My Research

Over the years, my research has covered a wide variety of areas and I highlight some of them below (see my CV for a full publication list). A common theme running through my research work has been nonlinearity. A nonlinear system is one whose outputs are not in direct proportion to their inputs (you will be very happy to win $100 million on the lottery, but likely you will not be twice as happy to win $200 million). Nonlinear systems can exhibit unexpectedly beautiful properties (e.g., when they generate fractal geometries) and feel much less artificial to my mind than do linear systems.

1. My PhD research was in the field of Einstein’s nonlinear general theory of relativity at the University of Oxford. My teachers were Roger Penrose and Dennis Sciama (himself a student of Paul Dirac). One of the main outcomes of my research was an expression for the energy and momentum of a gravitational wave, which could be defined in fully general circumstances. The expression was “quasi-local” which meant it could be defined in a small-region of space-time, but not at a point in space-time.

https://journals.aps.org/prd/abstract/10.1103/PhysRevD.18.4399

2. After my PhD, I changed fields, which I write about in The Primacy of Doubt. One of my first papers concerned the co-discovery with Michael McIntyre of the University of Cambridge of the world’s largest breaking waves: so-called Rossby waves in Earth’s Stratosphere. The tip of one of these breaking waves can extend tens of thousands of kilometres around the Earth. One of the key sources of these waves are the big mountain ranges in the Northern Hemisphere. The general lack of such breaking waves in the Southern Hemisphere is the key reason why the ozone hole was discovered in the Antarctic and not the Arctic.

https://www.nature.com/articles/305593a0

3. On a much smaller scale of tens of kilometres, gravity waves produced by flow over individual mountains can break a few km up in the atmosphere, effectively slowing the atmospheric circulation at these levels. These waves are too small in scale to be represented directly in weather and climate models. With Glenn Shutts and Richard Swinbank, we developed a simplified mathematical representation of orographic gravity wave drag. This had a major impact improving the skill of forecasts of the jet stream, and reducing the systematic errors of climate models.

https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.49711247406

4. At the beginning of my meteorological career, the African Sahel was suffering a devastating long-term drought. The 1985 Live Aid concert raised money to help bring food to those in need. But what caused the drought? One popular theory at the time was that it was caused by over-grazing of the land in the Sahel. However, with colleagues Chris Folland and David Parker, we showed it was in fact caused by decadal timescale variability in the tropical oceans, primarily in the tropical Atlantic Ocean.

https://www.nature.com/articles/320602a0

https://www.nature.com/articles/322251a0

5. One of my main contributions has been in pioneering the development of probabilistic ensemble prediction methods in weather prediction (I acknowledge my many colleagues on this in The Primacy of Doubt. The theoretical motivation for ensemble prediction comes from chaos theory: less the idea that chaotic systems are unpredictable in the long range, but more the idea that chaotic systems can, on occasion, be unpredictable even in the very short range. I write about this in The Primacy of Doubt.

https://rmets.onlinelibrary.wiley.com/doi/full/10.1002/qj.3383

6. I led a European Union climate project developing the first multi-model ensemble system of coupled ocean-atmosphere models for seasonal climate prediction. Multi-model ensembles are now used extensively in the Intergovernmental Panel on Climate Change reports. These ensembles have pros and cons as I discuss in The Primacy of Doubt.

https://journals.ametsoc.org/view/journals/bams/85/6/bams-85-6-853.xml

7. One important nonlinear phenomenon in the atmosphere are circulation regimes – anomalies in circulation patterns that can last weeks or even months or more. Such regimes are frequently associated with extreme weather. I argue that to be able to predict the impact of climate change on the regional scale, it is vital that models can predict such nonlinear regimes. This is still a problematic area in climate modelling.

https://journals.ametsoc.org/view/journals/clim/12/2/1520-0442_1999_012_0575_andpoc_2.0.co_2.xml

8. My own strong belief is that we will need much higher resolution climate models to advance our ability to predict climate change regionally (e.g., to simulate the statistics of these circulation regimes accurately). Providing the dedicated exascale computing facilities such high resolution models will need will likely require international collaboration to create some kind of “CERN for Climate Change”. The important EU Destination Earth programme, whose goal is the development of models with km-scale grids, arose directly from a meeting I held at the Royal Society to raise awareness of this issue.

https://www.nature.com/articles/515338a

https://www.pnas.org/doi/10.1073/pnas.1906691116

9. Although the equations of a weather or climate model are formally deterministic, there are good reasons (discussed in The Primacy of Doubt) for adding random noise to the equations (through what are called stochastic parametrisations). Such noise provides a representation of model uncertainty in ensemble predictions. However, it can also help reduce the systematic errors of such models.

https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.49712757202

https://www.nature.com/articles/s42254-019-0062-2

10. If we add noise to the equations, then we do not need to run our models using high-precision (64 bits) numerical representations of model variables. This contributes to inefficient code when models are run on big computers. The work I started in this area led to the European Centre for Medium Range Weather Forecasts reducing the numerical precision of its variables, which allowed it to increase the resolution of its models and thereby improve the skill of its forecasts, at no extra computation cost, for the benefit of billions around the planet.

https://doi.org/10.1098/rsta.2013.0391

https://rmets.onlinelibrary.wiley.com/doi/full/10.1002/qj.4181

11. My interests in the constructive role of noise in nonlinear systems got me interested in the brain. With computational neuroscientist Michael O’Shea from the University of Sussex, we proposed that the brain makes constructive use of noise in helping us become the creative species we are. I discuss this in The Primacy of Doubt.

https://www.frontiersin.org/articles/10.3389/fncom.2015.00124/full

12. Returning to my roots in fundamental physics, I now believe that the nonlinear fractal geometries of chaos theory underpin quantum physics. I write about this extensively in The Primacy of Doubt. Such geometries may provide an understanding of the experimental violation of Bell’s inequality in a deterministic setting without requiring Einstein’s “spooky action at a distance”. This, I feel, will be the route to synthesising quantum and gravitational physics. It’s something I will be pursuing vigorously in the years to come.

https://royalsocietypublishing.org/doi/full/10.1098/rspa.2019.0350

https://avs.scitation.org/doi/abs/10.1116/5.0060680