Single-Course English 10 ECTS

Environmental Modelling

Overall Course Objectives

This course aims to provide students the basic knowledge to work with mathematical models and apply them to environmental problems, providing the theoretical basis for subsequent applications in specialization courses. The course has four major elements: i) simple mass balances using big environmental datasets, ii) deterministic modelling using ordinary differential equations, iii) deterministic modelling using partial differential equations and iv) model optimisation, sensitivity analysis and uncertainty analysis. The course builds on a series of examples drawn from the field of environmental engineering and employs programming tools and languages (e.g., COMSOL Multiphysics, Python) to illustrate the general modelling principles. The course will teach students how to integrate observed data with models and apply them to describe environmental problems and evaluate model results .

Learning Objectives

  • Apply fundamental physical, chemical and biological knowledge to mathematically describe an environmental problem
  • Identify and describe the governing processes, boundary and initial conditions that are relevant to environmental problems.
  • Formulate mass balances, ordinary and partial differential equations based on process understanding
  • Employ numerical and analytical techniques, using programming and modelling tools to simulate environmental systems
  • Evaluate model results and their uncertainty
  • Understand model behaviour through sensitivity analysis
  • Apply parameter estimation by employing measured data
  • Communicate modelling results in a clear, concise, and convincing manner

Course Content

Topics will include selections from the following: Modelling terminology; model building process; zero-dimensional mass balances of environmental problems; environmental models based on coupled ordinary and partial differential equations, including modelling of mass and energy conservation and reactive transport, and models of microbial processes; sensitivity analysis; parameter estimation and optimisation; stochastic modelling; programming. Example cases are taken from the fields fate and effects of chemicals in the environment, groundwater flow and transport, and urban water systems.

Recommended prerequisites

Mathematics, chemistry, physics, and environmental processes (12102) or similar (basically the same prerequisites as required for admission to the MSc Environmental Engineering). Programming (mainly in Python)

Teaching Method

The underlying teaching philosophy is problem based learning. The core of the course consists of a series of tutorials and assignments, which should expose the students to the most important techniques used in environmental modelling. The tutorials and assignments are supported by focussed reading, discussion, and lectures.


The course is a mandatory general competence course for the MSc in Environmental Engineering.
It is recommended that MSc students complete the course in their first year of study.
3rd year BSc students are also welcome to take the course.

See course in the course database.





13 weeks




DTU Lyngby Campus

Course code 12104
Course type Candidate
Semester start Week 35
Semester end Week 48
Days Tues 8-12, Fri 13-17

15.000,00 DKK