## 2 Materials and Methods
### Climatic Elaborations and Wind-Driven Rain (WDR) Calculation  
Microenvironmental monitoring for St. Simeon church, such as T/RH, solar radiation, and wind direction/speed, as well as soil-water measurement, have been started since  
Figure 2: **(a–d)**: Sampling areas (green circles) of St. Simeon Church and visual inspection of the related deterioration patterns in areas (**I–VIII**).  
September 2019. However, due to some gaps in data collection caused by technical problems and the COVID-19 situation, this study utilized hourly weather data from nearby weather stations data from the weather API of Visual Crossing (www.visualcrossing.com) (8 September 2023). The Visual Crossing weather API is a comprehensive weather data collection, leveraging multiple sources and models to provide accurate weather predictions [40]. The collected weather data are created by aggregating information from public weather platforms and privately owned weather stations. In this study, the weather stations were located in Kayseri (30 km away) and Gulsehir district (55 km away).  
The hourly weather datasets were retrieved from the Visual Crossing platform for two specific time periods: the year from 1 October 2019 to 30 September 2020 (hygrothermal calendar that begins on October 1 st and ends on 30 September in the next year) [41], as well as a broader range covering 20 years from 2000 to 2020. From the long-term measured datasets, we specifically calculated the total and monthly amount of rainfall, the wind speed and direction, and the temperature trends.  
To determine the amount of rainwater likely to impact a wall, the semi-empirical method described in ASHRAE Standard 160 was used [41; 42]. This method uses hourly weather data, specifically rainfall horizontal amount, wind speed, and wind direction.  
Considering the site's open landscape and the church's geometric morphology, associate to a cone, a simplified \"free field\" model has been applied, disregarding certain factors that could affect the amount of water reaching the walls, such as the surrounding topography (buildings nearby), the building's height, and rain protection measures. The hourly wind-driven rain (WDR) on a simplification model \"free field\", indicated as rbv, [kg/(m\({}^{2}\cdot\)h)], was calculated by the following formula [41]:  
\[\mathbf{rbv}=\mathbf{FL}\times\mathbf{U}\times\mathbf{cos(\theta)}\times\mathbf{rh}\]  
where  
**FL**: an empirical constant, typically 0.2 kg s/(m\({}^{3}\cdot\)mm);  
**U**: the hourly mean wind speed [m/s];  
**rh**: the hourly rainfall [mm/h];  
\(\theta\): the angle between the wind direction and the normal to the wall surface [\({}^{\circ}\)].  
For calculating the annual mean wind-driven rain (WDR) based on long-term weather data, the following formula was applied [41]:  
\[\mathbf{rbvMY}=\mathbf{\Sigma(0.2\times\mathrm{U}\times\mathbf{cos\theta}\times\mathrm{rh })/\mathrm{N}}\]  
where  
**rbvMY**: annual mean WDR [kg/(m\({}^{2}\cdot\)a)];  
**\(\mathbf{\Sigma}\)**: summation over all hours where cos\(\theta\) is positive;  
**U**: hourly mean wind speed in m/s;  
\(\theta\): the angle between the wind direction and the normal to the wall surface [\({}^{\circ}\)];  
**rh**: hourly rainfall intensity in mm/h;  
**N**: number of years over which the data are collected.  
In order to consider the directional aspect of WDR, calculations were performed for the different facade orientations (South; North-East; North-West; South-West).  
For each church exposure, the WDR calculation was evaluated with respect to the real orientation of the wall expositions, considering the inclination of the single surface.