Course description: The course examines nonlinear motion in the atmosphere and ocean from the perspective of turbulence theory. We begin with a simplified system to illustrate how linear motion becomes chaotic with nonlinearity. Then we examine Kolmogorov’s theory of 3-D turbulence, and its extension to two dimensions. We consider the implications for weather predictability and discuss how geophysical effects (the earth’s rotation, stratification) alter the flows. Then we consider the dispersion of passive tracers, like volcanic ash and spilled oil, in turbulent flows.
Outcomes: The students will learn basic elements in statistics and chaos theory. The student will also learn how nonlinear processes fundamentally affect the dynamics of atmospheric and oceanic flows, in particular by making them unpredictable, requiring statistical descriptions. Nonlinear processes are central to many observed phenomena, such as storm interactions and the transport of heat, pollutants and biological material.
Structure: The course will be held over two weeks, with five three hour lectures the first week and four the second week. The lectures will be given via video link, so the students will be able to attend at their home institutions. Problems are given out underway, and the students will present the results each morning. The students will also make a final presentation on a topic of interest to them which is also relevant to the course. There is no exam. The course has its own compendium, though supplemental reading will be suggested.
Week 13, 2019 – Lectures Monday to Friday 9:15 – 12:00
Week 19, 2019 – Lectures Monday to Thurdsay 9:15 – 12:00, Presentations Friday 9:15 – 15:00
Lecture 1: Statistics in a nutshell; Fourier transforms
Lecture 2: Chaos in a simplified system
Lecture 3: Energy conservation, triad interactions
Lecture 4: Kolmogorov’s theory for 3-D turbulence
Lecture 5: 2-D turbulence
Day 10: Student presentations
Responsible: Joe LaCasce / UiO
International lecturer: Jonathan Lilly / Theiss Research
Max. no. of participants: 12 CHESS students (total participants 24)
Credit points: 3 ECTS
Registration form here. Deadline: 3 May
Submitted applicant list
Course description: This course introduces students to essential tools for analyzing any type of dataset from oceanography, atmospheric science, or climate. The centerpiece, called “distributional data analysis”, is a simple yet powerful method for delving into a potentially large, multivariate dataset by examining its statistics in two-dimensional slices. Elementary statistics for univariate or bivariate (e.g. velocity) datasets, simple filtering, data organization and manipulation techniques in Matlab, and data visualization strategies are all addressed. The course also provides innovative training in the mental factors of curiosity, imagination, and objectivity that are essential for observationalists. Students apply techniques to their own datasets, and learn further through homework problems and group exercises.
This will be the third time the course is offered. By popular demand, this iteration focuses on a greatly expanded version of the “low-tech” methods that form the foundation of the data analyst’s toolbox.
Structure: Lectures will be given in the mornings and lab sessions in the afternoons, allowing the students to apply the methods directly to data at once. In addition to a physical classroom in Oslo, lectures will also be available via video link. Students are expected to bring a dataset of any type that they would like to analyze for a course project. Multivariate datasets are encouraged. Model output is also acceptable. The students employ the statistical and time series analysis toolbox jLab developed by the instructor (http://jmlilly.net/jmlsoft.html). Course notes are available online at http://jmlilly.net/course (specifically chapters 1-8).
Outcome: At the end of the course, students will be well-prepared to begin efficiently analyzing any dataset they might encounter, while avoiding common pitfalls. Students gain practical experience through hands-on demonstrations and exercises in Matlab.