Reducing overharvest risk in the Brazilian Amazon: mixed-effects volume ratio models based on post-harvest measurements

Abstract Estimating commercial wood volume is fundamental to sustainable forest management in the Brazilian Amazon, supporting environmental licensing, harvest planning, and timber quantification. However, the region’s high biodiversity and structural complexity make accurate volume estimation difficult, particularly when generic fixed-factor models are applied. Although legal frameworks require site-specific equations after the first year of exploration, generic models are still widely used during the initial Annual Operational Plan (AOP) due to limited pre-harvest data, typically restricted to diameter at breast height (DBH), visually estimated stem height, and stem defects. In this context, this study aimed (i) to fit volume ratio models using post-harvest data for application from the second year of exploration onward and (ii) to evaluate, through volume simulation based solely on pre-harvest data, whether the best-fitted volume ratio model outperforms the generic equations commonly used in the first AOP. The study was conducted in five federal conservation units in the states of Pará and Rondônia, Brazil, comprising ~66 000 trees from 10 widely commercialized botanical genera, and using data collected during forest inventory and post-harvest log-scaling. Three-volume-ratio models (two nonlinear and one linear) were evaluated and compared with the Schumacher–Hall model. A mixed-effects framework was adopted, incorporating botanical genus as a random effect to account for the hierarchical data structure. Model performance was assessed using root mean square error expressed as a percentage, percentage bias, and equivalence tests. Additionally, total stem volume was simulated using only pre-harvest DBH and stem defects data. Volume ratio models incorporating post-harvest actual height data outperformed traditional approaches, whereas models excluding height data performed the poorest. Among the Schumacher–Hall formulations, the model based on visually estimated pre-harvest height exhibited errors exceeding 40%, highlighting the critical importance of accurate height information. Total stem volume simulations indicated similar performance between the best volume ratio and Schumacher–Hall models when only DBH and stem quality data were available. Overall, volume ratio models calibrated with post-harvest data demonstrated superior accuracy and reliability, representing a robust alternative for subsequent AOPs and offering potential gains in transparency and efficiency for forest management in the Brazilian Amazon.