Data Assimilation

METEO 527 Syllabus: Data Assimilation 

Department of Meteorology and Atmospheric Science

The Pennsylvania State University
University Park Campus
Semester: Spring 2019

Credits: 3.0

Instructor: Prof. Steven J. Greybush (lead instructor)
618 Walker Building
(Please include METEO 527 in the subject line of course-related email correspondence.) 

Guest Lecturers:
Prof. Fuqing Zhang
624 Walker Building 

Prof. John Harlim
214 MacAllister Building 

Course Information:
Course Hours:  Monday, Wednesday, Friday, 2:30 PM – 3:20 PM
Course Location: 110 Walker Bldg
Professor Office Hours: Monday 3:30-4:00 PM (618 Walker); By appointment
Course Description: Data assimilation is the process of finding the best estimate of the state by statistically combining model forecasts and observations and their respective uncertainties. 

Required Materials: None
Required textbooks: None
Recommended textbooks (on reserve in the EMS library):

  • Atmospheric Modeling, Data Assimilation, and Predictability, by Eugenia Kalnay (Cambridge University Press, 2003)

Internet materials and links: CANVAS 

Course Objectives: 

  1. To provide a conceptual and mathematical overview of the basic concepts, theoretical underpinnings, and research frontiers of data assimilation. 

Course Outcomes: 

  1. To demonstrate familiarity with the terminology, mathematical framework, assumptions, and conceptual understanding of data assimilation.
  2. To demonstrate familiarity with specific data assimilation methodologies, including variational techniques, ensemble kalman filters, and hybrid approaches.
  3. To demonstrate the ability to apply assimilation techniques to a dynamical system using computer programming.
  4. To demonstrate knowledge of current research frontiers in the field of data assimilation and predictability, including its applications to numerical weather prediction. 


This is a self-contained course and is designed for first year meteorology/math/stats/engineering graduate students or advanced undergraduate students. 

A basic knowledge of probability theory, calculus, linear algebra/matrices, and computer programming is expected. 

Data assimilation (DA) is the process of finding the best estimate of the state and associated uncertainty by combining all available information including model forecasts and observations and their respective uncertainties. DA is best known for producing accurate initial conditions for numerical weather prediction (NWP) models, but has been recently adopted for state and parameter estimation for a wide range of dynamical systems across many disciplines such as ocean, land, water, air quality, climate, ecosystem and astrophysics. Taking advantages of improved observing networks, better forecast models and high performing computing, there are two leading types of advanced approaches, namely variational data assimilation through minimization of a cost function, or ensemble-based data assimilation through a Kalman filter.  Hybrid techniques, parameter estimation, predictability, and ensemble sensitivity methods will also be covered. 

The material in this course may be relevant to those in engineering, statistics, mathematics, hydrology, earth systems science, atmospheric science, and many other fields that seek to integrate information from observations and models. 

This course is offered by faculty of the Penn State Center for Advanced Data Assimilation and Predictability Techniques (ADAPT;, with the goal to foster interdisciplinary collaborations in this important field. 

Assessment Tools:
Required written/oral assignments 

Several homework assignments / programming exercises (in MATLAB) will be assigned during the course to apply algorithms learned during lecture and gain hands on experience with these techniques. 

Students will work individually to complete a final research project / literature review on a topic approved by the instructors; guidelines and potential topics should be discussed with one of the instructors. Project results must be summarized in a short report (maximum 10-page double-spaced), and discussed in a 25-min presentation. Lecture time during the last few weeks of the semester will be used for presentations.

Examination Policy
There are no formal exams in this course. 

Grading Policy 

  • Participation 10%
  • Assignments / Programming Exercises 50%
  • Final Project 40% 

Attendance and Participation: Students are highly encouraged to attend all lectures and participate in all exercises.  Active, thoughtful contributions to class discussions are welcomed. 

Add / Drop Deadline is January 12. 

The course content, topics, and timeline listed here is intended as a guideline, and is subject to modification by the instructors. 

Course content: 

Weeks / Topics 


  • Overview of Data Assimilation (DA)
  • Review of Probability Theory and Bayes Theorem
  • Optimal Interpolation


  • Least Squares versus Maximum Likelihood Approaches
  • 3D-Var
  • Dynamical Systems and Chaos


  • Kalman Filter (KF)
  • Extended Kalman Filter (EKF)
  • Ensemble Kalman Filter (EnKF)


  • 4D-Var
  • Hybrid Filters
  • Application to High-Dimensional Systems and NWP
  • DA in Operational Centers
  • Ensemble Sensitivity


  • Parameter Estimation
  • Model Error
  • Special Topics in DA and Predictability
  • Particle Filters


  • Frontiers in Data Assimilation (student presentations) 

Lecture notes will often be placed on CANVS (, although students are ultimately responsible for their own note-taking. 

Attendance 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. 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:

Academic Integrity Statement: Academic integrity is fundamental not only to one’s experience at the university, but remains essential throughout one’s career.  Students are not to receive unauthorized assistance on any course quizzes or individual assessments.  Students are not to misrepresent the work of others as their own.  Serious offenses may warrant a zero on the assignment or assessment.

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 any sources (e.g. papers or solutions 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." 

If in doubt about how the academic integrity policy applies to a specific situation, students are encouraged to consult with the instructors. 

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

Weather Delays and Campus Emergencies: Campus emergencies, including weather delays, are announced on Penn State News: http:/ and communicated to cellphones, email, the Penn State Facebook page, and Twitter via PSUAlert (Sign up at: Students will not be required to attend class if campus is closed during any part of the scheduled class time. 

Safety: In the case of an emergency, we will follow the College of Earth and Mineral Sciences Critical Incident Plan (  In the event of an evacuation, we will follow posted evacuation routes and gather at the Designated Meeting Site.  Evacuation routes for all EMS buildings are available at  For more information regarding actions to take during particular emergencies, please see the Penn State Emergency Action Guides.

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: 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. 

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 to the course discussion forum. 

Acknowledgements: We would like to thank previous instructors of data assimilation courses for their contributions to the development and structure of this course.