METEO 597B Data Assimilation

Instructors: Prof. Steven J. Greybush (lead instructor), Prof. Fuqing Zhang, Prof. John Harlim, Course Hours: Monday, Wednesday, Friday, 2:30 PM – 3:20 PM, Course Location: 124 Walker Bldg

METEO 597B Syllabus: Data Assimilation 

Semester: Spring 2017
Credits: 3.0 


Prof. Steven J. Greybush (lead instructor)

  • 618 Walker Building

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: 124 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: ANGEL 

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 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%
  • 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. 


  • Week 1 Jan 9,11,13
  • Week 2 Jan 18, 20 Note Jan 16 is university holiday
  • Week 3 Jan 23, 25, 27
  • Week 4 Jan 30, Feb 1, 3
  • Week 5 Feb 6, 8, 10
  • Week 6 Feb 13, 15, 17
  • Week 7 Feb 20, 22, 24
  • Week 8 Feb 27, Mar 1, 3
  • Break Mar 6, 8, 10 Spring break
  • Week 9 Mar 13, 15, 17
  • Week 10 Mar 20, 22, 24
  • Week 11 Mar 27, 29, 31
  • Week 12 Apr 3, 5, 7
  • Week 13 Apr 10, 12, 14
  • Week 14 Apr 17, 19, 21
  • Week 15 Apr 24, 26, 28 Final Presentations

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

Course content: 



  • 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 ANGEL (, 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. Other legitimate reasons for missing class include religious observance, family emergencies, and regularly scheduled university-approved curricular or extracurricular activities.  Students who encounter serious family, health, or personal situations that result in extended absences should contact the of the Assistant Vice President for Student Affairs (AVPSA) and 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 may consult with their instructors and classmates for assistance with the course assignments, but the final product must represent their own work and be fully understood by the author.  Students in this class are expected to write their papers in their own words using proper citations.  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.

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.

Weather Delays and Campus Emergencies: 

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: Students will not be required to attend class if campus is closed during any part of the scheduled class time. 


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 Student Disability Resources (SDRODS) website provides contact information for every Penn State campus: ( For further information, please visit the 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 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.

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.