Instructor: Peter Bannon, TA: Robert Nystrom, Lectures: Mon., Wed., and Fri. at 12:20-1:10 p.m. 124 Walker Building

Examinations: Two midterms and a final exam are planned. The midterms are scheduled for Friday September 30th and Friday November 4th during class. Each mid-term will contribute 25% to your final grade, the final 35%.  

Problem Sets: Frequent problem sets will be given. Together the problem sets will contribute 15% to your grade. 


  1. Student participation (either in or out of class or online) is essential. Bonuses up to 5% of your grade will be assigned based on your individual level of participation. Anyone who misses class regularly without a reasonable excuse is, of course, unlikely to receive these points.
  2. Total scores are curved to determine the course grade.
  3. 10% penalty for problem sets turned in after 5 p.m. on the due date.
  4. No problem sets will be accepted after the answers are posted or discussed in class.
  5. Make-up exams by prior arrangement only.
  6. No make-up final except for a direct conflict.
  7. This course adopts the EMS College's academic integrity policy:

Prerequisites: Meteo 300. Concurrent: Meteo 431 

Textbooks: The recommended text is A First Course in Atmospheric Radiation by Petty. 

Lectures: Mon., Wed., and Fri. at 12:20-1:10 p.m. 124 Walker Building

Lecturer: Peter R. Bannon, 521 Walker Building, 863-1309 Office hours: Mon., Wed., Fri. 1:30-2:30 p.m. or whenever my door is open or by appointment.

Teaching Assistant: Robert Nystrom, 601 Walker Building Office hours: Mon. 2:30-4:00 p.m.; Tues. 10:00-11:30 a.m.


  • Andrews, D. G., 2000:  An Introduction to Atmospheric Physics. Cambridge, 229 pp. QC863.A596 2000
  • Bohren, C.F., 1987: Clouds in a Glass of Beer. New York, John Wiley, 195 pp. QC861.2.B64 1987
  • Bohren, C.F., 1991:  What Light Through Yonder Window Breaks?  New York, John Wiley, 190 pp.  QC871.B64 1991
  • *Bohren, C. F., and E. E. Clothiaux, 2006:  Fundamentals of Atmospheric Radiation. Wiley, 472 pp.
  • Fleagle, R. G., and J. A. Businger, 1980:  An Introduction to Atmospheric Physics. Second Edition.  New York, Academic Press, 432 pp. QC880.F53 1980
  • Goody, R. M., 1995: Principles of Atmospheric Physics and Chemistry. New York, Oxford University Press, 324 pp. QC861.2.G66 1995 
  • Hartmann, D. L., 2016: Global Physical Climatology. Second Edition. San Diego, Academic Press, 485 pp.  QC981.H32 1994 
  • Liou, K. N., 1980: An Introduction to Atmospheric Radiation. New York, Academic Press, 392 pp.  QC912.3.L56
  • *Petty, G. W., 2006: A First Course in Atmospheric Radiation. Second Edition. Sundog Publishing. QC912.3P48 2004 
  • *Wallace, J. M., and P. V. Hobbs, 2006: Atmospheric Science. An Introductory Survey. Second Edition. New York, Academic Press, 483 pp.  QC861.2.W34 

*  On reserve in the EMS Library 

Fundamentals of Radiation

  • The wave-particle duality of radiation
    • Electromagnetic waves
      • Plane waves: wavelength, frequency, phase, and polarization
      • Speed of light
      • Electromagnetic spectrum, dipole radiation
    • Quantum mechanical particles: Photons: Planck’s relation
  • Description of the radiation field
    • Geometry of radiation: Angles and solid angles
    • Radiance (intensity) and Irradiance (flux)
  • Radiation in thermodynamic equilibrium (TE)
    • Planck function: Wien’s law and Stefan-Boltzmann Law
    • Effective, color, and brightness temperatures
  • Solar radiation
    • Solar spectrum, solar constant, effective temperature
    • Distribution of insolation
  • Terrestrial radiation 

Interaction of radiation and matter I

  • Absorptivity, reflectivity, transmissivity, and emissivity
  • Kirchhoff's law: Local thermodynamic equilibrium (LTE);
    • Black, gray, and white bodies
  • Radiative properties of surfaces
  • Scattering: Specular and diffuse reflection
  • Refraction: Index of refraction
  • Planetary and surface albedo 

Planetary Energy Balance

  • Global radiative equilibrium
  • A simple model of the "greenhouse effect"
  • Global energy balance

Radiative Transfer: Absorption

  • Absorption of radiation: 
    • Absorption coefficient, absorption cross section
    • Law of absorption, optical path length
    • Probabilistic interpretation of absorption
      • Photon mean free path, penetration depth
    • Transmissivity and absorptivity
  • Plane parallel atmosphere: Normal vs. oblique path lengths
  • Absorption of UV solar radiation by ozone
    • UV-A, B, C, UV Index, erythemal efficiency
  • Shortwave atmospheric heating
  • Dobson spectrophotometer: Remote sensing of ozone 

Interaction of radiation and matter II

  • Molecular energies
  • Energy transitions
  • Discrete spectra of gases: Absorption and emission spectra
  • Continuous spectra of liquids and solids 

Radiative Transfer: Absorption and Emission

  • Schwarzschild equation and its formal solution
  • Spectrum of outgoing longwave radiation (OLR)
  • Remote sensing of water vapor
  • Remote sensing of temperature: Weighting function
    • Effective emission level and brightness temperature
  • Longwave atmospheric heating 

Radiative Transfer: Scattering

  • Atmospheric scattering
    • Size parameter, scattering efficiency, and phase function
    • 3 regimes: Rayleigh, Mie, and geometric optics
  • Single scattering: Sunlight, skylight, and airlight
  • Multiple scattering:
    • Equation of radiative transfer
    • Two-stream approximation: Schuster's model

Clouds and Radiation

  • Cloud properties
  • Clouds and visible radiation
  • Clouds and near infrared radiation
    • Radiative transfer: Scattering and absorption
      • Equation of radiative transfer
      • Extinction, single scattering albedo
  • Clouds and longwave radiation
    • Radiative transfer: Emission, scattering, and absorption
  • Clouds and radio waves: RADARS 

Radiation and Climate

  • Radiative equilibrium
  • Radiative-convective equilibrium: Convective adjustment
  • Radiative-dynamical equilibrium
  • Clouds and climate
  • Aerosols and climate 

Insolation and the Earth-Sun Geometry

  • The earth's orbit
    • Kepler’s laws: Eccentricity, perihelion, and aphelion
  • The earth's rotation and the seasons
    • Angular rotation rate, obliquity, longitude of perihelion
  • Time: Local time, standard time, equation of time
  • Distribution of insolation
    • Solar zenith angle: declination angle, hour angle
      • Sunrise and sunset
    • Daily mean insolation, Annual mean insolation
  • Orbital theory of climate change 

*  Please note that this outline serves only as a general guide to the course. The actual topics covered may vary at the discretion of the instructor.

EXPECTATIONS AND POLICIES FOR METEO 436: As a student majoring in Meteorology, you are expected to have a reasonable background in mathematics (through differential equations) and physics (mechanics, electricity and magnetism) before studying atmospheric physics. Students with weak backgrounds in these fundamental disciplines are advised to postpone enrollment in this course. 

Each student is expected to keep up with the subject matter and to participate actively and effectively in class.  Participation may take the form of responding to questions posed by the instructor or of asking content-related questions in or out of the classroom. Exams serve to test not only your general knowledge of the subject matter, but also your ability to apply that knowledge to solving new problems.

Homework, assigned approximately weekly, must be turned in on time.  Outside assignments may be challenging, but they nevertheless constitute an important way to learn. Reading from the required text is essential. Experience also suggests that rewriting your class notes within a day or so of each lecture leads to significantly enhanced learning of complex material. Remember that what you get out of any endeavor is proportionate to the effort you put in. 

Reminder about academic integrity: Cheating and plagiarism are serious offenses that may be grounds for failing an assignment, an exam, or even the course. Collaboration with classmates can be an effective way of learning, especially when you are the one teaching others. In any case, the final work must be your own, a clear expression of your level of understanding. Please review the College policies related to academic integrity on the web at: 


  • The problem set is due by 5 p.m. on the due day (you can slide them under my office door). No homeworks will be accepted if they are turned in after the problems have been discussed in class, the graded problem sets returned, or their solutions posted.
  • Please try to write in complete sentences and explain what you are doing and why you are doing it.  This practice has several benefits:
    • It gives you practice in writing in general and in writing on scientific issues in particular.
    • The explanation may uncover a flaw in your thinking that you can fix before the homework is turned in.
    • If the grader knows what you're thinking, then it will be easier to correct any errors in logic.  This feedback will help you in the long run.
    • The problem set will be easier to read later, say, when you're studying for an exam.
  • It is not necessary to submit every step in a mathematical derivation unless you wish to have it for your own use at a later point or you wish the grader to help you find an error. A sketch of the analysis will suffice for grading purposes.
  • You may collaborate with your classmates on a problem set. Note that collaborate means "to work together."  It does not mean to copy.  You are here to learn, not to get a grade.  After working together, you should write up your results independently.
  • Try to embed your equation into a sentence and punctuate it with either a comma or a period (if it is at the end of the sentence). For example:
    The equation of state for an ideal gas of N molecules in a volume V is P V  = N k T , (1) where k is the Boltzmann constant.
  • Number your equations if you need to refer to them. Equation (1) is an example.
  • Check your spelling and your grammar.
  • Avoid abbreviations and jargon.
  • The use of clean, stapled, 8 ½” x 11” sheets and legible handwriting is appreciated. Never hand in a rough draft.  Avoid dividing a page into columns, unless you are making a table. 
  • The plans are for 12 problem sets this semester. Your total problem set grade will be based on your 10 best scores. 

Objectives and Outcomes for Meteo 436 

Objectives for Meteo 436:

  1. Students can demonstrate how radiative processes are related to atmospheric structure and phenomena
  2. Students can demonstrate the ability to apply atmospheric radiative principles quantitatively to atmospheric problems 

Outcomes for Meteo 436:

  1. Students can demonstrate knowledge of absorption, emission, and scattering properties along with the equations for radiance, irradiance, and solid angle
  2. Students can demonstrate a basic grasp of the integro-differential form of the radiative transfer equation by providing a physical interpretation
  3. Students can solve the integro-differential form of the radiative transfer equation for simplified atmospheres such as attenuation-only with no scattering
  4. Students can demonstrate the use of simplified solutions of the integro-differential form of the radiative transfer equation to basic remote sensing of the atmosphere
  5. Students can show the link of atmospheric irradiance to atmospheric heating and cooling 

Program Objectives

  1. To produce graduates who possess quantitative, scientific reasoning skills that can be applied to atmospheric problems.
  2. To produce graduates who have a general knowledge of a range of atmospheric phenomena and applications, and have expertise in one or more program subdisciplines or related interdisciplinary areas.
  3. To produce graduates who are equipped to contribute to solving problems in the atmospheric sciences and related disciplines, through service in business or as educators, researchers, and leaders in academia, government, the private sector, and civil society. 

Program Outcomes

  1. Graduates can demonstrate skills for interpreting and applying atmospheric observations.
  2. Graduates can demonstrate knowledge of the atmosphere and its evolution.
  3. Graduates can demonstrate knowledge of the role of water in the atmosphere.
  4. Graduates can demonstrate facility with computer applications to atmospheric problems.
  5. Graduates can demonstrate skills for communicating their technical knowledge. 

EMS Syllabus Statements 

Prerequisites: Students who do not meet these prerequisites may be disenrolled according to Administrative Policy C-5. if they do not have the proper prerequisite override. Students who re-enroll in the course after being dis-enrolled according to this policy are in violation of Item 15 on the Student Code of Conduct:

Assistance with Textbooks: Penn State honors and values the socioeconomic diversity of our students. If you require assistance with the costs of textbooks for this course, contact the Office of Student and Family Services (120 Boucke Building, 863-4926, For additional need related to socioeconomic status please visit

Academic Integrity:  

Students in this class are expected to write up their problem sets individually, to work the exams on their own, and to write their papers in their own words using proper citations.  Class members may work on the problem sets in groups, but then each student must write up the answers separately.  Students are not to copy problem or exam answers from another person's paper and present them as their own; students may not plagiarize text from papers or websites written by others.  Students who present other people's work as their own will receive at least a 0 on the assignment and may well receive an F or XF in the course.  Please see: Earth and Mineral Sciences Academic Integrity Policy:, which this course adopts. To learn more, see Penn State's "Plagiarism Tutorial for Students."

Course Copyright:  

All course materials students receive or to which students have online access are protected by copyright laws. Students may use course materials and make copies for their own use as needed, but unauthorized distribution and/or uploading of materials without the instructor’s express permission is strictly prohibited. University Policy AD 40, the University Policy Recording of Classroom Activities and Note Taking Services addresses this issue. Students who engage in the unauthorized distribution of copyrighted materials may be held in violation of the University’s Code of Conduct, and/or liable under Federal and State laws.

Accommodations for Students with Disabilities:

Penn State welcomes students with disabilities into the University's educational programs. Every Penn State campus has an office for students with disabilities. The Office for Disability Services (ODS) website provides contact information for every Penn State campus: ( For further information, please visit the Office for Disability Services website ( 

In order to receive consideration for reasonable accommodations, you must contact the appropriate disability services office at the campus where you are officially enrolled, participate in an intake interview, and provide documentation based on the documentation guidelines ( If the documentation supports your request for reasonable accommodations, your campus’s disability services office will provide you with an accommodation letter. Please share this letter with your instructors and discuss the accommodations with them as early in your courses as possible. You must follow this process for every semester that you request accommodations.


This course abides by the Penn State Attendance Policy E-11:, and Conflict Exam Policy 44-35: Please also see Illness Verification Policy:, and Religious Observance Policy: Students who miss class for legitimate reasons will be given a reasonable opportunity to make up missed work, including exams and quizzes  Students are not required to secure the signature of medical personnel in the case of illness or injury and should use their best judgment on whether they are well enough to attend class or not; the University Health Center will not provide medical verification for minor illnesses or injuries. Other legitimate reasons for missing class include religious observance, military service, family emergencies, regularly scheduled university-approved curricular or extracurricular activities, and post-graduate, career-related interviews when there is no opportunity for students to re-schedule these opportunities (such as employment and graduate school final interviews). Students who encounter serious family, health, or personal situations that result in extended absences should contact the Office of Student and Family Services for help: Whenever possible, students participating in University-approved activities should submit to the instructor a Class Absence Form available from the Registrar's Office:, at least one week prior to the activity.

Weather Delays: 

Campus emergencies, including weather delays, are announced on Penn State News and communicated to cell phones, email, the Penn State Facebook page, and Twitter via PSUAlert (Sign up at:

Syllabus and Paper Acknowledgement Forms
All students must sign and return the Syllabus Acknowledgement Form during the first week of the semester.

Penn State E-mail Accounts

All official communications from Penn State are sent to students' Penn State e-mail accounts. Be sure to check your Penn State account regularly, or forward your Penn State e-mail to your preferred e-mail account, so you don't miss any important information. 

Deferred Grades

If you are prevented from completing this course within the prescribed amount of time, it is possible to have the grade deferred with the concurrence of the instructor. To seek a deferred grade, you must submit a written request (by e-mail or U.S. post) to your instructor describing the reason(s) for the request. It is up to your instructor to determine whether or not you will be permitted to receive a deferred grade. If, for any reason, the course work for the deferred grade is not complete by the assigned time, a grade of "F" will be automatically entered on your transcript.

Military Personnel

Veterans and currently serving military personnel and/or spouses with unique circumstances (e.g., upcoming deployments, drill/duty requirements, disabilities, VA appointments, etc.) are welcome and encouraged to communicate these, in advance if possible, to the instructor in the case that special arrangements need to be made.

Technical Requirements:

For this course, we recommend the minimum technical requirements outlined on the Dutton Institute Technical Requirements page (, including the requirements listed for same-time, synchronous communications. If you need technical assistance at any point during the course, please contact the ITS Help Desk (


The term "Netiquette" refers to the etiquette guidelines for electronic communications, such as e-mail and bulletin board postings. Netiquette covers not only rules to maintain civility in discussions, but also special guidelines unique to the electronic nature of forum messages. Please review some general Netiquette guidelines that should be followed when communicating in this course. 

Disclaimer Statement

Please note that the specifics of this Course Syllabus can be changed at any time, and you will be responsible for abiding by any such changes. Changes will be posted.