## 4 Comparison of Light-Tube Optical Properties under Arbitrary and Homogenous Skies
### Clear and Overcast Skies  
It is a natural goal of all the luminance models to mimic a momentary sky state as accurately as possible. Of all cases, the clear and overcast skies represent the best conditions to test different models, because we avoid random errors that can originate from the missing information on the cloud arrangement. The common requirement is to test the models on real data and in situations that regularly occur in nature. We have used the optical data taken in Bratislava, Slovakia. Of all the data taken during a reference year we have selected two days that are well representative for clear and overcast conditions. The horizontal global (\(G_{h}\)) and diffuse (\(D_{h}\)) irradiance data needed to run [PERSON]'s model are shown in Tables 1 and 2. Note that the dew point temperature is calculated from the relative humidity RH and real temperature \(t\) using Equation (11) in [28]. The sky clearness index \(\varepsilon\) and sky brightness \(\Delta\) computed for both the clear and overcast skies are presented in Tables 3 and 4, showing that \(\varepsilon\) is one when the cloud fraction approaches unity. However, \(\varepsilon\) can fluctuate as a result of the evolving atmospheric turbidity (see e.g., Table 3). The aerosol optical depth has increased shortly before noon, but then remained constant and equal to that of the morning value (0.11). Peak values at noon normally occur due to intensified turbulent mixing in the boundary layer or due to the change of wind direction. The wind direction is often associated with changes of aerosol content and origin, especially if the measuring site is surrounded by different pollution sources. This was just the case in our field experiment that has been performed in the city of Bratislava with many industrial and anthropogenic emission sources. Other evidence for a transform of aerosol system is that the single-scattering albedo of aerosol particles (\(\omega_{0}\)) has changed abruptly when \(\tau_{a}\) achieved peak values. The transition from \(\omega_{0}\)\(>\) 0.7 in the morning to \(\omega_{0}\)\(\approx\) 0.4 at noon can be interpreted as a contamination of the local aerosol population by highly absorbing particles, most probably due to emissions from close industrial sources. At the same time, the asymmetry parameter of aerosol particles \(g\prime\) drops down from almost 0.9 to 0.7 and then to 0.4, meaning that the concentration of the small particles has increased. This is consistent with the experimental studies indicating that most of the absorbing particles (e.g., some fractions of carbonaceous species) are small in size [29; 30]. The values of \(\tau_{a}\) which are all found to be nearly zero under overcast sky conditions (Table 4) indicate that the aerosol content was at the detection limit. This is not surprising, because low-level clouds with a base below 2 km are often rainy and contribute to the efficient removal of tiny particles in the under-cloud atmosphere through frequent rainfall. The accuracy of the UMRP model is demonstrated in Tables 3 and 4, where the parameter Dev is obtained by matching the modelled to the measured irradiance data. The deviation obtained is as low as 1%, implying that UMRP is capable of simulating both clear and overcast sky conditions with exceptional accuracy.