Aim
The mathematical tools and models that engineers has long used e.g. for designing factories is today also used to describe natural systems and how human activities affect these systems. Mathematical models, e.g. of the climate regulation mechanisms of our earth, currently has a great impact on what we conceive to be politically, economically and socially feasible.

The aim with this course is that the student should learn to identify as well as orally, graphically and mathematically describe feedbacks in biogeochemical systems, thereby achieving a deep understanding for the limitations of the mathematical models that politicians and scientists refer to.

Knowledge and understanding
For a passing grade the student must

• identify crucial feedbacks of a given system and visualize these graphically in a Causal Loop Diagram (CLD)

• based on a CLD for a given system determine Reference Behaviour Patterns (RBP) for the system, i.e. be able to analyse what dynamic behaviour that is typical for the class off systems that can be described by a similar CLD.

Skills and abilities
For a passing grade the student must

• build a mathematical model for a simple biogeochemical system and be able to critically analyse the uncertainty and sensitivity associated with the model.

• be able to discuss the difference between uncertainty and variability, uncertainty in model structure and uncertainty in model parameterization as well as what epistemological uncertainty is.

• orally and in writing be able to disseminate model results in a short and concise manner.

Judgement and approach
For a passing grade the student must

• have a scientific and critical attitude towards mathematical models of natural systems have a fundamental insight into how mathematical models influence policy and politics

Contents
The course is built upon a number of simulation tasks. The simulation tasks can concern e.g. soil acidification/recovery, eutrophication, the global carbon cycle, etc. and cover chemical and physical processes as well as ecological processes and population dynamics. Each simulation task is supported by an overview of relevant theory. The course also cover more general theoretic aspects including

Systems Analysis: Causal Loop Diagrams (CLD), reinforcing and balancing feedback loops, Reference Behaviour Patterns (RBP).

The fundamentals of: Model robustness and deterministic chaos. Uncertainty/sensitivity analysis. Monte Carlo simulation and sampling strategies. Spatial and temporal variability. Classification of sources of uncertinaty. Population dynamics: Intensity based models, individually based models and cohort models.

Literature
Reference literature, simulation task specific compendiums available as handouts or as PDF-files.