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

Instantons and Fluctuations in a Lagrangian Model of Turbulence

We perform a detailed analytical study of the Recent Fluid Deformation (RFD) model for the onset of Lagrangian intermittency, within the context of the Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) path integral formalism. The model is based, as a key point, upon local closures for the pressure Hessian and the viscous dissipation terms in the stochastic dynamical equations for the velocity gradient tensor. We carry out a power counting hierarchical classification of the several perturbative contributions associated to fluctuations around the instanton-evaluated MSRJD action, along the lines of the cumulant expansion. The most relevant Feynman diagrams are then integrated out into the renormalized effective action, for the computation of velocity gradient probability distribution functions (vgPDFs). While the subleading perturbative corrections do not affect the global shape of the vgPDFs in an appreciable qualitative way, it turns out that they have a significant role in the accurate description of their non-Gaussian cores.Comment: 32 pages, 9 figure

The Onset of Intermittency in Stochastic Burgers Hydrodynamics

We study the onset of intermittency in stochastic Burgers hydrodynamics, as characterized by the statistical behavior of negative velocity gradient fluctuations. The analysis is based on the response functional formalism, where specific velocity configurations - the viscous instantons - are assumed to play a dominant role in modeling the left tails of velocity gradient probability distribution functions. We find, as expected on general grounds, that the field theoretical approach becomes meaningful in practice only if the effects of fluctuations around instantons are taken into account. Working with a systematic cumulant expansion, it turns out that the integration of fluctuations yields, in leading perturbative order, to an effective description of the Burgers stochastic dynamics given by the renormalization of its associated heat kernel propagator and the external force-force correlation function.Comment: 10 pages, 6 figure

A Random Multifractal Tilling

We develop a multifractal random tilling that fills the square. The multifractal is formed by an arrangement of rectangular blocks of different sizes, areas and number of neighbors. The overall feature of the tilling is an heterogeneous and anisotropic random self-affine object. The multifractal is constructed by an algorithm that makes successive sections of the square. At each $n$-step there is a random choice of a parameter $\rho_i$ related to the section ratio. For the case of random choice between $\rho_1$ and $\rho_2$ we find analytically the full spectrum of fractal dimensions

Kinematics of a Spacetime with an Infinite Cosmological Constant

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant \Lambda is discussed by using Inonu-Wigner contractions of the de Sitter groups and spaces. When \Lambda --> infinity, spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c --> infinity is further considered, the kinematical group in this case being a modified Galilei group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology.Comment: RevTex, 7 pages, no figures. Presentation changes, including a new Title. Version to appear in Found. Phys. Let