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E-grāmata: Radiative Transfer in Coupled Environmental Systems: An Introduction to Forward and Inverse Modeling

(University of Bergen, Norway), (Stevens Institute of Technology, Hoboken, USA)
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Radiative Transfer in Coupled Environmental Systems: An Introduction to Forward and Inverse ModelingPalielināt
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Radiative Transfer in Coupled Environmental Systems This book discusses radiative transfer in coupled media such as atmosphere-ocean systems with Lambertian as well non-Lambertian refl ecting surfaces at the lower boundary.



The spectral range from the ultraviolet to the microwave region of the electromagnetic spectrum is considered, and multi-spectral as well as hyperspectral remote sensing is discussed. Solutions of the forward problem for unpolarized and polarized radiation are discussed in considerable detail, but what makes this book unique is that formulations and solutions of the inverse problem related to such coupled media are covered in a comprehensive and systematic manner.

This book teaches the reader how to formulate and solve forward and inverse problems related to coupled media, and gives examples of how to solve concrete problems in environmental remote sensing of coupled atmosphere-surface systems.

From the contents:





Inherent Optical Properties (IOPs) Basic Radiative Transfer Theory Forward Radiative Transfer Modeling The Inverse Problem Applications
Preface xi
Acknowledgments xiii
1 Introduction
1(6)
1.1 Brief History
1(1)
1.2 What is Meant by a Coupled System?
2(1)
1.3 Scope
3(1)
1.4 Limitations of Scope
4(3)
2 Inherent Optical Properties (IOPs)
7(78)
2.1 General Definitions
7(4)
2.1.1 Absorption Coefficient and Volume Scattering Function
7(1)
2.1.2 Scattering Phase Function
8(3)
2.2 Examples of Scattering Phase Functions
11(3)
2.2.1 Rayleigh Scattering Phase Function
11(1)
2.2.2 Henyey--Greenstein Scattering Phase Function
11(2)
2.2.3 Fournier--Forand Scattering Phase Function
13(1)
2.2.4 The Petzold Scattering Phase Function
14(1)
2.3 Scattering Phase Matrix
14(10)
2.3.1 Stokes Vector Representation IS = [ I, Q, U, V]T
16(4)
2.3.2 Stokes Vector Representation I = [ I||, I, U, V]T
20(2)
2.3.3 Generalized Spherical Functions
22(2)
2.4 IOPs of a Polydispersion of Particles -- Integration over the Size Distribution
24(5)
2.4.1 IOPs for a Mixture of Different Particle Types
25(1)
2.4.2 Treatment of Strongly Forward-Peaked Scattering
26(2)
2.4.3 Particle Size Distributions (PSDs)
28(1)
2.5 Scattering of an Electromagnetic Wave by Particles
29(6)
2.5.1 Summary of Electromagnetic Scattering
30(1)
2.5.2 Amplitude Scattering Matrix
31(1)
2.5.3 Scattering Matrix
32(2)
2.5.4 Extinction, Scattering, and Absorption
34(1)
2.6 Absorption and Scattering by Spherical Particles -- Mie--Lorenz Theory
35(6)
2.7 Atmosphere IOPs
41(7)
2.7.1 Vertical Structure
41(1)
2.7.2 Gases in the Earth's Atmosphere
42(1)
2.7.3 Molecular IOPs
43(2)
2.7.4 IOPs of Suspended Particles in the Atmosphere
45(1)
2.7.5 Aerosol IOPs
45(2)
2.7.6 Cloud IOPs
47(1)
2.8 Snow and Ice IOPs
48(5)
2.8.1 General Approach
48(2)
2.8.2 Extension of Particle IOP Parameterization to Longer Wavelengths
50(1)
2.8.3 Impurities, Air Bubbles, Brine Pockets, and Snow
51(2)
2.9 Water IOPs
53(10)
2.9.1 Absorption and Scattering by Pure Water
53(1)
2.9.2 Absorption and Scattering by Water Impurities
54(2)
2.9.3 Bio-Optical Model Based on the Particle Size Distribution (PSD)
56(7)
2.10 Fresnel Reflectance and Transmittance at a Plane Interface Between Two Coupled Media
63(5)
2.10.1 Stokes Vector of Reflected Radiation
65(1)
2.10.2 Total Reflection
65(2)
2.10.3 Stokes Vector of Transmitted Radiation
67(1)
2.11 Surface Roughness Treatment
68(9)
2.11.1 Basic Definitions
68(2)
2.11.2 Reciprocity Relation and Kirchhoff's Law
70(1)
2.11.3 Specular Versus Lambertian and Non-Lambertian Reflection at the Lower Boundary
71(1)
2.11.4 Scattering, Emission, and Transmission by a Random Rough Surface -- Kirchhoff Approximation
72(1)
2.11.4.1 Rough Dielectric Interface
72(4)
2.11.5 Slope Statistics for a Wind-Roughened Water Surface
76(1)
2.12 Land Surfaces
77(8)
2.12.1 Unpolarized Light
78(4)
2.12.2 Polarized Light
82(3)
3 Basic Radiative Transfer Theory
85(32)
3.1 Derivation of the Radiative Transfer Equation (RTE)
85(3)
3.1.1 RTE for Unpolarized Radiation
85(2)
3.1.2 RTE for Polarized Radiation
87(1)
3.2 Radiative Transfer of Unpolarized Radiation in Coupled Systems
88(2)
3.2.1 Isolation of Azimuth Dependence
89(1)
3.3 Radiative Transfer of Polarized Radiation in Coupled Systems
90(3)
3.3.1 Isolation of Azimuth Dependence
91(2)
3.4 Methods of Solution of the RTE
93(17)
3.4.1 Formal Solutions
94(2)
3.4.2 Single-Scattering Approximation
96(4)
3.4.3 Successive Order of Scattering (SOS) Method
100(2)
3.4.4 Discrete-Ordinate Method
102(3)
3.4.5 Doubling-Adding and Matrix Operator Methods
105(4)
3.4.6 Monte Carlo Method
109(1)
3.5 Calculation of Weighting Functions -- Jacobians
110(7)
3.5.1 Linearized Radiative Transfer
110(2)
3.5.2 Neural Network Forward Models
112(5)
4 Forward Radiative Transfer Modeling
117(20)
4.1 Quadrature Rule -- The Double-Gauss Method
117(3)
4.2 Discrete Ordinate Equations -- Compact Matrix Formulation
120(3)
4.2.1 "Cosine" Solutions
120(2)
4.2.2 "Sine" Solutions
122(1)
4.3 Discrete-Ordinate Solutions
123(14)
4.3.1 Homogeneous Solution
123(5)
4.3.2 Vertically Inhomogeneous Media
128(1)
4.3.3 Particular Solution -- Upper Slab
129(4)
4.3.4 Particular Solution -- Lower Slab
133(1)
4.3.5 General Solution
134(1)
4.3.6 Boundary Conditions
135(2)
5 The Inverse Problem
137(68)
5.1 Probability and Rules for Consistent Reasoning
137(3)
5.2 Parameter Estimation
140(23)
5.2.1 Optimal Estimation, Error Bars and Confidence Intervals
140(7)
5.2.2 Problems with More Than One Unknown Parameter
147(10)
5.2.3 Approximations: Maximum Likelihood and Least Squares
157(3)
5.2.4 Error Propagation: Changing Variables
160(3)
5.3 Model Selection or Hypothesis Testing
163(5)
5.4 Assigning Probabilities
168(13)
5.4.1 Ignorance: Indifference, and Transformation Groups
168(5)
5.4.2 Testable Information: The Principle of Maximum Entropy
173(8)
5.5 Generic Formulation of the Inverse Problem
181(1)
5.6 Linear Inverse Problems
182(4)
5.6.1 Linear Problems without Measurement Errors
183(2)
5.6.2 Linear Problems with Measurement Errors
185(1)
5.7 Bayesian Approach to the Inverse Problem
186(5)
5.7.1 Optimal Solution for Linear Problems
189(2)
5.8 Ill Posedness or Ill Conditioning
191(9)
5.8.1 SVD Solutions and Resolution Kernels
192(5)
5.8.2 Twomey--Tikhonov Regularization -- TT-Reg
197(1)
5.8.3 Implementation of the Twomey--Tikhonov Regularization
198(2)
5.9 Nonlinear Inverse Problems
200(5)
5.9.1 Gauss--Newton Solution of the Nonlinear Inverse Problem
201(2)
5.9.2 Levenberg--Marquardt Method
203(2)
6 Applications
205(58)
6.1 Principal Component (PC) Analysis
205(2)
6.1.1 Application to the O2 A Band
206(1)
6.2 Simultaneous Retrieval of Total Ozone Column (TOC) Amount and Cloud Effects
207(8)
6.2.1 NILU-UV Versus OMI
209(1)
6.2.2 Atmospheric Radiative Transfer Model
210(1)
6.2.3 LUT Methodology
210(1)
6.2.4 Radial Basis Function Neural Network Methodology
210(1)
6.2.5 Training of the RBF-NN
211(1)
6.2.6 COD and TOC Values Inferred by the LUT and RBF-NN Methods
211(2)
6.2.7 TOC Inferred from NILU-UV (RBF-NN and LUT) and OMI
213(1)
6.2.8 Summary
214(1)
6.3 Coupled Atmosphere--Snow--Ice Systems
215(10)
6.3.1 Retrieval of Snow/Ice Parameters from Satellite Data
216(2)
6.3.2 Cloud Mask and Surface Classification
218(1)
6.3.2.1 Snow Sea Ice Cover and Surface Temperature
218(1)
6.3.3 Snow Impurity Concentration and Grain Size
219(6)
6.4 Coupled Atmosphere--Water Systems
225(7)
6.4.1 Comparisons of C-DISORT and C-MC Results
226(1)
6.4.2 Impact of Surface Roughness on Remotely Sensed Radiances
226(2)
6.4.3 The Directly Transmitted Radiance (DTR) Approach
228(1)
6.4.4 The Multiply Scattered Radiance (MSR) Approach
229(1)
6.4.5 Comparison of DTR and MSR
230(2)
6.5 Simultaneous Retrieval of Aerosol and Aquatic Parameters
232(5)
6.5.1 Atmospheric IOPs
233(1)
6.5.2 Aquatic IOPs
234(1)
6.5.3 Inverse Modeling
235(2)
6.6 Polarized RT in a Coupled Atmosphere--Ocean System
237(12)
6.6.1 C-VDISORT and C-PMC Versus Benchmark -- Aerosol Layer -- Reflection
239(1)
6.6.2 C-VDISORT and C-PMC Versus Benchmark -- Aerosol Layer -- Transmission
239(3)
6.6.3 C-VDISORT and C-PMC Versus Benchmark -- Cloud Layer -- Reflection
242(1)
6.6.4 C-VDISORT and C-PMC Versus Benchmark -- Cloud Layer -- Transmission
242(3)
6.6.5 C-VDISORT Versus C-PMC -- Aerosol Particles -- Coupled Case
245(1)
6.6.6 C-VDISORT Versus C-PMC -- Aerosol/Cloud Particles -- Coupled Case
245(4)
6.6.7 Summary
249(1)
6.7 What if MODIS Could Measure Polarization?
249(14)
6.7.1 Motivation
249(1)
6.7.2 Goals of the Study
250(1)
6.7.3 Study Design
250(2)
6.7.4 Forward Model
252(1)
6.7.5 Optimal estimation/Inverse model
252(2)
6.7.6 Results
254(6)
6.7.7 Concluding Remarks
260(3)
A Scattering of Electromagnetic Waves
263(24)
A.1 Absorption and Scattering by a Particle of Arbitrary Shape
264(7)
A.1.1 General Formulation
264(1)
A.1.2 Amplitude Scattering Matrix
265(1)
A.1.3 Scattering Matrix
266(2)
A.1.4 Extinction, Scattering, and Absorption
268(3)
A.2 Absorption and Scattering by a Sphere -- Mie Theory
271(16)
A.2.1 Solutions of Vector Wave Equations in Spherical Polar Coordinates
272(3)
A.2.2 Expansion of Incident Plane Wave in Vector Spherical Harmonics
275(2)
A.2.3 Internal and Scattered Fields
277(10)
B Spectral Sampling Strategies
287(10)
B.1 The MODTRAN Band Model
289(1)
B.2 The k-Distribution Method
290(3)
B.3 Spectral Mapping Methods
293(1)
B.4 Principal Component (PC) Analysis
294(1)
B.5 Optimal Spectral Sampling
294(3)
C Rough Surface Scattering and Transmission
297(16)
C.1 Scattering and Emission by Random Rough Surfaces
297(16)
C.1.1 Tangent Plane Approximation
298(2)
C.1.2 Geometrical Optics Solution
300(1)
C.1.2.1 Stationary-Phase Method
301(12)
D Boundary Conditions
313(18)
D.1 The Combined Boundary Condition System
313(2)
D.2 Top of Upper Slab
315(2)
D.3 Layer Interface Conditions in the Upper Slab
317(8)
D.3.1 Interface Between the Two Slabs (Atmosphere--Water System)
319(6)
D.4 Layer Interface Conditions in the Lower Slab
325(1)
D.5 Bottom Boundary of Lower Slab
325(6)
D.5.1 Bottom Thermal Emission Term
327(1)
D.5.2 Direct Beam Term
327(1)
D.5.3 Bottom Diffuse Radiation
328(1)
D.5.4 Bottom Boundary Condition
329(2)
References 331(16)
Index 347
Knut Stamnes is professor of physics in the Department of Physics and Engineering Physics, and Director of the Light and Life Laboratory at Stevens Institute of Technology in Hoboken New Jersey. Stamnes began his career in upper atmospheric physics, and has since specialized in atmospheric radiation, remote sensing, and climate-related studies. He is a fellow of the OSA, a member of the AGU, EGU, and SPIE, and was elected member of the Norwegian Academy of Technological Sciences in 2009.

Jakob J. Stamnes is professor of physics in the Department of Physics and Technology at the University of Bergen, Norway. He is fellow of the OSA, founding member and fellow of the EOS (European Optical Society), a member of the SPIE, EGU, and the Norwegian Physical Society, and was elected member of the Norwegian Academy of Technological Sciences in 2009.
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