Significant decline of mesospheric water vapor at the NDACC site Bern in the period 2007 to 2018

The middle atmospheric water vapor radiometer MIAWARA is located close to Bern in Zimmerwald (46.88° N, 7.46° E, 907m) and is part of the Network for the Detection of Atmospheric Composition Change (NDACC). Initially built in the year 2002, a major upgrade of the instruments spectrometer allowed to continuously measure middle atmospheric water vapor since April 2007. Thenceforward to May 2018, a time series of more than 11 years has been gathered, that makes a first trend estimate possible. For the trend estimation, a robust multi-linear parametric trend model has been used. The trend 5 model encompasses a linear term, a solar activity tracker, the El Niño–Southern Oscillation (ENSO) index, the quasi-biennial oscillation (QBO) as well as the annual and semi-annual oscillation. In the time period April 2007 to May 2018 we find a significant decline in water vapor by −0.6±0.2ppmdecade−1 between 61 and 72km. Below the stratopause level (∼ 48km) a smaller reduction of H2O of up to −0.3± 0.1ppmdecade−1 is detected.

Boulder (Colorado) since 1980. This data comes from balloon frost-point hygrometer (FPH) measurements that are launched usually once per month. A weighted, piecewise regression analysis of the 30-year record from 1980 to 2010 by Hurst et al.
(2011) revealed an average increase by 1.0 ± 0.2 ppm in the altitude range between 16 and 26 km. About a quarter of the H 2 O increase could be attributed to changes in the methane (CH 4 ) concentration. Methane can easily be transported from the surface upward into the stratosphere where its oxidation is a major in-situ source of water vapor. 10 Compared to water vapor, stratospheric ozone gathered much higher scientific attention in regard of its long-term development after the detection of the Antarctic ozone whole in 1985 (Farman et al., 1985). Two years later in 1987 the Montreal Protocol has been signed to protect the ozone layer by banning and regulating the production of numerous substances that are responsible for ozone depletion. Numerous trend studies on ozone were published in the past years (e.g. Eckert et al., 2014;Moreira et al., 2015;Steinbrecht et al., 2017;Ball et al., 2018) showing how ozone developed in the course of time. 15 Drift-corrected ozone trends from MIPAS (Michelson Interferometer for Passive Atmospheric Sounding) space-borne observations (July 2002 to April 2012) range from negative (up to −0.41 ppm decade −1 ) in the tropical stratosphere to positive (+0.55 ppm decade −1 ) at southern mid-latitudes (Eckert et al., 2014). A 20-year continuous mapping of the stratospheric ozone layer at the NDACC site Bern could be achieved. A recent trend analysis by Moreira et al. (2015) showed that ozone recovered by about 3 % decade −1 at an altitude of 40 km within the time period 1997 to 2015. Steinbrecht et al. (2017) calcu-20 lated ozone trends for larger number of ground-based NDACC site observations by different techniques such as FTIR (Fourier-Transform-Infrared-Spectrometer), microwave radiometry or lidar. They found positive trends between 35 and 48 km altitude in the tropics as well as in the the 35 to 65°latitude bands of the Northern and Southern Hemisphere. More specifically, ozone mixing ratios at 42 km increased by 1.5 (tropics) and 2-2.5 (mid-latitudes) % decade −1 , respectively. Although total column measurements of ozone show that the ozone layer stopped to decline across the globe, there is some evidence from satellite 25 observations that lower stratospheric ozone continued to decline within 60°N to 60°S after 1998, resulting in downward trend of stratospheric ozone columns (Ball et al., 2018).
In order to understand detected water vapor trends in the middle atmosphere, models and measurements are both important.
A 40-year (1960-1999) model simulation with the coupled chemistry-climate model (CCM) ECHAM resulted in a global mean stratospheric H 2 O increase by 0.7 ppm between 1980 and 1999 (Stenke and Grewe, 2005). Trend estimates in lower 30 stratospheric water vapor strongly differentiate between the NOAA (National Oceanic and Atmospheric Administration) FPH observations at Boulder and merged zonal mean satellite measurements as pointed out by Lossow et al. (2018). The differences reach up to 0.5 ppm decade −1 and change the signs from positive for the in-situ observations to negative for the processed satellite data. But not only the observations do not agree, also extensive trend estimates from simulations show discrepancies for the location of Boulder and the corresponding zonal mean latitude band around 40°N. An intercomparison of ground-35 based microwave and satellite linear trends in the lower mesosphere at an altitude of about 53 km (0.46 hPa) within different extended periods shows no consistent picture between the different observations. The following stations were considered in the study by Nedoluha et al. (2017) (Microwave Limb Sounder), SCIAMACHY (Scanning Imaging Absorption Spectrometer for Atmospheric Chartography), SMR (Sub-Millimeterwave Radiometer), SOFIE (Solar Occultation For Ice Experiment) and different data subversions of those. At none of the comparison sites a uniform result of only positive or negative trends could be retrieved. This might be related to the problem that the time periods cover different ranges. Regarding Fig. 8 in Nedoluha et al. (2017) the trends at Bern range from +16 to −5 % decade −1 . However, the majority of H 2 O time series, including Aura/MLS, exhibit small positive 10 relative trends in the range 1-7 % decade −1 . At the 0.46 hPa pressure level the multi-linear regression model used in our study does not produce a significant trend at the 95 % confidence level.
Still it is unclear how mesospheric water vapor develops in a changing climate. Therefore it is very important to continue the observations especially from those instruments that already have long records such as the microwave NDACC instruments at Mauna Loa (Hawaii),   (Kämpfer et al., 2012). Atmospheric pressure decreases exponentially with altitude and this information is reflected in the H 2 O line shape. The obtained spectra are used to retrieve water vapor profiles by means of radiative transfer calculations and the Optimal Estimation Method as described in Rodgers (2000) using the retrieval software package ARTS/qpack (Eriksson et al., 2005;Buehler et al., 2018). As spectroscopic H 2 O model a combination of 25 the H2O-MPM93 model from Liebe et al. (1993), for the pressure broadened half line width, and recent entries in the JPL (Jet Propulsion Laboratory) line catalog, for the lower state energy and line strength at 300 K, is taken. MIAWARA is continuously operated on the roof of the building for Atmospheric Remote Sensing in Zimmerwald (46.88°N, 7.46°E, 907 m a.s.l.), which is close to Bern, since September 2006. The reason why we only use data since April 2007 is a major upgrade of the instrument from optoacoustic to Fast Fourier Transform (FFT) spectrometry. In the course of this upgrade the spectral resolution increased  (Scheiben et al., 2014;Lainer et al., 2017Lainer et al., , 2018.

Measurement stability
The total spectrometer bandwidth is 1 GHz, but only a narrow part of maximal 250 MHz is in general usable in the retrieval 5 procedure due to baseline artifacts at the wings of the H 2 O spectrum. However, the reduced bandwidth is sufficient for the retrieval of water vapor in the middle atmosphere and even less is needed for the mesosphere. In order to guarantee a high stability of the spectral measurements we further constrain the bandwidth to 80 MHz around the central frequency of MIAWARA.
Changes in tropospheric opacity due to local weather variability affects the sensitive altitude region of the water vapor profile retrieval. In order to make the retrieved data independent of environmental conditions, we use a special H 2 O retrieval with a 10 variable integration time of the spectral information to reach a constant measurement noise (0.01 K) of the water vapor spectra.
Further, we set the measurement response to 80 % to derive a quite stable upper and lower limit of the measurements. This approach generates profiles with a time resolution of typically a few hours in winter and up to 1-2 days during summer.
The a priori water vapor information is derived from a monthly mean zonal mean climatology using Aura/MLS v2.2 data over 4 years between 2004 and 2008. The most recent Level2 Aura/MLS data (v.4.2) are used to initialize pressure, temperature 15 and geopotential height within the MIAWARA H 2 O retrieval. The vertical resolution of the instrument varies between 11 km in the stratosphere and 14 km in the mesosphere (Deuber et al., 2005). An instrument validation against Aura/MLS v3.3 with more than 1000 seasonal separated profile comparisons can be found in Lainer et al. (2015). An area of 800 × 400 km (E/W × N/S) has been used as spatial coincident criterion for the satellite overpasses. In the pressure range of 2-10 hPa the relative differences are below 3 % and between 0.05-2 hPa the analysis revealed negative biases of MIAWARA compared to Aura/MLS 20 of up to −10 %.
With Fig. 1 we show the overall development of the MIAWARA residuals in a bandwidth of 80 MHz. The shown residuals are defined as the difference between the observed difference spectrum and the modeled spectrum from the retrieved profile and is illustrated as residuum brightness temperature fluctuations T R . Especially measurements at lower altitudes like in the stratosphere are particularly dependent on a good baseline fitting over a broad frequency range. Overall two differnt baseline fittings are performed. A polynomial fit of fifth order and a sinus fit with 6 coefficients guarantee a stable removal of baseline 5 artefacts on our calibrated spectra.
The 3-D top plot in Fig. 1 shows Starting from autumn 2010 the T R signature changes due to a hardware and measurement cycle upgrade, that made it possible to retrieve H 2 O profiles in a higher temporal resolution while maintaining the same thermal noise level of the measured difference 10 spectrum. The upgrade of the measurement cycle had no effect on the overall homogeneity of the water vapor time series, also because the measurements were always conducted with the same FFT spectrometer. Since no critical parts of the instrument's receiver chain were replaced in the investigated time period, a thorough homogenization of the data has not been computed for this investigation. The band-like structure in the residuals is a very tiny pattern and hardly visible in a 2-dimensional plot. The pattern is likely related to temperature changes within the instrumental signal path, like microwave absorbers that are operated 15 at the ambient temperature or periodically changes in the tropospheric attenuation affecting the H 2 O line strength. However, the T R differences that make the band-structure are very small (below 1 · 10 −2 K) and will not effect the water vapor retrieval and the trend estimation.
In particular the histograms below the 3-D plot show the PDF (probability density function) of the binned (bin width: Alltogether it shows indirectly that the fitting of the baseline during the retrieval process is correct and stable.
Beside baseline artifacts which are not fitted correctly, it is known that the retrieval averaging kernels A can have an impact on the H 2 O profile product. For a long-term measurement-based trend study it is of importance that any variability of A does 25 not imply a data drift, which could induce an artificial trend. Accordingly we investigate this issue by a sensitivity trend test in Section 3.1. For the trend model it is very important to assess a reasonable uncertainty of the microwave radiometer measurements and thus the overall error of the monthly mean water vapor profiles. Two different types of errors were considered. The first type is the natural variability, which can be approximated by the standard error σ std of the monthly mean H 2 O profiles. The second type is the instrument related observational error σ obs that belongs to the random error and depends on the thermal noise on the water vapor spectra. The observational error is calculated during the retrieval computation. Both errors were then combined in 5 the following way to get a total monthly mean error profile σ tot for the initialization of the trend model:

H 2 O data and error handling
The third panel (c) of Fig. 3 shows the temporal evolution of the total error at an altitude of 70 km. At this altitude the error predominantly fluctuates around 0.3 ppm.
3 Trend model description 10 We performed the trend analyses of the water vapor data through a robust multilinear parametric trend estimation method + e · F 10.7 (t) + f · M EI(t) 20 + m=3 n=2 c n · sin 2π · t l n + d n · cos 2π · t l n where t represents the time, a and b the constant term and the slope of the fit. The sum term consists of two sine and cosine functions with the period length l n , including the annual and semi-annual oscillations (l 1 = 182.5 d and l 2 = 365 d) . All coefficients (a, b, c 1 , c 2 , c 3 , d 1 , d 2 , d 3 , e and f ) are fitted against the water vapor monthly mean time series in order to estimate the linear variations.
For the water vapor trend analyses, the multi-linear regression model needs the monthly mean profiles together with their uncertainties as input. Figure

Averaging kernel sensitivity test
Here we describe a performed test on an artificial water vapor profile time series in order to check if the variability of the MIAWARA averaging kernels can induce a data drift that might be misinterpreted as a trend. The averaging kernel matrix A is defined as It represents the sensitivity of the retrieved statex to the difference in the true atmospheric state x. The measured microwave spectrum is denoted as y. In our case we use a time series of one constant artificial H 2 O profile x art of 5 ppm at 50 pressure levels between 10 and 0.01 hPa at the same time steps as the original MIAWARA profiles werê A has to be given on the grid of x a and is interpolated to the grid of x, conserving the measurement response. The artificial 20 convolved water vapor time seriesx art (2007-04 to 2018-04) was then used to calculate monthly mean profiles that could be used as input to the trend model described in Section 3. No significant trend has been generated by the convolution process with the MIAWARA v301 averaging kernels, the retrieval version for the main trend analysis. In conclusion this means that the variability of A has no effect on the result of the trend estimate presented in Section 3.2. 25 After having shown that MIAWARA is measuring with a high instrumental stability, we are confident to present the trend result from the multi-linear parametric trend model (von Clarmann et al., 2010). Figure 4 shows the estimated water vapor trend profiles in absolute (left) and relative (right) values. The latter is calculated relative to the mean H 2 O profile between

H 2 O trend estimate
April 2007 and May 2018. Although the pressure range of the trend profile goes from 0.01 to 10 hPa in the two plots, equivalent to 30-80 km, we restrict the trustworthy trend results to the altitudes of the MIAWARA radiometer which are to a degree of 80 % 30 a priori independent. These lower and upper limits are marked by the horizontal red lines and are located at 0.03 and 2.5 hPa.
At higher and lower altitudes the trend turns towards zero which is to be expected due to the fact that the MIAWARA mixing ratios gradually approach the climatology of Aura/MLS a priori values and those exhibit no long-term variability. Further not at every pressure level between the red lines a significant trend result could be obtained. This circumstance is expressed by the dashed green boxes by encompassing two altitude regions where the trend is two times larger than the uncertainty. According to Tiao et al. (1990) this is equivalent to a significance on the 95 % confidence level.

5
Below the stratopause from 1 to 2.5 hPa (42-48 km) a small but still significant negative trend, maximizing at 2 hPa could be determined. A mean linear decline rate of −2.5 · 10 −3 ppm month −1 results in −0.3 ± 0.1 ppm decade −1 (in relative units: −4 ± 1.2 % decade −1 ) or a total loss of ≈ 0.33 ppm in the analyzed measurement period. This result is contradictory to explanations presented in North et al. (2015), where the increase of methane in the last decades is expected to also increase the water vapor content in the stratosphere by photodissociation and oxidation. On the other hand it has been pointed out, that the current  We are not able to give an explanation towards the reasons for the detected H 2 O decline below the stratopause and in the mesosphere. The complexity of interactions between dynamics and chemistry is hardly addressable by observations alone.
Numerical investigations will be needed to unravel the impacts of the different processes.
The fact that a lot of inconsistent results are published, regarding the evolution of middle atmospheric water vapor, it will be of great importance to continue with measurements from various ground-based observation sites. Although satellite missions, 5 like EOS Aura, can provide data for almost the whole globe (82°S to 82°N), however the maintenance of the long-term stability and lifetime is limited and complicates trend studies.     where the MIAWARA data is to ∼ 80 % a priori independent.