Absorption with significant pressure and temperature differences

Introduction Conclusions References


Introduction
O 2 O 2 has been widely used in remote sensing to retrieve aerosol and cloud information from spectroscopic measurements using ground based (Wagner et al., 2002(Wagner et al., , 2004;;Frieß et al., 2006;Irie et al., 2008Irie et al., , 2009;;Clémer et al., 2010) and space instruments (Acarreta et al., 2004;Sneep et al., 2008).The advantage of O 2 O 2 for such measurements is that its concentration is directly proportional to the square of the oxygen concentration (R1).
The nature of molecular interactions in the O 2 O 2 collisional complex is still debated (Sneep et al., 2006) and the equilibrium constant, K eq , in (R1) is not known.As a result, Figures only the "pseudo", not the true concentration of the O 2 O 2 collisional complex can be determined.After application of the ideal gas law the "pseudo" O 2 O 2 column are easily calculated when atmospheric temperature, pressure and specific humidity profiles are known.
O 2 O 2 absorption can be accurately measured by the differential optical absorption spectroscopy (DOAS) technique due to several absorption bands in the UV and visible parts of the spectrum (e.g., ≈ 343, 360, 380, 477, 532, 577, 630 nm, Wagner et al., 2002) assuming availability of accurate "pseudo" absorption cross section, σ, as a function of T and P .The problem with the laboratory measurements of σ is related to the need to have long paths and/or higher pressures compared to atmospheric conditions for sufficient absorption.Despite numerous laboratory measurements of σ(O 2 O 2 ) in UV and visible spectral regions (Salow and Steiner, 1934;Greenblatt et al., 1990;Volkamer, 1996;Newnham and Ballard, 1998;Hermans et al., 2011;Sneep and Ubachs, 2003;Sneep et al., 2006;Thalman and Volkamer, 2013), the question of their applicability to atmospheric conditions remains unanswered.Only Thalman and Volkamer (2013) made σ (O 2 O 2 ) laboratory measurements at the pressure close to ambient (825 hPa).Their σ(O 2 O 2 ) at 295 K agree with the Hermans et al. (2011) σ(O 2 O 2 ) at 296 K within the instrumental measurement errors.The main confusion arises from the fact that under low aerosol conditions approaching a near pure Rayleigh atmosphere multi axis DOAS measurements (MAX-DOAS) of O 2 O 2 differential slant column density, ∆SCD, require a "correction factor" of about 0.75-0.89 to reproduce the O 2 O 2 ∆SCD modeled by different radiative transfer algorithms while using Hermans et al. (2011) σ(O 2 O 2 ) at 296 K (Table 1).
The σ dependence on temperature potentially originates from two sources: temperature dependence of K eq and temperature dependence of the true absorption cross section.Pfeilsticker et al. (2001) assumed that temperature dependence is solely due to K eq .Thalman and Volkamer (2013) demonstrated that the integral of the stronger absorption lines is temperature independent, while the line shape and peak values exhibit some temperature dependence.Introduction

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Full In this study we investigate the pressure and temperature dependence of the cross section peak values and line shape using actual field DOAS measurements of O 2 O 2 optical depth.We further assess the bias introduced by the temperature dependence of σ (O 2 O 2 ) on the DOAS fit, and discuss a possible solution.Using non-scattered directsun (DS) photons for σ measurements is very desirable, since O 2 O 2 optical depth is observed under actual atmospheric conditions and the photon path is well defined.Aircraft measurements in the free troposphere are advantageous, since they detect mainly Rayleigh scattered photons and facilitate a more straightforward comparison with Radiative Transfer Model (RTM) calculations.
This study presents O 2 O 2 "DOAS apparent" cross sections derived from DS and airborne MAX-DOAS (AMAX-DOAS) measurements for the 335-390 and 435-490 nm wavelength ranges.Pressure dependence was evaluated from DS data collected at three sites with roughly the same O 2 O 2 effective temperature (∼ 266 K) and pressures of 780, 925 and 1013 hPa.Temperature dependence of O 2 O 2 σ was examined from the ground-based DS and AMAX-DOAS measurements.DS data were collected at seven sites where O 2 O 2 T ranged from 247-275 K. AMAX-DOAS measurements were made between 9 and 13.2 km at near pure Rayleigh scattering conditions with O 2 O 2 T between 232 and 244 K.
The paper is organized in the following sections.Section 2 explains the methodology to calculate the normalized VOD and peak O 2 O 2 cross section using the DOAS technique.Section 3 describes the DS and AMAX-DOAS instrumentation, measurement sites and DOAS settings.Section 4 presents results.Conclusions are outlined in Sect. 5. Introduction

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Full  1) (Platt, 1994;Danckaert et al., 2012).DOAS separates the strongly wavelength dependent molecular absorption cross-section structure (σ i (λ)) of the absorbing gases from the weak wavelength dependence of the aerosol and molecular scattering and absorption (wide band extinction).
The DOAS technique does not require prior knowledge of Rayleigh and aerosol extinction to derive differential slant column densities (∆SCD i ) of a gas i , since the wide band extinction can be approximated by a low-order polynomial function (P Lo ).Unwanted instrumental stray light is removed as an offset term in Eq. (1).∆SCD i , the low-order polynomial function and offset are simultaneously fitted by a non-linear least squares algorithm to the difference between the logarithms of the attenuated (I) and reference (I ref ) spectra.The reference spectrum used in DOAS analysis is typically a solar spectrum measured by the same instrument under the lowest available slant path and abundance conditions.
The total vertical column density (CD) measured in any DOAS observation geometry is related to ∆SCD according to Eq. ( 2), where SCD REF is the SCD in the reference spectrum and the air mass factor (AMF) is the photon path enhancement relative to the Introduction

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Full The AMF for DS measurements is almost wavelength independent for most solar zenith angles (SZA) and can be easily estimated using the geometrical approximation, that is roughly equal to 1/ cos(SZA) (for the equation used in this study see Cede et al., 2006).
For weak absorbers with an almost constant vertical CD, such as O 2 O 2 , an increase in ∆SCD from DS measurements is mainly due to an increase in the photon path length (AMF).For this type of absorbers, the Langley Plot method is used to estimate SCD REF .
For MAX-DOAS measurements the AMF is wavelength dependent and is a function of atmospheric composition and scattering conditions and requires RTM.The main complication in MAX-DOAS AMF calculations arises from insufficient knowledge of aerosol micro/macro properties and spatial distribution.This is not a problem for modeling of a pure Rayleigh atmosphere.
To simplify further discussion we introduce a specific notation that is followed through the remainder of the paper.
1.All quantities that exhibit strong wavelength dependence are depicted as vectors: 2. All quantities that exhibit very small or no wavelength dependence are expressed as scalars: CD -"pseudo" column density derived from a specific fitting window [molecule 2 cm −5 ]; 3. All "true" or theoretically estimated quantities from the "true" measurements are expressed using " * " superscript: Introduction

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Full 8. Goodness of the linear fit between two quantities is expressed as the coefficient of determination (R 2 ).R 2 is rounded to two or three decimal places.In case of R 2 = 1.00 or 1.000 less than 0.5 % or 0.05 % of the variation cannot be explained by the linear model.

Pressure and temperature dependence
The DOAS technique can be applied to evaluate pressure and temperature dependence of a laboratory measured molecular absorption cross section for gases with known CD * , using remote sensing atmospheric observations with well defined AMFs.Introduction

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Full This is accomplished by evaluating the normalized τ (Eq. 3) calculated from the DOAS fitted radiance/irradiance as a function of T or P (Wagner et al., 2002). Where: - τ RESIDUAL is the residual optical depth that is not attributed to any known absorption by the DOAS analysis at wavelength λ in each measurement.
The main assumption of the approach is that OD of all species absorbing in the specific wavelength window are accounted for and the residual OD is only due to the variation in the cross section of the species of interest.Any significant differences in shape between the true O 2 O 2 cross section and the fitted σ should be captured in the residual optical depth."Broad" differences will be "masked" by the combination of the polynomial and offset fits.As a result the derived cross section in Eq. ( 3) is a "DOAS apparent" cross section which might not exactly match the true cross section.
In this study, the QDOAS software package (Danckaert et al., 2012) is used to derive the ∆SCD and τ from DS measurements and WinDOAS (Fayt and Van Roozendael, 2001) for the analysis of aircraft measurements.
To evaluate a potential pressure dependence of σ, we use a DS Fraunhofer spectrum, measured at a higher altitude (lower pressure) location, as a reference spectrum Introduction

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Full to analyze DS data collected at lower altitudes (higher pressure).The main requirements are high signal to noise ratio in the measurements at all locations and the same O 2 O 2 T * .DOAS derived ∆SCDs are then compared to ∆SCD * estimated from T , P and SH profiles at the corresponding sites.
To evaluate temperature dependence of σ, both DS and AMAX-DOAS data are used.
For DS observations a reference Fraunhofer spectrum measured at the smallest SZA is applied to the data collected at the same site.For the AMAX-DOAS measurements, a spectrum, collected at ceiling altitude (13.2 km) pointing 10 Richland, WA and Goddard Space Flight Center (GSFC/NASA), Greenbelt, MD.Temperature, pressure and specific humidity profiles were composed for each site from the following sources to ensure consistent vertical CD * calculation from the surface to the TOA: surface pressure, temperature and relative humidity measured by Vaisala Weather Transmitter WXT520; radio soundings launched at nearby sites twice a day (00:00 and 12:00 UTC, available at http://weather.uwyo.edu/upperair/sounding.html).During some field campaigns frequent ozonesonde measurements were also available (UAF, JPL, UAH).Introduction

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Full   MFDOAS spectra were analyzed in two wavelength regions 335-390 nm and 435-490 nm to evaluate the ∼ 360 and 477 nm absorption lines.Table 3 lists all fitting parameters and laboratory measured higher resolution molecular absorption cross sections used in DOAS analyses after convolution with the MFDOAS instrument transfer function.All cross sections were fitted as non-differential cross sections to remove dependence on the polynomial order used to estimate cross section broad band ab-Introduction

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Full A single, site specific, reference Fraunhofer spectrum was selected to analyze all the data available at the corresponding site (for the same instrument configuration).This reference spectrum was calculated as an average of spectra collected during a 30 min interval around a small SZA.Since O 2 O 2 CD * can vary by a few percent during a particular day due to diurnal pressure/temperature changes only days with relatively constant surface P were selected as reference days.Langley plot method to derive SCD REF was applied only to the DS spectra collected during these reference days.
Pressure dependence was examined by using a reference spectrum measured at JPL located at 2.3 km a.s.l. with surface pressure of 780 hPa to analyze data collected at WSU (925 hPa) and GSFC (1013) with O 2 O 2 T * ≈ 266 K.

AMAX-DOAS measurements of O 2 O 2 in a near pure Rayleigh atmosphere
The TORERO field experiment (Tropical Ocean tRoposphere Exchange of Reactive halogen species and Oxygenated VOC, January-February 2012) provided an opportunity to measure and assess O 2 O 2 absorption in a Rayleigh atmosphere by means of the University of Colorado airborne MAX-DOAS instrument (Baidar et al., 2013).TORERO deployed a unique selection of chemical in-situ and remote sensing instruments aboard the National Science Foundation/National Center for Atmospheric Research Gulfstream V aircraft (NSF/NCAR GV) over the Eastern Pacific Ocean.We have measured ambient temperature, pressure, water vapor and ozone (all by in-situ sensors), aerosol size distributions by an Ultra High Sensitivity Aerosol Spectrometer (UHSAS), as well as temperature profiles by the Microwave Temperature Profiler (MTP) (Denning et al., 1989;Lim et al., 2012), and aerosol extinction profiles by High Spectral Resolution LI-DAR (HSRL, Eloranta et al., 2008).Four cameras provide information on cloudiness forward, sideways, and below the aircraft.Research flight 05 (RF05) was conducted on 29 January 2012 from/to Antofagasta, Chile over the Southern Hemisphere subtropical Pacific Ocean, where the aircraft probed very clear air during a case study from 18:06-18:30 UTC (9-13.2km altitude; SZA of 12.4-12.0 • , 92.4-92.1 • E/29.7-29.9 • S).Introduction

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Full The ambient temperature varied from 235.4-214.3K.The corresponding O 2 O 2 effective temperatures, calculated for 360/477 nm using box-AMFs and measured T , P , SH, ranged from 243.4/239.3-235.3K/232.4K (see Table 2).The camera data shows only sparsely scattered boundary layer clouds.The aerosol extinction profile measured by the HSRL at 532 nm showed sub-Rayleigh aerosol extinction values above the aircraft.
The aerosol content in the stratosphere was nominally zero, i.e. the measured aerosol backscatter cross section is too small to derive any extinction values.Below the aircraft, aerosol extinction was sub-Rayleigh above 1.5 km, and agreed very well (better 0.01 km −1 ) with Mie calculations below 1.5 km (see Fig. 1).Mie calculations were constrained by measured size distributions, and used to better quantify the low aerosol extinction values in the free troposphere, FT, as well as to estimate the wavelength dependence of aerosol extinction at the O 2 O 2 wavelengths.The mean aerosol number density between 9 and 13.2 km was 5.8 ± 1.7 cm −3 .The average aerosol size distribution over this altitude range had an effective radius, R e = 0.11 ± 0.02 µm.Mie code was initiated assuming a constant refractive index, n, at all sizes and wavelength dependencies as described in Massie and Hervig (2013).Sensitivity studies varied n ∼ 1.55 (sea salt), ∼ 1.30 (ice) and ∼ 1.56 (mineral dust).The aerosol extinction values (sea salt) averaged between 9 and 13.2 km are 4.6 × 10 −4 km −1 (532 nm), 5.2 × 10 −4 km −1 (477 nm), and 6.7 × 10 −4 km −1 (360 nm), respectively.These numbers are 1 to 2 orders of magnitude lower than the extinction due to molecular (Rayleigh) scattering at the O 2 O 2 wavelengths (see Fig. 1).The atmospheric radiation state can be described in good approximation as a Rayleigh atmosphere.AMAX-DOAS measures scattered sunlight spectra from well-defined lines of sight.The limb scanning telescope has a FOV of 0.17 using the WinDOAS software package (Fayt and van Roozendael, 2001) for two wavelength windows: 350-387.5 nm (with a gap between 366 and 374.5 nm to minimize Ring effect) and 445-485 nm using (1) the Hermans cross section at 296 K (Hermans et al., 2011) and (2) the Thalman and Volkamer cross sections at 293 K and 203 K (Thalman and Volkamer, 2013).These analysis settings are optimized to retrieve robust ∆SCDs over the wide range of atmospheric conditions encountered during a typical 8 h flight time.A summary of analysis settings and cross sections used can be found in Table 3.One spectrum collected at 13.2 km altitude was used as a reference Fraunhofer spectrum to analyze all data (see Table 2).The reference elevation angle is upward looking (EA 10

Direct sun measurements
SCD REF were calculated from the DS measurements at each site in the UV and visible fitting windows using the Langley plot method.Figure 2 shows Langley plots for the reference data analyzed in 435-490 nm with the settings described in Table 3. Linear regression analysis shows high correlation between the DS ∆SCD and ∆AMF with R   (Thalman and Volkamer, 2013) some deviation from "1" is expected while fitting σ(O 2 O 2 ) at a single T. The observed divergences from "1" are 2.9 % at 360 nm and 1.6 % at 477 nm To evaluate the effect of aerosol extinction below the aircraft on the linear correlation between the measured ∆SCD and estimated SCD * (SCD REF and slope), we recalculated AMFs and SCD * including the extinction profiles derived from Mie theory.In the RTM aerosols are described by single scattering albedo (0.97 at 360 nm, 0.98 at 477 nm) and g-parameter (0.75-0.7 for 0-13 km).The extinction profile is taken from the Mie calculations for the sea salt case (see Fig. 1).For the aerosol scenario, agreement between the measured SCD REF and estimated SCD * REF slightly improves (0.9 % at 360 nm and 0.8 % at 477 nm), but slope deviations from "1" increase to 5.2 ± 5 % at 360 nm and 2.6 ± 1 % at 477 nm.DS measurements indicate a clear increase in DOAS normalized VOD at 360 and 477 nm, at a rate of 5 ± 2 % per 30 K, from 275 to 247 K. Similar trends are observed over all DS sites regardless of their dramatic differences in NO 2 , HCHO, H 2 O and O 3 columns.The spread of the derived "DOAS apparent" peak σ(O 2 O 2 ) of the 477 nm band (±1 %) is within the error of O 2 O 2 CD * from T , P , SH profiles (1.6 %).More variability is observed for the peak σ(O 2 O 2 ) of the 360 band (±2 %) due to a lower SNR in the UV part of the spectrum, and higher sensitivity to the DOAS fitting parameters.The AMAX-DOAS data exhibits a similar trend when using the Hermans et al. (2011) cross section between 231 and 244 K.   fitted O 2 O 2 ∆SCD is buffered by the fact that the integral O 2 O 2 absorption (integral over the wavelength window of each band) does not depend on temperature (Thalman and Volkamer, 2013).The temperature induced corrections required to bring DS and AMAX-DOAS VCDs to the model values are significantly smaller than the corrections reported for the boundary layer MAX-DOAS observations in the literature (0.94 ± 0.02 vs. 0.75 ± 0.1, see Table 1).When using two σ (203 and 293 K) the temperature dependent bias in the measured VCDs is essentially zero within errors at 477 nm.This illustrates the importance of (1) accounting for the temperature dependence of the O 2 O 2 cross section during the DOAS fit and (2) accurately representing the atmosphere in the RTM (results including aerosol are better compared to the Rayleigh case).

σ(O
The UV region, however, is more sensitive to the DOAS fitting parameters and does not show a clear improvement in the retrieved VCDs while using two σ (203 and 293 K).This is especially pronounced for DS measurements (Fig. 8) where several percent underestimation of the VCD is observed.AMAX-DOAS data seem to be less sensitive and show only a few percent underestimations that are insignificant within the low error bars., polynomial order (3, 4 and 5, depending on the ∆λ), offset order (0 and 1), and σ(O 3 ) (single temperature vs. two temperatures).

Error analysis of DS and AMAX
One standard deviation of the SCD REF derived from all fitting scenarios is reported as SCD REF error.For the visible spectral window this is about 1 % and 2.4 % for the UV.
The noise in the residual OD (Eq. 3) was significantly reduced by averaging daily measurements.This resulted in SNR increase in irradiance between 5-27 times depending on the observation schedule.
The total error in the normalized daily VOD and VCD is derived from the DOAS sensitivity scenarios and CD * ±1.6 % as one standard deviation.It is about 3.5 % for UV and 2.1 % for the visible wavelength regions.

Aircraft MAX-DOAS
The DOAS fitting error of ∆SCD(O 2 O 2 ) is the main error source for the AMAX-DOAS data.Error values listed in as shown in Fig. 3 and detailed in Table 4.These offsets agree within error bars with those computed from RTM for a Rayleigh atmosphere, or for an atmosphere containing aerosols (see Table 4).
The excellent agreement between DS DOAS (no RTM) and AMAX-DOAS (uses RTM) is not trivial, given the need for radiative transfer calculations, and active control of telescope pointing with AMAX-DOAS observations (Baidar et al., 2013).For example, a 1 % uncertainty in the Rayleigh scattering cross section used in the RTM directly translates into an error of the same order in the predicted O 2 O 2 SCD.A recent laboratory study extends knowledge about Rayleigh scattering cross sections at UV wavelengths (Thalman et al., 2014), and confirms that the cross sections that underlie our RTM are correct within very small error bounds (< 1 %).This is noteworthy, since variations in the Rayleigh scattering cross-sections had been found around 4 % at 477 nm when comparing empirical fits of previous measurements in the literature with theory (Thalman et al., 2014).We conclude that any systematic bias from using the RTM to interpret the AMAX-DOAS measurements is not due to the representation of Rayleigh scattering, and limited by the small remaining uncertainty due to aerosols.Missing knowledge on aerosol distribution and properties in the atmosphere presents a fundamental limitation to determining SCD REF for AMAX-DOAS measurements.

AMTD Introduction Conclusions References
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Full The difference in SCD REF between a Rayleigh or aerosol atmosphere introduces a systematic error of about 2 % in modeled VCD and VOD values (see Figs. 6 and 8).We consider this to be the limit at which our data can be considered accurate.The overall errors for both DS and AMAX-DOAS are comparable, particularly after averaging of AMAX-DOAS ∆SCD(O 2 O 2 ).The effect of σ(O 2 O 2 ) temperature dependence on the fitted O 2 O 2 ∆SCD is buffered by the fact that the integral O 2 O 2 absorption (integral over the wavelength window of each band) does not dependent on temperature (Thalman and Volkamer, 2013).SCD retrieved from DS and AMAX-DOAS measurements were within 6 % of the model/T , P , SH SCD even at temperatures below 250 K.This suggests that σ(O 2 O 2 ) cross sections do not contribute to creating the need for correction factors of 25 ± 10 % reported in the literature for some PBL MAX-DOAS measurements where the effective O 2 O 2 temperatures are expected to be between 265 K (zenith) to 275 K (1-2 • EA).
T -dependent bias in ∆SCD can be reduced by simultaneously fitting σ(O 2 O 2 ) at different temperatures, which becomes increasingly important for measurements with effective O 2 O 2 temperatures below 250 K as is the case for AMAX-DOAS measurements.Fitting σ(O 2 O 2 ) at 203 and 293 K improved AMAX-DOAS results in both UV and visible wavelength regions.Introduction

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Full  Full  Full  Full  Full  Full    Full were analyzed using AMAX-DOAS settings (Table 3).AMAX-DOAS data is averaged and 894 binned for 2K increments for a pure Rayleigh atmosphere and including aerosols.3).AMAX-DOAS data is averaged and binned for 2 K increments for a pure Rayleigh atmosphere and including aerosols.
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | spectroscopy (DOAS) for weak absorbers is based on the modified Beer-Lambert law which describes solar radiation attenuation due to molecular and aerosol absorption and scattering, Eq. ( Discussion Paper | Discussion Paper | Discussion Paper | CD * -"pseudo" column density calculated from the temperature (T ), pressure (P ) and specific humidity (SH) profiles [molecule 2 cm −5 ]; τ * -theoretical O 2 O 2 "pseudo" absorption optical depth: τ * = σ • CD * ; T * -O 2 O 2 "pseudo" profile and box-AMF weighted effective temperature [K]; 4. Differential quantities are expressed using a "∆" prefix; 5. Quantities integrated along the photon path (slant) are expressed using an "S" prefix, quantities integrated along the vertical direction (vertical) have no prefix notation; 6. Quantities describing the reference spectrum are expressed using "REF" as subscript: CD REF -CD in the reference spectrum; T * REF -O 2 O 2 "pseudo" profile weighted effective temperature at the reference time [K]; τ REF -O 2 O 2 "pseudo" absorption optical depth in the reference spectrum; 7. The word "pseudo" is omitted while referring to O 2 O 2 parameters.
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | • and is actively angle stabilized to better 0.2• accuracy in real time(Baidar et al., 2013;Dix et al., 2013).Two synchronized spectrograph-detector units (Acton SP2150/PIXIS400B CCD) simultaneously observed the spectral ranges from 330-470 nm (0.7 nm Full Width Half Maximum (FWHM) optical resolution) and 430-680 nm (1.2 nm FWHM optical resolution).O 2 O 2 ∆SCDs were retrieved by application of a non-linear least squares DOAS fitting routine Introduction Discussion Paper | Discussion Paper | Discussion Paper | 000 for the visible wavelength region and better than 0.980 for UV.The final error in the SCD REF derived from the UV and visible wavelength windows was determined as one standard deviations of SCD REF calculated from ∆SCDs with different DOAS fitting parameters (e.g.polynomial order, offset order, fitting window boundaries).The estimated relative error in SCD REF from the visible wavelength region is about 1 % and from the UV wavelengths is about 2.4 %.Derived SCD REF from DS measurements agree with the SCD * REF within these errors.4.1.2AMAX-DOAS measurements SCD REF in the AMAX reference Fraunhofer spectrum, measured at 13.2 km and 10 • EA, was calculated from the linear correlation between the measured ∆SCD and modeled SCD * at 360 and 477 nm assuming pure Rayleigh scattering conditions (Fig. 3, upper panel).SCD * accounted for an altitudinal dependence of O 2 O 2 CD * .The slant column amount contained in the reference, SCD REF , is the absolute value of Discussion Paper | Discussion Paper | Discussion Paper | the intercept.Linear regression parameters are summarized in 2 O 2 ) pressure dependence from DS measurements To investigate the effect of pressure on the O 2 O 2 VOD we used the Fraunhofer reference spectrum collected over JPL (7 July 2007) to analyze the reference spectra collected over WSU, Pullman, WA (11 September 2007) and GSFC, Greenbelt, MD (23 May 2007).The estimated ∆SCD * over WSU relative to JPL reference column is 0based on the calculated CD * from T , P , SH profiles and AMFs of the corresponding measurements.DOAS retrieved ∆SCD from 435-490 nm window in the WSU spectrum from 11 September 2007 and in GSFC spectrum from 23 May 2007 relative to Discussion Paper | Discussion Paper | Discussion Paper |

4. 3
Temperature dependence of observed τ(O 2 O 2 )Since no pressure dependence was observed between 780 and 1013 hPa, we combined data from all sites for DS and from AMAX-DOAS measurements to determine the temperature dependence of σ(O 2 O 2 ).O 2 O 2 from DS measurements (Eq. 3) were averaged to produce single daily values.CD * calculated from T , P and SH profiles were interpolated on a DS daily time grid.The AMAX-DOAS data were binned and averaged within 2 K increments to derive vertical column densities.CD * was calculated from simultaneous in-situ temperature and pressure measurements, corrected by insitu water vapor data.Above the aircraft the temperature profile was extended using MTP data and RAQMS model pressure.

Figure 5
Figure 5 provides an example of the of the AMAX-DOAS spectral fit in the UV and visible windows for O 2 O 2 effective temperatures of 239.7±0.4K at 360 and 234.8±0.5 K

Figure 6
Figure 6 shows vertical optical depths at 360 (A) and 477 nm (B), derived from DS and AMAX-DOAS measurements over all sites, and normalized by VOD * .Normalization by VOD * is done to remove differences in spectral resolution between the MFDOAS and AMAX-DOAS instruments.It also allows to detect any systematic differences in DOAS retrieved τ(O 2 O 2 ) as a function of temperature relative to the fitted Hermans et al. (2011) σ(O 2 O 2 ) at 296 K. DS measurements indicate a clear increase in DOAS normalized VOD at 360 and 477 nm, at a rate of 5 ± 2 % per 30 K, from 275 to 247 K. Similar trends are observed over all DS sites regardless of their dramatic differences in NO 2 , HCHO, H 2 O and O 3 columns.The spread of the derived "DOAS apparent" peak σ(O 2 O 2 ) of the 477 nm

Figure 7
Figure 7 shows the comparison between O 2 O 2 peak σ(T * ) of 360 and 477 nm bands derived from DS and AMAX-DOAS measurements using Hermans et al. (2011) σ (this work) and published σ.Peak values derived in this work and Thalman and Volkamer (2013) agree within the DS and AMAX-DOAS errors for both bands at 233, 253 and 273 K. Error budgets for the DS and AMAX-DOAS O 2 O 2 peak σ (T) of 360 and 477 nm bands are summarized in Table 5 (for the detailed discussion of errors see Sect.4.5).Sneep et al. (2006) peak σ (230 K) at 477 nm is 18 % lower than the observed values in this study.Osterkamp et al. (1998) and Wagner et al. (2002) measured O 2 O 2 absorptions under atmospheric conditions.Osterkamp et al. (1998) peak σ (256 K) at

Figure 8
shows measured VCD normalized by VCD * in case of fitting one σ (Hermans et al., 2011, at 296 K) and two σ (Thalman and Volkamer, 2013, at 203 and 293 K) for DS and AMAX-DOAS measurements at 360 (A) and 477 nm (B).The inverse of the normalized VCD can be interpreted as "correction factors" necessary to bring the measured VCDs to "true" VCD * .In case of fitting a single σ at 296 K the CFs are temperature-dependent and range from 1 ± 0.02 at 275 K to 0.94 ± 0.02 at 231 K for both UV and visible spectral regions.The effect of temperature to bias the 10034 Discussion Paper | Discussion Paper | Discussion Paper | The main source of error in DS τ(O 2 O 2 ) measurements is DOAS fitting error of ∆SCD(O 2 O 2 ).Since DS AMF(O 2 O 2 ) is wavelength independent at most SZA, retrieval in any of the wavelength regions where O 2 O 2 has a significant absorption should produce the same ∆SCD.In practice, DOAS fitting parameters such as order of the polynomial function, mimicking Rayleigh and Mie extinction, exact fitting window boundaries, offset correction, uncertainties in cross sections of other trace gases absorbing in the same wavelength region, errors in instrument transfer function and wavelength Discussion Paper | Discussion Paper | Discussion Paper | calibration introduce errors in ∆SCD.
Discussion Paper | Discussion Paper | Discussion Paper | DS and AMAX-DOAS measurements of O 2 O 2 absorption optical depths under actual Earth atmospheric conditions in two wavelength regions (335-390 nm and 435-490 nm).DS irradiance measurements were made by the research grade MFDOAS instrument from 2007 to 2014 at seven sites with significant pressure (778-1020 hPa) and O 2 O 2 profile weighted temperature (247-275 K) differences.Aircraft MAX-DOAS measurements were conducted by the University of Colorado airborne MAX-DOAS instrument on 29 January 2012 over the Southern Hemisphere subtropical Pacific Ocean.Scattered solar radiance spectra were collected at altitudes between 9 and 13.2 km, with O 2 O 2 effective temperatures of 231-244 K, and near pure Rayleigh scattering conditions.The data were evaluated to understand temperature and pressure dependence of the O 2 O 2 molecular absorption cross section using vertical O 2 O 2 column densities calculated from atmospheric sounding, in-situ data and/or model temperature and pressure profiles adjusted by the surface observations.DS data interpretation involves a simple geometric calculation of AMF.AMAX-DOAS observations, on the other hand, require RT modeling of atmospheric conditions to estimate AMF.Based on the atmospheric DS observations, there is no pressure dependence of the O 2 O 2 cross section within MFDOAS errors (3 %).A temperature dependence in σ(O 2 O 2 ) from 231 to 275 K was observed at about 9 ± 2.5 % per 44 K rate in both wavelength regions from DS and AMAX-DOAS measurements.The change in band shape described by Thalman and Volkamer (2013) was observed under atmospheric Discussion Paper | Discussion Paper | Discussion Paper | conditions in both DS and AMAX-DOAS datasets.Derived peak O 2 O 2 cross sections of 360 and 477 nm bands were compared to the recent laboratory measured O 2 O 2 cross sections of Thalman and Volkamer (2013) at 233, 253 and 273 K.The agreement between the peak O 2 O 2 cross sections at both wavelengths is within 3 %.The combined observations of DS and AMAX-DOAS measurements support the fact that laboratory measured O 2 O 2 cross sections are well suited for DOAS observations under typical atmospheric conditions.

Figure 6 .
Figure 6.Vertical optical depth at 360 (A) and 477 nm (B), derived from DS and AMAX-DOAS measurements over all sites, and normalized by the VOD * calculated from sonde/measured/model temperature, pressure and specific humidity profiles as a function of O 2 O 2 effective temperature.AMAX-DOAS data is averaged and binned for 2 K increments for a pure Rayleigh atmosphere and including aerosols.Table 3 lists DOAS settings.

Figure 7 .
Figure 7. Collision induced absorption cross section of O 2 O 2 at 360 (A) and 477 nm (B) recorded in literature since 1990 at their corresponding spectral resolutions.DS and AMAX DOAS derived peak cross sections (this work) are scaled to 0.3 nm FWHM, using Hermans et al. (2011) 296 K. 895

Figure 8 .
Figure 8. DS and AMAX-DOAS derived VCD from DOAS fitting in the UV (A) and visible (B) spectral windows using σ(O 2 O 2 ) by (1) Hermans et al. (2011) 296 (black symbols) and (2) Thalman and Volkamer (2013) at 203 and 293 K (red symbols), and normalized by VCD * calculated from model (AMAX) and measured T , P and SH profiles.DS UV spectra, collected with U340 filter, were analyzed using AMAX-DOAS settings (Table3).AMAX-DOAS data is averaged and binned for 2 K increments for a pure Rayleigh atmosphere and including aerosols.
∆sτ is the DOAS fitted O 2 O 2 τ at effective measurement temperature T

Results and discussion 4.1 O 2 O 2 reference slant optical depth in direct sun and AMAX-DOAS measurements
Deutschmann et al., 2011), a fully spherical Monte Carlo RTM, for 360 and 477 nm.Radiation fields were constrained by in-situ pressure, temperature, water vapor, ozone, MTP temperature profiles, and stratospheric profiles of NO 2 and O 3 taken from the Real-time Air Quality Modeling System (RAQMS)(Piers et al., 2007).The O 2 O 2 vertical profile was calculated as the square of the O 2 concentration based on measured temperature and pressures and corrected for water vapor concentration.Ocean surface albedo was set to 5 % at 360 nm and to 8 % at 477 nm.Solar and observation geometry were input variables for the RTM.Introduction Estimation of sτ REF in Eq. (3) requires determination of SCD REF from DS and AMAX-DOAS data.SCD REF are calculated from the DOAS fitted ∆SCD using Hermans et al. σ(O 2 O 2 ) at 296 K by applying the Langley Plot method.SCD REF is then multiplied by σ to determine sτ REF .
• ) to minimize the slant column amount contained in the reference, SCD REF .Spectra were measured with elevation angle (EA) 0 • (i.e.horizontal and parallel to flight altitude) during ascent; further three upward angle scans (1 • , 2 • , 5 • ) at constant flight altitude (13.2 km) were included in the analysis.Radiative transfer calculations were performed with McArtim (Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 4

Table 4 .
The modeled SCD REF values agree with the SCD REF inferred from the measurements within 1.7 % at 360 nm and 1.6 % at 477 nm.The slope of the linear correlation is expected to be unity if there is no temperature dependence of σ(O 2 O 2 ), and atmospheric conditions are correctly described by the model.Given the small temperature dependence of the O 2 O 2 cross section shape ) without any significant spectral structure.Corresponding ∆SCD retrieved in the 335-392 nm fitting region were (0.688 ± 0.014) and (0.579 ± 0.014) × 10 3 molecules 2 cm −5 .Residual ODs in UV were about two times larger than in visible due to smaller signal-to-noise ratio (SNR) in the UV part of the MFDOAS spectrum compared to the visible.Some of the residual structure in UV is probably the result of incomplete removal of stray light due to scattering of photons with longer wavelength within the spectrograph.Hoya U340 filter was added after 2008 to improve SNR in the UV.Figure4shows DOAS apparent σ(O 2 O 2 ) estimated from the T , P , SH profiles at the two sites.The agreement between the derived σ(O 2 O 2 ) at 1013 and 925 hPa (relative to 780 hPa) and Hermans laboratory measured σ(O 2 O 2 ) at 296 K (after convolution with MFDOAS ITF) is better than 3 %.We conclude that σ(O 2 O 2 ) does not exhibit a pressure sensitivity between 780 and 1013 hPa within typical DOAS instrumental and fitting errors.

Accounting for temperature dependence of measured τ(O 2 O 2 ) in DOAS fit
477 nm agrees with the results presented here within the measurement errors.Wagner et al. (2002) O 2 O 2 peak σ (242 K) are 25 % and 12 % larger than the derived values in this study for 360 and 477 nm correspondently.
temperature.Figure3and Table 4 also show effect of more accurately accounting for temperature dependence of σ on correlation between AMAX measured ∆SCD and modeled SCD.The results for Rayleigh and aerosol cases at 477 nm are comparable to fitting O 2 O 2 σ at a single T within corresponding errors.The slopes are indistinguishable from unity and the SCD REF are within less than 1 % of the modeled SCD * REF .Fitting two O 2 O 2 cross sections has a more pronounced effect on the slope and SCD REF at 360 nm.Derived slopes decrease both for pure Rayleigh and aerosol cases by about 7 %, which brings the slope for the aerosol case within 2 % of unity.While the temperature dependence in the combined ∆SCD vs. SCD * is reduced the recalculated SCD REF are slightly underestimated: by less than 7 % for pure Rayleigh case and 5 % for aerosol case.
Table 5 summarizes DS normalized τ(O 2 O 2 ) errors calculated for different DOAS fitting scenarios accounting for variability in CD.An error associated with DS AMF comes from the uncertainty in SZA ephemeris and O 2 O 2 effective height calculation.The error in SZA calculation is 0.02 • and error in O 2 O 2 effective height is less than 200 m.This translates to an error of less than 0.1 % at SZA < 80 • which increases to 2 % at 88 • SZA.Since most measurements contributing to the final results come from the observations at SZA < 80 • we assume AMF error of 0.1 %.Error in the total CD * calculated from the T , P , SH profiles is determined as one standard deviation of CD * variability at a specific T .Yearly average relative error is about 1.6 % To evaluate ∆SCD and SCD REF errors associated with the DOAS fitting parameters we varied the wavelength fitting windows Table 5 are representative for individual measurements with a 15 s time resolution.Statistical averaging of individual spectra can be used to further reduce this error.The total errors of 5.2 % at 360 nm and 2.4 % at 477 nm are therefore 10036 Introduction upper limits, particularly in the UV.AMAX-DOAS data shown in Figs. 6 and 8 is taken from EA 0 • measurements only.Unlike for the DS measurements, Eq. (3) was directly applied to the AMAX-DOAS ∆SCD results without prior averaging.To reduce scatter VOD and VCD data included in Figs. 6 and 8 are averages and standard deviations of binned data in 2 K increments.The AMF error is due to the statistical nature of the Monte Carlo RTM McArtim (statistical uncertainty).McArtim was initiated several times with identical settings and variations are small.The error in the total O 2 O 2 CD * is directly representative of the error in our temperature measurements; errors due to pressure measurements are negligible.The major source of uncertainty is related to assumptions about SCD REF .We assess this error by determining SCD REF experimentally from the offsets of linear fits of measured ∆SCD(O 2 O 2 ) over modeled SCD(O 2 O 2 ) Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

Table 2 .
O 2 O 2 vertical column density and effective temperature at the observation sites during Direct Sun and aircraft MAX-DOAS measurement periods.

Table 3 .
DOAS analysis parameters used in direct sun and aircraft MAX-DOAS analysis.

Table 5 .
Error budget of the 360 and 477 nm band peak O 2 O 2 σ(T ) derived from DS and AMAX-DOAS measurements.
a < 3.5 % b < 2.3 % a < 0.9 % b a Maximum relative error from Table 4. b Maximum relative error weighed by the relative contribution of the SCD ref to the overall; SCD = dSCD + SCD ref ; weighed relative error = (SCD ref /SCD) • SCD ref, error ; the ratio SCD ref /SCD is on average 0.51 and 0.39 at 360 nm and 477 nm, respectively.Introduction Table 3 lists DOAS settings.
Table 3 lists DOAS settings.Introduction