VVZ API is not affiliated with ETH Zurich. Data might be outdated or incorrect. Please view the official ETHZ Vorlesungsverzeichnis for binding information.

701-0461-00L 3 Credits BSC , MSC D-USYS , D-ERDW , D-CHAB
You're viewing possible stale or outdated data. Please check the latest semester for more up-to-date information.

Numerical Methods in Environmental Sciences

Numerische Methoden in der Umweltphysik

Lecturers & Examiners: Prof. em. Dr. Christoph Schär, Dr. Christian Zeman
VVZ CR n/a

Last Updated: 2026-02-05 15:48:48

Abstract

This lecture imparts the mathematical basis necessary for the development and application ofnumerical models in the field of Environmental Science. The lecture material includes an introduction into numerical techniques for solving ordinary and partial differential equations, as well as exercises aimed at the realization of simple models.

Objective

This lecture imparts the mathematical basis necessary for the development and application of numerical models in the field of Environmental Science. The lecture material includes an introduction into numerical techniques for solving ordinary and partial differential equations, as well as exercises aimed at the realization of simple models.

Content

Classification of numerical problems, introduction to finite-difference methods, time integration schemes, non-linearity, conservative numerical techniques, an overview of spectral and finite-element methods. Examples and exercises from a diverse cross-section of Environmental Science. Three obligatory exercises, each two hours in length, are integrated into the lecture. The implementation language is Python (previous experience not necessary: a Phython introduction is given). Example programs and graphics tools are supplied.

Resources

Lecture Notes

Per Web aufLink

Literature

List of literature is provided.

Learning Materials (Links)

General Information

Language
German
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 60 minutes
Aids
4-seitige, handschriftliche Zusammenfassung.Fachneutrales Wörterbuch für fremdsprachige Studierende erlaubt.

Course Components

Type Title Time & Place Hours
lecture with exercise Numerische Methoden in der Umweltphysik
  • Thu 08:15-10:00 (CHN E 46)
2 h weekly

Offered In

  • Earth and Climate Sciences Bachelor
  • Environmental Sciences Bachelor (Students can choose between one Bachelor thesis of 10KP or two Bachelor theses of 5KP each. In principle, all professors and lecturers involved in the teaching of the Environmental Sciences degree programme are entitled to supervise a Bachelor's thesis (BA). BA in the area of social sciences and humanities can only be supervised by lecturers who teach in this area. The same applies to BA in the field of natural sciences and technology. If the thesis is supervised by a person who does not teach in the Environmental Sciences degree programme or who does not have ETH lecturer status, then the student has to fill in the "Form for supervisors of a Bachelor thesis who do not teach in the Environmental Sciences degree programme" Link)
    • Specialization in an Environmental System
      • Atmosphere and Climate (The following courses are highly recommended as preparation for the Specialization in Atmosphere and Climate: 701-0106-00L Mathematik V: Angewandte Vertiefung von Mathematik I - III (Spring semester) 402-0048-00L Fortgeschrittene Physik für Umwelt- und ErdwissenschaftlerInnen (Spring semester) These courses should be successfully completed during the second year.)
  • Interdisciplinary Sciences Bachelor
    • Physical-Chemical Direction
      • 3. Semester (Physical-Chemical Direction)
        • Electives (The Bachelor's programme in Interdisciplinary Sciences allows students to choose from any subject taught at a Bachelor level at ETH Zurich. In consultation with the Director of Studies of Interdisciplinary Sciences, every student must establish his/her own individual study programme at the beginning of the 2nd year. See the Programme Regulations 2018 for further details.)
  • Environmental Sciences Master
  • Atmospheric and Climate Science Master
    • Electives (The students are free to choose individually from the entire course offer of ETH Zürich and the universities of Zürich and Bern.)
      • Prerequisites (The definition of prerequisites is part of the admission procedure for the master studies. You are informed by the admission office as to what courses of the section «prerequisites» you have to catch up with. You are accredited for these courses in the electives block of the master studies.)