## 4 Artificial Soiling Test with Pollen
### Results
Hence, concerning the optical behavior of the glass coupons soiled with pollen, by assuming the following approximation for the absorbance due to pollen:  
\[A_{\text{POLLEN}}\sim A_{\text{s}\text{o}\text{i}\text{e}\text{l}}\text{ - }A_{\text{c}\text{e}\text{l}} \tag{4}\]  
and substituting the terms of the right-hand side with these definitions:  
\[A_{\text{s}\text{o}\text{i}\text{e}\text{l}}\text{ (\%)}=100\text{ - }T_{\text{s}\text{o}\text{i}\text{e}\text{l}}\text{ (\%)}\text{ - }R_{\text{s}\text{o}\text{i}\text{e}\text{l}}\text{ (\%)} \tag{5}\]  
\[A_{\text{c}\  
where \(A\), \(T\), and \(R\) refer to absorbance, transmittance, and reflectance, respectively, and the subscripts \"pollen\", \"clean\", and \"soiled\" refer only to pollen, to the glass coupon in a clean state, and to the glass coupon soiled with pollen, respectively.  
Then, the absorbance spectra of the cypress pollen itself (\(A_{\text{POLLEN}}\)) were calculated and represented (Figure 11), confirming an intense UV absorption which increased with the pollen mass density (\(\rho_{\text{A}}\)). This optical behavior would be attributable to the exine, namely the outermost part of the pollen grain wall, which is known to absorb UV light [108]. The major component of the exine is sporopolenin, a complex biopolymer containing UV-absorbing phenolic compounds such as p-coumaric acid and ferulic acid [109]. Given that exineless pollen is restricted to some water-pollinated marine plants [23], this optical behavior should be expected wherever soiling occurs by pollen deposition. However, the absorption intensity would vary not only with the amount of deposited pollen, but also with the vegetal species producing it depending on the thickness of the exine relative to the whole pollen grain size. This absorption peak should be also expected in the event of soiling by fern spores, mosses, and some green algae, provided that their sporoderms also contain sporopolenin [23].  
Next, the averaged transmittance (\(T_{\text{AVE}}\)) was obtained by averaging the normalized transmittance (\(T_{\text{NORM}}\)) over the 300-1200 nm (instead of the 300-1800 nm) wavelength range. This wavelength interval was chosen because it covers the spectral response of the most common PV technologies [110]. As a result, Figure 12 clearly shows a linear correlation between the pollen mass density (\(\rho_{\text{A}}\)) and the averaged transmittance (\(T_{\text{AVE}}\)) for the 26 analyzed pollen samples. This result agrees with other artificial soiling tests performed with different pollutants (generically referred to as \"dust\") which showed, at least for low dust densities, a nearly linear relationship between the dust density and both the light transmission and (in case of uniform soiling) the PV efficiency [7; 96; 111]. Nevertheless, some of them reported a deviation from linearity beyond a certain level of soiling. That was because when a portion of the arriving dust particles settled down on the previously deposited ones rather than on a clean surface area, the resulting increase on the dust mass density did not cause as much proportion of light obstruction as observed in an earlier stage [50; 51]. From our experimental results, it can be concluded that, in the case of there being a saturation point [96; 112] for soiling by pollen, it would exist for a cypress pollen mass density (\(\rho_{\text{A}}\)) above 9.1 g/m\({}^{2}\). Concerning outdoor pollen deposition, pollen mass densities of 0.4-0.5 g/m\({}^{2}\) have been reported for 30\({}^{\circ}\)-tilted glass samples during a pollen bloom in a Mediterranean rural area with extensive olive crops [12] (i.e., pollen grains about 20 um in size with a minor content of pollenkitt [44]).  
Figure 11: Absorbance spectra of cypress pollen (\(A_{\text{POLLEN}}\)) as a function of the pollen mass density (\(\rho_{\text{A}}\)).  
According to Figure 12, the results of the artificial soiling test achieved a fair good least-square linear fitting (coefficient of determination: R\({}^{2}\) = 0.9897) which provided the following correlation with a percentage error of \(\pm\)1.4%:  
\[T_{\rm AVE}\left(\%\right)=99.7-3.8\cdot\rho_{\rm A}\left(\rm g/m^{2}\right) \tag{8}\]  
This confirmed the experimental reproducibility of our artificial soiling test procedure.