Accuracy of a DTM derived from full-waveform laser scanning data under unstructured eucalypt forest: a case study

A Digital Terrain Model (DTM) is fundamental for extracting several forest canopy structure metrics from data acquired with small-footprint airborne laser scanning (ALS). This modern remote sensing technology is based on laser measurements from a laser system mounted on an aircraft and integrated with a geodetic GNSS receiver and an inertial measurement unit (IMU) or inertia navigation system (INS). In the context of a research project for deriving forest inventory parameters and fuel variables under eucalypt stands in Mediterranean climates, the vertical precision of the DTM obtained by automatic filtering of full-waveform ALS data had to be evaluated. The DTM accuracy estimation on a study area with peculiar characteristics, which are often avoided in related studies, will also allow verifying the performance of full- waveform ALS systems. The accuracy estimation is carried out in a novel way. By novel way, it is meant an exhaustive, well-planned collection of reliable control data in forest environment. The collection of the control data involves the production of DTM on 43 circular plots (radius = 11.28m) using total stations and geodetic GNSS receivers. These DTM, with a total of 3356 points, allowed one to evaluate consistently and reliably the vertical accuracy of the terrain surface produced with ALS under a eucalypt forest. This global accuracy, expressed by the Root Mean Square Error (RMSE) of the vertical differences between the field surveyed surface and the ALS derived DTM surface is 0.15m (mean=0.08m and std=0.09m). This impressive value indicates that, for an ALS point cloud density of 10pts/m2 and footprint of 20 cm, the methodology used to extract the DTM from full- waveform ALS data under an unstructured eucalypt forest is very accurate. In this article it is addressed both the strategy adopted to collect the control data and the quality assessment of the DTM produced by means of the ALS data

Some Aspects of the Exact Foldy-Wouthuysen Transformation for a Dirac Fermion

The Foldy-Wouthuysen transformation (FWT) is used to separate distinct components of relativistic spinor field, e.g. electron and positron. Usually, the FWT is perturbative, but in some cases there is an involution operator and the transformation can be done exactly. We consider some aspects of an exact FWT and show that, even if the theory does not admit an involution operator, one can use the technique of exact FWT to obtain the conventional perturbative result. Several particular cases can be elaborated as examples