One model to rule them all: A nationwide height–diameter model for 91 Spanish forest species

Abstract

Accurately characterizing tree allometry is essential for sustainable forest management to predict forest growth and yield, monitor long-term stand dynamics and assess the impacts of disturbances. Among different allometric attributes, past studies have focused on understanding the relationships between tree height and diameter at breast height (dbh), also known as height–diameter (h–d) relationships. Both variables are commonly used to estimate and predict tree and stand metrics (e.g., total volume, biomass and carbon) as well as to assess site productivity. Under limited budget and time constraints, h–d models, which predict tree heights using dbh measurements, provide a practical and cost-effective alternative. In this study, a mixed-effects h–d model was developed for making species-specific predictions for 91 tree species across broad geographic areas in Spain. A total of 1,512,721 observations were collected from the Spanish National Forest Inventory sample plots for analysis. Results indicate that the final model, selected from a pool of 95 candidates, provides unbiased predictions of total tree height based on the 95% confidence interval of mean bias. In addition to dbh, the inclusion of site qualitative variables (stand origin, species mixture and biogeographic region) in the model plays an important role in improving the model predictability. For a given tree dbh, trees in plantations and pure stands tend to achieve greater heights than those in natural and mixed stands. Regional variation is species-dependent, while the Alpine region with a higher wind speed and cooler temperature tends to exhibit shorter trees compared to other regions. The proposed models are simple in structure and rely on easily-obtainable predictors, making them useful for field application and minimizing the need for complex measurements. This study provides an alternative quantitative tool for forest practitioners and managers when predicting total tree heights for diverse forest ecosystems across a wide range of geographic regions.