Note on rotational-Raman scattering in the O 2 Aand B-bands

Abstract. Quantifying the impact of rotational-Raman scattering (RRS) on the O2 A- and B-bands is important as these bands can be used for cloud and aerosol characterization for trace-gas retrievals including CO2 and CH4. In this paper, we simulate the spectral effects of RRS for various viewing geometries and instruments with different spectral resolutions. We also examine how aerosols affect the amount of RRS filling-in. We show that the filling-in effects of RRS are relatively small, but not negligible, in these O2 absorption bands, particularly for high-spectral-resolution instruments. For comparison, we also compare and contrast the spectral signatures of RRS with those of terrestrial chlorophyll fluorescence.


Introduction
Near-InfraRed (NIR) retrievals of trace-gas concentrations, such as of CO 2 and CH 4 , as well as terrestrial chlorophyll fluorescence often use information derived from O 2 A and B absorption band measurements (e.g., Reuter et al., 2010;Yoshida et al., 2011;Crisp et al., 2012;Guanter et al., 2010;O'Dell et al., 2012).Additive signals that contribute to satellite-measured top-of-the-atmosphere (TOA) radiance in the O 2 A-and B-bands can bias these retrievals.One type of additive signal that can produce a filling-in of deep telluric NIR absorption features, such as those in the O 2 A-and B-bands, is atmospheric rotational-Raman scattering (RRS) of N 2 and O 2 molecules.RRS has been neglected in the NIR spectral region, because the amount of atmospheric molecular scattering is low at these wavelengths.RRS effects in the O 2 A-band have been quantified in the literature (Sioris and Evans, 2000).RRS filling-in effects have also been compared with those of fluorescence for several solar Fraunhofer lines in the visible and near infrared (Sioris et al., 2003).However, RRS effects are worthy of further consideration, owing to the high accuracy and precision requirements placed on CO 2 retrievals to be used for carbon assessment (e.g., Crisp et al., 2004).
Recent advances in the satellite retrieval of chlorophyll fluorescence in the NIR (Guanter et al., 2007(Guanter et al., , 2010(Guanter et al., , 2012;;Joiner et al., 2011Joiner et al., , 2012;;Frankenberg et al., 2011a,b) also call into question the role of RRS in this spectral region.For example, Joiner et al. (2011Joiner et al. ( , 2012) ) examined the filling-in of various solar Fraunhofer lines in the NIR and found the effects to be generally small, but not negligible.Frankenberg et al. (2012) showed that systematic biases in xCO 2 can be as large as 1 ppm if chlorophyll fluorescence in the O 2 A-band, amounting to 1 % to the continuum level radiance, is neglected.While RRS was not considered in that paper, it produces similar spectral effects on TOA radiances and should be examined in that context.
In this paper, we detail the effects of RRS in the O 2 Aand B-bands under various conditions.For comparison, we simulate the effects of chlorophyll fluorescence in the same bands.We also examine the impact of aerosol and thin clouds on both RRS and fluorescence additive signals within these absorption bands.2008).LIDORT-RRS allows for accurate radiative transfer (RT) calculations in the presence of cloud/aerosol scattering.Oxygen absorption coefficients are calculated using a lineby-line code with spectroscopic absorption line parameters from the HIgh-resolution TRANsmission (HITRAN) molecular absorption database (Rothman et al., 2005) and the Voigt line shape profile.A single mid-latitude profile of temperature/pressure was used in the computation of the absorption coefficients.
For reference, Fig. 1 shows the rotational-Raman spectra of N 2 and O 2 computed as in Joiner et al. (1995) at a temperature of 273 K for an excitation wavelength near the O 2 A-band (760 nm).The rotational-Raman lines peak at around ±3-4 nm from the excitation wavelength and extend to approximately ±10 nm.Therefore, the spectral response of RRS is not the same as that for an additive signal as is more the case for chlorophyll fluorescence.However, the overall spectral effects of the RRS and fluorescence signals are similar, as will be shown below.

Chlorophyll fluorescence
The TOA fluorescence signal is calculated approximately using the quasi-single scattering approximation, i.e., where I f0 is the fluorescence radiance at the surface (assumed to be isotropic), θ is the viewing zenith angle (VZA), τ a (λ) and τ R (λ) are the absorption and Rayleigh optical thicknesses of the atmosphere, respectively, and τ s = τ (1 − g) is the scaled aerosol optical thickness, where τ is the aerosol optical thickness (assumed to be spectrally independent within the O 2 A-band) and g is the asymmetry parameter of the aerosol phase function.For non-absorbing wave-lengths, this approach is applicable for low values of the scaled scattering optical thickness.The far-red fluorescence radiance feature at the canopy level is approximated by a Gaussian function similar to Subhash and Mohanan (1997) and Zarco-Tejada et al. (2000); i.e., I f0 (λ) = I fp exp[−(λ − λ 0 ) 2 /(2σ 2 )], where λ 0 = 736.8nm and σ = 21.2 nm for the O 2 A-band and λ 0 = 685.2nm and σ = 9.6 nm for the O 2 B-band.We assume a peak fluorescence value I fp = 2 mW m 2 sr −1 nm −1 at a solar zenith angle (SZA) of 45 • for both bands.This gives a surface fluorescence radiance at 762 nm of ∼ 1.0 mW m 2 sr −1 nm −1 .This value of surface fluorescence radiance near the O 2 A-band is typical of observed terrestrial chlorophyll fluorescence values within the O 2 A-band spectral range and corresponds to approximately 1 % of the continuum level radiance at a surface albedo of 30 %.

Satellite instrument simulation
Quasi-monochromatic computations are carried out at a spectral sampling of 0.01 nm, that of the solar irradiance reference spectrum from Chance and Kurucz (2010) in which high-spectral-resolution spectra were convolved with a Gaussian response function with a full width at half maximum (FWHM) of 0.04 nm.For evaluation purposes, we also perform a limited number of RT computations with higher spectral resolution and sampling (sampled at 0.001 nm) using the solar irradiance spectrum from kurucz.harvard.edu/sun/irradiance2005/irradthu.dat in Appendix C. The latter sampling requires an order of magnitude more computational resources for a given calculation.
Computed TOA radiances are convolved with Gaussian response functions having various values of the FWHM.The chosen FWHMs (0.03, 0.1, 0.5, and 1 nm) are representative of existing and future satellite instruments.They include high-spectral-resolution instruments such as the Fourier Transform Spectrometer (FTS) on the Japanese Greenhouse gases Observing SATellite (GOSAT) (Kuze et al., 2009) and the Orbiting Carbon Observatory 2 (OCO-2) (Crisp et al., 2004) and moderate-spectral-resolution instruments such as the SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) instrument aboard EnviSat (Gottwald et al., 2006) and the proposed FLourescence EXplorer (FLEX) (Rascher, 2007).However, note that convolution of these instrument response functions with the solar spectrum of Chance and Kurucz (2010) (that has spectral resolution similar to our highest spectral resolution simulation) will somewhat underestimate solar line filling as shown in Appendix C.
For reference, the solar irradiance spectrum convolved with the chosen response functions is shown in Fig. 2 in the spectral ranges selected around the O 2 A-and B-bands.It is seen that these spectral ranges contain several deep Fraunhofer lines.RRS fills in Fraunhofer lines due to spectral  transport of energy from wavelengths in the vicinity of the lines.The filling-in is larger for deeper lines.

Surface specification and viewing geometries
For simplicity, we assumed a spectrally independent Lambertian surface with reflectivities R = 30 % in the O 2 Aband and 5 % in the O 2 B-band.These values are typical for vegetated surfaces.The TOA simulations are performed for three solar zenith angles (20, 45, and 70 • ) at various viewing zenith and azimuth angles appropriate for typical satellite observations.ances are small as compared with the elastic radiances, I e .The inelastic radiances are positive within the O 2 A-band where the amount of outgoing Raman scattered light from those wavelengths is less than the amount of incoming Raman scattered light from excitation wavelengths in the surrounding continuum.The reverse is true of wavelengths near to or in the shoulders surrounding the O 2 A-band.

RRS effects for molecular scattering only
Figure 4 shows the percent difference between the total and elastic radiances, also known as the filling-in factor, i.e., I rrs /I e × 100 (in %) (Joiner et al., 1995) for wavelengths in and surrounding the O 2 A-and B-bands.Within deep telluric O 2 A-band absorption lines where elastic radiances are small, the filling-in can be as large as 2 % for high-spectral-resolution instruments.Note that the filling-in does not decrease linearly with increasing FWHM within the O 2 A-band.For relatively low-resolution instruments (FWHM = 1 nm), the maximum filling-in within the O 2 A-band is < 0.2 %.
It can be seen that values of the RRS filling-in in the O 2 B-band are significantly lower than in the O 2 A-band despite    the fact that there is more atmospheric scattering at the O 2 B-band.This is explained by the fact that absorption lines in the O 2 A-band are much deeper than in the O 2 B-band.Thus, the filling-in from Raman scattered light coming from excitation wavelengths in the surrounding continuum in terms of percent of radiance is larger in the O 2 A-band than in the O 2 B-band.The remainder of the paper will therefore focus primarily on the filling-in of the O 2 A-band.

RRS viewing angle dependences
The VZA dependence of the maximum RRS filling-in at wavelengths with large RRS effects within the O 2 A-band (760-762 nm) is shown in Fig. 5 for SZA = 45 and 70 • at azimuth angle of 90 • .The RRS filling-in increases with VZA, owing to increased photon path lengths and thus increased probability of Raman scattering.At SZA = 45 • , the filling-in at 60 • VZA doubles as compared with that at nadir.

Comparison of RRS and fluorescence spectral signatures
Figure 6 shows the TOA fractional fluorescence radiance (defined as a ratio of fluorescence radiance to elastic radiance) computed for SZA = 45 • and observations at nadir at wavelengths in and surrounding the O 2 A-and B-bands.For this viewing geometry and a substantial amount of assumed chlorophyll fluorescence (2 mW m −2 sr −1 nm −1 at the two emission peaks), the fractional fluorescence signal is significantly higher than that of RRS.The spectral effects of fluorescence and RRS filling-in are similar within this spectral region though some small differences are observed.For example, the fluorescence spectral response contains a slight tilt across this wavelength range, owing to the Gaussian shapes of the emission features.
The relative ratio of fluorescence to RRS filling-in within the O 2 A-band depends upon the FWHM.At high spectral resolution (FWHM = 0.03 nm), the fractional fluorescence signal exceeds that of RRS by a factor of about 2 at the center of the O 2 A-band, while at FWHM = 1.0 nm fluorescence is larger than RRS by a factor of 6.4.Note that we have subtracted the fluorescence signal in the continuum from the total fluorescence signal to enhance the spectral comparison with RRS effects.
The O 2 B-band is spectrally located near the peak of the 685 nm fluorescence emission feature.Therefore, the total percentage of the contribution of fluorescence to the TOA radiance is much higher in the O 2 B-band as compared with the O 2 A-band.However, when the fluorescence signal is normalized with respect to the continuum, the relative fluorescence contribution to the TOA radiance in the O 2 B-band is somewhat lower than in the O 2 A-band.This is explained by A direct comparison of the spectral RRS and fluorescence signals at wavelengths in and surrounding the O 2 A-and B-bands is shown in Fig. 7 for FWHM = 0.1 nm along with the radiance response for a surface pressure change of 3 hPa.Again for clarity, the fluorescence spectral response has been normalized with respect to the continuum value.A value of 0.5 mW m −2 sr −1 nm −1 is used for the peak fluorescence.At this low level of fluorescence radiance, the fractional RRS and fluorescence signals are similar, and both are also similar in magnitude to the small surface pressure change.However, there are some subtle differences.For example, surface pressure change does not fill in solar Fraunhofer lines, whereas both RRS and fluorescence produce a solar filling-in signal.It should be noted that the spectral RRS, fluorescence, and response for a surface pressure change in the O 2 B-band are

Aerosol and cloud effects on RRS
We carried out RT computations in the presence of aerosol/cloud with various optical depths and layer heights.Aerosol/cloud scattering is assumed to be in accordance with the Henyey-Greenstein (H-G) phase function with an asymmetry factor of 0.7 for aerosol and 0.85 for clouds.The simplified H-G phase function is adequate for our purpose of examining the qualitative effects of aerosol/cloud on RRS and fluorescence.We characterize the aerosol scattering effect on RRS (fluorescence) through a fractional difference of the TOA inelastic (fluorescence) radiance between aerosol and aerosol-free cases: (I r (τ ) − I r (τ = 0))/I e (τ = 0) × 100 (in %), where I r is either RRS I rrs or fluorescence I f radiance and    τ is the aerosol optical depth.Figure 8 shows the fractional difference of the TOA inelastic radiance for a nonabsorbing aerosol plume with τ = 1.0.The aerosol plume has a geometrical thickness of 1 km with a plume-top height of 3 km.In general, the aerosol effect on RRS is small.The presence of aerosol increases inelastic radiance within oxygen absorption lines and decreases it beyond the absorption lines, i.e., in the continuum.The total aerosol effect is complex because of two opposing tendencies.Aerosol partly screens the atmosphere below the plume, decreasing photon path lengths.However, aerosol also increases photon path length, owing to scattering between the bright ground and aerosol layer.The relative increase of the inelastic radiance owing to aerosol is larger for lower values of the FWHM.The aerosol effect on inelastic radiance depends on aerosol optical depth and height.RT computations for τ = 0.15 show that the effect decreases by a factor of ∼ 4 as compared with τ = 1.0.Increase of the aerosol plume height also decreases the aerosol effect on RRS.For example, the aerosol effect at τ = 1.0 decreases by a factor of ∼ 1.8 when the aerosol height increases from 3 to 10 km.
We looked at the cloud effect on RRS in terms of the maximum of the fractional inelastic radiance difference between cloudy and cloud-free cases.The presence of low-altitude clouds substantially increases the cloud effect on RRS with increasing cloud optical depth (COD).Varying COD from 1 to 50 enhances the cloud effect on RRS by a factor of approximately 2. For brighter clouds, i.e., optically thicker clouds, the increase of photon paths above the cloud due to reflection from the cloud prevails over the decrease of RRS due to screening of the atmosphere below the cloud.The presence of high-altitude clouds mostly decreases the cloud effect on RRS with increasing COD; i.e., screening of the atmosphere below the cloud plays the main role.Sioris and Evans (2000) with their definition of filling-in (see text).Bottom: filling-in computed for the same conditions with our definition and different spectral resolutions.clouds can slightly increase the cloud effect on RRS as compared with cloud-free case.This case is quite similar to the aerosol effect discussed in the previous paragraph.
The aerosol effect on the TOA fluorescence is quite simple: the presence of aerosol reduces the fluorescence signal according to Eq. ( 1).The fractional TOA fluorescence radiance difference between aerosol and aerosol-free cases, i.e., the difference normalized by the TOA radiance, significantly depends on wavelength.It is interesting that the presence of aerosol reduces the fractional fluorescence signal most substantially in the spectral range of strong absorption.and variations in surface pressure.At moderate solar zenith the magnitude of RRS filling-in is similar to that from a terrestrial chlorophyll fluorescence emission with the peak value of ∼ 0.5 mW m −2 sr −1 nm −1 or from a surface pressure change of ∼ 3 hPa.The RRS filling-in of O 2 absorption lines increases for larger SZAs and VZAs.The percentage of RRS filling-in in the O 2 B-band is less than in the O 2 A-band.The presence of a low-altitude aerosol plume may slightly increase inelastic radiance and thus increase RRS filling-in.For an aerosol plume with τ = 1 and height of 3 km, the fractional RRS filling-in increases by about 30 % in the center of the O 2 A-band as compared with the aerosol-free atmosphere.

RRS
Note that our definition of RRS filling-in differs from that of Sioris and Evans (2000), who define it as a percentage        of the continuum radiance.We provide an example of direct comparison of both definitions in Appendix A. Use of different definitions of filling-in may lead to somewhat different conclusions regarding the importance of RRS, particularly within the O 2 A-band.Our calculations and definition lead to the conclusion that while the RRS effect is small it may be non-negligible even at moderate solar zenith angles with respect to fluorescence and surface pressure retrievals relevant also to xCO 2 retrievals.However, this conclusion may depend upon the level of instrumental noise for a given instrument, particularly for high-spectral-resolution instruments that resolve deep absorption lines.For such instruments, high values of the RRS filling-in, defined as the ratio of inelastic radiance to elastic radiance, may be close to the noise level within the cores of deep absorption lines that produce low radiances.land.We note that the surface albedo dependence may produce some spatial structure in the observed filling-in from space-based instruments.

Fig. 1 .
Fig. 1.Rotational-Raman spectra of (a) N2 and (b) O2 for excitation wavelength 760 nm.Line strengths are normalized such that the sum over all lines is equal to unity.

Fig. 1 .
Fig. 1.Rotational-Raman spectra of (a) N 2 and (b) O 2 for excitation wavelength 760 nm.Line strengths are normalized such that the sum over all lines is equal to unity.

Fig. 4 .
Fig. 4. Percentage filling-in from RRS for SZA = 45 • , at nadir, for wavelengths in and around the O 2 B-band and surface reflectivity 0.05 (top) and O 2 A-band and surface reflectivity 0.3 (bottom).

Fig. 4 .
Fig. 4. Percentage of filling-in from RRS for SZA = 45 • , at nadir, for wavelengths in and around the O 2 B-band and surface reflectivity 0.05 (top) and O 2 A-band and surface reflectivity 0.3 (bottom).

Fig. 6 .Fig. 6 .
Fig. 6.Percentage contribution of fluorescence emission to TOA radiance for SZA = 45 • , at nadir, for wavelengths in and surrounding the O 2 B-band and surface reflectivity 0.05 (top) and O 2 A-band and surface reflectivity 0.3 (bottom).

Fig. 7 .
Fig. 7. Comparison of fractional radiance effect of RRS (red), fluorescen (∆P s ) of 3 hPa (green) for FWHM = 0.1 nm, SZA = 45 • , at nadir, for w B-band and surface reflectivity 0.05 (top) and O 2 A-band and surface normalized to a value of zero at 686 nm (top) and 758 nm (bottom).

Fig. 7 .
Fig. 7. Comparison of fractional radiance effect of RRS (red), fluorescence (blue), and surface pressure change ( P s ) of 3 hPa (green) for FWHM = 0.1 nm, SZA = 45 • , at nadir, for wavelengths in and surrounding the O 2 B-band and surface reflectivity 0.05 (top) and O 2 A-band and surface reflectivity 0.3 (bottom).All curves normalized to a value of zero at 686 nm (top) and 758 nm (bottom).

Fig. 9 .Fig. 10 .
Fig. 9. Top: RRS filling-in computed for conditions similar to Sioris of filling-in (see text); Bottom: Filling-in computed for the same cond spectral resolutions.

Fig. 9 .
Fig.9.Top: RRS filling-in computed for conditions similar toSioris and Evans (2000) with their definition of filling-in (see text).Bottom: filling-in computed for the same conditions with our definition and different spectral resolutions.

Fig. 10 .Fig. 10 .
Fig. 10.RRS signal defined as a percentage of the spectral elasic radiance versus the RRS signal defined as a percentage of the continuum level radiance at 758 nm.Every point represents a wavelength around the O 2 A-band.Only positive filling-in values are shown.Input parameters are similar to those used in Fig. 4.

Fig. 12 .
Fig. 12.Similar to Fig. 4 but computed with the higher spectral samplin

Fig. 12 .
Fig. 12.Similar to Fig. 4 but computed with the higher spectral sampling