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1. Course title

Continuum theory applications in snow and ice research
Continuum theory applications in snow and ice research
Continuum theory applications in snow and ice research

2. Course code


Aiemmat leikkaavat opintojaksot 535039 Continuum theory applications in snow and ice research, 5 op.

3. Course status: optional

-Which degree programme is responsible for the course?
Master's Programme in Atmospheric Sciences

-Which module does the course belong to?
ATM300 Advanced Studies in Atmospheric Sciences (optional for Study Track in Geophysics of the hydrosphere)

-Is the course available to students from other degree programmes?

4. Course level (first-, second-, third-cycle/EQF levels 6, 7 and 8)

Master’s level, degree programmes in medicine, dentistry and veterinary medicine = secondcycle
degree/EQF level 7
Doctoral level = third-cycle (doctoral) degree/EQF level 8

-Does the course belong to basic, intermediate or advanced studies (cf. Government Decree
on University Degrees)?
Advanced studies

5. Recommended time/stage of studies for completion

-The recommended time for completion may be, e.g., after certain relevant courses have
been completed.

Can be taken earlier, but it is recommended to take the course at an advanced stage

6. Term/teaching period when the course will be offered

-The course may be offered in the autumn or spring term or both.
-If the course is not offered every year, this must be indicated here.
-Specification of the teaching period when the course will be offered

Given every second year (even years) in the spring term (next spring 2022)

7. Scope of the course in credits

5 cr

8. Teacher coordinating the course

Thomas Zwinger

9. Course learning outcomes

-Description of the learning outcomes provided to students by the course
- See the competence map (

• Background information on problems in cryospheric science, mainly focused on ice sheet and glacier flow and elastic

deformation of ice

• General Introduction to continuum mechanics:

• Basic definitions. Different vector products. Vector transformations. Different notations. Invariants of tensors.

• Balance Equations in general

• Material and local time derivatives. Reynolds transport theorem. Discontinuities on surfaces. Conservation of mass/linear- and angular momentum/energy. Closure relations

• Dimensional analysis: non-dimensional groups, scaling and expansion of equations (in particular to Stokes equation)

• Similarity relations

• Fluids (rheology of ice in detail), solids linear elasticity, heat transfer

• anisotropic behaviour

• Numerical solution of continuum problems:

• Numerical methods (finite difference, volume and element method), basics of solution of linear systems, discussion of sources of errors to approximations (discretization/truncation error), types of boundary conditions

• Applications: We use a FEM package (Elmer/Ice) for setting up numerical simulations of  some of these topics: Alpine Glacier response to climate change, Ice sheet dynamics, short-time linear response of ice, thermal-structure in ice.

10. Course completion methods

-Will the course be offered in the form of contact teaching, or can it be taken as a distance
learning course?
-Description of attendance requirements (e.g., X% attendance during the entire course or
during parts of it)
-Methods of completion

The course consists of a mixture of lectures and exercises. As these are tightly connected, it is recommended to attend both not to detach from the topics. Definitely, this course is not able to be completed as a distance learning course.

11. Prerequisites

-Description of the courses or modules that must be completed before taking this course or
what other prior learning is required

We expect basic knowledge of mathematics (calculus) and basic computational skills (we use LINUX), hence earlier courses in these disciplines should have been accomplished.

12. Recommended optional studies

-What other courses are recommended to be taken in addition to this course?
-Which other courses support the further development of the competence provided by this

It is recommended (but not mandatory) to attend the course ATM343 Glaciology in advance

13. Course content

-Description of the course content

The course consists of a mixture of lectures and exercises. The aim is to introduce the theoretical concepts and immediately do the exercises to deepen the understanding. In the end of the course the students will take on a project that demands the application of the transferred knowledge.

14. Recommended and required literature

-What kind of literature and other materials are read during the course (reading list)?
-Which works are set reading and which are recommended as supplementary reading?

The course will be supported by material distributed via Moodle (incl. lecture slides)

Main literature the course is based on (for continuum mechanic theory and glaciological models):

    Greve, R. & Blatter H., Dynamics of Ice Sheets and Glaciers, Springer, 2009

For project work it might be possible that we study certain scientific articles, which will be provided in case

15. Activities and teaching methods in support of learning

-See the competence map (
-Student activities
-Description of how the teacher’s activities are documented

Weekly lectures and and exercises (individual work).

16. Assessment practices and criteria, grading scale

-See the competence map (
-The assessment practices used are directly linked to the learning outcomes and teaching
methods of the course.

The final grade is based on the exercise results and the performance within a project work at the end of the course.

17. Teaching language


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