Estimation of coniferous forest aboveground biomass with aggregated airborne small-footprint LiDAR full-waveforms

Haiming Qin; Cheng Wang; Xiaohuan Xi; Jianlin Tian; Guoqing Zhou

doi:10.1364/OE.25.00A851

1. Introduction

Forests, as a principal component of terrestrial ecosystems, are the largest carbon pool and carbon sink on land. They also play an important role in carbon cycle, water cycle, and energy exchange [1,2]. Forest aboveground biomass (AGB) is one of the main biophysical parameters to evaluate forest productivity and to assess carbon sequestration rates [1, 3, 4]. Therefore, accurate estimation of forest AGB is critical for quantifying terrestrial carbon, controlling greenhouse gases, and keeping forest sustainably managed [4–7]. However, up to now, it has still been a challenging task to accurately and rapidly estimate forest AGB.

Traditional measurement methods, such as field measurement and volume model estimation method, can acquire accurate forest AGB. However, these methods are time consuming, labor intensive and destructive, and thus they cannot be applied over large areas [8]. Remote sensing can overcome the above shortcomings, and has been widely used to estimate forest AGB in recent years [9]. Passive optical remote sensing imagery has been used to extract many vegetation indices, such as the normalized difference vegetation index (NDVI) and the ratio vegetation index (RVI), to estimate forest biomass [10–13]. However, passive optical imagery cannot acquire forest vertical structure information due to low penetration ability, and the vegetation indices are often saturated in dense canopy [14]. Synthetic Aperture Radar (SAR) has the ability to penetrate the forest canopy, and it has been used to estimate forest AGB by the backscatter coefficient [15–17], correlation coefficient [18, 19], and forest height [20, 21]. However, complex data processing technology and signal saturation limit its application in large scale [22].

LiDAR is an active remote sensing technique that can capture more forest vertical structure information [23, 24]. Moreover, it can easily overcome the saturation problem that exists in optical remote sensing and SAR [25]. Therefore, LiDAR has been recognized as the optimal remote sensing technique for forest structural parameters estimation [26], and it has been used to estimate many forest structural parameters, such as LAI [27], height [28], biomass [29], etc. In recent years, forest biomass has been estimated by discrete-return LiDAR metrics, such as height and density related metrics [30]. Lefsky et al. estimated the forest AGB using LiDAR-derived maximum canopy height, mean canopy height, median canopy height, and quadratic mean canopy height (QMCH) by a simple linear model, and results indicated that QMCH had the best prediction accuracy [31]. Riggins et al. extracted multiple height percentiles (5, 15, 25, 35, 45, 55, 65, 75, 85, 95, and 100th percentiles) from airborne discrete-return LiDAR data to estimate forest biomass by a regression-tree model, and the determination coefficients (R²) of the training data set and the testing data set were 0.83 and 0.72 respectively [32]. Garcia et al. used discrete-return LiDAR height and intensity metrics to estimate forest biomass, and results indicated that an intensity-based model provided higher prediction accuracy [4]. Discrete-return LiDAR has been widely used to estimate forest AGB, but it has the disadvantage of only recording several limited returns, which may limit the accuracy of forest AGB estimation to some degree.

The recent development of full-waveform LiDAR system has provided new opportunities for forest AGB estimation [24]. Full-waveform LiDAR can record the entire backscattered energy, so it can acquire more detailed forest vertical structure information. Up to now, several studies have successfully estimated forest AGB by full-waveform LiDAR data. Drake et al. calculated the LiDAR canopy height, height of median energy (HOME), height/median ratio (HTRT), and simple ground return ratio (GRND) from airborne large-footprint LiDAR data to predict tropical forest AGB by a stepwise regression method, and results showed that the R² value between the field-measured AGB and predicated AGB was 0.93 [33]. Pirotti et al. predicted the tropical forest biomass using three levels of full-waveform LiDAR metrics - peak-level, pulse-level, and plot-level - and results indicated that the height of median target count (HOMTC) performed the best [34]. Cao et al. estimated subtropical forest biomass using both discrete and full-waveform LiDAR-derived metrics, including height statistic metrics, density measures, waveform distance (WD), number of peaks (NP), front slope angle (FS), etc., and results indicated that height metrics were the best predictors of forest AGB [35]. However, all these studies explored the ability of full-waveform LiDAR data in the estimation of hardwood forest AGB. Few studies have estimated the coniferous forest AGB using airborne full-waveform LiDAR data so far. Moreover, previous studies failed to extract more metrics from full-waveform LiDAR data to estimate the forest AGB. This stimulates us to investigate effective methods that use small-footprint full-waveform LiDAR data to extract more information to retrieve coniferous forest AGB.

The objective of this study is to extract a suite of new metrics from airborne small-footprint full-waveform LiDAR data and to evaluate the ability of these metrics in estimating coniferous forest AGB. To achieve this goal, four main steps were carried out: (1) preprocessing the airborne small-footprint full-waveform LiDAR data, including de-noising, smoothing, and normalization; (2) acquiring the return energy profile from a large pseudo waveform and generating the foliage profile based on the Geometric Optical and Radiative Transfer (GORT) model; (3) extracting a series of new metrics based on the return energy profile and foliage profile; and (4) estimating forest AGB with the newly proposed metrics by regression analyses and assessing the estimation accuracy of these models. The main innovation in this study is that return energy profile and foliage profile based metrics are first proposed to estimate coniferous forest AGB, which provides a new way to estimate forest AGB with small-footprint full-waveform LiDAR data.

2. Materials

2.1 Study area

The study site called Dayekou is located in Heihe Basin, Gansu Province, China (Fig. 1). The terrain is mountainous, with an elevation range of 2729 m - 3123 m above sea level. The study area is situated in a temperate continental climate zone with an annual mean temperature of 3.9 °C and an annual mean precipitation of 264.8 mm. The main land cover type is evergreen coniferous forest, and the dominant forest specie is Picea crassifolia. The study area was chosen by the “Watershed Allied Telemetry Experimental Research (WATER)” project, and the field measurement data and airborne LiDAR data were all collected as part of this project [36].

Fig. 1 Airborne ortho charged coupled device (CCD) image of the study area and the distribution of field plots.

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2.2 Field measurements

Field measurement was conducted in June 2008. Two field plots, which were called the line-plot and super-plot, were selected. The line-plot was a sample line consisting of 19 subplots with the size of 20 m × 20 m, and the distance between the subplots was 50 m. The super-plot was a sample square of 100 m × 100m, and it was divided into 16 subplots with the size of 25 m × 25 m. A total of 35 subplots were used in this study. For each subplot, the tree height and diameter at breast height (DBH) of each tree were measured using a laser hypsometer and a tape measure, respectively. A real-time kinematic GPS (RTK GPS) was used to measure the centre coordinate of each subplot.

Tree aboveground biomass components, including stem biomass, branch biomass, leaf biomass, and fruit biomass, were all calculated based on the DBH and tree height according to the empirical allometric Eqs. (1)-(4) [37]. The AGB of each tree was calculated as the sum of stem biomass, branch biomass, leaf biomass, and fruit biomass. Subplot forest AGB was the sum of the AGB of each tree within the subplot.

s t e m b i o m a s s = 0.0478 \times {(D^{2} \times H)}^{0.8665}

b r a n c h b i o m a s s = 0.0061 \times {(D^{2} \times H)}^{0.8905}

l e a f b i o m a s s = 0.2650 \times {(D^{2} \times H)}^{0.4701}

f r u i t b i o m a s s = 0.0342 \times {(D^{2} \times H)}^{0.5779}

where D is the DBH (cm) and H is the tree height (m).

2.3 Airborne LiDAR data

Airborne small-footprint full-waveform LiDAR data of the study area were acquired using a LiteMapper-5600 system on June 23, 2008. The pulse frequency was 50 kHz with a wavelength of 1550 nm. The flying altitude was approximately 800 m above ground level with a beam divergence of 0.5 mrad, so that the footprint size was approximately 0.4 m. The average pulse density was approximately 3.43 pulses/m².

3. Methods

The technical flow chart of the methods applied in this research is presented in Fig. 2. This figure summarizes the steps of the forest AGB estimation using airborne small-footprint full-waveform LiDAR data. The three main procedures were waveform processing, LiDAR metrics extraction, and forest AGB estimation.

Fig. 2 Technical flow chart of the methods applied in this research.

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3.1 Waveform processing

To extract reliable and accurate full-waveform LiDAR metrics for forest AGB estimation, raw waveform data should first be processed. The waveform processing procedure was performed in three steps: waveform preprocessing, return energy profile generating, and foliage profile generating.

3.1.1. Waveform preprocessing

There were some background noises that did not include any information of the earth surface in the raw waveform data. To acquire the actual waveform signal, these background noises should be removed first. The mean of the background noises was calculated from the raw waveform based on the frequency histogram [38], and then the mean background noise was subtracted from the raw waveform data to retrieve the actual waveform [39]. The actual waveform still contains noises due to the limitations of sensor capacity [27]. To reduce the noise and obtain the smoothed waveform, waveform smoothing was also performed using a Gaussian filter in this study [24, 27]. The sample waveforms were shown on Fig. 3, including original waveform, de-noised waveform, and smoothed waveform.

Fig. 3 The sample waveforms: (a) original waveform; (b) de-noised waveform; (c) smoothed waveform.

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Gaussian decomposition was performed to obtain the point cloud data from full-waveform LiDAR data [40]. Then the adaptive triangular irregular network (TIN) filter embedded in TerraScan software was conducted to acquire the ground and non-ground points [41]. The ground points were used to generate the DTM with a resolution of 0.5 m.

3.1.2. Return energy profile generating

Over the whole process of the LiDAR data acquisition, the behaviour of the laser device might be changed slightly, and the atmospheric conditions might also be changed [39]. Therefore, the emitted pulses and atmospheric conditions might be different, which would lead to different returned waveforms, even if the earth surface is homogeneous [27, 39]. To remove these effects, each preprocessed waveform was normalized according to Duong et al. [39] For each waveform, the return energy at moment i, $V_{i}$ , was divided by the total return energy $V_{T}$ , and then the normalized value at moment i, $V_{N} (i)$ , was obtained based on Eq. (5).

V_{N} (i) = \frac{V_{i}}{V_{T}} with V_{T} = \sum_{i = 1}^{N} V_{i}

where N is the number of waveform bins, and the first bin starts from the ground or the bottom objects which intercept the pulse.

In dense vegetation regions, single small-footprint full-waveform data often acquire faint ground returns, which are the result of reduced energy levels due to obscurant scattering, attenuation and absorption [27, 42]. The faint ground returns would affect the estimation accuracy of vegetation structure parameter [27]. Several studies have demonstrated that waveform aggregating is an effective method for faint ground return detection and enhancement [3, 42]. To obtain accurate full-waveform LiDAR metrics, the normalized waveforms within each plot were all aggregated to generate the return energy profile. First, the corresponding ground elevation of each waveform was extracted from the DTM. Next, the relative heights of all waveform bins in each normalized waveform were calculated based on the corresponding ground elevation and the elevation of the first bin, so that a new waveform was generated. Then, all the new waveforms within each plot were directly aggregated to obtain a pseudo large waveform. Therefore, the return energy profile was generated in the end. The sample small-footprint waveforms and the aggregated pseudo waveform of one plot were shown on Fig. 4, and the pseudo large waveforms of all the 35 plots were shown on Fig. 5.

Fig. 4 The sample small-footprint waveforms (a) and the aggregated pseudo waveform (b) of one plot.

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Fig. 5 The pseudo large waveforms of the 35 plots.

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3.1.3. Foliage profile generating

The foliage profile can reflect the vegetation growth status and describe the forest vertical distribution condition. According to Tang et al [43], the foliage profile was retrieved from the return energy profile based on the GORT model. The LAI can be retrieved from return energy profile based on the gap theory [44–46] which quantifies the relationship between LAI and the gap probability for horizontally homogenous canopy layers according to Eq. (6) [43].

P (θ) = e^{\frac{- G (θ) \cdot L A I}{\cos (θ)}}

where _{$P (θ)$}is the gap probability within canopy with a view zenith angle of _$θ$, _{$G (θ)$}is the projection coefficient representing unit leaf area on the canopy layer perpendicular to the view direction. For the airborne waveform LiDAR data, we assume the viewing zenith angle is constant at 0, and hence we only need information of gap probability and projection coefficient to obtain LAI [43].

According to Ni-Meister et al. [47], the canopy closure profile was derived from the return energy profile based on Eq. (7). The canopy closure at height z was computed as the canopy return energy from the canopy top to height z divided by the total return energy including ground return energy. Then, the cumulative leaf area index profile was retrieved based on the Beer-Lambert law using Eq. (8). Finally, the cumulative leaf area index profile was differentiated to obtain the foliage profile according to Eq. (9).

f cov e r (z) = \frac{E_{v} (z)}{E_{v} (0) + \frac{ρ_{v}}{ρ_{g}} E_{g}}

L A I_{c u m} (z) = - \frac{\log (1 - f cov e r (z))}{G * Ω}

f o l i a g e_p r o f i l e (z) = \frac{d L A I_{c u m} (z)}{d z}

where

f cov e r (z)

is the canopy coverage from the canopy top to height z,

E_{v} (z)

and

E_{v} (0)

are the canopy return energy from the canopy top to height z and the canopy return energy from the canopy top to height 0, respectively,

E_{g}

is the ground return energy,

ρ_{v}

and

ρ_{g}

are the vegetation reflectance and ground reflectance respectively,

\frac{ρ_{v}}{ρ_{g}}

is the adjust factor which is used to reduce the effect of the reflectance difference on return energy, and it is set as 2.5 according to Tang et al [43].

L A I_{c u m} (z)

is the cumulative leaf area index from the canopy top to height z.

G

is the projection coefficient. Assuming a random foliage distribution within the canopy, we set the

G

projection coefficient to be 0.5 [48].

Ω

is the clumping index, which is set as the mean clumping index value of 1.61 for needleleaf and evergreen forest according to Chen et al [49].

f o l i a g e_p r o f i l e (z)

is the foliage profile at height z.

3.2. LiDAR metrics extraction

Two kinds of metrics, return energy profile metrics and foliage profile metrics, were extracted from full-waveform LiDAR data to estimate the forest AGB. The metrics used in this study and the corresponding metric descriptions are reported in Table 1.

Table 1. LiDAR metrics used for forest AGB estimation.

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3.2.1. Return energy profile metrics extraction

Twelve new return energy profile metrics were proposed to estimate the forest AGB in this study. Several metrics could be directly extracted from the return energy profile as shown in Fig. 6(a), such as the sum of canopy return energy (totalCE), the maximum canopy return energy profile amplitude (maxCE), the maximum height of the return energy profile (maxH_E), and the corresponding height of maxCE (H_maxCE). The ratio of totalCE and total return energy (R_{CE_TE}) was calculated as the quotient of totalCE and the sum of the return energy, and its calculation method is shown in Eq. (10). Energy weighted canopy height (H_Eweight) was calculated as the sum of the product of the canopy return energy and height at each bin divided by totalCE, and its calculation method is shown in Eq. (11). The energy height percentiles, EH25, EH50, EH75, and EH95, were the corresponding heights at which the cumulative canopy return energy was 25, 50, 75, and 95 percent of the totalCE, respectively. Two return energy bounding volumes, Volume_maxHE and Volume_HEweight, were calculated as the product of maxCE and maxH_E and the product of maxCE and H_Eweight, respectively, and their calculation equations are shown as Eq. (12) and Eq. (13).

R_{C E_T E} = \frac{t o t a l C E}{t o t a l E}

H_{E w e i g h t} = \frac{\sum_{i = 1}^{N} (H_{i} \times C E_{i})}{t o t a l C E}

V o l u m e_{\max H E} = \max C E \times \max H_{E}

V o l u m e_{H_{E w e i g h t}} = \max C E \times H_{E w e i g h t}

where _{$t o t a l E$} is the sum of return energy,

C E_{i}

is the canopy return energy at bin i,

H_{i}

is the height at bin i, and N is the number of bins.

Fig. 6 Representations of several metrics extracted from the return energy profile (a) and from the foliage profile (b).

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3.2.2. Foliage profile metrics extraction

Thirteen new foliage profile metrics were proposed to estimate the forest AGB in this study. A part of these metrics could be extracted from the foliage profile directly as shown in Fig. 6(b), such as the sum of foliage area (totalF), the maximum foliage profile amplitude (maxF), the maximum height of foliage profile (maxH_F), the corresponding height of maxF (H_maxF). The height of the canopy base (H_base) corresponds to the greatest decrease in the foliage profile, detected as the position of the minimum value of the foliage profile derivation. Then the height of the crown (H_crown) can be calculated as the difference between maxH_F and H_base. Foliage area weighted canopy height (H_Fweight) is calculated as the sum of the product of the foliage area and height at each bin divided by totalF, and its calculation method is shown in Eq. (14). The foliage height percentiles, FH25, FH50, FH75, and FH95, are the corresponding heights at which the cumulative foliage area was 25, 50, 75, and 95 percent of totalF respectively. Two foliage area bounding volumes, Volume_maxHF and Volume_HFweight, are calculated as the product of maxCF and maxH_F and the product of maxCF and H_Fweight, respectively, and their calculation equations are shown as Eq. (15) and Eq. (16).

H_{F w e i g h t} = \frac{\sum_{i = 1}^{N} (H_{i} \times F_{i})}{t o t a l F}

V o l u m e_{\max H F} = \max C F \times \max H_{F}

V o l u m e_{H_{F w e i g h t}} = \max C F \times H_{F w e i g h t}

where _{$F_{i}$}is the foliage area at bin i, _{$H_{i}$}is the height at bin i, and N is the number of bins.

3.3. Forest biomass estimation

A correlation analysis was conducted to assess the correlation between each full-waveform LiDAR metric and field-measured AGB, and the correlation coefficient (R) was calculated according to Eq. (17) . The LiDAR metrics with the R values larger than 0.5 were all selected to estimate forest AGB, and the simple linear regression analysis was carried out to examine the capability of each selected LiDAR metric in estimating forest AGB. Stepwise multiple regression is a commonly-used and effective method to eliminate the multicollinearity issue and select the optimal regression equation, which has been widely used to estimate forest AGB [50, 51]. To estimate forest AGB more accurately, stepwise multiple regression models were developed to estimate the forest AGB by the two sets of LiDAR metrics (i.e., return energy profile metrics and foliage profile metrics) both independently and in combination. In this study, the stepwise multiple regression employed the approach of bidirectional elimination. This method first contained only the independent variable most relevant to the dependent variable, then, the choice of predicative variables is carried out by an automatic procedure. In each step, a variable is considered for addition to or subtraction from the set of explanatory variables based on the F-tests and t-tests. After the process of selecting explanatory variables, a forest AGB estimation model was established based on the selected metrics.

To assess the prediction accuracy of a forest AGB estimation model, the leave-one-out cross-validation method (LOOCV) was performed, which is considered an effective tool when a small number of samples is available [52, 53]. The R², root mean square error (RMSE) (Eq. (18)), and bias (BIAS) (Eq. (19)) were calculated to evaluate the reliability of each forest AGB estimation model.

R = \frac{\sum_{i = 1}^{n} (x_{i} - \bar{x}) (y_{i} - \bar{y})}{\sqrt{\sum_{i = 1}^{n} {(x_{i} - \bar{x})}^{2} \cdot \sum_{i = 1}^{n} {(y_{i} - \bar{y})}^{2} \cdot}}

R M S E_{L O O C V} = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} {(x_{i} - y_{i})}^{2}}

B I A S_{L O O C V} = \frac{1}{n} \sum_{i = 1}^{n} (x_{i} - y_{i})

where _{$x_{i}$}is the field-measured AGB of sample i, _$\bar{x}$is the mean value of field-measured AGB, _{$y_{i}$} is the predicted AGB of sample i, _$\bar{y}$is the mean value of predicted AGB, and n is the number of samples.

4. Results

To investigate the relationship between each LiDAR metric and field-measured AGB, correlation analysis was conducted based on the 35 field-measured AGB against each LiDAR metric. The correlation coefficients of all LiDAR metrics and field-measured AGB are plotted in Fig. 7. Nine of the twenty-five LiDAR metrics suggested, including totalCE, maxCE, R_{CE_TE}, Volume_maxHE, totalF, H_base, Volume_maxHF, and Volume_HFweight, had negative correlations with field-measured AGB, and their R values were all between −0.5 and 0. All the rest of the metrics had positive correlations with field-measured AGB. The R values of field-measured AGB and two metrics, Volume_HEweight and H_crown, were both smaller than 0.5. The remaining fourteen metrics all had stronger correlations with field-measured AGB, with R values larger than 0.5. For all return energy profile metrics, H_Eweight and EH25 showed the highest correlation with field-measured AGB (R = 0.88), followed by EH50 (R = 0.86), EH75 (R = 0.80), H_maxCE (R = 0.75), EH95 (R = 0.64), and maxH_E (R = 0.54). TotalCE, maxCE, R_{CE_TE}, Volume_maxHE, and Volume_HEweight were all not sensitive to field-measured AGB. Among all the foliage profile metrics, H_Fweight had the most significant relationship with field-measured AGB (R = 0.89), followed by FH95 (R = 0.85), FH75 (R = 0.82), FH50 (R = 0.77), H_maxF (R = 0.74), FH25 (R = 0.72), and maxH_F (R = 0.54). totalF, maxF, H_base, H_crown, Volume_maxHF, and Volume_HFweight all had weak correlations with field-measured AGB.

Fig. 7 The correlation coefficient (R) of each LiDAR metric and field-measured AGB.

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A simple linear regression was performed to examine the ability of a single LiDAR metric in estimating forest AGB. The metrics that had R values larger than 0.5 with field-measured AGB were selected to develop a forest AGB estimation model, and the results are shown in Table 2. The R² values of the fourteen models ranged from 0.29 to 0.79, the RMSE_loocv values ranged from 12.83 Mg/ha to 23.59 Mg/ha, and the BIAS_loocv were all between −0.037 Mg/ha and 0.038 Mg/ha. A total of five single LiDAR metric-based AGB estimation models had R² values larger than 0.70, including the H_Eweight based model, EH25 based model, EH50 based model, H_Fweight based model, and FH95 based model. Among all the single metric based forest AGB estimation models, the H_Fweight based model was the best one, with the highest R² (0.79), the lowest RMSE_loocv (12.83 Mg/ha), and a small BIAS_loocv (−0.037 Mg/ha), followed by the H_Eweight based model (R² = 0.78, RMSE_loocv = 13.10 Mg/ha, BIAS_loocv = 0.001 Mg/ha) and the EH25 based model (R² = 0.77, RMSE_loocv = 13.33 Mg/ha, BIAS_loocv = 0.003 Mg/ha). maxH_E based and maxH_F based forest AGB estimation models all had the lowest R² (0.29) and the highest RMSE_loocv (23.59 Mg/ha). However, the BIAS_loocv of the maxH_F based AGB estimation model (0.003 Mg/ha) was larger than the maxH_E based AGB estimation model (0.002 Mg/ha). Therefore, the maxH_F based AGB estimation model was the worst AGB estimation model.

Table 2. Results of the forest AGB estimation models using a single LiDAR metric.

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To determine which combination of LiDAR metrics can explain the highest amount of variance in forest AGB, the stepwise multiple regression analysis was carried out. Among all the return energy profile metrics, H_Eweight and EH75 were selected by stepwise regression to establish the forest AGB estimation model, and the final model is shown in Eq. (20). From all the foliage profile metrics, only H_Fweight was selected to build the forest AGB estimation model, and the final model is shown in Eq. (21). When combining return energy profile metrics and foliage profile metrics, the forest AGB estimation model was established based on H_Fweight, Volume_maxHE, and H_Eweight, and the final AGB estimation model is shown in Eq. (22).

AGB = 3.555 + 23.490 * H_{Eweight} - 11 .0 30 * EH75

AGB = - 19 .0 92 + 1.288 * H_{Fweight}

AGB = - 29 .0 61 + 4 .0 27 * H_{Fweight} + 0.0 11 * {Volume}_{maxHE} - 26.63 * H_{Eweight}

The LOOCV method was performed to assess the accuracy of three forest AGB estimation models. Field-measured AGB versus the predicted AGB from return energy profile metrics based model, foliage profile metrics based model, and the combo model are plotted in Fig. 8(a), (b), and (c), respectively. For the three models, the combo model had the highest R² (0.85), the lowest RMSE_loocv (10.78 Mg/ha), and a small BIAS_loocv (0.72 Mg/ha). Therefore it is considered the optimal forest AGB estimation model. The return energy profile metrics based model had the second best AGB estimation accuracy, with an R² of 0.82, an RMSE_loocv of 11.84 Mg/ha, and a BIAS_loocv of 0.001 Mg/ha. The foliage profile metrics derived model had the lowest R² (0.79), the highest RMSE_loocv (12.83 Mg/ha), and a small BIAS_loocv (−0.036 Mg/ha); therefore, it is considered the third best AGB estimation model of the three models.

Fig. 8 Field-measured AGB vs. predicted AGB: (a) from the return energy profile metrics derived model (Eq. (14)); (b) from the foliage profile metrics derived model (Eq. (15)); (c) from the combo model (Eq. (16)).

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5. Discussion

For coniferous forests, He et al. estimated the forest AGB using discrete-return LiDAR metrics and explained 72.7% of the variance in AGB [54]. Li et al. combined the horizontal and vertical discrete-return LiDAR metrics to estimate the forest AGB and explained 71% of the variance in AGB [55]. Nie et al. used airborne discrete-return and full-waveform LiDAR metrics to retrieve forest AGB, and the full-waveform metrics explained 76% of the variance in AGB, meanwhile the combined metrics explained 81.5% of the variance in AGB [56]. In this study, return energy profile and foliage profile based metrics were first proposed to estimate coniferous forest AGB, and they explained 85% of the variance in AGB when combining the two sets of metrics. The higher forest AGB variability reported in our study owes to the introduction of new types of full-waveform LiDAR metrics, which provided more accurate and abundant forest vertical structure information.

Previous studies have found that LiDAR-derived height-related metrics can produce accurate forest AGB prediction [30, 50, 57]. To our knowledge, few studies have extracted height-related metrics from return energy profile and foliage profile. In this study, return energy profile and foliage profile based height-related metrics were proposed to estimate forest AGB for the first time, and results indicated that most of these metrics were strongly correlated with AGB, and thus these metrics were reliable predictors of forest AGB. These height-related metrics described the vertical structure of forest, and they contained abundant information about return energy vertical distribution and foliage vertical distribution, which were strongly related to forest AGB [43]. Therefore, return energy profile and foliage profile based height-related metrics can greatly improve the prediction accuracy of forest AGB compared with the height metrics in our studies.

Cao et al. [58] and Kulawardhana et al. [59] all found that none of the vegetation cover-related metrics were significantly correlated to biomass. Our study found that the new return energy profile based canopy cover-related metric, R_{CE_TE}, was also weakly correlated with forest AGB, which was in agreement with early studies. In this study, return energy profile based energy-related metrics (totalCE, maxCE) and foliage profile based foliage area-related metrics (totalF and maxF) were all first proposed to estimate forest AGB, which have not been explored up to now. But results indicated that all these metrics had weak correlations with forest AGB with negative R values. Therefore, the newly proposed return energy profile based energy-related metrics and foliage profile based foliage area-based metrics have no contribution to accurate forest AGB prediction.

Several studies have used the product of LiDAR derived height metric and canopy cover metric to estimate forest AGB, and results showed that these metrics can improve the prediction accuracy of forest AGB [47, 56]. These studies provided a novel way to design new LiDAR metrics for vegetation structure parameters estimation. However, there has been no study to use this kind of metrics extracted from return energy profile and foliage profile to estimate forest AGB at present. In this research, we firstly proposed the return energy profile based bounding volume-related metrics (Volume_maxHE and Volume_HEweight) and foliage profile based bounding volume-related metrics (Volume_maxHF and Volume_HFweight) to predict forest AGB. But these metrics all had low explanation ability in the variation of forest AGB. This may be caused by the inaccurate metric design, which is needed to be explored in the future.

Simple linear regression results showed that the metrics selected by the criterion of R values larger than 0.5 were all height-related metrics. Among all return energy profile metrics, H_Eweight explained 78% of the variance in forest AGB, which ranked highest in these metrics. For foliage profile metrics, H_Fweight was most relevant to forest AGB and it explained 79% of the variance in forest AGB. These findings indicated that H_Eweight and H_Fweight could express the typical forest height information, and they had great potential in estimating forest AGB, which had never been explored in previous studies. Energy height percentiles and foliage height percentiles were also first proposed to estimate forest AGB, and the explanation ability of some metrics in the variation of forest AGB were larger than 70%, which was better than the explanation ability of discrete-return LiDAR derived height percentiles in AGB variation [35]. These results indicated that energy height percentiles and foliage height percentiles could describe the forest vertical distribution information more accurately. In consequence, return energy profile and foliage profile derived height-related LiDAR metrics were most related to forest AGB, which was consistent with the results of previous studies [38, 47].

Like previous studies on forest biomass estimation [34], stepwise regression analysis was conducted to develop a more accurate forest AGB estimation model. The AGB estimation model derived from return energy profile metrics alone could explain 82% of the variation in AGB, with an RMSE_loocv of 11.84 Mg/ha, and containing two metrics, H_Eweight and EH75. A foliage profile metrics alone derived AGB estimation model only included one metric, H_Fweight, and it could explain 79% of the variation in AGB with an RMSE_loocv of 12.83 Mg/ha. The combo model took full advantage of the predictive ability of return energy profile metrics and foliage profile metrics, and it provided higher AGB estimation accuracy with R² = 0.85 (RMSE_loocv = 10.78 Mg/ha). Therefore, combining return energy profile metrics and foliage profile metrics could improve the accuracy of forest AGB estimation. The improvement might be due to more metrics being contained in the AGB estimation model by stepwise regression analysis.

6. Conclusions

In this study, a series of new return energy profile and foliage profile based metrics derived from airborne small-footprint full-waveform LiDAR data were proposed to estimate forest AGB. Return energy profile and foliage profile based height-related metrics were all strongly related to forest AGB, especially energy weighted canopy height, H_Eweight, and foliage area weighted height, H_Fweight. H_Eweight and H_Fweight could express the typical forest height information, and the correlation coefficients of them with field-measured forest AGB were all ranked the highest in return energy profile metrics and foliage profile metrics respectively. Energy height percentiles and foliage height percentiles could describe the forest vertical distribution information more accurately, and they had better explanation ability in AGB variation than discrete-return LiDAR derived height percentiles. The newly proposed energy-related metrics, foliage area-related metrics, and bounding volume-related metrics derived from the return energy profile and foliage profile were not all sensitive to forest AGB. Compared to if only one set of new LiDAR metrics was used, combining return energy profile metrics and foliage profile metrics could improve the accuracy of forest AGB estimation, and the optimal forest AGB estimation model contained H_Fweight, Volume_maxHE, and H_Eweight.

Above all, this study proposed a series of new full-waveform LiDAR metrics derived from the return energy profile and foliage profile to estimate forest AGB, and it did contribute to the improvement of estimation accuracy in forest AGB. Additionally, future works should focus on exploring the capability of the proposed metrics in this study in improving the AGB estimation accuracy of more forests types.

Funding

National Key R&D Program of China (No. 2017YFA0603002) and National Natural Science Foundation of China (Nos. 41671434, 41431179).

Acknowledgments

We thank the editor and anonymous reviewers for reviewing our paper.

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Estimation of coniferous forest aboveground biomass with aggregated airborne small-footprint LiDAR full-waveforms

Abstract

1. Introduction

2. Materials

2.1 Study area

2.2 Field measurements

2.3 Airborne LiDAR data

3. Methods

3.1 Waveform processing

3.1.1. Waveform preprocessing

3.1.2. Return energy profile generating

3.1.3. Foliage profile generating

3.2. LiDAR metrics extraction

3.2.1. Return energy profile metrics extraction

3.2.2. Foliage profile metrics extraction

3.3. Forest biomass estimation

4. Results

5. Discussion

6. Conclusions

Funding

Acknowledgments

References and links

Cited By

Figures (8)

Tables (2)

Equations (22)

Optics Express

Source	Metric ID	Metric description
Return energy profile	totalCE	The sum of canopy return energy
	maxCE	The maximum canopy return energy profile amplitude
	R_{CE_TE}	The ratio of totalCE and total return energy
	maxH_E	The maximum height of return energy profile
	H_maxCE	The corresponding height of maxCE
	H_Eweight	Energy weighted canopy height.
	EH25	25th energy height percentile
	EH50	50th energy height percentile
	EH75	75th energy height percentile
	EH95	95th energy height percentile
	Volume_maxHE	maxCE * maxH_E
	Volume_HEweight	maxCE* H_Eweight
Foliage profile	totalF	The sum of foliage area
	maxF	The maximum foliage profile amplitude
	maxH_F	The maximum height of foliage profile
	H_maxF	The corresponding height of maxF
	H_base	The height of canopy base
	H_crown	The height of crown
	H_Fweight	Foliage area weighted canopy height.
	FH25	25th foliage height percentile
	FH50	50th foliage height percentile
	FH75	75th foliage height percentile
	FH95	95th foliage height percentile
	Volume_maxHF	maxF * maxH_F
	Volume_HFweight	maxF * H_Fweight

Metric	Model	R²	RMSE_loocv (Mg/ha)	BIAS_loocv (Mg/ha)
maxH_E	AGB = −36.04 + 7.24*maxH_E	0.29	23.59	0.002
H_maxCE	AGB = 52.26 + 0.53* H_maxCE	0.56	18.56	0.038
H_Eweight	AGB = −30.51 + 13.03* H_Eweight	0.78	13.10	0.001
EH25	AGB = 26.66 + 9.93* EH25	0.77	13.33	0.003
EH50	AGB = −5.44 + 10.45* EH50	0.75	14.09	0.002
EH75	AGB = −50.13 + 11.92* EH75	0.63	16.93	−0.003
EH95	AGB = −87.85 + 12.11* EH95	0.41	21.50	−0.004
maxH_F	AGB = −34.6 + 7.24* maxH_F	0.29	23.59	0.003
H_maxF	AGB = 49.11 + 5.7* H_maxF	0.54	18.94	0.004
H_Fweight	AGB = −19.09 + 1.29* H_Fweight	0.79	12.83	−0.037
FH25	AGB = 61.9 + 16.28* FH25	0.52	19.48	0.001
FH50	AGB = 56.9 + 14.12* FH50	0.60	17.78	0.001
FH75	AGB = 53.17 + 12.6* FH75	0.67	16.10	0.001
FH95	AGB = 50.25 + 11.89* FH95	0.71	14.98	−0.002