1. Introduction
Tropical vegetation holds the lion’s share of the global terrestrial carbon (C) pool stored in aboveground plant biomass [
1]. However, due to a lack of ground data available for tropical forests, our knowledge on how much biomass is stored in these ecosystems is still highly uncertain. Such uncertainties arise because in spite of ongoing initiatives, only a small proportion of this vast and spatially variable ecosystem has, so far, been surveyed by traditional forest inventories [
2,
3].
A general technique to measure aboveground biomass (AGB) in situ is to destructively sample and extract basic structural variables of the vegetation at the individual level and then to develop calibrated allometric (size-to-mass) relationships for upscaling to the plot-level based on biometric vegetation parameters [
4,
5]. The main horizontal structural vegetation parameters collected in forest inventories are the tree diameter at breast height (DBH), the stem basal area (BA), and number of individuals (Ni); the main vertical variables are the total tree height (Ht), the commercial height (Hc), the leaf area index (LAI), and the canopy architecture [
4,
5,
6,
7,
8]. Each of these estimated parameters is associated with measurement errors; therefore, it is important to identify the underlying sources and relative magnitudes of uncertainty as respective errors will add up in compound estimates of vegetation biomass [
4]. Such errors are associated with uncertainties due to the deviation of tree trunks from a perfect circular shape (irregular trunks and/or buttresses) and to the rate of trunk circumference decline with height, branching patters, identification of highest point on a tree, as well as variability of wood density (ρ) among species and within species from different areas [
2,
3,
4]. For instance, it has been demonstrated that a 5% error in tree diameter and a 10% error in tree height and wood density can lead to a 21.6% uncertainty in estimates of aboveground biomass [
9]. This highlights the importance of assessing the respective measurement errors and also indicates that cumulative errors could propagate to even larger uncertainties when incorporated into allometric equations for estimating aboveground biomass [
5]. As a result, AGB estimates are dependent on the particular choice of allometric equations based on the set of variables used for parameterization [
10] because these parameters vary in relation to the spatial heterogeneity of tropical landscapes and among surveyed tree communities [
2,
3,
4].
Recently, novel technologies based on light detection and ranging (LiDAR) have proven successful for the calibration of allometric models and, thus, could represent a nondestructive alternative to traditional destructive sampling techniques [
11]. LiDAR technology is able to determine the distance between the instrument and a specific object by measuring the timespan between the emission and return of a laser beam with millimetric precision [
12] and, thus, is capable of creating three-dimensional images of a given object based on recording the returns of light pulses emitted from the device [
12,
13]. Depending on the scale of interest, three types of LiDAR are used for the analysis of vegetation structure in forest ecosystems, i.e., spaceborne, airborne, and terrestrial LiDAR. Spaceborne LiDAR is currently limited to 3 years of data and has a relatively large footprint of the order of tens of meters and, hence, does not provide wall-to-wall coverage. Airborne LiDAR provides higher spatial detail but covers relatively smaller spatial areas. Both have been successfully tested at the global [
14,
15], continental [
16], and national levels [
17] but are limited by cloud cover and penetration through the canopy. Terrestrial LiDAR is being used for a more detailed analysis of the complex vegetation structure sampled across smaller spatial areas (<1 ha) down to the level of single trees [
18,
19,
20]. At the plot level, terrestrial laser scanning (TLS) allows the extraction of biometric variables, such as, leaf, branch, and trunk volume, as well as canopy architecture, with remarkable accuracy [
12,
21,
22,
23].
So far, studies evaluating the structural parameters using TLS have been conducted mostly in temperate forest ecosystems [
19,
24,
25,
26], and this technique might be expected to be less successful in tropical forest ecosystems due to the high structural complexity of tropical vegetation [
11,
27,
28,
29,
30,
31]. One of the main limitations for laser-based technologies in forest environments is the occlusion of the laser beam by the vegetative material present in different layers of the forest stratum [
32,
33,
34,
35]. Moreover, the structural complexity of the environment was found to vary throughout the landscape in response to environmental gradients [
30,
31,
32,
33]. To cope with the resulting differences in complexity of structural parameters and to reduce the associated measurement errors between surveyed forest plots, the sampling protocols for each variable of interest have been established, focusing on standardization of methodologies among different forest sites and on a greater control of non-sample errors [
36,
37,
38,
39,
40,
41]. Accordingly, strategies for sampling campaigns conducted across tropical and temperate forest plots have been established that are capable of producing point clouds with a uniform point distribution and, thus, should allow for the intercomparison of metrics between instruments, plots, and over time [
42]. Indeed, TLS has been reported to yield reliable estimates of structural vegetation parameters across different tropical ecosystems and biogeographic regions, such as Amazonian lowland rainforests [
43,
44], mangrove forests in southeastern Brazil [
45], neotropical rainforests in Costa Rica [
31], and palaeotropical forests in Malaysia [
28,
29]. These studies often reported a higher accuracy of remotely sensed estimates than those applying conventional methods investigating the vegetation structure based on traditional forest inventories [
11,
46,
47]. However, to thoroughly assess the uncertainties of estimated vegetation biomass, it is necessary to compare the respective error metrics among different surveyed vegetation parameters and multiple methodologies applied under comparable in situ conditions and based on the same tree individuals.
To that end, we conducted an intensive measurement campaign in central-eastern Amazonian terra-firme forest (1) to compare the measurements of tree diameter and height obtained from traditional inventory techniques and laser-based electronic devices (i.e., terrestrial laser scanner, electronic caliper, and hypsometer); (2) to quantify the total error, the systematic error, and the random error for each of these techniques; and (3) to assess the overall uncertainty of the respective methods for estimating aboveground biomass in tropical forest ecosystems.
2. Materials and Methods
The study was conducted in the Cuieiras River Basin near the Experimental Station of Tropical Forestry (EEST) managed by the National Institute of Amazonian Research (INPA). The site represents one of the best-studied regions in the Central-Eastern Amazon and is located near “ZF-2” approx. 70 km north of Manaus, Brazil (2°36′32.67S; 60°12′33.48W;
Figure 1 and the following URL
https://www.inpa.gov.br/amazonface/arquivos/Amazon-FACE-Sciencie_Plan_Implementation_Strategy.pdf). According to Köppen-Geiger, the climate of the region is classified as a rainy tropical climate, with average monthly temperatures varying from 24 to 27 °C [
48]. The mean annual precipitation is 2400 mm with a dry period between July, August, and September when monthly precipitation is less than 100 mm [
48,
49]. The soils are clayic Latosol with high clay content and low natural fertility [
50]. The vegetation is characterized as a dense ombrophilous forest, and foregoing studies conducted in the same region reported that vegetation structure, i.e., stem density, canopy height, and aboveground biomass, is representative of the Amazonian terra-firme forest [
51]. The vegetation exhibits a median canopy height of 30 m, with emergent trees reaching 45 m; the individual stems reach up to 120 cm DBH; and the basal area reaches between 28–30 m
2 ha
−1 [
52]. The average canopy cover was 87–89% (dry/wet season), leaf area index of 5.3–6.2 m
2/m
2 (dry/wet season) and plot mean tree density (>10 cm DBH) was 708 individuals ha
−1. The main families found were Lecythidaceae, Sapotaceae, Arecaceae, Euphorbiaceae, Burseraceae, and Chrysobalanaceae. The largest number of species was found in Chrysobalanaceae, Sapotaceae, and Lauraceae [
53]. Tree individuals (inclusion limit DBH ≥ 10 cm) located in a permanent monitoring transect are monitored since 1996 by the Forest Management Laboratory at the National Institute for Amazonian Research (LMF/INPA). In this study, we evaluate traditional and laser-based inventory techniques based on surveying tree stems (n = 55; DBH ≥ 10 cm) located inside circular plots with 30 m in diameter (706 m
2) within a permanent monitoring transect managed by the National Institute of Amazonian Research (
Figure 1).
2.1. Measurements Obtained with Traditional Forest Inventory Techniques
For DBH, the tree circumference was measured at 1.30 m above ground level using a 5 m diameter tape (Forestry Supplies, Mississippi, USA). In the case of imperfections or buttresses, the point of measurement (POM) was moved up until the form of the stem normalized following the RAINFOR protocol [
38] and this observation was annotated in field worksheets. Additionally, the POM was marked with oil-based paint [
36,
38]. For Ht, the measurements were obtained with a tape measure of 50 m length (Irwin Tools, North Carolina, USA) at the highest possible point of the tree of interest that could be reached by a professional climber [
54,
55]. If the highest point was not reached by climbing, a measuring rod was used to reach the highest point of the crown.
In this study, the above-described traditional measurements (TM) of diameter and tree height were compared to estimates of Ht and DBH from multiple electronic devices, i.e., a laser rangefinder (TruPulse 360R, Laser Technology Inc., Colorado, USA;
Figure 2a) coupled to an electronic caliper (BT MEM, Masser OY, Rovaniemi, Finland;
Figure 2b) and connected to a portable computer (Getac T800, Hsinchu County, Taiwan;
Figure 2c) integrated via the so-called Field-Map
® software bundle (Institute of Forest Ecosystem Research Ltd., Prague, Czech Republic), as well as a terrestrial laser scanner (RIEGL VZ400, Riegl, Horn, Austria;
Figure 2d).
2.2. Measurements Obtained with the Field-Map Bundle
The field-map bundle is composed of three devices (
Figure 2a–c). For the evaluation of DBH, two perpendicular (90°) measurements were taken from the trunk at the largest and smallest diameters using an electronic caliper (
Figure 2b); at the same, POM as measured with the diameter tape. For the evaluation of Ht, a laser rangefinder (LR,
Figure 2a) was used to triangulate following the tangent method [
56]. The electronic devices are wirelessly connected to a portable computer (
Figure 2c) where data can be accessed directly in the field and extracted later via portable media (e.g., memory card or pen drive) or sent over wireless networks (Bluetooth). The Field-Map
® software interface allows the user to note additional observations for each measurement, e.g., change in POM, presence of imperfections, and buttress of the trunk. The device also determines the positions of each tree individual (
x,
y,
z coordinate system) by conducting distance measurements between respective tree individuals and a reflecting target in the center of the plot (considered as the center of the x, y, and z coordinates). This information is used by the Field-Map software to display the position of each tree on a two-dimensional map on the computer screen. Later on, this spatially explicit information was used to locate and co-register tree segments identified by the terrestrial laser scan.
2.3. Measurements Obtained with Terrestrial Laser Scanning
Terrestrial Laser Scanning
Three-dimensional scans were performed with the RIEGL VZ-400 laser scanner (
Figure 2d). The device has a vertical angle range of 30–130° and quickly acquires a large amount of data (300 kHz laser beam repetition rate) by recording multiple laser pulse returns (up to four returns per pulse emitted). The beam divergence of the laser is 0.35 mrad operating in the near infrared range (wavelength 1550 nm) and records targets within a range of 350 m. The scan settings were standardized across multiple scan positions throughout the plot. Briefly, we used a systematic sampling scheme using a central scanning location and further scanning sites in each cardinal direction to cover the plot area by conducting eight to ten overlapping scans with a mean distance below 10 m. Data were collected using the high-speed mode to obtain the maximum amount of laser return points per time, thus improving identification of the forest structure. Furthermore, additional scans were acquired at each scanning location with the instrument tilted 90° from the vertical position to fully sample the canopy. The collection time per position was approximately 2 min for the vertical position and for the tilted (90°) positions. To register the respective scans into a single point cloud, reflective targets made from reflective tape glued onto plastic cylinders 5 cm in diameter and 10 cm in height [
42] were distributed throughout the plot.
Registration of the Point Cloud
The scenes generated by each scan in the previous step were aligned in a common coordinate system forming a single point cloud for the entire plot (
Figure 3). This process is defined as the point cloud registration [
42,
57,
58]. The process was performed automatically using the RiSCAN PRO software [
59]. The program usually identifies at least four reflective targets shared by each scanning location, which is considered the minimum number to perform a reasonable coarse registration between two consecutive scans [
60]. However, the more reflective targets that can be detected during the scanning process, the better the automated registration procedure will perform (
Figure 3).
Acquisition of Biometric Variables from the Point Cloud
Following the procedure above, point coordinates for each individual tree were generated using open-source software for point cloud analysis (3D Forest version 0.42; available from
www.3dforest.eu; [
63]). The software extracts horizontal and vertical structural variables such as DBH, Ht, position of the tree, and volume of sections of the trunk, as well as canopy-related variables such as base height, crown depth, crown area, and volume. For the DBH estimation, we applied two methods: (i) Randomized Hough transformation (TLS
RHT) fitting a circle to the horizontal section of the trunk, with an adjusted number of iterations (standard setting n = 200) [
64], and (ii) least squares regression (TLS
LSR) with an algebraic estimation of the diameter and reduction of the quadratic distance of the adjusted circle [
65]. The two methods use only part of the point cloud, i.e., a 10 cm horizontal section of the trunk between 1.25 and 1.35 m above the lowest point determined by the digital terrain model [
63] (
Figure 4). For the extraction of diameters in a position different from the conventional POM (1.30 m), the stem curve command is able to determine the diameter in different positions of the trunk. The diameters in the stem curve command are located, relative to the base of the cloud, at 0.65 m, 1.3 m, 2 m, and every 1 m until the first bifurcation of the trunk. The stem curve command terminates when the estimated diameter is twice as large as the two diameters above, which indicates the crown expansion in the point cloud [
63].
For estimates of total tree height (Ht), the program offers two different approaches: (i) The “TLS Height” method defines the height by calculating the difference between the highest and the lowest points in the cloud along the z-axis (ii) the “TLS Length” method that computes the largest Euclidean distance between a point at the base of the cloud and the farthest point in any direction of the cloud, thus being the method of choice for analyzing inclined trees [
63] (
Figure 4).
2.4. Data Analysis
The relationship between traditional inventory measurements (TM) and laser-based estimates of tropical vegetation structure (i.e., tree diameter and tree height) obtained either with the Fieldmap bundle (FM) or the terrestrial laser scanner (TLS) was assessed using reduced major axis regression (RMA) [
66]. For each instrument, the total error, the systematic error (i.e., accuracy), and the random error (i.e., precision) were quantified [
56]. The total error (Equation (1)) was evaluated based on root mean square error (RMSE):
The systematic error (Equation (2)) or bias was calculated as the mean of the measurement error (Equation (2)) and represents “a mean of the differences between population measurements or test results and an accepted reference or true value” [
67]. It was calculated as follows:
The random error (Equation (3)) considers the variation of the measurement errors and represents the “statistical variance of an estimation methodology” [
68], calculated as follows:
Due to errors increasing in absolute terms with the DBH and Ht, all the abovementioned errors were calculated in a proportional way. The proportional total error, proportional systematic error, and proportional random error were calculated according to the following equations (Equations (4)–(6)):
where
Xobserved is the actual measurement for the desired variable, e.g., for DBH, the data obtained from the diameter tape (i.e., by calculating DBH from the circumference measurements) or for Ht obtained with a vertical tape measurement;
Xpredicted refers to the biometric data obtained with the electronic devices, i.e., FM and TLS; and
n the number of trees. Briefly, the systematic error indicates the tendency of an instrument to record results systematically above or below the actual value (i.e., precision), whereas the random error is the product of the variations in measurements that do not follow a fixed trend and the total error is the product of the estimate (systematic and random error) in relation to the observed in situ measurement (i.e., accuracy).
The DBH and Ht obtained through the conventional measurements and the instruments assessed in this study were used as input variables for allometric equations estimating tropical aboveground biomass (AGB). We selected two local equations, derived from central Amazonian inventory plots, and two pantropical equations extracted from the published literature [
5,
10,
69] (see references in
Appendix A Table A1). The local equation proposed by Higuchi et al. [
69] was used as a reference for calculating the error metrics among AGB estimates resulting from different allometric relationships evaluated in this study. The equation is based on fresh weight from destructively sampled trees and applies a correction factor of 0.6028 (1 − mean moisture content) [
70].