Mixed-effects height-diameter models for black pine (Pinus nigra Arn.) forest management

Key message Height-diameter models were developed specifically for Pinus nigra Arn., an important commercially species extending in the Mediterranean and central Europe region. The accuracy of the proposed models is expected to substantially improve the tree volume and total biomass estimations. Three types of nonlinear height-diameter models, simple, generalized mixed effects and fixed, were evaluated against independent data from even-aged black pine (Pinus nigra Arn.) natural stands located in Olympus National Park in Greece in an effort to accurately predict total tree height (h). A total of 3442 pairs of height-diameter data were collected from 66 randomly selected non-permanent plots. Using the diameter at breast height (d) as independent variable, a number of simple nonlinear mixed-effects models were fitted to select the most appropriate for further analysis. Continuously, basic stand parameters were added as predictors, so as to develop a generalized (h-d) model with increased applicability prospects. At that stage, a mixed-effects modeling approach was applied to improve height predictability based on the reduction of the Root Mean Squared Error (RMSE). The analysis showed that the inclusion of dominant height and dominant diameter as predictors improved the accuracy of the Chapman-Richards model. Moreover, the random components within the nonlinear (h-d) model explained a great part of the height variation, which was not possible to explain previously. The mixed-effects modeling approach provides an adequate framework for predicting the black pine tree height accurately, which could save intensive fieldwork.