## 2 Materials and Methods  
### Experimental Procedure  
The experiment was conducted on the roof of the Agricultural Research and Experiment Station building, Agriculture Engineering Department, King Saud University (Riyadh, Saudi Arabia, 46\({}^{\circ}\)47\({}^{\prime}\) E longitude and 24\({}^{\circ}\)39\({}^{\prime}\) N latitude). In order to evaluate the effect of the greenhouse shape and its orientation on the degradation behavior of the radiometric properties of the film cover, four greenhouse prototypes were used, each with a floor surface area of 2 m\({}^{2}\). Two prototypes were of the pitched-roof type, and the other two were of the tunnel type (Figure 1a). Wooden bars (a cross-section of 3 \(\times\) 3 cm\({}^{2}\) for each) were used to construct the prototypes; the dimensions of the greenhouse prototypes are illustrated, not to scale, in Figure 1a. Each prototype was covered with a 200 \(\upmu\)m thick LDPE film, which is popular in the local market and commonly used for cladding greenhouses in Saudi Arabia and the Arabian Peninsula. The LDPE film cover was produced and supplied by Napco Modern Plastics Products Company-Sack Division Ltd. (Dammam, Saudi Arabia); the film density is 0.93 g cm\({}^{-3}\); its melt flow index (MFI) of the raw material is 0.34 g/10 min; the MFI of the stabilized material is 11 g/10 min; the upper working temperature is 50-80 \({}^{\circ}\)C. The film includes different additives such as anti-UV, antioxidant, plasticizer, etc. However, the real film composition of the film was kept confidential by the supplier. Each prototype was mounted horizontally 0.5 m above the roof of the building using four identical wooden legs, each with a cross-section of 5 \(\times\) 5 cm (Figure 1a). The base of each prototype was kept without covering to permit air exchange between the inside and the outside of the greenhouse prototype (ventilation process). Two types (one duo-pitched-shaped and one tunnel-shaped) were oriented longitudinally in the N-S direction, and the other two were oriented longitudinally in the E-W direction. The four prototypes were exposed to arid climatic agents for one year (from 1 October 2019, to 1 October 2020) without cleaning to represent the practical situations of commercial greenhouses in the farms. Samples were taken periodically one month from each cover and tested in the laboratory in order to assess the degradation of their radiative properties due to prolonged exposure to arid climatic agents. One-year exposure to a harsh arid environment is sufficient to represent the degradation behavior of film covers. Six strips (each of 20 cm \(\times\) 20 cm) of the film cover were taken from six surfaces (one from each surface) of the duo-pitched-roof greenhouse prototype, and four similar strips were taken from the tunnel-type prototype. Figure 1: _Cont._  
In order to show the location of each strip on the cover for the two prototypes, the development of the cover surface of each prototype (orthographic) is illustrated in Figure 1b for the N-S orientation and in Figure 1c for the E-W orientation. Strips were cut carefully at the center of each surface; the samples were designated as s\({}_{1}\)-s\({}_{6}\) for the duo-pitched roof prototype and s\({}_{1}\)-s\({}_{4}\) for the tunnel-shaped prototype (Figure 1b,c). This procedure was performed periodically every one month to test the samples in the laboratory. The spectral transmittance (\(\tau_{\lambda}\)) and reflectance (\(\rho_{\lambda}\)) of each sample were measured at normal incidence using a Black-Comet (StellarNet Inc., Tampa, FL, USA) spectrophotometer, scanning between 200 and 1700 nm at 0.5 nm intervals in the UV-vis-IR range. The measured data were averaged at each 5 nm interval. The samples were re-fixed, using transparent sticker spices, at the same locations immediately after the measurements to work again as part of the film cover. The sticker spices were small enough and were fixed on the corners of the sample perimeter.