## 2 Materials and Methods
### Statistical Analysis and Multivariate Image Analysis  
In order to quantify the effect of biochar on root growth for each genotype, a non-destructive technique, e.g., a multivariate image analysis, was carried out according to [PERSON] et al. [29]. At the beginning of May, plants were extracted from pots and the images of roots and soil for each plant were acquired twice using a digital camera Nikon D750 at a high resolution and a color depth of 16 bits, saving the captured images in uncompressed RAW format. The images were acquired by photographing the basis and four external opposite sides. To create the final data set, a region of interest (ROI) of \(472\times 472\) pixels, representative of the whole sample surface, was extracted from each image using the Lightroom Classic CC 2018.  
The images were processed by PLS Toolbox 8.5 (Eigenvectors Research, Inc., Manson, WA, USA) for MATLAB R2016b (The MathWorks Inc., Natick, MA, USA). Red (R), green (G), blue (B) values, measures in the RGB space color, were calculated. A principal component analysis (PCA) on the RGB values was carried out, providing the pixel distribution in the score space (score plot). The first principal component (PC1) contained most of the original information, with a decreasing amount in the remaining score images. PC1 score image. PC1 score image was converted from the RGB space color into the HSI (hue, saturation, intensity) space color. Then, the Hue channel was extracted to obtain the hue image. A pixel segmentation in different intensity ranges, corresponding on different material (soil and root), was carried out to select roots. In this way, it was possible to quantify the percentage of roots present in each pot and for each cultivar.  
The influence of genotype, treatment and the two-way interaction on roots percentage or number of leaves or bines length or number of cones was tested using the technique of General Linear Models (GLM). The statistical model was:  
\[Y_{ij}\ =\ \ \beta_{0}+\ \beta_{1}\cdot\tau_{i}+\ \beta_{2}\cdot\delta_{j}+\ \beta_{3}\ \tau_{i}\cdot\delta_{j}+\ \varepsilon_{ij} \tag{1}\]  
where \(Y_{ij}\) = roots percentage or number of leaves or bines length or number of cones, \(\beta_{0}\) = mean effect common to all observations; \(\beta_{1,2,3}\) = unknown regression parameters; \(\tau_{i}\) = treatment (\(i\) = 1, 2; 1 = with biochar, 2 = without biochar); \(\delta_{j}\) = cultivar (\(j\) = 1, 2, 3; 1 = Hallertau Magnum, 2 = Perle, 3 = Spalter spalt); \(\varepsilon_{ij}\) = error term.  
GLM was also applied to monitor the plant development in time. The statistical model was:  
\[Y_{ijk}\ =\ \ \beta_{0}+\ \beta_{1}\ \tau_{i}+\ \beta_{2}\ \delta_{j}+\ \beta_{3}\ \gamma_{k}+\ \beta_{4}\ \tau_{i}\cdot\delta_{j}+\beta_{5}\tau_{i}\cdot\gamma_{k}+\ \beta_{6}\ \delta_{j}\gamma_{k}+\beta_{7}\ \tau_{i}\cdot\delta_{j}\gamma_{k}\ +\ \varepsilon_{ijk} \tag{2}\]  
where \(Y_{ijk}\) = diameter of shoots, \(\beta_{0}\) = mean effect common to all observations; \(\beta_{1,7}\) = unknown regression parameters; \(\tau_{i}\) = treatment (\(i\) = 1, 2; 1 = with biochar, 2 = without biochar); \(\delta_{j}\) = cultivar (\(j\) = 1, 2, 3; 1 = Hallertau Magnum, 2 = Perle, 3 = Spalter spalt); \(\gamma_{k}\) = time (\(k\) = 1,...,5; 1 = 30 June, 2 = 18 July, 3 = 27 July, 4 = 3 November, 5 = 21 November); \(\varepsilon_{ijk}\) = error term.  
Post hoc Tamhane test (\(p\) < 0.05) was carried out in order to evaluate differences between groups (with or without biochar) for each considered variable. Statistical analysis was performed with SPSS 20.0 software (SPSS, Inc., Chicago, IL, USA).