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Edited by: Cyril Pommier, INRA Centre Versailles-Grignon, France

Reviewed by: András Zlinszky, Institute of Ecology Research Center (MTA), Hungary; Eric R. Casella, Forestry Commission England, United Kingdom

This article was submitted to Technical Advances in Plant Science, a section of the journal Frontiers in Plant Science

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Forest carbon density is an important indicator for evaluating forest carbon sink capacities. Accurate carbon density estimation is the basis for studying the response mechanisms of forest ecosystems to global climate change. Airborne light detection and ranging (LiDAR) technology can acquire the vertical structure parameters of forests with a higher precision and penetration ability than traditional optical remote sensing. Combining top of canopy height model (TCH) and allometry models, this paper constructed two prediction models of aboveground carbon density (ACD) with 94 square plots in northwestern China: one model is plot-averaged height-based power model and the other is plot-averaged daisy-chain model. The correlation coefficients (^{2}) were 0.6725 and 0.6761, which are significantly higher than the correlation coefficients of the traditional percentile model (^{2} = 0.5910). In addition, the correlation between TCH and ACD was significantly better than that between plot-averaged height (AvgH) and ACD, and Lorey’s height (LorH) had no significant correlation with ACD. We also found that plot-level basal area (BA) was a dominant factor in ACD prediction, with a correlation coefficient reaching 0.9182, but this subject requires field investigation. The two models proposed in this study provide a simple and easy approach for estimating ACD in coniferous forests, which can replace the traditional LiDAR percentile method completely.

Forest carbon storage accounts for 82.5% of terrestrial vegetation carbon storage, which is the main component of the vegetation carbon sink (

Traditional optical remote sensing can extract the spectral information and horizontal structure information of vegetation. However, with increasing biomass, saturation occurs easily, which affects the estimation accuracy of forest carbon storage (

With the big-data progress and increasing storage space in recent years, airborne LiDAR has become an important means of forest resource surveys and carbon storage research (

There are two main approaches for the estimation of carbon density based on plots. One approach is the use of a variety of machine learning algorithms to establish the relationship between measured carbon density and LiDAR percentile metrics, which can make full use of the information contained in the point cloud to obtain increasing precision (

A multiple linear regression model based on LiDAR percentiles is a popular method for estimating forest carbon density or biomass, which is widely used and has acceptable precision in different forest area (e.g., ^{2}); ^{2} of 0.74 and 0.79 in 0.09 ha plots, respectively; ^{2} of 0.90 in 0.5 ha plots. Previous studies have demonstrated that the accuracy and form of percentiles models are closely related to the LiDAR instruments (

In this study, we attempt to find a simple plot-based LiDAR extraction parameter, establish allometry models of the aboveground carbon density (ACD) of the northern coniferous forest, and evaluate the accuracy of these models. The objectives of this study are (1) the selection of the best parameter for ACD prediction from the following three plot-based LiDAR extraction parameters: top of canopy height (TCH), AVG (plot-averaged height), and Lorey’s height (LorH); (2) the proposal of direct and indirect fitting models of TCH and ACD and comparison of their accuracy and (3) calculation of the ACD of the study area with the proposed models and comparisons of the results and spatial distribution characteristics.

The study was conducted 50 km southwest of Zhangye City, Gansu Province, Northwest China (

Study area and 94 plots.

The LiDAR data used in this study were acquired on June 2008 using a LiteMapper 5600 instrument that recorded up to five returns per pulse, along with their intensity. The average flight altitude was 3560 m, the relative height over ground was 760 m, and the flight speed was 227 km/h. The laser scanner adopted RIEGL LMS-Q560, and the wavelength was 1550 nm. The laser pulse width was 3.5 ns, and the laser pulse divergence angle was less than or equal to 0.5 mrad. The LiDAR point cloud used the WGS84 coordinate system and the UTM projection zone 47 in the northern hemisphere. To increase the point density, the flight was repeated seven times over the study area with a side overlap of approximately 90%. As a result, the average point cloud interval was decreased to 0.54 m, and the average point cloud density was 3.43/m^{2}.

Subsequently, a set of metrics (^{1}. The main processing steps were as follows: (1) the point cloud was filtered and classified to ground, trees and noise; (2) the normalized point cloud (NPC, also referred to as height above ground) was calculated; (3) height percentiles, density percentiles and canopy cover (CC) were derived from the NPC corresponding to each plot; (4) the digital surface model (DSM) and digital elevation model (DEM)were interpolated from the first echo and the last echo of the point cloud, respectively. The canopy height model (CHM) was the difference of the first two. (5) The TCH was extracted from the CHM based on each plot (the mean value of 400 pixels per plot).

Metrics derived from LiDAR and field investigation data.

TCH | Top of canopy height of plot | CHM (canopy height model) |

h25…h95 | Height percentiles | NPC (normalized point cloud) |

d25…d95 | Density percentiles | |

CC | Canopy closure | |

AvgH | Average height of plot | Field investigation |

LorH | Lorey’s height of plot | |

BA | Base area of plot |

In addition, in order to explore the effect of CHM pixel size on ACD prediction, we generated 10 CHMs from NPC, with pixel sizes from 1 to 10 m. When the pixel location of CHM corresponds to a laser point, the point’s height value is used as the pixel value. If the location corresponds to multiple laser points, the average value of height is used as the pixel value. For the pixels without corresponding laser point, inverse distance weighted (IDW) is adopted for interpolation, which can ensure smooth transition between the target pixel and surrounding pixels (

To calibrate and validate the models, the plot data were acquired simultaneously with the LiDAR data. A total of 94 square plots (20 m × 20 m), which included 5734 trees, were used. The four corners and the centre of each plot were measured using differential GPS (DGPS), and the error was less than 10 cm. For each tree with a diameter at breast height (DBH) greater than 5 cm, the tree type, diameter, height to crown base, crown width in cardinal directions, crown class, and crown transparency were measured. DBH was measured on all trees using a diameter tape, and the heights of all trees were measured using a laser ranging hypsometer with theoretical accuracy up to the decimeter level. Considering the canopy occlusion and human error, the average accuracy of the measured tree height was better than 0.5 m.

Using the species-specific allometry Eqs 1–4 in the study area (

where _{i}_{i} are the basal area and the height of the

The use of an allometry model is the main means of forest biomass calculation. This type of model is obtained by the regression of the sample forest harvesting and tree-measuring metrics and is a single-tree model for specific tree species in a specific region. The present work imitates the form of single-tree models at the plot level to find a suitable plot-level LiDAR metric to replace traditional tree-measuring metrics.

An idealized and simple tree allometry equation for special species is:

Since DBH is the most easily accessible and accurately measurable tree indicator, and there is an intrinsic relationship between the DBH and tree height, the model is widely used (

However, Eq. 6 cannot explain the variability of diameter and tree height growth caused by tree age, forest density, site conditions and management measures; the introduction of the tree height factor is necessary.

where

The essence of LiDAR is ranging, which can directly estimate tree height. Therefore, this paper applies Eqs 6 and 7 to Eqs 8 and 9, which are plot-averaged height-based allometry models, and fits the equations as follows:

where ACD represents the aboveground carbon density (Mg C ha^{–1}), and

Light detection and ranging is highly sensitive to the three-dimensional structure of forest, because laser pulses can penetrate the canopy and then record all echo signals from the ground to the canopy surface. Therefore, a series of LiDAR metrics, such as height percentile, density percentile, variation coefficient, etc., have been successively extracted to capture key information of forest canopy (

In this study, the height and density percentiles extracted from the NPC were used to regression fit the ACD calculated from the field investigation data. The model is as follows, and the independent variables are described in

All models in this study were fitted by the least squares (OLS) method (^{2}) and back-log root-mean-squared errors (RMSE) were employed to compare the performance of the models, and 10-fold cross-validation analysis was used to evaluate the stability of the models.

The study area was divided into a 20 m × 20 m grid using GIS software (

Fishnet for the study area.

Using the comparison between the simple power-law model (Eq. 8) of ACD and the three plot-averaged metrics (AvgH, LorH, and BA)calculated from the field inventory, we found that the BA explains 91.8% of the variation in ACD, which is much higher than the 39.5% explained by AvgH and 10.1% explained by LorH (^{2} value (0.9182) is reduced by 0.004 compared with the model-fitted ^{2} (0.9143), which indicates that the model using BA tends to be applicable and stable. This result means that, when we want to obtain the ACD of plots, we can discard the exhaustive field inventory data and only need to perform spatially explicit point-based measurements using the relascope or prism method.

Summary for ACD estimation using AvgH, LorH, and BA.

^{2} |
^{2} |
^{–1}) |
|||

ACD = aAvgH^{b} |
8.7899 | 0.8026 | 0.3945 | 0.3587 | 13.5561 |

ACD = aLorH^{b} |
7.8821 | 0.6691 | 0.1014 | 0.0614 | 15.9938 |

ACD = aBA^{b} |
1.6528 | 1.0345 | 0.9182 | 0.9143 | 5.5440 |

The linear relationship between ln(AvgH) and ln(ACD)

Moreover, although AvgH and LorH are the most commonly used plot-averaged height indicators, when they were applied in Eq. 8 to predict ACD, the effect was poor, with ^{2} values of 0.3954 and 0.1014, respectively, and RMSE values of 13.5561 (Mg C ha^{–1}) and 15.9938 (Mg C ha^{–1}), respectively; the results with AvgH are slightly better than those with LorH (

The plot-level LiDAR metric (TCH) was taken into the ideal simplest allometry (Eq. 8) and was subjected to log changes and linear fits. The result showed that TCH could explain 67.25% of the variation in ACD (

Using regression by ordinary least squares, we modeled variation in BA to TCH for 94 plots, with resulting values of ^{2} = 0.6066 and RMSE = 5.1749 m^{2} ha^{–1} (Eq. 10, ^{2} only increased by 0.0036, and RMSE increased by 0.1163 Mg C ha^{–1} (

Summary for ACD estimation using TCH only or TCH and BA’ in pairs.

^{2} |
^{2} |
^{–1}) |
||||

ACD = |
11.6592 | 0.8436 | – | 0.6725 | 0.6585 | 10.1427 |

BA’ = |
6.7117 | 3.6516 | – | 0.6066 | 0.5882 | 5.1749 (m^{2} ha^{–1}) |

ACD = |
0.9393 | 1.1977 | 0.0018 | 0.6761 | 0.6022 | 10.2590 |

The following result (Eq. 12) was obtained by the multiple regression fitting of the surveyed ACD of 94 plots and the LiDAR percentile metrics listed in

The ACD in the study area is closely related to h25 and d95. These two parameters can explain 59.1% of the ACD variation, with a RMSE of 11.6304 Mg C ha^{–1} (

^{–1}, which is slightly lower than the measured ACD. Furthermore, the range of predicted values of the TCH model is slightly smaller than the surveyed value range, which is larger than the range of the MLR model. Therefore, compared with the MLR model, the TCH model has a wider prediction range and can represent larger and smaller values of ACD.

All grid values in the study area were calculated using our proposed TCH allometry model and percentile model, and then maps of ACD were produced. ^{–1}, and the maximum value is 104.70 Mg C ha^{–1}, which is slightly larger than the values of 40.13 and 95.46 Mg C ha^{–1} from the percentile model. This resulted in an overall aboveground carbon reserve of the study area of 5535.54 Mg for the TCH model and 5433.06 Mg for the percentile model; the difference between the two models is only 1.89%. Although the accuracies of the TCH and the MLR models are not much different, the TCH model is much simpler and easier than the MLR model.

Study area carbon density map predicted using the TCH model

Our original purpose was to find a suitable plot-averaged LiDAR parameter and use existing allometry models to quickly and accurately predict the forest carbon density. The exponential model of TCH captures 67.25% of ACD changes (

Moreover, since the TCH is derived from the mean of the CHM based on the plots, the TCH is also subject to the pixel size. We extracted 10 CHMs from the LiDAR point cloud, with pixel sizes from 1 to 10 m, and then extracted the corresponding TCHs to fit the ACD. As the pixel size increased, ^{2} continually decreased, and the RMSE continually increased (^{2}, so the minimum pixel size was 1 m. In addition, we found that when the pixel sizes were 5 and 7 m, the fitting effect fluctuated slightly, but this fluctuation did not affect the overall law. The reason for this finding requires further study. Similarly, fitting accuracy is also limited by the size of the plot and the number of samples. A larger plot size means a smaller boundary effect, and a larger plot number means a smaller outlier influence (

Fitting trends of TCH and ACD under different CHM precisions. ^{2};

The three-dimensional visualization of the point cloud in plot no. 1 (

We also recognized a flaw in the ACD prediction at the plot scale. Whether in the field measurement phase, the plot-based TCH extraction phase, or the final ACD prediction phase, our resolution is fixed at 20 m × 20 m. This inevitably leads to the conversion of the continuous ACD distribution in nature into a discontinuous distribution, which may cause a large jump phenomenon at the boundary. Therefore, selecting the appropriate interpolation algorithm to restore the continuity of the ACD will help improve the prediction accuracy of our proposed models (

Finally, we must emphasize that although our proposed TCH-based allometric approach is an efficient LiDAR-assisted ACD prediction method, the allometry model used for plot calculation is generally targeted to a specific region and species (

Using the traditional allometry growth model theory, this paper proposed two models based on TCH extracted from LiDAR data. The first model was a simple power model (only using TCH) based on the diameter allometry, and the second model was a daisy-chain model (TCH → BA′ → ACD) based on diameter-height allometry. A comparison of the results suggested there was little difference in the fitting accuracy and error distribution between models. In addition, this paper compared the traditional LiDAR percentile method with the proposed method and found that the latter method had a higher precision, fewer parameters, more concise steps and more stable forms than the former method. Furthermore, the implicit hypothesis in our study, the traditional allometry model of individual trees can be extrapolated to the plot scale, was confirmed. The LiDAR-assisted ACD estimation method proposed in this study will accelerate the application of airborne LiDAR technology in forest carbon density measurements and provide an accurate data basis for forest ecosystem research.

Publicly available datasets were analyzed in this study. This data can be found here:

HH and WL: conceptualization, methodology, and writing-original draft preparation. HH: software, resources, and data curation. XZ and PZ: validation. HH and XZ: formal analysis. HH, WL, and XZ: investigation. QC: writing, review, and editing. HH and PZ: visualization. QC and PZ: supervision, project administration, and funding acquisition.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The authors would like to thank Northwest Institute of Eco-Environment and Resources (CAS) for support in LiDAR data acquisition and also thank Gansu Province Qilian Water Resource Conservation Forest Research Institute for support in field investigation.