## 2 Materials and Methods
### Data Analysis  
The spectral transmittance and reflectance (\(\tau_{\lambda,i}\) and \(\rho_{\lambda,i},\ i=1,\ 2,\ldots n\)) of each sample of the cover (\(n\) is the number of samples in each cover; \(n=4\) for the tunnel prototypes and \(n=6\) for the duo-pitched roof prototypes) were measured. The total transmittance (\(T_{\rm s}\)) and reflectance (\(R_{\rm s}\)) of each sample were estimated as the weighted average values of the corresponding spectral properties, using the spectral distribution of solar irradiance measured at the ground level (\(S_{\lambda}\) in W m\({}^{-2}\) nm) as a weighting function [19; 20] as follows:  
\[T_{\rm s}=\int_{\lambda=200}^{\lambda=2500}\tau_{\lambda}S_{\lambda}d\lambda/ \int_{\lambda=200}^{\lambda=2500}S_{\lambda}d\lambda \tag{1}\]  
In the same way as in Equation (1), the total reflectance of each sample in the cover (\(R_{\rm s}\)) was estimated by replacement with Equation (1). Numerical integration was carried out using the trapezoid rule [21]. Owing to the capacity of the available spectrophotometer, the upper limit of \(\lambda\) in Equation (1) was taken as 1700 nm instead of 2500 nm. This assumption  
Figure 1: Schematic diagram, not to scale, to illustrate: (**a**) front view of the two greenhouse prototypes used in the study; (**b**) development (orthographic) of the cover surfaces for the two prototypes in the N–S orientation to show the sample locations on the cover; (**c**) orthographic in the E–W orientation.  
does not affect the accuracy of the analysis because the remaining part of solar irradiance (\(S_{\lambda}\)), from 1700 nm to 2500 nm, is minor and can be neglected [22]. The total transmittance and reflectance of the cladding of the whole prototype (\(T\) and \(R\)) were obtained as the average values of the sample properties (\(T_{\rm s}\) and \(R_{\rm s}\)), weighted with respect to the relatively surface area, as: \(T=\sum_{i=1}^{n}T_{s,i}A_{i}/\sum_{i=1}^{n}A_{i}\), where \(A_{i}\) is the surface area, and \(n\) is the number of samples or the number of surfaces in the prototype. The absolute reduction in the cover transmittance (loss in transmittance) after a given period of exposure time \(t\) is defined as \(T_{\rm new}-T_{t}\), where \(T_{\rm new}\) is the transmittance of the new material to solar radiation (at \(t=0\)), and \(T_{\rm t}\) is the cover transmittance after a period of time \(t\). The relative loss in the cover transmittance (\(T\)) is defined by:  
\[\text{Relative loss in }T\left(\%\right)=\left[\left(T_{new}-T_{t}\right)/T_{ new}\right]\times 100 \tag{2}\]  
The degradation rate of the cover transmittance per day \(D\) (\(\%\)) is defined by:  
\[D(\%)=\frac{d}{dt}(T)\approx-\left[\frac{T_{t+\Delta t}-T_{t}}{\Delta t}\right] \tag{3}\]  
where \(\Delta t\) is the interval of time between two measurements (30 days in the present study). The daily integral of the global solar radiation, \(DSR\) (MJ m\({}^{-2}\)) is estimated as:  
\[DSR=\int_{t1}^{t2}SR(t)dt \tag{4}\]  
where \(t_{1}\) and \(t_{2}\) are the sunrise and sunset times.  
The Stats-Model library in Python was used to perform the statistical analysis. One-way and two-way ANOVA was applied to compare the degradation rates of the covers (i.e., four surfaces of the tunnel-type/six surfaces of the duo-pitched roof type) to explore the impact of both the shape and orientation of the greenhouse on the degradation rate of the cover optical properties.