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.
