Development of ingrowth models for forest types in South Korea

Figures & data

Figure 1. Sampling design for the Korean NFI.

Table 1. Summary of the ingrowth attributes by forest type.

Forest type	Total no. of sampling plots	Sampling plots with ingrowth	Sampling plots without ingrowth	Ingrowth ratio (%)
Coniferous Forest	2585	406	2179	15.7
Broad-leaved Forest	1364	270	1094	19.8
Mixed Forest	864	363	501	41.9

Table 2. Model forms used in this study to estimate the ingrowth probability.

Model no.	Model form
I	$P_i=\frac{1}{1\hspace{0.17em}+\hspace{0.17em}{e}^{b_0\hspace{0.17em}+\hspace{0.17em}{b}_{1}BA\hspace{0.17em}+\hspace{0.17em}{b}_{2}SI}}$
II	$P_i=\frac{1}{1\hspace{0.17em}+\hspace{0.17em}{e}^{b_0\hspace{0.17em}+\hspace{0.17em}{b}_1{D}_q\hspace{0.17em}+\hspace{0.17em}{b}_2\overline{H}}}$
III	$P_i=\frac{1}{1\hspace{0.17em}+\hspace{0.17em}{e}^{b_0\hspace{0.17em}+\hspace{0.17em}{b}_1{D}_q\hspace{0.17em}+\hspace{0.17em}{b}_{2}BA\hspace{0.17em}+\hspace{0.17em}{b}_{3}SI\hspace{0.17em}+\hspace{0.17em}{b}_{4}N}}$
IV	$P_i=\frac{1}{{\left(1\hspace{0.17em}+\hspace{0.17em}{e}^{b_0\hspace{0.17em}+\hspace{0.17em}{b}_{1}BA\hspace{0.17em}+\hspace{0.17em}{b}_{2}N\hspace{0.17em}+\hspace{0.17em}{b}_3{SC}_1\hspace{0.17em}+\hspace{0.17em}{b}_4\overline{D}{b}_{5}SI}\right)}^{1/L}}$
V	$P_i=\frac{1}{{\left(1\hspace{0.17em}+\hspace{0.17em}{e}^{b_0\hspace{0.17em}+\hspace{0.17em}{b}_{1}BA\hspace{0.17em}+\hspace{0.17em}{b}_2{D}_q\hspace{0.17em}+\hspace{0.17em}{b}_{3}PS\hspace{0.17em}+\hspace{0.17em}{b}_4{SC}_1}\right)}^{1/{\left(L\times F\right)}^{\omega }}}$
VI	$P_i=\frac{1}{{\left(1\hspace{0.17em}+\hspace{0.17em}{e}^{b_0\hspace{0.17em}+\hspace{0.17em}{b}_{1}BA\hspace{0.17em}+\hspace{0.17em}{b}_2{SC}_2\hspace{0.17em}+\hspace{0.17em}{b}_{3}N\hspace{0.17em}+\hspace{0.17em}{b}_{4}SI\hspace{0.17em}+\hspace{0.17em}{b}_5{D}_{\mathit{min}}}\right)}^L}$

$\overline{\mathrm{DBH}}$ = stand average diameter at breast height (cm); $D_{\mathit{min}}$ = minimum diameter (cm); $D_q$ = quadratic mean diameter (cm); $\overline{H}$ = average height (m); $BA$= basal area per hectare ($m^2/ha$); $N$ = number of trees per hectare (trees/ha); $PS$ = percent stocking; ${SC}_1$ = ratio of target species density (${N/ha}_{sp}$) over total stand density (${N/ha}_{\mathit{total}}$); ${SC}_2$ = ratio of target species basal area (${BA/ha}_{sp}$) over total stand basal area (${BA/ha}_{\mathit{total}}$); $SI$ = site index (reference age 30); $L$ = measurement interval length; $F$ = plot size factor; and $\omega$ = exponent to annual survival probability Sources. in model’s numerical order (Vanclay 1989; Qin 1998; Brovo et al. 2008; Adame et al. 2010; Li et al. 2011; Yang and Huang 2015).

Table 3. Model forms to estimate the ingrowth amount as the number of trees per hectare.

Model no.	Model form
I	$I_n=b_0\hspace{0.17em}+\hspace{0.17em}{b}_{1}BA\hspace{0.17em}+\hspace{0.17em}{b}_{2}SI$
II	$ln\left(I_n\right)=b_0\hspace{0.17em}+\hspace{0.17em}{b}_{1}ln\left(N\right)\hspace{0.17em}+\hspace{0.17em}{b}_2\left(1/{\overline{D}}^2\right)$
III^a	$I_n=b_0{e}^{b_{1}N\hspace{0.17em}+\hspace{0.17em}{b}_{2}BA\hspace{0.17em}+\hspace{0.17em}{b}_{3}SI\hspace{0.17em}+\hspace{0.17em}{b}_4{\overline{\mathit{DBH}}}^2\hspace{0.17em}+\hspace{0.17em}{b}_5\overline{\mathit{DBH}}}$
IV^a	$I_n=b_0{e}^{b_{1}ln\left(N\right)\hspace{0.17em}+\hspace{0.17em}{b}_{2}BA\hspace{0.17em}+\hspace{0.17em}{b}_3{SC}_2\hspace{0.17em}+\hspace{0.17em}{b}_4{\overline{\mathit{DBH}}}^2\hspace{0.17em}+\hspace{0.17em}{b}_5\overline{\mathit{DBH}}}$
V^b	$I_n=e^{\left(b_0\hspace{0.17em}+\hspace{0.17em}{b}_{1}BA\hspace{0.17em}+\hspace{0.17em}{b}_2\left(D_q\hspace{0.17em}\times \hspace{0.17em}PS\right)\hspace{0.17em}+\hspace{0.17em}{b}_{3}SI\hspace{0.17em}+\hspace{0.17em}{b}_4\sqrt{N}\right)}$
VI^b	$I_n=e^{\left(b_0\hspace{0.17em}+\hspace{0.17em}{b}_{1}BA\hspace{0.17em}+\hspace{0.17em}{b}_2\left(D_q\hspace{0.17em}\times \hspace{0.17em}PS\right)\hspace{0.17em}+\hspace{0.17em}{b}_{3}ln\left(PS\right)\hspace{0.17em}+\hspace{0.17em}{b}_4\sqrt{N}\right)}$
VII^b	$I_n=e^{\left(b_0\hspace{0.17em}+\hspace{0.17em}{b}_{1}BA\hspace{0.17em}+\hspace{0.17em}{b}_2{D}_q\hspace{0.17em}+\hspace{0.17em}{b}_{3}PS\hspace{0.17em}+\hspace{0.17em}{b}_4\left(D_q\hspace{0.17em}\times \hspace{0.17em}PS\right)\hspace{0.17em}+\hspace{0.17em}{b}_5\left(SI\hspace{0.17em}\times \hspace{0.17em}{SC}_1\right)\right)}$

Sources. in model’s numerical order (Vanclay 1989;

^aQin 1998; Adame et al. 2010; ^bYang and Huang 2015).

Note. The model symbol identical with that in Table 2.

Table 4. Estimated parameters and root mean square errors (RMSEs) for ingrowth probability models by forest type.

Forest type	Model no.	Estimates of the regression coefficients						RMSE
		$b_0$	$b_1$	$b_2$	$b_3$	$b_4$	$b_5$
Coniferous Forest	I	−2.2557	0.0016	0.3977	–	–	–	0.34
	II	−1.7217	0.1077	0.1140	–	–	–	0.34
	III	−1.3530	0.0412	0.0236	0.2236	−0.0005	–	0.33
	IV	−0.8575	0.1423	−0.0024	−0.0482	−0.0181	1.0125	0.34
	V	10.2682	0.0010	0.1262	0.0032	0.0664	−3.6200	0.34
	VI	−5.5621	0.0036	−0.5809	0.0002	0.0164	0.6384	0.31
Broad-leaved Forest	I	−1.3661	0.0256	0.2108	–	–	–	0.39
	II	−1.7254	0.0287	0.2098	–	–	–	0.39
	III	−1.0904	0.0352	0.0275	0.1444	−0.0003	–	0.39
	IV	0.6880	0.1029	−0.0011	−1.4441	0.0907	0.5239	0.39
	V	10.1598	0.0101	0.0656	−0.7113	0.5211	−3.2894	0.39
	VI	−9.7031	−0.0013	−0.4574	0.0006	0.0898	1.0695	0.34
Mixed Forest	I	−0.7254	0.0305	0.0180	–	–	–	0.49
	II	−1.8141	0.2693	−0.2727	–	–	–	0.41
	III	−5.8583	0.3562	−0.0679	−0.1180	0.0015	–	0.40
	IV	12.0020	0.0165	−0.0013	−17.8740	0.0315	0.5663	0.34
	V	2.4360	−0.0105	0.1020	−2.0260	−2.7752	−0.0597	0.35
	VI	−5.7086	−0.0089	−4.3589	0.0005	0.1391	0.7503	0.31

Table 5. Statistics of ingrowth probability estimated using ingrowth probability equations by forest type.

Forest type	Stand variables	No. of plots	Estimates of the ingrowth probability
			Mean	SD	Min	Max
Coniferous Forest	With ingrowth	406	0.54	0.0584	0.42	0.67
	Without ingrowth	2179	0.10	0.1484	0.00	0.49
Broad-leaved Forest	With ingrowth	270	0.58	0.0675	0.45	0.77
	Without ingrowth	1094	0.10	0.1477	0.00	0.46
Mixed Forest	With ingrowth	363	0.83	0.0950	0.50	0.93
	Without ingrowth	501	0.07	0.1313	0.00	0.48

Table 6. Estimated parameters and evaluation statistics for the ingrowth amount models by forest type.

Forest Type	Model No.	Estimates of the regression coefficients						$FI$	Evaluation Statistics
		$b_0$	$b_1$	$b_2$	$b_3$	$b_4$	$b_5$		$MD$	$\mathit{SDD}$	$\mathit{SED}$
Coniferous Forest	I	227.9786	−0.6746	−13.0942	–	–	–	0.43	−1.76	41.59	41.61
	II	0.5165	0.4385	86.1527	–	–	–	0.66	9.20	39.02	42.08
	III	280.8	0.0005	−0.0305	−0.1012	0.0014	−0.0445	0.63	−3.88	38.51	39.06
	IV	0.0709	1.0865	−0.0532	1.3211	0.0030	−0.0949	0.64	−0.76	37.10	37.12
	V	4.2188	−0.0363	0.0163	−0.0829	0.0460	–	0.64	−0.51	37.49	37.50
	VI	3.8021	−0.0515	0.0036	0.0512	0.0528	–	0.66	−1.52	38.84	38.88
	VII	6.6854	0.0078	−0.1510	−0.5310	0.0511	−0.0247	0.62	0.38	38.07	38.10
Broad-leaved Forest	I	289.5019	−0.6967	−19.3465	–	–	–	0.45	0.52	48.13	48.14
	II	−0.2741	0.5486	86.0060	–	–	–	0.62	11.20	44.08	45.61
	III	217.8000	0.0008	−0.0312	−0.1307	0.0011	−0.0436	0.67	3.24	36.78	36.91
	IV	0.0005	1.6133	−0.0360	1.8766	0.0011	−0.0375	0.67	−0.61	36.99	36.95
	V	2.5806	−0.0490	0.0546	−0.1297	0.0900	–	0.67	1.65	38.82	38.83
	VI	5.1459	−0.0088	−0.1229	2.4998	0.0414	–	0.67	2.26	38.40	38.40
	VII	3.3037	0.0391	−0.0510	5.2399	−0.2155	−0.1032	0.68	1.52	36.70	36.70
Mixed Forest	I	176.6465	−0.8467	−3.6772	–	–	–	0.41	0.28	44.86	44.88
	II	1.6843	0.3629	40.8072	–	–	–	0.46	8.79	48.65	51.47
	III	28.5452	0.0005	−0.0329	0.0607	−0.0027	0.1016	0.62	2.76	47.32	47.40
	IV	0.0052	1.1786	−0.0444	2.6638	0.0002	0.0061	0.70	−0.93	42.06	42.08
	V	1.6363	−0.0594	0.0660	0.0605	0.0810	–	0.64	−0.12	45.70	45.76
	VI	4.3994	−0.0291	−0.0217	2.2310	0.0440	–	0.68	0.25	41.91	41.92
	VII	4.6187	0.0050	−0.0989	1.7531	−0.0046	0.0085	0.67	0.50	43.68	43.69

Table 7. Ingrowth amount estimates of the number of trees per hectare based on the final ingrowth amount estimation equations by forest type.

Forest type	Stand con-dition	Stand variables									Estimated ingrowth (N/ha)
		$\mathit{Age}$	$D_q$$(cm)$	$BA$$(m^2/ha)$	$SI$	$N$$(\mathit{trees}/ha)$	$\overline{\mathit{DBH}}$$(cm)$	${SC}_1$	${SC}_2$	$PS$
Coniferous Forest	1	15	9.4	14.5	12	2933	8.0	0.87	0.91	0.91	362
	2	30	19.2	27.0	15	1147	18.6	0.79	0.80	0.87	49
	3	50	30.9	35.9	18	621	31.9	0.70	0.73	0.79	31
Broad-leaved Forest	1	15	9.4	14.5	13	2700	9.0	0.78	0.83	0.81	141
	2	30	16.8	23.4	15	1198	16.1	0.70	0.79	0.72	31
	3	50	26.6	32.1	18	716	25.7	0.65	0.71	0.68	5
Mixed Forest	1	15	9.4	14.5	12	2847	8.5	0.84	0.84	0.86	335
	2	30	18.0	25.2	15	1172	17.4	0.74	0.78	0.80	78
	3	50	28.8	34.0	18	669	28.8	0.68	0.72	0.74	30

Note. ${SC}_1$(density-based species composition) and ${SC}_2$(basal area-based species composition) have a range of zero to one.

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