Effects of denitrification on the distributions of trace gas abundances in the polar regions: a comparison of WACCM with observations

. Polar stratospheric clouds (PSCs) play a key role in the polar chemistry of the stratosphere. Nitric acid trihydrate (NAT) particles have been shown to lead to denitrification of the lower stratosphere. While the existence of large NAT particles (NAT "rocks") has been verified by many measurements especially in the Northern Hemisphere (NH), most current chemistry-climate models use simplified parameterizations, often based on evaluations in the Southern Hemisphere where the polar vortex is stable enough that accounting for NAT rocks is not as important as in the NH. Here, we evaluate the probability 5 density functions of various gaseous species in the polar vortex using one such model, the Whole Atmosphere Community Climate Model (WACCM), and compare these with measurements by the Michelson Interferometer for Passive Atmospheric Sounding onboard the Environmental Satellite (MIPAS/Envisat) and two ozonesonde stations for a range of years and in both hemispheres. Using the maximum difference between the distributions of MIPAS and WACCM as a measure of coherence, we find better agreement for HNO 3 when reducing the NAT number density from the standard value of 10 − 2 used in this model 10 to 5 × 10 − 4 cm − 3 for almost all spring seasons during the MIPAS period in both hemispheres. The distributions of ClONO 2 and O 3 are not greatly affected by the NAT density. The average difference of WACCM to ozonesondes supports the need to reduce the NAT number density in the model. Therefore, this study suggests to use a NAT number density of 5 × 10 − 4 cm − 3 for future simulations with WACCM.


15
Polar stratospheric clouds (PSCs) have been known for decades to play a key role in explaining the stratospheric ozone hole (Solomon et al., 1986;Solomon, 1999;Tritscher et al., 2021). Reactions on their surfaces lead to activation of chlorine reservoirs, known as chlorine activation. In addition, sedimentation of PSCs result in dehydration and denitrification of the lower stratosphere. Three types of PSCs with different composition and roles have been found to be important: liquid supercooled ternary solution droplets (STS, Carslaw et al., 1994) are major contributors to chlorine activation (e.g., Peter, 1997). Ice PSCs 20 lead to dehydration of the stratosphere (e.g., Kelly et al., 1989). Nitric acid trihydrate particles (NAT) dominate the irreversible removal of nitric acid (HNO 3 ) from the lower stratosphere via sedimentation, known as denitrification, thus potentially reducing the reformation of chlorine reservoir species which can affect ozone loss (e.g., Waibel et al., 1999).
The existence of NAT particles in the stratosphere has been verified by a variety of airborne measurements (Fahey et al., 1989;Voigt et al., 2000;Fahey, 2001;Molleker et al., 2014;Woiwode et al., 2016). Since the polar vortex in the Southern 25 Hemisphere (SH) generally is more stable than in the Northern Hemisphere (NH) (e.g., Schoeberl et al., 1992), the time period when denitrification can occur is much longer in the SH polar vortex than the NH. On the other hand, denitrification in the NH has been found to occur locally and the role of low-number density large-size NAT particles, so-called NAT rocks, has been discussed and verified by measurements (Fahey, 2001;Fueglistaler et al., 2002;Drdla and Müller, 2012;Adriani et al., 2004;Woiwode et al., 2014Woiwode et al., , 2016. These large particles can lead to significant sedimentation even on the shorter time scales needed 30 to explain the occurrence of low HNO 3 volume mixing ratios (VMR) in the NH spring.
Satellite instruments are able to provide measurements of PSCs and gaseous HNO 3 with daily near-global coverage Spang et al., 2018;Pitts et al., 2018;Santee et al., 2007;Wespes et al., 2022). Höpfner et al. (2006) found the first evidence of a NAT belt around the Antarctic Continent using the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) onboard the Environmental Satellite. Therefore, satellite measurements provide a unique opportunity for comparisons 35 of HNO 3 and denitrification with current chemistry-climate models in both hemispheres. They also allow study of the range of the probability distributions in the data for different years and conditions. Accounting for denitrification is an important process in chemistry-climate and in chemistry-transport models, which is why many parameterizations with different levels of detail have been developed to account for the microphysics and sedimentation of NAT particles in these models (e.g., Considine et al., 2000;Carslaw et al., 2002;Grooß et al., 2005;Wohltmann et al., 40 2010; Wegner et al., 2013;Zhu et al., 2015;Kirner et al., 2011;Weimer et al., 2021). Some models account for comprehensive microphysics of NAT particles (e.g., Zhu et al., 2015) to determine radii and concentrations which then redistribute gaseous HNO 3 . Others use an intermediate approach accounting not for the full microphysics but constraining the amount of NAT to a measured NAT distribution (e.g., Kirner et al., 2011;Weimer et al., 2021). In addition, there are models with diagnostic approaches, as suggested e.g. by Considine et al. (2000), where NAT is formed based on the available gaseous HNO 3 , sedi-45 mentation is computed and the solid HNO 3 of NAT ::::::: contained ::: in :::: NAT ::::::: particles : is released back to the gaseous phase within the same model time step.
The stadard ::::::: standard : version of the Whole Atmosphere component of the Community Earth System Model includes a diagnostic parameterization of NAT with a NAT number density set to a global value of 10 −2 cm −3 (Wegner et al., 2013).
However, Wilka et al. (2021) found that this value leads to an overestimation of gaseous HNO 3 in the NH for the extraordinarily 50 cold NH winter 2019/2020 in comparison to measurements of the Microwave Limb Sounder. They found a better agreement with the measurements using an adopted NAT number density of N NAT = 10 −5 cm −3 . Here, we investigate this further by applying an adapted version of the method by Zambri et al. (2021) to compare the distributions of various gaseous species within the polar vortex with MIPAS, which provided measurements during 2002 to 2012. MIPAS data is well suited to this task, because it provides high signal to noise local measurements over multiple years in both hemispheres, with good dynamic 55 range; other datasets may also be appropriate but here we use MIPAS for this initial test. Further, using MIPAS and varying the NAT number density of the model, we can also investigate its associated impact on HNO 3 , ClONO 2 and O 3 for many spring seasons in both hemispheres.  Gelaro et al., 2017). In this study, we use a horizontal resolution of 1.9 • latitude × 2.5 • longitude and 88 vertical levels up to about 140 km. In the component set "FWmaSD", a comprehensive chemistry for the middle atmosphere is included, as also used e.g. by Zambri et al. (2021).
Polar stratospheric clouds in WACCM are calculated using a diagnostic parameterization described by Considine et al. (2000), Kinnison et al. (2007) and Wegner et al. (2013). NAT particles are formed in thermodynamical equilibrium with the 70 gaseous H 2 O and HNO 3 below the NAT formation ::::::: threshold : temperature (Hanson and Mauersberger, 1988). Coexistence of NAT and STS is accounted for by allowing 20 % of HNO 3 to form NAT whereas the rest is available for STS (Wegner et al., 2013;Solomon et al., 2015). Sedimentation of the NAT particles, i.e. the vertical redistribution of gaseous HNO 3 , is calculated using a simple upwind scheme (Considine et al., 2000). The radius of the particles is determined in this scheme by using the amount of condensed HNO 3 and the NAT number density, which is a global parameter in this scheme. Larger NAT density 75 leads to smaller particles and vice versa, assuming the mass of HNO 3 condensed in NAT is constant in the grid box. Therefore, the NAT density is a parameter in this scheme that can be used to tune the denitrification in the model. Examination of observations of NAT particle number densities (Pitts et al., 2009(Pitts et al., , 2011 and an emphasis on HNO 3 data for the SH in 2005 led on in-situ measurements. In mountain waves, high NAT densities larger than 10 −2 cm −3 have been measured (e.g., Carslaw et al., 1998). Voigt et al. (2005) observed a NAT PSC with 10 −4 cm −3 . Here we have had the benefit of the unusual NH year 2020 and have placed more emphasis on both hemispheres to derive a parameterization that better represents the remaining gas phase HNO 3 in the maximum number of years and for both hemispheres. However, it is important to emphasize that the model's NAT parameterization is subject to multiple simplifications of complex microphysics. For instance, NAT particles 85 in a grid box with a horizontal extent of about 100 × 100 km 2 do not necessarily have the same radius but usually follow a multi-modal size distribution (e.g., Fahey, 2001). In addition, NAT particles are not allowed to grow or decrease :::::: change :::: their ::: size : over time or to be transported while interacting with the atmosphere by nucleation and (re-)sublimation and not all of the supersaturated amount of gaseous HNO 3 will become NAT. Therefore, observed NAT particle abundances may not be the best guide for this parameter choice. 90 We performed sensitivity simulations varying the NAT number density within the observed range from 10 −2 to 10 −5 cm −3 in the current version 6 of WACCM. We also performed a simulation excluding stratospheric heterogeneous reactions, apart from the reaction N 2 O 5 + H 2 O, to evaluate the impact of heterogeneous processes on the gas-phase species. The N 2 O 5 + H 2 O reaction rate is nearly independent of temperature, happens on nearly all aerosolsand ::: also :: on ::: the :::::::::: background :::::::: aerosols, does not directly affect the halogen chemistry ::: and :: is :::::::: important ::: for ::: the :::::::::: partitioning :: of ::::::: reactive ::::::: nitrogen :: in ::: the :::::::::: atmosphere which is why 95 we kept this reaction in that simulation. ::::::: Without ::: this ::::::: reaction, ::: the ::::::::: chemistry :: in ::: the ::::: model :::::: would :: be ::::::::: completely :::::::::: unrealistic. All simulations are summarized in Table 1. They cover the satellite period starting from 1979 to present.

MIPAS
The Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) operated in limb geometry on board the Environmental Satellite (Envisat) between July 2002 and April 2012 (Fischer et al., 2008). Envisat was placed in a sun-synchronous 100 polar orbit at an altitude of around 800 km with more than 14 orbits per day. MIPAS measured a variety of trace gases including HNO 3 , ClONO 2 and O 3 using a Fourier transform spectrometer in the infrared spectral range between 4.15 and 14.6 µm at tangent altitudes from 7 to 72 km (Fischer et al., 2008). The spatial resolution was approximately 3 km in the vertical and The method used to compare the MIPAS data with WACCM is based on the approach by Zambri et al. (2021). It takes advantage of WACCM's ability to provide output at the locations and times closest to the MIPAS profiles. In combination with interpolation of the MIPAS vertical levels to the WACCM altitudes, this enables a direct comparison of the two datasets. As a result, probability density functions (PDFs) can be evaluated in the spatiotemporal range of interest and compared to the 115 observations.
Since NAT formation and denitrification are strongly temperature-dependent and most efficient at the lowest temperatures, we compute PDFs for profiles inside the polar vortex, determined by MERRA2 using the Nash criterion (Nash et al., 1996).
As the sedimentation of the NAT particles takes several weeks (Tabazadeh et al., 2001), the largest effects of denitrification can be expected to be most amplified after the local winter, which is why we restrict our analysis to the early local spring, i.e.

Ozonesondes
We also compare the WACCM simulations to balloon-borne in-situ measurements of ozonesondes, made available by the 135 World Ozone and Ultraviolet Data Centre. They use an electrochemical concentration cell to measure ozone profiles with a precision of 3 to 5 % and an uncertainty of about ±10 % in the pressure range of interest here (Smit et al., 2007 profiles within the polar vortex. Averages and spread of the differences between WACCM and the observations are evaluated.
3 Impact on the distribution of gas-phase species In this section, we will analyze the influence of changing denitrification in WACCM on the trace gases HNO 3 , ClONO 2 and O 3 during early spring in both hemispheres. Generally, these species are expected to be influenced by a changed NAT number density because it leads to a redistribution of HNO 3 (lower HNO 3 at high altitudes and higher HNO 3 at lower altitudes). During early spring, HNO 3 is photolyzed and forms NO 2 which combines with ClO to form ClONO 2 . ClO is responsible for part of the catalytic ozone depletion and deactivated through this mentioned reaction :: by ::: the ::::::: reaction :::: into ClONO 2 .
As a starting point, Fig. 1 shows vortex-mean profiles of the HNO 3 VMR during the local spring months for both hemi-  Fig. 1, the NAT particles do not get large enough :: for ::: the ::::::::: simulated HNO 3 to compare well with the measured denitrification of the shown years. This means that larger HNO 3 VMRs than observed remain at higher altitudes at the end 155 of the timeseries, whereas the VMR is underestimated at lower altitudes. In contrast to this, with the smallest tested number density of 10 −5 cm −3 , HetAll.1e-5 in the last row, the HNO 3 VMRs become too low, which indicates that the NAT particles become too large. By using a number density of 5 × 10 −4 cm −3 (HetAll.5e-4 in the third row), the differences compared to MIPAS HNO 3 are smallest and the altitude regions of denitrification and renitrification are comparable to the measurements.
In order to generalize this comparison, Fig. 2 shows correlation plots of the HetAll simulations using different NAT number 160 densities compared to the MIPAS measurements for the whole pressure range (30 − 150 hPa) and all MIPAS years in the NH and SH. The simulation HetAll.5e-4 (green) has a relatively concise ::::::: compact : correlation with MIPAS in both hemispheres, whereas the other simulations show a larger spread :::::: scatter. The simulation HetAll.1e-2 shows too large HNO 3 VMRs due to too small NAT particles and as ::: that ::: are ::: too ::::: large :::::::: compared :: to ::: the ::::::::::: observations :::::: because ::: of :::: NAT ::::::: particles :::: that ::: are ::: too ::::: small. ::: As already suggested by Fig. 1, the NAT particles in the simulation HNO 3 ::::: VMRs :: in HetAll.1e-5 are too large and :::: small ::::::::: compared 165 :: to :::::: MIPAS ::: as : a ::::: result ::: of ::: too ::::: large :::: NAT :::::::: particles :::::: which lead to sedimentation below and to too small VMRs compared to MIPAS :: the :::::: shown ::::::: pressure ::::: range. As this figure includes the data of all MIPAS years and the whole pressure range, we will investigate the PDFs of this pressure range in the following, using the approach based on Zambri et al. (2021).    Tables 2 and 3 for NH and SH, respectively. The simulation with the minimum difference is highlighted for each year. Apart from some exceptions in the NH, the minimum difference occurs for the simulations using N NAT = 5 × 10 −4 cm −3 . This is another indication that this value improves denitrification and the distribution of HNO 3 in the polar vortex in both hemispheres. shows the minimum differences compared to the MIPAS distribution, see Table 2. In 2004, relatively warm temperatures in the NH stratosphere lead to small denitrification (Manney et al., 2005). As shown in Fig. 4a, this is reflected by the WACCM HNO 3 distributions which do not show large differences when changing the NAT density during that year. There seems to be a systematic difference between WACCM and MIPAS in this year, though, maybe due to a lower accuracy of the instrument or for instance due to a mismatch in the location of the polar vortex in the reanalysis data used for the model and the temperature There is also a clear signature of heterogeneous chemistry in the ClONO 2 distributions. The deactivation reaction forming

Probability density functions of HNO
is usually faster than the deactivation reaction forming HCl Cl + CH 4 → HCl + CH 3 , (R2) Figure 5. Same as Fig. 3, but for ClONO2.
Therefore, while the simulation without heterogeneous chemistry noHetAll.5e-4 generally shows ClONO 2 VMRs that are too low compared to MIPAS, it is notable that the maximum values are increased by about 1 ppbv and then are comparable to MIPAS in all simulations with heterogeneous chemistry.
Similar impacts can be seen in the distributions of ozone (O 3 ), shown in Fig. 6. Ozone VMRs are about 1 ppmv too large 225 in the SH for noHetAll.5e-4 compared to MIPAS. In the NH, the difference is smaller but ozone is still overestimated in the simulation without heterogeneous chemistry. Wilka et al. (2021) showed that the agreement of WACCM model calculations of Arctic spring ozone losses in 2020 with ozonesonde data was heavily dependent on the denitrification parameterization used in the model, providing an important check. Figure 7 displays comparisons between WACCM and ozonesonde data at Syowa and Eureka for their respective spring  7a), care must be taken in interpreting percentage differences; we also provide absolute differences for that reason. The Syowa sondes agree considerably better with the model when the NAT number density of 5 × 10 −4 cm −3 or less is used, compared to 235 Figure 6. Same as Fig. 3, but for O3.
larger values of this parameter. At Eureka, results are far less sensitive due to smaller ozone losses, except in very cold years (like 2020 shown in Wilka et al., 2021).
In summary, the results in this section showed that the diagnostic parameterization of NAT particles in WACCM is able to reflect the main features in the three key gas-phase species HNO 3 , ClONO 2 and ozone. When using a reduced NAT particle number density of N NAT = 5 × 10 −4 cm −3 compared to the standard WACCM setup, the difference in the cumulative density cannot be used for noisy data (such as N 2 O 5 and ClO in MIPAS) and we restricted the analysis to the gaseous species HNO 3 , The diagnostic parameterization of NAT in the WACCM model was shown to be able to reproduce the general shape of the MIPAS distributions for almost all years of the MIPAS period in the polar vortices of both hemispheres. There was a general overestimation of gaseous HNO 3 , though, when using the standard N NAT of 10 −2 cm −3 . Reducing this number concentration 255 to 5 × 10 −4 cm −3 was shown to also reduce the differences in the HNO 3 distributions between MIPAS and WACCM for almost all spring seasons in both hemispheres during the MIPAS period. Changes in the distributions of ClONO 2 and O 3 due to the new value of N NAT were either negligible or the differences were reduced. Mean differences between ozonesonde profiles and the WACCM simulations at the grid point closest to the sonde stations Syowa and Eureka were also shown to be decreased when reducing N NAT . Therefore, this study suggests the use of N NAT = 5 × 10 −4 cm −3 for future simulations : .
A simplified parameterization as applied in WACCM cannot capture all features of the distributions of all years. This was demonstrated by the years 2004 and 2012 where differences between the MIPAS and WACCM distributions were increased.
Further, there are many uncertainties in the detailed chemistry from one year to another that may also be important for denitrification and ozone loss, including for example volcanic particle inputs, gravity and planetary wave amplitudes, and changes in 265 circulation, to name only a few. It can also be seen that the smallest number density of 10 −5 cm −3 is comparable to measurements during the exceptionally cold northern winter 2019/2020 (Wilka et al., 2021). In addition, although overall differences in the PDFs are reduced with N NAT = 5 × 10 −4 cm −3 , the Kolmogorov-Smirnov test, used e.g. by Zambri et al. (2021) with a similar approach as in this study, will fail if not using a significance level α that is set to a very small value (O(10 −70 )).
Therefore, although the differences are decreased, the distributions of MIPAS and WACCM are still different in a statistical 270 sense, probably due to the simplifications in the NAT parameterization of WACCM.
Future studies could apply this methodology to other long-term satellite measurements to evaluate the usage of this new NAT number density for further years, although their precision has to be low enough to allow for comparisons with individual profiles. Nevertheless, as a follow-up of the publication by Wilka et al. (2021), we recommend using N NAT = 5 × 10 −4 cm −3 for future simulations with WACCM, indicating that NAT rocks play an important role, especially in the NH where we saw the 275 largest impact on changing the NAT number density.
Code and data availability. Instructions for the access to MIPAS data can be found at https://www.imk-asf.kit.edu/english/308.php (last access on 18 November 2022). Instructions how to download CESM version 2 can be found in Danabasoglu et al. (2020). Ozonezonde station data are publicly available through the World Ozone and Ultraviolet Data Center (WOUDC; WMO/GAW Ozone Monitoring Community, 2022). The scripts and data needed to create the figures of this paper can be found at https://g-27eb33.7a577b.6fbd.data.globus.org/ACP_ 280 Weimer_2022/ACP_Weimer_2022.tar.gz (last access on 7 December 2022).
Author contributions. MW added the comparison with MIPAS and wrote the first draft of the manuscript. DEK performed the simulations with WACCM used for the comparisons. CW added the comparison to ozonesondes. All authors contributed to prepare the manuscript.
Competing interests. The authors declare that they have no competing interests.
Acknowledgements. Michael Weimer and Douglas E. Kinnison were funded in part by NASA grant 80NSSC19K0952. Susan Solomon was 285 funded in part by grant no. 1906719 of the U.S. National Science Foundation (NSF). We would like to thank Brian Zambri for initiating this work and helping with the comparison to MIPAS. This material is based upon work supported by National Center for Atmospheric Research (NCAR), which is a major facility sponsored by NSF under the Cooperative Agreement 1852977. The CESM project is supported primarily by NSF. We would like to acknowledge support from the Svante cluster at MIT used for the comparison of model and the data, see https://svante.mit.edu/intro.html (last access 18 November 2022) for more information. We would like to acknowledge high-performance 290 computing support from Cheyenne and Casper provided by NCAR's Computational and Information Systems Laboratory (2019), sponsored by NSF.