The ozone radiometer GROMOS (GROund-based Millimeter-wave Ozone Spectrometer)
has been performing continuous observations of stratospheric ozone profiles since 1994
above Bern, Switzerland (46.95

For many decades it has been 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.

In 1985, massive ozone losses in measured column abundances during the
Antarctic spring were reported and heterogeneous chlorine chemistry on polar
stratospheric clouds (PSCs) were implicated for the loss (

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
(

The concerns regarding anthropogenic
depletion of stratospheric ozone increased the necessity for precise and
accurate measurements to monitor long-term trends in this species.
(

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 (

Ground-based millimetre-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 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 midlatitudes (46.95

We perform a trend study of our time series of stratospheric ozone profiles
through a new robust multilinear parametric trend estimation method
(

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 Sect. 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 Sect. 4. Section 5 deals with the characterisation of GROMOS uncertainty sources. The estimated trend is presented in Sect. 6, concluding with an overview of our result in an overall context. And finally, Sect. 7 is a summary of our findings.

GROMOS is an ozone
radiometer, located at the University of Bern (46.95

GROMOS is a 142 GHz total power radiometer observing at an elevation angle
of 40

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 frequency resolution varying from 200 kHz
at the line centre to 100 MHz at the wings. Figure

Measurement of the ozone spectrum line at 142 GHz at Bern on a winter day with the filter bench spectrometer. The integration time is 60 min.

In July 2009, an Acqiris fast Fourier transform spectrometer (FFTS) was added
as a back end to 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 Fig.

Ozone spectrum line at 142 GHz recorded by the Acqiris FFT spectrometer at Bern on a winter day. The integration time is 30 min. The red line represents the frequency binned.

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 (

GROMOS instrument specifications.

GROMOS measures the thermal microwave emission of a rotational transition of
ozone at 142.175 GHz. As the observed emission line is broadened by
pressure, the vertical distribution of ozone (approximately from 25 to
70 km) can be calculated from the shape of the observed spectrum in the
retrieval procedure. For the ozone profile retrieval of GROMOS, the
Atmospheric Radiative Transfer Simulator (ARTS2) (

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,

Example of an a priori profile and a retrieved ozone profile (left panel), averaging kernels (middle panel) and the measurement response (area of averaging kernels) (right panel) of the GROMOS retrieval for January, 2002.

The a priori profiles of ozone are from a monthly varying climatology based
on earlier ozone 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 off-diagonal 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

As GROMOS was upgraded with a fast Fourier transform spectrometer, harmonisation is needed between the time series measured by the original FB spectrometer and the time series recorded by FFTS. In order to ensure appropriate harmonisation, both spectrometers were measuring in parallel for over 2 years. According to Sect. 2.2, the FFTS offers high resolution besides stability and accuracy compared with FB. Therefore, we can use the data recorded by FFTS as a reference for the original FB data set.

The strategy carried out for the harmonisation of both data sets was to study
the bias between them in the time interval in which both spectrometers were
simultaneously measuring, i.e. from October 2009 to August 2011. In Fig.

Harmonisation of ozone profiles retrieved from the FB (red line in the left panel) and FFT (blue line in the left panel) spectrometers. The blue area (FFTS) and the red area (FB) are the standard deviation of the measurements. The bias between FB and FFTS is less than 5 % (middle panel) as derived from the overlap measurement (2009 to 2011) of ozone profiles at pressure levels from 30 to 0.3 hPa (valid altitude range of GROMOS, green box). The grey area in the middle panel is the standard deviation of the differences.

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 (Fig.

Harmonised time series of stratospheric ozone VMR profiles recorded by GROMOS from January 1997 to January 2015 above Bern, Switzerland.

A multilinear parametric trend model (

Power spectra of stratospheric ozone time series measured by GROMOS above Bern, Switzerland. The black dotted lines are the frequencies for the annual and semi-annual oscillation, the 11 years due to the solar cycle, the 2.4 years of the QBO and the 4.5 years of ENSO phenomenon. The magenta dotted lines are the frequencies of the overtones (3, 4, 7.2, 8.4 and 24 months).

With the aim to assess the linear variation of the time series within the
period covering January 1997 to January 2015, the coefficients

The inputs required by the trend estimation program are the ozone monthly
mean profiles and their uncertainty. An example of the fit is displayed in
Fig.

The first panel shows the trend fit at 10 hPa, with the GROMOS monthly mean data (blue line), the calculated fit (red line) and the related trend (black line). The second panel shows the residual and in the following panels the fitted signals of the proxies QBO (magenta line), solar F10.7 cm flux (red line) and ENSO (green line), at 10 hPa.

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 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 (

The criterion to indicate if an estimated trend is statistically significant
at the 95 % confidence level is that the absolute ratio of the trend to
its uncertainty is larger than 2 (

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 series is taken into account. The standard error of the
monthly mean contains uncertainties due to both measurement noise and
atmospheric variability. First the standard deviation was calculated:

To calculate the correlation lengths, we used the autocorrelation function (ACF) of Matlab, which provides us the time lags (correlation lengths) of the temporal autocorrelation function calculations. For stationary processes, the autocorrelation among any two observations only depends on the time lag. Therefore, the autocorrelation is 1 for the time lag equal to 0, since unlagged data are perfectly correlated with themselves. The collection of autocorrelations, autocorrelation function, computed for various lags exhibit a more or less gradual decay toward 0 as the time lag increases, reflecting the generally weaker statistical relationship between data points more remote from each other in time. The number of time lags of autocorrelated values within the 95 % confidence level are the correlation lengths within a month, used to calculate the DGF.

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 estimation. We have estimated this
profile with the result of past cross-validations of coincident data from
GROMOS, ozonesondes, nearby lidars and satellites (

Uncertainty budget of GROMOS used in the trend analysis. The red line is an example of monthly mean correlation length profile, in units of days, calculated for the time interval from October 2011 to October 2014. The magenta line is the monthly mean observation error profile, calculated for the same time interval. The blue line is the estimated instrumental error profile. And the black line represents the total contribution of the uncertainty of GROMOS.

Figure

Figure

Estimated ozone trend profile (in % decade

The estimated stratospheric trend results are able to support the evidence of
a shift toward increasing ozone in the middle and upper stratosphere at
northern midlatitudes also reported by previous studies
(

The WMO (2014, Table 2.4) reported a statistically significant
ozone increase of (3.9

Concerning
circulation changes as contributors to the stratospheric ozone increases,
recent studies have simulated changes in the Brewer–Dobson circulation (BDC)
in response to increasing greenhouse gases (

Regarding the lower mesosphere region,
our results are in agreement with recent trend estimations
(

We have constructed a harmonised ozone profile time series from GROMOS measurements since 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. Since July 2009 the spectral analysis has been done by a fast Fourier transform spectrometer. 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 20 hPa. The harmonisation has been done by taking the data set from the FFTS as a 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 index, the
quasi-biennial oscillation, the annual and semi-annual oscillation and
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 the 95 % confidence 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 (

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 timescales from 10 min to more than 20 years. The continuation in time of these measurements will help future generations to confirm findings through the intercomparison with other instruments and to understand the evolution of the ozone layer, which is extremely crucial for life on Earth.

This work was supported by the Swiss National Science Foundation under Grant 200020 – 160048 and MeteoSwiss GAW Project: “Fundamental GAW parameters measured by microwave radiometry”. Edited by: S. Godin-Beekmann