Series Editor: Alexander Kokhanovsky

Wendisch, M. / Brenguier, J.-L. (eds.)

**Airborne Measurements for Environmental Research**

**Methods and Instruments**

2013

Coakley Jr., J. A. / Yang, P.

**Atmospheric Radiation**

**A Primer with Illustrative Solutions**

2014

Kokhanovsky, A. / Natraj, V.

**Analytical Methods in Atmospheric Radiative Transfer**

2014

North, G. R. / Kim, K.-Y.

**Energy Balance Climate Models**

2014

Davis, A. B. / Marshak, A.

**Multi-dimensional Radiative Transfer**

**Theory, Observation, and Computation**

2015

Minnis, P. *et al.*

**Satellite Remote Sensing of Clouds**

2015

Stamnes, K. / Stamnes, J. J.

**Radiative Transfer in Coupled Environmental Systems**

**An Introduction to Forward and Inverse Modeling**

2015

Zhang, Z. *et al.*

**Polarimetric Remote Sensing**

**Aerosols and Clouds**

2015

Huang, X. / Yang, P.

**Radiative Transfer Processes in Weather and Climate Models**

2016

Tomasi, C. / Fuzzi, S. / Kokhanovsky, A.

**Atmospheric Aerosols**

**Life Cycles and Effects on Air Quality and Climate**

2016

Weng, F.

**Satellite Microwave Remote Sensing**

**Fundamentals and Applications**

2016

**The Authors**

*Prof. James A. Coakley Jr.*

Oregon State University

College of Earth, Oceanic, and Atmospheric Sciences

United States

*Prof. Ping Yang*

Texas A&M University

Department of Atmospheric Science

United States

**Cover picture**

Spiesz Design, Neu-Ulm

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**Paperback Print ISBN:** 978-3-527-41098-9

**Hardcover Print ISBN:** 978-3-527-41137-5

**ePDF ISBN:** 978-3-527-68144-0

**ePub ISBN:** 978-3-527-68146-4

**Mobi ISBN:** 978-3-527-68145-7

**CourseSmart ISBN:** 978-3-527-68390-1

**WTX ISBN:** 978-3-527-68391-8

This book is an introduction to atmospheric radiation. The focus is on radiative transfer in planetary atmospheres with particular emphasis on the Earth's atmosphere, the Earth's energy budget, and the role that radiation plays in climate sensitivity and climate change. The material is presented at the level expected of entering graduate students in the atmospheric sciences and most upper division undergraduates in the physical sciences. Students will need to have studied physics with calculus and methods for solving linear differential equations.

The goal of the book is to provide students with relatively simple physically based methods for calculating radiances and radiative fluxes at the Earth's surface and the top of the atmosphere and radiative heating rates within the atmosphere. It does so by following the approaches of two classical works: Rodgers and Walshaw [1], a treatment of infrared radiative transfer in the atmosphere, and Lacis and Hansen [2], a treatment of the transfer of solar radiation. Although more sophisticated treatments have appeared, these classical treatments embrace the physics of the problem. The difference in the modern and classical approaches is in the details with which scattering, absorption, and emission are treated and the numerical accuracy of the solutions to the radiative transfer equation.

The material presented in the book is intended to help students become familiar with relatively simple techniques that they can use to develop their intuition for the effects of scattering, absorption, and emission. A second goal is to alert students to the sensitivity of the Earth's climate to seemingly minor perturbations of the radiation budget. A third goal is to exercise a student's analytical skills. For the most part, the book's treatment is analytical. The use of large computer programs, while briefly described, is avoided. The emphasis is on helping students build an understanding that allows analytical manipulation rather than relying on computer exercises.

Problems at the end of each chapter are meant to be both interesting and instructive. They are intended to help students hone their understanding of the material covered in the chapter as well as in previous chapters. Some of these problems are rather simple but nonetheless helpful aids to learning; others will challenge students. The ordering of the problems is from the simple to the challenging. Occasionally, a problem will call for simple, straightforward numerical calculations that require the use of a spreadsheet or one of the widely used software programs for interactive computer analysis. These numerical exercises help students develop a sense of magnitudes for various processes.

This book grew from the “Class Notes” for a course on atmospheric radiation taught for more than 20 years at Oregon State University. Over the years, the notes evolved to better fit the needs of students and the time constraints of the 10-week quarter system. The book is not meant to be a reference book. Many fine references on atmospheric radiation already exist [3–8]. Teaching introductory courses from these references, however, has often proved difficult. Instructors are forced to select topics from what must seem to students as random pages from different sections of the books. Owing to time constraints, many sections of the books go untouched. In addition, some of the reference books are difficult for students to read. Some assume readers have far more advanced physical and mathematical knowledge and ability than have been acquired by many entering graduate students in the atmospheric sciences and upper division undergraduate students in the physical sciences. In fairness to the students, atmospheric radiation poses special challenges to those encountering the subject for the first time. New students often find bewildering the need for zenith angles, relative azimuth angles, solid angles, radiances, and irradiances. This book is meant to help them over the hurdles of what seems at first the horrendously complicated geometry, strange parameters, and esoteric terminology and units associated with radiative transfer.

The book might have been augmented with applications of atmospheric radiation to photochemical reactions, atmospheric optics, and a myriad of remote sensing problems. In addition, the treatment in the book is restricted to plane-parallel radiative transfer. Avoided are the consequences for remote sensing arising from the spatial variability of liquid water and ice within clouds. Also avoided are the 3-D radiative effects observed when clouds are present or nearby. Even without these topics, the short 10-week sprint of quarter systems will seem insufficient for dealing with the basics, let alone the potential applications of atmospheric radiation and 3-D radiative transfer effects.

The book includes some material such as radiometry (Section 2.3), elementary principles of light scattering (Section 3.3), and a description of molecular spectra (Sections 5.2 and 5.3). More than a few treatises have been written on each of these topics. The material in these sections is meant to provide students with some background in subjects to which they have had little, if any, exposure. Such material can be covered quickly in introductory courses, or even left to students to read on their own. Other additional material, marked *optional* (Sections 4.12–4.17), need not be covered at all. These sections briefly describe additional, more accurate solutions to the radiative transfer equation and numerical algorithms for solving radiative transfer problems. These sections are intended to serve as an introduction for students who pursue further studies in atmospheric radiation. This additional material might also serve for courses taught within the longer duration of semester systems.

I (JAC) am indebted to my coauthor for suggesting that the class notes be converted into an introductory textbook. I am even more indebted that he agreed to coauthor the book. Ping's contributions greatly extended and improved the material in the notes. He made the presentation more readable, more accurate, and more complete. Without Ping's involvement and the assistance and angelic patience of our editors at Wiley, Ulrike Fuchs and Ulrike Werner, the book would not exist. I am also indebted to the students of atmospheric radiation who struggled with the class notes over the years at Oregon State. Their struggles helped me see the need to seek better approaches for presenting the material. Former students will surely recognize many sections of this book from the notes. Some might even recognize how they contributed to the book through the added explanations, extra steps in derivations, improved diagrams, additional examples, and fewer mistakes. I doubt that this book is as helpful as some of my former students might have liked, but I hope that it satisfies the needs of most students new to atmospheric radiation. Furthermore, I am indebted to the many wonderful colleagues that I have encountered during my career in the atmospheric sciences. They have been immensely valuable in my education and development as a researcher and teacher. Some will surely recognize their contributions to my education in various sections of this book.

I am also grateful for the many years of funding support from Oregon State University, the National Science Foundation (NSF), National Aeronautic and Space Administration (NASA), National Oceanic and Atmospheric Administration (NOAA), and the Office of Naval Research (ONR). The funding made it possible for me and the students and postdocs who worked with me to probe techniques for extracting cloud and aerosol properties from satellite observations and pursue evidence for aerosol–cloud interactions. I am particularly grateful for my participation in NSF's Center for Clouds, Chemistry, and Climate (C^{4}) at the Scripps Institution of Oceanography and my many years of participation in NASA's Earth Radiation Budget Experiment and the Clouds and Earth's Radiant Energy System project. Without these experiences, this book would not have been possible. I thank the College of Oceanic and Atmospheric Sciences, now the College of Earth, Oceanic, and Atmospheric Sciences, for supporting my writing of the book and allowing me to teach and use a draft of the book in the course on Atmospheric Radiation after I had retired. In addition, I thank Texas A&M University and the Department of Atmospheric Sciences for supporting my visits to College Station while writing the book. Ping and the atmospheric sciences faculty made these visits enjoyable and memorable experiences.

I thank my wife and family for putting up with my absences during the past 3½ years that I spent transforming the notes into a book.

Corvallis, Oregon*Jim Coakley*

August 2013

One of my goals in the original planning for the Wiley series on Atmospheric Physics was to develop an introductory textbook on atmospheric radiation for senior undergraduate students with majors in the broad area of the geosciences. When Dr Alexander Kokhanovsky of the University of Bremen took over as editor of this series, he encouraged me to pursue this goal. I turned to Prof. James (Jim) Coakley for advice on such a textbook. In response, Jim shared with me the lecture notes he had developed throughout his 20 years of teaching atmospheric radiation at Oregon State University. I was impressed by the unique style of his lecture notes, especially his ability to explain physical concepts clearly without adopting the typical mathematically intensive approach found in most radiative transfer texts. I knew that Jim was thinking of retiring in a few years, and I did not want to see his excellent lecture notes go waste. Therefore, I urged Jim that he develop his lecture notes into a textbook. To my delight, he took my recommendation and invited me to assist him as a coauthor. I am grateful to have had this opportunity to work with Jim for two reasons. First, he is a very pleasant person to work with. He has welcomed the incorporation of many of my suggestions and additions into the final version of the book. Second, through working with him, I have learned a lot about how to teach atmospheric radiation effectively without over-reliance on mathematical equations.

In my opinion, this textbook is unique in three aspects. First, many important concepts are explained with simple models. For example, the greenhouse effect and the linkage of climate sensitivity to radiative transfer are demonstrated with a simplified window-gray model. Second, simple diagrams are used to define and explain physical quantities. And third, the materials covered in this textbook are designed to be accessible to readers who may not already have extensive training in physics and mathematics.

I am grateful to several researchers and graduate students at Texas A&M University, particularly, Lei Bi, Shouguo Ding, Chao Liu, Chenxi Wang, and Bingqi Yi, for their assistance in the preparation of some diagrams, specifically, Figures 1.7, 1.8, 1.9, 1.11, 1.12, 3.4, 3.5, 4.3, 4.9, 5.3, 5.4, 5.5, 5.12, and 7.6 used in this textbook.

I thank my mentors at Texas A&M University, Profs. Gerald North, George Kattawar, and Kenneth Bowman, for supporting my professional development. Over the years, I have learned atmospheric radiation, either theory or practical applications, from a number of people including Prof. Kuo-Nan Liou, Dr Warren Wiscombe, Prof. George Kattawar, Dr Michael King, Prof. Thomas Wilheit, Prof. Thomas Vonder Haar, and Prof. William L. Smith. My academic growth has substantially benefited from research with a number of collaborators, including (in alphabetical order) Anthony Baran, Bryan Baum, Andrew Dessler, Oleg Dubovik, Qiang Fu, Andrew Heidinger, Andrew Heymsfield, Yongxiang Hu, N. Christina Hsu, Hironobu Iwabuchi, Ralph Kahn, Xu Liu, Istvan Laszlo, Patrick Minnis, Michael Mishchenko, Shaima Nasiri, R. Lee Panetta, Steven Platnick, Jerome Riedi, Si-Chee Tsay, Manfred Wendisch, and Fuzhong Weng.

While writing this book, my research was supported by the National Science Foundation (NSF), National Aeronautics and Space Administration (NASA), National Oceanic and Atmospheric Administration (NOAA), and the Federal Aviation Administration (FAA). I would like to take this opportunity to thank Dr Hal Maring (NASA), Dr Lucia Tsaoussi (NASA), Dr Bradley Smull (NSF), Dr Chungu Lu (NSF), Dr A. Gannet Hallar (NSF), Dr Rangasayi Halthore (FAA), and Dr S. Daniel Jacob (FAA) for their support and encouragement.

As Jim already said in his preface, we sincerely thank our editors at Wiley, Ms. Ulrike Fuchs and Ms. Ulrike Werner, for their assistance and for being patient with us.

Last but not least, I thank my family for having endured my preoccupation with both working on the book and keeping up with my research over the past several years.

College Station, Texas *Ping Yang*

August 2013

- 1. Rodgers, C.D. and Walshaw, C.D. (1966) The computation of infra-red cooling rate in planetary atmospheres.
*Q. J. R. Meteorolog. Soc.*,**92**, 67–92. - 2. Lacis, A.A. and Hansen, J.E. (1974) A parameterization for the absorption of solar radiation in the Earth's atmosphere.
*J. Atmos. Sci.*,**31**, 118–133. - 3. Goody, R.M. and Yung, Y.L. (1989)
*Atmospheric Radiation Theoretical Basis*, Oxford University Press, New York. - 4. Thomas, G.E. and Stamnes, K. (1999)
*Radiative Transfer in the Atmosphere and Ocean*, Cambridge University Press, New York. - 5. Liou, K.N. (2002)
*Introduction to Atmospheric Radiation*, 2nd edn, Academic Press, New York. - 6. Bohren, C.F. and Clothiaux, E.E. (2006)
*Fundamentals of Atmospheric Radiation*, Wiley-VCH Verlag GmbH, Weinheim. - 7. Wendisch, M. and Yang, P. (2012)
*Theory of Atmospheric Radiative Transfer—A Comprehensive Introduction*, Wiley-VCH Verlag GmbH, Weinheim. - 8. Mishchenko, M.I., Travis, L.D. and Lacis, A.A. (2006)
*Multiple Scattering of Light by Particles–Radiative Transfer and Coherent Backscattering*, Cambridge University Press, New York.