Odd hydrogen response thresholds for indication of solar proton and electron impact in the mesosphere and stratosphere

. Understanding the atmospheric forcing from energetic particle precipitation (EPP) is important for climate simulations on decadal time scales. However, presently there are large uncertainties in energy-ﬂux measurements of electron precipitation. One approach to narrow these uncertainties is by analyses of EPP direct atmospheric impacts and their relation to measured EPP ﬂuxes. Here we use observations from the Microwave Limb Sounder (MLS) and Whole Atmosphere Community Climate Model (WACCM) simulations, together with EPP ﬂuxes from the GOES and POES satellites, to determine 5 the OH and HO 2 response thresholds to solar proton events (SPEs) and radiation belt electron (RBE) precipitation. Because of their better signal-to-noise ratio and extended altitude range, we utilize MLS HO 2 data from an improved ofﬂine processing instead of the standard operational product. We consider a range of altitudes in the middle atmosphere, and all magnetic latitudes from pole to pole. We ﬁnd that the nighttime ﬂux limits for day-to-day EPP impact detection using OH and HO 2 are 50 – 130 protons cm − 2 s − 1 sr − 1 ( E > 10 MeV) and 1.0 – 2.5 × 10 4 electrons cm − 2 s − 1 sr − 1 ( E = 100–300 keV ). Based on 10 the WACCM simulations, nighttime OH and HO 2 are good EPP indicators in the polar regions, and provide best coverage in altitude and latitude. Due to larger background concentrations, daytime detection requires larger EPP ﬂuxes and is possible in the mesosphere only. SPE detection is easier than RBE detection because a wider range of polar latitudes is affected, i.e. the SPE impact is rather uniform poleward of 60 ◦ while the RBE impact is focused at 60 ◦ . Altitudewise, the SPE and RBE detection are possible at ≈ 35–80 km and ≈ 65–75 km , respectively. We also ﬁnd that the MLS OH observations indicate a 15 clear nighttime response to SPE and RBE in the mesosphere, similar to the simulations. However, the MLS OH data are too noisy for response detection in the stratosphere below 50 km and the HO 2 measurements are overall too noisy for conﬁdent EPP detection on a day-to-day basis.


Introduction
Solar energetic particle precipitation (EPP) affects the polar atmospheric chemistry directly at the altitude region from upper 20 stratosphere to lower thermosphere. Ionization caused by precipitating protons and electrons leads to, e.g., production of odd hydrogen and odd nitrogen from ionic reactions, and subsequently to loss of ozone through catalytic reactions (Sinnhuber et al., 2012). There is evidence of EPP-driven variability in winter-springtime ozone (Andersson et al., 2014a; 1 2016), which could further connect to decadal variability of regional climate via modulation of polar vortex dynamics and the top-down coupling (e.g. Seppälä et al., 2014).
In atmospheric and climate modeling, EPP forcing can be defined using satellite-based particle flux observations (Matthes et al., 2017, and references therein). Solar wind proton fluxes are continuously measured by detectors aboard the GOES satellites in the geosynchronous orbit (https://www.ngdc.noaa.gov/stp/satellite/goes/). These measurements provide a good repre-5 sentation of proton forcing because MeV protons have enough rigidity, i.e. momentum/charge, to penetrate through Earth's magnetic field in polar regions and enter the atmosphere directly from the solar wind. Several studies have shown that the observed atmospheric effects can be well represented in models using the GOES proton observations if the relevant ion-neutral chemistry is considered as well (Jackman et al., 2001;Verronen et al., 2006;Funke et al., 2011;Andersson et al., 2016). For electron precipitation the situation is different. Electrons have less mass than protons and are captured by Earth's magneto- 10 sphere, e.g. in the radiation belts (Baker et al., 2018), from where they are eventually lost either to space or into the atmosphere.
Satellite-based observations of electron precipitation fluxes are being made from low-orbiting satellites but these measurements do not capture full spatio-temporal varibility, and also suffer from restricted measurement geometry and proton contamination, like in the case of the MEPED/POES instruments (Rodger et al., 2010a;van de Kamp et al., 2018). Atmospheric impacts seen in observations seem to indicate a need for a large adjustment of the electron forcing representation in simulations (Clilverd 15 et al., 2012;Randall et al., 2015). Thus atmospheric observations of EPP impact could help to understand the uncertainties in the electron flux data and how these flux observations relate to effects in the atmosphere (e.g. Verronen et al., 2011). Thus EPP detection limits for atmospheric data are valuable information.
Ground-based ionospheric observations provide the most direct measure of EPP atmospheric impact (e.g. Verronen et al., 2015;Heino et al., 2019), but in practice only satellite-based measurements can offer a global view. Measurement of odd 20 hydrogen species (OH, HO 2 ) are well-suited for monitoring EPP impacts due to their relative short chemical lifetime Damiani et al., 2010a). Satellite-based observations of OH were made continuously in 2004-2009 by the Microwave Limb Sounder (MLS) aboard the Aura satellite Pickett et al., 2008). They have since been used to study both solar proton events and electron precipitation Damiani et al., 2010a;Jackman et al., 2011;Andersson et al., 2012;Verronen et al., 2013;Jackman et al., 2014;Andersson et al., 2014b), particularly 25 at 60-80 km altitudes where largest EPP events can produce order-of-magnitude increases. Compared to the OH observations, MLS HO 2 measurements are being made since 2004 and thus provide a longer timeseries than the OH observations. However, the standard HO 2 data from operational processing have a lower signal-to-noise ratio and only cover the lower mesosphere and stratosphere (Pickett et al., 2008;Livesey et al., 2018). Thus the use of standard HO 2 data has been limited to large proton events Zou et al., 2018). An improved offline processing of HO 2 data provides better quality (Millán 30 et al., 2015), extending the altitude range to the mesopause and enhancing possibilities for studies of daily EPP impact.
In this paper, we use MLS observations of OH and HO 2 to determine EPP flux thresholds for impact detection in the stratosphere and mesosphere. Looking at different latitudes bands and altitudes individually, we first consider large proton events, which have a well-known flux from satellite observations, to develop a method for EPP threshold detection. We then apply the same method to medium-energy electrons for which the satellite based flux observations are not all-inclusive. We 35 compare satellite-data-based thresholds to those from the Whole Atmosphere Community Climate Model (WACCM, version 4), to discuss both limitations of the satellite data and EPP forcing in WACCM. Our results provide the limits of MLS OH and HO 2 for EPP detection and usability in EPP studies.

Data and models
The Microwave Limb Sounder (MLS) measures millimeter and submillimeter thermal emission from the Earth's limb atmo- 5 sphere, from which temperature, trace gases, and cloud ice are retrieved. Launched in July 2004 into a Sun-Synchronous near-polar orbit, the geographic latitude coverage of the measurements is from 82 • S to 82 • N on each orbit and measurements are made during both day and night conditions. The instrument is described in detail by Waters et al. (2006). A detailed description of MLS version 4 data products and quality is given by Livesey et al. (2018). The MLS target species in the stratosphere and mesosphere include OH and HO 2 . 10 For the version 4 OH data used in our study, the recommended pressure range of observations is 32-0.0032 hPa (approx. altitudes 25-95 km). At levels with p > 0.01 hPa, the vertical resolution of observations is 2.5 km. Version 2.2 data has been validated with balloon-borne remote-sensing instruments and with ground-based column measurements (Pickett et al., 2008;Wang et al., 2008). Instead of the standard HO 2 data, we use data from the offline processing described in detail and validated against other observations by Millán et al. (2015). This algorithm retrieves daily zonal means of HO 2 over an extended vertical 15 range by first averaging the radiances in 10 • bins, resulting in a better signal-to-noise ratio and an extended altitude range compared to the standard HO 2 data. The recommended pressure range for the offline HO 2 data is 10-0.0032 hPa (≈35-90 km), vertical resolution is about 4 km between 10 and 0.1 hPa, 8 km at 0.02 hPa and around 14 km for lower pressures.
Day and nighttime data are provided separately using measurement tangent point solar zenith angle limits < 90 • and > 100 • , respectively. 20 The Whole Atmosphere Community Climate Model (WACCM) is a chemistry-climate model that extends from the surface to about 5.9×10 −6 hPa (≈140 km) with horizontal resolution 1.9 • latitude by 2.5 • longitude. WACCM physics and atmospheric response to solar and geomagnetic forcing variations are described by Marsh et al. (2007). Details about WACCM version 4 coupled simulations and overview of the model climate can be found in Marsh et al. (2013). Here, we utilize WACCM-D, a variant of WACCM version 4 in which standard parametrization of EPP-driven odd hydrogen and odd nitrogen production is 25 replaced by a set of D-region ion chemistry reactions , and which reproduces better the observed OH response during EPP . We used WACCM-D in the specified dynamics scenario (SD-WACCM-D) forced with meteorological fields (temperature, winds, surface pressure) from Modern-Era Retrospective analysis for Research and Applications (MERRA, Rienecker et al., 2011). The daily atmospheric ionization rates due to 1-300 MeV solar protons are calculated based on flux data available from the National Oceanic and Atmospheric Administration (NOAA) Space Environ-30 ment Center (http://sec.noaa.gov/Data/goes.html) and the methodology discussed in Jackman et al. (2009). These are applied at geomagnetic latitudes > 60 • in both hemispheres. The daily zonal mean ionization rates at geomagnetic latitudes 40 • -72 • from precipitating 30-1000 keV electrons are taken from the APEEP proxy model which is recommended for the Coupled Model Intercomparions Project (van de Kamp et al., 2016;Matthes et al., 2017). We carried out a simulation for a period between 2000-2012 which covers the whole period of MLS OH observations. WACCM-D output, including OH and HO 2 , was saved at MLS measurement times and locations to ensure one-to-one match between the model and the measurements in the analysis.
EPP forcing patterns follow the geomagnetic latitudes, rather than the geographic ones, and the odd hydrogen response is 5 expected to show similar patterns due to its short chemical lifetime (e.g. Andersson et al., 2018). Thus we use a modified version of the HO 2 offline algorithm where the radiances were averaged using geomagnetic latitudes instead of geographic latitudes (for a definition of Altitude-Adjusted Corrected Geomagnetic Coordinates, see e.g. Shepherd, 2014). These geomagnetic latitudes are shown in Fig. 1. Before the analysis, the MLS OH and WACCM-D data were pre-processed the same way as it was done for HO 2 . The data were divided into daily daytime and nighttime sets using the same solar zenith angle limits and averaged zonally 10 after sorting observations into 10 • geomagnetic latitude bins, running from −85 • through to +85 • . Through this manuscript these bins are referred to by their central latitude, i.e. the latitude 40 • refers to the zonal average from geomagnetic latitudes It should be noted that due to separating the data both by latitude and by day/night conditions, there is sometimes little data available at the highest latitudes. For example, sometimes there is no nighttime data in June for latitude 80 • . The daily averages of existing data points at the high geomagnetic latitude bins may also be skewed towards lower geographic 15 latitudes. However, this should not affect our comparisons because WACCM-D was sampled at the MLS times and locations and binned in the same manner.
In the analysis, we use the pressure level grid from the MLS measurements, as sections of the MLS HO 2 and OH pressure grids are the same. Hence the overlapping sections of MLS HO 2 and OH values were selected, whereas the least-squares interpolation method recommended by Livesey et al. (2018) was used to convert WACCM-D data onto the MLS grid. The 20 same pressure grid allows for direct comparisons between the data sets. The MLS HO 2 offline data are provided in both mixing ratios (ppmv) and concentrations (molec./cm 3 ). Thus daily total density profiles can be calculated by dividing HO 2 concentrations by HO 2 mixing ratios. To ensure consistency between the data sets, MLS OH and WACCM-D data were converted from mixing ratios to concentrations using the same total densities from MLS HO 2 . For the general comparisons, the MLS HO 2 averaging kernels were applied to the WACCM-D HO 2 fields. As most of the averaging kernels are fairly 25 similar, only the daytime and nighttime kernels corresponding to magnetic equator were used and applied to all latitude bins.
MLS averaging kernels were not used on WACCM-D OH data because the effect was expected to be small. In the threshold detection, the MLS averaging kernels were not applied on WACCM-D HO x data.
In order to show the connection between EPP and odd hydrogen changes, we use proton flux measurements from the Geostationary Operational Environmental Satellite (GOES-11, https://www.ngdc.noaa.gov/stp/satellite/goes/) as a measure of 30 proton precipitation over the polar caps. Daily average fluxes of protons with energies greater than 10 MeV are used as an indicator because those directly affect atmospheric altitudes below about 90 km (for the relation between EPP energies and penetration altitudes, see Turunen et al., 2009, Figure 3). The measurements from the other GOES channels responding to higher proton energies correlate well with the >10 MeV channel (not shown), so we would not expect significant changes in our results if other proton energy channels were used. As a measure of electron precipitation, we use flux observations 35 from the Medium Electron Proton and Electron Detector aboard the Polar Orbiting Environmental Satellite (Evans and Greer, 2004). Daily average electron fluxes from an energy range between 100 keV and 300 keV, from the 50 • magnetic latitude bin, are used as indicator of radiation belt electron precipitation (RBE) affecting mesospheric altitudes. While the magnitude of RBE forcing will depend on latitude more than for the proton forcing, the 50 • latitude bin was selected because of its most pronounced atmospheric HO x impact (e.g. Verronen et al., 2011). The assumption here is that the RBE forcing will 5 vary similarly with magnetic activity across affected latitudes although the magntitude can differ. The electron flux data are exclusively from the zero-degree telescope and have been pre-processed to remove known quality issues (for a description, see Verronen et al., 2011, and references therein), e.g. data suffering from proton contamination have been excluded using the methods described by Rodger et al. (2010a).

10
First, we present an overall comparison between WACCM-D and MLS odd hydrogen data. We use monthly average concentrations to identify the main similarities and differences between the data sets, focusing on the shape, strength, and location of concentration peaks. These comparisons provide us information on the overall representation of odd hydrogen in WACCM-D, which can help to understand the differences in EPP detection thresholds.
Starting from the approach of Verronen et al. (2011), we use daily average data in EPP detection. However, Verronen et al. 15 (2011) studied only four selected RBE events. And although they demonstrated the correlation between EPP and OH, they did not use HO 2 data or pursue the detection limits. Before determining threshold values for the SPE and RBE detection, daily climatologies of OH and HO 2 concentrations were removed from the odd hydrogen data. Climatological values were calculated for each day of the year by first calculating daily average OH and HO 2 night and day concentrations of available data at each grid point, separately for WACCM-D and MLS. A nine-day moving average was then calculated to smooth the 20 time series and produce the final climatologies. After the climatology is removed, the background concentrations do not display seasonal variability, which makes it possible to combine EPP event periods from different seasons for the threshold detection.
Examples of this de-seasonalising effect can be seen in Fig. 2.
It should be noted that after the climatology is removed, the HO x concentrations still have variability from sources other than EPP, and these are included in the data in our analysis. For example, sudden stratospheric warmings (SSWs) contribute to 25 the year-to-year OH variability in the NH middle atmosphere (Damiani et al., 2010b). As our aim is to determine the general threshold values for SPE and RBE detection, we do not separate SSWs years in any particular manner. However, we consider SH and NH separately and only NH is regularly affected by SSWs.
For the SPE threshold determination, we selected data from all months during which the daily proton flux indicates an event, i.e. it exceeds the limit of 10 protons cm −2 s −1 sr −1 , see Fig. 3 (upper panel). All months used in the analysis are 30 listed in Table 1. Using data from the selected months, we applied a fitting method previously used by Verronen et al. (2011).
First, we plotted the SPE flux values against the climatology-free odd hydrogen concentrations (i.e. anomalies). Then a first degree polynomial was fitted to the HO x anomalies and the square root of the SPE fluxes. A limit for a significant SPE-driven enhancement in odd hydrogen concentration was calculated by adding the standard deviation of the concentrations to the median concentration. Since the concentrations are de-seasonalised, the median is expected to be close to zero. The addition of the standard deviation suggests that a concentration anomaly of one standard deviation from the climatology is significant and should be detected. We then find the SPE indicator value at the intersection of the limit and the linear fit; this is the detected SPE threshold flux value. Examples of the SPE threshold determination are shown in Fig. 4 (left panel). This process is applied for 5 each latitude bin and at each pressure level separately. To identify those thresholds that are reasonable, they are filtered using correlations between the square root of the SPE fluxes and odd hydrogen concentrations. All thresholds with corresponding correlation coefficient ≥ 0.35 are accepted as reasonable and the rest are discarded. This filtering effectively removes threshold values at lower latitudes where SPE impact is not expected.
The RBE threshold values are determined using the same method but with different RBE flux and correlation limits. RBE 10 months were found using an RBE flux limit of 1.5 × 10 4 electrons cm −2 s −1 sr −1 (see Fig. 3, lower panel), and data from these months are used in the analysis. However, the months having an SPE event, as defined in the previous paragraph, were excluded. The RBE fluxes from MEPED are not reliable during SPEs (Rodger et al., 2010a), and SPE forcing would likely interfere with the RBE threshold detection. Indeed, exclusion of SPE months leads to stronger correlations between the RBE flux and odd hydrogen concentrations (not shown). For a full list of the months used in the analysis, refer to Table 1. As with 15 SPEs, the RBE thresholds were found using linear fitting with square roots, as well as the median and the standard deviation of odd hydrogen data (see Fig. 4, right panel). For RBE events, threshold values with corresponding flux-concentration correlation coefficients ≥ 0.25 are accepted as reasonable.
As seen in Fig. 4 (left panel) at 0.1-0.2 protons cm −2 s −1 sr −1 , in some cases there is a large number of data points at low fluxes. To find out the impact to our analysis, we performed tests where we excluded these low-flux points. In general, 20 correlations between flux data and HO x concentrations get stronger, but thresholds increase due to larger standard deviation.
These effects would, however, not change our conclusions.

Overall comparison between WACCM-D and MLS
In general, WACCM-D and MLS compare reasonably well in the magnitude and spatio-temporal variability of OH and HO 2 . 25 In both MLS and WACCM-D daytime concentration profiles, there is a maximum in the stratosphere and mesosphere, which reflects the production being dependent on atomic oxygen and Lyman-alpha radiation, respectively. Figure 5  Latitude-wise, the strongest concentrations are found at lower latitudes with concentrations generally decreasing polewards 30 (not shown). Lower latitudes also show the clearest stratospheric and mesospheric maxima and less seasonal variability than the polar regions.
6 WACCM-D shows a stronger stratospheric OH peak by 10-20% and a weaker mesospheric OH peak by up to a factor of two. In WACCM-D, the vertical transition between the OH summertime peaks is more continuous, while in MLS data there is a clear minimum between them around 0.1 hPa. EPP detection in the summer mesosphere is likely harder from MLS than WACCM-D because of larger background concentrations. In wintertime, both WACCM-D and MLS show lower OH values than in summer, particularly in the mesospheric altitudes, while the altitude distributions and concentrations are very similar. 5 Similar observations can be made in daytime HO 2 data as well (Fig. 5). Of the two maxima in the concentration profiles, the mesospheric one in stronger in MLS HO 2 compared to WACCM-D, and MLS also has a clearer minimum between the two maxima at around 0.1 hPa. However the noisiness of MLS HO 2 data is evident at lower atmospheric levels. Note that the HO 2 data could be improved below the 1 hPa level by using the day-night difference (Livesey et al., 2018), but this was not done in our analysis. 10 The nighttime concentrations show some similarities and differences as well, as seen in the time series of monthly average concentrations from magnetic latitude 60 • S presented in Fig. 6. Overall, nightly concentrations are low in both MLS and WACCM-D. MLS HO 2 is a clear exception at lowest atmospheric levels, with much larger concentrations than in WACCM-D.
Note, however, that the nighttime HO 2 data are only valid from 1 to 0.0032 hPa, while from 10 to 1 hPa the concentrations are close to zero and only used to correct the daytime observations. Thus, these high values are likely an artefact of the low 15 signal-to-noise quality of the observations. Both WACCM-D and MLS show the characteristic OH peak in the mesosphere, produced at night from reaction between atomic hydrogen and O 2 . The peak is approximately at the same pressure level of 0.01 hPa, but its magnitude is larger and the seasonal variability is weaker in WACCM-D. In summer, the peak occurs at a higher altitude and is stronger in both WACCM-D and MLS, although the altitude variation is slightly less obvious in MLS data. The MLS OH data also shows oscillating 20 minima and maxima in summertimes at 0.1-0.01 hPa, but these may be an artefact of the observations and are not seen in WACCM-D.
For HO 2 , WACCM-D shows an upper mesospheric peak with a clear seasonal cycle, coinciding with the OH peak. In addition, there is another clear peak at around 0.5 hPa, with a seasonal cycle: a minimum in winter, and clear maxima in spring and autumn. MLS HO 2 data are noisy, and there are no clear patterns of seasonal variability. 25 Our WACCM-D/MLS HO 2 comparison results are similar to those by Millán et al. (2015), although it should be noted that they presented the data in geographic coordinates. WACCM-D and MLS clearly produce similar structural patterns. Daytime peak in the mesosphere is stronger in MLS, potential reasons including model deficiencies in chemistry, solar radiation, and meridional circulation from gravity waves (Millán et al., 2015). Nighttime differences are smaller than during day. Overall, the model and observations agree reasonably well so that EPP detection possibilities should be similar, at least in terms of 30 background level of HO x .  Fig. 7 (right column). At higher latitudes in both hemispheres, i.e. at 60 • -80 • , the correlations are distinctly high while at other latitudes there is essentially no correlation. In the polar regions, the nightly threshold values are typically 50-130 protons cm −2 s −1 sr −1 . At magnetic latitude 80 • S the thresholds are lower than elsewhere, i.e. 35-80 protons cm −2 s −1 sr −1 , which would make this latitude band the best for SPE detection. The lower overall background concentration, especially in the SH due to the geomagnetic latitude distribution, is making detection easier, which leads to 5 these lower thresholds. There are however larger variations at 80 • S as well, due to smaller amount of data available, causing weaker correlations in the MLS observations. Overall, WACCM-D and MLS show similarly distributed threshold values. Comparing the thresholds from OH, SPEs are detected lower into the atmosphere in WACCM-D than MLS data, i.e. from around 80 km down to about 35 km and 50 km, respectively. This is seen in both hemispheres, in both thresholds and correlations, and can be explained by the MLS OH data becoming noisier in the stratosphere. In WACCM-D, the thresholds from OH and 10 HO 2 are very consistent, although correlations are weaker in HO 2 in the Southern Hemisphere above 1 hPa.

SPE thresholds
Daytime SPE thresholds and correlations are shown in Fig. 8. Again, regions of high correlations are at high latitudes 60 • -80 • as expected. Because the daytime background concentrations of HO x are higher at most altitudes, the thresholds can be detected in a more restricted altitude range compared to nighttime. In WACCM-D, the detection can be done at 50-80 km.
Both the threshold values and the correlations are very similar for HO 2 and OH data, even more so than at nighttime. For MLS 15 OH, the correlations are overall lower than in WACCM-D and there is a larger disparity between NH and SH. No thresholds are detected in SH, and in NH a total of three grid points, all at latitude 80 • N, have high enough correlations to qualify as reasonable thresholds. The WACCM-D thresholds vary mostly from 85 to 130 protons cm −2 s −1 sr −1 , though there are many values up to 300 protons cm −2 s −1 sr −1 , while MLS OH thresholds range from 145 to 220 protons cm −2 s −1 sr −1 . Thus, the daytime threshold values are higher than for the nighttime and there is larger range of values as well. 20 We do not include MLS HO 2 in Figures 7-8, because we could not detect thresholds due to the noisiness of the data.
However, the correlations between MLS HO 2 data and the square root of the SPE indicator for both daytime and nighttime are shown in Fig. 9. The correlations are quite uniformly around zero, although there are some larger values seen in the NH high latitudes and altitudes. Nevertheless, no effect of proton precipitation is detectable in the MLS HO 2 data. In the threshold detection analysis, the MLS averaging kernels were not applied to the WACCM-D data. However, we tested their impact and 25 found that the averaging kernels lead to lower correlations overall and higher threshold values, especially at altitudes above 1 hPa. Thresholds could still be detected using WACCM-D data, especially in the NH (not shown).
In WACCM-D, the SPE forcing is applied uniformly at geomagnetic latitudes > 60 • , and in HO x the impact is detected at all the same latitudes. Observations also confirm this: the same latitude extent is seen in MLS OH observations at night. Verronen et al. (2007) used MLS OH data to study the latitudinal extent of the the proton forcing during the January 2005 SPE, 30 comparing the results to a 1-D atmospheric simulation. They found that the lowest geomagnetic latitude affected by the SPE varied between 57 • and 64 • during the event. This agrees with our results with SPE impact detected at latitude bins poleward of 55 • , NH and SH. On the other hand, Heino et al. (2019) compared the latitudinal extent of 62 SPEs using cosmic radio noise absorption from a chain of riometer (relative ionospheric opacity meter) observations to those calculated from WACCM-D ionospheric output. They concluded that WACCM-D tends to overestimate the SPE impact at geomagnetic latitudes > 66 • . 35 However, Heino et al. (2019) included a large number of smaller events which are expected to affect the highest latitudes only (e.g. Rodger et al., 2006). For the set of events considered by us, the SPE impact seems to cover all geomagnetic latitudes above 60 • .
The SPE threshold fluxes from our HO x analysis are of the order of 100 protons cm −2 s −1 sr −1 . Thus our results are in agreement with a recent simulation study of SPE-driven atmospheric impacts which suggested little effect from SPEs with a 5 smaller peak flux (Kalakoski et al., 2020). This detection limit means that of the 130 SPEs recorded in 2004-2018, 36 (28%) have a peak daily flux large enough for HO x -based atmospheric detection.

RBE detection
The thresholds and correlations for nightime RBE detection are shown in Fig. 10. In general, the HO x reaction to radiation belt electron precipitation is more limited in altitude and latitude compared to proton precipitation, which can be expected from  (Fig. 11). These thresholds are 2.16 and 2.50 ×10 4 electrons cm −2 s −1 sr −1 , at altitudes 0.0147 hPa and 0.0215 hPa, respectively, both at magnetic latitude 70 • N.
In an attempt to improve some of the results, five-day averaged data were also examined. A moving five-day average was calculated from the HO x data and analysed as above with the SPE and RBE indicators. This was done to remove some of the 25 noise, especially in the MLS HO 2 , but the results were not improved. The data smoothing effectively flattened out the daily concentration peaks caused by events, which generally led to slightly lower correlations with the SPE and RBE indicators.
Thus the daily values can be considered an optimal choice for EPP detection, taking into account that a typical SPE/RBE event duration is days.
Although RBE forcing in WACCM-D is applied at geomagnetic latitudes 40 • -72 • , the detection in HO x impact is only seen 30 at 55 • -65 • . Unlike the SPE forcing, RBE is not uniform over the latitude range but peaks at the heart of the outer radiation belt (van de Kamp et al., 2016). Thus, only this region can be used to detect HO x impact. In the MLS data, i.e. in the correlations shown in Fig. 10, the RBE extent in the NH seems to reach into neighboring bins outside 55 • -65 • although the correlation limit is not exceeded. This could indicate an underestimation in WACCM-D RBE forcing which is driven by the geomagnectic Ap index.
The RBE threshold fluxes are of the order of 10 4 electrons cm −2 s −1 sr −1 , i.e. 100 times larger fluxes than for SPEs. This is consistent considering that 100 keV electrons ionize about 100 times less molecules than 10 MeV protons while penetrating to about the same atmospheric altitude. Considering the time period 2004-2018, there are 192 days, i.e. 3.9% of all days, 5 which have RBE flux larger than the 10 4 threshold. Note that our RBE thresholds are an order of magnitude larger than those given by Verronen et al. (2011). Analyzing four large RBE events, they estimated that it is not possible to detect HO x impact from electron forcing less than 10-30 counts/s as measured by MEPED, and this count rate corresponds to fluxes of 1 − 3 × 10 3 electrons cm −2 s −1 sr −1 (Evans and Greer, 2004).

10
In this study we have used atmospheric HO x data as a detector of EPP impact in the mesosphere and stratosphere. In a sense, WACCM-D simulations have provided us with the theoretical thresholds for the detection, while MLS observations are the present reality that is affected also by the quality of the measurements.
Overall, SPE impacts can be well detected using average nighttime OH data from MLS. Based on the WACCM-D results, detection should be possible also at daytime and using HO 2 data. In practise, however, the current MLS data do not have good 15 enough signal-to-noise ratio to do this. RBE detection is possible as well, but only at nighttime and for more limited altitude and latitude ranges. While the SPE impact can be seen rather uniformly poleward of 60 • , the RBE impact is focused at 60 • . As with SPEs, only MLS OH observations can be used for confident RBE detection on a day-by-day basis.
Our analysis shows the extent of SPE atmospheric impacts, down to around 35 km and 50 km in WACCM-D and MLS, respectively. The noise in MLS observations likely causes the difference in the altitude extent. Below 50 km altitudes, MLS 20 HO x can not be reliably used to detect SPEs. Potentially, however, other species like Cl x or HNO 3 could provide better SPE detection capabilities in the stratosphere. For example, the simulations of SPE impacts by Kalakoski et al. (2020) showed enhancements in Cl x and HNO 3 between 1 and 0.01 hPa lasting around a week, and longer lasting (20-30 days) effects below the 1hPa level in HNO 3 .
We find thresholds for EPP detection using the GOES >10 MeV proton fluxes and POES 100-300 keV electron fluxes to be 25 around 50 -130 protons cm −2 s −1 sr −1 and 1.0 -2.5×10 4 electrons cm −2 s −1 sr −1 at nighttime. These flux values have to be exceeded to cause detectable HO x impact. This limits the data usability to relatively large events. Note, however, that this does not mean that EPP with smaller fluxes is insignificant for the atmosphere. If applied for longer periods of time, EPP below the threshold limit can cause cumulative impacts on chemically long-lived species like NO x .
Although the MLS HO 2 data were found to be too noisy for day-to-day EPP detection, they still have a great potential for 30 other purposes. For example, studies of solar-cycle variability in the mesosphere could greatly benefit from the long timeseries.
Also, it has been shown, e.g. by Jackman et al. (2014), that the MLS HO 2 data are useful when largest solar proton events are studied.
Code and data availability. MLS data are available from the NASA Goddard Space Flight Center Earth Sciences (GES) Data and Information Services Center (DISC, https://mls.jpl.nasa.gov/data). All model data used are available from corresponding author by request. CESM source code is distributed through a public subversion code repository (http://www.cesm.ucar.edu/models/cesm1.0/) Competing interests. Authors declare that no competing interests are present. as well as WACCM-D data used in the analysis is also shown below the graphs.         Table 1. Months included in the analysis, with dates of SPE and RBE flux peaks within each month also given. For peaks within five days of each other, only the date of the strongest is included. Dates marked by * indicate dates in months, where the event peak was in another month. RBE peak dates marked by × are not included in the analysis, due to SPE peak in the same month.