We present the analysis of annual average OH

We perform a multiple linear regression using the solar radio flux
F10.7

The mesopause of the Earth is one of the most variable regions in the
atmosphere. There are numerous different influences such as the solar
radiation and different types of waves (e.g. tides, planetary waves, gravity
waves) that affect the temperature in this region. Thus, the temperature
undergoes large variations on very different timescales from minutes to
years. The largest variation observed in temperature is the variation in
1 year. This seasonal variation is characterised by an annual, a
semi-annual, and a ter-annual component

Beside these variations of the mesopause temperature,

Because of this large number of influences and possible interactions the
analysis of the temperatures is not easy to interpret, but due to the
different timescales of the variations the different types of influences and
phenomena can sometimes be distinguished. In this paper we focus on the long-term
variations of the mesopause temperature on timescales larger than
10 years. We use OH

The paper is structured as follows. In Sect.

OH

Excited hydroxyl (OH

At the beginning of 2011 a newly built instrument was operated next to the
GRIPS-II instrument. Simultaneous measurements conducted over a few months
showed no significant differences between the two instruments. Unfortunately
a detector failure stopped the GRIPS-II measurements in mid-2011, but the new
instrument was able to continue the time series of nightly OH

The nightly average OH

By far the largest variation in this temperature series is the variation over
the course of a year. In order to evaluate the data with respect to long-term
dynamics with periods well above 1 year the seasonal variation has to be
eliminated first. Since the temperature series exhibits data gaps mostly due
to cloudy conditions, a simple arithmetic mean for each year is not
advisable. We follow the method used before in several analyses

GRIPS-II nightly average temperatures of 2009 plotted at the day of
year (DOY). The measurement data are shown in black and the harmonic fit
using Eq. (

Since there is a data gap of two years (2012–2013) in the GRIPS-II and
GRIPS-N measurements in Wuppertal and the last data points are derived from
measurements by a new instrument, one has to ensure that the

OH

Figure

The linear increase for each time series is shown in
Fig.

The latest analysis of the OH

Analysing periodicities in the time series of

An important quantity for the interpretation of a LSP is the so called false
alarm probability (FAP). The FAP gives the probability that a peak of height

Distribution for peak heights

Monthly average values of the solar radio flux F10.7 cm. The red dots mark the annual average values corresponding to the times of the GRIPS data points. The data were provided by Natural Resources Canada, Space Weather Canada.

We analyse the long-term trend and the correlation with the 11-year cycle in solar activity by means of a multiple
linear regression. For this and the following analyses the time coordinate is shifted such as the first data point (1988.5)
is set to zero. The annual average temperatures are described by

The upper panel of the figure shows the time series of annual
average OH

The obvious differences between fit and data series can also be seen in the
LSPs in Fig.

The Lomb–Scargle periodogram for the time series of annual OH

Residual for the temperature time series after removing the 11-year
solar cycle
(

The trend break and the correlation with the 11-year solar cycle are analysed
by describing the annual average temperatures as

Thus, Eq. (

We determine the best estimates for the parameters

The Lomb–Scargle periodogram for the time series of annual OH

We analyse the possibility of an oscillation instead of a trend break.
In order to get an idea about the oscillation we fit a
sinusoid of the form

The upper panel of the figure shows the time series of annual
average OH

Very prominent is the fact that the oscillation has a period of about 26
years with a minimum at about 2006 and a maximum at about 1993. This type of
oscillation with very similar parameters can be found on the sun. The
original solar cycle (Hale cycle) is a cycle with a period of about 22 years
and describes the reversal of the magnetic field of the sun. The solar polar
magnetic field of the sun is shown in
Fig.

The long periodic oscillation describes the largest part of the temperature
variability after detrending the temperature series with respect to the
11-year solar cycle. Thus, we analyse the temperature series

The Lomb–Scargle periodogram for the time series of annual OH

The upper panel of the figure shows the time series of annual
average OH

We analyse this possibility and add an oscillation to the temperature
description, which replaces the solar polar magnetic field. Since the
oscillation and the 11-year solar cycle are non-orthogonal functions, here we fit
all dependencies simultaneously. The equation transforms to

The Lomb–Scargle periodogram for the time series of annual OH

The upper panel shows the sensitivity to the solar activity derived
for different 11-year time intervals. All values are displayed at the middle
of the corresponding time interval. The error bars show the 1

In the former sections a constant sensitivity to the solar activity for the
complete observations was assumed. In order to study whether this assumption is
correct and the oscillation derived in Sect.

The results of the analysis are shown in Fig.

The lower panel of Fig.

There are numerous publications about the correlation of the 11-year cycle of
solar activity and temperatures in the mesopause region. A review is given by

Besides the fact that the derived values are in the expected range for the
northern middle to high latitudes, one new aspect with respect to the
correlation between 11-year solar cycle and mesopause temperatures has become
apparent. In the present study the correlation was determined for three solar
maxima including the comparably weak latest solar cycle 24. Our study shows
that the significant correlation between OH

Temperature trends in the mesopause region are reported in a number of
papers, and a review about numerous results is given by

The observed trend break can also be described using a long periodic
oscillation. In Sect.

Firstly, the solar polar magnetic field (Hale cycle) is used as one parameter
in a multiple linear regression with the second parameter being the solar
radio flux. The correlation coefficients are

Secondly, an independent oscillation is used to describe the OH

25-year oscillation of OH

The most important point here is that no additional linear trend can be
maintained. All long-term dynamics of the Wuppertal OH

The analysis by using different 11-year time intervals leads to two main
results. Firstly, the sensitivity to the solar activity is fairly stable
throughout the whole time period 1988–2015. There are some variations in
sensitivity but considering the uncertainties there are no significant
changes. The mean of the derived values is
(3.9

Secondly, the derived partial trend values show the same oscillation as the
derivative of the 25-year temperature oscillation. Thus, the analysis using
the 11-year time intervals confirms the result that, besides the 11-year solar
cycle, an oscillation of about 25 years is the second important component of
the OH

We present the analysis of the OH

The OH

One linear trend during the whole time interval (together with the sensitivity to the 11-year solar cycle) cannot
sufficiently explain all long-term dynamics found in the OH

The reversal of the temperature trend can also be described by a long periodic oscillation.
We present two possibilities
for this oscillation. Firstly, the solar polar magnetic field of the sun (Hale cycle) is used in a multiple linear
regression together with the solar radio flux as second parameter. The derived regression coefficients are

Caution has to be applied when estimating linear trends from data sets containing long-term variations. Trend results are quite sensitive to the length of the data interval used. In such a case a piecewise linear trend approach has to be used or the long-term variation has to be described in another appropriate way, e.g. by using an oscillation.

The GRIPS data used in this study can be obtained by request to the
corresponding author or to P. Knieling (knieling@uni-wuppertal.de). The
monthly average values of the solar radio flux F10.7 cm were provided by
Natural Resources Canada (Space Weather Canada) and were obtained from

This work was funded by the German Federal Ministry of Education and Research
(BMBF) within the ROMIC (Role Of the Middle atmosphere In Climate) project
MALODY (Middle Atmosphere LOng period DYnamics) under Grant no. 01LG1207A.
Wilcox Solar Observatory data used in this study was obtained via the web
site