065–3078. [CrossRef]

19. Martyshenko, K.V.; Yankovsky, V.A. IR band of O2 at 1.27 µm as the tracer of O3 in the mesosphere and lower thermosphere: Correction of the method. Geomagn. Aeron. 2017, 57, 229–241. [CrossRef] 20. Yankovsky, V.A.; Manuilova, R.O. Model of daytime emissions of electronically-vibrationally excited products

of O3 and O2 photolysis: Application to ozone retrieval. Ann. Geophys. 2006, 24, 2823–2839. [CrossRef] 21. Russell, J.P.; Lowe, R.P. Atomic oxygen proﬁles (80–94 km) derived from Wind Imaging Interferometer/Upper Atmospheric Research Satellite measurements of the hydroxyl airglow: 1. Validation of technique. J. Geophys. Res. 2003, 108, 4662. [CrossRef] 3 22. Yankovsky, V.; Vorobeva, E.; Manuilova, R. New techniques for retrieving the [O( P)], [O3] and [CO2] altitude proﬁles from dayglow oxygen emissions: Uncertainty analysis by the Monte Carlo method. Adv. Space Res. 2019, 64, 1948–1967. [CrossRef] 23. Edwards, D.P.; Lopez-Puertas, M.; Lopez-Valverde, M.A. Non-local thermodynamic equilibrium studies

of the 15-µm bands of CO2 for atmospheric remote sensing. J. Geophys. Res. Atmos. 1993, 98, 14955–14977. [CrossRef] 24. Hays, P.B. High-resolution optical measurements of atmospheric winds from space. 1: Lower atmosphere molecular absorption. Appl. Opt. 1982, 21, 1136–1141. [CrossRef][PubMed] 25. Hays, P.B.; Abreu, V.J. Absorption line proﬁles in a moving atmosphere—A single scattering linear perturbation theory. J. Geophys. Res. Atmos. 1989, 94, 18351–18365. [CrossRef] Remote Sens. 2019, 11, 2702 18 of 18

26. Abreu, V.J.; Bucholtz, A.; Hays, P.B.; Ortland, D.; Skinner, W.R.; Yee, J.H. Absorption and emission line shapes in the 02 atmospheric bands: Theoretical model and limb viewing simulations. Appl. Opt. 1989, 28, 2128–2137. [CrossRef] 1 27. Yee, J.H.; DeMajistre, R.; Morgan, F. The O2(b Σ) dayglow emissions: Application to middle and upper atmosphere remote sensing. Can. J. Phys. 2012, 90, 769–784. [CrossRef] 28. Anderson, G.P.; Berk, A.; Acharya, P.K.; Matthew, M.W.; Bernstein, L.S.; Chetwynd, J.H.J.; Dothe, H.; Adler-Golden, S.M.; Ratkowski, A.J.; Felde, G.W.; et al. MODTRAN4: Radiative transfer modeling for remote sensing. Proc. SPIE 2000, 4049, 176–183. 29. SABER—Sounding of the Atmosphere using Broadband Emission Radiometry. Available online: http: //saber.gats-inc.com/ (accessed on 30 October 2019). 30. Mlynczak, M.G.; Russell, J.M. An overview of the SABER experiment for the TIMED mission. Opt. Remote Sens. Atmos. 1995, 2, 5–7.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).