Modeling structural traits of Aleppo pine (Pinus halepensis Mill.) forests with low-density LiDAR

Figures & data

Figure 1. Locations of the ground data used in this study. Colors represent the number of plots per location, and the box summarizes the plot categories regarding historic land use. The Pinus halepensis Mill. coverage has been extracted from the IV National Forest Inventory Map National Forest Map 1:25,000 (2007–2017) (MAGRAMA 2012).

Table 1. Forest inventory summary of the measured and modeled variables, classified by historic land use and past cover.

Historic use	Dense forestland (N = 44)				Sparse forestland (N = 26)				Scrubland (N = 10)				Agricultural land (N = 33)
Statistic/variable	Min.	Max.	Mean	Std. Dev.	Min.	Max.	Mean	Std. Dev.	Min.	Max.	Mean	Std. Dev.	Min.	Max.	Mean	Std. Dev.
DBH (cm)	18.2	31.0	24.1	3.5	14.6	37.2	24.1	5.7	12.8	38.7	23.2	7.6	16.0	33.9	25.0	4.3
BA (m^2 ha^−1)	4.18	45.27	22.18	7.82	3.63	38.92	17.99	7.80	0.41	38.30	18.52	10.08	5.82	50.53	18.32	9.46
Hmean (m)	7.8	15.3	10.6	1.5	7.2	15.8	10.7	2.4	6.0	14.3	10.7	2.4	9.4	16.7	12.3	2.0
Hdom (m)	8.6	18.4	12.1	1.9	7.8	19.7	12.8	2.9	6.0	18.6	13.0	3.5	9.5	21.2	14.2	2.6
Age (years)	58	113	82	12	23	88	73	14	37	78	56	13	30	89	46	14
Density (trees ha^−1)	95	955	453	171	127	987	386	216	32	891	363	230	95	955	335	174
SI (m)	8.4	16.7	11.9	2.0	8.8	20.3	13.0	2.7	8.9	19.8	14.9	3.5	12.2	32.3	19.0	4.6
AGB (Mg ha^−1)	13.47	191.57	82.66	35.40	10.40	212.18	71.57	44.67	0.87	236.42	83.96	63.46	18.47	291.69	83.80	54.01
VOL (m^3 ha^−1)	18.32	229.09	104.89	41.42	17.04	219.93	89.31	45.21	2.31	240.63	98.58	62.92	22.63	303.36	99.11	56.32

Table 2. Pinus halepensis Mill. allometric and volumetric equations.

Item	Units	Expression	Equation	Reference
Stem	kg	$W_s=0.0139\cdot d^2\text{cdoth}$	(1(7) $\mathit{SI}=H_{\mathit{dom}}\cdot {\left(\frac{1-e^{-b\cdot A_0}}{1-e^{-\mathit{b}\cdot \mathit{A}}}\right)}^{\frac{1}{c}}$(7) )	Ruiz-Peinado et al. (2011)
Thick branches	kg	If d ≤27.5 cm then Z = 0; If d >27.5 cm then Z = 1 $W_{\mathit{b}7}=\left[3.926\cdot \left(\mathit{d}-27.5\right)\right]\text{cdotZ}$	(2(7) $\mathit{SI}=H_{\mathit{dom}}\cdot {\left(\frac{1-e^{-b\cdot A_0}}{1-e^{-\mathit{b}\cdot \mathit{A}}}\right)}^{\frac{1}{c}}$(7) )	Ruiz-Peinado et al. (2011)
Medium branches	kg	$W_{\mathit{b}2-7}=4.257+0.00506\cdot d^2\text{cdoth}-0.0722\text{cdotdcdoth}$	(3(9) $\mathit{RMSE}=\sqrt{\frac{\sum _{\mathit{i}=1}^n{\left(y_i-{\hat{y}}_{\mathit{i}}\right)}^2}{\mathit{n}}}$(9) )	Ruiz-Peinado et al. (2011)
Thin branches + needles	kg	$W_{\mathit{b}2+\mathit{n}}=6.197+0.00932\cdot d^2\text{cdoth}-0.0686\text{cdotdcdoth}$	(4(10) $\mathit{RRMSE}=\frac{\mathit{RMSE}}{\bar{y}}$(10) )	Ruiz-Peinado et al. (2011)
Above-ground Biomass	kg	$\mathit{AGB}=W_s+W_{\mathit{b}2-7}+W_{\mathit{b}2+\mathit{n}}$	(5(11) $\mathit{d}=4.7217+1.2407\cdot \mathit{h}+0.0392\cdot h^2$(11) )	Ruiz-Peinado et al. (2011)
Total Volume	dm^3	$\mathit{VOL}=47.45+0.0000257\cdot {\left(\mathit{d}\cdot 10\right)}^2\text{cdoth}$	(6(11) $\mathit{d}=4.7217+1.2407\cdot \mathit{h}+0.0392\cdot h^2$(11) )	MAGRAMA (2012)

Biomass yields in kilograms, volume in cubic decimeters. Diameter at breast height (d) in cm and total height (h) in meters. Equations 1(7) $\mathit{SI}=H_{\mathit{dom}}\cdot {\left(\frac{1-e^{-b\cdot A_0}}{1-e^{-\mathit{b}\cdot \mathit{A}}}\right)}^{\frac{1}{c}}$(7) to 5(11) $\mathit{d}=4.7217+1.2407\cdot \mathit{h}+0.0392\cdot h^2$(11) extracted from Ruiz-Peinado et al. (2011), Equation 6(11) $\mathit{d}=4.7217+1.2407\cdot \mathit{h}+0.0392\cdot h^2$(11) extracted from MAGRAMA (2012). For allometric equations, thick branches are of more than 7 cm in diameter, medium branches are between 7 and 2 cm in diameter, and thin branches are below 2 cm in diameter.

Table 3. Names of the variables computed for the ABA methodology.

avgHTagrn1	Mean	pct85HTagrn1	85th percentile
medianHTagrn1	Median	pct90HTagrn1	90th percentile
stdHTagrn1	Standard deviation	pct95HTagrn1	95th percentile
varHTagrn1	Variance	pct99HTagrn1	99th percentile
vcHTagrn1	Variation coefficient	pte1rn1	Percentage of first returns above 1 m
maxHTagrn1	Maximum	pte2rn1	Percentage of first returns above 2 m
minHTagrn1	Minimum	pte5rn1	Percentage of first returns above 5 m
skHTagrn1	Skewness	pte10rn1	Percentage of first returns above 10 m
ktHTagrn1	Kurtosis	pte15rn1	Percentage of first returns above 15 m
pct5HTagrn1	5th percentile	pte20rn1	Percentage of first returns above 20 m
pct10HTagrn1	10th percentile	fci2	First echo cover index at 2 m
pct25HTagrn1	25th percentile	fciavgHt	First echo cover index at average crown height
pct75HTagrn1	75th percentile	•	•

All the variables are computed for the first returns above ground (i.e. height above ground ≥ 2).

Table 4. Names of the variables computed for the ITD methodology.

proxyTPH	Number of detected treetops	Htpct90	90th percentile of individual heights
avgHt	Mean height of the trees	Htpct95	95th percentile of individual heights
medianHt	Median height of the trees	Htpct99	99th percentile of individual heights
Htpct75	75th percentile of individual heights	Htmax	Maximum individual height
Htpct80	80th percentile of individual heights	proxyBA	proxy of BA
Htpct85	85th percentile of individual heights	proxyAGB	proxy of AGB
–	–	proxyVOL	proxy of VOL

Figure 2. General overview of the methodologies applied in this study. In blue, are the method steps that involve ground data, in green are the steps that involve LiDAR data and in orange are the steps that involve both.

Table 5. Expressions to predict forest attributes for both LiDAR-based methodologies.

Method.	Forest Attribute	Expression	Núm.
Area-Based Approach	AGB (Mg ha^−1)	$\mathit{AGB}=65.2339-21.5444\cdot \mathit{avgHTagrn}1+1.9932\cdot \mathit{avgHTagrn}{1}^2+0.6983\cdot \mathit{pte}5\mathit{rn}1$	11
	VOL (m^3 ha^−1)	$\mathit{VOL}=63.4626-21.2720\cdot \mathit{avgHTagrn}1+1.8986\cdot \mathit{avgHTagrn}{1}^2+1.1192\cdot \mathit{pte}5\mathit{rn}1$	12
	TPH (trees ha^−1)	$\mathit{TPH}=299.9573-5.6318\cdot \mathit{vcHTagrn}1+603.3975\cdot \mathit{fciavgHT}$	13
	BA (m^2 ha^−1)	$\mathit{BA}=-5.2010+3.3765\cdot \mathit{pct}25\mathit{HTagrn}1$	14
	Hdom (m)	$H_{\mathit{dom}}=0.5694+0.9952\cdot \mathit{pct}95\mathit{HTagrn}1$	15
Individual-Tree Detection	AGB (Mg ha^−1)	$\mathit{AGB}=34.3894+1.6520\cdot \mathit{proxyAGB}$	16
	VOL (m^3 ha^−1)	$\mathit{VOL}=39.1917+1.6896\cdot \mathit{proxyVOL}$	17
	TPH (trees ha^−1)	$\mathit{TPH}=137.5623+1.6524\cdot \mathit{proxyTPH}$	18
	BA (m^2 ha^−1)	$\mathit{BA}=8.7911+1.5835\cdot \mathit{proxyBA}$	19
	Hdom (m)	$H_{\mathit{dom}}=1.1977+0.9077\cdot \mathit{HTpct}95$	20

Tree density model has been calculated for N = 106 plots, when measured TPH ≥ 750; RRMSE of the dominant height model has been obtained using the most extended definition of dominant height (domHtassb).

Figure 3. Maps of basal area (1), dominant height (2), volume (3) and above-ground biomass (4) for a forested area of the southwestern part of Ibiza Island. The maps have been generated using the models shown in Table 5 (ABA) and the resolution is 20 m.

Table 6. Goodness of fit in terms of R², RMSE, and RRMSE for all the models shown in Table 5 for both LiDAR-based methodologies.

Methodology	Forest Attribute	R^2	RMSE (m)	RRMSE (%)
Area-Based Approach	AGB (Mg ha^−1)	0.655	27.28	33.86
	VOL (m^3 ha^−1)	0.691	27.40	27.66
	TPH (trees ha^−1)	0.449	110	27.87
	BA (m^2 ha^−1)	0.623	5.35	27.05
	Hdom (m)	0.685	1.48	11.41
Individual-Tree Detection	AGB (Mg ha^−1)	0.508	32.55	40.40
	VOL (m^3 ha^−1)	0.539	33.40	33.71
	TPH (trees ha^−1)	0.226	130	33.00
	BA (m^2 ha^−1)	0.479	6.28	31.76
	Hdom (m)	0.704	1.44	11.10

Values are the result of a 500-repetition bootstrapping validation procedure. Tree density model has been calculated for N = 106 plots, when measured TPH ≥ 750; RRMSE of the dominant height model has been obtained using the most extended definition of dominant height (domHtassb).

Figure 4. Performance of the models of above-ground biomass (1), total volume (2), trees per hectare (3), basal area (4), and dominant height (5) regarding time lag (left, in blue), and pulse density (right, in green). Residuals are calculated as the observed value minus the predicted value. The whiskers represent the 5th and 95th percentiles of the distribution. The white numbers correspond to the median values, and the black numbers above each box correspond to the number of observations in each group. The tree density model has been calculated for N = 106 plots, when measured TPH ≥ 750; the dominant height represents the average height of the 100 thickest trees per hectare (domHtassb). The fitted resolution is 20 m.

Figure 5. Behavior of the most explanatory covariate of above-ground biomass (AGB, 1) and volume (VOL, 2) (avgHtagrn1) by land cover historic use. Regression is fitted using a linear model to prevent overfitting due to limited sample size of each level. The fitted resolution is 20 m.

Figure 6. Behavior of the most explanatory percentile of height (pct95HTagrn1) for the five different dominant height definitions tested, and by land cover historic use. R², RMSE, and RRMSE correspond to all data. The fitted resolution is 20 m.

Table 7. Tukey’s HSD test results (alpha 0.05) for the analysis of past use and land history effect on site index in meters for a base age of 80 years.

Historic land use and cover	Letter report of significance			Site index base age 80 years mean (m)
Agricultural land	A			19.0
Scrubland		B		14.9
Sparse forestland		B	C	13.0
Dense forestland			C	11.9

Levels not connected by the same letter are significantly different.

Ruiz-Peinado, R., Del Rio, M., & Montero, G. (2011). New models for estimating the carbon sink capacity of Spanish softwood species. Forest Systems, 20(1), 176–188. https://doi.org/10.5424/fs/2011201-11643

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Data availability statement

The PNOA LiDAR and orthophotography data is openly available at https://centrodedescargas.cnig.es/CentroDescargas/index.jsp. Forest inventory data is property of the landowners and managed by TERRAPI WORLD S.L. and will be available from the corresponding author (VARC) upon reasonable request.