Table 17 Summary table of all stand variables involved (modified based on Ciceu et al. 2020; Dănescu et al. 2016)

Tree

1

DBH _m

Mean value of the DBH(cm)

\(\frac{{\sum }_{j=1}^{n}{DBH}_{j}}{n}\)

\({DBH}_{j}\) is the diameter of tree j at breast height (cm)

\({H}_{j}\) is the tree height of tree j (m)

\(n\) is the number of trees measured

\({H}_{D}\) is the height of the tree with diameter (D) at breast height (m)

2

H _m

Mean value of the tree height (m)

\(\frac{{\sum }_{j=1}^{n}{H}_{j}}{n}\)

Stand

3

Dq

Quadratic mean DBH (cm)

\(\sqrt{{\sum }_{j=1}^{n}\frac{{DBH}_{j}^{2}}{n}}\)

4

Hq

Quadratic mean tree height (m)

\(\sqrt{{\sum }_{j=1}^{n}\frac{{H}_{j}^{2}}{n}}\)

5

DBH _max

Maximum DBH (thickest tree)

\(Max\left(DBH\right)\)

6

H _max

Maximum tree height (highest tree)

\(Max\left(H\right)\)

7

Range DBH

Range of the DBH

\(Max\left(DBH\right)-Min\left(DBH\right)\)

8

Range H

Range of the tree height

\(Max\left(H\right)-Min\left(H\right)\)

9

Range H_D

Difference between the tree height of the thickest tree and the thinnest tree

\(Max\left({H}_{D}\right)-Min\left({H}_{D}\right)\)

10

H _Dmax

Tree height of the thickest tree

\(Max\left({H}_{D}\right)\)

11

DBH _dom

Dominant DBH

Average DBH of the 3 thickest trees in each stand

12

H _dom

Dominant tree height

Average tree height of the 3 thickest trees in each stand

DBH diversity

13

Hd

Shannon index

\(-{\sum }_{j=1}^{Nd}\left({P}_{j}\times ln\left({P}_{j}\right)\right)\)

\(Nd\) is the number of diameter classes at breast height

\({P}_{j}\) is the proportion of the basal area of the j-th diameter class at breast height

14

GCd

Gini coefficient

\(\frac{{\sum }_{i=1}^{n}\left(2\times i-n-1\right)\times {BA}_{i}}{{\sum }_{i=1}^{n}\left(n-1\right)\times {BA}_{i}}\)

\({BA}_{i}\) is the basal area for the tree with rank i

\(i\) is the rank of a tree in ascending order from \(1,...,n\)

\(n\) is the total number of trees

15

Vard

Coefficient of variation of DBH

\(100\times \frac{{sd}_{DBH}}{\overline{DBH}}\)

\({sd}_{DBH}\) is the SD of the DBH

\(\overline{DBH}\) is the arithmetic mean diameter at breast height (cm)

Density and competition

16

BA

Basal area per hectare (m²ha⁻¹)

\(\frac{\frac{\pi }{40000}\left({\sum }_{j=1}^{n}{DBH}_{j}^{2}\right)}{S}\)

\(S\) is the stand area (ha)

\({DBH}_{j}\) is the diameter of tree j (cm) at breast height

17

BAL

Basal area of the largest trees (m²ha⁻¹)

Sum of the basal areas of the 3 thickest trees in each stand

18

N

The number of trees per hectare (Nha⁻¹)

19

SDI

Stand density index of uneven aged stands

\({\sum }_{j=1}^{n}\left({N}_{j}{\left(\frac{{DBH}_{j}}{25}\right)}^{1.605}\right)\)

\({N}_{j}\) is the number of trees in the diameter class j at breast height

\({DBH}_{j}\) is the middle of j diameter class at breast height (cm)

\(n\) is the total number of diameter classes at breast height

20

RD

The ratio of each individual DBH to Dq

\(\frac{DB{H}_{j}}{Dq}\)

Geographic information

21

ALT

Altitude (m)

22

lat

Latitude

23

lng

Longitude

Mixed stand

24

RBA

Proportion of the basal area of each species in relation to the total basal area

\(\frac{{BA}_{j}}{{BA}_{i}}\)

\({BA}_{j}\) is the basal area of tree species j in stand i

\({BA}_{i}\) is the total basal area in stand i

25

RN

Proportion of the number of each species in relation to the total number of trees

\(\frac{{N}_{j}}{{N}_{i}}\)

\({N}_{j}\) is the number of tree species j in stand i

\({N}_{i}\) is the total number of trees in stand i