Data Assimilation

METEO 527 Syllabus: Data Assimilation 

Department of Meteorology and Atmospheric Science
The Pennsylvania State University
University Park Campus 

Semester: Spring 2021
Credits: 3.0 

Prof. Xingchao (XC) Chen
601 Walker Building 

Course Information:
Course Hours:  Monday, Wednesday, Friday, 2:30 PM – 3:20 PM
Course Location: 101 Walker Bldg 

Before February 15th: METEO 527 is slated to follow a remote synchronous format (Zoom meeting)

Starting February 15th: METEO 527 is slated to follow an in-person format, while a remote synchronous section (Zoom meeting) will be provided 

Office Hours: Monday 3:30-4:00 PM; By appointment

Office Hours are slated to follow a remote synchronous format (Zoom meeting) 

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. 

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

Weeks / Topics

  • 1-2 
    Overview of Data Assimilation (DA)
    Least Squares versus Maximum Likelihood Approaches
    Optimal Interpolation
  • 3-4 
    Review of Probability Theory and Bayes Theorem
    Dynamical Systems and Chaos
  • 5-7
    Kalman Filter (KF)
    Extended Kalman Filter (EKF)
    Ensemble Kalman Filter (EnKF)
  • 8-10
    Hybrid Filters
    Application to High-Dimensional Systems and NWP
    DA in Operational Centers
    Ensemble Sensitivity
  • 11-13
    Parameter Estimation
    Model Error
    Special Topics in DA and Predictability
    Particle Filters
  • 14-15
    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:

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:, at least one week prior to the activity. 

Use the symptom checker of the Penn State GO app every day to see if you have any COVID-19 symptoms.  If you have COVID-19 symptoms or are otherwise not feeling well, DO NOT COME TO CLASS, and seek the advice of a medical professional as appropriate.  If you have been notified or know yourself that you have been in contact with someone who has tested positive for COVID-19, DO NOT COME TO CLASS and please make sure you have been reported as a close contact. I cannot stress this strongly enough. We are counting on you to help contain the spread of the virus (and other illnesses) on campus.  If you need to isolate (because you are infected) or quarantine (because you were a close contact to an infected person), the Student Support Services Office will let both of us know when you are allowed to attend class again.  If you attend class before the approved date, it will be a student conduct violation, because you are endangering the health of your classmates and me.  While you are in isolation or quarantine, I will work with you to help you maintain progress in the course as you are able.  [This may include participating remotely, watching the recorded class, and/or completing asynchronous course content.]  If you are not in class on your assigned day, you may be contacted by the instructor to check up on you and make sure you are okay. 

According to University guidelines, and because of the distancing procedures in place for in-person classes, if someone in the class tests positive, we will continue with our regularly scheduled classes. 

Academic Integrity Statement: 

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 Procedures:, 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 address 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.

Change in Normal Campus Operations:

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


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 (SDR) 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: 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. 

Reporting Educational Equity Concerns: 

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

Counseling and Psychological Services: 

Many students at Penn State face personal challenges or have psychological needs that may interfere with their academic progress, social development, or emotional wellbeing.  The university offers a variety of confidential services to help you through difficult times, including individual and group counseling, crisis intervention, consultations, online chats, and mental health screenings.  These services are provided by staff who welcome all students and embrace a philosophy respectful of clients’ cultural and religious backgrounds, and sensitive to differences in race, ability, gender identity and sexual orientation.  Services include the following: 

Mask Wearing: 

We know from existing scientific data that wearing a mask in public can help prevent the spread of COVID-19 in the community (Lyu and Wehby, 2020; CDC, 2020; Johns Hopkins Medicine, 2020). Just as you’re expected to wear a shirt and shoes to class every day, everyone -- including the instructor and TAs -- are required to wear a face mask in University buildings, including classrooms and labs. You MUST wear a mask appropriately (i.e., covering both your mouth and nose) in the building if you are attending class in person. Masks have been provided for students, faculty, and staff, and everyone is expected to wear one while on campus or out in the community. 

All students, faculty and staff are expected to maintain physical distancing (i.e., maintain at least six feet of space between individuals) when possible. Seating patterns and attendance patterns, including assigned seating and closed-off desks/chairs/room sections, have been established to help allow for this distance for your safety. It is also important to follow related guidance communicated by the University and via public postings/signage related to directional traffic flow and maximum occupancy of spaces. 

You are not permitted to consume food or drink in classrooms, except for water. If you must drink water, please be especially conscious of maintaining social distancing and minimizing the time your mask is moved aside. Or, better yet, use a water bottle with a built-in straw. Cooperation from EVERYONE will help control the spread of the virus and help us get back to the previous version of campus life as quickly as possible. 

Students with conditions that make it difficult to wear a mask or who choose not to wear a mask may participate in class remotely but may not attend class in person. This is to protect your health and safety as well as the health and safety of your classmates, instructor and the University community. Anyone attending class in person without a mask will be asked to put one on or leave. Refusal to comply with University policies is a violation of the Student Code of Conduct. Students who refuse to wear masks appropriately may face disciplinary action for Code of Conduct violations. See details here:

Centers for Disease Control and Prevention. (2020, April 3) Recommendation Regarding the Use of Cloth Face Coverings, Especially in Areas of Significant Community-Based Transmission.

Johns Hopkins Medicine. (2020, June 17) Coronavirus Face Masks & Protection FAQs.

Lyu, W. and Wehby, G.L. (2020, June 16) Community Use Of Face Masks And COVID-19: Evidence From A Natural Experiment Of State Mandates In The US. Health Affairs. 2003& 

Wellness Days: 

Wednesday, April 7th has been designated as a Wellness Day. No class meeting will happen, either in person or remotely, for that day, and no assignments will be due on that day. Students are encouraged to use the day 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.

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 (

Deferred Grades: 

If you are prevented from completing this course within the prescribed amount of time for reasons that are beyond your control, it is possible to have the grade deferred with the concurrence of the instructor, following Penn State Deferred Grade Policy 48-40 ( To seek a deferred grade, you must submit a written request (by e-mail or U.S. post) to the instructor describing the reason(s) for the request. Non-emergency permission for filing a deferred grade must be requested before the beginning of the final examination period. It is up to the instructor to determine whether or not you will be permitted to receive a deferred grade. If permission is granted, you will work with the instructor to establish a communication plan and a clear schedule for completion.  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. 


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.

Disruptive Behavior: 

Behavior that disrupts normal classroom activities will not be tolerated, in accordance with Items 9 and 14 in the Student Code of Conduct.

Mandated Reporting Statement: 

Penn State’s policies require me, as a faculty member, to share information about incidents of sex-based discrimination and harassment (discrimination, harassment, sexual harassment, sexual misconduct, dating violence, domestic violence, stalking, and retaliation) with Penn State’s Title IX coordinator or deputy coordinators, regardless of whether the incidents are stated to me in person or shared by students as part of their coursework.  For more information regarding the University's policies and procedures for responding to reports of sexual or gender-based harassment or misconduct, please visit Penn State's Office of Sexual Misconduct Prevention & Response website.

Additionally, I am required to make a report on any reasonable suspicion of child abuse in accordance with the Pennsylvania Child Protective Services Law

Diversity, Inclusion, and Respect: 

Penn State is “committed to creating an educational environment which is free from intolerance directed toward individuals or groups and strives to create and maintain an environment that fosters respect for others” as stated in Policy AD29 Statement on Intolerance. All members of this class are expected to contribute to a respectful, welcoming and inclusive environment and to interact with civility.

For additional information, see:

Accessible Syllabus: 

Notes: Any syllabus posted online (e.g. a Word/PDF file or an online syllabus) should make destinations clickable links such as is done throughout this page. Also, in order to comply with Penn State Policy AD69 (Accessibility of Penn State Web Pages,, PDF documents cannot be the sole source of presenting online information. Such documents include syllabi, homework assignments, and scanned notes.  

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 to the syllabus shall also be given to the student in written (paper or electronic) form. 

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