Advanced Statistical Meteorology

January 17, 2017
TR 2:30-3:45
METR 5433.002


Furtado, Jason
Associate Professor; Carlisle and Lurline Mabrey Presidential Professor


National Weather Center, Room 5930, 120 David L. Boren Blvd, Norman, OK 73072   View map


Spring 2017

Time: Tuesday and Thursday 2:30-3:45
Room: NWC 5930
Instructor: Furtado


Course DescripCon

Data analysis is a rou-ne part of many types of research in the atmospheric sciences. As such, having the right set of tools and the prowess on how to use those tools is an important part to understanding the behavior of the climate system.


This course offers an overview of some advanced sta4s4cal methods used to interpret data in the atmospheric and oceanic sciences. It is designed to be


an applied course: i.e., the goal is to gain a working knowledge of the sta4s4cal tools most commonly used in the atmospheric sciences.

Major topics to be covered include: (A) regression/ correla4on and epoch analyses; (B) 4me series analysis (e.g., power spectra, filtering, wavelet analysis);

  • matrix methods for signal decomposi4on (e.g., EOFs, CCA); and (D) objec4ve mapping and covariance


The course is intended for graduate students and senior undergraduates (with permission). Although previous knowledge of probability and sta4s4cs is required, a short background review will be provided at the start of the course. You should also have a working knowledge of a soPware package to analyze data (e.g., Python, MATLAB, IDL, NCL,

etc.). This will be important because of the highly-applied nature of the course.



Required Text

There is no required text for the class. Most of the class will be taught with my own personal notes. However, there are several sources and texts that will be useful (Textbooks will be available on reserve or you can purchase them):


  • Discrete Inverse and State Es0ma0on Problems – Carl Wunsch, Cambridge Press
  • Sta0s0cal Methods in the Atmospheric Sciences Second Edi0on – Daniel Wilks, Academic Press
  • Sta0s0cal Analysis in Climate Research – Hans von Storch and Francis W. Zwiers


Course Web Page

The web page will be accessible via hbps:// (log on using your OU 4+4). There you will find course materials (e.g., class notes, assignments, and even useful code snippets), grades, and other news and announcements about the course.


Homework Assignments:65%
Final Project:35%


Homework Assignments. There will be about 6-7 homework assignments throughout the semester. Homework assignments must be typed and stapled and electronically submibed through Canvas. All plots included with your assignment should have proper units, labels, colorbars, and cap4ons. These homework assignments are intended for you to apply the knowledge you learn in the course directly to data (either synthe4c or real). Some4mes, I will allow you to subs4tute your own research data (if applicable) in lieu of the provided data to complete a problem in the assignment. This is done so that you have a chance to actually see how to apply these techniques to your own research work. You may work with others on the assignments, but you must turn in your own work.


Final Project. The final project will be a paper and oral presenta4on in which you must use one or more sta0s0cal techniques learned in the course to answer a real research ques4on. The project is to be chosen based on a set of ques4ons that you would like to answer rather than the type of data analysis technique you would like to apply. You will be required to submit an abstract of your work for prior approval. More details will be provided in class.





A main goal of the course is to have you work with data using computer soPware packages and develop your own “sta4s4cal toolbox” for later use. All students who do not have a School of Meteorology (SoM) computer account may obtain one from Shawn Riley (NWC 5640). MATLAB is readily available for use on the MetLab worksta4ons. Python is open-source and can be installed on your own machine. Note: You are free to use whatever soPware package with which you feel most comfortable. I will primarily use Python and some MATLAB in this course for in-class examples, solu4ons, etc. If there are ques4ons or issues with access to soPware, please see me during the first week of class.


Course Style

The overall structure of the class will consist of lectures, both tradi4onal and interac4ve, covering the major topics. I will also present examples in class of using the actual techniques to analyze climate data. Ques4ons and interac4ons during class are welcome and highly encouraged. If you don’t ask ques4ons when things are unclear, then neither of us benefit from classroom lecture.



Reasonable AccommodaCon Policy

The University of Oklahoma is commibed to providing reasonable accommoda4on for all students with disabili4es. Students with disabili4es who require accommoda4on in this course are requested to speak with me as soon as possible. Students with disabili4es must be registered with the Office of Disability Services ( prior to receiving accommoda4ons in this course. The Office of Disability Services is located in Goddard Health Center, Suite 166 (Phone: 405.325.3852 or TDD only 405.325.4173).



Academic Misconduct

Chea4ng is strictly prohibited at the University of Oklahoma. Simply put, it devalues your degree and ends up marring your character and reputa4on. For specific defini4ons on what cons4tutes chea4ng, review the Student’s Guide to Academic Integrity at hbp:// If you are caught chea4ng, I am obligated to report it. Sanc4ons for academic misconduct include expulsion from the University and an F in this course. BOTTOM LINE: Don’t cheat – it’s not worth it.


To be successful in this class, all work must be yours and yours alone. You may work together on homework assignments, but you must submit your own original work for grading.


Religious Holidays

It is the policy of the University is to excuse absences of students that result from religious observances and to provide without penalty for the rescheduling of examina4ons and addi4onal required classwork that may fall on religious holidays. Any student who has a religious holiday fall on a day an assignment is due, please see me no later than one week before the deadline so as to make other arrangements.


Title IX Resources and ReporCng Requirement

For any concerns regarding gender-based discrimina4on, sexual harassment, sexual assault, da4ng/ domes4c violence, or stalking, the University offers a variety of resources. To learn more or to report an incident, please contact the Sexual Misconduct Office at 405.325.2215 (8 AM to 5 PM, Monday-Friday) or Incidents can also be reported confiden4ally to OU Advocates (405.615.0013) 24 hours a day, 7 days a week. Please be advised that a professor/GA/TA is required to report instances of sexual harassment, sexual assault, or discrimina4on to the Sexual Misconduct Office. Inquiries regarding non-discrimina4on policies may be directed to: Bobby J. Mason, University Equal Opportunity Officer and Title IX Coordinator at 405.325.3546 or For more informa4on, please visit  hbp://


Adjustments for Pregnancy/Childbirth Related Issues

Should you need modifica4ons or adjustments to your course requirements because of documented pregnancy-related or childbirth-related issues, please contact me or the Disability Resource Center at 405.325.3852 as soon as possible. Also, see hbp:// for answers to commonly asked ques4ons.



Course Outline – Emphasis will be on applying techniques to data!

I.            Review of Basic StaCsCcs + Least Squares Methods

(a)       Fundamental sta4s4cal measures / Sta4s4cal tests

(b)      Correla4on theory / Regression and correla4on analysis / Mul4-variate regression

(c)       Composite / Epoch analysis

(d)      Significance Tes4ng

(e)       Applica4ons of regression / correla4on theory, (e.g., func4on-fiwng and interpola4on).

II.          Matrix Methods

(a)       Linear algebra review (vector spaces, rank, orthogonality)

(b)      Empirical orthogonal func4ons (EOFs) / principal component analysis (PCA)

(c)       Extended and mul4variate EOFs

(d)      Maximum covariance analysis (MCA) & canonical correla4on analysis (CCA)

III.        Time Series Analysis

(a)       Autocorrela4on

(b)      Harmonic analysis, power spectral analysis, and significance tes4ng for spectral peaks

(c)       Cross-spectral analysis

(d)      Filtering and filter designs – Best prac4ces to use

IV.       AddiConal Topics (as Cme allows)

(a)       Covariance modeling and simple regression models (space and 4me)

(b)      Objec4ve Mapping / Kriging

(c)       Inverse modeling and methods

(d)      Wavelet analysis

Final PresentaCons will be done during the final week of classes and during the Final Exam Period – WEDNESDAY, MAY 10, 2017 1:30 – 3:30 PM


****NO CLASS: Jan 24, 26 (AMS Conference) —> Makeup classes will be scheduled.