## 4 Non-Unique Characterisation and Hygrothermal Behaviour  
It appears that the agreement between simulated and measured capillary absorption alone may not suffice to universally and dependably characterize the moisture storage and transport properties of building materials. This argument is further developed in this section, where the non-uniqueness of the parameter identification and its impact on hygothermal behaviour are targeted. To do so, it is shown below that the measured capillary absorption can also be reproduced with different parameter values. Subsequently, it is demonstrated that these different parameter values yield deviating hygothermal responses. This implies that the inverse identification based on capillary absorption exclusively suffers from non-identifiability [14,15], implying that the resulting characterisation of the material's moisture storage and transport properties may not be reliable. This non-uniqueness should of course not come as a surprise. The capillary absorption by a building material is typically described with a single value: the capillary absorption coefficient, which quantifies the slope of the linear moisture mass evolution in function of the square root of time. Fitting three independent parameters (K, m, and n; \(\alpha\) is determined via the initial moisture content) to one single target value is a textbook example of non-identifiability [14,15]. It is furthermore suggested below that these four parameters featuring in the unimodal van Genuchten-Mualem equations often do not suffice to capture the full complexity of the moisture storage and transport properties of building materials. In [16], the hygric properties of brick and mortar were described via independent bimodal and trimodal curves, comprising some 15-20 parameters, which would obviously only worsen the non-identifiability. Though demonstrating the uniqueness of inverse characterisation procedures can be somewhat complex [14,15], establishing their non-uniqueness is far more straightforward. If it can be confirmed that multiple sets of parameter values all minimise the objective function, then it must be concluded that the characterisation is non-unique and hence unreliable. Table 1 shows three parameter value that all satisfactorily reproduce the capillary absorption. The first is [1]'s OPS limestone original, and the two others are variations. The changes in their parameters values primarily reflect somewhat steeper moisture retention curves, still centred though at the same capillary pressure as [1]'s original. The intrinsic permeabilities were subsequently calibrated such that the variants reproduce the capillary absorption. Figure 3 illustrates the resulting moisture retention and permeability curves. It should be noted that the two variants were deliberately kept quite similar to the original to demonstrate the large impacts of small deviations on the hygric response. Compared to the hygric properties for other building materials in the literature [3, 4, 5, 6, 8, 14, 16], these are certainly not exceptional hygric property curves, implying that all are physically viable. For reasons discussed in Section 6, K fitting was not performed with FLoW1D; instead, the well-known hygothermal simulation tool Delphin was used [17]. These simulations were conducted for the same configuration as in [1]: a 5 cm thick slab, initially at 32% RH, with bottom water contact. Complementarily, three more hygrothermal cases were simulated: moisture redistribution, isothermal drying, and hygroscopic adsorption. In hygroscopic adsorption, the 5 cm thick slab started at 32% RH, and was exposed to a 100% RH environment with a 2 \(\times\) 10\({}^{-7}\) kg/m\({}^{2}\)sPa transfer coefficient at one surface. For isothermal drying, the 5 cm thick slab started at 100% RH and was exposed to a 32% RH environment with a 2 \(\times\) 10\({}^{-7}\) kg/m\({}^{2}\)sPa transfer coefficient at one surface. For moisture