Direct estimation of the rate constant of the reaction ClO + HO 2 → HOCl + O 2 from SMILES atmospheric observations

Diurnal variations of ClO, HO2, and HOCl were simultaneously observed by the Superconducting Submillimeter-Wave Limb-Emission Sounder (SMILES) between 12 October 2009 and 21 April 2010. These were the first global observations of the diurnal variation of HOCl in the upper atmosphere. A major reaction for the production of HOCl is ClO + HO2 →HOCl + O2 (Reaction(R1)) in extra-polar regions. A model study suggested that in the mesosphere, this is the only reaction influencing the amount of HOCl during the night. The evaluation of the pure reaction period, when only Reaction (R1) occurred in the Cly chemical system, was performed by checking the consistency of the HOCl production rate with the ClO loss rate from SMILES observation data. It turned out that the SMILES data at the pressure level of 0.28 hPa (about 58 km) in the autumn mid-latitude region (20–40 ◦ S, February–April 2010) during night (between modified local time 18:30 and 04:00) were suitable for the estimation of the rate constant, k1. The rate constant obtained from SMILES observations wask1(245 K)= (7.75± 0.25)×10−12 cm3 molecule−1 s−1. This result is consistent with results from a laboratory experiment and ab initio calculations for similar low-pressure conditions.


Introduction
The Reaction (R1) converts active chlorine monoxide (ClO) into hypochlorous acid (HOCl) as a short-lived reservoir in the atmosphere: ClO + HO 2 → HOCl + O 2 . (R1) The Reaction (R1) is the rate-limiting step of a catalytic ozone depletion cycle that causes about 7 % and 10 % of the ozone loss in the extra-tropical lower stratosphere and in the Arctic stratospheric vortex, respectively (Lee et al., 2002;Chipperfield et al., 1994).
Several laboratory studies on the rate constant of the Reaction (R1), k 1 , have been reported (Stimpfle et al., 1979;Knight et al., 2000;Nickolaisen et al., 2000;Hickson et al., 2007).k 1 has relatively large uncertainties compared with the rate constants of other major reactions in the atmospheric chemistry.For example, the k 1 value from Hickson et al. (2007) has an error of about 25 % (k 1 (296 K) = (6.4± 1.6) × 10 −12 cm 3 molecule −1 s −1 ), while the rate constant of the Cl + O 3 →ClO + O 2 reaction, k, has an error of about 10 % (k(298 K) = (1.21±0.13)×10−11 cm 3 molecule −1 s −1 ) (Seely et al., 1996).Table 1 shows k 1 and the error (1σ ) calculated from previous laboratory studies at 225 K (which corresponds to the typical temperature of the lower stratosphere).A discrepancy of a factor of 2 between the k 1 values from Stimpfle et al. (1979) and Knight et al. (2000) can be noticed.There is no consistency in the previous laboratory studies.One reason for this is that the quantification of the production of HO 2 and ClO in laboratory experiments is difficult.Large uncertainties and discrepancies of k 1 lead to uncertainties of the estimation of the ozone loss in the extratropical lower stratosphere and in the Arctic stratospheric vortex.
The validity of k 1 values from laboratory studies have been discussed using atmospheric observations and model calculations of HOCl.Several atmospheric observations of HOCl in the lower/middle stratosphere have been reported Published by Copernicus Publications on behalf of the European Geosciences Union.
Table 1.k 1 and the error (1σ ) calculated based on previous laboratory studies at 225 K.
A high-sensitivity remote sensing instrument named the Superconducting Submillimeter-Wave Limb-Emission Sounder (SMILES) on the International Space Station (ISS) performed the first simultaneous observations of the diurnal variations of HOCl, ClO, and HO 2 in the middle atmosphere.The observation period was between 12 October 2009 and 21 April 2010.The latitude and altitude coverage of the SMILES observations was nominally 38 • S-65 • N and 16-90 km, respectively.An overview of SMILES is given in Kikuchi et al. (2010).Details of the observation of O 3 and ClO are described in Kasai et al. (2013), Sato et al. (2012), and Sagawa et al. (2013).
In this paper, we directly derive k 1 from the diurnal variations of HOCl, ClO, and HO 2 observed by SMILES in the lower mesosphere.We evaluate the "purity" of Reaction (R1) using both of the rate of HOCl production and the rate of ClO loss.Here "purity" means that only the Reaction (R1) modifies the concentration of ClO and HOCl, and the effect of competitive reactions does not appear in the observation.This "purity" condition is essential for the accurate estimation of k 1 .It is difficult to obtain such a condition in stratospheric observations.In the stratosphere, several competitive reactions exist that modify the amount of HOCl and ClO.The photolysis of HOCl occurs during daytime, and ClO is consumed by the reaction ClO + NO 2 + M →ClONO 2 + M during nighttime.

Model calculation of Cl y chemistry in the lower mesosphere
In order to derive the rate constant of a chemical reaction from the observations of the concentrations of chemical species in the atmosphere, two basic approaches are possible.
a. Steady-state approach: if the reaction of interest is involved in the production or destruction of a chemical species that is at steady state, then the corresponding balance equation (chemical production = depletion) may be exploited.It can be solved for the unknown rate constant, if the rate constants of all other involved reactions and the concentrations of all the reactants are known.The disadvantage of this method is that, besides the reaction of interest, at least one more reaction is involved in the chemical equilibrium.That is why assumptions about the corresponding reaction rate constant(s) must be made.
b. Exploitation of the temporal evolution of the concentration of a chemical species: an estimate of the rate constant of the reaction of interest can be obtained from the rate of change of the concentration of a reactant or product of this reaction.This approach is especially useful if it is applied under conditions in which the concentration of a certain species is affected only by the reaction of interest, because then no assumptions about the rate constants of other reactions are needed.
We used approach (b) for the calculation of k 1 from the SMILES HOCl, ClO, and HO 2 observations.In order to find out under which conditions the temporal evolution of HOCl can be expected to be determined solely by the Reaction (R1), we ran the AWI (Alfred Wegener Institute) chemical box model at different altitudes.This model simulates 175 reactions between 48 chemical species in the stratosphere and mesosphere.We performed 3D runs, the last 24 h of which were used for the analysis.SMILES observations (bi-monthly mean data within latitude and altitude bins) were used for the initialization of these runs.For the species which were not observed by SMILES, initial mixing ratios were taken from Brasseur et al. (1999), Appendix C, with the exception of that of water vapour; its initial mixing ratio was adjusted such that the diurnally varying mixing ratio of ClO repeated every 24 h in the simulation.
These model runs yielded the following results: 1. Daytime conditions are not suitable for the application of method (b), because the photolysis of HOCl counteracts the Reaction (R1).present, because the concentrations of their reaction partners in the loss reactions are smaller than those in the stratosphere.

Nighttime conditions in
Figure 1 shows the corresponding model results for 0.28 hPa (58 km).After sunset Cl is quickly converted to ClO.Then, a slow conversion of ClO to HOCl occurs.As mentioned above, this is caused by the reaction of interest, ClO + HO 2 →HOCl + O 2 .
As the daytime loss reactions of HOCl (photolysis and reaction with atomic oxygen O) stop after sunset, the Reaction (R1) is the only reaction affecting HOCl after about 10 local time (LT) 18:30 in the present model run.That is why, after that time, the rate of the increase of [HOCl] together with the concentrations of ClO and HO 2 may be used to estimate k 1 .
After  ing HCl-to-ClO conversion.The earlier this analysis starts, the more data enter the analysis, making it more robust.The alternative calculation of k 1 may be helpful to detect and exclude effects in the data that are not caused by chemistry: for example, as the data corresponding to different local 30 times may be from different months (see Fig. 2), a seasonal variation of the data may result in a variation with local time not caused by chemistry.

Diurnal variation observed by SMILES
We obtained concentrations of ClO, HO 2 and HOCl from 35 the SMILES NICT level-2 product version 2.1.5(Sato et al., 2012;Sagawa et al., 2013;Kasai et al., 2013).VMRs (volume mixing ratios) of the species of interest were retrieved from the spectra observed in the stratosphere and the mesosphere.Data of at least two months are required to obtain all 40 local times at night because of the ISS orbit.
The 0.28 hPa pressure level (∼58 km) was used to investigate the lower mesosphere.We selected the latitude range between 20 • S and 40 • S and the season between February and April 2010 for our analysis by the following reasons: (1)

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The effect of the seasonal and latitudinal variability of the atmosphere is reduced, (2) the amount of HOCl was abundant in the mid-latitude autumn season (von Clarmann et al., 2012), and (3) SMILES has a denser data sampling around the 38 • S region.We extracted observations at a temperature 50 within 245 ± 1.4(1σ) K in order to reduce the variability of the calculated k 1 caused by the variability of the temperature.
The extracted SMILES data merge different latitudes and seasons that have a different relation between local times and solar zenith angles (SZA).This is why, throughout this The number density at a specific altitude was calculated by vertically interpolating the original data of level-2 VMR profiles.The vertical resolutions were about 6 km, 5 km, and 12 km for ClO, HO 2 , and HOCl respectively.The 1σ pre-65 cision of the derived number density was estimated to be ∼ 35 %, 90 %, and 120 % at 0.28 hPa (∼58 km) for single measurements of ClO, HO 2 , and HOCl in the nighttime, respectively.The variance of the number density was roughly 40 %, 110 %, and 170 % for ClO, HO 2 , and HOCl, respec-70 tively.These variances are larger than the 1σ precision of the single measurements because they include variabilities of the number density in the atmosphere.
The number of data was about 6,000 during the nighttime (MLT 18:00-06:00).This number is large enough for statis-75 tical analysis.
Figure 2 shows the diurnal variations of ClO, HO 2 , HOCl, and the sum of [ClO] and [HOCl] in the lower mesosphere (0.28 hPa).Individual observations and averages over 3.75 min are presented.The horizontal and vertical axes are  + [HO 2 ] by photolysis, and reactions involving O( 1 D) stop after sunset; HO x is converted to reservoir species by several reactions, e.g.OH + NO 2 + M →HNO 3 + M).
3. Nighttime conditions in the mesosphere are suitable for the analysis.
HOCl is produced by the Reaction (R1) on in the mesosphere during nighttime, and there is no competing production or destruction reaction.The Reaction (R1) occurs throughout the night: both reactants (ClO and HO 2 ) are present, because the concentrations of their reaction partners in the loss reactions are smaller than those in the stratosphere.
Figure 1 shows the corresponding model results for 0.28 hPa (58 km).After sunset Cl is quickly converted to ClO.Then a slow conversion of ClO to HOCl occurs.As mentioned above, this is caused by the reaction of interest, ClO + HO 2 →HOCl + O 2 .
As the daytime loss reactions of HOCl (photolysis and reaction with atomic oxygen O) stop after sunset, the Reaction (R1) is the only reaction affecting HOCl after about 18:30 local time (LT) in the present model run.That is why, after that time, the rate of the increase of [HOCl] together with the concentrations of ClO and HO 2 can be used to estimate k 1 .
After sunset there is a slow ClO production by HCl + OH →Cl + H 2 O and Cl + O 3 →ClO + O 2 .This slows down significantly by 20:00 and almost completely decays by midnight.This means that after 18:30, the rate of change of [ClO] is determined to an increasing degree by the Reaction (R1), until this is the only relevant reaction for ClO and, consequently, [ClO] + [HOCl] is nearly constant.That is why it is possible to derive an alternative estimate of k 1 from the rate of the decrease of [ClO] together with the concentrations of ClO and HO 2 .Here two effects compete; the later this analysis starts, the smaller the effect of the counteracting HCl-to-ClO conversion is.The earlier this analysis starts, the more data enter the analysis (making the analysis more robust).
The alternative calculation of k 1 may be helpful in detecting and excluding effects in the data that are not caused by chemistry; for example, as the data corresponding to different local times may be from different months (see Fig. 2), a seasonal variation of the data may result in a variation with local time not caused by chemistry.

Diurnal variation observed by SMILES
We obtained concentrations of ClO, HO 2 and HOCl from the SMILES NICT (National Institute of Information and Communications Technology) level 2 product version 2.1.5(Sato et al., 2012;Sagawa et al., 2013;Kasai et al., 2013).VMRs (volume mixing ratios) of the species of interest were retrieved from the spectra observed in the stratosphere and the mesosphere.Data for at least two months are required to obtain all local times at night because of the ISS orbit.
The 0.28 hPa pressure level (∼ 58 km) was used to investigate the lower mesosphere.We selected the latitude range between 20 • S and 40 • S and the season from February to April 2010 for our analysis for the following reasons: (1) the effect of the seasonal and latitudinal variability of the atmosphere is reduced, (2) the amount of HOCl was abundant in the mid-latitude autumn season (von Clarmann et al., 2012), and (3) SMILES has a denser data sampling around the 38 • S region.We extracted observations at a temperature within 245 ± 1.4(1σ ) K in order to reduce the variability of the calculated k 1 caused by the variability of the temperature.
The extracted SMILES data are from different latitudes and seasons, for which there are different relations between local times and solar zenith angles (SZA).This is why, throughout this study, a modified local time (MLT) of the SMILES observations is used.It is defined as follows: modified local time (MLT) = local time − local time corresponding to a SZA of 90 • + 18:00.According to this definition, the sunset at the Earth's surface (solar zenith angle = 90 • ) always occurs at 18:00 MLT independently of latitudes and seasons.
The number density at a specific altitude was calculated by vertically interpolating the original data of level 2 VMR profiles.The vertical resolutions were about 6 km, 5 km, and 12 km for ClO, HO 2 , and HOCl respectively.The 1σ precision of the derived number density was estimated to be ∼ 35 %, 90 %, and 120 % at 0.28 hPa (∼ 58 km) for single measurements of ClO, HO 2 , and HOCl in the nighttime, respectively.The variance of the number density was roughly 40 %, 110 %, and 170 % for ClO, HO 2 , and HOCl, respectively.These variances are larger than the 1σ precision of the single measurements because they include variabilities of the number density in the atmosphere.The number of data was about 6000 during the nighttime (18:00-06:00 MLT).This number is large enough for statistical analysis.
Figure 2 shows the diurnal variations of ClO, HO 2 , HOCl, and the sum of [ClO] and [HOCl] in the lower mesosphere (0.28 hPa).Individual observations and averages over 3.75 min are presented.The horizontal and vertical axes are the modified local time and the number density of each molecule, respectively.The lowest panel in Fig. 2 is the modified local time dependence of the number of the extracted SMILES data for each month.
The systematic error (bias) of SMILES NICT ClO data was estimated in a theoretical manner by Sato et al. (2012) and Sagawa et al. (2013).Theoretical estimations of the systematic errors are done by a forward-model simulation using a certain reference atmospheric state, and they do not include the actual measurement noise of SMILES observations in order to estimate the maximum impact of each error factor on the bias uncertainties.According to Sagawa et al. (2013), the systematic error for ClO is up to about 3 % at 0.28 hPa for the mid-latitude nighttime.In this study, we adopt the systematic error of 3 %, which is derived from the theoretical systematic error analysis of ClO, for all the considered species.The SMILES ClO, HO 2 , and HOCl products have been compared to other satellite measurements (Khosravi et al., 2013).However, due to the limitation in the number of compared instruments and due to the large difference in the sensitivity and observation local time of each instrument, it is not possible to determine which instrument has positive/negative bias errors.Despite such technical difficulties, the diurnal variation of the SMILES ClO, HO 2 , and HOCl show general agreement both in the quantity and shape (Khosravi et al., 2013).It is noted that more robust evaluation on the systematic error of our analysis will be addressed when further validation works of SMILES products are completed.

Method of the estimation
The results of our model calculation suggested that [ClO] + [HOCl] increases rapidly until about 18:30 and undergoes only a small increase (10 %) afterwards.As shown in Fig. 1, the sum of [ClO] + [HOCl] is nearly constant after that.This relation is equivalent to the following relation: We consider the Eq.(1) a necessary condition to prove the purity of Reaction (R1) in the atmosphere.The Reaction (R1) is a second-order reaction of ClO and HO 2 .Its reaction rate is represented with the help of the number densities of relevant species as: Eq. ( 1) is equivalent to: Equation ( 3) can be rewritten as follows using Eq. ( 2): The calculation of k 1 in Sects.4.2 and 4.3 will be based on Eqs. ( 2) and (4), respectively.In order to distinguish the results, the rate constants determined on the basis of Eqs. ( 2) and ( 4) will be denoted by c k 1 and c k 1 , respectively.Here the superscript c means "calculated".To fulfill the condition of Eq. ( 1), c k 1 and c k 1 must be identical.If other reactions affect either the increase of HOCl or the decrease of ClO, there can be some difference between c k 1 and c k 1 .

Calculation of c k 1 based on increase of HOCl
To calculate c k 1 based on the increase of HOCl, we start from Eq. ( 2).After substituting k 1 by c k 1 , the integration equation of Eq. ( 2) yields Using the trapezoidal rule, we obtain the following approximate solution of the integration Eq. ( 5): In these equations, [ClO] obs m and [HO 2 ] obs m are the mth observed number densities of ClO and HO 2 .t obs m is the mth elapsed time from the calculation start time.The intervals of t obs m+1 − t obs m are about 7 s.
[HOCl](t 0 ) is the initial value of HOCl at the calculation start time.The calculation is performed for various modified local time intervals from different start time to end time.The observation values of ClO and HO 2 were extracted for each time interval for the calculation of Eq. ( 7).
The rate constant of interested, c k 1 , and also [HOCl](t 0 ) are considered as variable parameters.The reason for not fixing [HOCl](t 0 ) is that there is a variability of the SMILES observation data of HOCl at the calculation start time for each time interval.c k 1 and [HOCl](t 0 ) are determined by the minimization of the following function χ 2 using the least-squares method:   The observation values of HOCl and the observation error of HOCl were extracted in the same time interval as in the calculation of Eq. ( 7).[HOCl] obs m is the mth observed number density and σ HOCl m is the mth observation error of HOCl.N is the number of data for each time interval.To reduce the effect of random errors from SMILES measurements, we ignored time intervals with a data volume less than 3000 (half of the total data number at night).We also obtained the calculated error (fitting error) of c k 1 from the optimization of c k 1 and [HOCl](t 0 ).

Calculation of c k 1 based on decrease of ClO
To calculate c k 1 based on the decrease of HOCl, we start from Eq. (4).After substituting k 1 by c k 1 , the integration equation of Eq. ( 4) yields www.atmos-chem-phys.net/14/255/2014/Atmos.Chem.Phys., 14, 255-266, 2014 Using the trapezoidal rule, we obtain the following approximate solution for the integration Eq. ( 9): In these equations, the rate constant of interest, c k 1 , and also [ClO](t 0 ) are considered as variable parameters.c k 1 and [ClO](t 0 ) are determined by the minimization of the following function, χ 2 , using the least-squares method: Similarly, calculated errors of c k 1 were obtained in parallel with the optimization of c k 1 and [ClO](t 0 ).

Results
Figure 3 shows the calculated c k 1 and c k 1 values in each modified local time interval.
In addition, the difference between c k 1 and c k 1 is presented.We denote this difference by The horizontal and vertical axes are the start and end times of the considered time intervals, respectively.The blank area represents the time intervals where the data numbers are less than the threshold of 3000 or k values are greater than 5.0 × 10 −12 cm 3 molecule −1 s −1 .

Evaluation of the purity of Reaction (R1) by k
As already described in Sect.4.1, k is an indicator of the purity of the Reaction (R1).k = 0 is necessary for the relation expressed in Eq. ( 1) to be fulfilled.
than 3000 (half of the total data number at night).We also obtained the calculated error (fitting error) of c k 1 from othe optimization of c k 1 and [HOCl](t 0 ).

Calculation of c k ′ 1 based on decrease in ClO
To calculate c k ′ 1 based on the decrease in HOCl, we start 5 from Eq. ( 4).After substituting k 1 by c k ′ 1 , the integration equation of Eq. (4) yields: Using the trapezoidal rule, we obtain the following ap-10 proximate solution of the integration Eq. ( 9): The rate constant of interested, c k ′ 1 , and also [ClO](t 0 ) are considered as variable parameters.c k ′ 1 and [ClO](t 0 ) are determined by the minimization of the following function χ 2 20 using the least-squares method: Similarly, calculated errors of c k ′ 1 were obtained in parallel with the optimization of c k ′ 1 and [ClO](t 0 ).

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Figure 3 shows the calculated c k 1 and c k ′ 1 values in each modified local time interval.In addition, the difference between c k 1 and c k ′ 1 is presented.We denote this difference by: The horizontal and vertical axes are the start and end time of the considered time intervals, respectively.The blank area represents the time intervals where the data numbers are less than the threshold of 3,000 or ∆k values are greater than 5.0 × 10 −12 cm 3 molecule −1 s −1 .Result 3 may be caused by two problems.One is the variability observed in the ClO data around 02:40 MLT.In Fig. 2, the ClO data around this modified local time show a relatively smaller number density compared to neighbouring modified local times (0.5 ×10 6 molecule cm −3 at 02:40 MLT while it is around 0.7 ×10 6 molecule cm −3 at neighbouring modified local times).Another one is the inhomogeneous local time sampling of SMILES in the extracted February-April data set.As shown in Fig. 2, the data for 21:00-00:00 MLT was quite evenly distributed throughout February, March, and April 2010, while that for 02:00-03:00 MLT mostly is from March 2010.Such a problem in result 2 between 00:45-01:45 MLT is also considered to be due to the inhomogeneous sampling.
The effect of photochemistry in the morning time causes relatively large k in the result 4 and the result 2. During sunrise ClO and HOCl start to decrease, and HO 2 starts to increase.This time range should be excluded from our analysis in order to ensure the purity of the Reaction (R1).
A good possibility exists that the modified local time interval of 18:30-04:00 MLT was the time in which the reaction ClO + HO 2 →HOCl + O 2 predominantly occurred in the Cl y chemistry.The sum of [ClO] and [HOCl] was near constant after 18:30 MLT in Fig. 2.However, as shown in Sect.2, the model calculation suggested that the ClO production by HCl + OH →Cl + H 2 O and Cl + O 3 →ClO + O 2 affected the sum of HOCl and ClO until 20:00 LT.The sum of HOCl and ClO in Fig. 1 increased by about 11 % after 18:30 LT.Thus, a noticeable difference occurred between the numerical analysis result using the SMILES observation data and the model calculation result.We considered this difference as caused by the following reason: although we used the modified local time to reduce effects of variabilities from latitude and season, some variabilities (e.g.water vapour) are still left.The ClO production by HCl + OH →Cl + H 2 O and Cl + O 3 →ClO + O 2 might still remain between 18:30 and 19:30 MLT, but did not appear in the SMILES observations.
As a conclusion, we derived from the SMILES data set that the modified local time interval of 18:30-04:00 MLT is the time in which the reaction ClO + HO 2 →HOCl + O 2 purely happens in the Cl y chemistry in the lower mesosphere.The condition of the SMILES data set used here is the pressure level of 0.28 hPa in the mid-latitude region (20-40 • S) in February-April 2010, having a temperature of 245 K.

Estimation of the rate constant of Reaction (R1)
In the modified local time interval of 18:30-04:00 MLT, the derived c k 1 and c k 1 range between 1.1 and 11.3 × 10 −12 cm 3 molecule −1 s −1 .This variability includes the irrelevant results as discussed in Sect.5.1.To reduce .Kuribayashi et al.: SMILES HOCl 7
Result 3 may be caused by two problems.One is the variility observed in the ClO data around MLT 02:40.In Fig. 2, e ClO data around this modified local time show a relvely smaller number density compared to neighbouring odified local times (0.5 ×10 6 molecule cm −3 at MLT 02:40 ile it is around 0.7 ×10 6 molecule cm −3 at neighbourg modified local times).Another one is the inhomogeneous cal time sampling of SMILES in the extracted Februaryril dataset.As shown in Fig. 2, the data for MLT 21:00-:00 was mixed well homogeneously between February, arch, and April, 2010 while that of MLT 02:00-03:00 ostly is from March 2010.Such a problem in result 2 beeen MLT 00:45-01:45 is also considered to be due to the homogeneous sampling.
The effect of photochemistry in the morning time causes latively large ∆k of the result 4 and the result 2. During nrise ClO and HOCl start to decrease, and HO 2 starts to crease.This time range should be excluded from our analis in order to ensure the purity of the Reaction (R1).
A good possibility exists that the modified local time interl of MLT 18:30-04:00 was the time in which the reaction O + HO 2 →HOCl + O 2 predominantly occurred in the As a conclusion, we derived from the SMILES dataset that the modified local time interval of MLT 18:30-04:00 is the time in which the reaction ClO + HO 2 →HOCl + O 2 purely 60 happens in the Cl y chemistry in the lower mesosphere.The condition of the SMILES dataset used here is the pressure level of 0.28 hPa in the mid-latitude region (20-40 • S) in February-April 2010, having a temperature of 245 K.

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In the modified local time interval of MLT 18:30-04:00, the derived c k 1 and c k ′ 1 range between 1.1 and 11.3 × 10 −12 cm 3 molecule −1 s −1 .This variability includes the irrelevant results as discussed in Sect.5.1.To reduce the effect of this variability on the estimation of k 1 , for the following calcula-70 tion we use the time range between start time of MLT 18:30-19:30 and end time of MLT 03:00-04:00 where the ∆k according to Eq. ( 13) value is closest to zero in Fig. 3. Figure 4 is a magnified figure of the ∆k shown in Fig. 3 in this time range.∆k is close to zero for start times near MLT 18:30.

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To estimate k 1 under the condition that ∆k approaches zero, we calculated average values of c k 1 and c k ′ 1 under the condition of ∆k ≤ x, where x is a variable threshold ranging from 0.01 to 2.5 × 10 −12 cm 3 molecule −1 s −1 in incre- the effect of this variability on the estimation of k 1 , for the following calculation we use the time range between start time of 18:30-19:30 MLT and end time of 03:00-04:00 MLT where the k according to Eq. ( 13) value is closest to zero in Fig. 3. Figure 4 is a magnified figure of the k shown in Fig. 3 in this time range.k is close to zero for start times near 18:30 MLT.
To estimate k 1 under the condition that k approaches zero, we calculated average values of c k 1 and c k 1 under the condition of k ≤ x, where x is a variable threshold ranging from 0.01 to 2.5 × 10 −12 cm 3 molecule −1 s −1 in increments of 0.01 × 10 −12 cm 3 molecule −1 s −1 .The average values of c k 1 and c k 1 under the condition of k ≤ x are denoted as c k1 (x) and c k 1 (x), respectively.The calculation of the standard deviation, σc k1 (x) and σc k 1 (x) , of c k1 (x) and c k 1 (x) was performed simultaneously.
Figure 5 shows the dependence of c k1 (x), c k 1 (x), σc k1 (x) , and σc k 1 (x) on x.The values of ck 1 (x) and ck 1 (x) and the values of σc k1 (x) and σc k 1 (x) converge in a case in which x approaches zero.We estimated the following limits: In this estimation, we linearly extrapolated the results shown in Fig. 5 to x = 0 × 10 −12 cm 3 molecule −1 s −1 .The dependence of k1 (0) and σ k1 (0) on how to take the value of increments of x or to extrapolate is much smaller than 1 % of k1 (0) and σ k1 (0) , respectively.The differences between the results of Eqs. ( 14) and ( 15) and between the results of Eqs. ( 16) and ( 17) are much smaller than 1 % of these limits.We used k1 (0) and σ k1 (0) as the k 1 and 1σ provided by the SMILES observations, respectively: Moreover, a comparison between the derived 1σ of k 1 and the uncertainties of c k 1 and c k 1 calculated in Sects.4.2 and 4.3 was performed.As described in Sect.4, the uncertainties (calculated errors) of c k 1 and c k 1 were calculated simultaneously with c k 1 and c k 1 , respectively.These uncertainties are denoted as σc k 1 and σc k 1 hereafter.The average values of σc k 1 and σc k 1 in the time range between start time of 18:30-19:30 MLT and end time of 03:00-04:00 MLT are σc k 1 is larger than σc k 1 because SMILES has less sensitivity to HOCl compared to ClO.If both σc k 1 and σc k 1 are the standard deviations of a Gaussian distribution and c k 1 and c k 1 are assumed to be statistically independent, then the joint distribution of c k 1 and c k 1 is the product of two Gaussian distributions.A short calculation shows that the selection of c k 1 and c k 1 according to the condition k ≤ x for x → 0 yields a Gaussian distribution with the following standard deviation σ G : 1 σ G was calculated to be 0.25 × 10 −12 cm 3 molecule −1 s −1 , and is consistent with 1σ of k 1 given in Eq. ( 18).This confirms that a reasonable estimate for the precision of the derived reaction rate constant was obtained.
The derived 1σ error of k 1 is attributable to the 1σ precisions of [ClO], [HOCl], and [HO 2 ] which are caused by the random errors in the single-scan spectrum of SMILES.There are systematic errors in [ClO], [HOCl], and [HO 2 ] observed by SMILES.As described in Sect.3, the systematic errors of ClO, HO 2 , and HOCl are another error source of the derived k 1 .The total impact on the rate constant of Reaction (R1) was estimated to be 4.3 % at maximum using 3 % for [ClO], [HO 2 ], and [HOCl] as the systematic errors (cf.Appendix A).Thus, the impact of systematic errors was slightly larger than that of the 1σ precision (3.3 %) of the derived k 1 in Eq. ( 18).
Figure 6 shows the time dependence of [HOCl] and [ClO] both for observations and calculations using the derived k 1 in Eq. ( 18).The lowest panel in Fig. 6 is the sum of observations ([HOCl] + [ClO]) and the sum of the optimized [HOCl](t 0 ) and [ClO](t 0 ).Both of them show good agreement with each other.

Comparison of k 1 with previous studies
We estimated k 1 using the SMILES atmospheric remote sensing data, which have advantages owing to the high in- strumental sensitivity and the long line-of-sight of the limb measurement from space.We compared our derived k 1 , hereafter denoted "SMILES k 1 ", with previous laboratory experiments (Stimpfle et al., 1979;Knight et al., 2000;Nickolaisen et al., 2000;Hickson et al., 2007), an ab initio calculation (Xu et al., 2003), and JPL 2011 recommendation (Sander et al., 2011).
Figure 7 shows the comparison of k 1 from our work and that from previous works.To see the detail number at 245 K, which we analyse in the presented study, we summarized the k 1 values with 1σ errors in Table 2.The value of the SMILES k 1 is consistent with the one from Hickson et al. (2007) and the ab initio value at 1 Torr from Xu et al. (2003) within the margin of error.The measurement of Nickolaisen et al. (2000) was performed under higher pressure (50-700 Torr), and the value of k 1 is larger than the other values which were performed under the condition of 0.21-1.7 Torr (except Stimpfle et al., 1979).A pressure dependence of the Reaction (R1) was noticed by Xu et al. (2003) due to the long lifetime of the reaction intermediate HOOOCl.As mentioned in Xu et al. (2003), the large value of Nickolaisen et al. (2000) might be caused by the pressure dependence.
The 1σ error of k 1 from the SMILES observation data is 2-10 times smaller than those of previous laboratory experiments at 245 K.In the laboratory experiments, the radical amount calibration is difficult because of the light source of the photolysis.The smaller 1σ error of the SMILES k 1 can be attributed to the fact that the SMILES k 1 was derived from the data set in which only the Reaction (R1) happened and other competitive radical reactions did not appear in the observation.noted as c k1 (x) and c k′ 1 (x), respectively.The calculation of the standard deviation, σck 1 (x) and σck′ 1 (x) , of c k1 (x) and c k′ 1 (x) was performed simultaneously.

Atmos
Figure 5 shows the dependence of c k1 (x), c k′ 1 (x), σck 1 (x) , and σck′ 1 (x) on x.The values of ck 1 (x) and ck ′ 1 (x) and the 5 values of σck 1 (x) and σck′ 1 (x) converge in the case that x approaches zero.We estimated the following limits:  analyze in the presented study, we summarized the k 1 values with 1σ errors in Tab. 2. The value of the SMILES k 1 is con-

Fig. 1 .
Fig. 1.Diurnal variation of the chlorine partitioning (HCl omitted) at 0.28 hPa altitude according to model calculations for 30 • S, 31 March. 25 55 study, a Modified Local Time (MLT) of the SMILES observations is used.It is defined as follows: Modified Local Time (MLT) = local time -local time corresponding to a SZA of 90 • + 18:00.According to this definition, the sunset at the Earth's surface (solar zenith angle = 90 • ) always occurs at 60 MLT18:00 independently of latitudes and seasons.
80the modified local time and the number density of each molecule, respectively.The lowest panel in Fig.2is the modified local time dependence of the number of the extracted SMILES data for each month.The systematic error (bias) of SMILES NICT ClO data 85 was estimated theoretically bySato et al. (2012) andSagawa et al. (2013).These theoretical estimations of the system-

Fig. 2 .
Fig. 2. Diurnal variation of the number density of ClO, HO2, HOCl, and the sum of [ClO] and [HOCl] at 0.28 hPa obtained by SMILES.Data from 20-40 • S between February and April 2010 are used in this study.Small dots represent the results from each single measurement of SMILES.Large dots show the smoothed temporal evolution with an average over 3.75 min.The modified local time dependence of the number of data is shown in the bottom panel.The number of data is integrated over every 0.5 h for February (red), March (green), and April (blue) separately.

Fig. 2 .
Fig. 2. Diurnal variation of the number density of ClO, HO 2 , HOCl, and the sum of [ClO] and [HOCl] at 0.28 hPa obtained by SMILES.Data from 20-40 • S from February to April 2010 are used in this study.Small dots represent the results from each single measurement of SMILES.Large dots show the smoothed temporal evolution with an average over 3.75 min.The modified local time dependence of the number of data is shown in the bottom panel.The number of data is integrated over every 0.5 h for February (red), March (green), and April (blue) separately.

Fig. 3 .
Fig. 3. Contour plots of c k 1 (top), c k ′ 1 (middle), and ∆k (bottom) calculated from SMILES observation dataset.c k 1 and c k ′ 1 are calculated in time periods from each start time (horizontal axis) to each end time (vertical axis).

Fig. 3 .
Fig. 3. Contour plots of c k 1 (top), c k (middle), and k (bottom) calculated from the SMILES observation data set.c k 1 and c k 1 are calculated in time periods from each start time (horizontal axis) to each end time (vertical axis).

Fig. 6 .
Fig. 6.Diurnal variation plot of ClO with average values (red) and calculation values using the rate constant of this work (black) in 0.28 hPa region (top).Diurnal variation plot of HOCl with average values (black) and calculation values using the rate constant of this work (red) in 0.28 hPa region (middle).Diurnal variation plot of the sum of ClO + HOCl with average values (green) and the sum of calculation values.

Fig. 6 .
Fig. 6.Diurnal variation plot of ClO with average values (red) and calculation values using the rate constant of this work (black) in 0.28 hPa region (top).Diurnal variation plot of HOCl with average values (black) and calculation values using the rate constant of this work (red) in 0.28 hPa region (middle).Diurnal variation plot of the sum of ClO + HOCl with average values (green) and the sum of calculation values.

Table 2 .
Comparison with previous studies.

Table 2 .
Comparison with previous studies.

Table A1 .
Impacts of the systematic errors.