Offered in association with Fenner School.

In this course the major model types used to represent environmental systems are studied. Mathematical emphasis on how they are constructed will use the theory of inverse problems while the practical emphasis uses systems methodology. The focus will be on hydrological systems and their basic processes, combined with the constraints imposed by the limitations of real observational data.

It will be assumed that students have a reasonable grasp of different model types (time series, PDE/ODE-based models, frequency domain models) as well as understanding of the issue of uncertainty in model inputs, structure and observed outputs.

The assessment of the course will be based on written reports on selected papers, as well as a project exploring a particular paper/model in more detail. The key component of the project will be proposing potential improvements in the work done, and doing at least some initial work on evaluating these improvements. This will include components of:

• analytical evaluation of model behaviour

• coding the original and improved versions of the model and conducting sensitivity analysis

• exploration of structure of uncertainty in model inputs.

• Propagating uncertainty in inputs through the model

Note: Graduate students attend joint classes with undergraduates but are assessed separately.

On satisfying the requirements of this course, students will have the knowledge and skills to:

1. Describe the basic processes and behaviour of different environmental systems and the major methods of modelling these (e.g. model family selection, model structure identification, parameter estimation, sensitivity assessment, optimisation).

2. Be able to apply the concept of tradeoffs and uncertainty sources in decision-making and optimisation through critical evaluation of case studies referring to hydrology, ecology, water quality and socioeconomics.

3. Evaluate the issues in building and evaluating models; formulate treatment of complex real-world problems (not just environmental problems); and select appropriate frameworks and methods to solve these, including using computer platforms and the statistical R package.

4. Communicate and engage with interest groups involved in a problem; and appreciate how integrated assessment can be used for managing our environment more sustainably, and the valuable role played by modelling.

5. Build a model of a system, drawing on an existing understanding of the typical behaviour of the system and available data.

6. Be able to critically evaluate the limitations of a model, and identify and conduct research that will enable improvements in the model.

Assessment will be based on:

• Five reviews of selected papers (50%; LO 1, 2)

• Two presentations (10%; LO 3, 4)

• Project (40%; LO 5 and 6)

36 lectures and regular tutorials

Bachelor degree; with second year Maths.

Third year Mathematics is required.