*3.4. Seasonal Dependence and Annual Mean of the Diurnal Cycle in ILW*

Figure 6 shows the absolute and the relative diurnal cycles in ILW with respect to the monthly mean. We define ΔILW in the same manner as ΔIWV as described in the subsection above. Compared to IWV, the diurnal cycle in ILW is more variable from month to month and relative amplitudes of 15 to 25% are reached especially during October, November and January. These strong diurnal cycles are connected with a break up of a cloud layer (stratus) at about 10:00 LT before noon and a relatively clear sky in the afternoon, which is consistent with our daily weather experience in Bern in late autumn and winter. The annual mean of the diurnal cycle (black dots) shows a minimum of about −10%, which occurs around noon. We suggest that this minimum is connected with the maximum evaporation or loss of cloud droplets at noon. During nighttime, a relative maximum of 9% is reached at around 03:00 LT.

Wood, R. et al. [37] reported diurnal ILW amplitudes of about 15–35% over the subtropical and tropical oceans observed by the Tropical Rainfall Measuring Mission Microwave Imager (TMI). The time of the ILW maximum is in the early morning (at 03:00 LT) and the time of the ILW minimum is at 15:00 LT, which is a bit later than for our measurements in Bern. They explain that the diurnal cycle in ILW is mainly driven by cloud solar absorption. Wood, R. [37] emphasize that the ILW measurements provide important constraints for models simulating the diurnal cycle of clouds. Snider, J.B. et al. [17] performed surface-based radiometric observations of water vapour and cloud liquid in the temperate zone and in the tropics. They found a sub-daily maximum of ILW at 05:00 LT and a minimum at 14:00 LT. The relative sub-daily variation of ILW was about 30%. In contrast with our study, Roebeling, R.A. et al. [16] reported diurnal variations in ILW values of the SEVIRI satellite experiment and ground-based microwave radiometers in France and England, which show increasing ILW values toward local solar noon.

**Figure 6.** Seasonal dependence of the diurnal cycle in ΔILW as a function of local time over Bern for the time interval 2004–2016. The upper panel shows the absolute diurnal cycle (Δ ILW = ILW − monthly mean of ILW) while the lower panel shows the relative diurnal cycle with respect to the monthly mean and in percent. The black dots indicate the annual mean of the seasonal curves.

The seasonal curves for June to August in Figure 6 show local maxima from 16:00–20:00 LT. We suggest that this effect could be due to diurnal water vapour convection during summer. This phenomenon was indicated by the increase of IWV during afternoon in Figure 5. Schlemmer, L. et al. [38] performed idealized cloud-resolving simulations for the study of mid-latitude diurnal convection over land. They found an increase of specific cloud water content from 15:00 to 21:00 LT at 2–3.5 km altitude. They explained that convection and evaporation determine the moisture content of the lower troposphere. Then, the moisture content regulates the timing and intensity of the diurnal convection.

#### *3.5. Seasonal Dependence and Annual Mean of the Diurnal Cycle in CF*

In the case of cloud fraction, we present and discuss only the diurnal variations ΔCF = CF − CF. Figure 7 shows the diurnal cycle in CF1 (thin liquid water clouds) in the upper panel and those of CF2 (thick supercooled liquid water clouds) in the lower panel. The diurnal cycle in ΔCF1 has a maximum of 2% at 10:00 LT. Generally, the sub-daily variation is less than 5%. The climatology of CF2 showed that the thick supercooled liquid water clouds mainly occur during winter. The lower panel of Figure 7 shows that the curves of December and January have a strong diurnal variation with a fast decrease of ΔCF2 at 10:00 LT. This means that the occurrence of the thick supercooled liquid water clouds is favored during the nighttime and in the morning hours until 10:00 LT. Possibly, a part of the clouds are depleted by insolation during the daytime. The amplitude of the diurnal cycle in CF2 is about 4% in December and January.

**Figure 7.** Seasonal dependence of the diurnal cycle in cloud fraction ΔCF1 (thin liquid water clouds) and ΔCF2 (supercooled thick liquid water clouds) as a function of local time over Bern for the time interval 2004–2016. The panels show ΔCF = (CF − monthly mean of CF). The black dots indicate the annual mean of the seasonal curves.

Figure 8 shows the diurnal cycle in CF3 (thick warm liquid water clouds) in the upper panel and those of CF4 (all liquid water clouds) in the lower panel. The strongest diurnal variation is found for CF3 and CF4 in October and November with deviations of about ±10% for CF4. Maximum values are reached at 07:00 LT and then a decrease starts towards the minimum, which is reached at 16:00 LT. Our daily experience with the cloud cover above Bern during autumn supports this objective measurement. Often, the clouds disappear around noon in autumn. A similar diurnal variation of cloud cover was derived by [13] from the ISCCP-C2 cloud climatology for the cloud category of maritime non-convective low-level clouds. "Maritime climate" may fit to Switzerland since it has a west coast climate and many lakes. The study of [13] showed that each cloud category has a different diurnal cycle. Min, M. and Zhang, Z. [39] presented a sinusoidal-like diurnal cycle in cloud fraction (five-year mean of SEVIRI observations over the southeast Atlantic). They found a slow 20% decrease of CF starting after sunrise and lasting until the evening.

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 [38].

The behavior of the annual mean of the diurnal cycle in Figure 8 (black dots) is a bit similar to those of ILW in Figure 6. Cloud solar absorption may explain the decrease of CF and the slightly negative values during the daytime.

**Figure 8.** Seasonal dependence of the diurnal cycle in cloud fraction ΔCF3 (warm thick liquid water clouds) and ΔCF4 (all liquid water clouds) as a function of local time over Bern for the time interval 2004–2016. The panels show ΔCF = (CF − monthly mean of CF). The black dots indicate the annual mean of the seasonal curves.

## *3.6. Seasonal Variation and Diurnal Cycle in Rain Fraction*

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/m2. At the edges of a time interval of rain, ILW increases or decreases within a short time from a small value to a high value or vice versa so that the choice of the threshold (e.g., 300, 400, or 500 g/m2) plays a marginal role for the calculation of rain fraction [32].

Figure 9a shows the seasonal variation in rain fraction which varies from about 4% in winter to about 11% in summer. Figure 9b depicts the diurnal cycle in ΔRF = RF − RF. Rain fraction is enhanced by a few percent in the late afternoon during the summer months of June and July. This diurnal cycle in rain fraction might be connected to diurnal convection and precipitation over land during summer as described by [38].

**Figure 9.** (**a**) seasonal variation in rain fraction (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. (**b**) seasonal dependence of the diurnal cycle in rain fraction ΔRF (for ILW as a function of local time over Bern for the time interval 2004–2016. The panel shows ΔRF = (RF − monthly mean of RF). The black dots indicate the annual mean of the seasonal curves.

#### **4. Conclusions**

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/m2. The sub-daily minimum of IWV is at 10:00 LT, while the maximum of IWV occurs at 19:00 LT. The relative amplitudes of the diurnal cycle in ILW are up to 25% in October, November and January, which is possibly related to a breakup of the cloud layer at 10:00 LT. The minimum of ILW occurs at 12:00 LT, possibly explained by the maximum loss of cloud droplets due to maximum insolation at noon. In the case of cloud fraction of liquid water clouds (CF4), maximum values of +10% are reached at 07:00 LT and then a decrease starts towards the minimum of −10%, which is reached at 16:00 LT in autumn. This breakup of cloud layers in the late morning and early afternoon hours during autumn seems to be typical for the weather in Bern. A similar behavior is observed for CF3 so that we conclude that mainly thick warm liquid water clouds are responsible for the described diurnal variation in autumn. Finally, the TROWARA observations show that rain fraction is enhanced in the late afternoon hours in June and July.

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.

**Acknowledgments:** 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.

**Author Contributions:** 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.

**Conflicts of Interest:** The authors declare no conflict of interest.
