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Table 4 Summary of the equations used for indirectly predicting SI as a function of the ten growth parameters

From: Rule-based vs parametric approaches for developing climate-sensitive site index models: a case study for Scots pine stands in northwestern Spain

Model label

Equation

Variables

ABC

\(SI_{abc}=\frac{\hat{a}}{1+\hat{b}t_{ref}^{-\hat{c}}}\)

\(\hat{a}\),\(\hat{b}\),\(\hat{c}\)

IP1

\(SI_{ip1}=\hat{h}_{ip} \frac{1 + \frac{1}{2 \hat{c} / (\hat{c} + 1) - 1}}{1 + \frac{\hat{t}_{ip} ^ c t_{ref} ^ {-\hat{c}}}{2 \hat{c} / (\hat{c} + 1) - 1}}\)

\(\hat{h}_{ip}\), \(\hat{t}_{ip}\), \(\hat{c}\)

IP2

\(SI_{ip2}=\hat{g}_{ip} \hat{t}_{ip}^{2\hat{c}}\frac{(1 + \frac{1}{2\hat{c} / (\hat{c} + 1) - 1})^2}{1 + \frac{\hat{t}_{ip} ^{ \hat{c}} t_{ref} ^ {-\hat{c}}}{2 \hat{c} / (\hat{c} + 1) - 1}}\frac{\hat{c} \hat{t}_{ip}^{2\hat{c}+1}}{2\hat{c} / (\hat{c} - 1) - 1}\)

\(\hat{g}_{ip}\), \(\hat{t}_{ip}\), \(\hat{c}\)

MMG1

\(SI_{mmg1}=\hat{h}_{mmg} \frac{1 + \frac{1}{\hat{c} - 1}}{1 + \frac{\hat{t}_{mmg} ^{\hat{c}} t_{ref} ^ {-\hat{c}}}{\hat{c} - 1}}\)

\(\hat{h}_{mmg}\), \(\hat{t}_{mmg}\), \(\hat{c}\)

MMG2

\(SI_{mmg2}=\hat{mmg} \hat{t}_{mmg} \frac{1 + \frac{1}{\hat{c} - 1}}{1 + \frac{\hat{t}_{mmg} ^{ \hat{c}} t_{ref} ^ {-\hat{c}}}{\hat{c} - 1}}\)

\(\hat{mmg}\), \(\hat{t}_{mmg}\), \(\hat{c}\)

MMG3

\(SI_{mmg3}=\hat{h}_{mmg} \frac{1 + \frac{1}{\hat{c} - 1}}{1 + \frac{(\hat{h}_{mmg}/\hat{mmg}) ^{ \hat{c}} t_{ref} ^ {-\hat{c}}}{\hat{c} - 1}}\)

\(\hat{mmg}\), \(\hat{h}_{mmg}\), \(\hat{c}\)