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701-0461-00L 3 Credits BSC , MSC D-USYS , D-ERDW , D-CHAB

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Numerical Methods in Environmental Physics

Numerische Methoden in der Umweltphysik

Lecturers & Examiners: Prof. em. Dr. Christoph Schär, Dr. Christian Zeman

VVZ CR n/a

Last Updated: 2026-02-05 16:01:02

Abstract

This lecture conveys 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 using the computer language Python.

Objective

Ability to develop simple numerical schemes and to implement these schemes using the programming language Python. Ability to critically use more complex numerical models.

Content

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

Resources

Lecture Notes

Per Web aufLink

Literature

List of literature is provided.

Learning Materials (Links)

Main link
Information

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
- Majors
  - Major: Climate and Water (Advisor of the BSc-major "Climate and Water" is Dr. Hanna Joos, Institute for climate and atmosphere (IAC).)
    - Advanced
Environmental Sciences Bachelor
- 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
- Major in Atmosphere and Climate
  - Prerequisites
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.)