Allometric relationships between total height and diameter for volume estimation of bottomland hardwood oaks in Arkansas

Bottomland hardwood (BLH) forests are a unique ecosystem that plays an important role in the provision of ecosystem services, both ecologically and economically. This study modeled allometric relationships between total tree height and diameter at breast height (DBH) for seven oak species ( Quercus spp.), including overcup ( Quercus lyrata ), cherry bark ( Quercus pagoda ), Nuttall ( Quercus texana ), Shumard ( Quercus shumardii ), water ( Quercus nigra ), willow ( Quercus phellos ), and post oaks ( Quercus stellata ) that prevail in BLH forests in the Lower Mississippi Alluvial Valley region of eastern Arkansas. Twelve candidate models (Schumacher, Bufford, Curtis, Meyer, Micment, Power, Logistic, Weibull, Chapman, Gompertz, Ratkowsky, and Prodan) were fitted using data from 2,762 individual trees across 34 Forest Inventory and Analysis (FIA) plots collected between 2015 and 2023. The results showed that the three-parameter Weibull model was the best-fitting model based on the relative rank sum scores and was therefore selected as the base model for further analysis. To account for interspecific variability, a nonlinear mixed-effects model was developed using the Weibull function with species as a random effect. The mixed-effects model performed better than the fixed-effects global models, with R 2 = 0.79 and RMSE = 3.34 m. Furthermore, volume validation analysis revealed that mixed-effects model estimates were more consistent with the observed data. In contrast, global model estimates tended to underestimate volume in larger diameter classes (DBH > 50 cm). Additionally, applying response calibration to a subsample of trees localized these predictions and consistently reduced prediction errors relative to the uncalibrated population-average model. These findings suggest that the mixed-effects Weibull model is a robust and precise tool for predicting tree height and estimating volume for oak species in BLH forests of this region, providing a baseline for predicting biomass stock of these oak species and contributing to the development of biometric models to guide forest inventory, silvicultural practices, and forest management.