Table 5 Models of bark volume (Bv) with bark thickness at breast height (BTBH) and stem volume over-bark (Vob) for Eq. 10 (Meyer 1946). The statistical significance is indicated by: NS: p ≥ 0.1; *: p < 0.05; **: p < 0.01; ***: p < 0.001. R2 is the coefficient of determination. RMSErel is the relative Root Mean Square Error. AIC is the Akaike Information Criterion. PME is the propagation of measurement error for Norway spruce only. BP-test is the p-value of the Breusch-Pagan test without the structuration of the variance and with the structuration of the variance. The models in bold correspond to the models finally retained in this study. Standard errors are given in Appendix Table 10
Species | Model | a | b | c | d | e | σ | 𝜃 | R2 | RMSErel (%) | AIC | PME | BP-test without | BP-test with |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
silver fir | Eq. 17 | 1.364 *** | -0.00101 *** | / | / | / | 9.51 ⋅ 10− 3 | 0.885 | 0.95 | 24.70 | -3308 | / | 2 ⋅ 10− 50 | 0.09 |
Eq. 18 | 1.534 *** | 0.0009592 *** | / | / | / | 9.23 ⋅ 10− 3 | 0.889 | 0.95 | 24 | -3344 | / | 4 ⋅ 10− 40 | 0.11 | |
Eq. 10 | 0.945 *** | / | / | / | / | / | / | 0.89 | 39.1 | / | / | / | / | |
Eq. 11 | 1.849 *** | / | 1.139 *** | 0.9048 *** | 0.8589 *** | 9.41 ⋅ 10− 3 | 0.876 | 0.96 | 23.5 | -3330 | / | 4 ⋅ 10− 39 | 0.10 | |
Norway spruce | Eq. 17 | 1.3 *** | / | / | / | / | 8.22 ⋅ 10− 3 | 0.875 | 0.95 | 23.3 | -3718 | 24.97 | 1 ⋅ 10− 28 | 0.90 |
Eq. 18 | 1.475 *** | 0.000827 *** | / | / | / | 8.22 ⋅ 10− 3 | 0.880 | 0.95 | 25.3 | -3714 | 24.3 | 1 ⋅ 10− 29 | 0.84 | |
Eq. 10 | 0.943 *** | / | / | / | / | / | / | 0.92 | 34.9 | / | / | / | / | |
Eq. 11 | 0.7942 *** | / | 1.069 *** | 0.818 *** | 0.9594 *** | 7.92 ⋅ 10− 3 | 0.869 | 0.96 | 21.8 | -3772 | 64.8 | 2 ⋅ 10− 30 | 0.91 | |
Douglas fir | Eq. 17 | 0.9958 *** | 0.003118 *** | / | / | / | 9.83 ⋅ 10− 3 | 0.926 | 0.95 | 20.8 | -1669 | / | 2 ⋅ 10− 21 | 0.70 |
Eq. 18 | 1.07 *** | 0.005459*** | / | / | / | 1.08 ⋅ 10− 2 | 0.870 | 0.95 | 21.4 | -1628 | / | 8 ⋅ 10− 22 | 0.61 | |
Eq. 10 | 0.921 *** | / | / | / | / | / | / | 0.89 | 29.3 | / | / | / | / | |
Eq. 11 | 0.2608 *** | / | 1.1 *** | 0.5981 *** | 0.9866 *** | 7.63 ⋅ 10− 3 | 0.956 | 0.95 | 16.7 | -1815 | / | 1 ⋅ 10− 21 | 0.20 | |
sessile oak | Eq. 17 | 1.228 *** | -0.0004375 *** | / | / | / | 1.05 ⋅ 10− 2 | 0.946 | 0.91 | 24.7 | -6764 | / | 2 ⋅ 10− 49 | 0.76 |
Eq. 18 | 1.386 *** | 0.001027 *** | / | / | / | 1.04 ⋅ 10− 2 | 0.942 | 0.91 | 24.4 | -6812 | / | 8 ⋅ 10− 47 | 0.85 | |
Eq. 10 | 0.921 *** | / | / | / | / | / | / | 0.87 | 30 | / | / | / | / | |
Eq. 11 | 0.3399 *** | / | 1.077 *** | 0.7273 *** | 1.112 *** | 9.78 ⋅ 10− 3 | 0.935 | 0.92 | 22.7 | -7003 | / | 5 ⋅ 10− 63 | 0.61 | |
pedunculate oak | Eq. 17 | 1.17 *** | / | / | / | / | 1.02 ⋅ 10− 2 | 0.925 | 0.91 | 29.3 | -2325 | / | 3 ⋅ 10− 12 | 0.36 |
Eq. 18 | 1.353 *** | / | / | / | / | 1.05 ⋅ 10− 2 | 0.915 | 0.91 | 29.9 | -2303 | / | 5 ⋅ 10− 33 | 0.13 | |
Eq. 10 | 0.922 *** | / | / | / | / | / | / | 0.87 | 35.4 | / | / | / | / | |
Eq. 11 | 0.8077 *** | / | 1.229 *** | 0.7352 ** | 0.8744 *** | 9.76 ⋅ 10− 3 | 0.908 | 0.92 | 27.5 | -2378 | / | 2 ⋅ 10− 28 | 0.18 | |
European beech | Eq. 17 | 1.214 *** | / | / | / | / | 5.68 ⋅ 10− 3 | 0.839 | 0.94 | 25.7 | -8049 | / | 2 ⋅ 10− 60 | 0.0030 |
Eq. 18 | 1.386 *** | 0.0007332 *** | / | / | / | 5.59 ⋅ 10− 3 | 0.845 | 0.94 | 26.4 | -8053 | / | 1 ⋅ 10− 61 | 0.0006 | |
Eq. 10 | 0.973 *** | / | / | / | / | / | / | 0.87 | 42.6 | / | / | / | / | |
Eq. 11 | 0.4478 *** | / | 1.018 *** | 0.7834 *** | 1.031*** | 5.18 ⋅ 10− 3 | 0.811 | 0.95 | 22.1 | -8298 | / | 1 ⋅ 10− 56 | 0.003 |