Inverse Theory and its Application in Atmospheric Remote Sensing

Syllabus for METEO 597
Inverse Theory and its Application in Atmospheric Remote Sensing

Term: Spring 2021

Instructor: Dr. Bill Bristow
Time: TR 1:35 PM to 2:50 PM
Office: Walker 621
Office Hours: MW 2:30 PM-4:00 PM, T 3:00 PM-4:00 PM, or by appointment

Room: Zoom

Credit Hours: 3

Description:In physical sciences, we often seek a description of parameters such as a wind field or temperature profile, as continuous functions of position and/or time based upon a finite collection of measurements. Often those measurements come from remote sensing instruments and may be only indirectly related to the parameter of interest. Inverse theory concerns the mathematical techniques that enable researchers to use the available information in those data to build models of the parameters of interest. This course will introduce the principles of inverse theory and apply them to remote sensing observations. The theory and techniques presented will be general, however the example applications will be drawn from atmospheric remote sensing. Students will develop a set of tools and apply them to analyze sample data sets from remote sensing instruments.


  • Geophysical Data Analysis: Discrete Inverse Theory by William Menke, Fourth Edition, Academic Press 2018. (required)
  • Discrete Inverse Problems: Insight and Algorithms by Per Christian Hansen, Society for Industrial and Applied Mathematics, 2010. (reference)
  • Inverse Methods for Atmospheric Sounding: Theory and Practice by Clive D. Rodgers, World Scientific Publishing 2000. (reference)

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 Care and Advocacy (120 Boucke Building, 863-4926, For additional need related to socioeconomic status please visit

Grading:Final grade based upon

Exercises (20%)
Programming Assignments (50%)
Final project (30%)

Tentative Lecture Schedule:

  • Jan 19th Course Introduction
  • 21st Probability and Measurement Error I
  • 26th Probability and Measurement Error II
  • 28th Remote sensing inverse problems
  • Feb 2nd The L2 Norm and Simple Least Squares
  • 4th A Priori Information and Weighted Least Squares
  • 9th Wellness Day
  • 11th Computational Aspects and Regularization
  • 16th Resolution and Generalized Inverses
  • 18th Backus-Gilbert Inverse - Resolution vs Variance
  • 23rd Maximum Likelihood Principle
  • 25th Inexact Theories
  • Mar 2nd Nonuniqueness and Localized Averages
  • 4th Vector Spaces and Singular Value Decomposition
  • 9th Equality and Inequality Constraints
  • 11th Wellness Day
  • 16th L1, L2 Norm Problems and Linear Programming
  • 18th Iterative Regularization
  • 23rd Nonlinear Problems: Grid and Monte Carlo Searches
  • 25th Nonlinear Problems: Newton's Method
  • 30th Nonlinear Problems: Simulated Annealing
  • Apr 1st Empirical Orthogonal Functions
  • 6th Continuous Problems
  • 8th Linear Operators
  • 13th Frechet Derivatives
  • 15th Application Examples
  • 20th Ionospheric Radar Imaging
  • 22nd TBD
  • 27th Student Project Presentations
  • 29th Student Project Presentations 

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 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. To learn more, see Penn State's Academic Integrity training.

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. For example, uploading completed labs, homework, or other assignments to any study site constitutes a violation of this policy. 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. For example, uploading completed labs, homework, or other assignments to any study site constitutes a violation of this policy.

Disability Accommodation: Penn State welcomes students with disabilities into the University's educational programs. Every Penn State campus has an office for students with disabilities. Student Disability Resources (SDR) website provides contact information for every Penn State campus. For further information, please visit Student Disability Resources 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: See documentation guidelines ( If the documentation supports your request for reasonable accommodations, your campus 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 as possible. You must follow this process for every semester that you request accommodations.

Attendance: Regular attendance is critical for building on the skills and knowledge developed throughout the class. Students who participate have a more complete understanding of the material presented and are more likely to succeed in the class. This is true whether your attendance is in person or remote. The University recognizes that, on exceptional occasions, students may miss a class meeting to participate in a regularly scheduled university-approved curricular or extracurricular activity (such as field trips, debate trips, choir trips, and athletic contests), or due to unavoidable or other legitimate circumstances such as illness, injury, military service, family emergency, religious observance, participation in local, state, and federal government elections, or post-graduate, career-related interviews when there is no opportunity for students to re-schedule these opportunities (such as elections or employment and graduate school final interviews). In all cases, you should inform me in advance, when possible. Missing class, even for a legitimate purpose, may mean there is work that cannot be made up, hurting your grade in this class. Students who encounter serious family, health, or personal situations that result in extended absences should contact the Office of the Assistant Vice President for Student Affairs (AVPSA) and Student Care and Advocacy for help: You should be prepared to provide documentation for participation in University-approved activities, as well as for career-related interviews. You should submit to the instructor a Class Absence Form: absence v3.pdf, at least one week prior to the activity.

Wellnes Days:Tuesday, 2/9 and Thursday, 3/11 have been designated as Wellness Days. No class meeting will happen, either in person or remotely, for those two days, and no assignments will be due on those days. Students are encouraged to use these days to focus on their physical and mental health. Please see for university sponsored events focusing on wellness that may be of interest to you. See Canvas and the course syllabus for any work that may be due before the next class meeting. Educational Equity: Penn State takes great pride to foster a diverse and inclusive environment for students, faculty, and staff. Acts of intolerance, discrimination, or harassment due to age, ancestry, color, disability, gender, gender identity, national origin, race, religious belief, sexual orientation, or veteran status are not tolerated and can be reported through Educational Equity via the Report Bias webpage (

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