Table 2 The nonlinear ITH-DBH functions tested by this study

(M1)

\( ITH=1.3+\left({H}_0-1.3\right)\frac{\left(1-{e}^{-{b}_0d}\right)}{\left(1-{e}^{-{b}_0{d}_0}\right)} \)

Meyer (1940) modified by Cañadas et al. (1999)

(M2)

\( ITH=1.3+{\left({b}_0\left(\frac{1}{d}-\frac{1}{d_0}\right)+{\left(\frac{1}{H_01.3}\right)}^{\frac{1}{2}}\right)}^{-2} \)

Loetsch et al. (1973) modified by Cañadas et al. (1999)

(M3)

\( ITH=1.3+\left({H}_0-1.3\right){\left(1+{b}_0\left({H}_0-1.3\right)\left(\frac{1}{d}-\frac{1}{d_0}\right)\right)}^{-1} \)

Prodan (1965) modified by Tomé (1989)

(M4)

\( ITH=1.3+{b}_0{H}_0^{b_1}{d}^{b_2{H}_0^{b_3}} \)

Hui and Kv (1993)

(M5)

\( ITH={H}_0\left(1+\left({b}_0+{b}_1{H}_0+{b}_2 Dg\right){e}^{b_3{H}_0}\right)\left(1-{e}^{\frac{b_4d}{H_0}}\right) \)

Soares and Tomé (2002)

(M6)

\( ITH=1.3+\left({b}_0{H}_0^{b_1}\right){\left(1-{e}^{-{b}_2{\left(\frac{N}{BA}\right)}^{b_3}d}\right)}^{b_4} \)

Richards (1959) modified by Sharma and Parton (2007)

(M7)

\( ITH={\left({1.3}^{b_0}+\left({H}_0^{b_0}-{1.3}^{b_0}\right)\frac{\left(1-{e}^{-{b}_1d}\right)}{\left(1-{e}^{-{b}_1{d}_0}\right)}\right)}^{\frac{1}{b_0}} \)

Schnute (1981) modified by Castedo Dorado et al. (2006)