Trend analysis of the 20 years time series of stratospheric ozone proﬁles observed by the GROMOS microwave radiometer at Bern

. The ozone radiometer GROMOS (GROund-based Millimeterwave Ozone Spectrometer) performs continuous observations of stratospheric ozone proﬁles since 1994 above Bern, Switzerland (46.95 ◦ N, 7.44 ◦ E, 577 m). GROMOS is part of the Network for the Detection of Atmospheric Composition Change (NDACC). From November 1994 to October 2011, the ozone line spectra were measured by a ﬁlter bench (FB). In July 2009, a Fast-Fourier-Transform spectrometer (FFTS) has 5 been added as backend to GROMOS. The new FFTS and the original FB measured in parallel for over two years. The ozone proﬁles retrieved separately from the ozone line spectra of FB and FFTS agree within 5% at pressure levels from 30 to 0.5 hPa, from October 2009 to August 2011. A careful harmonisation of both time series has been carried out by taking the FFTS as the reference instrument for the FB. This enables us to assess the long-term trend derived from stratospheric ozone observa- 10 tions at Bern. The trend analysis has been performed by using a robust multilinear parametric trend model which includes a linear term, the solar variability, the El Niño - Southern Oscillation (ENSO) index, the quasi-biennial oscillation (QBO), the annual and semi-annual oscillation and several harmonics with period

1 Introduction 20 For many decades it is known that the stratospheric ozone layer shields the Earth's surface from harmful solar ultraviolet radiation (UV), thus enabling life on Earth and protecting humans and the biosphere against adverse effects. Molina and Rowland (1974) were the first to propose that this protective layer could be depleted by anthropogenic emission of chlorofluorocarbons (CFCs) to the atmosphere. The photodecomposition of CFCs and other long-lived organic molecules in the From the late 1990s, there were some measurements and model calculations indicating a turnaround in the decreasing ozone, suggesting that the negative ozone trends in the stratosphere would level out or even become positive (Newchurch et al., 2003). Nevertheless, during this recovery phase, ozone levels will also be affected by the expected anthropogenic increases in abundances of other 40 ozone-relevant gases (carbon dioxide (CO 2 ), methane (CH 4 ), and nitrous oxide (N 2 O)) as well as by the natural influences of volcanic eruptions, solar activity, and the natural variability in the Earth's climate (WMO, 2014).
The concerns regarding anthropogenic depletion of stratospheric ozone increased the necessity for precise and accurate measurements to monitor long term trend in this specie. (Parrish et al., 1992). 45 Passive millimeter wave radiometry has been used to monitor the vertical distribution of atmospheric trace gases since the early 1970s (Palm et al., 2010). The need for continuous monitoring of the stratospheric response to anthropogenic trace gas releases, performed by a well defined set of instruments, led to the foundation of the Network for the Detection of Stratospheric Change (NDSC) (now Network for the Detection of Atmospheric Composition Change -NDACC) in 1991. The ozone ra-50 diometer GROMOS is part of the NDACC, hence our more than 20 years harmonised time series are available via http://ftp.cpc.ncep.noaa.gov/ndacc/station/bern/hdf/mwave/ Ozone time series from the GROMOS microwave radiometer were used for comparisons with lidar, ozonesondes and collocated satellite observations and for detection of long-term trends (Dumitru et al., 2006;Steinbrecht et al., 2006;Steinbrecht et al., 2009;Keckhut et al., 2010;van Gijsel et al., 55 2010; Studer et al., 2013;Delcloo and Kreher, 2013;WMO, 2014).
Ground-based millimeter wave radiometry is a powerful technique for trace gas measurements due to its low sensitivity to weather conditions and aerosol contamination. Since ozone radiometers measure the thermal microwave emission of ozone in the middle atmosphere, they do not require external illumination sources, such as laser pulses or the solar irradiance. The measurements can therefore 60 be made throughout day and night. Among other advantageous technical features, the more than 20 years of continuous observations and the privileged location of the instrument offer us a pretty clear vision of the distribution of ozone in the northern mid-latitudes (46.95 • N, 7.44 • E, 577 m).
We perform a trend study of our time series of stratospheric ozone profiles through a new robust multilinear parametric trend estimation method (von Clarmann et al., 2010). The program minimises a 65 cost function in order to estimate the linear trend of a time series. The cost function consists of the quadratic norm of the residual between a regression model and the measured time series, weighted by the inverse covariance matrix of the data errors. Error correlations between data points are supported, making the program suitable for consideration of auto-correlated residuals. This generic trend method takes the entire effect of correlated residuals into account but it does not correct them. The 70 method is particularly useful when a time series is constructed of multiple datasets where different calibration standards and other errors with systematic components have to be considered. Further, this method takes into account autocorrelated residuals which are caused by atmospheric variability on time scales larger than the sampling distance of the data but not described properly by the multilinear trend model chosen. Since the related additional autocorrelated error term can change the 75 weight of the data points, its inclusion does not only lead to a larger, more realistic, error estimate but can slightly change the trend estimate, too. The regression model consists of an axis intercept, a linear trend, sine waves, and several proxies. Unknown biases between data subsets are handled by assigning a fully correlated error term to each data point of one of the data subsets. With this trend analysis tool a complete treatment of the uncertainties is assured, making this trend analysis 80 particularly valuable to confirm the aforementioned ozone turnaround with a representative station in central Europe. Trend studies of ozone profiles based on ground-based microwave measurements are rare. In fact, since Steinbrecht et al., 2006 we are not aware of any other publication, therefore, the purpose of this paper is to present a new trend estimation based on stratospheric ozone profiles measured by a ground-based microwave at northern midlatitudes (46.95 • N, 7.44 • E, 577 m).

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The present study is organised as follows: the description of the instrument, the measurement technique, the spectrometer upgrade and the retrieval method are presented in Section 2. Section 3 summarises the procedure carried out for the harmonisation of ozone profiles, followed by a detailed description of the trend estimation method in Section 4. Section 5 deals the characterisation 90 of GROMOS uncertainty sources. The estimated trend is presented in Section 6, concluding with an overview of our result in an overall context. And finally, Section 7 is a summary of our findings.

Spectrometer upgrade
The spectral analysis was performed by a filter bench (FB) spectrometer from November 1994 to October 2011. The 45-channel FB had a total bandwidth of 1.2 GHz with individual filters with a 115 frequency resolution varying from 200 kHz at the line centre to 100 MHz at the wings. Figure 1 shows as an example a calibrated spectrum recorded on a winter morning in 2011 by the FB spectrometer, with an integration time of 60 minutes. In July 2009, an Acqiris Fast-Fourier-Transform Spectrometer (FFTS) was added as backend to 120 GROMOS. The FFTS covers a total bandwidth of 1 GHz with 32768 channels, giving a frequency resolution of around 30.5 kHz. A sample of a calibrated ozone spectrum is given in Figure 2. It shows the ozone line recorded by the FFTS on the same winter morning as the FB spectrum ( Figure   1). The integration time is 30 minutes and no frequency binning is applied in the blue curve whereas the red line represents the 15 MHz frequency binned spectrum. Compared to the FB, the FFTS has a high resolution not only in the centre but also in the line wings. The stability time of our whole radiometer system was improved compared to the FB (Müller et al., 2009). The FB required much more maintenance by the operator and in spite of this individual channels were disturbed from time to time so that the measured line spectrum was not usable. With 130 the aim to ensure a proper harmonisation of the two datasets, both spectrometers were measuring in parallel for over two years. Afterwards the FB was turned off and FFTS is now used to continue the ozone time series. Table 1 summarises the characteristics of GROMOS radiometer.  The Qpack2 derives the best estimate of the vertical profile of ozone volume mixing ratio (VMR) by using the Optimal Estimation Method (OEM) (Rodgers, 1976), and taking into account the uncertainties of the measured ozone spectrum, the a priori profile and the a priori covariance matrix. The

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OEM further provides a characterisation and formal analysis of the uncertainties (Rodgers, 1990).
Prior to the inversion, a tropospheric correction for the tropospheric attenuation (mainly due to water vapour) of stratospheric ozone emission is applied to the calibrated spectra by assuming an isothermal troposphere with a mean temperature, T mean . T mean depends upon the temperature profile as well as on the absorption profile at a specific frequency. Since the number den-150 sity is highest at low altitudes and the absorption is highest near the ground, T mean has a value close to the temperature of the lower troposphere (Ingold et al., 1998). The transmission factor where τ is the opacity, is estimated from the offresonance emission T B,wing at the wings of the spectrum and the expected brightness temperature above the troposphere T B,strat (Peter, 1997). The knowledge of the tropospheric opacity permits the 155 so-called tropospheric correction, which means that the effect of tropospheric attenuation is removed from the measured line spectrum (Studer et al., 2014). The inversion is performed for all spectra if the tropospheric opacity is lower than 1.6, i.e. transmission factor larger than 0.2 (Studer et al., 2013). In the standard retrieval, the time resolution is 30 minutes, which gives sufficient signal-tonoise ratio (approximately 30; measurement noise is around 0.7 K and brightness temperature at the  The a priori profiles of ozone are from a monthly varying climatology based on earlier ozone 170 measurements at Bern. As diagonal elements of the a priori covariance matrix we assume a relative error around 35% at 100 hPa. The error decreases in the lower stratosphere up to 28%. Then it increases linearly from 35% in the upper stratosphere to 70% in the lower mesosphere. The offdiagonal elements exponentially decrease with a correlation length of 3 km. The line shape used in the retrieval is the representation of the Voigt line profile from Kuntz (1997). Spectroscopic 175 parameters to calculate the ozone absorption coefficients were taken from the JPL catalogue (Picket et al., 1998) and the HITRAN spectroscopic database (Rothman et al., 1998). The atmospheric temperature and pressure profiles are taken from the 6 hourly of the European Centre for Medium-Range Weather Forecast (ECMWF) operational analysis data and are extended above 80 km by monthly mean temperatures of the CIRA-86 Atmosphere Model (Fleming et al., 1990). The total 180 error includes systematic error and random error as well as the smoothing term. The systematic error originates from the tropospheric correction, calibration error due to systematic errors in the load temperatures, errors due to baseline features, spectral parameters, etc. The random error includes e.g. the thermal noise on the spectra. An error analysis has been performed by Peter (1997). The uncertainty resulting from the tropospheric correction is smaller than 5% (Ingold et al., 1998). The 185 total error is of the order of 7% for the stratosphere and increases toward the lower and upper altitude limit: up to 10% at 20 km and up to 30% at 70 km. The smoothing term is due to the limited altitude resolution. The GROMOS radiometer is described in more detail by Peter (1997).
8 3 Harmonisation strategy for the ozone profiles As GROMOS was upgraded with a Fast-Fourier-Transform Spectrometer, an harmonisation is needed 190 between the time series measured by the original Filter Bench (FB) spectrometer and the time series recorded by FFTS. In order to ensure an appropriate harmonisation, both spectrometers were measuring in parallel for over two years. According to subsection 2.2 Spectrometer Upgrade, the FFTS offers high resolution besides stability and accuracy compared with FB. Therefore, we can use the data recorded by FFTS as reference for the original FB data set.

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The strategy carried out for the harmonisation of both data sets was to study the bias between them  On the basis of this harmonisation process, we have generated a time series of more than 20 years of stratospheric ozone profiles observed by GROMOS over Bern, Figure 5. Undoubtedly, Figure 5 210 provides an extremely clear view of the evolution of stratospheric ozone over the last two decades at a central Europe station, and hence at northern mid-latitudes. Further the annual cycle of ozone can be observed in the stratosphere as well as an increase of mid-stratospheric ozone in last years. y(t) = a+b·t+c 1 ·qbo 1 (t)+d 1 ·qbo 2 (t)+e·F 10.7(t)+f ·M EI(t)+ m n=2 (c n ·sin( 2π · t l n )+d n ·cos( 2π · t l n )) (1) where t is time, a and b represent the constant term and the slope of the fit, respectively. The

Uncertainty considerations
Before analysing the estimated trends, the uncertainties affecting the ozone profiles recorded by GROMOS must be considered, analysed and taken into account. We have considered three types of uncertainties. The first one is the uncertainty of the natural variability that is approximated by 260 the standard error of the monthly mean. The second one is the observation error, which is obtained from the propagation of the thermal noise of the brightness temperature into the ozone profile. The observation error corresponds to the random error, calculated during the retrieval procedure, which is due to the thermal noise on the spectra. The third way to assess the uncertainties is based on cross-validations of GROMOS with satellites and ground-based instruments (Dumitru et al., 2006, 265 Steinbrecht et al., 2006, Studer et al., 2013 andKreher, 2013).
The criterion to indicate if an estimated trend is statistically significant at the 95% of confident level is that the absolute ratio of the trend to its uncertainty is larger than 2 (Tiao et al., 1990).
The large number of GROMOS measurements per month allows a robust assessment of the uncertainty from natural variability, where the effect of the autocorrelation among data points within the 270 series is taken into account. The standard error of the monthly mean contains both uncertainties due to measurement noise and atmospheric variability. First the standard deviation has been calculated, where n is the number of measurements per month, x the ozone mixing ratio, andx its monthly mean. Then the variability within the month has been analysed for autocorrelations between the To calculate the correlation lengths we have used the autocorrelation function (ACF) of Matlab, which provides us the time lags (correlation lengths) of the temporal autocorrelation function calcu- Finally, we assume an uncorrelated monthly instrumental uncertainty. The aim is to take into account the bias between GROMOS and other instruments, and thereby to get a realistic uncertainty 295 estimation. We have estimated this profile with the result of past-cross validations of coincident data from GROMOS, ozonesondes, nearby lidars and satellites (Dumitru et al., 2006, Steinbrecht et al., 2006, Studer et al., 2013 andKreher, 2013). Past cross-validations show a systematic uncertainty of about 5 to 10% for our instrument. Around 5% between 10 and 1 hPa and tending to roughly 10% toward the lower and upper stratosphere. The strongest point of this estimation 300 method relies on the fact that these validation reports and inter-comparisons cover all the 20 years of GROMOS measurements. Both for the period in which the spectral analysis was done by the filter 13 bench spectrometer (Dumitru et al., 2006, Steinbrecht et al., 2006, as for the period of the new Fast-Fourier-Transform Spectrometer (Studer et al., 2013, Delcloo andKreher, 2013).   The estimated stratospheric trend results are able to support the evidence of shift toward increasing ozone in the middle and upper stratosphere at northern mid-latitudes also reported by previous studies (Vigouroux et al., 2008;Nair et al., 2013;Huang et al., 2014;WMO, 2014;Tummon et al., 2015;330 and references therein). On the other hand, other recent studies (Eckert et al., 2014;Vigouroux et al., 2015;Harris et al. 2015; and references therein) have found positive but not significant trend in our location. But we have to be careful about these discrepancies since it could arise from differences in treatment and propagations of uncertainties, selection of data, ozone measurement techniques, statistical approach, latitudinal and altitudinal extent and/or the time period covered in the trend study.

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The WMO (2014, Table 2.4) reported a statistically significant ozone increase of (3.9 ± 1.3) (% Observations of changes in temperature and ozone over the past three to five decades are suggestive of increased upwelling of air in the tropical lower stratosphere. This is consistent with model simulations, which robustly simulate long-term increases in the tropical upwelling due to past green-375 house gas increases (WMO, 2014). Ozone in the tropical lower stratosphere shows little response to ODS, because conversion of ODS into reactive chlorine and bromine is small in this region. Instead, tropical lower stratospheric ozone is more affected by the strength of tropical upwelling of air from troposphere to stratosphere caused by the shallow branch of the BDC (WMO, 2014). Additionally, sification of the BDC, together with weakening of the subtropical mixing barrier as an explanation of their age of air temporal evolution. Therefore, the acceleration of both branches of BDC could be one of the contributors to the aforementioned stratospheric ozone increase in northern mid-latitudes.
Regarding the lower mesosphere region, our results are in agreement with recent trend estimations (Kyrölä et al., 2013;Remsberg, 2014 and references therein;Tummon et al., 2015). They have 385 found statistically significant negative trends above 55 km in the northern mid-latitudes through the SAGE II (Stratospheric Aerosol and Gas Experiment) version 7 data and by the combined SAGE II-GOMOS (Global Ozone Monitoring by Occultation of Starts) data set.

Conclusions
We have constructed an harmonised ozone profile time series from GROMOS measurements since

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November 1994 up to now. The need for such harmonisation is due to the spectrometer upgrade performed in 2009. From November 1994 to October 2011, the ozone line spectra were measured by a filter bench spectrometer (FB). Since July 2009 the spectral analysis is done by a Fast-Fourier-Transform Spectrometer (FFTS). Both spectrometers were measuring parallel in order to ensure a proper harmonisation. A bias between both data sets has been identified, being less than 5% above 395 20 hPa. The harmonisation has been done by taking the data set from the FFTS as reference for the FB. The combined data set time series was then analysed for trends in the stratosphere.
A mutilinear parametric trend model was used to analyse this time series of stratospheric ozone profiles. This model includes a linear term, the solar variability, the El Niño -Southern Oscillation (ENSO) index, the quasi-biennial oscillation (QBO), the annual and semi-annual oscillation and 400 several harmonics with period lengths between 3 and 24 months. The trend results for the period between January 1997 and January 2015 show statistically significant trends at 95% level at pressure levels around 5 and 0.2 hPa. Our estimated trend profile is in agreement with other northern midlatitude trend estimations from other ground-based and satellite instruments (Vigouroux et al., 2008;Nair et al., 2013;Kyrölä et al., 2013;Huang et al., 2014;Remsberg, 2014  This study also demonstrates the reliability of GROMOS measurements for providing stratospheric ozone profiles. Allowing us the adequate study of the characterisation of ozone variability on time scales from 10 minutes to more than 20 years. The continuation in time with these measurements will help future generations to confirm findings through the intercomparison with other instruments 410 and to understand the evolution of the ozone layer that is extremely crucial for life on Earth.