Mixed-effects generalized height-diameter model: A tool for forestry management of young sweet chestnut stands uri icon


  • Conception of the study, data analysis, drafting of the manuscript and critical revision: MSP, LN, CRGD. Contributed materials: MSP, LN. The authors are grateful to the Foundation for Science and Technology (FCT, Portugal) for financial support by national funds FCT/ MCTES to CIMO (UIDB/00690/2020); AGRO Program, Project 267: Sustainable Management of Chestnut Forested Areas in High-Forest and Coppice Systems; Project PTDC/AGRCFL/68186/Mixed forests: Modeling, dynamics and geographical distribution of productivity and carbon storage in mixed forest ecosystems in Portugal; Project PDR2020-101-031671 GO_FTA: Afforestation of agricultural lands with + value, financial support of FEADER and Portuguese Government.
  • Height is a key variable for forest management. However, tree height measurements are expensive and timeconsuming, requiring more effort to measure in the forest than diameter breast height measurements. Indeed, height-diameter (h-d) models are increasingly used to overcome the difficulty in measuring tree heights. Therefore, more accurate h-d models are increasingly needed. The mixed-effects modeling approach is a mainstream method to estimate h-d models. This technique was used to model the h-d relationship in the first 24 years of growth of sweet chestnut (Castanea sativa Mill.) high-forest stands for timber production. A dataset of 10,868 h-d observations and 57 plots of local-inventory data were considered individually. Simple mixed-effects models considering a grouping structure in the data (plot-level) were obtained, and generalized mixed-effects models were developed by expanding the fixed structure of simple mixed-effects models with stand-level variables. Several alternative model forms were tested in terms of accuracy, applicability and measurement effort. Different alternatives for calibrated predictions of tree height at plot level were analyzed, and considerations on the tradeoff between easy-to-use equations in the field practice and high-accuracy equations for forest inventory were tested. The selected Richards M1a generalized mixed-effects model simultaneously provides fixed and random parameters to estimate the chestnut tree height from tree diameter and stand-level variables using the same model. The analysis showed that the inclusion of dominant height and dominant diameter as predictors improved the accuracy of the Richards model. The Draudt method was one of the best approaches to improve tree-level height prediction accuracy using mixed-effects. The applied approach is quite feasible in 100–500 m2 plots. The use of these models and the suggested calibration process will significantly reduce the effort and costs of fieldwork teams to measure heights for forest management planning while ensuring high accuracy. This effort is greater the greater the forest density and, therefore, greater for young stands than for adult stands.

publication date

  • June 1, 2022