Table 4 Attributes of the different models of bark thickness at breast height (BTBH). Model following Eq. 8 is shown when altitude effect is significant. 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. The models in bold correspond to the model finally retained in this study. It must be remembered that the different parameters a to d are model-dependent. Standard errors are given in Appendix Table 9

silver fir

Eq. 4

-2.691 ***

-0.4013 ***

1.057 ****

/

0.71

30.3

-228055

/

Eq. 5

0.04036 ***

-0.1022 ***

0.4081 ***

-0.0003595 ***

0.72

30

-228593

/

Eq. 6

0.000844 ***

0.02087 ***

0.01906 ***

-0.02074 ***

0.72

30.3

-228170

/

Eq. 7

0.02473 ***

0.9021 ***

/

/

0.71

30.4

-227940

/

Eq. 8

/

0.892 ***

5.838 ⋅ 10^− 06***

0.0199 ***

0.73

29.5

-229444

/

Norway spruce

Eq. 4

-3.227 ***

0.2666 ***

0.7861 ***

/

0.69

32.3

-391076

4.49

Eq. 5

0.02452 ***

0.08554 ***

-0.04756 NS

− 8.34 ⋅ 10^− 05 NS

0.71

31.5

-393323

5.12

Eq. 6

0.00187 ***

0.01356 ***

0.03483 ***

-0.03145 ***

0.7

32.2

-391443

5.67

Eq. 7

0.02408 ***

0.8723 ***

/

/

0.69

32.4

-391007

0.84

Eq. 8

/

0.8178 ***

5.218 ⋅ 10^− 06***

0.01859 ***

0.72

30.7

-395525

0.19

Douglas fir

Eq. 4

-2.996 ***

0.8389 ***

0.8468 ***

/

0.76

32

-152100

/

Eq. 5

0.01911 ***

0.1259 ***

-0.1548 NS

0.0005875 ***

0.76

32.3

-151799

/

Eq. 6

0.001364 ***

0.02312 ***

0.03851 ***

-0.009671 *

0.76

32

-152133

/

Eq. 7

0.04552 ***

1.1180 ***

/

/

0.77

30.5

-153769

/

sessile oak

Eq. 4

-2.878 ***

-0.0314 NS

0.6863 ***

/

0.66

27.9

-401069

/

Eq. 5

0.01264 ***

0.4552 ***

-0.9218 ***

/

0.68

27.5

-402398

/

Eq. 6

0.002125 ***

0.03915 ***

-0.02089***

0.006342 ***

0.66

27.9

-401006

/

Eq. 7

0.02748 ***

0.6759 ***

/

/

0.67

27.9

-401172

/

pedunculate oak

Eq. 4

-2.777 ***

-0.1084 ***

0.7357 ***

/

0.68

27

-351586

/

Eq. 5

0.02695 ***

0.2846 ***

-0.5018 ***

-0.0002738 ***

0.69

27

-351588

/

Eq. 6

0.00166 ***

0.04279 ***

-0.02609***

0.009523 ***

0.68

27

-351552

/

Eq. 7

0.02858 ***

0.6958 ***

/

/

0.68

26.8

-351992

/

European beech

Eq. 4

-3.775 ***

0.00143 NS

0.8498 ***

/

0.64

38.7

-431527

/

Eq. 5

0.01327 ***

0.05339 ***

-0.1006 **

-0.0001094 ***

0.66

37.6

-434014

/

Eq. 6

0.0004547***

0.01204 ***

0.0008586 NS

-0.002298 ***

0.64

38.7

-431563

/

Eq. 7

0.01149 ***

0.8516 ***

/

/

0.65

37.3

-434761

/

Eq. 8

/

0.8844 ***

3.134 ⋅ 10^− 06***

0.01023 ***

0.68

36

-437788

/