## 2 Materials and Methods
### Metrics and Indicators  
The effect of external weather conditions on indoor microclimates has been studied in numerous studies [25; 43; 44; 45; 46]. This research examined eight indicators from the relationships between T\({}^{\circ}\)C, RH%, dew point temperature [T\({}_{\rm P}\)], and mixing ratio [MR] in the 13 case studies, as indicated in Table 3. Initially, the temperature (\({}^{\circ}\)C) and relative humidity (RH%) data were calculated using statistical measures (daily averages, minimum, maximum, and standard deviations) to quantify the baseline microclimate conditions prior to the in-depth analysis. While thermo-diffusion moisture movement due solely to temperature gradients is considered negligible [47], vapor pressure gradients (driven by temperature and humidity differences) are the dominant factors that enable the detection of moisture in porous materials. It should be noted that the importance of calculating each indicator was evaluated under theoretical conditions, which were distinct from the actual degradation state of materials in the case studies. In practice, the presence of salts, contaminants, or prior damage (e.g., micro-cracking) can significantly alter moisture behavior, modifying the relative importance of indicators. For instance, hygroscopic salts can amplify moisture uptake even at a moderate RH [48] while pre-existing damage can enable moisture transport, effectively bypassing vapor diffusion mechanisms by providing preferential pathways for liquid water infiltration [49]. Despite these complexities, the evaluation of each indicator demonstrates the progression of nearly all degradation mechanisms in porous materials. As a direct quantification of condensation risk, Dew Point Depression (difference between the air temperature and the dew point temperature at a given pressure level) was analyzed. The dew point was calculated using the Magnus formula, a commonly adopted empirical equation in building science and conservation, which offers reliable accuracy within the range of 0 \({}^{\circ}\)C to 60 \({}^{\circ}\)C, with a marginal deviation of \(\pm\)1 \({}^{\circ}\)C at subzero temperatures. While hygrometers can provide direct hourly measurements of dew point, their use carries a high risk of data loss and signal noise due to the extended drying time required for accurate sensor readings. The margin of 2.5 \({}^{\circ}\)C between dry air and dew point requires the high accuracy level of data loggers (0.2 \({}^{\circ}\)C, as explained in Appendix B) and the dew point calculation aligned with ASHRAE's precautionary guidelines [50]. The interdependence of T\({}^{\circ}\)C and RH% has been examined through various indexes [51; 52]. Within the scope of this study, a critical zone was defined as two conditions of high temperature (>25 \({}^{\circ}\)C) and relative humidity (>60%) and low temperature (T \(\approx\) 0 \({}^{\circ}\)C) and high relative humidity (>60%), which affect salt dissolution-recrystallization and freeze  
Figure 1: The comparison of ARPA data recorded in 2022 and external data loggers installed in San Giacomo Church in Como. Data has been processed to reduce noise and peaks. (**a**) Comparison of temperature data recorded by the external prob and ARPA data. (**b**) Comparison of relative humidity data recorded by the external prob and ARPA data. thaw damage. Consequently, the calculation of RH fluctuation is of importance for detecting prolonged high variations. Temperature gradients alone cannot reliably indicate surface moisture in historic porous materials. Diurnal temperature fluctuations can lead to material stress, microcracking, and subsequent moisture ingress. To investigate building materials' hygrothermal buffering performance, the damp effect was proposed, which is the relationship between internal and external daily variations in RH and the mixing ratio (MR): <0 indicates uncontrolled damping, 0-0.25 indicates very low damping, 0.25-0.5 indicates low damping, 0.5-0.75 indicates moderate damping, 0.75-1 indicates high damping, and 1 indicates full damping.