Matching remotely sensed and field-measured tree size distributions

Abstract

Undetected trees and inaccuracies in the predicted allometric relationships of tree stem attributes seriously constrain single-tree remote sensing of seminatural forests. A new approach to compensate for these error sources was developed by applying a histogram matching technique to map the transformation between the cumulative distribution functions of crown radii extracted from airborne laser scanning (ALS) data and field-measured stem diameters (dbh, outside bark measured at 1.3 m aboveground). The ALS-based crown data were corrected for the censoring effect caused by overlapping tree crowns, assuming that the forest is an outcome of a homogeneous, marked Poisson process with independent marks of the crown radii. The transformation between the cumulative distribution functions was described by a polynomial regression model. The approach was tested for the prediction of plot-level stem number (N), quadratic mean diameter (DQM), and basal area (G) in a managed boreal forest. Of the 40 plots studied, a total of 18 plots met the assumptions of the Poisson process and independent marks. In these plots, the predicted N, DQM, and G had best-case root mean squared errors of 299 stems·ha−1 (27.6%), 2.1 cm (13.1%), and 2.9 m2·ha−1 (13.0%), respectively, and the null hypothesis that the mean difference between the measured and predicted values was 0 was not rejected (p > 0.05). Considerably less accurate results were obtained for the plots that did not meet the assumptions. However, the goodness-of-fit of the predicted diameter distribution was especially improved compared with the single-tree remote sensing prediction, and observations realistically obtainable with ALS data showed potential to further localize the predictions. Remarkably, predictions of N showing no evidence against zero bias were derived solely based on the ALS data for the plots meeting the assumptions made, and limited training data are proposed to be adequate for predicting the stem diameter distribution, DQM, and G. Although this study was based on ALS data, we discuss the possibility of using other remotely sensed data as well. Taken together with the low requirements for field reference data, the presented approach provides interesting practical possibilities that are not typically proposed in the forest remote sensing literature.