Table 12 PBIRROL model—sub-models for growth projection (annual tree diameter growth in both distance-dependent and distance-independent versions and dominant height growth)

Annual tree diameter growth (over bark)

Annual tree diameter potential growth equation

 \( {i}{{{d}}_{\mathrm{pot}}}=\left( {20.94348+1.7417{S_h}25} \right){{\left( {\frac{{{d}{t_1}}}{{20.94348+1.7417{S_h}25}}} \right)}^{{{{{\left( {\frac{{{t_1}}}{{{t_2}}}} \right)}}^{1.1325 }}}}}-{d}{t_1} \)

 with t ₂ = t ₁ + 1

 R ² = 0.995; \( R_{\mathrm{adj}}^2 \) = 0.995; RMS = 0.328; mean PRESS = 0.201; mean APRESS = 0.460; n = 52

Distance-independent annual tree diameter growth equation

 \( \operatorname{d}{t_2}=\operatorname{d}{t_1}+{i}{{{d}}_{\mathrm{pot}}}\,{{\mathrm e}^{{-0.1893+0.00245G>d+0.7052\frac{d}{{d}{g}}+0.8475\bar{{c}} {r}-0.00054N}}} \)

 with t ₂ = t ₁ + 1

 R ² = 0.998; \( R_{\mathrm{adj}}^2 \) = 0.998; RMS = 0.155; mean PRESS = 0.022; mean APRESS = 0.322; n = 453

Distance-dependent annual tree diameter growth equation

 \( \operatorname{d}{t_2}=\operatorname{d}{t_1}+{{\mathrm{id}}_{\mathrm{pot}}}\,{e^{{30.447+0.00472G>d+0.6749\frac{d}{{d}{g}}+0.8885\bar{{c}} {r}-0.00053N}}}\,\frac{1}{{1+{e^{{30.6228+0.0325F4H\_U}}}}} \)

 with t ₂ = t ₁ + 1

 R ² = 0.998; \( R_{\mathrm{adj}}^2 \) = 0.998; RMS = 0.155; mean PRESS = 0.023; mean APRESS = 0.324; n = 453

Dominant height growth equation

 \( {h_{\mathrm{dom}}}{t_2}=19.62270345{{\left( {\frac{{{h_{\mathrm{dom}}}{t_1}}}{19.62270345 }} \right)}^{{{{{\left( {\frac{{{{\bar{t}}_1}}}{{{{\bar{t}}_2}}}} \right)}}^{2.24166088 }}}}} \)

 with \( {{\bar{t}}_2}\ne {{\bar{t}}_1}+1 \)

 R ² = 0.9737; \( R_{\mathrm{adj}}^2 \) = 0.972; RMS = 0.202; mean PRESS = 0.020; mean APRESS = 0.346; n = 58