Heightdiameter

Height-diameter, commonly referred to as the height–diameter relationship, is an allometric concept used in forestry and ecology to describe how a tree's height (H) relates to its trunk diameter measured at breast height (DBH). It captures general allometry of tree form and is essential for estimating height when direct measurement is difficult, as well as for modeling biomass and carbon stocks. The relationship varies with species, age, site conditions, and competitive status.

A variety of mathematical forms are used to represent the H–DBH curve. Linear models (H = a + b·DBH) are simple but often insufficient; nonlinear models such as H = a·DBH^b are common because height growth accelerates with diameter in many species. More flexible functions, including logistic or generalized logistic forms, can capture a leveling off of height at large diameters. In practice, models are fitted to local data, and sometimes species- or site-specific random effects are included.

Data collection typically involves measuring DBH at 1.3 meters above ground and estimating height using clinometers, hypsometers, laser devices, or advanced remote sensing methods. Model fitting uses regression techniques, with attention to heteroscedasticity, outliers, and cross-validation. Mixed-effects models are frequently employed to accommodate variation among species and sites.

Applications of height–diameter relationships include biomass and carbon stock estimation, growth and yield modelling, forest inventories, and as inputs for ecological and remote-sensing models. Limitations include species- and site-specificity, age-related changes, measurement error in height, and potential bias when applied beyond the data range used to calibrate the model.