A Primer on Clustering of Forest Management Units for Reliable Design-Based Direct Estimates and Model-Based Small Area Estimation

Abstract

This study employs clustering analysis to group forest management units using auxiliary, satellite imagery-derived height metrics and past wall-to-wall tree census data from a natural, uneven-aged forest. Initially, we conducted an exhaustive exploration to determine the optimal number of clusters k, considering a wide range of clustering schemes, indices, and two specific k ranges. The optimal k is influenced by various factors, including the minimum k considered, the selected clustering algorithm, the clustering indices used, and the auxiliary variables. Specifically, the minimum k, the Euclidean distance metric, and the clustering index were instrumental in determining the optimal cluster numbers, with algorithms exerting minimal influence. Unlike traditional validation indices, we assessed the performance of these optimally defined clusters based on direct estimates and additional criteria. Subsequently, our research introduces a twofold methodology for Small Area Estimation (SAE). The first approach focuses on aggregating forest management units at the cluster level to increase the sample size, thereby yielding reliable design-based direct estimates for key forest attributes, including growing stock volume, basal area, tree density, and mean tree height. The second approach prepares area-level data for the future application of model-based estimators, contingent on establishing a strong correlation between target and auxiliary variables. Our methodology has the potential to enhance forest inventory practices across a wide range of forests where area-level auxiliary covariates are available.