Estimating forest stand density and structure using Bayesian individual tree detection, stochastic geometry, and distribution matching

Abstract Errors in individual tree detection and delineation affect diameter distribution predictions based on crown attributes extracted from the detected trees. We develop a methodology for circumventing these problems. The method is based on matching cumulative distribution functions of field measured tree diameter distributions and crown radii distributions extracted from airborne laser scanning data through individual tree detection presented by Vauhkonen and Mehtatalo (2015). In this study, empirical distribution functions and a monotonic, nonlinear model curve are introduced. Tree crown radius distribution produced by individual tree detection is corrected by a method taking into account that all trees cannot be detected. The evaluation is based on the ability of the developed model sequence to predict quadratic mean diameter and total basal area. The studied data consists of 36 field plots in a typical boreal managed forest area in eastern Finland. The suggested enhancements to the model sequence produce improved results in most of the test cases. Most notably, in leave-one-out cross-validation experiments the modified models improve RMSE of basal area 13% in the full data and RMSE of quadratic mean diameter and basal area 69% and 11%, respectively, in pure pine plots. Better modeling of the crown radius distribution and improved matching between crown radii and stem diameters add the operational premises of the full distribution matching.