## 5 Inadequate Unimodal van Genuchten-Mualem Equations  
Various sensitivity analyses [18; 19; 20] have stressed the necessity of using accurate hygric properties for the reliable simulation of the hygrothermal response of building materials. [PERSON] et al. [19] showed that minute changes in the capillary range--5% on moisture retention and 1% on liquid permeability--already substantially affect the drying behaviour. [PERSON] et al. [20] revealed that minor variations in the hygroscopic range--20% on sorption isotherm and 20% on vapour permeability--significantly impact the buffering behaviour. Any parameterized description of the moisture storage and transport properties of building materials thus needs to be precise. Additionally, it is shown below that the unimodal van Genuchten-Mualem equations mostly do not meet this criterion. Accordingly, we fitted independent hygric properties with these equations, revealing sizeable deviations between the originals and the unimodal van Genuchten-Mualem fits. Figure 5 shows the moisture retention and liquid permeability curves of three sandstones (Cotta, Posta, and Hildesheim), the properties of which were taken from the Delphin material database. The figure additionally depicts the unimodal van Genuchten-Mualem fits. For these, a least-squares-optimisation was executed, wherein deviations of saturation degree and liquid permeability were brought together in linear and logarithmic fashions, respectively. This confrontation of original and fitted data clearly reveals that van Genuchten-Mualem description was lacking, as it could not capture all complexities of the hygric properties of building materials. It should be noted that the original moisture retention curves, which were desorption curves, did not start from the saturated moisture content but instead from a lower effective maximum moisture content [6]. To not handicap the fitting from the start, these effective maximum moisture contents--which were lower than the saturated moisture contents--were adopted for the parameter fitting. It can also be shown that the use of bimodal van Genuchten-Mualem equations was not satisfactory. In the discusser's experience, the van Genuchten-Mualem equations led to far better results when working with two or three modes while simultaneously employing independent parameters for the moisture retention and liquid permeability curves; however, this necessitates a far larger set of parameters [16]. A second fallacy of [1]'s hygric property description regards vapour permeability; see Equation (3). Predictions of the vapour permeability at 25% RH based on this equation yielded values of 5.4 \(\times\) 10\({}^{-11}\), 4.2 \(\times\) 10\({}^{-11}\), and 4.7 \(\times\) 10\({}^{-11}\) kg/msPa for the Cotta, Posta, Hildesheim sandstones, respectively. Measurements in the Delphin material database provided values of 1.0 \(\times\) 10\({}^{-11}\), 1.2 \(\times\) 10\({}^{-11}\), and 1.4 \(\times\) 10\({}^{-11}\) kg/msPa, respectively--roughly 3-5 factors lower. It should thus be concluded that the parameterisation suggested in [1], based on van Genuchten-Mualem for liquid storage and transport and on a non-correction for tortuosity for vapour transport, cannot accurately represent the hygric properties of building materials. Given that small deviations in the hygric properties may yield highly different moisture responses [18; 19; 20] (see also Section 4), such inaccuracies should be avoided. The authors of [1] could argue though that researchers are free to adopt more complex descriptions  
Figure 5: (**left**) Original (from Delphin material database) versus van Genuchten-Mualem-fitted moisture retention curves for three sandstones; (**right**) original (from Delphin material database) and van Genuchten-Mualem-fitted liquid permeability curves for three sandstones. with (many) more parameters--if desired. This would, however, be inconsistent with their previous and future work on this topic [21,22].