## 3 Materials and Methods
### Validation of the Modified Miami Model
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Literature data**} & \multicolumn{3}{c}{**Parameters**} & \multicolumn{2}{c}{**Output**} & \\ \hline
**Species** & **MAT** & **MAP** & **BM\({}_{\rm max}\)** & **BM\({}_{\rm max}\)** & **MAT\({}_{\rm mat}\)** & **ABM** & \(r^{2}\) & **References** \\ \hline  & \({}^{\circ}\)C & mm & Mg ha\({}^{-1}\)a\({}^{-1}\) & Mg ha\({}^{-1}\)a\({}^{-1}\) & \({}^{\circ}\)C & Mg ha\({}^{-1}\)a\({}^{-1}\) & - & \\ \hline  & 0.0 & 718 * & 4.5 & & & & 4.8 & & \\  & 2.0 & 718 * & 6.2 & & & & 5.7 & & \\ Norway & 4.0 & 718 * & 7.9 & & & 6.8 & & \\ spruce & 6.0 & 718 * & 9.6 & & & 8.0 & & \\  & 8.0 & 718 * & 11.3 & & & & 8.0 & & \\  & 10.0 & 718 * & 13.0 & & & 7.0 & & \\ \hline  & 4.6 & 632 & 6.4 & & & & 6.0 & & \\  & 5.9 & 750 & 6.2 & & & 7.0 & & \\ Reed canary & 6.9 & 657 & 6.0 & & & 7.1 & & \\ grass & 7.6 & 514 & 5.5 & & & 4.7 & & \\  & 8.2 & 477 & 6.2 & & & 3.8 & & \\  & 8.4 & 547 & 6.2 & & & 4.8 & & \\ \hline  & 7.6 & 783 & 11.8 & & & 13.7 & & \\  & 7.8 & 578 & 15.1 & & & 14.6 & & \\  & 8.3 & 630 & 14.7 & & & 17.0 & & \\  & 8.9 & 634 & 15.4 & & & 16.7 & & \\  & 9.6 & 689 & 18.5 & & & 18.1 & & \\  & 9.6 & 769 & 12.6 & & & 21.2 & & \\ \multirow{2}{*}{_Miscanthus_} & 9.6 & 766 & 17.5 & & & 21.1 & & \\  & 9.8 & 660 & 21.0 & & & 16.6 & & \\  & 10.4 & 594 & 19.6 & & & 12.9 & & \\  & 10.4 & 594 & 12.5 & & & 12.9 & & \\  & 10.5 & 676 & 19.6 & & & 16.3 & & \\  & 11.5 & 813 & 34.3 & & & 20.6 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Literature data, parameters and output of the final modified Miami model. MAT, mean annual temperature; MAP, mean annual precipitation; BM\({}_{\rm max}\), maximal above-ground biomass production of a species in dry matter; MAT\({}_{\rm mat}\), mean annual temperature of the native distribution area of a species; ABM, modeled above-ground biomass production of a species in dry matter; \(r^{2}\), coefficient of determination for the final model. The values for the coefficient of determination (\(r^{2}\)) in Table 1 are between 0.41 and 0.90. Nevertheless, the small amount and small range of data may reduce the representative significance of the coefficient of determination. Therefore, the coefficient of determination for the different species, the paired samples correlation (\(t\)-test), was also used to increase the parameters by combining all the literature data presented in Table 1 under a single variable and comparing them to modeled data. For this purpose, the species-specific parameters (MAT\({}_{\text{nat}}\) and BM\({}_{\text{max}}\)) were exchanged either (1) by using the literature data directly as species-specific parameters or (2) by using average variables over all species for the parameters. 1. The literature data were compared to modeled data using each single MAT\({}_{\text{nat}}\) and BM\({}_{\text{max}}\) value in the literature directly as a species-specific parameter. The coefficient of determination of this modification was \(r^{2}=0.903\) with \(p<0.0001\). 2. The literature data were compared to the modeled data using as parameters the average MAT\({}_{\text{nat}}\) and BM\({}_{\text{max}}\) values from the literature data. The coefficient of determination of this modification was \(r^{2}=0.759\) with \(p<0.0001\). For the paired sample comparisons (1) and (2), it could not be excluded that the two groups (the literature data and the modeled data) were equal, and this supports the hypothesis that the modified Miami model can be used to estimate the ABM. Thus, the results of the paired sample comparisons support the results of the validation based on the approximation process (Table 1), _i.e.,_ that it is possible to estimate the ABM of a single species with the modified Miami model using species-specific variables. To see the effect of the species-specific variables and the relation between the MAT (Equation 4) and MAP (Equation 5) functions (Equation 7), 3D graphs were drawn for Norway spruce and _Miscanthus_ (Figure 4) using the species-specific parameters introduced above.