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Dr. M. Disney
PB 113, Dept. Geography UCL

## Term 1 2017-18 (15 credits): Course outline & timetable

### Staff: Dr M. Disney (MD, convenor), Dr. Jon Iliffe (JI).

Contact
MD: mathias.disney@ucl.ac.uk
JI: j.iliffe@ucl.ac.uk

## Course Aims

• To provide an introduction to mathematical and computational methods for modelling applications, both analytical and numerical;
• To provide a general framework for the problems and issues of developing forward and inverse models;
• To provide practical analytical and numerical skills for both forward and inverse modelling;
• To provide example applications of the techniques covered;
• To cover generic issues arising in application of analytical and numerical approaches including discretisation, detail vs computation time, stochastic processes etc.;
• To provide exposure to numerical tools that are used in a wide range of modelling applications.

## Content

A detailed outline of the course, plus reading lists, timetables etc is given here (PDF).

Moodle: GEOGG121 but note these pages are the most up-to-date resource for this module. The module will provide an introduction to a range of fundamental concepts and principles for handling and manipulating data. The module will cover:

• Elementary differential and integral calculus and its applications (equations of motion, areas and volumes etc)
• Linear algebra and matrix methods, including computational issues (decomposition for eg) and generalised linear models
• Overview of statistical methods
• Introduction to ODEs and their applications
• Numerical methods, Bayesian parameter estimation, model fitting, numerical optimisation, including Monte Carlo & Bayesian methods
• Time series analysis and spatial methods

The main sessions include:

```    - Introduction to calculus methods (JI)
- Introduction to linear algebra, matrices (JI)
- Statistics and further statistics (JI)
- Least Squares and further least squares (JI)
- Introduction to differential equations (MD)
- Linear models, inversion methods and applications (MD)
- Non-linear models, parameter estimation, curve fitting (MD)
- Introduction to Bayesian parameter estimation methods (MD)
- Introduction to Monte Carlo methods & misc methods(MD)
```

## Format

The course is a mixture of lectures and practical sessions. There will be a range of practical sessions and problem solving classes, including assessment of submitted problems (in Dr. Iliffe's component of the course), and guided computer practical sessions (Dr. Disney's component of the course). Students are expected to take notes as they see fit during practical sessions (not just lectures), and to put in additional practical time outside timetabled sessions to consolidate their work.

## Assessment

Assessed coursework for the first part of the course, handed in online; 2 hour unseen examination for the second part, which takes place at the start of Term 2.

Example exam papers are provided here, including a mock paper from the first year of the course and some papers including model answers. The format of the exam is to answer TWO questions from a total of 5, in 2 hours. As you'll see the questions are a mixture of simple calculations, explanation and discussion of some of the methods covered in the second half of the module:

## Learning outcomes

At the end of the course students should:

• Understand the general requirements for forward and inverse modelling in environmental sciences
• Have a sound grasp of some of the fundamental methods required for scientific data analysis.
• Understand and be able to apply a range of mathematical and technical concepts and methods to environmental modelling problems
• Be aware of the strengths and limitations of some of the more common mathematical and technical approaches in modelling
• Demonstrate knowledge and understanding of a range of mathematical and computational modelling tools
• Have some knowledge of the wider literature, both technical and theoretical, covering implementation and application of the methods covered in the course

## Lecture Materials and Practical Pages (MD)

• Differential equations: Lecture notes (PDF, PPTX)
• Differential equations: Practical
• Model fitting I: linear models. Lecture notes (PDF, PPTX); Lewis's notes on linear modelling (docx); some additional notes on linear models and methods.
• Model fitting I: linear model inversion practical
• Model fitting II: non-linear models. Lecture notes (PDF, PPTX); Gastellu et al. (2003); Saich et al. (2003); some additional notes on non-linear model inversion.
• Model fitting II: non-linear inversion practical
• Bayesian methods, Monte Carlo intro and revision: Lecture notes (PDF)
• Bayesian exercises: practical 1 Jupyter notebook, practical 2 Jupyter notebook. You should copy and run these locally.
• Monte Carlo exercise: Practical Jupyter notebook. Copy and run locally also.

The Bible
• Numerical Recipes: free online out-of-print versions. Start here and you won't go far wrong.

Some interesting papers

• Chib & Greenberg (1995) Understanding Metropolis-Hastings, Chib and Greenberg; an older but thorough description (somewhat technical).
• Dowd (2007) Bayesian statistical data assimilation for ecosystem models using Markov Chain Monte Carlo; an example of MCMC in action, not too technical.
• Kondo and Miura (2010) Reaction-Diffusion Model as a Framework for Understanding Biological Pattern Formation, a really nice review of the subject, plus supplementary material with a downloadable model to play with.

Material and examples are taken from some of these texts. Where a text is key, this will be detailed in the lectures and/or practicals, along with web links.

Barnsley, M. J., 2007, Environmental Modeling: A Practical Introduction, CRC Press, 432pp.
Boas, M. L., 198s (2nd ed) Mathematical Methods in the Physical Sciences, Wiley, 793pp.
Boeker, E. and van Grondelle, R., 2001, Environmental Science, Physical Principles and Applications, 2nd ed, Wiley.
Campbell, G. S. and J. Norman (1998) An Introduction to Environmental Biophysics, Springer NY, 2nd ed.
Croft, A., Davison, R. & Hargreaves, M. (1996) Engineering Mathematics, 2nd ed., Addison Wesley.
Flake, W. G., 2000, Computational Beauty of Nature, MIT Press.
Gauch, H., 2002, Scientific Method in Practice, CUP.
Gershenfeld, N., 2002, The Nature of Mathematical Modelling, CUP.
Goodchild, M.F., Parks, B.O. and Steyaert, L.T. 1993 Environment al Modelling with GIS, Oxford: Oxford University Press.
Hardisty et al., 1993, Computerised Environmental Modelling: A practical introduction using Excel, John Wiley and Sons.
Haynes-Young, R. and Petch, J. 1986 Physical Geography: its nature and methods, (London: Harper Row).
Kirkby, M. J., Naden, P. S., Burt, T. P. and Butcher, D.P. 1993 Computer Simulation in Physical Geography, (Chichester: John Wiley and Sons).
Monteith, J. L. and Unsworth, M. H., Principles of Environmental Physics, Edward Arnold.
Riley, K. F., M. Hobson & S. Bence (2006) Mathematical Methods for Physics & Engineering, 3rd ed., CUP.
Sivia, D. S., with J. Skilling, 2008 (2nd ed) Data Analysis: A Bayesian Tutorial, OUP, 246pp.
Wainwright, J. and Mulligan, M., 2004, Environmental modelling: finding simplicity in complexity, Chichester, Wiley.

•   Maintained by Mathias Disney Last Updated: Nov 2014

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