EXPLORATION OF THE
SOLAR SYSTEM
BY
INFRARED REMOTE SENSING
Second edition
R. A. HANEL
B. J. CONRATH
D. E. JENNINGS
and
R. E. SAMUELSON
Cambridge University Press
Contents
Introduction to first edition page xi
Introduction to second edition xv
1 Foundation of radiation theory 1
1.1 Maxwell’s equations 2
1.2 Conservation of energy and the Poynting vector 4
1.3 Wave propagation 5
1.4 Polarization 13
1.5 Boundary conditions 14
1.6 Reflection, refraction, and the Fresnel equations 17
1.7 The Planck function 21
1.8 The Poynting vector, specific intensity, and net flux 25
2 Radiative transfer 27
2.1 The equation of transfer 28
a. Definitions and geometry 28
b. Microscopic processes 29
c. The total field 37
d. The diffuse field 40
2.2 Formal solutions 42
2.3 Invariance principles 44
a. Definitions 44
b. The stacking of layers 45
c. Composite scattering and transmission functions 47
d. Starting solutions 49
2.4 Special cases 50
a. Nonscattering atmospheres 50
b. Optically thin atmospheres 51
2.5 Scattering atmospheres; the two-stream approximation 52
a. Single scattering phase function 52
b. Separation of variables 53
c. Discrete streams 54
d. Homogeneous solution 55
e. Outside point source 56
3 Interaction of radiation with matter 58
3.1 Absorption and emission in gases 59
a. The old quantum theory 59
b. The Schr ¨odinger equation 60
c. Energy levels and radiative transitions 62
3.2 Vibration and rotation of molecules 64
3.3 Diatomic molecules 66
a. Vibration 67
b. Rotation 72
c. Vibration–rotation interaction 75
d. Collision-induced transitions 78
3.4 Polyatomic molecules 80
a. Vibration 80
b. Rotation 86
c. Vibration–rotation transitions 90
3.5 Line strength 93
3.6 Line shape 99
3.7 Solid and liquid surfaces 103
a. Solid and liquid phases 103
b. Complex refractive indices 105
3.8 Cloud and aerosol particles 110
a. Asymptotic scattering functions 110
b. Rigorous scattering theory; general solution 113
c. Particular solutions and boundary conditions 117
d. The far field; phase function and efficiency factors 122
4 The emerging radiation field 129
4.1 Models with one isothermal layer 129
a. Without scattering 129
b. With scattering 132
4.2 Models with a vertical temperature structure 140
a. Single lapse rate 141
b. Multiple lapse rates 144
4.3 Model with realistic molecular parameters 148
5 Instruments to measure the radiation field 152
5.1 Introduction to infrared radiometry 154
5.2 Optical elements 155
5.3 Diffraction limit 166
5.4 Chopping, scanning, and image motion compensation 170
a. D.C. radiometers 170
b. Chopped or a.c. radiometers 179
c. Image motion compensation 185
5.5 Intrinsic material properties 188
a. Absorbing and reflecting filters 188
b. Prism spectrometers 190
c. Gas filter, selective chopper, and the pressure modulated
radiometer 192
5.6 Interference phenomena in thin films 194
a. Outline of thin film theory 195
b. Antireflection coatings 198
c. Beam dividers 200
d. Interference filters and Fabry–Perot interferometers 204
5.7 Grating spectrometers 209
5.8 Fourier transform spectrometers 220
a. Michelson interferometer 220
b. Post-dispersion 240
c. Martin–Puplett interferometer 243
d. Lamellar grating interferometer 247
5.9 Heterodyne detection 249
5.10 Infrared detectors in general 253
5.11 Thermal detectors 255
a. Temperature change 255
b. Noise in thermal detectors 260
c. Temperature to voltage conversion 264
5.12 Photon detectors 272
a. Intrinsic and extrinsic semiconductors 273
b. Photoconductors and photodiodes 274
c. Responsivities 275
d. Noise in photon detectors 277
e. Circuits for photon detectors 278
f. Detector arrays 280
5.13 Calibration 281
a. Concepts 281
b. Middle and far infrared calibration 284
c. Near infrared calibration 291
d. Wavenumber calibration 293
5.14 Choice of measurementtechniques 294
a. Scientific objectives 294
b. Instrument parameters 296
6 Measured radiation from planetary objects up to Neptune 301
6.1 Instrument effects 301
6.2 The terrestrial planets 305
6.3 The giantplanets 317
6.4 Titan 325
6.5 Objects without substantial atmospheres 333
a. Tenuous atmospheres 333
b. Surfaces 334
7 Trans-Neptunian objects and asteroids 342
7.1 Pluto and Charon 342
7.2 Comets 346
7.3 Asteroids 349
8 Retrieval of physical parameters from measurements 352
8.1 Retrieval of atmospheric parameters 352
8.2 Temperature profile retrieval 355
a. General consideration 355
b. Constrained linear inversion 356
c. Relaxation algorithms 360
d. Backus–Gilbertformulation 361
e. Statistical estimation 365
f. Limb-tangent geometry 367
8.3 Atmospheric composition 368
a. Principles 369
b. Feature identification 369
c. Correlation analysis 370
d. Abundance determination 371
e. Profile retrieval 372
f. Simultaneous retrieval of temperature and gas abundance 376
g. Limb-tangent observations 378
8.4 Clouds and aerosols 380
a. Small absorbing particles 381
b. Titan’s stratospheric aerosol 382
8.5 Solid surface parameters 385
a. Surface temperature 385
b. Thermal inertia 388
c. Refractive index and texture 392
8.6 Photometric investigations 394
a. Introduction 394
b. The Bond albedo 396
c. Thermal emission 402
9 Interpretation of results 405
9.1 Radiative equilibrium 405
a. Governing principles 406
b. The solar radiation field 407
c. Thermal radiation and the temperature profile 410
d. General atmospheric properties 413
9.2 Atmospheric motion 420
a. Governing equations 421
b. Mars 428
c. The outer planets 436
d. Venus 442
9.3 Evolution and composition of the Solar System 444
a. Formation of the Solar System 445
b. Evolution of the terrestrial planets 450
c. Evolution of the giant planets 452
9.4 Energy balance 457
a. The terrestrial planets 459
b. The giantplanets 459
Closing remarks 465
Appendices
1 Mathematical formulas 467
2 Physical constants 471
3 Planetary and satellite parameters 472
References 475
Abbreviations 511
Index 513
Introduction to first edition
The adventof spaceflighthas ushered in a new era of Solar System exploration. Man has walked on the Moon and returned with soil samples. Instrumented probes have descended through the atmospheres of Venus and Mars. The Mariner, Pioneer, Venera, Viking, and Voyager space flight programs have provided opportunities to study the planets from Mercury to Neptune and most of the satellites. Remote sensing investigations have been conducted with unprecedented spatial and spectral resolutions, permitting detailed examinations of atmospheres and surfaces. Even for the Earth, space-borne observations, obtained with global coverage and high spatial, spectral, and temporal resolutions, have revolutionized weather forcasting, climate research, and the exploration of natural resources.
The collective study of the various atmospheres and surfaces in the Solar System constitutes the field of comparative planetology. Wide ranges in surface gravity, solar flux, internal heat, obliquity, rotation rate, mass, and composition provide a broad spectrum of boundary conditions for atmospheric systems. Analyses of data within this context lead to an understanding of physical processes applicable to all planets. Once the general physical principles are identified, the evolution of planetary systems can be explored.
Some of the data needed to address the broader questions have already been collected. Infrared spectra, images, and many other types of data are available in varying amounts for Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, and many of their satellites. It is now appropriate to review and assess the techniques used in obtaining the existing information. This will not only provide a summary of our presentcapabilities, butwill also suggestways of extending our knowledge to better address the issues of comparative planetology and Solar System evolution. Remote sensing is an interdisciplinary task. Theories of radiative transfer, molecular quantum mechanics, atmospheric physics, photochemistry, and planetary geology overlap with the design of advanced instrumentation, complex data processing, and a wide range of analysis methods. The purpose of this book is to bring many of these disciplines together with emphasis on the acquisition and interpretation of thermal infrared data. We address the advanced student and active researcher in the field. It is our intent to examine the basic principles in some depth. To meet this goal we strive to develop a consistent and essentially self-contained review. It is necessary to be highly selective in choosing illustrative cases because the development of each is fairly complex.
Although some in situ measurements have been made, planetary investigations have largely been restricted to remote sensing of emitted and reflected radiation. Planets emit most of their thermal radiation in the middle and far infrared while re- flected sunlight dominates their visible and near infrared spectra. Planetary spectra, recorded from orbiting or fly-by spacecraft, make it possible to simultaneously obtain good horizontal and vertical resolutions of both atmospheric composition and thermal structure. These quantities and their gradients lead to a description of energetic and dynamical processes characteristic of each atmosphere. High resolution images at visible and infrared wavelengths display cloud patterns, which manifest this dynamical activity and provide highly complementary information to the spectral data. Ground-based astronomy has contributed additional information, with the significant advantage of providing observations over relatively long time spans.
Emitted and reflected radiation fields can be regarded as coded descriptions of planetary atmospheres and surfaces. Radiative transfer theory provides a means of transforming the codes into intelligible terms. This approach requires an understanding of electromagnetic radiation and its interaction with matter. Chapters 1 through 3 are directed towards these ends. A review of Maxwell’s equations, wave propagation, polarization, reflection, refraction, and the Planck function is undertaken in Chapter 1. In Chapter 2 the equation of radiative transfer is derived in a form suitable for remote sensing from space, and various solutions of the transfer equation are obtained. In Chapter 3 we examine the interaction of radiation with matter. Quantum mechanical concepts, the principles of vibrational and rotational spectra, and other tools necessary to understand planetary spectra are developed. Investigation of matter in condensed phases – solid surfaces, ice crystals, and liquid droplets – requires an understanding of the emission and reflection of radiation at surfaces characterized by a complex index of refraction and such topics as the Mie theory.
With the tools developed in Chapters 1 through 3, it is possible to construct models of the emission and reflection of gas layers over a solid surface. Such models, with increasing complexity, including scattering, are the subject of Chapter 4. However, it is impossible to separate a study of planetary systems by remote sensing from the instruments which record the data. Inferences of atmospheric and surface parameters require the analysis of observed spectra, which have been subjected to modifications characteristic of the instruments used. In Chapter 5 we consider concepts of remote sensing instruments. The discussion of certain principles and techniques is supplemented with specific examples of instruments, such as the Thematic Mapper and the Voyager infrared spectrometer. Special attention is given to radiometric calibration. Examination of scientific objectives and instrumental techniques leads to a discussion of trade-offs between spatial and spectral resolution, signal-to-noise ratio, data rate, and other parameters. gnal-to-noise ratio, data rate, and other parameters. In Chapter 6 we consider instrumental effects, such as spectral resolution and signal-to-noise ratio, and discuss data from the terrestrial and the giant planets in a qualitative manner. In Chapter 7 we examine methods for interpreting spectroscopic and radiometric data produced by real instruments in terms of physical properties of atmospheres and surfaces. Emphasis is placed on the retrieval of thermal structure, gas composition and cloud properties of the atmospheres, and thermal properties and texture of surfaces. Limitations on the information content inherent in measured quantities are assessed.
In Chapter 8 we associate measured quantities with the underlying physical processes. The connection between thermal equilibrium and the vertical temperature profile is investigated. Dynamical regimes are explored with emphasis on wind fields and circulations. Certain aspects of Solar System composition, internal heat sources, and the concept of global energy balance are discussed in the context of planetary evolution.
In Appendix 1 we list some of the properties of vectors and mathematical functions used in the text. Important physical constants are listed in Appendix 2. The most important planetary and satellite parameters, such as dimensions and composition, are summarized in Appendix 3.
Throughout the book we adopt the International System (SI), with the basic units of meter, kilogram, second, ampere, mole, and kinetic temperature (kelvin). However, we make exceptions in deference to common usage. For example, in atmospheric physics and specifically in meteorology the bar and millibar are firmly entrenched in the literature as units of pressure; we retain these here. The corresponding SI unit, the pascal (newton per square meter, or N m−2), which equals 10−5 bar, is only slowly gaining acceptance in the planetary literature
The SI unit of intensity, the candela, is defined (1985) as the luminous intensity in a given direction of a source that emits at 540 × 1012 hertz (Hz) and has a radiant intensity in that direction of 1/683 watt per steradian (W sr−1). Although the candela should be a convenient unit in the discussion of radiative processes, it is not used in planetary astronomy or in the field of remote sensing. Hence we follow tradition and express the spectrally integrated intensity in W cm−2 s−1; t he spectral intensity itself is then expressed in W cm−2 sr−1/cm−1 (we prefer to retain this explicit expression rather than use the equivalent term W cm−1 sr−1). The term spectral radiance is synonymous with specific or spectral intensity.
Another exception concerns the units of wavenumber and wavelength. Radio astronomy is a rather modern branch of science and has easily adopted the SI (e.g., flux in W m−2), while spectroscopy is an old discipline of physics. The roots of spectroscopy lie deep in the nineteenth century, when the Gaussian system ruled with the centimeter as the unit of length. The common spectroscopic unit of wavenumber is, therefore, cm−1; wavelength is usually measured in µm. We follow that tradition.
In writing this book the authors gained from numerous discussions with many colleagues and friends. Several have made specific comments on the manuscript.We would like to acknowledge contributions from W. Bandeen, G. Birnbaum, R. Born, M. Flasar, P. Gierasch, G. Hunt, T. Kostiuk, V. Kunde, J. Mangus, J. Mather, J. Pearl, and D. Reuter. J. Guerber and L. Mayo helped with computer programming. We also appreciate the encouragement and patience of the editor S. Mitton and his staff atCambridge University Press.
The following journals and publishers have given permission to reproducefigures:
Applied Optics. Optical Society of America, Washington DC: Figs. 5.2.10, 5.3.2, 5.8.2, 5.8.3, 5.8.9, 5.8.10, and 5.8.12.
The Astrophysical Journal. The University of Chicago Press, Chicago IL: Figs.3.8.2, 7.3.4, and 7.3.5.
Icarus. Academic Press, Orlando FL: Figs. 5.9.1, 6.2.2, 6.2.9, 7.3.3, 7.5.1, 8.2.2,and 8.2.3.
Journal of Atmospheric Sciences. American Metereological Society, Boston MA:Fig. 8.2.4.
Journal of Geophysical Research. American Geophysical Union, Washington DC: Figs. 6.2.5, 6.2.6, 6.2.7, and 6.4.1.
Nature. Macmillan Magazines Ltd, London: Figs. 5.12.5, 6.4.2, 6.4.3, and 6.5.1.
Proceedings of the Twenty-first Astronautical Congress. North Holland Publishing Co.: Fig. 6.2.4.
Canadian Journal of Physics. National Research Council of Canada: Fig. 3.3.6.
Science. American Association for the Advancement of Science. Washington DC: Figs. 6.2.8, 6.2.11, 6.3.3, and 7.5.2.
Spectrometric Techniques III. Academic Press, Orlando FL: Fig. 5.8.5.
Satellites of Jupiter. University of Arizona Press, Tucson AZ: Fig. 6.5.4.
We also thank the authors for making this material available.
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