The Stuff Backscatter Random Fields Are Made Of

• Published in: Spatial Analysis for Radar Remote Sensing of Tropical Forests Vol. 1; pp. 73 - 93
• Main Authors: De Grandi, Gianfranco (Frank), De Grandi, Elsa Carla
• Format: Book Chapter
• Language: English
• Published: CRC Press 2021
• Edition: 1
• Subjects: SRTM DEM; Dense Tropical Forest; Backscattering Coefficient; Co-polarized Channels; Backscatter Simulation; Real SAR Data; PALSAR Image; InSAR Coherence; Total Backscattering Coefficient; HH Polarization; Real SAR Image; Radar Backscatter; Radiative Transfer; Microwave Domain; Specific Intensity; Object Based Change Detection; Integro Differential Equation; Branch Categories; Total Backscatter; Direct Scattering; SAR Image; Radiative Transfer Theory; InSAR Observation; Plane Parallel Medium; Diffuse Intensity
• ISBN: 0367259400; 9780367742669; 0367742667; 9780367259402
• DOI: 10.1201/9780429290657-7

Radar backscatter random fields will be the playground for spatial analysis theory and practice that will be developed throughout the book. A random field is the realization of a random process in a 2-dimensional space (i.e. a radar image). To understand the origin of the points that fill the radar image is a prerequisite for the development of further analysis on the statistical properties of their ensemble. How the points in the radar field are shadows of the illuminated target's physical properties (more specifically, of a dense tropical forest) is evidenced in this chapter by a wave scattering model. The principles of electromagnetic wave transport theory are outlined. The specific intensity, a differential descriptor of the local properties in space and time of the energy associated with a wave traveling and interacting with matter, is introduced. The basic building block of wave scattering modeling, the equation of transfer, an integro-differential equation that governs the two energy flow processes in a volume - absorption and scattering - is then presented. As an illustrative example, propagation through a plane parallel medium is worked out. The numerical solution of the equation of transfer provides a number of test cases, showing, for example, the angular dependence of the diffuse intensity. The main principles underpinning a wave scattering model for layered vegetation based on transport theory are explained next. The model was developed by the University of Texas at Arlington in the 1990s, and is referred to as the UTA model. The model's view of the vegetation layer consists of an ensemble of dielectric cylinders or discs that are "visible" by the radiation in the microwave domain, distributed stochastically in a volume that is layered in one dimension. The solution of the transport equations, given a medium description, provides estimates of the backscattering coefficients as a function of wavelength, incidence angle and polarization. The potential of the modelling approach for gaining insight into a controlled situation on the dependence of the backscattering measures from the target properties and the instrumental parameters (polarization, incidence angle) is proved with a modeling exercise: backscatter simulation for a dense tropical forest. Mapping of the model's view of the forest into the components of the vegetation (branches, trunks, leaves, soil properties) is a key step for arriving at a realistic model. The way this step can be undertaken is discussed. A number of model runs are then presented, for studying the outcome under different instrument and target configurations (P-, L-, C- band, HH, HV, VV polarizations, flooding conditions). In particular, the total backscattering coefficient is partitioned into components resulting from each category of scattering elements (leaves, branches, trunks), and for two scattering mechanisms - direct and indirect scattering. This virtual separation of the overall physical phenomenon is of great importance for the interpretation of experimental radar observations. Considerations prompted by the modeling exercise will support the findings related to spatial analysis in the chapters that follow. This chapter provides evidence on how the points in the radar field are shadows of the illuminated target's physical properties by using a wave scattering model. The principles of electromagnetic wave transport theory are outlined. The basic building block of wave scattering modeling, the equation of transfer, an integro-differential equation that governs the two energy flow processes in a volume - absorption and scattering - is then presented. The solution of the transport equations, given a medium description, provides estimates of the backscattering coefficients as a function of wavelength, incidence angle and polarization. The potential of the modelling approach for gaining insight into a controlled situation on the dependence of the backscattering measures from the target properties and the instrumental parameters is proved with a modeling exercise: backscatter simulation for a dense tropical forest.