*2.1. The Microwave Radiometer TROWARA*

Observations of the TROpospheric WAter RAdiometer (TROWARA) are central to our study. Peter, R. et al. [19,20] described the design and the construction of the TROWARA instrument, which is a dual-channel microwave radiometer. Two ferrite circulator switches at each frequency switch between the antenna and noise diodes where the latter are taken as hot and cold reference loads. A radiometer model was developed based on measurements of the reflection and transmission coefficients of all radiometer components up to and including the ferrite switches [20]. Tipping calibrations are carried out with an external mirror in order to correct the sky brightness temperature calculated by the model. The instrument is sufficiently stable that a tipping calibration is only necessary once every few weeks.

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◦N, 7.44◦E, 575 m a.s.l.). The indoor operation of TROWARA permits the measurement of IWV even during rainy periods. TROWARA's antenna receives the atmospheric radiation through a microwave transparent window and is pointing the sky at a zenith angle of 50◦ towards the southeast.

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

$$T\_{B,i} = T\_c e^{-\tau\_i} + T\_{man,i}(1 - e^{-\tau\_i}),\tag{1}$$

where *TB*,*<sup>i</sup>* is the observed brightness temperature of the *i*-th frequency channel (e.g., 21 GHz). *τ<sup>i</sup>* is the opacity along the line of sight of the radiometer, and *Tc* is the contribution of the cosmic microwave background. The effective mean temperature of the troposphere is given by *Tmean*,*<sup>i</sup>* [21,22].

Equation (1) leads to the opacities

$$\tau\_{i} = -\ln\left(\frac{T\_{B,i} - T\_{mcam,i}}{T\_c - T\_{mean,i}}\right),\tag{2}$$

where the radiances *TB*,*<sup>i</sup>* are observed by TROWARA.

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

$$
\pi\_i = a\_i^{\prime\prime} + b\_i^{\prime\prime} \text{IV} \mathcal{V} \mathcal{V} + c\_i^{\prime\prime} \text{II} \mathcal{W}\_{\prime} \tag{3}
$$

where the coefficients *a* and *b* are not really constant since they can partly depend on air pressure. As shown by [22], the coefficients can be statistically derived by means of coincident measurements of radiosondes and fine-tuned at times of periods with a clear atmosphere. The coefficient *c* is the mass absorption coefficient of cloud water. It depends on temperature (and frequency), but not on pressure. It is derived from the physical expression of Rayleigh absorption by clouds [22]. Once the coefficients are determined, combined opacity measurements at 21 and 31 GHz permit the retrieval of IWV and ILW from Equation (3). Thus, a dual channel microwave radiometer can monitor IWV and ILW with a time resolution of 6–11 s and nearly all-weather capability during daytime and nighttime.

The physical temperature at the cloud base is derived for optically thick clouds (ILW > 30 g/m2) from measurements of an infrared radiometer channel at a wavelength of *λ* = 9.5–11.5 μm. The narrowband infrared radiometer is a Heitronics KT15.85D pyrometer of type A, which

was calibrated by the manufactor for the signal temperature range from −100 to +100 ◦C [23]. Temperature resolution, filter curve, view of field, radiometer model at low temperatures and other characteristics of the Heitronics KT15.85D are described in [23]. The temperature resolution is less than 2 ◦C for target temperatures from −100 to +100 ◦C and a response time of 1 s.

The antenna coil of TROWARA has a full width at half power of 4◦ and is pointing the sky at a zenith angle of 50 ◦ towards the southeast. The view direction is constant, and the microwave and infrared channels of TROWARA observe the short-term temporal variations of the brightness temperature in the same volume of the atmosphere. This contributes to the high sensitivity of TROWARA for cloud detection. Cossu, F., Mätzler, C. and Morland, J. [22,24] give further details of the sensors and the retrieval technique.

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. [24] determined the instrumental noise *σnoise* = 0.77 g/m<sup>2</sup> of TROWARA from the noise of ILW during 245 days in which the sky was free of clouds. We emphasize that this is a remarkable sensitivity for a microwave radiometer. If an ILW value exceeds the 3*σnoise* level, then we are confident by 99.7% that the ILW value was generated by a cloud and not by instrumental noise. Thus, ILW > 3*σnoise* = 2.3 g/m2 is the criterion for the existence of a cloud. In contrast to the ILW series, the time series of IWV have been used since 1994 for trend analyses [25,26].

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<sup>2</sup> and the total observation time. The high spatio-temporal variability of clouds floating through the fixed line-of-sight of TROWARA requires a high temporal resolution of about 10 s for the cloud flag. CF for different categories of liquid water clouds were derived by [27] using the TROWARA measurements. TROWARA's coincident ILW and infrared brightness temperature measurements allow separation of the liquid water clouds into four categories:


Quite similar criteria for the separation of supercooled liquid water clouds were described by [28]. The critical point is that the derived cloud distributions are possibly biased towards the low level clouds since the infrared channel mainly sees the cloud base of thick clouds. Mätzler, C. et al. [29] avoided this bias by using additional satellite data for the cloud-top temperature.

Hirsch, E. et al. [30] determined the microphysical and optical properties of thin liquid water clouds and emphasized that these clouds should be considered in climate studies since they are frequent and they change the radiative forcing of the climate system. Measurements indicated that the downwelling infrared radiance of a thin liquid water cloud is about 60% greater than that of clear sky. Thin liquid water cloud areas often occur at the edges of and in the inter-region between clouds (*twilight* zone of clouds).

Since TROWARA is not sensitive to ice clouds, CF of TROWARA is in general smaller than that of synoptic observations. Cossu, F. [24] found a CF difference of about 17% between TROWARA and synoptic observations in the same region over a period of six years. In addition, TROWARA may not see some of the very thin and tenuous clouds that are still visible by the naked eye.

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 *thin* and *thick* refer to the magnitude of the optical depth at microwave frequencies that are proportional to the liquid water path. The terms should not be misunderstood by the geometrical thickness of the clouds, which is not measured by the microwave radiometer. A statistical cloud type study was performed by [31] for Payerne. Payerne is representative for Bern since Payerne is located just 40 km west of Bern in the Swiss plateau. About 38% of the clouds classified by a sky camera have the type Sc (stratocumulus), while 17% are cirrus-cirrostratus (Cr-Cs) and 12% are cirrocumulus-altocumulus (Cc-Ac). Bernet, L. et al. [31] also found that the relationship between the ILW value and the cloud type is ambiguous. Cumulus and cirriform clouds generally have a small ILW, but no tendency for stratiform clouds was found.
