*2.2. Data Analysis*

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/m2 is used for ILW. This means that, in the presence of rain droplets, we take the value 400 g/m<sup>2</sup> as an estimate of the ILW of the cloud droplets. During precipitation, TROWARA overestimates ILW of the cloud droplets because of the strong microwave emission from the rain droplets (*d* > 0.2 mm). This is the reason why we take an upper threshold of 400 g/m<sup>2</sup> for vertically integrated cloud liquid water path during rainy periods. Generally, the results are not sensitive to the choice of the threshold as it was investigated by [32]. Furthermore, the rain periods are a small fraction of about 7% of the whole measurement time. Monthly means of IWV are well defined because of the continuous monitoring of IWV by TROWARA.

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 *fc* = *fp* ± 10%*fp*, where *fp* is the central frequency. More details about the bandpass filtering are given by [33].

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.
