Current address: K. Hocke, IAP, University of Bern, Sidlerstr. 5, CH-3012 Bern, Germany

The TROpospheric WAter RAdiometer (TROWARA) is a ground-based microwave radiometer with an additional infrared channel observing atmospheric water parameters in Bern, Switzerland. TROWARA measures with nearly all-weather capability during day- and nighttime with a high temporal resolution (about 10 s). Using the almost complete data set from 2004 to 2016, we derive and discuss the diurnal cycles in cloud fraction (CF), integrated liquid water (ILW) and integrated water vapour (IWV) for different seasons and the annual mean. The amplitude of the mean diurnal cycle in IWV is 0.41 kg/m

Clouds and aerosols continue to contribute the largest uncertainty to estimates and interpretations of the Earth’s changing energy budget [

The physical description of clouds involves microphysics and nonlinear radiative-dynamic processes over temporal scales from about 1 s to 1 decade and spatial scales from about 1 m to 1000 km. Observing and modelling of the Earth’s cloud distribution is still a challenge, even though large efforts have been undertaken in meteorology, atmospheric research, and climate sciences [

In the following, we focus on the diurnal cycle in integrated liquid water (or liquid water path). Two research communities are active in investigating the diurnal variation of cloud liquid water (ILW). The first group are scientists who generate world maps of cloud coverage, outgoing radiation, and rainfall data from polar-orbiting satellites imaging the Earth in the ultraviolet, visible, infrared, and microwave range [

There is no doubt that weather forecast and regional climate projections will not be correct if a fundamental process such as cloud formation and its diurnal variation is incorrectly simulated by the numerical model. Bergman, J.W. et al. [

There are only a few studies investigating the diurnal variation in ILW by means of ground-based microwave radiometers. This is rather surprising since ground-based microwave radiometers are well suited for the continuous measurement of ILW during the daytime and nighttime in all seasons. Thus, data sets of microwave radiometers are convenient for intercomparisons with results from polar-orbiting satellites, other ground-based instruments (e.g., lidar), and models. A review of meteorological applications of ground-based microwave and millimeter wavelength radiometry was given by [

Ground-based microwave radiometers are well suited for measurement of the diurnal cycle in atmospheric water parameters. We suggest that modellers and observers should take more advantage of ground-based microwave radiometers for research and validation studies of the diurnal cycle in ILW. Here, we analyse the long-term time series of integrated liquid water, integrated water vapour, and cloud fraction observed by the TROWARA radiometer, which is located in Bern on the Swiss Plateau.

Observations of the TROpospheric WAter RAdiometer (TROWARA) are central to our study. Peter, R. et al. [

TROWARA provides the vertically-integrated water vapour (IWV) and vertically-integrated cloud liquid water (ILW), also known as liquid water path (LWP). TROWARA is operated inside a temperature-controlled room on the roof of the EXWI building of the University of Bern (46.95

The two microwave channels are at 21.4 GHz (bandwidth 100 MHz) and 31.5 GHz (bandwidth 200 MHz). The 21.4 GHz frequency is more sensitive to microwaves from water vapour, and the 31.5 GHz frequency is more sensitive to microwaves from atmospheric liquid water.

The radiative transfer equation of a non-scattering atmosphere can be expressed as

Equation (

For a plane-parallel atmosphere, the opacity is linearly related to IWV and ILW

The physical temperature at the cloud base is derived for optically thick clouds (ILW

The antenna coil of TROWARA has a full width at half power of 4

TROWARA delivered an almost uninterrupted time series of ILW since 2004, with a time resolution of 11 s until end of 2009 and 6 s afterwards. Clouds are detected in the line of sight of TROWARA with the time resolution of the ILW series. Cossu, F. [

CF (cloud fraction) is easily determined in the time domain—for example, CF is the quotient of the time intervals when ILW > 2.3 g/m

CF1: thin liquid water clouds (2.3 g/m

CF2: thick supercooled liquid water clouds (ILW > 30 g/m

CF3: thick warm liquid water clouds (ILW > 30 g/m

CF4: all liquid water clouds (ILW

Quite similar criteria for the separation of supercooled liquid water clouds were described by [

Hirsch, E. et al. [

Since TROWARA is not sensitive to ice clouds, CF of TROWARA is in general smaller than that of synoptic observations. Cossu, F. [

The present study is not a cloud type study that would require the evaluation of coincident observations by ceilometer, lidar, radiosonde and hemispherical sky camera. In our study, the terms

Hourly means of IWV, ILW, CF1, CF2, CF3 and CF4 were obtained by averaging of the 10 s sampling data. An upper threshold of 400 g/m

The arithmetic mean is removed from the time series of IWV, ILW or CF. Then, the Fast Fourier Transform (FFT) power spectra are obtained by folding these time series with a Hamming window and by applying zero padding at the beginning and end of the time series. The FFT power spectra are normalized by the power of the strongest spectral component, which is either the annual or the semi-annual oscillation.

Next, we derive amplitude spectra by means of bandpass filtering. The time series are filtered with a digital non-recursive, finite impulse response (FIR) bandpass filter performing zero-phase filtering by processing the time series in forward and reverse directions. The number of filter coefficients corresponds to a time window of three times the central period, and a Hamming window has been selected for the filter. Thus, the bandpass filter has a fast response time to temporal changes in the data series. The variable choice of the filter order permits the analysis of wave trains with a resolution that matches their scale. The bandpass cutoff frequencies are at

Climatologies of the time series are obtained by sorting the data for the month and taking the mean and the standard deviation. The mean diurnal cycles are obtained by sorting the data for the month and the hour of the day (in local time). Again, the arithmetic means of the sorted ensembles are taken. In order to intercompare the seasonal curves, we subtract the monthly mean values.

We evaluated in total about 48 million samples of TROWARA measurements from 2004 to 2016 (sampling rates are between 6 and 11 s). The number of samples of IWV or ILW is about 48 million. The number of samples with cloud occurrence (group CF4) is about 24 million. The number of samples of the group CF1 is about 7 million. The number of samples of CF2 is 6 million, and the number of samples of CF3 is about 10 million. The number of samples of rain (ILW

The climatologies of IWV, ILW, CF1, CF2, CF3 and CF4 above Bern from 2004 to 2016 are shown in

The normalized FFT power spectra of the complete time series of fluctuations provide information on the occurrence and the strength of the diurnal and semi-diurnal cycles with respect to the annual oscillation. Only in the case of ILW, the semi-annual oscillation is stronger than the annual oscillation, and so we normalize ILW by the power of the semi-annual oscillation. The FFT power spectra mainly provide information on the phase-locked fluctuations, e.g., phase-locked to the daily or annual cycle of solar radiation. Thus, many intermittent short-term fluctuations may average out by taking the spectrum over the time interval 2004–2016. This is the reason why we show next the amplitude spectrum obtained by a wavelet-method.

The amplitudes of the diurnal and semidiurnal oscillation in IWV are known to 5

In the case of ILW, we see a peak of the diurnal cycles that is rather close to those of the semi-annual oscillation, which is the dominant oscillation. There are several other significant oscillations with peaks closely above the red line, e.g., the semi-diurnal oscillation. In the cases of CF1, CF2, CF3 and CF4, we find significant diurnal cycles. The semi-diurnal cycle is well present for CF2 and CF4.

As a supplement to the FFT power spectra, we derive amplitude spectra by means of the fast response bandpass filter that takes care of phase-unlocked oscillations, which may persist only about time intervals of a few wave periods.

Morland, J. et al. [

Analyzing a GPS ground station network in Spain, Ortiz de Galisteo, J.P. et al. [

Ortiz de Galisteo, J.P. et al. [

Dai, A. et al. [

Wood, R. et al. [

The seasonal curves for June to August in

In the case of cloud fraction, we present and discuss only the diurnal variations

In the case of CF3 in June, there seems to be an increase in the late afternoon, which might be connected to diurnal convection and cloud formation as described by [

The behavior of the annual mean of the diurnal cycle in

Analogously to cloud fraction, one can define rain fraction (RF), which is a measure of the occurrence of rain droplets in the measurements of TROWARA. Here, rain or rain droplets occur if the ILW measurements of TROWARA are greater than or equal to 400 g/m

The TROpospheric WAter RAdiometer (TROWARA) continuously measured cloud fraction (CF), integrated liquid water (ILW) and integrated water vapour (IWV) in Bern in Switzerland from 2004 to 2016. For our study, we derived hourly means from the TROWARA data sampled every 10 s. We presented and discussed the diurnal cycles in cloud fraction (CF), integrated liquid water (ILW) and integrated water vapour (IWV) for different seasons and the annual mean. Furthermore, we divided CF into four categories: thin liquid water clouds (CF1), thick supercooled liquid water clouds (CF2), thick warm liquid water clouds (CF3) and all liquid water clouds (CF4).

The amplitude of the mean diurnal cycle in IWV is 0.41 kg/m

The study showed that long-term measurements of a microwave radiometer equipped with an additional infrared channel objectively provide information on the diurnal cycle in six atmospheric water parameters. This information is of great interest for cross-validations with satellite data, high-resolution reanalyses and model simulations.

The study was supported by Swiss National Science Foundation under Grant No. 200021-165516. We are grateful to all technicians and scientists of the Institute of Applied Physics for designing, building and operating the TROWARA instrument over the last two decades. We thank the reviewers for valuable comments and corrections.

Klemens Hocke carried out the spectral analysis. Francisco Navas-Guzmán and Christian Mätzler took care of the radiometer. All authors contributed to the interpretation of the data set.

The authors declare no conflict of interest.

Number of samples of integrated water vapour (IWV), rain (ILW

Climatologies of integrated water vapour (IWV), integrated liquid water (ILW) and cloud fraction (CF) of four cloud categories (defined in the text) observed by the TROWARA radiometer in Bern from 2004 to 2016. The error bars indicate the standard deviation of the monthly mean from year to year.

Fast Fourier Transform (FFT) power spectra (blue line) of the temporal fluctuations of IWV, ILW and CF in Bern for the time interval from 2004 to 2016. The spectra are normalized by the power of the maximum (power of the annual or semi-annual oscillation). The yellow line is the mean of the spectrum averaged over 1000 frequency grid points. The red line is the five sigma level of confidence. A significant diurnal cycle shows up as a blue spike at 1 cycle/day in each parameter. A significant semidiurnal cycle (at 2 cycles/day) is present for IWV and CF4.

Amplitude spectra of IWV, ILW and CF over Bern for the time interval 2004–2016 obtained by a fast response bandpass filter. The red line marks the position of the diurnal cycle. The short-term variability of fluctuations with periods <10 days is high for ILW and CF.

Seasonal dependence of the diurnal cycle in

Seasonal dependence of the diurnal cycle in

Seasonal dependence of the diurnal cycle in cloud fraction

Seasonal dependence of the diurnal cycle in cloud fraction

(