## 2 Materials and Methods
The partial water vapour pressure of the ambient air (AVP), ventilation air (VVP), and air in the attic (AtVP) was determined using physical relationships. The resulting measurements were pairwise correlated using Pearson coefficients of correlation. Specific timelines were analysed using linear regression analysis. The graphs covering the time span of a whole year were smoothed using moving averages to the power of 288. This corresponds to an average of measurements over 24 h.  
The dew-point temperature of the air in the ventilation layer was determined according to Equations (1) and (2), and the partial water vapour pressure was determined using well-known relationships. The equilibrium moisture content of wood (EMC), on the basis of the relative moisture content of the surrounding air, was estimated according to Equation (3) [28]. The roof construction was evaluated for 365 days starting 24 November 2017 using the simulation program Delphin 5.8.1 (Bauklimatik Dresden Software GmbH) for coupled heat, air, and moisture transport in a two-dimensional consideration. A section with a length of 30 cm, including three roof battems, was considered in the model (Figure 2). The materials larch wood for the shingles with a density of 550 kg/m\({}^{3}\) (absolutely dry) and spruce wood for the battems and the sheathing with a density of 425 kg/m\({}^{3}\) (absolutely dry), and a horizontal air layer with an inclination of 38\({}^{\circ}\) for the ventilation layer were considered. The physical material parameters were used as documented by Bauklimatik Dresden Software GmbH [29] and [PERSON] et al. [30]. The two shingle layers were simplified by considering two layers of wood with a thickness of 15 mm. The simplification consists of neglecting thin air gaps between shingle layers (a result of wood warping and shrinking) which would ease water input to and moisture dry-out from the lower shingle layer. The moisture ab- and desorption of the sheathing was limited by applying a high water conduction resistance value (\(5\times 10^{15}\) m/s) on the surface corresponding to the roofing underlay. The temperature of the exterior air (AAT), its relative humidity (AAM), the attic air temperature (AtAT), and its humidity (AtAM) were imposed on the simulation model as boundary conditions using the measured values. A roof pitch of 38\({}^{\circ}\) and western orientation was considered. Hourly values of precipitation, global radiation, and wind velocity were integrated in the model using meteorological data from St. Wolfgang/Austria (measuring point 9 km from the building site) [31]. In the measuring period, precipitation of 1160 L/m\({}^{2}\) and 1956 h of sunshine were recorded. The air stream in the ventilation layer was integrated as a laminar flow. A linear relationship between a pressure gradient between the ventilation layer openings and the air flow was assumed. Pressure differences of 5 Pa (0.12 m/s), 3 Pa (0.06 m/s), and 10 Pa (0.25 m/s) between the air in- and outlet of the modeled domain were considered. Longwave radiation across the cavity between the alternate surfaces was considered using an emissivity of 0.9 for both surfaces (shingles and sheathing). The model domain was discretized using variable discretization (smaller elements at material boundaries) with a minimum element width of 1 mm, which resulted in 1054 elements considered in the model (Figure 2). All results derived from the model are marked with an \"m\" below to avoid confusion with measured values. The temporal course of VAT_m, VAM_m at the specified position according to Figure 2 (equivalent to the sensor position), was modeled as an averaged value of 20 finite elements (\(30\times 30\) mm). The model values of SST were determined at the position of the sensor, averaging eight finite elements (length between to roof battems, 75 mm). Moreover, the moisture flux (liquid water, vapour diffusion, and convection) was integrated over time at the lower shingle layer's lower surface (Dry-out_w_m).