# Building Tree Allometry Relationships Based on TLS Point Clouds and Machine Learning Regression
## 4 Discussion  
The main objective of this work is to model the allometric relationships--DBH = \(\Phi\)(H) or DBH = \(\Psi\)(H, CD)--of teak trees located in the Coastal Region of Ecuador. Such models are important components for calibrating remote sensing products used to estimate natural forest stocks. In fact, AGB estimates at tree level could be obtained from airborne and spaceborne sensors by only extracting some key variables such as tree height and crown diameter. This remote sensing-oriented approach is gaining importance in recent years [18] because it enables large-scale mapping of AGB for forest management and monitoring [10; 28] in the context of mitigating climate change (REDD monitoring programmes) [5; 29]. It is worth noting that this is the exact opposite of what is common in traditional fieldwork based inventories, where DBH is usually easier and cheaper to measure than tree height, especially due to the difficulty of locating tree tops inside closed-canopy forests [30]. Figure 3: Examples of plots of DBH predicted/observed values for test datasets (455 teak trees not used for training) given by four allometric models in which the explanatory variables are H and CD. **(a)** Linear regression (R\({}^{2}\) = 87.99%); **(b)** Decision Tree Regression (R\({}^{2}\) = 79.75%); **(c)** Random Forest Regression (R\({}^{2}\) = 89.63%); **(d)** Gradient Boosting Regression (R\({}^{2}\) = 91.01%). The red line refers to the 1:1 line. Most allometric models to estimate AGB at tree level are based on knowing the DBH value. This is the case of the generalized pantropical AGB model proposed by [PERSON] et al. [17] given by the following equation:  
\[\text{AGB}=0.0673\Big{(}\rho\text{DBH}^{2}\text{H}\Big{)}^{0.976}, \tag{6}\]  
where AGB represents estimated aboveground biomass (kg), DBH is diameter at breast height (cm), H is tree height (m), and \(\rho\) is wood density (g cm\({}^{-3}\)). The same occurs with specific models developed for the estimation of AGB of teak trees such as those proposed by [PERSON] [31] or [PERSON] [32] that also have DBH as an explanatory variable. However, it is not possible to directly measure DBH from airborne or spaceborne sensors, a drawback that could be overcome if we counted on reasonably accurate allometric models to estimate DBH from variables that can be extracted from remote sensing techniques such as H and CD [4; 19; 33; 34; 35]. This requires accurate algorithms to extract the position and height of each tree within a study plot as well as methods aimed at automated tree crown delineation [15]. Machine learning methods have been widely applied to develop AGB prediction models from different remote sensing data sources such as optical satellite imagery, UAV stereo-imagery, airborne hyperspectral images, ALS (airborne laser scanning), and spaceborne SAR [15; 16; 25; 26; 36; 37]. However, there are very few published works comparing the results offered by traditional linear least squares regression with those provided by machine learning methods in relation to modeling tree height-diameter allometry. Most of these studies test some formulation of artificial neural networks (ANN) [38; 39; 40] or even Deep Learning (DL) approaches [30; 41], which generally showed greater precision than traditional linear regression methods. For example, [PERSON] et al. [40] successfully applied a new approach for using ANN machine learning to synthesize spatiotemporal tree measurement data collected in a boreal forest in central Canada to model DBH-H and DBH-H-age relationships for six dominant tree species. [PERSON] and [PERSON] [30] trained a complex DL algorithm with 100 neurons distributed into six, seven or nine hidden layers for predicting tree heights in a tropical rain forest of Nigeria. They found that DL approach outperformed the results provided by nonlinear least squares and nonlinear mixed-effects models.