1975 • 265 Pages • 4.07 MB • English

Posted April 14, 2020 • Uploaded
by sarai.flatley

PREVIEW PDF

Page 1

LIGHT SCATTERING I N PLANETARY ATMOSPHERES B Y V. V. SOBOLEV Tra n s l a t e d b y WILLIAM M. IRVINE w i t h t h e c o l l a b o r a t i o n o f M i c h a e l G e n d e l a n d A d a i r P . L a n e P E R G A M O N PRESS O X F O R D • N E W Y O R K . T O R O N T O • S Y D N E Y B R A U N S C H W E I G

Page 2

Pergamon Press Ltd. , Headington Hil l Hal l , Oxford Pergamon Press Inc. , Maxwel l H o u s e , Fairview Park, Elmsford, N e w York 10523 Pergamon of Canada Ltd. , 207 Queen's Quay West , Toronto 1 Pergamon Press (Aust . ) Pty. Ltd. , 19a Boundary Street, Ruschutters Bay, N . S . W . 2011 , Australia Pergamon Press G m b H , Burgplatz 1, Braunschweig 3300, West Germany Copyright © 1975 Pergamon Press Ltd; All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of Pergamon Press Ltd. First edit ion 1975 Library of Congress Cataloging in Publicaton Data Sobolev , Viktor Viktorovich. Light scattering in planetary atmospheres . (International series o f monographs in natural phi losophy, v. 76). Translation of Rasseyanie sveta v atmosferakh planet Includes bibliographies. 1. Planets—Atmospheres . 2. Light—Scattering. 3. Radiat ive transfer. I. Title. QB603.A85S6213 1975 51.5'6 74-13852 I S B N 0 - 0 8 - 0 1 7 9 3 4 - 7 . Printed in Hungary

Page 3

LIST OF TABLES Table 1.1. Phase function x(y) for polydisperse spherical particles with refractive index m = 1.38. Table 2.1. Relation between X and k for isotropic scattering. Table 2.2. Values of single scattering albedo A as a function of g and k. Table 2.3. The function <p(rf) and its moments. Table 2.4. Values of the albedo A(£) for the phase function x(y) = 1 + cos y+P2(cos y) and X = 0.99. Table 3.1. Function 99(77, r 0) for X = 1. Table 3.2. Function y)(rj, r0) for X = 1. Table 4.1. Surface albedo ^(^o) (in %) for an atmosphere of large optical thickness T 0, small true absorption k, a phase function with x± = 2 and an underlying surface albedo a. Table 6.1. Function 0„(t , r 0) for r 0 = 0.3 (isotropic scattering). Table 6.2. Function cpn(Z, ^o) for r 0 = 0.3 (isotropic scattering). Table 6.3. Function ^r t(t, T 0) for r 0 = 0.3 (isotropic scattering). Table 6.4. Source function B(t, £, r0)/.S for r 0 = 0.3, A = 1 and isotropic scattering. m Table 6.5. The function 0 ( r , r 0) for A = 1, r 0 = 1 and two sample three-term phase functions. m Table 7.1. The function H (rj) and its moments for X = 1 and two sample three-term phase functions. Table 7.2., Values of the function q>™{rj) for X = 1 for two sample three-term phase func- tions. Table 7.3., Plane albedo A(0 of a semi-infinite atmosphere with single scattering albedo X for two sample three-term phase functions. Table 7.4., The function u(r]) for single scattering albedo X and two sample three-term phase functions. Table 7.5. Values of the function u0(rj) for the Henyey-Greenstein function (1.16). 0 Table 7.6. Reflection coefficient Q (rj, £) for the Henyey-Greenstein phase functions with g = 0.25 (above main diagonal) and g = 0.50 (below diagonal). Table 8.1., The relation between the parameters X and k in the approximate theory. Table 9.1. Values of the quantity /(^, 77, TT)/ / (1 , 1, n) for a three-term phase function. Table 9.2.. Values of the quantities As, Ag and q for a three-term phase function. Table 9.3. Values of the function C(rj9 rj, n) for three phase functions. Table 9.4. Exact and approximate degree of polarization for a Rayleigh scattering atmosphere. ix

Page 4

X LIST OF TABLES Table 9.5. ^V alues of the quantities x(y) and y(y) for m = 1.38. Table 9.6. ^V alues of the function <5(r0, a) entering eq. (9.83). Table 9.7. ^V alues of functions G0(a, *i ) , Gi(a) and F(<x). Table 11.1. Values of the function b(u, ip). Table 11.2. Brightness of a planet close to the terminator for isotropic scattering. Table 11.3. Brightness at the zenith for scattering according to the Rayleigh phase function.

Page 5

FOREWORD I N RECENT times the launching of space rockets has led to a significant growth of interest in planetary investigations. Whereas astrophysicists once studied primarily stars, nebulae, and galaxies, at present a considerable part of their effort is directed toward the determination of the nature of the planets. The application of a variety of astrophysical methods has already yielded valuable results in this area. Progress in the study of the planets depends not only upon the collection of new observa- tional data, but also upon development of the theory used to interpret the data. It is from solar radiation scattered in the planetary atmospheres that we derive most of our informa- tion about the planets. Consequently, the theory of multiple scattering of light, otherwise known as the theory of radiative transfer, is necessary for the interpretation of planetary observations. This theory is important for the physics of planets for another reason. The process of transfer of solar radiation in the planetary atmosphere determines to a significant extent the physical state of the atmosphere. In order to calculate various quantities characterizing this state, it is thus necessary to use the theory of radiative transfer. Theoretical astrophysicists have been developing radiative transfer theory for a long time. However, they have been primarily concerned with stellar atmospheres, within which the scattering of light is isotropic. In the atmospheres of the planets, light scattering by an elemen- tary volume is anisotropic. This fact severely complicates the theory. Nevertheless, in recent years the theory of radiative transfer for anisotropic scattering has made considerable pro- gress and has been increasingly used in the study of planetary atmospheres. The present monograph has been written for the purpose of summarizing the results of work in this area. The monograph is concerned mainly with the theory of radiative transfer for anisotropic scattering. The first eight chapters deal with the general problem of multiple scattering of light in an atmosphere consisting of plane-parallel layers illuminated by parallel radiation. In the following two chapters, the theory is applied to the determination of the physical characteristics of planetary atmospheres. The last chapter discusses the theory of radiative transfer in spherical atmospheres, which is necessary for the interpretation of observations made from spacecraft. The emphasis in the monograph on the theory rather than its application is easily under- stood; the theory is designed not only for the interpretation of existing observational data, but also for that to be gathered in the future. One must also bear in mind that the theory of radiative transfer is utilized in related sciences, such as meteorology and oceanology, and also in certain branches of physics and chemistry. xi

Page 6

xii FOREWORD This monograph is the second book by this author dealing with the theory of radiative transfer. The first book, entitled Radiative Transfer in the Atmospheres of Stars and Planets 1 (Gostekhizdat, 1956), " is devoted to a wide range of questions (radiative transfer with frequency redistribution, nonstationary scattering of radiation, etc.). Since then, the theory has developed so fast that at present the examination of each of these questions may be the subject for a separate monograph. The solution of one such problem is examined in the present book. The previous book, for the sake of brevity, will henceforth be referred to as TRT (with reference to the chapter and page). The author wishes to express his thanks to his colleagues in the Department of Astro- physics at Leningrad University for their assistance in the preparation of the manuscript and for their critical remarks. V . V . SOBOLEV t Published in English as A Treatise on Radiative Transfer ( D . V a n Nostrand, 1963).

Page 7

TRANSLATOR'S PREFACE THE present monograph is the first complete text devoted solely to the study of radiative transfer in planetary atmospheres. It has clearly been written at an appropriate time and fills an important need. In fact, as the author points out, the theory also has direct applica- tions in fields as varied as oceanology and neutron physics. The order of presentation is described most fully by the author in his Concluding Re- marks. The fundamental physical problem considered is the multiple scattering of radiation within an atmosphere. The discussion is thus applicable to the region of the spectrum from the near ultraviolet through the near infrared, for which atmospheric thermal radiation is either negligible or assumed known a priori and all scattering processes are assumed to be coherent in frequency. The treatment is a macroscopic one, so that the microscopic processes of excitation and emission by atoms and molecules are described only in terms of the aver- age properties of an elementary volume. The author concentrates his attention on analytical procedures, approximate and asymptotic as well as exact. The reader interested in the special problems associated with the transport of thermal radiation in the terrestrial atmosphere may wish to consult the textbook by R. M. Goody: Atmospheric Radiation (Oxford, 1964). In the translation we have attempted to remain faithful to the style of the original, while making the book easily accessible to as wide as possible an English speaking audience. The result will hopefully be useful to graduate students and to scientists in fields other than astronomy, as well as to the professional astrophysicist. We have taken some liberties with paragraphing, where English and Russian practice differ. Of greater importance, we have added new or explanatory material at several points, most obviously in the Addendum to Chapter 10, but also to a small degree in Chapter 1 and at a few other places. Some recent work by the author, published since the Russian edition of this monograph, has been included in the Appendix. Only two points of terminology require comment. Following the classic example of Chandrasekhar we have used phase function for the Russian scattering indicatrix (sometimes translated as scattering diagram). The choice of illumination (see page 16) rather than such alternative English terms as irradiance or simply incident flux was less clear-cut, but follows the precedent set in the translation of Professor Sobolev's earlier monograph on radiative transfer. We are very grateful to Professor Sobolev for providing the initial impetus for this trans- lation, and to him and his colleagues for their labors in correcting a first draft of the manu- script and for proof-reading the final equations. The completion of the English manuscript xiii

Page 8

xiv TRANSLATOR'S PREFACE would have been impossible without the dedicated hard work of Ms. Kathleen Carr and Ms. Maryellen Maesano. One of us (W. M. I) wishes to gratefully acknowledge support from the U.S. National Aeronautics and Space Administration and the gracious hospitality of Professor O. E. H. Rydbeck, Director of the Onsala Space Observatory, Chalmers University of Technology, Sweden, where this work was completed. University of Massachusetts, Amherst W. M. IRVINE M. GENDEL A. P. LANE

Page 9

LIST OF SYMBOLS Symbol Description Introduced on page a particle radius 3 a surface albedo 74 AO atmospheric (plane) albedo 18 geometric albedo 178 A spherical albedo 18 spherical albedo in presence of planetary surface 8 3 relative source function deep within a semi-infinite m atmosphere 25 B source function 9 S source function in presence of reflecting surface 75 B* source function for inhomogeneous atmosphere illuminated from below 67 B° source function averaged over azimuth 11,25 source function for mth azimuthal component of radiation field 11 25 E illumination 16 Ek exponential integral 14 g parameter characterizing forward elongation of Henyey-Green- stein phase function 5 H radiation flux 16 //-function for mth azimuthal component of radiation field 2 1 , 9 4 H* scale height 215 Kv) relative intensity of radiation deep within a semi-infinite atmosphere 25 i intensity of radiation 6 intensity of radiation in presence of reflecting surface 75 1 I mean intensity of radiation 161 p intensity of radiation averaged over azimuth 11 ,25 r intensity of mth azimuthal component of radiation field 11 h intensity of radiation diffusely reflected by planetary surface 75 XV

Page 10

Xvi LIST OF SYMBOLS intensity diffusely reflected at frequency v within absorption line 181 k parameter describing decay of radiation field in deep layers 25 K absorption coeficient for a single molecule 183 m stelar magnitude 17 m index of refraction 2 Pi Legendre polynomial 3 Pm mth azimuthal component of phase function 1 pm asociated Legendre polynomial 1 q phase integral 178 n Sun-planet distance 17 r2 Sun-Earth distance 17 rv absorption line profile 181 T 212 To optical distance from planetary surface to observer within spherical atmosphere 29 u(rj) relative transmision coeficient 35 u radiant energy density 15 uoiv) relative transmision coeficient for pure scatering 4 u{n) 72 v ilumination of plane planetary surface 57 ilumination of total (spherical) planetary surface 83 K Vs in presence of reflecting surface 83 w equivalent width 181 *(r) phase function 2 phase function for molecular scatering 191 phase function for particulate scatering 191 Xl coefficient of second term in Legendre expansion of phase function 3 m X (V) X-function for mth azimuthal component of radiation field 21, 107, 112 y reflection function of planetary surface 75 y(r) 190 Ym{n) F-function for mth azimuthal component of radiation field 21, 107, 112 Z size parameter 3 a absorption coeficient 1 a phase angle 175 scatering angle 2 y b ratio of molecular scattering coefficient to total scattering coeficient 191 A Earth-planet distance 17 e emision coeficient 6 coeficient of true emision 8 cos #o 10

Planetary Atmospheres

1971 • 408 Pages • 11.72 MB

Transfer of Polarized Light in Planetary Atmospheres: Basic Concepts and Practical Methods

2004 • 264 Pages • 5.87 MB

Light Scattering Reviews, Volume 11: Light Scattering and Radiative Transfer

2016 • 522 Pages • 16.25 MB

Springer Series in Light Scattering: Volume 3: Radiative Transfer and Light Scattering

2019 • 227 Pages • 5.33 MB

Springer Series in Light Scattering: Volume 1: Multiple Light Scattering, Radiative Transfer

2018 • 369 Pages • 11.83 MB

reflection and transmission of polarized light by planetary atmospheres

2005 • 257 Pages • 2.93 MB

Light Scattering Properties of Asteroids and

2005 • 283 Pages • 4.19 MB

Absorption, scattering and emission of light by small particles

2004 • 128 Pages • 1.92 MB

Scattering, Absorption, and Emission of Light by Small Particles

2004 • 128 Pages • 1.92 MB

Springer Series in Light Scattering: Volume 2: Light Scattering, Radiative Transfer and Remote

2018 • 301 Pages • 6.78 MB

Planetary Systems in Polarized Light

2016 • 114 Pages • 12.77 MB

Light Scattering Properties of Asteroids and Cometary Nuclei

2005 • 283 Pages • 4.19 MB

Sixteenth Conference on Electromagnetic & Light Scattering

2017 • 153 Pages • 7.12 MB

Multiple Scattering of Light by Particles. Radiative Transfer and Coherent Backscattering

2016 • 508 Pages • 19.09 MB

Light Scattering by Ice Crystals: Fundamentals and Applications

2016 • 460 Pages • 26.85 MB

Experiments in Light Scattering

2013 • 90 Pages • 9.03 MB