Table 10 PBIRROL model—sub-models for tree volume prediction over bark (tree volume, tree volume ratio to any top merchantable limit and tree bole diameters)

Tree volume equation (over bark)

 \( v = 0.01437 + 0.00003293{d^2}h \)

 R ² = 0.913; \( R_{\mathrm{adj}}^2 \) = 0.912; RMS = 0.003; mean PRESS = −0.0002; mean APRESS = 0.027; n = 314

Tree volume ratio equation to any top height limit

 \( {r_h}=1+\left[ {-0.9201\frac{{{{{\left( {h-{h_d}} \right)}}^{2.8138 }}}}{{{h^{2.7901 }}}}} \right] \)

 with r _h —volume ratio (v _m/v) below h _d

 R ² = 0.9847; \( R_{\mathrm{adj}}^2 \) = 0.987; RMS = 0.001; mean PRESS = −0.003; mean APRESS = 0.026; n = 2,038

Tree volume ratio equation to any top diameter limit (over bark)

 \( {r_d}={e^{{-1.152{{{\left( {\frac{{{d_h}}}{d}} \right)}}^{3.7455 }}}}} \)

 with r _d —volume ratio (v _m/v) below d _h

 R ² = 0.928; \( R_{\mathrm{adj}}^2 \) = 0.928; RMS = 0.008; mean PRESS = −0.002; mean APRESS = 0.059; n = 2,038

Compatible tree taper equation (over bark)

 \( {d_h}=d{{\left[ {63,580.17\left( {\frac{1}{{{d^2}h}}} \right){{{\left( {\frac{{h-{h_d}}}{h}} \right)}}^{346.5 }}+1.151001{{{\left( {\frac{{h-{h_d}}}{h}} \right)}}^{1.7452 }}} \right]}^{0.5 }} \)

 R ² = 0.950; \( R_{\mathrm{adj}}^2 \) = 0.950; RMS = 3.606; mean PRESS = 0.238; mean APRESS = 1.264; n = 2,353