Ian Roulstone's home page

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I obtained my BSc in Theoretical Physics from Queen Mary College, University of London, and my DPhil in Mathematical Physics from Oxford University (New College; title of thesis ``A twistor description of the infrared problems of classical fields'', supervised (at various stages) by Andrew Hodges, Roger Penrose and Paul Tod). I spent the years 1989-2003 working as a research scientist at the Met Office, and during my last five years with the Office I worked at the Joint Centre for Mesoscale Meteorology at Reading University. During my career at the Met Office I became very much involved with establishing collaborative projects, which linked the Office to individuals, groups and networks within the academic community. I joined the Department of Mathematics at the University of Surrey in January 2004.

I am a Fellow of the Royal Meteorological Society (co-editor of the Society's Quarterly Journal from 2003-2008 and Chair of the Publications Committee 2006-2008). I am also a member of the London Mathematical Society (Programme Committee 2010-) and a Fellow of the Royal Astronomical Society.

Research Interests

Applied Differential Geometry and Analysis ; Hamiltonian Mechanics ; Control Theory ; Geometric Integration, and the application of these subjects to Meteorology , Numerical Weather Prediction and Data Assimilation .

The Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, hosted a six month programme from 8th July to 19th December 1996 on the Mathematics of Atmosphere and Ocean Dynamics. During that time, over 250 scientists participated in the Programme. This programme initiated many new collaborative projects involving the Met Office, various universities, and other operational forecasting centres. Some of the outcomes of this programme can be found in the two-volume collection of research articles and tutorial material, edited by myself and John Norbury , entitled Large-Scale Atmosphere-Ocean Dynamics; vol. 1 Analytical methods and numerical models and Large-Scale Atmosphere-Ocean Dynamics; vol. 2 Geometric methods and models, published by Cambridge University Press in August 2002.

Collaborative Projects and Networks

I am a co-theme leader of Data Assimilation in the new Natural Environment Research Council's (NERC) National Centre for Earth Observation (NCEO). The NCEO has overall responsibility for NERC's suite of Earth observation centres of excellence. These centres use data from Earth observation satellites to monitor both global and regional changes in the environment, and to develop a detailed understanding of these changes so that future environmental conditions can be predicted. The overall aim of Data Assimilation is to synthesize Earth observation with output from numerical weather prediction and climate models for a number of applications involving environmental prediction. These applications are highly challenging scientifically and technically, and offer considerable benefits to society.

Another recent project, involving colleagues at Aston University, University College London, and at the Met Office, was VISDEM: Variational Inference in Stochastic Dynamic Environmental Models --- funded by the EPSRC. A press release can be found here, and further technical details are available here. At Surrey, Dr. Renata Retkute and myself worked on the Hamiltonian formulation of four-dimensional variational data assimilation.

Another area of interest to me is the application of differential geometry to problems in hamiltonian fluid mechanics. I am working with John Gibbon (Imperial College London) on the transformation properties of the 3D Euler equations using quaternionic geometry. I have long-standing collaborations with Michael Sewell (Reading), Michael McIntyre (DAMTP, Cambridge) and Volodya Roubtsov (Angers), investigating the properties of hamiltonian models of nearly geostrophic flows in terms of contact and Kaehler geometries. There are a number of applications: one is is in a branch of numerical analysis known as geometric integration, and another is the subject of the EPSRC-funded research network Wave-Flow Interactions .


Sylvain Delahaies

PhD Students

I co-supervise David Fairbairn and Matthew Wakeling who are funded by Surrey's EngD programme and the Met Office. David is supervised by Professor Andrew Lorenc , and his project is on long-window 4D variational data assimilation. Matthew is supervised by Dr John Eyre , and his project is on the variational assimilation of satellite imagery.

Former PhD Students (Surrey)

Alison Rudd

Sylvain Delahaies


Recent papers:

Delahaies, S.B., Roulstone, I and Nichols, N.K. 2013 Regularisation of a carbon cycle model-data fusion problem. Submitted to SIADS.

Fairbairn, D., Pring, S.R., Lorenc, A.C. and Roulstone, I. 2012 A comparison of 4D-Var with ensemble data assimilation methods. Accepted by Q. J. R. Meteorol. Soc., and is available on-line

Roulstone, I., White, A.A. and Clough, S. 2013 Geometric invariants of the horizontal velocity gradient tensor and their dynamics in shallow water flow. Submitted to Quart.J.R.Meteorol.S.

Chuter, A.M., Aston, P.J., Skeldon, A.C. and Roulstone, I. 2013 Tipping Points for Forests, Using the Data Assimilation Linked Ecosystem Carbon Model, DALEC. Submitted to Biogeosciences.

Fletcher, S.J., Nichols, N.K. and Roulstone, I. 2010 Flow-dependent balance conditions for incremental data assimilation: elliptic operators (submitted to Quart.J. R. Meteorol. Soc.)


NEW!! Invisible in the Storm: the role of mathematics in understanding weather , by Ian Roulstone and John Norbury. Published by Princeton University Press, March 2013.

REVIEWS: "Mathematicians Ian Roulstone and John Norbury demystify the maths behind meteorology. Trailblazers' work is vividly evoked, from eighteenth-century mathematician Leonhard Euler on hydrostatics to physicist Vilhelm Bjerknes's numerical weather prediction. The pace cranks up with twentieth-century advances such as Jule Gregory Charney's harnessing of the gargantuan ENIAC computer for his work in the 1940s and 1950s on forecasting pressure patterns."--Nature

"[O]ne of the great strengths of the book is the way it picks apart the challenge of making predictions about a chaotic system, showing what improvements we might yet hope for and what factors confound them."--Philip Ball, Prospect

Large-scale atmosphere-ocean dynamics: Volumes I and II, edited by John Norbury and Ian Roulstone. Cambridge University Press 2002.

A selection of preprints:

Roulstone and Sewell 1996 Potential Vorticities in Semi-Geostrophic Theory

McIntyre and Roulstone 1996 Hamiltonian Balanced Models: Constraints, Slow Manifolds and Velocity Splitting

Roubtsov and Roulstone 1997 Examples of quaternionic and Kaehler structures in Hamiltonian models of nearly geostrophic flow (J. Phys. A)

Roubtsov and Roulstone 2001 Holomorphic structures in hydrodynamical models of nearly geostrophic flow (Proc. R. Soc. Lond. A.)

McIntyre and Roulstone 2002 Are there higher-accuracy analogues of semi-geostrophic theory?

Byrom and Roulstone 2002 Calculating vertical motion using Richardson's equation

Dixon and Roulstone 2003 Controlling imbalance within VAR by use of a weak constraint

Lorenc, Roulstone and White 2003 On the choice of control fields in VAR

Cullen, Douglas, Roulstone and Sewell 2005 Generalised semi-geostrophic theory on a sphere (J. Fluid Mech.)

White, Hoskins, Roulstone and Staniforth 2005 Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic (Quart. J. R. Meteorol. Soc.)

Gibbon, Holm, Kerr and Roulstone 2006 Quaternions and particle dynamics in the Euler fluid equations (Nonlinearity)

Wlasak, Nichols and Roulstone 2006 Use of potential vorticity for incremental data assimilation (Quart. J. R.Meteorol. Soc.)

Watkinson, Lawless, Nichols and Roulstone 2007 Weak constraints in four-dimensional variational data assimilation (Met. Zeits.)

Hyper-Kaehler geometry and semi-geostrophic theory, with Delahaies, published in Proc. R. Soc. Lond. A.(2009)

Kaehler geometry and Burgers' vortices, with Banos, Gibbon and Roubtsov, published in Proc. Math. Inst. Natl. Acad. Sci. Ukraine (2009)

A geometric interpretation of coherent structures in Navier-Stokes flows, with Banos, Gibbon and Roubtsov, published in Proc. R. Soc. Lond. A. (2009)

Rudd, A.C., Roulstone, I. and Eyre, J. 2012 A simple column model to explore anticipated problems in variational assimilation of satellite observations, J. Environmental Modelling & Software, 27-28: 23-39. http://dx.doi.org/10.1016/j.envsoft.2011.10.00

Roulstone, I. and Sewell, M.J. 2012 Complex contact and lift transformations. J. Geometry and Physics., Volume 65, March 2013, 55-65.

Hobbies and Pastimes

Church Bellringing ; Walking in the Yorkshire Dales (and elsewhere) --- and driving there in my Aston Martin

17th May, 2013