Reference: Meterology and Atmospheric Physics, Vol. 78, 287-289, 2001.

Book Review

**Thomas, G. E. and Stamnes, K.: Radiative Transfer in the Atmosphere and
Ocean.**__ __Cambridge University Press, 1999, 517 pp, US $ 85.00

Several decades ago, at the University of Munich, I had the pleasure to attend a series of graduate level lectures on dynamic meteorology, which were given by the late Professor Bernhard Haurwitz. The question came up which textbook would serve best as a reference book for the student. Then Professor Haurwitz made the startling remark that there are two types of textbooks. The first type is written by an author who wishes to show how much he knows. He has long forgotten that in past days he was a student himself struggling with a new and difficult subject. When writing his book he has not kept the student’s difficulties in his mind as often as he should. The second type is written by an author who knows just as much about the subject as the author of the first type, but he keeps the student in mind all the time. He refrains from such discouraging remarks as the following: By straightforward application of basic theory we obtain the desired result. Often statements of this type hide the fact that many difficult mathematical steps are required to obtain the answer.

The book by Thomas and Stamnes is of the second type. It is written for the student who really wishes to comprehend the basic theory and learn how to apply it. The subject matter of radiative transfer requires some skill in handling mathematical techniques. At the senior level the modern student of meteorology and of related sciences usually has acquired the mathematical background needed to read this book. He is familiar with the theory of orthogonal polynomials, solution techniques of differential equations and has some basic knowledge of linear algebra etc. Nevertheless, the authors don’t take any chance by assuming that the student has all the important mathematical facts at his fingertips. By giving some detailed information, for example on Legendre polynomials, they carefully lead the student to the desired result.

Radiative transfer has reached a high point of development and can be applied to various important disciplines ranging from Greenhouse warming to stellar atmospheres and ocean optics. This book provides the basic theory of radiative transfer in a form that can be well absorbed by the serious student. The authors make it a point not only to derive the basic equations, but they present them in a form which is ready for applications. They take great care to show the validity range of various approximations and state when the approximate solution can be used to advantage instead of evaluating the time consuming complete solution. Approximate solutions are usually required in climate modeling and boundary layer predictions.

One particularly valuable aspect of this book is the unified treatment of radiative transfer in atmospheres and oceans since the basic concepts are quite similar. The authors carefully discuss the problem of boundary conditions, which need to be specified at the interface between the atmosphere and the ocean. This book contains much valuable material on the state-of-art computational methods inclusive a very thorough treatment of the discrete-ordinate technique and of the correlated k-band absorption method.

The book of more than 500 pages is subdivided into twelve chapters presenting various important topics and aspects of radiative transfer. We will now list these and give a brief description of each chapter or group of chapters for those who might be interested to purchase this reasonably priced book.

Chapter 1 presents very carefully the basic concepts of radiation. The spectrum and the role of absorption bands is discussed to give a first impression of the complexity of spectral integrations and the computation of radiative fluxes and heating rates. In order to carry out such computations it is necessary to have some basic knowledge of the vertical structure of planetary atmospheres. Realistic models of the vertical distribution of atmospheric pressure, particles, gas concentrations and air density are given which employ the hydrostatic equation and the ideal gas law. These formulas are well-known to meteorology students, but they will be quite helpful to students of related disciplines. Similar formulas are given for the ocean where the concept of salinity plays an important role. The basic formulas of the optical line of path is presented as a preparation for the introduction of the optical path.< /P>

Chapter 2 introduces some basic facts such as the relation between radiative intensity and flux. The authors are not satisfied by merely giving mathematical definitions which can also be found in general meteorology textbooks. They construct a solid physical basis by presenting some theorems on the intensity of the radiation field by using a number of suitable figures. The extinction law is introduced together with formulas describing the optical path. A first form of the radiative transfer equation (RTE) is presented. Chapter 3 broadens the concepts introduced in the previous chapter by discussing the scattering effect, which is a part of extinction. The authors give a thorough discussion why scattering occurs and introduce the scattering phase function. A brief treatment of Rayleigh and Mie-Debye scattering is given. A thorough derivation of the Mie formulas requires much effort and time. The writer of this review article had to sacrifice a good part of his course work time to derive these formulas in detail with the help of Stratton’s book on electromagnetic theory.

Chapter 4 introduces the absorption concept applied to solid, aqueous and gaseous media. Moreover, the Planck radiation law is derived which contains the Wien and Rayleigh-Jeans limits. The frequency integration of the Planckian law is carried out to yield the Stefan-Boltzmann law. The topics involving the Planck radiation law are also subject of many physics courses. A detailed treatment of absorption by triatomic molecules such as water and carbon dioxide is involved and requires more than an introductional knowledge of quantum mechanics. Since meteorology students usually do not have such a knowledge the authors omit this difficult topic. They restrict their discussion to the two-level atom. Much can be learned from such a discussion about the basic radiative processes such as spontaneous and stimulated emission and the role of the Einstein coefficients. Omitting a detailed quantum-mechanical discussion, it is still possible to describe basic aspects of molecular absorption as manifested by the existence of molecular lines and bands. The authors give a simplified description and present some basic formulas for the computation of line intensities. Today all important spectral line data for major atmospheric absorbers are tabulated for a reference temperature. The required formulas are given to calculate the line intensities for arbitrary temperatures.

Chapter 5 deals with the principles of radiative transfer. Among the important subtopics of this chapter is an excellent discussion of Kirchhoff’s law. A thorough treatment is given how to handle various types of ground reflection. The RTE and its solution for a non-scattering medium is discussed for a slab geometry, and multiple scattering is introduced.

Chapters 6-9 represent some of the major research interests of the authors and form the core of this book. In these chapters the difficult problems of multiple scattering is handled with great care. This involves a splitting of the radiation field into diffuse and direct radiation. Boundary conditions are discussed as well as the removal of the azimuthal dependency of the radiative intensity by expanding the radiation field in terms of a Fourier type series. The removal of the azimuthal dependency becomes possible since the scattering function can be expanded as a series of Legendre polynomials. The addition theorem for spherical harmonics plays a fundamental role as already expounded in the famous book on Radiative Transfer by S. Chandrasekhar (1949).

A great deal of effort is expended in presenting two-stream approximate solutions of the Eddington type and the refined delta-two-stream approximations. The transfer problem is discussed by specifying a number of prototype problems for which solutions are given. The accuracy of various versions of the two-stream method is discussed with the help of tables. The discrete ordinate method (DOM) has become very popular within the last two decades. This method has been discussed in great detail. Barring trivial reformulations, all essential mathematical steps are shown to the point of numerical implementation into the atmosphere-ocean model. A description of the most accurate computational procedures, known as adding-doubling and the matrix operator method, is given. The optical properties of various cloud types have been formulated so that the optical path and the scattering functions can be computed.

Chapter 10 discusses the transmission in spectrally complex media. The RTE and the various solutions are given for monochromatic radiation. For practical calculations the monochromatic solution is of little interest. For the interpretation of satellite data entire spectral intervals must be modeled. For climate studies, boundary layer predictions or weather prediction models it is absolutely necessary to integrate the transfer equation over the entire spectrum. This is a very time consuming task which is carried out only for benchmark purposes for idealized atmospheres by integrating along the profile of all individual spectral lines. The overlapping effect of neighboring and distant spectral lines must be accounted for.

For practical applications spectral line and band models must be employed. The book presents a discussion on the transmission in an isolated Lorentz spectral line for which the exact Ladenburg and Reiche solution is known. The actual derivation is not given but can be found in many available textbooks. The Ladenburg and Reiche formulas provides the opportunity to introduce the important concepts of strong and weak line limits. Various band models are introduced. Among these is the famous Elsasser band model which is as infinite array of identical spectral lines. The advantage of this spectral model is that an analytic solution exists for band transmission. A brief discussion is given of the random band model which is also known as the Goody-Meyer model. Presently, the so-called correlated-k method is used for spectral integrations since it is accurate and fast. This method is described in the required detail.< /P>

Chapters 11 and 12 give various applications of the radiative transfer theory such as the computation of heating rates for clear-sky conditions and computations of terrestrial cooling rates. The effect of radiative heating and cooling rates in idealized clouds is briefly discussed. On the basis of the formal theory presented in earlier chapters, the authors describe the role of radiation in climate and consider radiative equilibrium problems inclusive radiative-convective equilibrium, radiative forcing due to clouds and aerosol and related topics.

The book ends with an appendix on glossary of symbols, physics constants, tables of model atmospheres, ocean optics terminology and a brief mathematical treatment on reflection and transmission at an interface. This text includes many illuminating figures and examples of various transfer problems. At the end of each chapter a brief summary is given. Numerous problems of variable degree of difficulty and a list of notes conclude each chapter.

Reading this book took a good deal of time. Nevertheless, I was greatly rewarded by my perseverance. Summarizing, this book contains a large amount of knowledge on radiative transfer theory and its applications. The material is very well presented and one is never left alone with an unfinished mathematical discussion. As customary, a number of steps in various derivations are left as student exercises.

It seems to be an unfortunate fact of life that no book as technical as this one can be written free of minor errors. This book is no exception. The remarkably few errors I found can be easily detected and do not present any problem to the reader. I would find it degrading to the book and to the authors to list these.

This book should not be missing on the desk of any person seriously interested in radiative transfer. If I were still actively engaged in teaching a course on Radiative Transfer on the graduate level, I would certainly use this book as a basic text and recommend it very highly to my students. I am sure that both instructor and student can profit a great deal from studying this excellent work.

Wilford Zdunkowski

Mainz, Germany