Abstract
Ochroma pyramidale (Cav. ex. Lam.) Urb. (balsa-tree) is a commercially important tree species that ranges from Mexico to northern Brazil. Due to its low weight and mechanical endurance, the wood is particularly well-suited for wind turbine blades, sporting equipment, boats and aircrafts; as such, it is in high market demand and plays an important role in many regional economies. This tree species is also well-known to exhibit a high degree of variation in growth. Researchers interested in modeling the height–diameter relationship typically resort to using ordinary least squares (OLS) to fit linear models; however, this method is known to suffer from sensitivity to outliers. Given the latter, the application of these models may yield potentially biased tree height estimates. The use of robust regression with iteratively reweighted least squares (IRLS) has been proposed as an alternative to mitigate the influence of outliers. This study aims to improve the modeling of height–diameter relationships of tree species with high growth variation, by using robust regressions with IRLS for data-sets stratified by site-index and age-classes. We implement a split sample approach to assess the model performance using data from Ecuador’s continuous forest inventory (n = 32,279 trees). A sensitivity analysis of six outlier scenarios is also conducted using a subsample of the former (n = 26). Our results indicate that IRLS regression methods can give unbiased height predictions. At face value, the sensitivity analysis indicates that OLS performs better in terms of standard error of estimate. However, we found that OLS suffers from skewed residual distributions (i.e., unreliable estimations); conversely, IRLS seems to be less affected by this source of bias and the fitted parameters indicate lower standard errors. Overall, we recommend using robust regression methods with IRLS to produce consistent height predictions for O. pyramidale and other tree species showing high growth variation.
Highlights
Our findings suggest that models that do not stratify are out-performed by models that stratified by age—these results were consistent in both ordinary least squares (OLS) and iteratively reweighted least squares (IRLS)
These results using the Näslund model are consistent with other empirical studies e.g., [45], which suggests a certain flexibility of this model to describe the height–diameter relationships; namely, the mathematical design of this model appears to allow for better residual distribution—when evaluated directly from a linear model fit that does not isolate for the influence of the variable h (Figure 7)
This result appears to be supported by models that stratify for site-index classes and those that do not stratify; namely, these two model specifications appear to exhibit greater variability for h and diameter at breast height (DBH)—this suggests a relative gain in accuracy (SEE%) when compared to models that stratify by site and age classes (Table 6)
Summary
(balsa-tree) is a large Malvaceae pioneer tree species native from tropical forests. This species can reach 30–40 m in height, 60–120 cm in diameter at breast height (DBH), and crowns up to 40 m at the age of 15 years. O. pyramidale is popularly known as balsa-tree and balsa-wood, with natural distribution throughout America, from southern Mexico to Bolivia, northern Brazil and the Antilles [1,2]. Due to its low weight (the density ranges between 0.06 and 0.38 g cm−3 ) and mechanical resistance, the wood of O. pyramidale is commonly used in wind turbine propellers, sports equipment, ships, and aircrafts [3]. Balsa-wood has been in high demand on the international market, mainly Europe, China, and United States. The species is planted in commercial reforestation programs and in mixed plantations to restorage degraded areas [2,4,5]
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