**1. Introduction**

Clouds and aerosols continue to contribute the largest uncertainty to estimates and interpretations of the Earth's changing energy budget [1]. There is a consensus in the climate research community that man-made global warming is amplified by an increase of water vapour in a warmer world [2]. The Earth's radiation budget between the incoming short-wave radiation of the Sun and the outgoing longwave radiation of the Earth is strongly influenced by the spatio-temporal distribution of clouds. Differing assumptions about how the Earth's cloud distribution is maintained for doubling of the CO2 concentration in the atmosphere lead to estimated increases of global mean surface temperature in the range from 1.5 to 4.5 ◦C [2].

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 [3,4]. Diurnal variations in atmospheric water parameters are of high interest for measurement and

atmospheric modelling since one day is the shortest regular period by which the Earth's surface and atmosphere absorb energy from the Sun. Cloud formation and rainfall depend on orography and land-sea contrast [5]. The phase of the diurnal variation can change significantly within a small horizontal distance. Parameterisation of cloud formation and rainfall is difficult since these phenomena depend for example on the variable surface flux of moisture, orography, convective processes, turbulence, eddies and the growth of the planetary boundary layer during the daytime

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 [5–9]. Since the diurnal variations of cloud parameters and rainfall have strong amplitudes of about 10% or larger, construction of world maps and climatic trend analyses of cloud parameters from satellite observations have to correct for offsets caused by a varying local solar time at the observation places. The second group are atmospheric modellers who use the periodic signal of the diurnal cycle in atmospheric water to test the quality of weather and climate models. The models often provide incorrect phases and amplitudes of the diurnal variations of rainfall, cloud cover and ILW reflecting errors in the parameterization of clouds, convective processes, surface moisture flux, and microphysics [10,11].

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. [12] analysed that the cloud diurnal contribution to time-average surface energetics is as much as 20 W m−<sup>2</sup> in a regional climate (Amazon basin) after deforestation, which caused a shift from a high cloud distribution to a low cloud distribution. Cross-validation studies fostered the progress in remote sensing, data analysis, and modelling. Observed and simulated diurnal variations were compared [9,13]. Numerous cross-validations were organized within the Global Energy and Water Experiment (GEWEX) and the International Satellite Cloud Climatology project (ISCCP) [14].

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 [15]. Roebeling, R.A. et al. [16] compared the diurnal variation in liquid water path derived from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) on board Meteosat-8 with those observed by two ground-based microwave radiometers of the CloudNET in northern Europe and found a good agreement. Snider, J.B. et al. [17] presented diurnal variations in IWV and ILW observed with ground-based microwave radiometers operating near 20, 23, 31, and 90 GHz. Cross-validation with coincident measurements of infrared brightness temperature of the sky confirmed the diurnal variations in ILW obtained by microwave radiometers. In addition, the observed diurnal variations in ILW are in a qualitative agreement with expectations from theory and satellite observations that a maximum of cloud liquid water occurs before sunrise in oceanic areas during summer [9]. Model simulations by [18] showed quite similar shapes of the diurnal cycles in CF and ILW for marine boundary layer clouds with a maximum at 06:00 LT and a minimum at 18:00 LT.

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. Section 2 describes the instrument and the measurement technique as well as the data analysis. Section 3 shows the climatology of IWV, ILW and CF averaged over the time interval 2004–2016. Furthermore, we discuss the results from the spectral data analysis of the time series. Section 3 also presents the diurnal cycles in IWV, ILW and CF. Conclusions are given in Section 4.
