Interactive comment on “ Stratospheric and mesospheric HO 2 observations from the Aura Microwave Limb Sounder ” by L .

Abstract. This study introduces stratospheric and mesospheric hydroperoxyl radical (HO2) estimates from the Aura Microwave Limb Sounder (MLS) using an offline retrieval (i.e. run separately from the standard MLS algorithm). This new data set provides two daily zonal averages, one during daytime from 10 to 0.0032 hPa (using day-minus-night differences between 10 and 1 hPa to ameliorate systematic biases) and one during nighttime from 1 to 0.0032 hPa. The vertical resolution of this new data set varies from about 4 km at 10 hPa to around 14 km at 0.0032 hPa. A description of the methodology and an error analysis are presented. Comparisons against the Whole Atmosphere Community Climate Model (WACCM), the Superconducting Submillimeter-Wave Limb-Emission Sounder (SMILES) and the Far Infrared Spectrometer (FIRS-2) measurements, as well as photochemical simulations, demonstrate the robustness of the retrieval and indicate that the retrieval is sensitive enough to detect mesospheric HO2 layers during both day and night. This new data set is the first long-term HO2 stratospheric and mesospheric satellite record and it provides needed constraints to help resolve the O3 deficit problem and the "HOx dilemma".


Introduction
Since 1985, when for the first time the now famous O 3 hole was reported (Farman et al., 1985), the stratospheric O 3 layer has received massive scientific attention.Although it peaks in the lower stratosphere, this layer extends well into the meso-sphere where O 3 chemistry is controlled by catalytic cycles involving the HO x (HO 2 , OH and H) family (Brasseur and Solomon, 2005): where the net effect of these two reactions is simply which destroys O 3 without changing the abundance of the catalyst, X, which in this case is either OH or H.The presence of the HO x family in the middle atmosphere is a consequence of the transport of H 2 O and CH 4 from the troposphere to higher altitudes.The production of HO x species in the middle atmosphere is primarily due to O 3 photolysis: and, above 60 km, by photodissociation of H 2 O by absorption of UV radiation (particularly in the Lyman-alpha region and the Schumann-Runge bands), where H turns into HO 2 due to the three-body reaction The removal of HO x is mainly through the self-reaction and the partitioning between OH and HO 2 above ∼ 40 km is primarily driven by where the H produced in Reaction (R12) is quickly converted to HO 2 by Reaction (R8).
Despite the apparent simplicity of the HO x chemistry, models were not able to give a complete picture of its chemistry in the middle atmosphere: Summers et al. (1997) reported that OH satellite observations by the Middle Atmosphere High Resolution Spectrograph Investigation (MAHRSI) were 30 to 40 % lower than the values computed using standard photochemical models.Sandor et al. (1998) reported that mesospheric ground-based microwave measurements of HO 2 were 23 to 47 % higher than photochemical model predictions at midday, agreed with the model values prior to 09:00 LT, and were 70 to 100 % higher immediately after sunset.Jucks et al. (1998) using simultaneous OH and HO 2 balloon observations by the Far Infrared Spectrometer (FIRS-2) reported that OH agreed reasonably well with model estimates, a conclusion supported by Pickett et al. (2008), while HO 2 was 25 % higher than the model estimates.However, Canty et al. (2006) concluded that, at least between 25 and 60 km, the HO x Microwave Limb Sounder (MLS) and FIRS-2 observations were reasonably well described by photochemical models.In addition to these modelling discrepancies (a problem known as the HO x dilemma), models have consistently underpredicted the amounts of O 3 at such altitudes, an issue known as the O 3 deficit problem (Crutzen and Schmailzl, 1983;Solomon et al., 1983;Eluszkiewicz and Allen, 1993;Summers et al., 1997;Varandas, 2004;Siskind et al., 2013).
There have been many suggested solutions for the "HO x dilemma" and the O 3 deficit problem in the literature (e.g.Miller et al., 1994;Jucks et al., 1998;Varandas, 2004); however, difficulties persist, in part because there are very few observations of HO 2 in the mesosphere.To date, there are four mesospheric data sets available: (1) 6 days spread between April 1992 and December 1996 measured by the Kitt Peak National Radio Astronomy Observatory (NRAO) (Sandor et al., 1998), (2) the Sub-Millimeter Radiometer (SMR) aboard the Odin satellite data set (Baron et al., 2009), which consists of one observation period of 24 h each month between October 2003 and December 2005, (3) the Superconducting Submillimeter-Wave Limb-Emission Sounder (SMILES) data set (Kikuchi et al., 2010), which provides daily coverage from 38 • S to 65 • N between October 2009 and April 2010, and (4) the standard MLS data set (Pickett et al., 2006(Pickett et al., , 2008)), which provides coverage mostly from 55 • S to 55 • N, up to 0.046 hPa and only during daytime.
In this study, we introduce a new data set of global observations of stratospheric and mesospheric HO 2 from the MLS instrument.This new offline (i.e.run separately from the standard MLS algorithm) retrieval extends the HO 2 vertical range well into the mesosphere (up to 0.003 hPa or ∼ 90 km), which, in addition to the standard MLS H 2 O, OH and O 3 , potentially allows the MLS data set to study the HO x -O 3 chemical system to provide insights for the long-standing O 3 deficit problem.To date, this data set provides 10 years of data and, in the near future, it will be publicly available for download in a daily-based hierarchical data format (HDF).In the next section we give an overview of the MLS instrument as well as the MLS HO 2 measurements.Section 3 presents the offline retrieval approach and describes its vertical resolution, precision, and systematic uncertainties.Comparisons between the offline MLS HO 2 data set and global climate model simulations, balloon-borne and satellite data sets are shown in Sect. 4. Lastly, the offline HO 2 data are compared to the results of a 1-D photochemical model to investigate whether standard reaction rates can model the extended HO 2 vertical range.Section 5 provides a summary.

MLS HO observations
The Microwave Limb Sounder (MLS) is, in essence, a small radio telescope on board the Aura satellite which was launched into a polar sun-synchronous orbit in July 2004.MLS measures limb millimetre and submillimetre atmospheric thermal emission at 120 different tangent altitudes from the ground to about 95 km every 24.7 s.It covers latitudes between 82 • S and 82 • N, providing near-global observations with roughly half of these measurements during daytime (∼ 13:45 LT), and the other half during nighttime (∼ 01:45 LT), except near the poles where the observations transition between daytime and nighttime conditions and vice versa.The incoming radiance is collected by a 1.6 m antenna which directs it onto four heterodyne radiometers covering spectral regions near 118, 191, 240 and 640 GHz (a fifth radiometer located at 2.5 THz is fed by a separate antenna).The radiant flux measured by the GHz radiometers is then analysed by 22 filter banks and four digital autocorrelator spectrometers.Most of these filter banks were designed to measure essentially a single spectral line, despite the double side band nature of the radiometers (i.e. each filter bank measures two different spectral regions, one on each side of the local oscillator).Furthermore, these banks have narrower filters at the band centre than at the extremes allowing them to measure the strong pressure broadening at microwave frequencies.A more detailed description of the Aura MLS instrument is given by Waters et al. (1999Waters et al. ( , 2006)).
HO 2 is measured by two of these filter banks, known as band 28 and band 30, centred at the 649.72 and 660.50 GHz HO 2 lines.These filter banks consist of 11 channels with widths varying from 6 to 32 MHz, giving a total width of around 200 MHz.An example of the observed radiances is shown in Fig. 1.The ∼ 1 K HO 2 signal is relatively small compared to the individual limb radiance precision which varies from 2 K at the bands edges to 4 K at the band centre (grey dotted line), hence some averaging is required to obtain HO 2 abundances with a useful signal to noise ratio.The clear tilt in band 30 is due to the proximity of an O 3 line.As mentioned above, HO 2 is one of the MLS products retrieved with the standard algorithm described in Livesey et al. (2006a).Briefly, the algorithm uses the optimal estimation technique (Rodgers, 2000) retrieving one profile for each scan using a two-dimensional approach.The smallness of the HO 2 signal translates to a retrieved product usable only between 10 and 0.046 hPa.For greater pressures, the signal is lost due to pressure broadening (Fig. 1 shows how the lines broaden rapidly as the pressure increases) and stronger emissions from O 3 .For smaller pressures the signal is indistinguishable from the noise.
The latest version (V3.3) of the MLS HO 2 standard product (Pickett et al., 2008;Livesey et al., 2011) produces ∼3500 abundance profiles daily with typical precisions varying from 0.15 ppbv (52 × 10 6 cm −3 ) at 10 hPa to 3 ppbv (5 × 10 6 cm −3 ) at 0.046 hPa for measurements zonally averaged and binned in a 10 • latitude bin.Due to the seasonality of HO 2 , these values can change up to 10 % depending on the pressure level observed.Its vertical resolution varies from 4 to 10 km between 10 and 0.046 hPa.In this pressure range, since negligible HO 2 is expected at night (∼ 1:45 a.m.LT for MLS at the equator), it is recommended to use the nonzero nighttime abundances as an indication of systematic biases (i.e.affecting both day and night retrievals).Hence, the HO 2 day-minus-night difference should be used as a better estimate of the daytime HO 2 than taking the daytime measurements at face value.During summer and winter, this restricts the usable HO 2 standard product data to between roughly 55 • S and 55 • N, where MLS observes both daytime and nighttime data.In addition to the MLS HO 2 product the MLS HO 2 product, this day-minus-night difference approach to ameliorate biases has been used successfully for the BrO and OH MLS products (Livesey et al., 2006b;Pickett et al., 2008;Millán et al., 2012).

Offline retrieval
For this study, an HO 2 offline retrieval has been developed similar to that described by Millán et al. (2012).In essence, we compute a daily zonal mean of the radiances, for band 28 and 30, from which we retrieve daily HO 2 concentrations.The daily zonal mean radiances are formed by collocating them into 10 • latitude bins, sorting them into daytime and nighttime using solar zenith angles (SZAs) lower than 90 • and greater than 100 • .Those radiances having SZAs between 90 and 100 • are disregarded to avoid twilight measurements.These sorted radiances are then averaged onto a vertical grid with six pressure levels per decade (spacing of ∼ 3 km) using the tangent pressure retrieved by the standard algorithm.
The retrieval uses the optimal estimation technique as described by Rodgers (2000) assuming an HO 2 a priori of zero, an a priori precision of 20 ppbv and using the corresponding daily zonal means of temperature, O 3 , HNO 3 and HCl from the standard MLS algorithm (version 3.3) as part of the atmospheric state.In addition to this constraint, a Twomey-Tikhonov regularization (Tikhonov, 1963;Twomey, 1963) is used to reduce noise and smooth the profiles at the expense of some vertical resolution.Furthermore, at each pressure level, a constant baseline is retrieved for each band to correct any instrument baselines as well as to take care of the water vapour continuum contribution.The best retrievals were found when doing a joint band 28 and 30 retrieval as opposed to doing retrievals using only band 28 or only band 30, even despite the O 3 line influencing band 30.
The offline daytime HO 2 estimates are confined to a pressure range between 10 and 0.0032 hPa with day-minus-night differences used as a measure of daytime HO 2 for pressures between 10 and 1 hPa where the nighttime values exhibit non-zero values indicative of biases.Note that a visual inspection of the 10 • bin monthly average profiles has shown, overall, no sings of a discontinuity at 1 hPa when using this approach.The offline nighttime HO 2 estimates are confined to a pressure range between 1 and 0.0032 hPa.
Figure 2 shows monthly (January 2005) zonal means for the standard and offline HO 2 data sets in volume mixing ra-  2008), here shown as the day-minus-night difference as recommended by the MLS data guidelines (Livesey et al., 2011).
The MLS offline (bottom) is the data set introduced here.In this case, the day-minus-night difference has been taken only between 10 and 1 hPa, which is the reason why this data set can be extended to 10 hPa.The left column shows the data in VMR and the right one in number density.
tio (VMR) and density units.The temperature used to convert the data from VMR to number density is the same zonal mean temperature from the standard MLS algorithm that is used as part of the atmospheric state.As can be seen, the offline retrieval has two distinct improvements over the standard product: (1) an extended pressure range, which enables the measurements of the mesospheric local maxima that occur at around 0.02 hPa at most latitudes, and (2) an extended latitudinal coverage, making it possible to measure the polar regions, where in the summer one the HO 2 maximum lies.Furthermore, as shown in the following sections, the offline retrieval also estimates HO 2 during night between 1 and 0.0032 hPa.Note that the standard MLS product is smoother because it is highly constrained due to the poor signal-to-noise ratio of the individual radiance profiles.Daytime averaging kernels for the HO 2 offline retrieval at the equator (those at other latitudes are very similar).The black line is the integrated area under each kernel: values near unity indicate that most information was provided by the measurements while lower values indicate that the retrieval was influenced by the a priori.The dashed grey line is a measure of the vertical resolution of the retrieved profile (derived from the FWHM of the averaging kernels approximately scaled into kilometres).

Vertical resolution
Figure 3 shows typical averaging kernels for the HO 2 offline retrieval.These kernels delimitate the region of the atmosphere from which the information is contributing to the retrieved values at a given pressure level.As such, their full width at half maximum (FWHM) is a measure of the vertical resolution.The offline HO 2 product has a vertical resolution of about 4 km between 10 and 0.1 hPa, 8 km at 0.02 hPa and around 14 km for smaller pressures.The vertical resolution of this offline retrieval is similar to that of the HO 2 standard product for the pressure range where they overlap.The integrated kernel shows that most of the information arises from the measurements.

Error assessment
The total error in the retrieved product is a combination of the random noise in the measurements, the smoothing error, and the errors due to systematic uncertainties, such as instrumental and calibration errors and forward model and retrieval approximations.
Figure 4 displays the offline HO 2 expected precision for daily, monthly and yearly profiles of measurements averaged over a 10 • latitude bin.The expected precision is the error due to the combination of the random noise in the measurements and the a priori uncertainty and is given by the diagonal elements of the covariance matrix of the retrieved state (Rodgers, 2000).For measurements averaged over a 10 • latitude bin, for both the daytime and nighttime data, the daily HO 2 precision ranges from 0.09 ppbv (29×10 6 molec cm −3 ) at 10 hPa to 1.4 ppbv (2.2 × 10 6 molec cm −3 ) at 0.046 hPa, and up to 7.7 ppbv (1 × 10 6 molec cm −3 ) at 0.003 hPa.Due to the temporal variability of HO 2 , these precision values can change seasonally up to 40 % depending on the pressure level observed.This variability is greater than the one found in the standard MLS product because the standard product is highly constrained due to the poor signal-to-noise ratio.Although significant averaging such as monthly means is needed to achieve usable HO 2 estimates, the retrieval algorithm presented in this study uses daily zonal mean radiances, instead of weekly or monthly, in order to enable averaging different combination of days as needed.
Figure 5 summarizes the impact of the dominant systematic uncertainties for the offline MLS HO 2 product.These arise from instrumental issues such as uncertainties in the radiometric calibration, the field of view (FOV) characterization, the spectroscopy parameters, the pointing knowledge, the temperature profile used, the contaminant species errors, such as the O 3 line influencing band 30, and the retrieval approximations (a complete list and a more detailed discussion of the systematic error analysis is given by Read et al., 2007, Appendix A).The contribution of these uncertainties to the total HO 2 error was estimated using end-to-end calculations.For each systematic error a full day (∼ 3500 profiles) of perturbed radiances was generated and binned into 10 • zonal bins and processed by the offline algorithm.Each perturbation corresponds to either 2σ estimates of uncertain-ties in the relevant parameter, or an estimate of their maximum reasonable error based on instrument knowledge.Comparisons of these results with those using unperturbed radiances are a measure of the impact of each systematic error source.The comparison between the unperturbed noise-free radiances run, and the "true" model atmosphere estimates the errors due to the retrieval numerics, which, in other words, is a measure of error due to the retrieval formulation itself, in this case, mostly an smoothing error.
The impact of typically small error sources, such as (but not limited to) errors due to the spectrometer nonlinearities, uncertainties in the MLS spectral filter position, and the antenna transmission losses, has been quantified with a simple analytical model of the MLS measurement system (Read et al., 2007, Auxiliary material).Unlike the end-to-end estimates, these calculations only provide a multiplicative error.
Between 10 and 0.1 hPa, both for the daytime and nighttime case, the total systematic error is around 0.04 ppbv (up to ∼ 10 × 10 6 molec cm −3 ).In this region, the main source of systematic bias arises from radiometric and spectroscopy uncertainties, in particular due to standing waves.Standing waves are a consequence of multiple reflections in the MLS optics of the hot and cold targets used as part of the radiometric calibration (Jarnot et al., 2006).For pressures smaller than 0.1 hPa, the main source of bias and scatter are retrieval numerics, which, although unsatisfactory, is understandable given the ∼ 14 km vertical resolution in this region.Around 0.0032 hPa, the total error is as large as 1.2 ppbv (∼ 0.2 × 10 6 molec cm −3 ) .
As already mentioned, between 10 and 1 hPa, the effects of the systematic biases can be diminished by subtracting the nighttime retrieved values from the daytime, taking advantage of the pronounced HO 2 diurnal variation below ∼ 1 hPa where negligible HO 2 is expected during night.

Results
In this section we compare the offline HO 2 data set with balloon-borne and other satellite measurements, as well as with global climate and photochemical model simulations.In making these comparisons, i.e. when showing the absolute or percentage differences between the data sets, the MLS averaging kernels has been applied to properly compare them.Furthermore, when comparing against the global climate or the photochemical model simulations, their high vertical resolution has been reduced to the MLS one using a least square fit as described by Livesey et al. (2011, Sect. 1.9).In these comparisons, no altitude extrapolation has been applied to any data set.To alleviate biases in the MLS offline HO 2 data, the day-minus-night differences are used as a measure of daytime HO 2 for pressures between 10 and 1 hPa.

Comparison with balloon-borne instruments
Figure 6 compares the MLS offline and the Far Infrared Spectrometer (FIRS-2) HO 2 data.The MLS HO 2 profile corresponds to day-minus-night differences averaged over a 20 • latitude bin centred at 30 • N averaged over 10 days centred on the day of the balloon flight.The mean SZA of this profile is ∼ 32 • .The FIRS-2 profile shown was taken on the 20 September 2005 in Fort Sumner, New Mexico, USA (34.5 • N).In that flight, the balloon stayed aloft at around 38 km for nearly 24 h.The FIRS-2 profile with the closest SZA to the MLS one is displayed, in this case ∼ 31 • .FIRS-2 is a thermal emission far-infrared Fourier transform spectrometer developed at the Smithsonian Astrophysical Observatory.It measures emission spectra between 75 and 1000 cm −1 with high interferometric efficiency.It retrieves HO 2 from 43 rotational transitions between 110 and 220 cm −1 (Jucks et al., 1998).The retrieval algorithm first estimates slant columns and then, in an onion-peeling fashion, a singular value decomposition routine is used to retrieve mixing ratios on a 1 km vertical grid (Johnson et al., 1996).The total systematic errors for the retrieved HO 2 are estimated to be 3 %.
Overall, the two instruments agree on the HO 2 vertical structure, with increasing HO 2 with height (in the VMR rep-resentation).However, there seems to be an bias between them, with the MLS data in the lower bound.This might be due to the differences between the FIRS-2 single profile and the MLS zonal mean profile.In SD-WACCM (see Sect. 4.3 for the model description), these differences (i.e.comparing a single profile versus a zonal mean profile at this location) are around 30 %. Quantitatively, the MLS offline data agree with the FIRS-2 data within their uncertainties -a result also found by Pickett et al. (2008) using the standard MLS HO 2 product.

Satellite intercomparison
Comparisons of monthly means were made with those from the Superconducting Submillimeter Wave Limb Emission Sounder (SMILES).SMILES is a 4 K cooled radiometer on board the Japanese Experiment Module (JEM) on the International Space Station (ISS) that performed atmospheric observations from October 2009 to April 2010.It measured, on a time-sharing basis, two of three frequency bands: 624.32-625.52GHz (band A), 625.12-626.32GHz (band B) and 649.12-650.32GHz (band C) covering tangent heights between 10 and at least 60 km about 1600 times per day covering mostly from 65 • N to 38 • S. HO 2 retrievals are based on radiances from band C which measures an HO 2 line centred The FIRS profile corresponds to the one with the closest SZA to the MLS (daytime only) data.The MLS (grey shaded region) and FIRS-2 errors represent a combination of precision and accuracy.The left column shows the data in VMR and the right one in number density.The differences shown in the bottom panels are FIRS-2 − MLS or (FIRS-2 − MLS) 100 / MLS (both in VMR units).The MLS averaging kernels were applied to the FIRS-2 data to fairly compare the two.The error margins (dashed lines) in the difference subplots correspond to the MLS and FIRS-2 errors added in quadrature.at 649.7 GHz (the same line measured by the upper side band of MLS band 28).The ISS follows a non-sun-synchronized circular orbit with an inclination of 51.6 • which allowed SMILES to make measurements at local times that drifted ∼ 20 min earlier each day covering the entire diurnal cycle in a period of about 2 months (Kikuchi et al., 2010).In this study we use the HO 2 retrievals from the research processor (version 3.0.0)developed by NICT (National Institute of Information and Communications Technology).This version is an outcome of the latest calibrated radiances which includes an improved determination of the tangent height (e.g.Ochiai et al., 2013).These HO 2 retrievals have been used for intersatellite comparisons (Khosravi et al., 2013) and for a reaction rate estimation (Kuribayashi et al., 2014).They have a vertical resolution varying from 4 to 5 km at 35 and 55 km, respectively.The estimated precision of a single profile was estimated to be better than 30 % in the vertical range 20-86 km.In this study, only retrieval levels with a measurement The MLS averaging kernels were applied to the SMILES data to fairly compare the two.The differences shown are SMILES − MLS or (SMILES − MLS) 100 / MLS (both in VMR units).Note that there are no HO 2 SMILES data available for December 2009.As before, to alleviate biases in the MLS HO 2 data, the day-minus-night differences are used as a measure of daytime HO 2 for pressures between 10 and 1 hPa.From left to right, the data sets shown are: MLS, SMILES, SMILES with the MLS average kernels, the absolute difference and the percentage difference.
response greater than 0.8 and lower than 1.2 have been used to avoid altitudes influenced too much by the a priori (Baron et al., 2011).
Figures 7 and 8 show daytime and nighttime comparisons (monthly means and the differences of the monthly means), respectively.To alleviate biases in the MLS HO 2 data, the day-minus-night differences are used as a measure of daytime HO 2 for pressures between 10 and 1 hPa.Note that only SMILES measurements made within half an hour local time of the MLS measurements were used in this comparison.During daytime, the retrieval top-level difference is as much as 80 %; however, at around 0.02 hPa (the mesospheric local maxima height), the difference is overall less than ±30 %.The retrieval top-level differences will need to be explored further, to investigate whether they are due to retrieval artifacts (both retrievals are more sensitive to the a priori at these levels), calibration uncertainties or sampling differences (unlike MLS, SMILES data are not regularly distributed); this will require a joint effort from the MLS and SMILES teams.During nighttime, the overall differences are around 30 % with localized spikes due to the small nighttime values.Overall, below around 0.1 hPa these HO 2 estimates agree within their uncertainties.Comparisons against SMR were not performed for two reasons: (1) the SMR mesospheric data mentioned in Sect. 1 are not publicly available and (2) SMR ascending-and descending-node times are about 6.00 a.m. and 6.00 p.m., just during sunrise and sunset, which complicates the comparison.

Comparison with a global climate model
The Whole Atmosphere Community Climate Model (WACCM Version 4) is a fully interactive chemistry climate model in which the radiatively active gases affect heating and cooling rates and therefore dynamics (Garcia et al., 2007).It simulates the atmosphere from the Earth's surface to the thermosphere.For this analysis, the model was run with a horizontal resolution of 1.9 • × 2.5 • in latitude and longitude, and a vertical coordinate purely isobaric in the stratosphere with a variable spacing of 1.1 to 1.75 km using meteorological fields derived from the Goddard Earth Observing System 5 (GEOS-5) analyses.The use of offline meteorological fields, a capability described by Lamarque et al. (2012), allows WACCM to perform as a chemical transport model, thus facilitating comparisons with observations.The WACCM chemical module is based on the 3-D chemical transport Model of Ozone and Related Tracers (MOZART), Version 4 (Kinnison et al., 2007).The of this Speci-Dynamics WACCM (SD-WACCM/GEOS-5) run were then sampled to the corresponding MLS observation time.
Figure 9 shows a daytime monthly (January 2005) mean comparison between the offline MLS data and the SD-WACCM simulations both in VMR and density units.To alleviate biases in the MLS HO 2 data, the day-minus-night differences are used as a measure of daytime HO 2 for pressures between 10 and 1 hPa.As can be seen, MLS and SD-WACCM display similar VMR structures with a gradient from the winter pole towards the summer pole.Note that, to properly compare the data with the model simulations, Fig. 9 also shows the SD-WACCM simulations convolved with the offline MLS averaging kernels reducing the SD-WACCM high vertical resolution using a least square fit as described by Livesey et al. (2011, Sect. 1.9).
In Fig. 9, the HO 2 VMR peak between 0.05 and 0.01 hPa reflects the mesospheric source -Reaction (R8) following Reaction (R7).The latitudinal gradient is a consequence of the varying SZA and the H 2 O distribution, which also shows a latitudinal gradient due to the meridional circulation.The height of this peak is set by the balance between the thin air density at higher altitudes and the weakening of the UV irradiance responsible for the H 2 O photolysis at lower altitudes, which leads to smaller HO 2 production.
In the stratosphere, as H 2 O photolysis becomes less important and the H abundance decreases, HO 2 mainly forms from the transformation of OH through reactions with O 3 -Reaction (R6).This source is reflected in the HO 2 number density peak in the stratosphere and has a similar shape to the peak of OH (e.g.Pickett et al., 2008) but at lower altitudes due to the O 3 maximum height in the lower stratosphere.
Even though the offline MLS data set and the SD-WACCM simulations display similar structures (see Fig. 9), they differ in magnitude.The offline MLS data suggest that there is more mesospheric HO 2 than predicted by the model, particularly at ∼ 0.02 hPa, which requires further investigation.To alleviate biases in the MLS HO 2 data, the day-minus-night differences are used as a measure of daytime HO 2 for pressures between 10 and 1 hPa.The MLS averaging kernels were applied to the SD-WACCM data set to fairly compare the two.The left column shows the data in VMR and the right one in number density.From top to bottom, the data sets shown are: SD-WACCM, SD-WACCM with the MLS averaging kernels, MLS and the absolute and percentage differences.The differences shown are SD-WACCM − MLS or (SD-WACCM − MLS) 100 / MLS (both in VMR units).
These differences correspond to SD-WACCM values smaller than the retrieved values by 50 % near the summer pole and smaller than 80 % near the winter pole (where SD-WACCM estimates near zero values).
To investigate whether these discrepancies, particularly the ∼ 4 ppbv difference at around 50 • S, were due to measurement errors or due to assumptions in the SD-WACCM model, we compared measured MLS radiances to synthetic radiances computed using the offline MLS data and the SD-WACCM values.The SD-WACCM simulated radiances were smaller than the measured radiances by ∼ 40 %, outside the radiance error.Although MLS calibration errors cannot be ruled out, this is unlikely due to the magnitude of the offset and because this type of discrepancy cannot be found in the nighttime monthly mean comparison (Fig. 11).Hence, these simulations suggest that there is more mesospheric HO 2 than modelled at around 0.02 hPa.Furthermore, as can be seen in the latitude/time cross-section shown in Fig. 10, the behaviour found in Fig. 9 (a 50 % difference near the summer pole and more than 80 % near the winter one) repeats itself.These discrepancies might be due to a variety of reasons, for example: (1) our understanding of middle atmospheric chemistry may not be complete, and (2) there might be due to differences between recent solar spectral irradiance (SSI) satellite measurements (Snow et al., 2005;Harder, 2010) and most parametrizations.These SSI measurements display a larger variability in solar UV irradiance which cannot be reconstructed with SSI models, including the model of Lean et al. (2005), used in this SD-WACCM run (Marsh et

2013
).These SSI measurement-model differences have been proven to affect the HO x photochemistry (Haigh et al., 2010;Merkel et al., 2011;Ermolli et al., 2013); more UV irradiance leads to an enhancement of O 3 photolysis as well as H 2 O photodissociation, which leads to more HO x production through Reactions (R4)-(R8).Further, Wang et al. (2013) showed that using a solar forcing derived from these SSI measurements the modelled OH variability agrees much better with observations.Lastly, (3) these discrepancies might be related to the WACCM representation of the mean meridional circulation which has been shown to have some deficiencies (Smith et al., 2011;Smith, 2012), suggesting that the gravity wave parametrization needs to be modified.In addition, Garcia et al. (2014) have shown that adjusting the Prandtl number, used to calculate the diffusivity due to gravity waves, significantly alters the CO 2 SD-WACCM simulations, improving the agreement with satellite measurements.Such adjustment should also affect the H 2 O and hence the HO x chemistry.Figure 9 also shows that SD-WACCM underpredicts HO 2 by about 20-30 % between 1 and 0.1 hPa.This result agrees with previous studies (Sandor et al., 1998;Khosravi et al., 2013) but contradicts the result of the study by Canty et al. (2006).The apparent model overestimation near 0.2 hPa is probably related to the MLS change in vertical scan pattern near this pressure level.
In Fig. 9 in the number density subplots, between 10 and 0.1 hPa, both the offline MLS data set and the SD-WACCM simulations behave in a similar manner both in structure and in magnitude; however, due to the small HO 2 signal in the MLS radiances, the offline MLS retrieval is noisier.The lack of a peak at ∼0.02 hPa in the SD-WACCM data set reflects the smaller mesospheric concentrations in this data set.
Figure 11 shows the nighttime monthly mean comparison.As in the daytime comparison, both data sets show similar structures with a narrower HO 2 layer in the upper mesosphere as well as a gradient from the winter to the summer pole.As during daytime, HO 2 is principally formed through the three-body reaction of H with O 2 -Reaction (R8); however in this case, due to the lack of photodissociation of H 2 O, the H available is the one generated at sunlit latitudes (in this case, in the Northern Hemisphere), transported at high altitudes towards the winter pole where it descends and reacts with O 2 at night (in this case, in the Southern Hemisphere) (Pickett et al., 2006).As in daytime, despite having similar structures, both data sets differ in magnitude.Overall, the nighttime differences are smaller than the daytime differences with SD-WACCM underpredicting the midlatitude summer regions by as much as 30 % and overestimating by as much as 50 % over the polar winter regions.
The strong contrast, around 6 ppbv, between the daytime and the nighttime HO 2 mesospheric peaks demonstrates the capability of the new offline retrieval to invert large mesospheric variations.

Photochemical model comparisons
Figure 12 shows a comparison between the HO 2 estimates from MLS offline and model simulations using the Caltech/JPL-Kinetics 1-D photochemical model.This model covers from the surface to 130 km in 66 layers.It has vertical transport (including eddy, molecular and thermal diffusion) and coupled radiative transfer (Allen et al., 1981(Allen et al., , 1984)).The kinetic parameters for the calculation of rate constants and photolysis rates were specified according to JPL 2011 recommendations (Sander et al., 2011).The model was run in a diurnally varying mode with no transport until the HO x concentrations were repetitive -which means that a steady state was reached.Two model runs are shown: Kinetics 1 which constrains the model using MLS measurements of H 2 O, O 3 , and temperature to test the HO x production and loss balance as well as the HO x partitioning, and Kinetics 2 which, in addition, constrains the model using MLS OH measurements to mostly test the HO x partitioning -Reactions (R10)-(R12).
As shown in Fig. 12, in the upper mesosphere (pressures smaller than 0.1 hPa), the Kinetics 1 simulations do not reproduce the magnitude of the measured peak, underestimating it by as much as 60 %.On the other hand, Kinetics 2 shows an improvement in the modelling of this peak, reducing the underestimation to less than 40 %.These discrepancies coincide with the ones discussed in the previous section, strongly suggesting that they are related to the model assumptions rather than to measurement errors.As with the SD-WACCM simulations, several factors could be the reason for this discrepancy: it might be due to limitations in our current understanding of middle atmospheric chemistry and/or due to the deficiencies in the model solar spectral irradiance used, in this case Rottman (1982).Also, considering that Kinetics 2 (the run testing the HO x partitioning) represents the measured HO 2 better, these simulations might suggest that the modelling problems are related to the HO x production and loss balance rather than to the HO x partitioning.In the upper stratosphere and lower mesosphere (between 1 and 0.1 hPa) for the most part the photochemical model underpredicts HO 2 by around 20 %, concurring with the SD-WACCM simulations as well as with previous studies (Sandor et al., 1998;Khosravi et al., 2013) but contradicting the result of the study by Canty et al. (2006).

Summary
We have introduced a stratospheric and mesospheric HO 2 data set derived from the Aura MLS using an offline retrieval algorithm.This offline HO 2 data set has three distinct improvements upon the standard MLS HO 2 : (1) an extended pressure range, allowing measurements of the mesospheric peak local maxima that occur at around 0.02 hPa at most latitudes, (2) an extended latitudinal coverage, which allows to measure the poles, where the HO 2 maximum lies, and (3) nighttime HO 2 estimates.
The offline retrieval uses zonal mean MLS radiance spectra divided into daytime (SZA ≥ 90 • ) and nighttime (SZA ≤ 100 • ) which are then inverted using the optimal estimation technique to produce daily zonal mean HO 2 profiles from 10 to 0.0032 hPa during daytime and from 1 to 0.0032 hPa during nighttime.The MLS non-zero nighttime HO 2 abundances between 10 and 1 hPa were used as measure of systematic biases in the retrievals.Assuming that these biases are constant throughout day and night, we used the dayminus-night differences, only at these pressure levels, as a more accurate daytime HO 2 estimate.The vertical resolution of this data set is about 4 km between 10 and 0.1 hPa, 8 km at 0.02 hPa, and around 14 km for smaller pressures.Daily precision ranges from 0.1 ppbv in the upper stratosphere to up to 8 ppbv in the upper mesosphere, dropping to ∼ 1.4 ppbv and ∼ 0.5 ppbv for monthly and yearly averages, respectively.Between 10 and 0.1 hPa, for both daytime and nighttime cases, the total systematic error is around 0.04 ppbv (up to ∼ 10 × 10 6 molec cm −3 ), while for smaller pressure levels the systematic error is as big as 1.2 ppbv (∼ 0.2 × 10 6 molec cm −3 ).
Comparison with the balloon-borne FIRS-2 measurements revealed that both data sets agree within their uncertainties, however there seems to be an offset with MLS on the low www.atmos-chem-phys.net/15/2889/2015/side.Comparisons with SMILES were found to agree both in structure and magnitude within the uncertainties below 0.02 hPa.Qualitatively, the offline MLS HO 2 agrees well with the SD-WACCM model.Quantitatively, however, the offline MLS HO 2 exceeds the model by up to 100 % in the mesosphere during day (in regions where SD-WACCM estimates near-zero values) and up to 40 % at night.Also, between 1 and 0.1 hPa, SD-WACCM underpredicts HO 2 by about 20-30 %, agreeing with previous studies (Sandor et al., 1998;Khosravi et al., 2013) but contradicting the result of the study by Canty et al. (2006).
Using the Caltech/JPL-Kinetics 1-D photochemical model we found similar results.In the upper mesosphere, we found an underestimation by the model by as much as 60 %, and in the upper stratosphere/lower mesosphere an underestimation by about 20 %.These results strongly suggest that these discrepancies are related to the model assumptions rather than to measurement errors.
The results presented in this study show that this new data set, in addition to the standard MLS OH, H 2 O and O 3 measurements, offers the possibility to study the impact of the HO x family upon the mesospheric O 3 as well as the HO x dilemma.Furthermore, this retrieval, or a similar one using geomagnetic latitudes to sort the radiances, may help to understand the impact of solar proton events and energetic electron particles upon the HO x family by comparing averages of days impacted by these events with averages of non-impacted days.

Figure 1 .
Figure 1.Average MLS radiance as detected by bands 28 (top) and 30 (bottom), separated into daytime (solid line) and nighttime (dashed line) measurements.Average is from 55 • S and 55 • N and for limb tangents at 10 and 4.6 hPa for January 2005.The dotted grey line is the expected single-scan noise.

Figure 2 .
Figure 2. January 2005 zonal mean for MLS HO 2 data sets.The MLS V3.3 data set (top) is the standard product described byPickett et al. (2008), here shown as the day-minus-night difference as recommended by the MLS data guidelines(Livesey et al., 2011).The MLS offline (bottom) is the data set introduced here.In this case, the day-minus-night difference has been taken only between 10 and 1 hPa, which is the reason why this data set can be extended to 10 hPa.The left column shows the data in VMR and the right one in number density.
Figure3.Daytime averaging kernels for the HO 2 offline retrieval at the equator (those at other latitudes are very similar).The black line is the integrated area under each kernel: values near unity indicate that most information was provided by the measurements while lower values indicate that the retrieval was influenced by the a priori.The dashed grey line is a measure of the vertical resolution of the retrieved profile (derived from the FWHM of the averaging kernels approximately scaled into kilometres).

Figure 4 .
Figure 4. Expected precision for daily (D), weekly (W), monthly (M) and yearly (Y) MLS HO 2 offline data averaged over a 10 • latitude bin.Precision expected in MLS HO 2 offline data averaged over a 10 • latitude bin for a day (D), a week (W), a month (M) and a year (Y).The left column shows the data in VMR and the right one in number density.The black lines show typical HO 2 profiles, daytime in solid and nighttime dashed.These profiles are a yearly average over all latitudes of the SD-WACCM model (see Sect. 4.3 for the model description).

Figure 5 .
Figure5.Estimated impact of various families of systematic error sources on the MLS offline HO 2 observations.Cyan lines correspond to uncertainties in the MLS radiometric and spectral calibration.Purple lines denote uncertainties associated with the MLS FOV and antenna transmission efficiency.Green lines denote errors in the spectroscopic databases and due to the forward model approximations.The impact of the uncertainties in the MLS pointing are depicted by the red lines.The yellow lines correspond to errors in the retrieved MLS temperature, while the blue lines show the impact of the retrieved errors in contaminant species.Errors due to retrieval formulation are shown in grey.The black lines are the root sum squares of all the biases or the scatters shown.The top panel corresponds to the daytime part of the orbit while the lower panel corresponds to the nighttime part.The left panels show the biases and additional scatter introduced by each family of systematic errors in VMR while the right panels show them in number density.

Figure 6 .
Figure 6.Comparison of MLS offline and FIRS-2 HO 2 data from 20 September 2005 at 34.5 • N. The MLS data correspond to the day-minus-night average of 15-25 September 2005 for the 20 • latitude bin centred at 30 • N.The FIRS profile corresponds to the one with the closest SZA to the MLS (daytime only) data.The MLS (grey shaded region) and FIRS-2 errors represent a combination of precision and accuracy.The left column shows the data in VMR and the right one in number density.The differences shown in the bottom panels are FIRS-2 − MLS or (FIRS-2 − MLS) 100 / MLS (both in VMR units).The MLS averaging kernels were applied to the FIRS-2 data to fairly compare the two.The error margins (dashed lines) in the difference subplots correspond to the MLS and FIRS-2 errors added in quadrature.

Figure 7 .
Figure7.Monthly daytime zonal mean comparisons between MLS offline and SMILES HO 2 data for October 2009 to April 2011.The MLS averaging kernels were applied to the SMILES data to fairly compare the two.The differences shown are SMILES − MLS or (SMILES − MLS) 100 / MLS (both in VMR units).Note that there are no HO 2 SMILES data available for December 2009.As before, to alleviate biases in the MLS HO 2 data, the day-minus-night differences are used as a measure of daytime HO 2 for pressures between 10 and 1 hPa.From left to right, the data sets shown are: MLS, SMILES, SMILES with the MLS average kernels, the absolute difference and the percentage difference.

Figure 8 .
Figure 8.As Fig. 7, but for nighttime data.Note that the large positive percentage differences shown for April 2010 close to 20 • S and 20 • N are due to underestimations by the MLS retrieval.

Figure 9 .
Figure9.January 2005 monthly daytime zonal mean for the MLS offline HO 2 observations and the SD-WACCM model.To alleviate biases in the MLS HO 2 data, the day-minus-night differences are used as a measure of daytime HO 2 for pressures between 10 and 1 hPa.The MLS averaging kernels were applied to the SD-WACCM data set to fairly compare the two.The left column shows the data in VMR and the right one in number density.From top to bottom, the data sets shown are: SD-WACCM, SD-WACCM with the MLS averaging kernels, MLS and the absolute and percentage differences.The differences shown are SD-WACCM − MLS or (SD-WACCM − MLS) 100 / MLS (both in VMR units).

Figure 10 .
Figure 10.Daytime latitude/time cross-sections of the MLS offline HO 2 observations and the SD-WACCM model for 2005 at 0.014 hPa.As in Fig.9, the MLS averaging kernels were applied to the SD-WACCM data set to fairly compare the two.From top to bottom, the data sets shown are SD-WACCM, SD-WACCM with the MLS averaging kernels, MLS and the absolute and percentage differences.The differences shown are SD-WACCM − MLS or (SD-WACCM − MLS) 100 / MLS (both in VMR units).

Figure 12 .
Figure 12.Daytime MLS offline HO 2 estimates for April 2005 and model results using JPL11 kinetics.Kinetics 1 is a photochemical model run constraining H 2 O, O 3 and temperature while Kinetics 2 constrains H 2 O, O 3 , temperature and OH.The differences shown are Kinetics − MLS or (Kinetics − MLS) 100 / MLS.In the difference subplots, to properly compare the model runs with MLS, a least square fit has been used to reduce the model resolution and the corresponding averaging kernels has been applied.The dashed grey lines show the MLS precision as well as the 20 and 40 % percentage regions.