Retrieval and validation of vertical LAI profile derived from airborne and spaceborne LiDAR data at a deciduous needleleaf forest site

Figures & data

Figure 1. The framework for retrieval and validation of the LAI profiles derived from DHP, TLS, ALS, and GEDI.

Figure 2. The location of the study area. The left panel (a) shows the locations of all measurements and the GEDI footprints (Background Google Earth Image obtained by CNES/Airbus on June 29, 2018). The right panel shows two field pictures taken near a measurement tower (42°24′N, 117°18′E, yellow triangle in (a) during (b) leaf-on (September 6, 2020) and (c) leaf-off (April 24, 2021) seasons, respectively.

Figure 3. (a) The sampling strategy within a plot with five elementary vertical sampling points (VSPs) located at the center and four cardinal points, respectively; (b) a diagram of the portable measurement system at different heights (1.5–13.5 m) with 2 m interval; (c) field pictures were taken at 1.5–13.5 m with 2 m interval, respectively, on September 9, 2020. The upward DHP is within the red circle.

Table 1. DHP, TLS, ALS, and GEDI data used in the study. N is the number of plots for DHP and TLS and the number of footprints for GEDI, respectively.

	Acquisition date
	2018 (leaf-on)	2019 (leaf-off)	2020 (leaf-on)	2021 (leaf-off)	(leaf-on)
DHP	-	-	September 4–10 (N=23)	April 21–24 (N=23)	September 3–9 (N=12)*
TLS	-	-	September 5 (N=1)	-	-
ALS	September 5–17	-	-	-	-
GEDI	-	May 21 (N=23)	August 24 (N=11)	-	-

Note: *There are 11 plots in the GEDI footprints, one in the TLS site.

Figure 4. Upward DHP images acquired at different heights (1.5–13.5 m) with 2 m interval from the same vertical sampling point (VSP) in (a) leaf-on season (September 8, 2020) and (b) leaf-off season (April 25, 2021), respectively.

Table 2. The parameters of airborne LiDAR system and flight.

Acquisition date	September 5–17, 2018
Sensor	Riegl LMS-Q680i
Beam wavelength (nm)	1550
Beam divergence (mrad)	0.5
Footprint (m) @1000 m altitude	0.5
Altitude (m)	1000
Pulse repetition frequency (kHz)	240
Point density (m^−2) @1000 m altitude	4
Scan angle	≤30°

Table 3. Various LiDAR indices derived from the ALS return number and intensity*.

Name	Equation	Description	References
Light penetration index from returns (LPIR)	$LP{I}_R\left(i\right)=\frac{{\sum }^{R_{\le z}}}{{\sum }^{R_{\le z+dz}}}$	The ratio of returns going through the layer dz to those reaching the height z + dz.	(Bouvier et al. 2015)
Light penetration index from return intensity (LPIInt)	$LP{I}_{Int}\left(i\right)=\frac{{\sum }^{I}n{t}_{\le z}}{{\sum }^{I}n{t}_{\le z+dz}}$	The ratio of return intensity going through the layer dz to those reaching the z + dz.	(Luo et al. 2018)
Light penetration index combining returns and return intensity (LPIRI)	$LP{I}_{RI}\left(i\right)=\frac{1}{2}\left(1+\frac{1}{LP{I}_R\left(i\right)}+\frac{{\rho }_g}{{\rho }_v}\ast \frac{1-LP{I}_{Int}\left(i\right)}{LP{I}_{Int}\left(i\right)}\right)$	Combine the LPIR and LPIInt at each height interval.	This study
Fractional cover index from returns (FCIR)	$FC{I}_R\left(i\right)=\frac{{\sum }^{R_{>z}}}{{\sum }^{R_{all}}}$	The ratio of returns above height z to all returns.	(Riano et al. 2004)
Fractional cover index from return intensity (FCIInt)	$FC{I}_{Int}\left(i\right)=\frac{{\sum }^{\hspace{0.17em}}In{t}_{>z}}{{\sum }^{\hspace{0.17em}}In{t}_{all}}$	The ratio of return intensity above height z to all return intensity.	(Hopkinson and Chasmer 2009)
Fractional cover index combining returns and return intensity (FCIRI)	$FC{I}_{RI}\left(i\right)=\frac{1}{2}\left(\frac{{\sum }^{R_{>z}}}{{\sum }^{R_{all}}}+\frac{{\sum }^{I}n{t}_{>z}}{{\sum }^{I}n{t}_{all}}\right)$	Combine the FCIR and FCIInt at each height interval.	This study
Above and below ratio index from returns (ABRIR)	$ABR{I}_R\left(i\right)=\frac{{\sum }^{R_{>z}}}{{\sum }^{R_{\le z}}}$	The ratio of returns above height z to those below height z.	(Sumnall et al. 2021)
Above and below ratio index from return intensity (ABRIInt)	$ABR{I}_{Int}\left(i\right)=\frac{{\sum }^{I}n{t}_{>z}}{{\sum }^{I}n{t}_{\le z}}$	The ratio of return intensity above height z to those below height z.	(Sumnall et al. 2016)
Above and below ratio index combining returns and return intensity (ABRIRI)	$ABR{I}_{RI}\left(i\right)=\frac{1}{2}\left(\frac{{\sum }^{R_{>z}}}{{\sum }^{R_{\le z}}}+\frac{{\sum }^{I}n{t}_{>z}}{{\sum }^{I}n{t}_{\le z}}\right)$	Combine the ABRIR and ABRIInt at each height interval.	This study

Note: * Subscripts R and Int denote ALS return and intensity, respectively, and RI indicates the new index combining both ALS return and intensity. $z$ represents the height, and $dz$ is the height interval.

Figure 5. Relationships between the DHP layered and cumulative LAI (September 2020 and 2021) and various ALS (September 2018) indices from the training data. (a-c) and (g-i) the canopy fractional cover indices from return (FCI_R), intensity (FCI_Int), and both (FCI_RI), respectively; (d-f) and (j-l) the above and below ratio indices from return (ABRI_R), intensity (ABRI_Int), and both (ABRI_RI), respectively. The vertical color bar in (a) and (g) indicates the different heights for layered LAI and cumulative LAI, respectively. The index values are normalized to 0–1. The black line represents the regression line.

Figure 6. Comparison of the layered LAI estimated from ALS (September 2018) with the validation DHP data (September 2020 and 2021) during the leaf-on season. (a-c) 34 plots with the Beer-Lambert method; (d-i) 17 plots with the linear regression method.

Table 4. Comparison of statistics between the LAI profiles derived from various ALS indices (Table 3) and those from DHP (34 plots, 238 heights) during the leaf-on season.

Indices	Model	Modeling			Validation
		N	R^2	RMSE	N	R^2	RMSE	Bias
(a) Layered LAI (Figures 5 & 6)
LPIR	equation (6)(6) $LA{I}_i=\frac{1}{G}\ast ln\left(1+\frac{{\rho }_g}{{\rho }_v}\ast \frac{1-LPI\left(i\right)}{LPI\left(i\right)}\right)$(6)	-	-	-	238	0.86	0.15	0.06
LPIInt	equation (6)(6) $LA{I}_i=\frac{1}{G}\ast ln\left(1+\frac{{\rho }_g}{{\rho }_v}\ast \frac{1-LPI\left(i\right)}{LPI\left(i\right)}\right)$(6)	-	-	-	238	0.86	0.14	−0.07
LPIRI	equation (8)(8) $LA{I}_i=\frac{1}{G}\ast ln\left(LP{I}_{RI}\left(i\right)\right)$(8)	-	-	-	238	0.86	0.13	0.00
FCIR	$LAI=1.94\ast FCI+0.08$	119	0.88	0.10	119	0.88	0.11	−0.01
FCIInt	$LAI=2.37\ast FCI+0.09$	119	0.86	0.11	119	0.87	0.11	0.00
FCIRI	$LAI=2.13\ast FCI+0.08$	119	0.87	0.11	119	0.88	0.11	−0.01
ABRIR	$LAI=0.52\ast ABRI+0.09$	119	0.82	0.13	119	0.86	0.12	0.00
ABRIInt	$LAI=0.95\ast ABRI+0.10$	119	0.77	0.15	119	0.81	0.14	−0.01
ABRIRI	$LAI=0.66\ast ABRI+0.09$	119	0.81	0.13	119	0.83	0.13	−0.01
(b) Cumulative LAI (Figures 5 & 7)
LPIR	equation (6)(6) $LA{I}_i=\frac{1}{G}\ast ln\left(1+\frac{{\rho }_g}{{\rho }_v}\ast \frac{1-LPI\left(i\right)}{LPI\left(i\right)}\right)$(6)	-	-	-	238	0.89	0.27	0.06
LPIInt	equation (6)(6) $LA{I}_i=\frac{1}{G}\ast ln\left(1+\frac{{\rho }_g}{{\rho }_v}\ast \frac{1-LPI\left(i\right)}{LPI\left(i\right)}\right)$(6)	-	-	-	238	0.86	0.19	−0.28
LPIRI	equation (8)(8) $LA{I}_i=\frac{1}{G}\ast ln\left(LP{I}_{RI}\left(i\right)\right)$(8)	-	-	-	238	0.89	0.23	−0.10
FCIR	$LAI=2.36\ast FCI+0.24$	119	0.89	0.19	119	0.92	0.17	−0.03
FCIInt	$LAI=2.95\ast FCI+0.27$	119	0.86	0.22	119	0.91	0.19	−0.04
FCIRI	$LAI=2.64\ast FCI+0.26$	119	0.88	0.20	119	0.91	0.19	−0.05
ABRIR	$LAI=0.61\ast ABRI+0.28$	119	0.83	0.25	119	0.89	0.21	−0.05
ABRIInt	$LAI=1.06\ast ABRI+0.32$	119	0.75	0.29	119	0.84	0.26	−0.06
ABRIRI	$LAI=0.78\ast ABRI+0.30$	119	0.81	0.26	119	0.87	0.23	−0.06

Figure 7. Comparison of the cumulative LAI estimated from ALS (September 2018) with the validation DHP data (September 2020 and 2021) during the leaf-on season. (a-c) 34 plots for Beer-Lambert; (d-i) 17 plots for linear regression method.

Figure 8. Comparison of the layered LAI derived from ALS (September 2018) and TLS (September 2020) during the leaf-on season.

Figure 9. Vertical LAI maps (1 km × 1.5 km) Figure 2derived from the ALS using LPI_RI (September 2018) over the study area (red box in Figure 2).The color bar indicates the LAI values.

Figure 10. The vertical LAI profiles derived from (a) DHP (September 2020 and 2021) and ALS (September 2018) during the leaf-on (34 plots) and leaf-off (23 plots in April 2021) seasons, and (b) TLS and GEDI V2 during the leaf-on (1 plot for TLS in September 2020, and 11 plots for GEDI in August 2020) and leaf-off (23 plots for GEDI in May 2019) seasons. The ALS LAIs were derived from LPI_RI. The line and shades represent the mean and standard deviation values, respectively. Subscripts “on” and “off” indicate the leaf-on and leaf-off seasons, respectively.

Table 5. The mean LAI at different heights and the total LAI obtained from DHP, TLS, ALS, and GEDI V2 at different seasons, respectively. The ALS LAIs were derived from LPI_RI. The values of the standard deviations are shown in the brackets. All LAI profile data are from Figure 10.

System	Acquisition date	Height (m)							Total LAI
		1.5–3.5	3.5–5.5	5.5–7.5	7.5–9.5	9.5–11.5	11.5–13.5	>13.5
DHP	September 2020 and 2021 (leaf-on)	0.12 (0.05)	0.12 (0.04)	0.11 (0.05)	0.14 (0.06)	0.20 (0.10)	0.32 (0.14)	0.92 (0.34)	1.92 (0.35)
	April 2021 (leaf-off)	0.11 (0.03)	0.08 (0.03)	0.08 (0.03)	0.07 (0.05)	0.09 (0.04)	0.09 (0.04)	0.59 (0.14)	1.12 (0.17)
TLS	September 2020 (leaf-on)	0.03	0.01	0.02	0.04	0.22	0.43	1.12	1.87
ALS	September 2018 (leaf-on)	0.04 (0.05)	0.04 (0.03)	0.08 (0.06)	0.15 (0.09)	0.26 (0.12)	0.37 (0.14)	0.99 (0.35)	1.98 (0.42)
GEDI	-	0–5	5–10			10–15		>15	-
	21 May 2019 (leaf-off)	0.07 (0.06)	0.27 (0.08)			0.18 (0.07)		0.16 (0.05)	0.68 (0.16)
	24 August 2020 (leaf-on)	0.14 (0.06)	0.33 (0.23)			0.72 (0.12)		0.71 (0.29)	1.90 (0.29)

Figure 11. Comparison of the layered LAI at (a) all heights, (b) 0–15 m, and (c) > 15 m and (d) the cumulative LAI derived from GEDI V2 (August 2020) with the DHP measurements (September 2021) during the leaf-on season (11 plots).

Figure 12. Comparison of the layered LAI at (a) all heights, (b) 0–15 m, and (c) > 15 m and (d) the cumulative LAI derived from GEDI V2 (May 2019) and DHP (April 2021) during the leaf-off season (23 plots).

Figure 13. Comparison of the cumulative LAI derived from ALS (September 2018) and GEDI V2 (August 2020) during the leaf-on season (11 footprints).

Figure A1. An example intensity image (in raw digital number) for 3 pairs of adjacent footprints (#1, #9 and #10) selected from Figure 2. Left: bare ground returns; right: forest returns. The average return intensity of each footprint is shown in the lower right corner.

Table A1. The average return intensities (in raw digital number) for ρ_v/ρ_g calculated from 10 pairs of adjacent footprints (Figure 2). The values of the standard deviations are shown in the brackets.

	#1	#2	#3	#4	#5	#6	#7	#8	#9	#10	Average
Rv1	0	0	0	0	0	0	0	0	0	0	0 (0)
Rv2	37.56	35.30	32.34	30.23	34.81	33.14	31.07	57.33	33.26	33.94	35.90 (7.42)
Rg1	127.86	99.61	108.12	119.27	118.15	105.73	117.65	195.61	102.10	155.07	124.90 (28.03)
Rg2	87.02	68.70	79.51	95.15	78.08	71.91	88.87	136.61	67.49	125.22	89.86 (22.34)
ρv/ρg	0.92	1.14	1.13	1.25	0.87	0.98	1.08	0.97	0.96	1.14	1.04 (0.12)

Figure B1. (a) The vertical LAI profiles derived from TLS (September 2020) and DHP (September 2021) during the leaf-on season. (b) The scatterplot between the TLS and DHP. The subscript “on” indicates that the data were obtained in the leaf-on season.

Figure B2. Comparison of the layered (a) and cumulative (b) LAI profiles derived from GEDI V2 (August 2020) and TLS (September 2020) during the leaf-on season.

Figure C1. The 2 m LAI profiles derived from the GEDI V2 waveform data during the leaf-on (11 footprints) and leaf-off (23 footprints) seasons.

Table C1. The mean and total LAI values obtained from the 2 m GEDI LAI profiles (Figure C1). The standard deviation values are shown in the brackets.

GEDI	Height (m)										Total LAI
	1.5–3.5	3.5–5.5	5.5–7.5	7.5–9.5	9.5–11.5	11.5–13.5	13.5–15.5	15.5–17.5	17.5–19.5	19.5–21.5
Leaf-on	0.07 (0.04)	0.05 (0.05)	0.08 (0.12)	0.15 (0.12)	0.21 (0.07)	0.32 (0.07)	0.39 (0.09)	0.32 (0.09)	0.21 (0.11)	0.12 (0.13)	1.94 (0.36)
Leaf-off	0.04 (0.02)	0.02 (0.01)	0.05 (0.01)	0.06 (0.02)	0.08 (0.02)	0.09 (0.03)	0.14 (0.04)	0.09 (0.04)	0.07 (0.06)	0.04 (0.04)	0.65 (0.16)

Table D1. Typical field measured canopy and ground reflectance ratio (ρ_v/ρ_g) for different species used in the RAMI-IV during the leaf-off season* (Widlowski et al. 2015). The last row shows the mean (standard deviation) of the values.

Species	ρv/ρg
Maple	0.69
Birch	0.90
Alder	0.69
Ash	0.68
Linden	0.68
Poplar	0.74
Norway spruce	0.59
All	0.71 (0.09)

Note: *Data source: http://rami-benchmark.jrc.ec.europa.eu/HTML/RAMI-IV/RAMI-IV.php.

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Data availability statement

The field measurement data in this study are available from the corresponding author, Y.W., upon reasonable request.