Estimating the impact of the 1991 Pinatubo eruption on mesospheric temperature by analyzing HALOE (UARS) temperature data

The Mt. Pinatubo eruption in 1991 had a severe impact on the Earth system with a well-documented warming of the tropical lower stratosphere and a general cooling of the surface. This study focuses on the impact of this event on the mesosphere by analyzing solar occultation temperature data from the Halogen Occultation Experiment (HALOE) instrument on the Upper Atmosphere Research Satellite (UARS). Previous analysis of lidar temperature data found positive temperature anomalies of up to 12.9 K in the upper mesosphere that peaked in 1993 and were attributed to the Pinatubo eruption. Fitting the 5 HALOE data according to a previously published method indicates a maximum warming of the mesosphere region of 3.3 K and does not confirm significantly higher values reported for that lidar time series. An alternative fit is proposed that assumes a more rapid response of the mesosphere to the volcanic event and approximates the signature of the Pinatubo with an exponential decay function having an e-folding time of 6 months. It suggests a maximum warming of 5.5 K if the mesospheric perturbation is assumed to reach its peak 4 month after the eruption. We conclude that the HALOE time series probably captures the decay 10 of a Pinatubo-induced mesospheric warming at the beginning of its measurement period.

100 km in 1993. This was attributed to the Pinatubo eruption in June 1991. Kalicinsky et al. (2016) reported annual averaged OH(3-1) rotational temperature above Wuppertal (51.3 • N) with a strong peak in 1991. They added a vertical line marking the Mt. Pinatubo eruption to their graph but did not discuss a connection between the Pinatubo eruption and the temperature signature further in their paper. Offermann et al. (2010) also noticed a temperature maximum in 1991 after de-trending the OH(3-1) Wuppertal temperature time series, which they connected with the eruption of Mt. Pinatubo and Cerro Hudson. 30 Analysing Rayleigh lidar data, Keckhut et al. (1995) observed a significant warming of 5 K in the mesosphere from 60 -80 km in the summer of 1992 and 1993 and at 44 • N. They associated this finding with the Pinatubo eruption. Similarly, annually averaged temperature data from the High Resolution Doppler Imager on the Upper Atmosphere Research Satellite (UARS) exhibited a 5 K warming at 100 km in the years 1992 and 1993 which might be related to the Pinatubo eruption according to the authors (Thulasiraman and Nee, 2002). 35 In a recent modelling study Ramesh et al. (2020) employed the Whole Atmosphere Community Climate Model version 6 (WACCM6) model to investigate the long-term variability of middle atmospheric temperature and zonal wind caused by different drivers, including volcanic perturbations of the stratospheric aerosol optical depth. The simulations showed volcanic perturbations to the atmospheric temperature field reaching up into the lower thermosphere. However, these responses were not significant in many latitude-altitude regions and the underlying physico-chemical processes were not discussed in Ramesh Some researchers concluded that no episodic perturbation from the Pinatubo eruption is evident in their mesospheric temperature data. Remsberg (2009) did not consider an episodic forcing for the analysis of HALOE temperature time series at altitudes up to 80 km starting in 1991. Remsberg and Deaver (2005) acknowledged the interpretation by She et al. (1998) of the temperature increase as being caused by Pinatubo although they fitted an 11 year solar cycle-like term to this peak (Rems-45 berg et al., 2002b). Bittner et al. (2002) reported OH(3-1) rotational temperatures in 87 km altitude at 51.3 • N and fitted one year of data with a regression, moved the analysis window by half a year and kept repeating the procedure. They found a clear perturbation in the phases of the seasonal fits in the middle of 1991 that vanished half a year later. A correlation between the volcanic eruption and the temperature signal, however, was considered inconclusive. They could not reproduce the findings from She et al. (1998) and Keckhut et al. (1995) but speculated that this discrepancy could be due to the location of the ground-50 based measurements. According to the authors, the mountains close to the measurement site of Ford Collins used in the study of She et al. (1998) could enhance gravity wave formation -a possible route for energy transfer from the stratosphere to the mesosphere. This paper is structured as follows. In section 2 we describe the HALOE temperature data set and the regression approaches chosen in this study to model the temperature data. Section 3 describes the main results of the regression analysis, followed by 55 a discussion of the implications of the detected temperature signals in section 4. Conclusions are presented in section 5.

Data and data analysis
The impact of the atmospheric perturbation by the Pinatubo eruption on mesospheric temperature is estimated in this work by using temperature data from the Halogen Occultation Experiment (HALOE) (Russell III et al., 1993) on board the Upper Atmosphere Research Satellite (UARS) (Reber et al., 1993). HALOE started its scientific observations using solar occultation 60 on October 11, 1991 (Russell III et al., 1993) and should be able to track a potential remaining signature from the Pinatubo eruption. The NASA temperature data product was retrieved from the CO 2 transmission in the altitude range between approximately 35 and 85 km (e.g., Hervig et al., 1996;Remsberg, 2009). HALOE took about 15 sunrise and 15 sunset measurements every day. Due to the non-sun-synchronous orbit of the UARS spacecraft, the latitudes of HALOE occultation measurements changed slowly from day to day. Latitudes between 50 • N and 50 • S are typically covered in each month. Depending on the UARS yaw cycle, latitudes up to 80 • are covered in one hemisphere.
In this study we used HALOE level 2 (Version 19) temperature data from the NASA Goddard Earth Sciences Data and Information Services Center website (https://disc.gsfc.nasa.gov) and the F10.7cm solar flux provided by the Laboratory for Atmospheric and Space Physics Interactive Solar Irradiance Data Center (https://lasp.colorado.edu/lisird/data/penticton_radio_flux/) as a solar proxy.

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The HALOE files contain the retrieved temperature at 0.3 km spacing, the latitudes and the classification of the measurement as sunset and sunrise measurements, respectively (Thompson and Gordley, 2009). Only temperatures between 43 and 87 km altitudes and with values not equal to 0 were used. All temperature data was divided into sunset and sunrise measurements and each data set was zonally and daily averaged and binned in 10 • latitude bins. Afterwards, the mean values of the sunset and sunrise data set for each latitude and altitude bin, mean ss and mean sr , were calculated to correct the data according to 75 equation 1 which is adapted from Remsberg et al. (2002b).
T sr,corr = T sr + (mean ss − mean sr )/2. (1) The corrected sunset and sunrise data T ss,corr and T sr,corr were combined to a single data set. If both sunset and sunrise data exist for the same latitude-altitude bin, the average of both values was taken. Subsequently, the monthly average was obtained.
If not stated otherwise, a fit was applied including a constant and linear term, seasonal terms, a solar proxy and an episodic 80 perturbation term. The seasonal terms account for the annual (P year ), semi-annual (P semiyear ), 4-months (P 4months ) and 3months (P 3months ) oscillations while the F10.7cm solar proxy was used to include the solar contribution (S F 10.7cm ) term. Two different approaches are proposed and compared. The first approach adopts an expression for the episodic perturbation term from She et al. (1998) which is also considered as the last term in equation 2

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with P year = 1 year, P semiyear = 0.5 years, P 4months =0.33 years and P 3months = 0.25 years. The parameters t 0 , t 1 and t 2 indicate the delay, rise and decay time (She et al., 2015) and were varied as described in the text below.
During the analysis of the HALOE temperature data it became apparent that for some altitude-latitude bins there appeared to be an anomalous enhancement of the temperature values right at the beginning of the time series in October 1991. This temperature anomaly was found to decay roughly exponentially. This finding motivated the use of an alternative fitting approach 90 based on two consecutive fit functions. After the constant, linear, seasonal and the solar contributions are accounted for in equation 3 an exponential decay function is fitted to the residual from the first fit in order to capture a potential volcanic perturbation, as can be seen in equation 4.
All fits were performed with equal weights and the amplitude of the solar proxy was limited to positive values, including zero.
Confidence intervals for the regression coefficients were determined with a jackknife method. If the confidence interval does not include zero than the regression coefficient is considered significant. This method is described in more detail in Appendix A1.
This study analyses the HALOE temperature data for a potential Pinatubo-related episodic warming in the mesosphere. In our 100 first approach, we include a perturbation term in our fit routine that was suggested by a Na lidar study (She et al., 1998) that reported a strong temperature perturbation. We can now compare our results to their findings. Figure 1 presents the HALOE temperature time series at 40 ± 5 • N and 86 km, similar to the location of the lidar station at 41 • N and the altitude reported in the lidar study (She et al., 1998). HALOE measurements from 76.5 km to 99 km are merged with the MSIS (Mass Spectrometer -Incoherent Scatter) climatology. According to Remsberg et al. (2002a) the HALOE temperatures up to 87.5 km altitude can be 105 assumed to be almost completely independent of MSIS and can thus be used for a direct comparison. The time series was fitted according to equation 2, containing a constant and a linear term, seasonal terms, a solar proxy and the episodic perturbation term. The parameters t 0 to t 2 that define the perturbation term are chosen according to the literature (She et al., 1998). The resulting fit is drawn as a green curve over the data. Figure 1 clearly shows that the fit successfully captures the measured data points. Figure 2 shows the residual determined by subtracting the fit from the actual data points. No modulation or remaining 110 signature is visible in the residual which further suggests that the fit is based on valid assumptions.
We now focus on the amplitude of the episodic perturbation term. The amplitude of the perturbation is negative (-2.3 K) and indicates a cooling between 1992 -1994 in contrast to the warming reported previously (She et al., 1998). Although the fit as a whole was performed successfully, the amplitude and sign of the term that captures the episodic perturbation contradict previous findings.   The analysis was expanded to the middle atmosphere from 45 to 87 km altitude and from 50 • S to 50 • N. The variables t 0 to t 2 are now treated as fit parameters. In contrast to the amplitude of the episodic term, they are only allowed to vary in defined ranges (2.7 ≤ t 0 ≤ 3.3, 0.2 ≤ t 1 ≤ 0.4 and 0.9 ≤ t 2 ≤ 2.9) on the basis of a previous lidar study (She et al., 1998).
The amplitude of the episodic perturbation for the middle atmosphere is presented as a contour plot in Figure 3. Its magnitude and sign might hint to a Pinatubo-induced temperature signature in the atmosphere. A grey color indicates that this area is not  If the two fits are compared throughout the upper mesosphere, however, it is apparent that the inclusion of the episodic 145 perturbation term adapted from the literature also captures the high temperatures at the beginning of the time series in some cases (column in the middle in Figure S1 of the supporting information). This term, however, strongly focuses on the time segment around 1993, whereas the exponential decay function specifically decreases the residual temperature at the start of the measurement series in most cases (last column in Figure S1 in the supporting information) and will therefore be explored further.   To compare the alternative fit with the perturbation term adopted from the literature (She et al., 1998), Figure 6 shows the temperature of fit F 3 (t Oct91 ) in a contour plot with t Oct91 being October 1991. We chose to report the value of the function at that time because it is more comparable with the amplitude of the perturbation term than the constant C 0 which is the intersection with the y axis, representing January 1990. The temperature of F 3 (t Oct91 ) is highest in the upper mesosphere above 80 km and between 10 • S and 20 • N with a maximum positive value of 5.5 K, as can be seen in Figure 6. Another area 155 with significant positive temperatures lies between 10 -20 • N between 70 -80 km. The lower mesosphere in the southern hemisphere shows positive values between 50 -30 • S and 50 -65 km. As t Oct91 is deliberately chosen as October 1991 it is, however, not quantitatively comparable to the amplitude of the perturbation function shown in the graph of Figure 3. Figure 6 nevertheless shows that, at least for the HALOE data set that started the observation four months after the Pinatubo eruption, an exponential decay function is an alternative to the episodic perturbation term suggested by a previous study (She et al., 160 1998). It further indicates that a positive temperature anomaly is present in the tropical upper mesosphere at the beginning of the HALOE time series, which may be related to the eruption of Mt. Pinatubo. Possible mechanisms are discussed in the following section. Figure 6. A positive temperature of 5.5 K was found in the upper mesosphere above 80 km and at 20 • N when an exponential decay function was applied. This temperature is the value of fit F3(tOct91) at tOct91, i.e. October 1991, assuming that the peak of the perturbation occurred four month after the eruption.

Discussion
This study compares two approaches to fit a perturbation signal potentially caused by the Pinatubo eruption in June 1991 165 to the HALOE temperature series in the middle atmosphere. They differ considerably in the assumed time that the volcanic perturbation needs to reach the upper mesosphere. Na lidar temperatures over Fort Collins (40.6 • N, 105.1 • W) showed a strong mesospheric warming peaking in 1993 (She et al., 1998) that could not be reproduced using the HALOE data set. There are, however, uncertainties in comparing a ground-based measurement with zonally averaged satellite data using a 10 • latitude bin for the case of the HALOE analysis. Keckhut et al. (1995) reported Rayleigh lidar measurements at 44 • N from 30 -80 km  (Bittner et al., 2002). They appear 6 months after the eruption and vanished half a year later (Bittner et al., 2002). Another publication used the OH*(3-1) rotational temperatures from both Wuppertal and Hohenpeißenberg and showed a positive anomaly in 1991 in fitted mean temperatures that disappeared in 1992 (Offermann et al., 2010). Bittner et al. (2002) speculated that the Pinatubo-induced temperature signal in the mesosphere might not be homogeneous in the zonal direction so that ground-based measurements differ because of a zonal asymmetry. Such a potential asymmetry, however, is 180 disregarded in our HALOE analysis because the limited number of daily sunset and sunrise measurements requires zonal averaging.
First results of a tropical volcanic eruption, that injects twice as much SO 2 as the Pinatubo, with the upper-atmosphere icosahedral non-hydrostatic (UA-ICON) model (Borchert et al., 2019) suggest that the strongest response in the upper mesosphere appears approximately 6 months after the eruption (Hauke Schmidt, personal communication, August, 24 2021). Interestingly,

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it also started to fade away and is barely visible two years after the eruption which further supports the hypothesis that volcanic perturbations can rapidly reach the mesosphere. Although the simulation showed the strongest perturbation in December we decided to report the value of F 3 (t) for October because single time series show high residual temperatures before the month of December. Both observation and simulation provide evidence that support our assumption of an early temperature signal in the mesosphere. As the HALOE instrument only started operating four months after the eruption, it is suggested that it may 190 only detect the decay of the already fading signal.
It is nontrivial to separate a Pinatubo-related signature from other natural contributions (such as a solar signal) when analysing temperature data and this issue could potentially explain some of the disagreements in the observations. The 11-year solar cycle exhibited a maximum around 1990 with several solar flares occurring in June 1991 (Rank et al., 1994). Remsberg atmosphere is approximately in phase with solar UV flux measurements for most altitudes. We therefore use the F10.7 cm solar flux as a solar proxy in our fit routine and limit its amplitude to positive values including zero. This should capture the contribution from the 11-year solar cycle in order to separate its effect from the volcanic terms. Another type of interfering signal was observed for OH* temperatures in the mesopause when Kalicinsky et al. (2016) found a 25-year oscillation of unknown origin with an amplitude of (1.95±0.44) K that has a maximum in 1993. They saw both the 25 year oscillation and 200 a temperature peak in 1991 that coincided with the Pinatubo eruption. These findings emphasize that any solar or non-solar signal must be carefully separated from a Pinatubo perturbation for each temperature time series.
An increase in the mesospheric temperature due to a strong volcanic eruption would indicate a coupling mechanism that transports the signal in the lower stratosphere up to the mesosphere. A simulation performed by Rind et al. (1992) showed that the radiative warming of the tropical lower stratosphere after a volcanic eruption enhanced the static stability of the troposphere region. In addition, a rapid dynamic coupling was reported, e.g. by Smith and Mullen (2020) who used WACCM6 simulation to demonstrate that perturbations in the winter stratosphere impact the summer mesosphere via a wave-driven inter-hemispheric coupling in just a few days. Although the early simulations by Rind et al. (1992) hinted at a dynamical mechanism that links a volcanically induced warming of the lower stratosphere with a subsequent warming of the upper mesosphere, further studies are necessary and currently underway to examine these processes.

Conclusions
The HALOE temperature time series for the mesosphere region was analyzed for a potential perturbation caused by the eruption of Mount Pinatubo in June 1991. The data was fitted with a regression that accounted for a constant and linear term, annual, semi-annual, 4-month and 3-month oscillations, as well as the F10.7cm solar proxy. Two methods to estimate a potential volcanic signal were compared. The first expanded the regression and included a perturbation term first proposed in a lidar 225 study (She et al., 1998). Using the parameters reported in that lidar study for 86 km and comparing it to HALOE data at a similar altitude and latitude resulted in an amplitudes with opposite sign; indicating a cooling instead of a warming. HALOE data for the entire mesosphere was subsequently fitted using ranges for the perturbation parameters t 0 to t 2 that were defined by the values found and discussed in the aforementioned publication (She et al., 1998). A maximum positive amplitude of 3.3 K was observed that was significantly lower than reported by these authors. Differences are, however, expected because a 230 ground-based measurement is compared with zonally averaged occultation measurements using a 10 • latitude bin.
Our analysis revealed anomalous positive temperature anomalies at some latitudes in the upper mesosphere during the first months of the HALOE time series starting in October 1991. For this reason, a second fit method was applied to fit the de-seasonalized data with an exponential decay function having an e-folding time of 6 months. This approach suggests a volcanic warming of up to 5.5 K if the peak of the signature is assumed to be reached in October 1991, four months after the 235 eruption. It indicates that HALOE probably measure (only) the decay of a mesospheric perturbation that was forced by the Pinatubo eruption and also suggests a more rapid response of the mesosphere to the volcanic event in agreement with other observations (Kalicinsky et al., 2016;Offermann et al., 2010). Data availability. The HALOE level 2 version 19 temperature data used in this paper is available on the NASA website (https://disc.gsfc.nasa.gov, Russell III and James (1999)). Two IDL routines were used for the subsequent data analysis, namely the IDL routine MPFUNFIT.PRO that was 240 released by Craig Markwardt (http://cow.physics.wisc.edu/craigm/idl/fitting.html) and the IDL reading function READ_HALOE_L2.PRO that was obtained from NASA (https://mls.jpl.nasa.gov/data/readers.php). The Laboratory for Atmospheric and Space Physics (LASP) provided the F10.7cm solar flux that is used as a solar proxy in this paper (http://lasp.colorado.edu/lisird/data/penticton_radio_flux/).