# Stand Structure Impacts on Forest Modelling
## 4 Diameter at Breast Height and Basal Area  
Diameter is always measured in forest inventories. Both diameter at breast height and basal area (corresponding to the area of the circle with diameter equal to diameter at breast height) are two key variables in the evaluation of the growth of trees, stands and forests. Forest inventories enable the evaluation of diameter (and basal area) variation with successive surveys. Yet, the drawback is that it is not possible to predict future growth, whether in time or in space. Thus, diameter and basal area models were, and still are, developed to monitor and predict growth. Several examples will be explored regarding the influence of stand structure on modelling at tree level. Several authors have studied the influence of composition (pure vs mixed) on diameter models. Ref. [46] discussed model performance for young mixed stands of _Picea abies_, _Betula pendula_ and _Betula pubescens_, subject to four different precommercial thinnings in Norway. The models for pure stands did not predict accurately diameter growth in mixed stands. The same authors stressed the effect of plot size on modelling. In small plots the contiguous trees (outside the plot) affected the trees in the plot and, consequently, its dimensions, and bias may arise in the estimation of diameter and dominant height. Ref. [47] and Ref. [48] stated that the different tree allometry in mixed stands, due to the variability between species, and thus growth, is better captured when models are developed per tree species. Ref. [49] studied diameter growth in even-aged mixed _Picea abies_, _Abies_ spp. and _Fagus sylvatica_ and pure _Fagus sylvatica_ stands in twelve long term thinning trials in Slovakia. The authors compared nonlinear ordinary least square regression and nonlinear mixed effect models. The latter outperformed the former because it was better suited for data with hierarchical structure, which resulted in more accurate predictions and, at the same time, maintained biological plausibility. Similar results were attained by Ref. [50]. The mixed models advantages were twofold: they enabled the detection of the increase in the increments in diameter after thinning and the accommodation of the differences in diameter growth due to the species and their proportions, stand development stage and site quality [49; 50]. Ref. [51] analysed diameter increment cores of 1240 dominant trees of long time series from both pure and mixed stands of _Fagus sylvatica_ in thirteen European countries in mountain forests using mixed models. The models were able to accommodate the differences in diameter growth in pure and mixed stands (with higher slope for the former than for the latter) and along an elevation gradient (growth decreased with elevation). Ref. [52] modelled the radial growth on pure and mixed stands of _Picea crassifolia_ and _Betula platyphilla_ in China. The linear mixed effects models were able to accurately estimate the radial growth and differentiated it according to competition and diversity. The increase in competition resulted in the reduction of the radial growth for both species, radial growth depended on the tree size and that of the neighbours, and diversity in species positively affected the radial growth of _Picea crassifolia_, although the competition by the neighbours influenced the extent of the positive effects. Other authors studied the effect of structure (even-aged vs uneven-aged) on diameter models. Ref. [53] evaluated the effect of selective cutting on diameter increment with forest inventory data and multiple least square models in _Picea abies_ stands in Norway. The authors referred that the models developed for even-aged stands resulted in an overestimation of about 20% when applied to the uneven-aged stands. The bias was the largest after the selective cut when the diameter growth rate was the lowest.