Modelling height-diameter relationships in complex tropical rain forest ecosystems using deep learning algorithm

Modelling tree height-diameter relationships in complex tropical rain forest ecosystems remains a challenge because of characteristics of multi-species, multi-layers, and indeterminate age composition. Effective modelling of such complex systems required innovative techniques to improve prediction of tree heights for use for aboveground biomass estimations. Therefore, in this study, deep learning algorithm (DLA) models based on artificial intelligence were trained for predicting tree heights in a tropical rain forest of Nigeria. The data consisted of 1736 individual trees representing 116 species, and measured from 52 0.25 ha sample plots. A K-means clustering was used to classify the species into three groups based on height-diameter ratios. The DLA models were trained for each species-group in which diameter at beast height, quadratic mean diameter and number of trees per ha were used as input variables. Predictions by the DLA models were compared with those developed by nonlinear least squares (NLS) and nonlinear mixed-effects (NLME) using different evaluation statistics and equivalence test. In addition, the predicted heights by the models were used to estimate aboveground biomass. The results showed that the DLA models with 100 neurons in 6 hidden layers, 100 neurons in 9 hidden layers and 100 neurons in 7 hidden layers for groups 1, 2, and 3, respectively, outperformed the NLS and NLME models. The root mean square error for the DLA models ranged from 1.939 to 3.887 m. The results also showed that using height predicted by the DLA models for aboveground biomass estimation brought about more than 30% reduction in error relative to NLS and NLME. Consequently, minimal errors were created in aboveground biomass estimation compared to those of the classical methods.

Modelling joint distribution of tree diameter and height using Frank and Plackett copulas

Bivariate distribution models are veritable tools for improving forest stand volume estimations.Their accuracy depends on the method of construction.To-date,most bivariate distributions in forestry have been constructed either with normal or Plackett copulas.In this study,the accuracy of the Frank copula for constructing bivariate distributions was assessed.The effectiveness of Frank and Plackett copulas were evaluated on seven distribution models using data from temperate and tropical forests.The bivariate distributions include:Burr III,Burr XII,Logit-Logistic,Log-Logistic,generalized Weibull,Weibull and Kumaraswamy.Maximum likelihood was used to fit the models to the joint distribution of diameter and height data of Pinus pinaster(184 plots),Pinus radiata(96 plots),Eucalyptus camaldulensis(85 plots)and Gmelina arborea(60 plots).Models were evaluated based on negative log-likelihood(-ΛΛ).The result show that Frank-based models were more suitable in describing the joint distribution of diameter and height than most of their Plackett-based counterparts.The bivariate Burr III distributions had the overall best performance.The Frank copula is therefore recommended for the construction of more useful bivariate distributions in forestry.