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

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Numerical Methods in Environmental Sciences

Numerische Methoden in der Umweltphysik

Lecturers & Examiners: Prof. em. Dr. Christoph Schär, Dr. William Barton Sawyer

VVZ CR n/a

Last Updated: 2026-02-05 15:06:21

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 Matlab (previous experience not necessary: a Matlab introduction is given). Example programs and graphics tools are supplied.

Resources

Lecture Notes

Is provided (CHF 10.- per copy).

Literature

List of literature is provided.

General Information

Language: German
Levels: BSC , DS , MSC
Frequency: Yearly recurring

Examination

Type: session examination
Mode: written 60 minutes
Aids: 10-seitige, handschriftliche Zusammenfassung

Course Components

Type	Title	Time & Place	Hours
lecture with exercise	Numerische Methoden in der Umweltphysik	Thu 08:15-10:00 (HG E 41) 23.11 Date 08:15-10:00 (HG D 12) 30.11 Date 08:15-10:00 (HG D 12) 11.01 Date 08:15-10:00 (HG D 12) 25.01 Date 08:15-10:00 (HG D 12)	2 h weekly

Offered In

Earth Sciences
- Advanced Studies (These courses normally have to be attended in the 5th or the 7th semester. The complementary courses are sumarized at the end.)
  - Major in Geophysics (Cc)
  - Major in Climate Sciences and Hydrology
    - Major in Climatology (Cd1)
      - Compulsory (List 1.1):
    - Major in Hydrology (Cd2)
      - Compulsory (List 1.2):
Earth Sciences Bachelor (Information on the Bachelor: )
- BSc 5. Semester
  - Major in Climate and Water: Electives
    - Major in Climate and Water: Core Courses (From the list of core courses offered in winter and summer semester 14 credit points must be aquired.)
Environmental Sciences Bachelor
- 5. Semester
  - Specialization in an Environmental System
    - Atmosphere and Climate
Interdisciplinary Sciences Bachelor
- Physical-Chemical Direction
  - 3. Semester (Physical-Chemical Direction)
    - Compulsory elective subjects (Further combinations of Compulsory elective subjects arising upon specific written request by the students and permission by the Director of studies.)
- Biochemical-Physical Direction
  - 3. Semester (Biochemical-Physical Direction)
    - Compulsory elective subjects (Further combinations of Compulsory elective subjects arising upon specific written request by the students and permission by the Director of studies.)
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.)