## 2 Materials and Methods
The MOE, MOR, and HB were determined using the universal material testing machine Zwick Z050 (Zwickkoell GmbH, Ulm, Germany; maximum load of 50 kN). Variations in basic density and moisture content variation, called the moisture gradient, were determined starting from the 72 battems, which were sawn in the radial direction from the cross-sectional slices (see before). The samples were stored in airproof plastic bags. From each batten, 2-4 cubes (dimensions of 20 \(\times\) 20 \(\times\) 20 mm) were sawn between the pit and bark, with the number of cubes depending on the diameter of the original log. The first cube was always taken immediately under the bark, and the following cubes were taken towards the pit at a distance of 20 mm each. If the log diameter did not allow for a 20 mm distance between the third and fourth cubes, the fourth cube was taken with a smaller distance from the third cube. The basic density and moisture gradient were determined from the same samples. The basic density of wood (kg/m\({}^{3}\)) was determined using the oven-dry method, according to standard ISO 13061-2 [34]. A color analysis was performed on HB specimens according to standard ISO/CIE 11664-4 [40] with a portable spectrophotometer (Konica Minolta 2600d, Osaka, Japan). In the CIELAB color space, L* indicates lightness from black to white, a* represents the red/green coordinate, and b* represents the yellow/blue coordinate. Two measurements were taken from each specimen on its outer edge. The specimens were conditioned in a weather chamber approximately 1 week before the measurements. The color difference between the reference trees and burned trees was calculated using the CIE76 color difference formula:  
\[\Delta E_{ab}^{*}=\sqrt{\left(\Delta L^{*}\right)^{2}+\left(\Delta a^{*} \right)^{2}+\left(\Delta b^{*}\right)^{2}} \tag{8}\]  
where \(\Delta E_{ab}^{*}\) is the color difference, and \(\Delta L^{*}\), \(\Delta a^{*}\), and \(\Delta b^{*}\) are the differences in the corresponding CIELAB coordinates. Descriptive statistics of the density and mechanical properties and the Pearson correlation between them are reported. Linear mixed-effect models (LMMs) were used to determine the variability in the mechanical properties, moisture gradient, color, and effects of selected factors on them:  
\[A_{i}=b_{0}+dmg_{j}+h_{k}+r+\rho_{a}+r*\rho_{a}+u_{s}+u_{ts}+\varepsilon, \tag{9}\]  
\[MC=b_{0}+dmg_{j}+h_{k}+r+\rho_{b}+dmg_{j}*r+r*\rho_{b}+u_{s}+u_{ts}+\varepsilon, \tag{10}\]  
\[C_{m}=b_{0}+dmg_{j}+h_{k}+r+dmg_{j}*r+u_{s}+u_{ts}+\varepsilon, \tag{11}\]  
where \(A_{i}\) is the modulus of elasticity (GPa), modulus of rupture (MPa), or Brinell hardness (N/mm2); \(MC\) is the moisture content (%); \(C_{m}\) is the CIELAB color coordinate \(L^{*}\), \(a^{*}\), or \(b^{*}\); \(b_{0}\) is the intercept; \(dmg_{j}\) is the fire damage class; \(h_{k}\) is the height class; \(r\) is the dummy term of the radial position (sapwood); \(\rho_{a}\) is the air-dry density (kg/m3); \(\rho_{b}\) is the basic density (kg/m3); \(r*\rho_{a}\) is the interaction term of the radial position and air-dry density; \(dmg_{j}*r\) is the interaction term of the fire damage class and radial position; \(r*\rho_{b}\) is the interaction term of the radial position and basic density; \(u_{s}\) is the random stand effect; \(u_{ts}\) is the random tree effect; and \(\varepsilon\) is the random error term. The LMM allows for the inclusion of dependent fixed effects (such as fire damage and radial position) and more than one source of random variation (such as tree and stand-level effect) in the model [41]. The fire damage class was included as a fixed factor in all models. The linear mixed-effects model (MIXED) procedure in IBM SPSS Statistics fits the model to the data. Normal probability distributions were tested and therefore assumed in the models. The accuracy of the predictions of the linear model was determined by calculating the proportion of explained variance (R2), bias, and root mean square error (RMSE) using only the fixed effects.