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1998 | Book

Basic Concepts Read chapter Read first chapter

Terrestrial Radiative Transfer

Modeling, Computation, and Data Analysis

Authors: Harriet H. Natsuyama, Sueo Ueno, Alan P. Wang

Publisher: Springer Japan

Included in: Professional Book Archive

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About this book

In this book we share our work with those who are faced with the challenging problem of studying the earth's atmosphere and the interactions between the atmosphere and the earth's surface. While there are some excellent books on this topic written from the physical point of view, those discussing the modeling and computational aspects are few and far between. Our book is intended to bridge this gap so that students as well as investigators will be able to understand and apply practical ways of determining solutions. Radiative transfer theory, on which this book is based, is elegant, and great minds have contributed to its richness. Instead of duplicating the clas­ sical references, we have taken a different approach: We have developed the in­ variant imbedding approach, both analytically and computationally, because of its attractiveness for producing numerical solutions. Having witnessed the transition to the computer age, we know that a new attitude to mathemati­ cal formulation is required. The one that we endorse is a model stated in the form of a Cauchy problem: a system of ordinary differential equations with a complete set of initial conditions. We chose this approach because it is well suited to implementation on digital computers.

Table of Contents

Frontmatter
1.. Basic Concepts
Abstract
We introduce basic concepts for the modeling of radiative transfer using the invariant imbedding approach. We show, for a one-dimensional reflection problem, how an initial value problem is formulated. We obtain a differential equation with the independent variable being the thickness, and an initial condition, for thickness zero. We describe the numerical procedure for integrating this equation. Tables of reflection functions are presented. Cauchy-initial value-problems for source and internal intensity functions are also treated. This chapter serves as an introduction to the more advanced concepts in Appendix A, as well as the remaining chapters of this book.
Harriet H. Natsuyama, Sueo Ueno, Alan P. Wang
2.. Inhomogeneous Plane-Parallel Atmospheres
Abstract
This chapter builds upon the physical descriptions of scattering processes of Chapter 1. It develops via invariant imbedding techniques effective mathematical and computational models of diffuse reflection and transmission due to multiple scattering in vertically stratified media. It treats the determination of internal diffuse intensities without use of the unstable equations of transfer and the computation of source functions without having to solve their ill-conditioned integral equations. Furthermore, internal and external intensity fields as well as source functions due to vertically inhomogeneous distributions of emitting sources are obtained. The emphasis here is to obtain exact Cauchy problems which are well solved computationally and to present samplings of the extensive numerical results that have been obtained. Cauchy problems are initial value problems for systems of differential equations and are attractive for computational solution.
Harriet H. Natsuyama, Sueo Ueno, Alan P. Wang
3.. Inverse Problems
Abstract
In addition to model building, as we did in the earlier chapters, we care very much about fitting observations, i.e., indirect measurements, to models. This is at the core of remote sensing, temperature retrieval, prospecting for oil, medical diagnosis, and other inverse problems. In this chapter we present several methods for the systematic formulation of inverse problems, and we give explicit computational procedures for carrying them out. We study their effectiveness and their robustness with respect to errors in observations, in models, in initial estimates. We present results of numerous computational experiments. Studies such as these serve in the planning of experiments. The benefits of analysis in the planning stages of a project can help to avoid unfruitful experiments and inferior designs.
Harriet H. Natsuyama, Sueo Ueno, Alan P. Wang
4.. Anisotropic Scattering
Abstract
Terrestrial atmospheres are neither isotropic nor homogeneous. In this chapter, we first take up a model of anisotropic scattering in an inhomogeneous slab, assuming that the local scattering is described by a function of only the incident and scattered polar angles and the vertical coordinate. This function is readily parameterized to approximate phase functions that vary from isotropic to highly elongated and anisotropic. Next we discuss a phase function that can be expanded in a series of Legendre polynomials and Cauchy problems for reflection and transmission functions that are also expanded in a similar series. Such a series approximation is appropriate for mildly anisotropic phase functions. Then we consider some inverse problems of estimating phase functions based on radiation measurements. There are also some approximate formulas that are rather useful and accurate. Finally, we take up diffuse reflection in a three-dimensional medium. Numerical results are presented in graphs and tables.
Harriet H. Natsuyama, Sueo Ueno, Alan P. Wang
5.. Finite Orders of Scattering
Abstract
When remote sensing of the atmosphere is performed at wavelengths whose optical thickness is small or when the albedo for single scattering is small, then reflected, transmitted, and internal intensities can be computed through an approximate method which enumerates the intensity fields up to a finite number of scatterings. Results are also useful for approximating the general problem and for understanding the physical effects of the order of scattering.
Harriet H. Natsuyama, Sueo Ueno, Alan P. Wang
6.. Scattering Matrix
Abstract
In previous chapters, we developed the invariant imbedding technique for multiple scattering in a vertically stratified plane parallel medium. Many advantages of this technique have been discussed. The purpose of this chapter is to extend invariant imbedding techniques by introducing scattering matrix analysis. The scattering matrix relates inputs to outputs. Such an extension gives us a physical understanding of complex multiple scattering. This approach provides a more solid mathematical structure. This also provides us with a new tool to solve more complicated problems such as time-dependent radiative transfer. Scattering matrix analysis lays the foundation of computational methods, several as presented in this chapter. It also leads us naturally to discuss and solve the inverse problems which are used in other chapters.
Harriet H. Natsuyama, Sueo Ueno, Alan P. Wang
7.. Atmospheric Correction
Abstract
The apparent radiance of ground reflection as measured by a remote sensor differs from the intrinsic surface radiation because of the presence of the intervening atmosphere. Methods are developed in this chapter to remove the atmospheric effects from measured data taken in air and in space.
Harriet H. Natsuyama, Sueo Ueno, Alan P. Wang
8.. Topographic Effects in Terrestrial Remote Sensing
Abstract
The surface radiance distribution measured in remote sensing from space differs from its value at the ground because of the presence of the atmosphere [l]–[9]. The removal of atmospheric effects from space-based images of the earth improves the accuracy of the classification of the ground objects. A further correction is needed for mountainous terrain. The topographic effect refers to the obscuration of terrestrial information due to the effect of terrain on the reflectance at the surface. The radiative transfer problem is very difficult to solve precisely.
Harriet H. Natsuyama, Sueo Ueno, Alan P. Wang
9.. Searchlight Problem
Abstract
The searchlight problem is concerned with the target reflection from a point source at the top of the atmospheric layer. In this chapter we develop methods to recover the true target reflection from the observed data which consists of the background light and the multiple scattering in the atmospheric layer. After the construction of the mathematical model of initial value problems based on invariant imbedding, we also establish approximation solutions and simulation results.
Harriet H. Natsuyama, Sueo Ueno, Alan P. Wang
10.. Transfer of Radiation with Spherical Symmetry
Abstract
This chapter on radiative transfer in a spherical shell medium is in two parts: first, the construction of linear-operator equations and their reduction to a class of functional equations; then, the description of numerical techniques for dealing with the functional equations and the presentation of computational results. These analytical and computational results are applicable to terrestrial and stellar atmospheres. In the analytical theory, we treat with inhomogeneous anisotropically scattering shells with internal or external illumination, and with reflecting or absorbing cores. The computational results presented herein are for homogeneous shells, and can be extended to inhomogeneous and anisotropically scattering ones.
Harriet H. Natsuyama, Sueo Ueno, Alan P. Wang
11.. Bibliography
Harriet H. Natsuyama, Sueo Ueno, Alan P. Wang
Backmatter
Metadata
Title
Terrestrial Radiative Transfer
Authors
Harriet H. Natsuyama
Sueo Ueno
Alan P. Wang
Copyright Year
1998
Publisher
Springer Japan
Electronic ISBN
978-4-431-68527-2
Print ISBN
978-4-431-70206-1
DOI
https://doi.org/10.1007/978-4-431-68527-2