


Dr. M. Disney
PB 113, Dept. Geography UCL
Term 1 201415 (15 credits): Course outline & timetable
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 uptodate 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)
 Nonlinear 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:
2011: mock exam paper
2011: actual, with model answers
2012: resit with model answers
2013: actual, with model answers
2014: actual, with model answers
2015: actual, with model answers
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
Timetable (dates/locations)
Lecture Materials and Practical Pages (MD)
Differential equations: Lecture notes (PDF, PPTX)
Differential equations: Practical
Bayesian methods: Lecture notes (PDF, PPTX)
Bayesian methods practicals: practical 1, practical 2
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: nonlinear models. Lecture notes (PDF, PPTX); Gastellu et al. (2003); Saich et al. (2003); some additional notes on nonlinear model inversion.
Model fitting II: nonlinear inversion practical
Monte Carlo methods, and revision: Lecture notes (PDF); Lecture notes (PPTX)
Monte Carlo methods: Practical
Reading list
The Bible
Numerical Recipes: free online outofprint versions. Start here and you won't go far wrong.
Some interesting papers
Chib & Greenberg (1995) Understanding MetropolisHastings, 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) ReactionDiffusion 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.
HaynesYoung, 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.
