Comparison of Parameter Estimation Methods Based on Two Additive Biomass Models with Small Samples

Accurately estimating tree biomass is crucial for monitoring and managing forest resources, and understanding regional climate change and material cycles. The additive model system has proven reliable for biomass estimation in Chinese forestry since it considers the inherent correlation among variables based on allometric equations. However, due to the increasing difficulty of obtaining a substantial amount of sample data, estimating parameters for the additive model equations becomes a formidable challenge when working with limited sample sizes. This study primarily focuses on analyzing these parameters using data extracted from a smaller sample. Here, we established two additive biomass model systems using the independent diameter and the combined variable that comprises diameter and tree height. The logarithmic Nonlinear Seemingly Uncorrelated (logarithmic NSUR) method and the Generalized Method of Moments (GMM) method were applied to estimate the parameters of these models. By comparing four distinct approaches, the following key results were obtained: (1) Both the GMM and logarithmic NSUR methods can yield satisfactory goodness of fit and estimation precision for the additive biomass equations, with the root mean square error (RMSE) were significantly low, and coefficients of determination (R-2) were mostly higher than 0.9. (2) Comparatively, examining the fitted curves of predicted values, the GMM method provided better fitting than the NSUR method. The GMM method with the combined variable is the most suggested approach for the calculation and research of single-tree biomass models with a small sample size.

Automated summary

Accurate estimation of tree biomass is crucial for monitoring and managing forest resources, understanding regional climate change and material cycles. This study analyzes parameters for additive biomass model systems using smaller sample data and establishes two models based on independent diameter and a combined variable of diameter and tree height. By comparing four different approaches, it is found that both the GMM and logarithmic NSUR methods provide satisfactory goodness of fit and estimation precision, with the GMM method yielding better fitting. The GMM method with the combined variable is suggested for calculation and research of single-tree biomass models with small sample sizes.