Retrieval of carbon dioxide vertical profiles from solar occultation observations and associated error budgets for ACE-FTS and CASS-FTS

An algorithm is developed to retrieve the vertical profile of carbon dioxide in the 5 to 25 km altitude range using mid-infrared solar occultation spectra from the main instrument of the ACE (Atmospheric Chemistry Experiment) mission, namely the Fourier transform spectrometer (FTS). The main challenge is to find an atmospheric phenomenon which can be used for accurate tangent height determination in the lower atmosphere, where the tangent heights (THs) calculated from geometric and timing information are not of sufficient accuracy. Error budgets for the retrieval of CO2 from ACE-FTS and the FTS on a potential follow-on mission named CASS (Chemical and Aerosol Sounding Satellite) are calculated and contrasted. Retrieved THs have typical biases of 60 m relative to those retrieved using the ACE version 3.x software after revisiting the temperature dependence of the N 2 CIA (collision-induced absorption) laboratory measurements and accounting for sulfate aerosol extinction. After correcting for the known residual high bias of ACE version 3.x THs expected from CO 2 spectroscopic/isotopic inconsistencies, the remaining bias for tangent heights determined with the N 2 CIA is −20 m. CO2 in the 5–13 km range in the 2009–2011 time frame is validated against aircraft measurements from CARIBIC (Civil Aircraft for the Regular Investigation of the atmosphere Based on an Instrument Container), CONTRAIL (Comprehensive Observation Network for Trace gases by Airline), and HIPPO (HIAPER Pole-to-Pole Observations), yielding typical biases of−1.7 ppm in the 5–13 km range. The standard error of these biases in this vertical range is 0.4 ppm. The multiyear ACE-FTS data set is valuable in determining the seasonal variation of the latitudinal gradient which arises from the strong seasonal cycle in the Northern Hemisphere troposphere. The annual growth of CO 2 in this time frame is deermined to be 2.6±0.4 ppm year −1, in agreement with the currently accepted global growth rate based on ground-based measurements.


Introduction
Besides water vapor, carbon dioxide is the most important greenhouse gas.Its concentration in the atmosphere has been rising at an increasing rate for decades (Hofmann et al., 2009), with a rate of 1.66-2.44ppm year −1 in the 2009-2012 period for the background global mean (http://www.esrl.noaa.gov/gmd/ccgg/trends/global.html).There is growing global concern about the consequential climate change with its broad spectrum of impacts on life across the planet.Efforts to curb the atmospheric growth of this greenhouse gas are difficult because of its long atmospheric lifetime and our dependence on fossil fuels.Nonetheless, a thorough scientific understanding of the budget of CO 2 , a gas innate to Published by Copernicus Publications on behalf of the European Geosciences Union.life on this planet, is needed.To address this need, a wide range of measurements (concentrations, fluxes, isotopes) and modeling tools are being developed.Satellite-based remote sensing provides a global view, although the vertical distribution of CO 2 , which is a very important piece of observational information, is sparse or lacking.CO 2 volume mixing ratio (VMR) profiles in the mesosphere (above ∼ 70 km) and lower thermosphere have been retrieved globally from observations by the Atmospheric Chemistry Experiment -Fourier transform spectrometer (ACE-FTS) where tangent heights are determined from geometric information (Beagley et al., 2009;Emmert et al., 2011).Because this approach is generally not of sufficient quality in the lower stratosphere and troposphere to measure CO 2 , limb-viewing thermal infrared sounders such as the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS, Fischer et al., 2008) and High Resolution Dynamics Limb Sounder (HIRDLS, Gille et al., 2008) use CO 2 simply for tangent height and temperature determination and sacrifice the opportunity to measure the VMR profile.
This was also the case with ACE-FTS until recently (Foucher et al., 2009).ACE-FTS is onboard SCISAT, a satellite in a low Earth orbit, which was launched in August 2003.The measurements are performed at sunrise and sunset using the solar occultation technique, which, by the design of the experiment, provides the following three advantages which ultimately translate into retrieval accuracy: 1. high signal-to-noise ratio, 2. self-calibration, and 3. a single, geometric path length at each tangent height.
The spectral range is 750-4400 cm −1 (2.3-13.3µm) and the spectral resolution is 0.02 cm −1 .The orbital inclination of 74 • results in better coverage of high latitudes, but the tropics are probed in four different months of the year, covering the four seasons.More than a decade after launch, ACE-FTS continues to have a signal-to-noise ratio (SNR) of ∼ 400 in the 4 µm region, as determined by analysis of spectra at the highest tangent heights (130-150 km).In the other relevant spectral region (7 µm), the SNR is 300 to 400 (e.g., Châteauneuf et al., 2005).
In this work, we improve the retrieval of vertical profiles particularly via major improvements to the tangent height determination.We also perform comprehensive error budgets for ACE-FTS and the FTS on the proposed CASS (Chemical and Aerosol Sounding Satellite) mission (Melo et al., 2013).

Method
Retrieval of CO 2 and tangent height in this work builds on previous algorithm development by Boone et al. (2005), Foucher (2009), Foucher et al. (2009Foucher et al. ( , 2011)), and Rinsland et al. (2010).As discussed by Boone et al. (2005), below ∼ 43 km, tangent heights (THs) cannot be accurately determined from the geometric information (satellite position and instrument viewing angle) and thus atmospheric observables are exploited for this purpose.The ACE version 2.2 (v2.2) and v3.x (v3.0 and v3.5) retrieval algorithms (Boone et al., 2005(Boone et al., , 2013) ) use CO 2 absorption lines, but the retrieval problem becomes circular if one wants to retrieve CO 2 VMR using THs determined with absorption by this molecule.Other atmospheric molecules which have thermal infrared absorption and could possibly be used for tangent height determination include O 2 and N 2 because their VMRs are well known, and constant through the troposphere and stratosphere.The O 2 magnetic dipole and electric quadrupole vibrational fundamental bands, the N 2 electric quadrupole vibrational fundamental, and the O 2 and N 2 collision-induced absorption (CIA) vibrational fundamentals are essentially the five options excluding CO 2 .In theory, the O 2 and N 2 lines would be preferable to N 2 CIA because there would be no bias due to non-opaque clouds and the upper altitude would be much higher (e.g., 48 km for N 2 quadrupole versus ∼ 25 km for N 2 CIA).If we could demonstrate that the VMR of N 2 could be retrieved accurately using its quadrupole lines, then one would expect that tangent heights retrieved from these lines would also be accurate.However, even though nonlocal thermodynamic equilibrium in N 2 absorption measurements below 35 km is expected to be a small-to-negligible effect (e.g., Goldman et al., 2007), the retrieval of N 2 from the quadrupole line does not have the necessary precision and suffers from a low bias at the lowest altitudes.We were able to improve the N 2 VMR retrieval from the quadrupole lines compared to those retrieved using the ACE-FTS v3.x algorithm by adding lines with higher rotational quantum numbers, but ultimately the retrieval remained significantly biased relative to the expected 78 % VMR of N 2 (see also Goldman et al., 2007); the N 2 line parameters are not satisfactory.Regarding O 2 , we found that the retrieval could not be extended below 15 km because of saturating H 2 O lines, and therefore the O 2 magnetic dipole and electric quadrupole lines did not meet our goal of retrieving into the troposphere globally.This same interference would affect a TH retrieval using the O 2 CIA.
ACE-FTS has a circular field of view of 1.25 mrad with a diameter of 3 to 4 km at the tangent point.Vertical sampling distance is dependent on the tangent height and the angle between the satellite velocity vector and the line-ofsight, namely the beta angle.In the troposphere and lowermost stratosphere, the vertical sampling is typically ∼ 1 km.ACE-FTS profiles are not perfectly vertical since the satellite motion results in a difference in the satellite position for each tangent point.For low beta angles, the horizontal displacement of the tangent point during a limb scan is negligible, but for high beta angles, it can reach 400 km over the 5-25 km altitude range.The modified global fitting method is used (Boone et al., 2005), and tangent heights are retrieved simultaneously with CO 2 VMRs.The ACE-FTS v3.x retrieval software was adapted for this application.One of the main modifications was to fit the scale and slope parameters (Boone et al., 2005) for the microwindows targeting CO 2 but not for the microwindows targeting N 2 CIA.

Atmos
Considering all of the microwindows listed in Tables 1-2 below, the significant interferers are 18 O 12 C 16 O, 17 O 12 C 16 O, 12 CH 4 , 13 CH 4 , 14 N 14 N 16 O, 15 N 14 N 16 O, 14 N 14 N 18 O, H 2 17 O, and HDO.For these species, the vertical profiles of VMR, normalized by their standard natural isotopic abundance, are assumed to be equal to the VMR of their respective primary isotopologue, recovered using version 3.x of the ACE-FTS retrieval software (Boone et al., 2013).The sensitivity to this assumption is checked as part of the error budget (Sect.2.3).

N 2 CIA modelling and uncertainties
The Lafferty et al. (1996) N 2 CIA cross-section spectra measured in the laboratory at five temperatures are considered to be the best available for temperatures below 300 K according to Richard et al. (2012).The stated uncertainties in the Lafferty et al. (1996) absorption coefficients are in the 0.71 % to 0.9 % range if the uncertainty in the background spectra is added in quadrature to the uncertainty from the absorption spectra.Menoux et al. (1993) state the uncertainty in their measurements above 2470 cm −1 rises from 5 % (near the band center) to 10 %.The empirical model proposed by Lafferty et al. (1996) is: where ν is the wavenumber (cm −1 ), T is the temperature (K), and T 0 is the reference temperature of 296 K. B 0 and β 0 are the model parameters which are independent and dependent on temperature, respectively.B 0 represents the absorption coefficient of N 2 -N 2 at 296 K while β 0 represents its temperature dependence at this reference temperature.In reality, β 0 is determined using the spectra at five different temperatures in the range 228.2-272.1 K available in the highresolution transmission (HITRAN) 2012 database (Rothman et al., 2013), and the empirical law in Eq. ( 1).We determine the best β 0 (ν) on the 0.25 cm −1 grid of the Lafferty et al. (1996) measurements by absolute difference minimization of Eq. ( 1) at each wavenumber increment independently.This involves interpolating B 0 (ν) from Table 1 of Lafferty et al. (1996) to the 0.25 cm −1 grid.We then average the best β 0 (ν) in 5 cm −1 bins in the 2130 to 2600 cm −1 range to reduce noise.This results in the pink curve in Fig. 1.In order to test the precision of the empirical model, we obtain five spectral simulations of B 0 by dividing the five observed B(T ) spectra by the exponential function on the right hand side of Eq. ( 1) inserting the appropriate T in each case as well as the best-fit β 0 spectrum (obtained using the spectra at all five temperatures).The standard deviation of the five B 0 (ν) spectra is a measure of the consistency of the observed spectra and also reflects any inaccuracy in the empirical model.Lafferty et al. (1996).The pink squares were determined in this work, while previous attempts were made by Hartmann (Lafferty et al., 1996) in blue-grey and Foucher (2009) in dark blue using the same data set.Also shown in green is the temperature-dependence model parameter determined here using the less precise measurements of Menoux et al. (1993).
The relative uncertainties in B 0 based on the standard deviation is similar to the quoted uncertainty (see above), except that at the low and high (ν > 2480 cm −1 ) frequency ends of the band, the relative uncertainty clearly exceeds 1 %, similar to the frequency-dependence of the uncertainty found by Menoux et al. (1993).
We also determined the temperature dependence from the data set provided by Menoux et al. (1993) but it did not improve the retrieved tangent heights when applied for wavenumbers ≤ 2600 cm −1 (the upper limit of Lafferty's published measurements).We use the Menoux et al. (1993) measurements to determine the density-normalized N 2 -N 2 CIA coefficients at 296 K and their temperature dependence (following Lafferty et al., 1996) in order to extend the N 2 CIA empirical model out to 2640 cm −1 .The temperaturedependence spectra that we obtained independently using the Menoux et al. (1993) and Lafferty et al. (1996) N 2 CIA spectra are more consistent, particularly near 2500 cm −1 , than the temperature-dependence spectra obtained previously (Lafferty et al., 1996;Foucher, 2009) as shown in Fig. 1.
For this work, we have applied a uniform increase to the B 0 spectrum of Lafferty et al. (1996) of 0.9 % and additionally by 0.1 % and 0.2 % at 2500 and 2505-2510 cm −1 , respectively.These increases are within the uncertainties stated by Lafferty et al. (1996) (discussed above) or the variation of the five B 0 estimates as a function of wavelength.Lafferty et al. (1996) published the following fit to the temperature dependence of the relative N 2 collision efficiency with O 2 versus collision with itself (N 2 ) of (2) Absorption due to N 2 -H 2 O collisional complexes (Baranov et al., 2012) is neglected.This is a safe assumption for the upper troposphere and lower stratosphere where water vapor is typically < 0.1 % of air by volume.Using Eqs. ( 1)-( 2) and the temperature dependence shown in Fig. 1, as well as 0.7808 and 0.2095 for the VMRs of N 2 and O 2 , we obtained a slightly modified version of Eq. (8) of Lafferty et al. (1996).

Retrieval setup and microwindows
The HITRAN 2012 database (Rothman et al., 2013) is used in this work whereas ACE v3.x relies on HITRAN 2004 (with some updates) (Boone et al., 2013).

Cloud detection
Cloud detection is carried out as a pre-processing step before the CO 2 profile retrieval.Following Foucher (2009) adjacent tangent heights exceeds an empirically determined value of 0.0689, a cloud is assumed to be present.Similarly at 2505.5 cm −1 , if the change in transmittance between adjacent tangent heights exceeds 0.076, a cloud is assumed to be present.Foucher (2009) used 0.1 as a threshold for both cloud microwindows.The CO 2 retrieval is not applied to cloudy occultations.These empirical settings are very stringent for the purpose of reducing cloud-related error in the determination of THs to a level where it is not a dominant source of CO 2 retrieval error (see Sect. 2.3).Some false positives may be present (i.e., occultation is flagged as cloudy when it is not).Out of 16 676 available occultations in the 2009-2011 time period, 77 % are deemed to be cloudy and not processed and an additional 15 % are cloudy only at 2505.5 cm −1 and are processed (see below).The remaining 8 % constitute the cloud-free data set.

Tangent heights
To retrieve tangent heights via the N 2 CIA, we use the 12 microwindows in Table 1.For the microwindows at 2505, 2492.1, and 2462 cm −1 , the central frequencies and widths were specified in Foucher et al. (2009).The center frequencies for the first and third microwindows were obtained via private communication with Foucher. Foucher et al. (2011) mentioned the use of a microwindow at 2430 cm −1 .We have optimized the microwindow center and width in terms of interfering absorption.We find that the tangent heights retrieved using the microwindow at 2462 cm −1 were inconsistent with those retrieved from higher frequencies (> 2492 cm −1 ).To remedy this likely spectroscopic issue, we have added five narrow microwindows within this 30 cm −1 gap to help smoothly transition between these two inconsistent microwindows.In choosing these narrow microwindows, we avoided strong lines due to 14 N 14 N 16 O, 14 N 14 N 18 O, and 12 CH 4 so that the depth due to absorption at the line center is < 7.5 % (at ACE-FTS resolution) for any remaining lines for the tangent height ranges given in Table 1.It is clear that Foucher et al. (2009Foucher et al. ( , 2011) also avoided strong interfering absorption since the microwindow centered at 2462 cm −1 lies in the band center of the ν 1 + 2ν 2 band of 14 N 2 16 O (which does not have a Q branch), and the microwindow at 2500.7 cm −1 lies in between the 2ν 1 and ν 1 + 2ν 2 bands of 14 N 2 16 O.N 2 O is an important interferer in between these two frequencies, with transmittance between adjacent lines not reaching 100 % due to overlapping wings.We have modified the combined range of the 12 N 2 CIA microwindows to span from 5 to 25 km. Figure 3a and b illustrate the microwindows used for tangent height determination at a low and high TH, respectively.
Since the first guess for tangent heights comes from ACE v3.x data, it is important to consider the finding of Foucher (2009) that there was a discontinuity at 12 km in ACE v2.2 data with regard to the altitudes, temperatures, and pressures obeying hydrostatic equilibrium.This discontinuity is located at the transition between pressure and temperature (p, T ) data retrieved from ACE-FTS and obtained from the assimilated meteorological fields provided by the Canadian Meteorological Centre (CMC).However, we searched for such a discontinuity in the v3.x data in the lower atmosphere, and found that the atmospheric p and T , and altitudes obey hydrostatic equilibrium with no apparent discontinuity at the altitude of this transition.

CO 2
For CO 2 retrieval, we have relied exclusively on 18  would arise with multiple CO 2 isotopologues.Low-J lines of the 20002←00001 band of 18 O 12 C 16 O from both the P and R branches are used.Specifically, in the P branch, the selected lines correspond to 3 ≤ J ≤ 6.In the R branch, the selected lines correspond to 2 ≤ J ≤ 30.. At J = 30, the lower state energy is 342.3089cm −1 and thus R branch transitions for an initial rotation quantum number of J ≤ 30 are weakly sensitive to temperature (Foucher, 2009).Any significant 18 O 12 C 16 O lines in the N 2 CIA microwindows have lower state energies of < 300 cm −1 and thus serve to increase the temperature-insensitive CO 2 signal.To increase the CO 2 signal at the higher altitudes, we included seven low-J lines in the 1371-1386 cm −1 region (10001←00001) with microwindow settings from the ACE v3.x retrieval of 18 OC 16 O.Information on all 27 CO 2 microwindows is in Table 2. Figure 3c and d show the CO 2 microwindows used at a low and high TH in the region of the 20002←00001 band of 18 O 12 C 16 O, respectively.The line intensities in the HITRAN 2012 spectroscopic database are from a model for both the ν 1 fundamental and the 20002←00001 band.Because the line intensity uncertainties in HITRAN 2012 are conservatively set to > 20 % for all lines mentioned above, we have compared the line intensities to ones measured in the laboratory (Toth, 1985;Teffo et al., 2003;Malathy Devi et al., 1984) to serve as an alternative estimate of their uncertainty.To summarize, the agreement on the line intensities in the 10001←00001 band is < 1 %, except for the weakest line at 1371.757715 cm −1 which differs by 1.6 %; however, the semi-empirical model relies on Toth's measurements (Teffo et al., 2002), so the validation is far from independent and the measurements have never been repeated to our knowledge.For the 20002←00001 band, the agreement is not as good, with the standard deviation of relative differences being 2.5 % and the mean bias being −2.2 % (i.e., HITRAN 2012 line intensities are lower than those measured by Malathy Devi et al., 1984).The comparison with the more recent Teffo et al. (2003) measurements show a larger bias (−6 %) but reduced scatter (standard deviation of 0.8 %).The level of agreement for the 20002←00001 band is not sufficient to allow for a measurement of CO 2 VMR with an overall uncertainty of 1-2 %.Unfortunately, the lines from the ν 1 fundamental band are too strong to be used in the midtroposphere.
The optical thickness inside a microwindow contains contributions from lines that are up to 40 cm −1 outside the nearest microwindow edge (instead of 2.5 cm −1 ) used in the ACE v3.x retrieval algorithm.This is necessary because of contributions from the far wings of strong lines such as those belonging to the ν 3 band of 12 C 16 O 2 , whose line shape is sub-Lorentzian.Instead, we use a Voigt profile for all bands and discuss the impact of this assumption in Sect.2.3.

Aerosol extinction
If ignored, aerosol absorption can bias the retrieved THs by several hundred meters, rendering the simultaneously retrieved CO 2 of little scientific value.Thus, aerosol transmittance is determined empirically and used to correct observed transmittances in the N 2 CIA microwindows.This correction is necessary since aerosol extinction is not included in the forward model.The four spectral points (on the 0.02 cm −1 measurement grid) at the low frequency end of the 2637 cm −1 microwindow are used to determine the observed total transmittance (Fig. 4), thereby reducing the signal-tonoise ratio by a factor of ∼ 2 compared to a single spectral point.Note that this microwindow covers the full TH range of the retrieval (5-25 km).Thus, it provides the information on the aerosol contribution over this same range.The total transmittance is assumed to be the product of the aerosol transmittance and combined transmittance of the various gases.The combined gas phase transmittance is determined using simulations with the ACE forward model (Boone et al., 2005  using the atmosphere and THs retrieved with the v3.x algorithm, except that the assumed CO 2 VMR profile comes from a model which accounts for seasonal, altitudinal, and latitudinal variations (Boone et al., 2013).Dividing the observed total transmittance by the modelled gaseous transmittance yields the aerosol transmittance at ∼ 2637 cm −1 .This is assumed to be equal to the aerosol transmittance in all of the N 2 CIA microwindows (essentially 2430-2510 cm −1 ), which appears to be a reasonable assumption if the aerosol is assumed to be pure sulfuric acid or even a 64 % by weight aqueous solution of H 2 SO 4 (Nash et al., 2001), which is typical of stratospheric aerosol at 210 K (Clapp et al., 1997).
Clouds are screened so the transmittance attributed to aerosol is unlikely to be due to water in solid or liquid form.Sulfate is the predominant aerosol in the stratosphere (Murphy et al., 2006) and also in the upper troposphere for cloud-free marine locations.Over land with strong convection, carbonaceous aerosols may dominate the aerosol burden in the upper troposphere (Froyd et al., 2009).We have not studied the absorption spectrum in the 2430-2640 cm −1 region by the latter aerosol type, but with the large number of classes of organics (Froyd et al., 2009), it is likely that some of them have spectrally dependent absorption in this wavenumber range.

Error budget -ACE-FTS
We begin the error budget description with a review of the available literature on error analysis for ACE-FTS CO 2 retrieval.Rinsland et al. (2010) retrieved the partial column of CO 2 in the 7-10 km range and determined the error contribution due to several important sources such as measurement noise, temperature profile, nitrogen continuum absorption coefficients, CO 2 line intensities, aerosol absorption, CO 2 isotopologue correction, ACE-FTS ILS (instrument line shape) function, and TH shift.Foucher et al. (2009Foucher et al. ( , 2011) ) and Foucher (2009)  Before delving into each error source, we list sources which are not including in the current error budget.The uncertainty on the N 2 VMR was not considered because it was expected to be trivial in the 5-25 km retrieval range.Rayleigh scattering was not considered since at a tangent height of 5.5 km, the transmittance is 0.9984 at our highest wavenumber of 2637 cm −1 .Another source of error which was neglected was H 2 O continuum absorption and it warrants further investigation.There is no bias if the H 2 O continuum transmittance at ∼ 2637 cm −1 is equal to its transmittance in the N 2 CIA microwindows.For a worst-case scenario of a tropical atmosphere at TH = 5.5 km, the transmittance simulated with MODTRAN5.2(Berk et al., 2005) is 0.9671 at 2637 cm −1 and maximizes at 0.9859 at 2507 cm −1 over the N 2 CIA microwindow range (2430-2507 cm −1 ).Another source of error relates to the modelled gas phase transmittance at ∼ 2637 cm −1 .Uncertainty in the transmittance at ∼ 2637 cm −1 due to each gaseous absorber can be implicitly taken into account in the error budget by propagating VMR and spectroscopic uncertainties through the retrieval.
The uncertainty due to spectroscopic parameters of the interferers was not considered and should be considered in future work.Similarly, the uncertainties on spectroscopic parameters for the target gas ( 18 O 12 C 16 O) were also not considered, except for the line intensities, since it is expected to be the more important spectroscopic source of bias.First, we address individual sources of error that affect retrieved CO 2 exclusively via TH uncertainty which we group into error sources which relate to N 2 CIA, aerosols, and finally, the sub-Lorentzian line shape of the ν 3 band of 12 C 16 O 2 .Following these TH-related error sources, the remaining sources of error are then discussed in order of decreasing significance (error variance integrated over the retrieval range), although errors on assumed atmospheric state parameters are grouped together.
Biases in TH tend to lead to biases in CO 2 of the same sign.Because pointing errors dominate over all other error sources when tangent heights offsets are > 70 m, it is possible to empirically determine the CO 2 sensitivity from a linear regression of TH offset versus CO 2 VMR using all altitudes.Each TH offset is determined by the difference between our retrieved TH and the corresponding ACE v3.x TH.In doing so over a large number of occultations, we obtain a CO 2 sensitivity to tangent height offsets of 0.09 ppm m −1 from the slope term of the linear regression.Using the mean TH offset profile from Fig. 5 and this sensitivity, we can empirically translate the TH bias profile to a TH-related CO 2 bias profile (Fig. 6).The TH precision, quantified by the standard deviation of the TH differences in Fig. 5, was not considered because we expect that, in general, ACE-FTS CO 2 profiles need to be averaged for scientific purposes, particularly in the upper troposphere where individual TH precision may be ∼ 140 m.
Next, we analyze the individual sources of TH-related error, which are mostly related to errors in model inputs.Perturbing the N 2 absorption coefficient spectrum by a constant value of 0.9 %, which is the upper limit of the quadraturesum of the uncertainties stated by Lafferty et al. (1996) as discussed in Sect.2.1, we find a bias that grows with decreasing TH.We are not sure how to interpret this other than that the retrieved THs at the top of the retrieval range might have some sensitivity to CO 2 absorption, particularly in the N 2 CIA microwindows where slope and offset terms are not fitted.The resulting CO 2 uncertainty increases from ∼ 2 ppm to ∼ 4 ppm from the top to the bottom of the retrieval range.
By switching between the N 2 CIA T -dependence we obtained from the two best low-temperature N 2 CIA laboratory measurements (Lafferty et al., 1996;Menoux et al., 1993) to wavenumbers as high as 2600 cm −1 , we obtain an estimate of the related uncertainty (including random and systematic differences).The test was done on one occultation and the resulting TH offset profile was converted to a CO 2 error by multiplying by the sensitivity of 0.09 ppm m −1 .One of the largest errors occurs just below 18 km which Note that each occultation does not provide data at all altitudes because of the TH sampling is typically 1-2 km but varying with beta angle and the lowest tangent height is often determined by the altitude of high, optically thick clouds.
is the upper altitude limit of a wide microwindow centered at 2492.1 cm −1 because of the differences that appear near 2485 cm −1 in Fig. 1.Errors of similar magnitude appear below 10 km again due to an oscillation in the temperature dependence derived from the noisier Menoux et al. (1993) measurements.N 2 -O 2 absorption coefficients in the region of the N 2 CIA fundamental band are currently not included in HITRAN 2012 (Richard et al., 2012).Using the variation of 4 of Menoux et al., 1993) over six temperatures and perturbing the extreme temperature values by their uncertainties in opposite directions, we obtained a slightly different best fit that ultimately translates to biases of < 0.5 ppm in retrieved CO 2 at all altitudes.
Aerosol extinction is derived from the noisy measurements.The standard deviation (σ ) of the total observed transmittance for the four spectral points used for aerosol correction (see above) is a measure of the noise in the observed aerosol extinction.We propagated +1σ observational noise at each tangent height through the retrieval and found the CO 2 sensitivity is ±0.06 ppm.
We also considered the impact of a bias in the assumed spectral dependence of aerosol extinction in the 2430-2637 cm −1 region, which may occur if the chemical composition of the aerosols is not dominated by sulfuric acid (e.g., liquid water, ice water (Clapp et al., 1997), and organic aerosol).There are a variety of different aerosol types, particularly in the troposphere, but even the mass fraction of water and its physical state (ice or liquid) are ∼ 3200 cm −1 to 2637 cm −1 could affect the slope of the aerosol extinction in the 2430-2637 cm −1 range (Clapp et al., 1997).The slope is currently assumed to be 0 (i.e., scaling factor of 1 between 2637 cm −1 and the N 2 CIA microwindows) at all THs.To consider a different scaling factor, we first convert the "observed" aerosol transmittance (see above) to an optical depth, then multiply by the scaling factor and convert back to a transmittance to account for the exponential nature of Beer's law.The CO 2 sensitivity is determined using the tangent height offsets multiplied by the CO 2 sensitivity to TH error of 0.09 ppm m −1 .We tested a scaling factor of 0.9 at all THs and found a maximum CO 2 bias of 6 ppm at the top of the retrieval range since N 2 CIA decreases exponentially with height but aerosol extinction is observed to be generally linear with altitude in the stratosphere for volcanically unperturbed conditions (e.g., Sioris et al., 2010;Doeringer et al., 2012).Variability of the scaling factor with altitude was not considered.

Atmos
Testing the effects of residual cloud contamination on the retrieval was challenging because the forward model does not simulate clouds.We made several attempts to identify occultations for which clouds were barely flagged in the hope of creating a subset of occultations with such borderline clouds to assess biases in TH and CO 2 due to residual cloud contamination.Some of these clouds could include volcanic aerosol plumes due to the Sarychev eruption (Doeringer et al., 2012) which affected our period of study (2009)(2010)(2011).In fact, two occultations were used for case studies in Doeringer et al. (2012), namely sunsets 31 976 and 31 868, and each of these was found to have cloud tops at exactly the same tangent height as shown in that paper (e.g., their Fig. 4).This is true for both cloud products (970 and 2505.5 cm −1 ).The best test we devised was to take occultations with the following conditions: 1. Cloud tops occur at exactly the same altitude at 970 and 2505.5 cm −1 .
2. Transmittance at cloud top is in the range of 0.82 to unity in cloud microwindow (a) (tran cld top,a ), where a is 970 or 2505.5 cm −1 .
3. Transmittance in the other microwindow at cloud top in the range of 0 to tran cld top,a .
We collected 20 cases fulfilling the above conditions with the cloud top altitude being between 15 and 16 km.The average transmittance was 0.84 and 0.85 at 970 and 2505 cm −1 , respectively.We retrieved THs and CO 2 VMR for these cloudy cases and found the tangent heights were not biased in any detectable way relative to Fig. 5, particularly near 15 km (or below) where the bias would have been mostly likely to appear.The thin clouds are expected to affect the CO 2 retrieval only via TH biases.Thus, the residual cloud contamination is essentially zero given the current, stringent cloud flagging.
Finally, the sub-Lorentzian line shape in the ν 3 band of 12 C 16 O 2 was considered.Note that the lowest frequency in any N 2 CIA microwindow is 2429.21cm −1 and the range considered outside of the microwindow is 40 cm −1 , so only 29 weaker lines of this ν 3 band can contribute.We find the difference in retrieved THs and CO 2 VMR is trivial if the sub-Lorentzian line shape is selected given the 40 cm −1 range limitation.
In summary, the seven theoretical sources of error which affect CO 2 via errors in retrieved TH are: The largest error source is the fifth one by far.Error sources 1, 3, 5, and 6 result in CO 2 biases whereas error sources 2 and 4 involve random error and result in CO 2 retrieval error whose sign varies with altitude.Figure 6 shows errors for both empirical and theoretical approaches as negative in magnitude, since the former approach indicates that THs retrieved from the N 2 CIA are biased low.
The CO 2 retrieval error averaged in the vertical direction (5-25 km) is −5.0 ± 4.5 ppm (±1σ ) for the empirical method and −5.6 ± 1.7 ppm for the quadrature-summed individual contributions, indicating that the two methods produce similar errors and neither method shows a strong difference between the troposphere and stratosphere (> 17 km), whereas if the water vapor continuum (mentioned above) was a large source of error related to TH determination, there would be a major difference in the magnitude of errors from the empirical method across the hygropause (∼ 8-12 km, depending on latitude).Note that the magnitude of the fifth source of error above was simply tested with an ad hoc and TH-independent scaling factor of 0.9 based on laboratory measurements of sulfuric acid absorption (Nash et al., 2001).Given that it is a major source of error among these individual TH-related terms, and the sufficient agreement between the empirically derived TH-related error and quadrature-summed theoretical error (within the altitudinal variability of the latter), the contribution from this error source has probably been reasonably estimated.
Biases in the CO 2 line intensities will lead to opposite biases of the same relative magnitude in retrieved CO 2 VMR.Each CO 2 microwindow targets one strong line of 18 O 12 C 16 O.To test the sensitivity of retrieved CO 2 to uncertainties in the intensities of these targeted lines, the available measured line intensities from Malathy Devi et al. (1984) and Teffo et al. (2002) for 20002←00001 and the ν 1 fundamental band, respectively, were used.Propagating this difference in CO 2 line intensities (measured instead of modelled) results in a 5 ppm negative bias in retrieved CO 2 VMR above 15 km and a 5-6 ppm negative bias below 15 km.The larger bias is expected below 15 km since the lines of the 20002←00001 band (∼ 2600 cm −1 region) are, on the whole, more biased relative to HITRAN 2012 than the lines of the fundamental band, and only the lines of the 20002←00001 band are used there.
To study the impact of the first guess CO 2 profile, we did three independent tests and, at each altitude, retained the largest of the three perturbations at that altitude.The first test was to switch between the default of using the first guess from the a priori model (Keppel-Aleks et al., 2012) for Total Carbon Column Observing Network (TCCON, Wunch et al., 2011) retrievals, which will be used in ACE v4.0 retrievals (Boone et al., 2013), versus the CO 2 first guess profile used in ACE v3.x retrievals.The TCCON a priori model captures the latitudinal, seasonal, and long-term variation of CO 2 VMR.The second test involved increasing the ACE v4.0 CO 2 profile by a factor of 1.0402 to account approximately for the atmospheric enrichment of 18 O 12 C 16 O due to fractionation (Wiegel et al., 2013).The third test used the VMR of 17 O 12 C 16 O within its retrieved range (55-96 km).These tests show a weak sensitivity of the least-squares inversion approach to the first guess of CO 2 even at the top altitude, partly because the profile above the retrieval range is scaled by a retrieved constant (Boone et al., 2005).
For each interfering molecule, we performed similar tests to the CO 2 first guess VMR tests described above.First, we positively perturb the assumed water vapor profile by its retrieval uncertainty (< 5 % below 80 km).This results in a ∼ 0.1 ppm error in CO 2 with no obvious altitude dependence.The second test relates to isotopic variation.In the default retrieval, we assume for each isotopologue of water vapor that its VMR is given by the VMR of the primary isotopologue (multiplied by the isotopic ratio of their natural abundances).There are no significant lines in any of our CO 2 or N 2 CIA microwindows due to H 2 16 O.There are only two lines due to any water isotopologue which absorb strongly into the dry stratosphere.One belongs to HDO and the other is due to H 2 17 O, and both appear in the region of the 18 O 12 C 16 O ν 1 fundamental band.To test the impact of assuming the VMR based on H 2 16 O and the standard isotopic ratio, which essentially is testing for the difference in profile shape due to atmospheric fractionation of a given isotopologue, we assume the ACE v3.x HDO VMR profile divided by its natural abundance.This is a worst-case scenario since atmospheric fractionation is stronger for HDO than H 2 17 O, and HDO is a minor absorber in the TH ranges of eight other microwindows whereas H 2 17 O absorption is negligible except for the single strong line mentioned above.Note that we attempted to retrieve HDO simultaneously but the retrieved HDO profiles were not of sufficient quality in the stratosphere, likely because the one strong line is insufficient.A maximum CO 2 sensitivity of 11 ppm is found at the top of the retrieval range where the fractionation effect is strongest, decreasing rather steadily to 0.3 ppm at 11 km when looking at an average of 10 difference profiles (to obtain a clearer H 2 O fractionation signal).Thus, the impact on CO 2 of the atmospheric fractionation of water vapor is greater than that of the H 2 16 O VMR retrieval uncertainty at all altitudes.The use of the HDO VMR profile shape leads to an improved CO 2 profile shape and removes oscillations in individual CO 2 profiles that dampen with decreasing altitude.This shall be used as the first guess for water vapor in future work.
CH 4 affects both N 2 CIA and CO 2 microwindows.For CH 4 , the ACE v3.x single profile retrieval uncertainty below 25 km is ≤ 3 %.Propagating this uncertainty profile (positive perturbation in the 5-75 km range) through the TH and CO 2 retrieval algorithm leads to a consistent negative bias in retrieved CO 2 of ∼ 0.2 ppm.According to ACE-FTS measurements, the isotopic fractionation between 12 CH 4 and 13 CH 4 is negligible (see also Rice et al., 2003) and the impact on retrieved CO 2 is ∼ 0.04 ppm.
Finally, for N 2 O, the ACE v3.x single profile retrieval uncertainty below 25 km is ≤3 %.Propagating this uncertainty profile (positive perturbation over the N 2 O retrieval range of 5-95 km) leads to a bias that changes sign, being negative above 11 km and positive below.The magnitude of the bias is always ≤ 0.7 ppm.An error in temperature translates into an air number density error since the latter is calculated using the ideal gas law.CO 2 bias due to air density bias is expected to dominate over the CO 2 bias relating to the temperature dependence of the CO 2 absorption, and the more temperature-sensitive N 2 CIA, which has an indirect effect via the tangent heights.ACE-FTS retrieved temperatures (v2.2) have been validated by Sica et al. ( 2008) who found differences of 2 K in the stratosphere and upper troposphere.Schwartz et al. (2008) found ACE-FTS temperatures to be 5-7 K warmer between 0.1 and 0.02 hPa (mesosphere) and 10 K warmer at 0.001 hPa (∼ 96 km) relative to the Microwave Limb Sounder on Aura.Garcia-Comas et al. ( 2012) found MIPAS and ACE-FTS temperatures to agree within 2 K up to 55 km (3 K in polar winter).They also found agreement within 3 K in the lower mesosphere, 3-4 K at 70-75 km, and within 5 K in the upper mesosphere.All of these preceding references for the quality of ACE-FTS temperatures used v2.2 data.In the only study using v3.x temperatures, Sheese et al. ( 2012) compared with OSIRIS and found 5 K differences in the 55 to 80 km range.Boone et al. (2013) illustrate and discuss the improvements to the temperatures retrieved from ACE-FTS between v2.2 and v3.x.Below 15 km, temperatures are assumed from the analysis provided by the Canadian Meteorological Centre (CMC).According to Côté et al. (1998), these temperatures have biases of 2 K at pressures less than 500 hPa.As a worstcase scenario, we introduced a discontinuity in the temperature profile with a bias of opposite sign to the temperature bias (retrieved from ACE-FTS data) above 15 km.Specifically, the following temperature bias profile was assumed: Applying this assumed perturbation yields height retrieval errors of −50 m at the highest altitudes (18-22 km), and positive retrieved height errors in the range of 10-40 m below 14 km.The change of the sign of the height error relates to the opposing temperature bias (above and below 15 km) as listed above.The CO 2 retrieval bias due to this perturbed temperature profile is dominated by the air density perturbation particularly at the lowest temperatures (i.e., tropopause) where the relative change in air density of a +2 K perturbation will be greatest.The sensitivity of CO 2 to temperature biases is reduced by the fact that there are canceling biases due to air density biases and TH-related biases (via N 2 CIA).The CO 2 retrieval bias reaches a local maximum in magnitude of +1.2 % at 16 km and this is the only altitude where the bias is significant relative to the retrieval uncertainty.There is a maximum at 5 km of +1.4 %.
Errors in pressure can impact the CO 2 retrieval algorithm because of pressure broadening of absorption lines.Below 15 km, the pressure assumed in the CO 2 retrieval comes from the CMC analysis (Côté et al., 1998).To obtain a reasonable pressure uncertainty, we took the geopotential height bias of the forecast at 100 hPa (∼ 16 km) of 25 m (Qaddouri and Lee, 2011) and converted this to a relative error of ∼ 0.16 % and assumed that this corresponds to the relative pressure bias.Below this altitude, the relative geopotential height biases are actually smaller.We applied this ∼ 0.16 % pressure bias to all altitudes up to 150 km.The resulting impact on CO 2 VMR was rather random, with a standard deviation of 0.99 ppm and height-averaged bias of 0.08 ppm.
To test the effect of the half-width of the instrument function, we independently changed each of the three parameters in the empirical expression used by Boone et al. (2013) for self-apodization by 2.86 % based on worst-case spectral resolution variability determined at four wavenumbers along the ACE-FTS spectral range (Châteauneuf et al., 2005).CO 2 VMR was sensitive mostly to the third parameter (biases of up to 1.3 ppm), with the sensitivity decreasing slightly from this upper limit at the top of the retrieval range where the width of the ILS exceeds the widths of the absorption lines to a relatively constant value of 1.1 ppm below 13 km where the widths of the absorption lines can exceed the ILS width.
To test the sensitivity of CO 2 to observation noise, we increased the noise in existing real ACE-FTS data without any TH-dependence by adding uniform noise, which is 1/454th of the signal.In combination with the existing real noise, which is 1/400th of the signal (Châteauneuf et al., 2005), we estimate that the final SNR would be reduced to approximately 300.We find that changing the SNR from 400 to 300 made a difference of up to 1.6 ppm in the retrieved CO 2 with the greatest impact at the top of the profile, where the CO 2 lines are less deep, and also below 7 km, where absorption saturation leads to smaller transmittance signal changes per unit change in CO 2 VMR.
Regarding the wavelength calibration, we tested the impact of changing the first guess of the wavelength calibration by 1/30th of the ACE-FTS spectral resolution.Larger perturbations are unrealistic given the accuracy of the wavelength calibration and the accuracy of the spectroscopic line parameters that are used.The retrieval is not expected to have much sensitivity to the first guess of the wavelength calibration because the wavelength calibration is determined again With respect to the overall error budget, it was necessary to avoid double-counting certain sources of error.These sources of error are the empirically derived TH-related error and the observational noise in the 2637 cm −1 microwindow.For the former, we preferred the theoretically derived TH-related error profile because the empirically derived one is based on 129 occultations and the sample sizes are very small at the lowest THs (because sunset and sunrise occultations stop and start, respectively, at the top of optically thick clouds).An additional error contribution was added in quadrature into the overall error budget to account for the uncertainty of the relative isotopic fraction of 18 O 12 C 16 O caused by its atmospheric variability. 18O 12 C 16 O is enriched in the troposphere by a relatively constant value of ∼ 4.1 % (Kawagucci et al., 2008) relative to standard mean ocean water (SMOW), which is the standard used in HITRAN2012 for CO 2 isotopic abundances.This factor varies with the abundance of O 1 D and thus, particularly in the stratosphere, it is a function of altitude, latitude, season and proximity to the polar vortex.In the stratosphere, using data from Kawagucci et al. (2008), we have taken this factor into account.We calculated a mean and standard deviation for this enrichment factor of 4.3 ± 0.2 %.We have used this measure of variability in order to account for this uncertainty source when reporting total CO 2 error based on 18 O 12 C 16 O measurements for all altitudes > 10 km and have assumed no related error in the troposphere.In the stratosphere, the uncertainty propagated to total CO 2 is 0.8 ppm.The median absolute value of latitude for ACE-FTS CO 2 data is 61 • , where the tropopause is at 10 km in the Southern Hemisphere and 9 km in the Northern Hemisphere (SPARC, 1998).
The assumed water vapor profile is the dominant source of error at the top of the retrieval range.The contribution of aerosol extinction relative to N 2 CIA is at a maximum in the lower stratosphere, near the Junge layer and this source of error dominates in the 18-21 km range. 18O 12 C 16 O line intensity uncertainties dominate at all other altitudes, except at the temperature extremes, where the T -dependence of the N 2 CIA becomes dominant.Figure 7 shows the total error ranges between 6 and 11 ppm.Many sources of error could be reduced with improved knowledge of forward model inputs.

Error budget -CASS
The proposed CASS mission (Melo et al., 2013) is under consideration by the Canadian Space Agency.The objectives of the mission are: 1. "climate and ozone balance monitoring" and 2. improved "knowledge of atmospheric processes driving climate and its changes".The CASS-FTS is very similar to the ACE-FTS, both consisting of Michelson interferometers, which use a pair of moving cube corner mirrors on a V-shaped scan arm.The optical path is folded in this design to give a double pass of the beams in each arm of the interferometer resulting in high spectral resolution for a compact size.The CASS-FTS has the same spectral sampling (0.02 cm −1 ) as the ACE-FTS and also uses the solar occultation technique to measure transmittance spectra in the 750-4400 cm −1 range.A tangent height range of 5 to 100 km is expected.The CASS orbit will likely have a lower inclination than ACE, offering better coverage of tropical and mid-latitudes.CASS-FTS is accompanied by solar imagers with the potential to independently provide improved pointing knowledge (Melo et al., 2013).Thus the error budget for CASS is different than the error budget for ACE with respect to uncertainties in TH and also in the temperature profile.
The CASS-FTS total CO 2 uncertainty (∼ 7-8 ppm) is not significantly lower than for ACE at most altitudes, but the magnitude depends strongly on the assumed tangent height uncertainty (Fig. 8).If the CASS imagers (or other methods) can achieve tangent height biases significantly better than 50 m, this will yield smaller biases in the retrieved CO 2 VMR profile.Furthermore, the TH precision for CASS is expected to be much better than the TH precision via the N 2 CIA shown as horizontal bars in Fig. 5. Gordley et al. (2009) find a precision of ±0.02 arcsec is achievable (e.g., 0.27 m at 20 km) with various bias sources which are significantly larger.This suggests that N 2 CIA could be used to correct the TH bias but the spacing between successive tangent heights could be determined via refraction measurements using the imaged sun.
Temperature target accuracy for CASS-FTS is 2 K between 10-50 km and 4 K between 50-100 km and 5-10 km.Propagation of this temperature bias leads to a CO 2 bias of Figure 8.Total CO 2 error budget for CASS-FTS, plus dominant individual terms.TH uncertainty is labelled "TH".The combination of TH and CO 2 line intensity uncertainties is labelled "TH+CO2_line_inten" and serves to demonstrate that these two sources of error account for the majority of the total error.

Atmos
+1.7 % at 5 km, decreasing to 1 % at 6 km, and < 1 % above 8 km.Temperature is only a significant source of error at 9 km relative to retrieval uncertainties.The CASS-FTS temperature target accuracy is sufficient to achieve the CO 2 target accuracy in the absence of other error sources.

Post-processing data filters
CO 2 retrieved from ACE-FTS is generally reliable (see Sect. 3).However, on rare occasions the retrieved profile can be implausible.This may be a result of the aerosol extinction correction which may fail as transmittance at 2637 cm −1 approaches zero at low tangent heights.There may be other causes as well (e.g., missing or corrupt data).Thus from any of the results shown below, we exclude a small fraction of points with negative CO 2 VMR.Also, we remove data points where the CO 2 VMR uncertainty is reported as 0.00 or > 1 000 000 ppm (i.e., uncertainty calculation failed).Finally, we removed points with VMR > 620 ppm which filters clearly anomalous values (see below).We have been very conservative so as to not remove any high CO 2 values that could result from rapid lofting of enhancements at the surface to heights of > 5 km.

Validation method
Data from the following in situ sources are used: HIPPO (HIAPER Pole-to-Pole Observations) (Wofsy et al., 2011), CONTRAIL (Comprehensive Observation Network for Trace gases by Airline) (Machida et al., 2008), and CARIBIC (Civil Aircraft for the Regular Investigation of the atmosphere Based on an Instrument Container) (Schuck et al., 2009).
Multiple instruments on the five HIPPO measurement campaigns were used to measure CO 2 (Wofsy et al., 2011); however, in this work we only use the CO2.X data product.CO2.X data is primarily made up of measurements from the quantum cascade laser spectrometer, with gap filling from the Observations of the Middle Stratosphere instrument (Daube et al., 2002).The HIPPO campaigns produced ∼ 150 days of flight data, sampling 9 of 12 calendar months with good latitudinal and altitudinal coverage.
We used CONTRAIL measurements made by the continuous CO 2 measuring equipment (CME) carried aboard commercial passenger aircraft.The CONTRAIL CO 2 measurements used in this work were made with a non-dispersive infrared (NDIR) gas analyzer (Licor 840).
For CARIBIC, air samples are collected from commercial aircraft flights using an automated system.The samples obtained are analyzed in a laboratory using a gas chromatograph equipped with a flame ionization detector, for which CO 2 is converted to CH 4 using a nickel catalyst prior to analysis (Schuck et al., 2009).
ACE-FTS single profile measurements are compared with monthly 10 • zonal means of in situ data in 1 km vertical increments.Validation opportunities cover the 5.075-13.999km range of ACE altitudes and years 2009 to 2011.If more than one correlative instrument provides a validation opportunity in the same year and month, latitude band, and height interval, then we avoid duplication by selecting only data from one correlative instrument, in the following priority sequence: HIPPO, CONTRAIL, and CARIBIC.The difference between these three instruments at ACE-FTS CO 2 geolocations is < 1.0 ppm.CARIBIC appears to have slightly more variability than the other in situ data sets.HIPPO is preferred because of its latitudinal and vertical coverage.The ACE-FTS retrieved VMR of 18 O 12 C 16 O is converted to total CO 2 (i.e., all isotopologues) by dividing by its SMOW isotopic abundance fraction.In the troposphere (z ≤ 10 km), we also divide by 1.0402 (Wiegel et al., 2013) which accounts for the difference between the SMOW standard and the more appropriate Pee Dee Belemnite (PDB) standard.For the stratosphere (z > 10 km), we divide the ACE total CO 2 VMR by 1.04314 instead to account for a minor contribution from atmospheric fractionation in the stratosphere.Post-processing data filters (see Sect. 2.5) are applied.

Retrieved tangent heights
Using the improved temperature dependence of the N 2 CIA and accounting for aerosol extinction in the N 2 CIA microwindows, we found improved pointing accuracy relative to using the temperature dependence of Foucher (2009)  the N 2 CIA temperature dependence of Foucher ( 2009) leads to a low bias of 200 m relative to ACE-FTS v3.x tangent heights.The impact of neglecting the aerosol extinction in the N 2 CIA microwindows introduces altitude-dependent TH offsets that become very apparent if the TH retrieval spans a sufficient range (5-25 km).This is discussed in Sect. 4. Boone et al. (2005) report a residual ∼ +100 m difference in THs retrieved independently using 18 O 12 C 16 O and 16 O 12 C 16 O microwindows with the ACE v2.2 retrieval software, after correcting for an apparent high bias of 3.5 % in the VMR of the rarer isotopologue.This correction factor was increased to +4.3 %, which is a more representative value for the isotopic enrichment of 18 O 12 C 16 O in the stratosphere (Wiegel et al., 2013;Kawagucci et al., 2008) for ACE v3.x retrievals.Thus, ACE v3.x THs would be expected to have this high bias reduced to +43 m assuming the latter correcting factor.Thus, the −61 m bias versus ACE v3.x THs shown in Fig. 5 is reduced to −18 m when the ACEv3.xTH high bias due to CO 2 isotopic inconsistencies is considered.
Using the HITRAN 2012 line list for the retrieval of THs using the ACE v3.x software leads to a decrease in THs of 62 ± 8 m in the 15-25 km range relative to the use of the default line list which is an updated version of HITRAN 2004.Similarly, below 15 km where 18 O 12 C 16 O lines are exclusively used for ACE v3.x TH retrieval (Boone et al., 2013), a larger TH decrease of 118 ± 45 m is observed.
Finally, the ACE v3.x THs are biased low because of the low-biased CO 2 VMR profile due to the underestimated growth rate of 1.50155 ppm year −1 of CO 2 (Boone et al., 2005).To study this effect, we have used the TCCON a priori CO 2 .Foucher et al. (2009) noted that the seasonal cycle of CO 2 in the troposphere could lead to seasonally varying biases in the mid-tropospheric THs.By replacing the default CO 2 VMR profile with profiles from the TCCON a priori CO 2 for the Northern Hemisphere mid-latitude in April and October, we find that the THs above 10 km are not sensitive to the seasonal cycle of CO 2 , consistent with Foucher et al. (2009), but exhibit sensitivity to the low bias in assumed CO 2 VMR due to the underestimated growth rate.The bias in THs due to assumed CO 2 is +40 ± 20 m at 25 km, partly due to the assumption of a constant VMR profile in the stratosphere (20-60 km), whereas the TCCON a priori profiles shows a 4.5 ppmv increase from 60 km down to 20 km.This bias in TH grows steadily to ∼ +110 m at the tropopause (10 km).In summary, two changes have been included in the ACE v3.x TH retrieval to make the resulting THs more accurate: 1. spectroscopic update and 2. assumed CO 2 VMR profile.
The two changes have opposite effects that are of the same magnitude both above and below 15 km.Thus the ACE v3.x tangent heights are essentially unchanged within 50 m (for altitude above 7 km) when both of these effects are taken into account simultaneously.

Validation of CO 2 profiles versus latitude with in situ data
Figure 9 shows a three year (2009-2011) CO 2 median profile from cloud-free data.Figure 10 shows a histogram of the cloud-free data points using all retrieval altitudes, justifying our use of 620 ppm as a cut-off (see Sect. 2.5).We validate individual data points by latitude and altitude with in situ data from airborne sensors.Using only clear-sky data, certain latitude regions provided few validation opportunities, especially in the troposphere.Therefore, we attempted to expand the number and spatial coverage of validation opportunities by including a subset of data which was flagged as cloudy at 2505.5 cm that occur in all seasons.Most of these aerosols likely include water-ice which absorbs in the 2100-3600 cm −1 region (Clapp et al., 1997) and forms at temperatures below 210 K (depending on mass fraction of sulfate relative to water-ice).
Based on the 2505.5 cm −1 cloud flag, these aerosols are observed to exist in a narrow layer between 13 and 15 km.We retrieved CO 2 VMR from all occultations belonging to this subset of data using v3.0 inputs for 2009 and up to September 2010 and v3.5 inputs after September 2010 until the end of 2011.This was necessary since v3.0 data is not valid beyond September 2010 (Boone et al., 2013).The retrieved CO 2 profiles show a high bias of 8 ppm at 13.5 and 7 ppm at 14.5 km, and no significant impact on this 21-month median profile at all other altitudes (not shown).We validate this "cloudy" data set as well, which greatly improves our ability to detect latitudinal biases at lower altitudes.Longitudinal variations are not validated.The annual growth (Fig. 11) validates the stability of the retrieved CO 2 versus time.Furthermore, it demonstrates that small increases of 2-3 ppm year −1 are detectable when averaging vertically over the lower stratosphere.
The global median bias including all latitudes and altitudes is −1.7 ± 0.4 ppm (± standard error, SE). Figure 12 shows that between 7 and 12 km, the only significant biases occur at 8 km (6.2 ± 2.3 ppm) and negative biases of 2.3 ± 0.5 ppm over the 9-12 km range.At 5-6 km, there are too few coincidences (N ≤ 13) to determine whether the bias is statistically significant.The negative bias in the 9-12 km region is driven by known negative CO 2 bias of 5 ± 3 ppm due to tangent height offsets (Fig. 6).At 13 km, the positive bias of 7 ± 1 ppm (±SE) is due to aerosol-related biases in the cloudy cases.The cause of the positive bias at 8 km is not known, but the bias is < 2 % of CO 2 .
Figure 13 shows the validation by latitude band for ACE-FTS data points below 13.0 km.All latitude bands also show a negative bias of ∼ 5 ± 5 ppm.Again, the sign and magnitude of the negative bias at most latitudes is expected.
We focus on the latitude bands with the most validation opportunities (Fig. 13), namely high and mid-latitudes, in order to examine the altitude dependence of any latitudinal bias.At southern mid-latitudes, the validation indicates significant negative biases only at 10 to 12 km of 5 ± 3 (N = 28), 4 ± 2 ppm (N = 40), and 6 ± 4 ppm (N = 32), respectively (Fig. 14).The sign and magnitude are expected based on tangent height bias.At 13 km, the sign and magnitude of the positive bias of 3 ± 3 ppm is expected from aerosol-related biases in the cloudy subset (∼ 8. offset of 5 ppm from low-biased THs.At all other altitudes, the biases are statistically insignificant. For Northern Hemisphere mid-latitudes, samples sizes are small (N < 20) below 9 km.The bias is consistent with southern mid-latitudes in the 9-12 km range.At 13 km, given that the validation opportunities are almost entirely for cloudy cases, the +8.5 ppm expected bias due to aerosols (discussed above) is added on a negative bias of ∼ 5 ppm from tangent heights.Thus a positive bias of 3.5 ppm is expected, which agrees with the observed 3.4 ± 2.7 ppm bias (±SE).
For northern high latitudes, the validation sample size is small (N ≤ 12) below 9 km.The sample sizes are adequate (N ≥ 20) in the 9-12 km range.Between 10 and 12 km, a negative bias of 1 ± 1 ppm is observed, similar to midlatitudes, and at 13 km, a positive bias of 11 ± 2 ppm is found, slightly larger than other latitude bands and caused by cloudy points.The high bias (∼ 1 %) at northern high latitudes at 9 km largely determines the global bias at 8-9 km (Fig. 12).As mentioned, its cause is not understood.
At southern high latitudes, the sample size is sufficient only at 12-13 km.At 12 km, the bias is not significant, whereas at 13 km, a positive bias of 5 ± 3 ppm is found, similar to other latitudes, and almost entirely due to the positive bias relating to lower stratospheric aerosols.

Conclusion and future work
There are four major advances in this work over the previous work (e.g., Foucher et al., 2011 and references therein): 1. the transmittance due to sulfate aerosol is considered 2. significantly improved temperature-dependence of N 2 CIA 3. addition of several narrow N 2 CIA microwindows to improve retrieval of the TH vector 4. no use of a priori information for regularization of the retrieved profile.
If sulfate aerosol transmittance is neglected, the TH offsets relative to ACE v3.x have a gradient versus TH of several hundred meters because the contribution of aerosol absorption relative to N 2 CIA grows with increasing TH.N 2 CIA decreases quadratically with decreasing air density (i.e., increasing TH) due to the bimolecular nature of the absorption whereas aerosol absorption is expected to decrease more linearly as aerosol extinction is proportional to air density for background cases.Foucher (2009) found such a TH offset gradient as well and used averaged vertical profiles of TH offsets to correct for their neglect of aerosol absorption.Their method is susceptible to aerosol variability which can be significant given recent volcanic activity (Sioris et al., 2010;Doeringer et al., 2011).
A consistent spectrum of the temperature-dependence coefficient for the N 2 CIA is found between the measurements of Lafferty et al. (1996) and Menoux et al. (1993).The use of Hartmann's temperature-dependence led to THs that were offset by > 1 km from those obtained using the ACE v3.x retrieval.This necessitated the re-analysis of Lafferty et al. (1996) data to obtain a much improved temperature dependence spectrum (Foucher, 2009).Using Foucher's temperature dependence, we obtain a mean TH offset of −200 m relative to ACE v3.x with no significant vertical gradient, whereas using the temperature dependence determined here, the TH offset is further reduced, typically to less than 100 m.
The retrievals shown in Foucher et al. (2009Foucher et al. ( , 2011) ) show a strong dependence on the a priori profiles particularly above 20 km, which, in turn, leads to reduced variability in retrieved CO 2 compared with our work.Specifically, if we use their small set of N 2 CIA microwindows, we also find a kink in the retrieved CO 2 profile near 16 km (Foucher et al., 2011) which we find to be related to inconsistencies between N 2 CIA microwindows.This kink is damped in their retrieval by constraining CO 2 to the a priori profiles.We find a much larger anomaly appears at the same altitude in our retrieved CO 2 profiles and the vertical profile of TH offsets (averaged over a large number of occultations).Using an improved and more extensive set of N 2 CIA microwindows (Table 1), significant kinks are largely reduced.
Future endeavors should include the simultaneous retrieval of the B 0 and β 0 parameters from the measurements of Lafferty et al. (1996).Ideally the simultaneous retrieval of these spectral quantities could be performed on a finer grid than 5 cm −1 .Then, the CO 2 retrieval could be repeated using N 2 CIA parameters on a finer grid.This may capture some of the weak, fine structure in the N 2 CIA that has been the subject of much investigation (e.g., Lafferty et al., 1996;Moreau, 1999).Microwindows could be added to retrieve non-primary isotopologues of interfering species simultaneously and accurately.There are ∼ 500 000 available CO 2 lines in HITRAN 2012.Additional microwindows for CO 2 should be sought to improve detection in the upper troposphere where CO 2 retrieval uncertainties grow exponentially.For example, the retrieval uncertainty, which is a statistical output of the leastsquares retrieval algorithm, can be as small as 1.0 ppm at 10 km (Antarctic stratosphere), whereas at 5 and 6 km, the minimum statistical uncertainty in the cloud-free data set grows to 11 and 5 ppm, respectively.

Atmos
Next, we discuss whether the ACE-FTS CO 2 data set presented here is sufficiently precise to detect natural variability on monthly and annual time scales, a large latitudinal scale, or vertically within a 5 km range (7-12 km) in the upper troposphere and lower stratosphere.Detecting CO 2 variations over shorter spatial and temporal scales becomes more challenging.The small-scale variability is determined by looking at the variability about the monthly mean, calculated in 10 • latitude bins and 1 km vertical increments.Using the HIPPO data set, natural small-scale variability reaches a maximum of 4.3 ppm (standard deviation, N = 64) at 5.5 km at 85 • N in July 2011.However, monthly-scale temporal variability can be determined by looking at variations between consecutive months (for the same altitude and latitude).At an annual time scale, time-dependent measurement biases (i.e., drifts) are much smaller than the annual increase in CO 2 .Natural yearto-year variations are small, on the order of 2.5 ppm year −1 , but ACE-FTS CO 2 has a high degree of temporal stability and can be used to detect this level of change.This is possible due to the self-calibrating nature of the solar occultation measurements.
As discussed in Sect.3.2 (Fig. 12), biases versus altitude between 7 and 12 km are on the order of 9 ppm.Natural variations in this altitude range can reach 8 ppm in April 2010 at 65 • N (according to HIPPO data).The vertical gradient in the boreal early spring is mostly due to the strong seasonal cycle in the Arctic mid-troposphere.
Biases versus latitude (maximum bias difference of 8.8 ppm between the tropics and the southern polar region shown in Fig. 13) approaches the natural latitude gradient of 9.2 ppm at 5.5 km in April 2010 (maximum and minimum at 85 • N and 65 • S, respectively, according to HIPPO).ACE-FTS CO 2 bias differences between southern high latitudes and northern mid-latitudes are on the order of 5 ppm at 12 km (Fig. 14).According to in situ observations (Fig. 15, left panel), the latitude gradient between 45 • N and 65 • S at 10 km in boreal spring is 6 ppm. Figure 15 shows the 6 and 4 ppm gradient at 9.5 and 10.5 km, respectively, using differences between CONTRAIL and HIPPO observations from these two latitude bands.According to the ACE-FTS retrievals, the gradients are of 5, 6, 4, and 1 ppm at 9.5, 10.5, 11.5, 12.5 km, respectively.The decreasing latitudinal gradient with height is expected at 12.5 km because both latitude bands are in the stratosphere at this altitude, where the gradients are smaller because they are not as sensitive to local sources and sinks as the upper troposphere.This latitudinal gradient disappears toward the end of boreal summer at 10 km due to the strong biospheric uptake at northern extratropical latitudes (Fig. 15 of ACE-FTS due to tangent height offsets also appears in Fig. 15.Also, the consistency between boreal summer and spring CO 2 VMR near the tropopause in the ACE-FTS data is encouraging. The vast majority of ACE-FTS CO 2 profiles which extend below 6.5 km are located in the Antarctic, which is a region of no flux, and the Southern Ocean, which has one of the smallest posterior errors of any region (Pak and Prather, 2001;Baker et al., 2006).This presents a challenge for constraining fluxes from satellite-based upper tropospheric profile measurements.The present scientific value of the ACE-FTS CO 2 data lies mostly in providing continuous global monitoring of the vertical profile in the upper troposphere and lower stratosphere with good temporal stability and small retrieval uncertainties in the stratosphere as expected from a solar occultation FTS.Taking annual means further magnifies the difference in uncertainties between the troposphere and stratosphere because clouds limit the fraction of occultations which provide tropospheric data.

Figure 3b .
Figure 3b.Same as Fig.3a, except for TH = 23.72 km, at which tangent height, two N 2 CIA microwindows are used.

Figure 4 .
Figure 4. Transmittance contributions from various gaseous absorbers in the 2637 cm −1 microwindow at TH = 6.3 km.Other gases may provide trivial contributions.The portion of the microwindow used to determine aerosol transmittance is shown in dark blue.The corresponding transmittance value of 0.75 is meaningless (only the wavenumber range is relevant).

Figure 5 .
Figure 5. TH differences (this work minus ACE v3.x) averaged over 120 randomly selected occultations covering latitudes in the range 80 • N to 68 • S and spanning from January 2009 to January 2011.The error bars indicate the standard deviation of these differences.Note that each occultation does not provide data at all altitudes because of the TH sampling is typically 1-2 km but varying with beta angle and the lowest tangent height is often determined by the altitude of high, optically thick clouds.

Figure 6 .
Figure 6.CO 2 VMR uncertainty versus altitude due to tangent height uncertainty from two different methods."TH-empirical" propagates the observed TH differences versus those retrieved using the ACE v3.x algorithm, and "TH-theoretical" includes all of the individual sources of TH-related error added in quadrature.

Figure 7 .
Figure 7. Overall error budget for ACE including TH-related contributions.

Figure 10 .
Figure 10.Histogram of retrieved cloud-free CO 2 VMR at all altitudes (5-25 km), globally, in the 2009-2011 time frame.Outside of this range, the frequency distribution tends to be random (no resemblance to a Gaussian).

Figure 12 .Figure 13 .
Figure 12.Validation results by height, combining all latitudes.The error bar is the standard error of the bias.Sample sizes (N ) are > 20 in the 7-13 km range.

Figure 14 .
Figure 14.Same as Fig. 12 but only for high and mid-latitude regions.

Figure 15 .
Figure15.On the left -latitudinal gradient in CO 2 VMR observed in boreal spring using satellite-based observations (ACE-FTS) and in in situ data(HIPPO and CONTRAIL).All measurements are from the year 2010.The 45 • N band comprises measurements from 30-60 • N for both ACE-FTS and CONTRAIL.Medians are shown for ACE-FTS to reduce sensitivity to outliers while averages are shown for HIPPO and the error bars are the standard errors for both instruments.For CONTRAIL, we plot the average three sub-bands (30-40, 40-50, and 50-60 • N), and each error bar represents the standard error of the three sub-band averages at that altitude.ACE-FTS data points between 13.0 and 15.0 km are excluded due to aerosol extinction (affects THs).Vertical bins of 1.5 and 2 km are used above 15.0 km to improve samples sizes per bin, particularly above 19.0 km for the ACE-FTS profiles of March to April 60-90 • S and May 45 • N, respectively.On the right -same as left panel but for boreal summer.HIPPO measurements are from the year 2011, so we subtract 2 ppm to account for the annual growth.
, right panel).Thus the latitudinal gradient has a seasonal variation.The low CO 2 bias www.atmos-meas-tech.net/7

Table 1 .
N 2 CIA microwindows: Center frequencies, widths, and tangent height ranges in order of increasing lower TH limit.

Table 2 .
CO 2 microwindows: Center frequencies, widths, and tangent height ranges in order of increasing center frequency.

. Meas. Tech., 7, 2243-2262, 2014 www
important considerations because solid state absorptions tend to be broad and the proximity of the ice O-H stretch near .atmos-meas-tech.net/7/2243/2014/ two non-primary isotopologues of N 2 O (listed in Sect.2) is considered, assuming the differences in profile shape between isotopologues are real.The magnitude of the bias reaches 1.8 ppm at 19.5 km.The CO 2 VMR sensitivity to N 2 O changes appears to be via the microwindows targeting the 18 O 12 C 16 O 20002←00001 band (i.e., not indirectly via TH changes).
The effect of fractionation of Atmos.Meas.Tech., 7, 2243-2262, 2014 www.atmos-meas-tech.net/7/2243/2014/ −1 but not at 970 cm −1 .These are not tropospheric clouds, but rather polar, lower stratospheric aerosols Annual growth of CO 2 versus altitude using yearly medians from the cloud-free data set.Error bars show the standard error for 2010.Between 12 and 25 km and over all latitudes, the growth rate is 2.1 and 2.8 ppm year −1 , or 2.47 ± 0.67 ppm year −1 averaged over2009-2011.