Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology, Karlsruhe, Germany
Corresponding author: M. Höpfner, Institute for Meteorology and Climate Research, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Karlsruhe, Germany. (email@example.com)
 The effect of collision-induced absorption by molecular oxygen (O2) and nitrogen (N2) on the outgoing longwave radiation (OLR) of the Earth's atmosphere has been quantified. We have found that on global average under clear-sky conditions the OLR is reduced due to O2 by 0.11 Wm−2 and due to N2 by 0.17 Wm−2. Together this amounts to 15% of the OLR-reduction caused by CH4 at present atmospheric concentrations. Over Antarctica the combined effect of O2 and N2 increases on average to about 38% of CH4 with single values reaching up to 80%. This is explained by less interference of H2O spectral bands on the absorption features of O2 and N2 for dry atmospheric conditions.
 It is a widespread notion that both main constituents of the atmosphere, molecular nitrogen (N2) and molecular oxygen (O2) ‘exert almost no greenhouse effect’ [Le Treut et al., 2007]. Their contribution is mainly ascribed to indirect effects like the pressure-broadening of CO2-lines in the infrared [Lacis et al., 2010; Goldblatt et al., 2009]. Thus, N2 and O2 are sometimes not considered as natural greenhouse gases even in case of low water vapor conditions [Lacis et al., 2010].
 Due to their symmetry, homonuclear diatomic molecules like N2 and O2 do not exhibit a static electric dipole moment, such as H2O, nor is there the possibility to induce vibrationally a dipole moment, as in the case of CO2. Thus, there are no strong infrared absorption bands due to dipole transitions as in the case of the major greenhouse gases. However, as discovered by Crawford et al. , collision- induced absorption leads to weak absorption features of N2 and O2 in the infrared [e.g., Hartmann et al., 2008].
 Due to the atmospheric concentration of atmospheric N2 (O2) that is about 2000 (550) times higher than that of CO2 and about 4.4 × 105 (1.2 × 105) times more abundant than CH4, even the weak infrared absorption of N2 (O2) can become radiatively important.
 The collision-induced fundamental vibration-rotation band at 6.4 μm is the major absorption signature of O2 in the thermal infrared. Timofeyev and Tonkov  reported that at distinct wavelengths near the band center, O2 absorption may affect the atmospheric zenith transmission by up to 9% for dry atmospheric conditions. This effect is strongly modulated by the atmospheric water vapor content since the O2 spectral signature is situated in the same spectral region as one of the most important H2O infrared absorption bands (ν2 bending). In the atmosphere the infrared signal of O2has first been detected through balloon-borne limb-sounding observations [Rinsland et al., 1982].
 N2has two major bands influencing the infrared radiation: the collision-induced rotovibrational fundamental band at 2400 cm−1and the collision-induced rototranslational band at 100 cm−1. In the atmosphere, the mid-infrared absorption of N2 was first observed by Susskind and Searl by use of ground-based FTIR measurements.Rinsland et al. confirmed these observations by analysis of balloon-borne limb solar occultation spectra. A further detailed analysis of the mid-infrared continuum signals of O2 and N2has been performed on basis of space-borne observations byRinsland et al. .
 The N2absorption band in the sub-mm range has been analysed in atmospheric measurements byPardo et al. . They used ground-based Fourier transform spectroscopy at Mauna Kea to determine the continuum like absorption up to frequencies exceeding 1 THz.
 In various line-by-line radiative transfer calculations for the validation of radiation codes used within climate models [e.g.,Fomin et al., 2004; Collins et al., 2006; Iacono et al., 2008] or for the exact modeling of outgoing longwave radiation [Buehler et al., 2006] the effects of collision-induced continua of N2 and O2 have mostly been taken into account by use of continuum parameterizations like the Mlawer, Tobin, Clough, Kneizys, and Davis (MT_CKD) model [Clough et al., 2005]. However, we are not aware of any publications on the quantification of the effect of O2 and N2 on the outgoing longwave radiation flux (OLR). In the following, after a description of the used radiative transfer model we show spectrally resolved typical simulations of atmospheric transmission and OLR for a standard atmospheric situation. Then, the globally resolved net effects of O2 and N2on OLR are discussed and at the end a comparison with an independent line-by-line model is presented.
2. Radiative Transfer Simulations
 For the simulation of broadband infrared spectra at the top of the atmosphere the radiative transfer model KOPRA [Stiller, 2000] has been applied. KOPRA is an accurate and fast line-by-line model being used for the analysis of spectrally high resolved satellite remote sensing observations like the IR-limb emission sounder MIPAS [Fischer et al., 2008] or the IR-nadir instrument IASI [Keim et al., 2009]. Beside the indirect model validation via the validation of the retrieved atmospheric parameters, KOPRA has successfully been compared to various independent radiative transfer models [e.g., Tjemkes et al., 2003]. For the calculations shown within this paper we have used spectroscopic data from HITRAN 2008 [Rothman et al., 2009]. Continuum contributions for water vapor and CO2 are parameterized according to the MT_CKD model version 2.5.2 [Clough et al., 2005]. The collision induced continuum by O2 is based on the empirical model by Thibault et al. . The continuum by N2 near 2300 cm−1 is calculated according to Lafferty et al. . The collision induced rototranslational absorption by N2 at around 100 cm−1 is taken from the MT_CKD version 2.5.2 implementation which is based on Borysow and Frommhold  and Boissoles et al. . All following KOPRA radiative transfer calculations have been performed on a spectrally high resolved variable wavenumber grid with a grid width down to 0.0005 cm−1 [Kuntz and Höpfner, 1999]. For the figures the high-resolved spectra have been smoothed with a 2 cm−1 wide boxcar function.
3. Calculation for a Standard Atmosphere
Figure 1a shows the atmospheric zenith transmission between 10 cm−1 and 2500 cm−1 (4 μm–1000 μm) for single gases H2O, CO2, O3, N2O, CH4, O2 and N2and their combination for a typical atmospheric mid-latitude situation [Remedios et al., 2007] as calculated with KOPRA. It is obvious that in case of O2 a maximum reduction of the atmospheric transmission by 40% (around 1550 cm−1) and in case of N2 by 50% at 2330 cm−1 and 80% at 100 cm−1 is reached. The mean zenith transmission of single gas atmospheres is reduced by 2.6% due to O2 and by 8.3% due to N2, in comparison to 1.9% by e.g. CH4. For a zenith angle of 80° an atmosphere consisting only of N2 and O2 would even be opaque by O2 absorption between 1500–1650 cm−1, and by N2 absorption in the regions 20–200 cm−1 and 2230–2470 cm−1. The mean transmission would be reduced by 14.2% due to O2 and by 25.7% due to N2, compared to 6.9% by CH4 and 92.5% by H2O.
 The effect of O2 and N2on the outgoing longwave radiation flux (OLR) at the top of the atmosphere (assumed at 80 km altitude) is estimated by integrating radiance calculations at different nadir angles (0°, 20°, 40°, 60°, 81°) taking into account Earth's sphericity. (The radiances between 81° and 90° have been neglected since those lines-of-sight do not hit the earth any more but correspond to limb views).
 In the following we discuss the net contribution to the OLR by different gases with respect to an atmosphere composed of the full set of species. This means that a gas with an absorption band in the same spectral region as a strong band of another species has less effect on the OLR than in case of less overlapping spectral signatures. As can be seen in Figure 1a, the collision induced absorption band of O2 is covered by the ν2 H2O absorption, the rotovibrational band of N2 at 2400 cm−1 by the strong 4.3 μm CO2 absorption and the rototranslational band of N2 at 100 cm−1 by absorption mainly due to H2O.
 Results are presented in Figure 1bas the difference between OLR calculations where a single gas has been omitted and the OLR values where all gases are included (ΔOLR(gas x) = OLR(all without gas x)–OLR(all)). Mind that ‘omitted’ and ‘without gas x’ here mean that the gas is set to be infrared-inactive but still contributes to the atmospheric density and pressure.
 As indicated in Figure 1b, ΔOLR(O2) = 0.05 Wm−2 and ΔOLR(N2) = 0.11 Wm−2. Thus, the natural greenhouse effect of oxygen and nitrogen together are about 10% of that of CH4 (ΔOLR(CH4) = 1.55 Wm−2). Mind that the mean tropospheric concentration of CH4 used in these calculations was 1.8 ppmv.
 To evaluate the effect of overlapping spectral signatures on the relative contribution to OLR reduction we simulated the pure hypothetical case of single gas atmospheres. Here, compared to the flux for an infrared-inactive atmosphere (365.7 Wm−2), each of N2 and O2 reduces the OLR by 2.8 Wm−2 and CH4 by 4.3 Wm−2. The effect of both major atmospheric constituents together would exceed the OLR-reduction due to CH4 by a factor of 1.3. This drop from a factor of 1.3 to 10% in relative importance of N2 and O2 compared to CH4 is caused by the overlapping bands of H2O and CO2in a real atmosphere. To demonstrate how strong this importance is modulated by temperature and water-vapor content of the atmosphere a realistic global situation is described in the following.
4. Global Picture
 In this section we investigate the OLR reduction by N2 and O2 in relation to CH4globally for a real atmospheric situation. As an example, October 16th, 2007 has been chosen arbitrarily. ECMWF T106 analysis for 6 UT of temperature and humidity has been applied to produce altitude profiles at cloud-free locations. To reduce the number of broad-band line-by-line calculations globally a 5° longitude × 5° latitude grid has been used. Within each grid-cell we have chosen the cloud-free profile nearest to the grid center. In case there has been no cloud-free situation, no calculation has been performed for the related grid cell. For all other gases (CO2, O3, N2O, CH4, O2, and N2), standard profiles have been used [Remedios et al., 2007].
 The calculations for an atmosphere containing the full set of gases are presented in Figure 2 and in Table 1. In Figure 2 (top) the OLR reduction due to oxygen relative to that of methane ΔOLR(O2)/ΔOLR(CH4) is shown, and Figure 2 (bottom) demonstrates the similar effect for nitrogen ΔOLR(N2)/ΔOLR(CH4). With exception of the southern polar region the values vary around 6% for O2 and 9% for N2. Global mean relative OLR reductions are 6.0% and 9.2% for O2 and N2, respectively (Table 1).
Table 1. Cloud-Free Global and Antarctic (70°–90°S) Means of the OLR, the Absolute OLR Reduction and the OLR Reduction Relative to That of CH4for Realistic All-Gas Atmospheresa
ΔOLR(gas x) = OLR(all without gas x)–OLR(all), ΔOLRrelCH4(gas x) = .
All w/o H2O
All w/o CO2
All w/o O3
All w/o N2O
All w/o CH4
All w/o O2
All w/o N2
All w/o H2O
All w/o CO2
All w/o O3
All w/o N2O
All w/o CH4
All w/o O2
All w/o N2
 Over Antarctica, maximum values for ΔOLR(O2)/ΔOLR(CH4) of around 30% and for N2 of up to 50% are reached. Mean values for latitudes poleward of 70°S are 16.1% for O2 and 21.9% for N2 as listed in Table 1. This large contribution to the natural greenhouse effect relative to the one exhibited by CH4 is due to the extremely low humidity over the southern polar region, such that spectral signatures of water vapor interfere less with those of O2 and N2.
5. Model Evaluation
 The accuracy of KOPRA simulations of the OLR reduction due to O2 and N2 relative to CH4 has been evaluated by comparison with independent calculations performed with the ARTS radiative transfer model [Buehler et al., 2005; Eriksson et al., 2011]. Like KOPRA, ARTS is a line-by-line model which has been applied recently for the modeling of OLR at the top of the atmosphere [Buehler et al., 2006]. For nadir view, a comparison dataset has been calculated on basis of 42 altitude profiles of pressure/temperature and trace gases (H2O, O3, CO2, N2O, CH4, O2, N2) [Garand et al., 2001]. Figure 3 shows the comparison for ΔOLR(O2)/ΔOLR(CH4), ΔOLR(N2)/ΔOLR(CH4) and the sum of both.
 In general both models compare reasonably well: the mean values for O2 are 6.4%(KOPRA) vs. 6.1%(ARTS) and for N28.1%(KOPRA) vs. 6.0%(ARTS), respectively. Differences are explained by different set-ups of the two models. First, the frequency grid of the ARTS simulations has been coarser (0.3 cm−1) than that of KOPRA (min 5 × 10−4 cm−1). A sensitivity analysis using a degraded frequency grid of 0.3 cm−1 for KOPRA showed a reduction of the total effect from 14.5% to 13.5%, thus approaching the lower values of ARTS. Remaining differences are likely due to the application of different spectroscopic databases (ARTS: HITRAN 2004, KOPRA: HITRAN 2008) and continuum models (ARTS: MT_CKD_1.0, KOPRA: MT_CKD_2.5.2). An update within the MT_CKD_2.5.2 model concerns e.g. the increase of the N2 continuum in the 0–350 cm−1 range [Pardo et al., 2001; Boissoles et al., 2003; Pardo et al., 2005]. This probably explains the stronger relative effect of N2 compared to that of O2 within the KOPRA simulations compared to ARTS. In summary, the model intercomparison confirms the relative large effects on OLR by O2 and N2 as deduced from KOPRA simulations.
 This work challenges a common perception on the negligible role of O2 and N2 as natural greenhouse gases in the Earth's atmosphere compared to species like CH4 or N2O. It is in fact the large abundance of oxygen and nitrogen which compensates for their only weak interaction with infrared radiation through collision-induced absorption bands. We have shown that for hypothetic atmospheres consisting of only single gases the natural greenhouse effect of O2 and N2 together would be larger than that of CH4 by a factor of around 1.3. For a realistic atmospheric composition this effect is reduced through shading of O2 and N2 absorption bands mainly by spectral signatures of H2O and, to a less extend, by CO2. Still the net global OLR reduction of oxygen and nitrogen together is with 0.28 Wm−2 about 15% of that due to CH4. However, for dry atmospheric situations like over the Antarctic continent the effect of O2 and N2 even reach up to 80% of the influence of CH4 for a realistic atmospheric composition.
 An atmospheric situation with increased values of N2 has been proposed as possible solution for the ‘Faint Young Sun’ paradox by Goldblatt et al. . Repeating their calculation of longwave radiative forcing we obtained similar values for a doubling of N2 concentrations (≈12 Wm−2). We investigated this effect for single absorbers and found reductions of the OLR by 9.4, 5.1, 4.6 and 1.9 Wm−2 for H2O, CO2, N2, and CH4. The relatively large value in case of N2is due to collision-induced continuum absorption which scales with the square of concentration while the dependence of strong absorption bands on line-width is much smaller. Thus, we object to the view that the radiative forcing of N2 increase operates only indirectly by broadening the absorption lines of other gases [Goldblatt et al., 2009]. Actually it is a combination of this indirect effect and the direct impact through collision-induced absorption.
 Finally we would like to stress that this work concerns only the contribution of N2 and O2 to the natural greenhouse effect. In no way does it affect the importance of CH4 and other anthropogenically affected gases with respect to global climate change.
 The Atmospheric and Environmental Research (AER) Radiative Transfer Working Group is acknowledged for making their continuum models publicly available.
 The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.