Diurnal cycle of short-term fluctuations of integrated water vapour above Switzerland

The TROpospheric WAter RAdiometer (TROWARA) continuously measures integrated water vapour (IWV) with a time resolution of 6 seconds at Bern in Switzerland. During summer, we often see that IWV has temporal fluctuations during daytime while the night-time data are without fluctuations. The data analysis is focused on the year 2010 where TROWARA has a good data quality without data gaps. We derive the spectrum of the IWV fluctuations in the period range from about 1 to 100 min. The FFT spectrum with a window size of 3 months leads to a serious underestimation of the spectral amplitudes of the 5 fluctuations. Thus, we apply a band pass filtering method to derive the amplitudes as a function of period Tp. The amplitudes are proportional to T 0.5 p . Another method is the computation of the moving standard deviation with time window lengths from about 1 to 100 min. Here, we get similar results as for the band pass filtering method. At all periods, the IWV fluctuations are strongest during summer while they are smallest during winter. We derive the diurnal variation of the short-term IWV fluctuations by applying a moving standard deviation with a window length of 10 min. The daily cycle is strongest during the 10 summer season with standard deviations up to 0.22 mm at about 14:00 CET. The diurnal cycle disappears during winter time. Using the meteorological weather station at Bern, we derive the diurnal cycle of the short-term fluctuations of the specific kinetic energy ek. Since these data have a temporal resolution of 10 min, we apply a 20 min-moving standard deviation. The derived short-term ek fluctuations can be regarded as a proxy of turbulent kinetic energy (TKE). During summer time, the 20 min-moving standard deviation of ek increases during daytime and has a similar diurnal cycle like the short-term IWV 15 fluctuations. Thus, we conclude that the diurnal cycle of the short-term IWV fluctuations is caused by turbulence associated with large convective heating during daytime in summer.


Introduction
The spatio-temporal variability of integrated water vapour (IWV) on scales of less than 10 km and hours was assessed by 20 Steinke et al. (2015) using various instruments and atmospheric numerical simulations. The model runs showed IWV variabilities of the order of 0.4 mm (or kg m −2 ) for differences in space of 3-4 km or time of 10-15 min during the presence of a boundary layer. Passive microwave radiometry can provide a high temporal resolution of 10 seconds for IWV measurements. Steinke et al. (2015) reported about standard deviations of IWV observed by microwave radiometers exceeding 1 mm even at short time scales of a few minutes. To our knowledge there are no other studies on the IWV variability at very short scales from 1 to 20 min. Since the short-term IWV fluctuations are likely connected with atmospheric waves and turbulence, we expect a seasonal and diurnal variation of the IWV variability which was not investigated by Steinke et al. (2015) and others. However, 5 Steinke et al. (2015) suggested that the short-term IWV variability at time scales of 15 min or less is induced by atmospheric turbulence which was simulated by their high-resolution model.
The TROpospheric WAter RAdiometer (TROWARA) has measured continuously integrated water vapour (IWV) with a time resolution of 6 seconds at Bern in Switzerland since 2009. In the time from 1994 to 2008 the temporal resolution was 10 seconds. Thus, it is no problem to analyse the IWV variability at Bern on time scales from 1 to 100 min as function of local 10 time and season. The short-term IWV variability is possibly connected with the growth of the atmospheric boundary layer during daytime in summer. Convective heating and associated turbulence generate variable vertical winds and circulation cells leading to a variable vertical water vapour flux during daytime. We expect that IWV can significantly change during daytime if the antenna beam of the radiometer transects an updraft or downdraft region in the lower troposphere. Numerical simulations (Stull, 1988;Yamada and Mellor, 1975) show that the turbulent kinetic energy (TKE) has a strong diurnal cycle with increases 15 of TKE from 0.05 J kg −1 at night-time to about 1 J kg −1 at daytime. The maximum occurs at a height of about 300 m above the surface. This increase of TKE is associated with the presence of a convective mixed layer during daytime reaching from the surface to 1.5 km or higher. Lüdi and Magun (2002) determined turbulence parameters in the lower troposphere by analyzing the scintillations of a microwave link between a transmitter and a receiver.
The diurnal cycle in IWV over Bern was described by Hocke et al. (2017) using hourly data of the TROWARA radiometer.

20
The diurnal cycle in IWV goes from about -0.5 mm (relative to the daily mean value) in the morning hours to about +0.5 mm during the evening hours. This IWV variation is less than 5%, and it can be assumed that the diurnal cycle in IWV has no direct influence on the diurnal cycle of short-term IWV variability. Nevertheless, the diurnal cycle in IWV can be understood as a residual upward flux of tropospheric water vapour during daytime so that the accumulation of IWV achieves a maximum in the evening hours.  the observations. Generally, vertical profiles of specific humidity or relative humidity can be used to determine the height of the atmospheric boundary layer as described by Seidel et al. (2010). The boundary layer is assumed to be moister than the free troposphere so that the vertical gradient of humidity becomes minimal (extreme) at the height level of the atmospheric boundary layer. This vertical gradient method of humidity also shows that there is a connection between IWV and the moist boundary layer.

35
The aim of the present study is to give mean values of the amplitudes of the short-term IWV fluctuations in the period range from 1 to 100 min. These mean values may guide modeling studies about water vapour convection and circulation cells in the lower troposphere. Further, we derive the dependence of the short-term IWV variability on the season and the local time.
Section 2 describes the TROWARA radiometer and the weather station of the University of Bern. Section 3 explains the data analysis to obtain the amplitudes or the moving standard deviation of the IWV variability. Section 4 presents the results on 5 the short-term IWV variability and the standard deviation of the specific kinetic energy where the latter is derived from the horizontal wind speed measurements of the weather station. Concluding remarks are given in section 5.

TROWARA
Our study is focused on the IWV observations of the TROpospheric WAter RAdiometer (TROWARA). TROWARA is a dual-10 channel microwave radiometer, and its design and construction were described by Peter and Kämpfer (1992) and Morland (2002). Two ferrite circulator switches at each frequency channel of the radiometer perform the change from the antenna to the noise diodes. The noise diodes serve as hot and cold reference loads. The developed radiometer model considers the measurements of the reflection and transmission coefficients of all radiometer components including the ferrite switches (Morland, 2002). In addition, a tipping curve calibration is performed by using the variable brightness temperature of the clear sky at 15 different elevation angles of the antenna. The instrument is very stable so that the tipping curve calibration is only required 2 or 3 times per year.
TROWARA measures the vertically-integrated water vapour (IWV) which is also known as precipitable water vapour. Further, TROWARA provides the vertically-integrated cloud liquid water (ILW), also known as liquid water path. The instrument is operated inside a temperature-controlled room on the roof of the building for Exakte Wissenschaften (EXWI) of the University 20 of Bern (46.95 • N, 7.44 • E, 575 m a.s.l.). The antenna receives the atmospheric radiation inside the room through a microwave transparent window. This indoor operation of TROWARA allows the measurement of IWV even during rainy periods.
The antenna beam of TROWARA has a full width at half power of 4 • and is pointing the sky at an zenith angle of 50 • towards south-east. At 1 km above surface, the horizontal diameter of the sounding volume of TROWARA is about 170 m. The view direction is constant, so that short-term temporal variations of the brightness temperature, IWV and ILW are well monitored 25 with a time resolution of 6 seconds. TROWARA's IWV measurement has nearly all-weather capability during day and nighttime. The ILW measurement cannot be carried out in presence of rain droplets. Thus, the ILW measurement is restricted to cloud droplets (ILW < 0.4 mm). Details of the TROWARA instrument and the retrieval technique are provided by Cossu et al. (2015) and Mätzler and Morland (2009).
In the following, we briefly explain the measurement principle and the retrieval. The microwave channel of TROWARA at The radiative transfer equation of a non-scattering atmosphere is where τ i is the opacity of the i-th frequency channel (e.g., 21 GHz) along the line of sight of the radiometer. T B,i is the 5 observed brightness temperature, and T c is the brightness temperature of the cosmic microwave background. T mean,i denotes the effective mean temperature of the troposphere (Ingold et al., 1998;Mätzler and Morland, 2009).
The equation 1 can be solved for the opacities where the TROWARA observations yield the radiances T B,i .

10
In a plane-parallel atmosphere, the opacity is linearly related to IWV and ILW where the coefficients a and b partly depend on air pressure. Mätzler and Morland (2009)

20
(2017) analysed diurnal cycles in IWV, ILW and cloud fraction by using all informations of TROWARA which also has an infrared radiometer channel at 9.5 -11.5 µm. The present study only uses the IWV measurements of the year 2010 when the performance of TROWARA was very good.

Weather station
The weather station is located on the roof of the building Exakte Wissenschaften of the University of Bern. The coordinates

Results and discussion
The main effect investigated in the present study is that short-term IWV fluctuations occur at daytime in summer (June -August) while they disappear at night. Figure 1a shows a convective cloud system which appears near to Bern in the afternoon of 28 June 2010. We assume that water vapour convection, turbulence and convection cells induce the short-term fluctuations of IWV. Figure    Another method to characterize the IWV fluctuations is the moving standard deviation with a variable time window length.
The time window length is a bit similar to the period. The four seasonal spectra of the standard deviation SD are shown as function of the time window length in Fig. 4. Using the SD method, we find a similar power law P ∼ f −1 as indicated by the magenta line. The SD values in Fig. 4 are about two times larger than the amplitude values in Fig. 3. In the following, we only present results derived by the SD method. The SD values in Fig. 4 are in a good agreement with those of Fig. 8 in Steinke et al. 5 (2015). The weather station at University of Bern is used to investigate if the diurnal variation of SD of IWV is related to the diurnal cycle of the short-term fluctuations of specific kinetic energy e k . Such a relationship is likely since the heating of the Earth's surface during daytime in summer, leads to increased turbulence, convection, and upward water vapour flux during daytime.
The increased water vapour flux is possibly associated with short-term IWV fluctuations observed by TROWARA.
We derive e k by assuming e k (t) ∼ 0.5(u(t) 2 +v(t) 2 ) where we neglect the small vertical wind component since the weather 15 station measures the horizontal wind speed. The moving standard deviation of e k is computed with a time window of 20 min. Figure 6 shows the results. It is obvious that the curves have their daily maxima in the afternoon hours around 14:00 CET. In so far, the short-term fluctuations of specific kinetic energy e k might be the cause for the diurnal cycle of the IWV fluctuations.
It is obvious that the spring curve (red) is larger than the summer curve (black) in Fig. 6. This effect can be due to stronger advection in spring than in summer. We can show that the specific kinetic energy is larger during the spring months than during 20 the summer months. Figure 7 shows the climatologies of e k and SD of e k which are maximal during the spring months. This is in agreement with the order of curves in Fig. 6. However, since the annual maximum of IWV is in the summer months, the maximal water vapour convection occurs during summer and not during spring. The daily cycle of the short-term fluctuations of e k explains the daily cycle of the short-term IWV fluctuations.

25
During summer, we often see that IWV has temporal fluctuations during daytime while the night-time data are without fluctuations. We derive the spectrum of the IWV fluctuations in the period range from about 1 to 100 min. The FFT spectrum with a window size of 3 months leads to a serious underestimation of the spectral amplitudes of the fluctuations. Thus, we apply a band pass filtering method to derive the amplitudes as a function of period T p . The amplitudes are proportional to T 0.5 p corresponding to a power law P ∼ f −1 where f is the frequency. Another method is the computation of the moving standard 30 deviation (SD) with time window lengths from about 1 to 100 min. Here, we get similar results as for the band pass filtering method. At all periods, the IWV fluctuations are strongest during summer while they are smallest during winter. However, the mean SD value is smaller than 0.5 mm for time window lengths less than 90 min. We derive the diurnal variation of the short-term IWV fluctuations by applying a moving standard deviation with a window length of 10 min. The daily cycle is strongest during the summer season with standard deviations up to 0.22 mm at about 14:00 CET. The diurnal cycle disappears during winter time. Using the meteorological weather station at Bern, we derive the diurnal cycle of the short-term fluctuations of the specific kinetic energy e k . Since these data have a temporal resolution of 10 min, we apply a 20 min-moving standard deviation. The derived short-term e k fluctuations can be regarded as a proxy of turbulent kinetic energy (TKE). During summer, 5 the 20 min-moving standard deviation of e k increases during daytime and has a similar diurnal cycle like the short-term IWV fluctuations. Thus, we conclude that the diurnal cycle of the short-term IWV fluctuations is caused by turbulence associated with large convective heating during daytime in summer. The observed behaviour of the short-term IWV fluctuations is useful for modeling studies on water vapour convection in the atmospheric boundary layer. Day ticks are at 0:00 UT.