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Dynamics of tropical convection and the large-scale tropical circulation

Prof Douglas Parker (SEE), Dr Juliane Schwendike (SEE), Lorenzo Tomassini (Met Office)

Project partner(s): Met Office

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This project will advance our theoretical understanding of the most important dynamical processes in the tropical atmosphere, namely the interactions between convective clouds and their large-scale environment. This is one of the most critical unsolved theoretical questions in climate science, and we seek an ambitious and capable mathematician or physicist with an interest in solving real-world problems.

Deep convection in the tropics is the engine-room of the global climate, communicating energy, momentum and water between the major climatic systems (earth, atmosphere and ocean). Convection is really the driver of the tropical circulation, and tropical-extratropical transitions are important for weather prediction all over the globe. Convective clouds also deliver heavy rainfall and winds, and are the drivers of much of the severe weather experienced in the tropics. Despite their importance, these clouds remain very poorly predicted, and their feedback on the climate system is one of the biggest uncertainties in weather and climate prediction. The cloud systems are able to self-organise, through fluid-dynamical interactions, so that elements on the scale of 10km can organise into systems lasting many hours or days, on scales of 100s of kilometres. The project will use observations, numerical model simulations and mathematical theory to advance our understanding of how these storms interact with the circulation systems of the Earth’s tropics.


This is a mathematical and theoretical project which will explore the relationship between atmospheric circulation and convective (cumulonimbus) storms in the atmosphere. The project will exploit the new generation of numerical modelling products, in the form of very high resolution atmospheric simulations with an operational weather prediction model. These model simulations will be used to test and develop mathematical models for the ways in which latent heating in clouds influences atmospheric circulation, on scales from a few kilometres (individual thunderstorms) up to a few thousand kilometres (e.g. waves, cyclones and monsoons).

Figure 1: Cumulus congestus clouds, and a rare pileus cloud (the “cap” on the congestus) observed in a research flight during the African Monsoon Multidisciplinary Analysis (AMMA) experiment in 2006. These clouds transport water vapour, momentum and other atmospheric constituents very rapidly through the troposphere. They also release latent heat and moisten the air, pre-conditioning the air for future storms.

Water plays a remarkable role in the dynamics of the Earth’s atmosphere. Water is abundant in the atmosphere, in its three phases; gas, liquid and solid. When water changes from one phase to another, latent heat is released or taken up by the air parcels, and the air is warmed or cooled. These latent heating processes play a fundamental role in the dynamics of many severe storms. Cumulonimbus storms (including thunderstorms), for example, are driven by the latent heat released as the air rises in the cloud. In larger-scale storms, the exact contribution of latent heating to the storm intensity is generally not well understood. The storms lead to dramatic changes in the atmospheric flows on scales of 10s of kilometres, but we lack good models of how these effects integrate up to the scales of regional weather and climate systems such as monsoons. At the same time as the cloud processes are influencing the large-scale circulation, they are also moving water around, as a fundamental part of the global water cycle. For instance, severe storm winds lead to very strong uptake of water from the ocean surface (Fig. 2), and rapid transport of this water through the atmosphere.

Figure 2: Storm conditions off the north of Scotland, observed during a research flight on 1 December 2011. The high winds over the surface cause very strong fluxes of moisture into the atmosphere. In turn, the moisture feeds clouds, which influence the storm dynamics and the surface winds. The dominant wavelength seen in this image was around 80-100 m. Figure courtesy of Tim Baker.

It is not just latent heating in clouds which contributes to storm intensity. Cooling of the air by evaporation of falling precipitation (snow or rain) can lead to intense downdraughts, which cause severe wind squalls when they descend to the Earth’s surface and spread out laterally (Fig. 3). Such squalls can generate winds of 100 kt (115 mph), and are also implicated in the generation of tornados. Some of our recent work, studying storms in Africa, has argued that these low level winds may also make a substantial contribution to large-scale water vapour transport. Other processes such as long-wave radiation from the cloud-tops, also contribute to the instability which drives the convection. A key uncertainty in climate science is to understand how such processes will change in a future climate, when the long-wave radiation changes, and the warmer air is able to hold more water vapour. Indeed, it is found that climate simulations have key sensitivities to the way in which the convection is represented (Tomassini et al. 2015).

Figure 3: Left, the “arcus” cloud marking the edge of the cold outflow expanding concentrically at low levels from a severe cumulonimbus storm over Africa – the precipitation can be seen on the left of the image. Right, a statistical average of the northward heat fluxes generated by such outflows, in a numerical modelling study.

The mathematics of water vapour conversions in the atmosphere is deep and challenging. Over large parts of the atmosphere, away from clouds, water vapour is moved as a passive tracer and its properties can be described by the body of theory related to tracer transport. Even where cloud processes are concerned, there are near-conserved quantities describing water vapour transport (equivalent potential temperature; effectively the entropy of the moist air). However, when phase changes of water occur, we have to deal with functional relationships which are highly nonlinear even non-differentiable. The mathematics of these systems is under-explored.

Once convective clouds have formed, they have a violent impact on atmospheric circulation. The vertical velocities carry air through the depth of the troposphere in a few minutes, and lead to the generation of intense circulations (vorticity and potential vorticity) on the storm scale. In many parts of the world, those circulations lead to natural hazards such as tornados. The circulations also undergo complex fluid-dynamical transformations, including deformation, merging and “cascades” between spatial scales, so that the effects of a single storm on the 10km scale influence the environment on continental scales of 1000s of km. We still only have rudimentary understanding of these processes.

Objective, aims and approach of the project

The objective of the project is to advance our theoretical understanding of the dynamics of tropical convective clouds and their environment.

There are a number of directions the research can take, but some important opportunities are available to us.

Many tropical environments are characterised by widespread fields of cumulonimbus storms. These storms are known to dominate the energy balance of tropical circulations, but we have a poor understanding of their feedbacks with those circulations. We will develop theoretical tools to characterise the cascades of energy and enstrophy from the convective scale (a few km) up to the regional scales (see Fig. 4).

We have the opportunity to interrogate the latest generation of “convection-permitting” models of the tropical atmosphere, which have revolutionised our ability to model tropical systems by simultaneously simulating individual storms (on km scales) and the large-scale circulations in which they exist (1,000s of km). We also have access to the latest generation of satellite measurements of tropical clouds, and data from recent field experiments in Africa and India. We aim to use these model and observational data to test and advance theoretical understanding of the tropical dynamics.

Figure 4: A field of potential vorticity caused by many organised cumulonimbus storms, in a model simulation of conditions over West Africa, at 4 km resolution. Each storm generates a coherent, but complex pattern of potential vorticity. We aim to understand the influence of these storm-scale patterns on the large-scale circulation.

Using these tools and methods we can address a range of research questions, such as the following.

  1. How do the dipoles and quadrupoles of circulation (perhaps characterised by potential vorticity, PV) generated by resolved (or "permitted") storms on the 10km scale project onto the PV of the large-scale flow? There are integral constraints on the PV budget: if a tropical storm generates a given PV field (on the 5-km grid), how does this project onto vorticity and circulation (on the large scale)?
  2. How does the diurnal cycle of solar heating and convection influence the circulations? Do the circulation (PV) dipoles and quadrupoles merge, or somehow mix, once the convection dies down in the morning? Is PV destroyed by mixing, or does it merge to large scales, or something else? State of the art “PV tracer methods” could be a really good way to explore and understand the diurnal cycle in circulation.
  3. Is there coherent contribution of the fine-scale (10km) circulation anomalies to the large-scale circulation through Reynolds-averaged terms, like <v'PV'>? Other papers in geophysical fluid dynamics (e.g. Scott and Dritschel 2012) have shown how barotropic turbulence will act to accelerate a jet. Do similar processes from tropical storms act to accelerate tropical jets? Can they explain feedbacks with the African Easterly Jet (AEJ)?

We expect to develop the theory of water processes in storms, and to use high resolution (“convection-permitting”) numerical weather prediction solutions to test and refine our ideas. These model simulations provide for the first time an opportunity to test high-level mathematical concepts against data which faithfully simulate the organisation and interactions of deep convection. We have some nice tools to use to analyse the model data, including the analysis of Lagrangian “PV tracers” and the use of storm tracking.

This PhD project is a new collaborative research venture between the supervisors, who are based in School of Earth and Environment and at Leeds and the Met Office. Doug has studied the interaction of convection with tropical and midlatitude circulations for more than 20 years: although his first degree was in mathematics, most recently his work has been observationally based, including intensive field experiments in Africa, India and the UK, and working with the new generation of computer modelling capability. Doug brings to the project supervision substantial experience studying the dynamics of real storms, in the atmosphere and in computer models. Juliane works on the mathematical and numerical modelling of tropical weather systems. She has a particular expertise in the dynamics of tropical cyclones (hurricanes and typhoons), in which the convective clouds play an essential and complex role. Lorenzo is a mathematician, and a Senior Scientist at the Met Office. He researches the ways small-scale moist diabatic processes interact with the atmospheric circulation, how this interaction influences regional precipitation patterns, and how convective organisation is shaped by, and feeds back on, the larger scales. With his work he also supports and informs the development of the global configuration of the Met Office Unified Model. Through partnership with the Met Office, results of the project will be communicated to, and hopefully influence the community of scientists developing the next generation of weather and climate models. We aim that this project will develop advanced theoretical understanding of water vapour processes in tropical storms and circulations, with practical applicability.

We have an established partnership with the UK Met Office, and through Lorenzo’s supervisory role this project will be conducted in close collaboration with colleagues at the Met Office. Regular study visits to the Met Office will be encouraged. The project will also benefit from links with several UK and international projects in which we are partners. Directly-relevant projects include:

  • AMMA is a massive international programme of research into the environment and climate of West Africa. Within AMMA, there is a strong network of scientists working on tropical storms and their role in the regional water cycle. A new offshoot of AMMA, AMMA-2050, is exploring future changes in storms and the water cycle.
  • The Future Climates for Africa (FCFA) is a £20 million research programme to refine 10-40-year climate projections for Africa, with relevance to African development. Within FCFA the group in Leeds are working on understanding the ways in which new models of tropical convection may improve our predictions of the kinds of weather which matter to vulnerable people in Africa (e.g. the most extreme storms; droughts).
  • ParaCon is a joint programme of work between the Met Office and UK universities to develop the next generation convection scheme for the Met Office’s weather and climate models. In Leeds we are working on the representation of the fluid dynamics of cloud systems in the new scheme.
  • GCRF African Science for Weather Information and Forecasting Techniques (GCRF African SWIFT) is an £8 million collaboration between UK and African partners to improve operational weather predictions for Africa. By improving our fundamental understanding of tropical convective dynamics, this PhD project will contribute to SWIFT’s aims of improving weather predictions for vulnerable people in Africa.

The student on this PhD project will have opportunities to be involved in all of these projects, as appropriate to the evolving research programme. This is likely to involve opportunities to work in Africa, in association with summer schools and forecasting knowledge-exchange events. There is an active group of researchers here in Leeds working on these and related projects.

We seek an enthusiastic mathematician with a genuine interest in real-world problems. Please get in touch with the supervisors directly, for informal discussion of the project.


The successful PhD student will have access to a broad spectrum of training workshops put on by the Faculty that include an extensive range of training workshops in numerical modelling, through to managing your degree, to preparing for your viva. A full listing is available through

The student on this project will also have the opportunity to attend international training and knowledge-exchange events in Africa as part of the GCRF African SWIFT project.


Strong mathematical background, e.g. excellent first degree or Master’s degree in Mathematics or Physics.

Further reading

Garcia-Carreras L; Parker DJ (2011) How does local tropical deforestation affect rainfall?, Geophys. Res. Lett., 38, doi:10.1029/2011GL049099.

Hoang LP; Reeder MJ; Berry GJ; Schwendike J (2016) Coherent Potential Vorticity Maxima and Their Relationship to Extreme Summer Rainfall in the Australian and North African Tropics, JOURNAL OF SOUTHERN HEMISPHERE EARTH SYSTEMS SCIENCE, 66, pp.424-440.

Marsham JH; Knippertz P; Dixon NS; Parker DJ; Lister GMS (2011) The importance of the representation of deep convection for modeled dust-generating winds over West Africa during summer, Geophys Res Lett, 38, doi:10.1029/2011GL048368.

Scott, R. K. & Dritschel, D. G. 2012. The structure of zonal jets in geostrophic turbulence. Journal of Fluid Mechanics. 711, 576-598.

Schwendike J, Jones SC (2010) Convection in an African Easterly Wave over West Africa and the eastern Atlantic: A model case study of Helene (2006), Q. J. R. Meteorol. Soc., 136, 364-396.

Taylor CM; Belusic D; Guichard F; Parker DJ; Vischel T; Bock O; Harris PP; Janicot S; Klein C; Panthou G (2017) Frequency of extreme Sahelian storms tripled since 1982 in satellite observations, Nature, 544, pp.475-478. doi:10.1038/nature22069.

Tomassini L, Parker DJ, Stirling A, Bain C, Senior C, Milton S (2017), The interaction between moist diabatic processes and the atmospheric circulation in African Easterly Wave propagation, Q. J. R. Meteorol. Soc., under review.

Tomassini L, Voigt A, Stevens B (2015), On the connection between tropical circulation, convective mixing, and climate sensitivity, Q. J. R. Meteorol. Soc., 141, 1404-1416.

Tomassini L, Field PR, Honner R, Malardel S, McTaggart-Cowan R, Saitou K, Noda AT, Seifert A (2017), The “Grey Zone” cold air outbreak global model intercomparison: a cross-evaluation using large-eddy simulations, J. Adv. Model. Earth Syst., 9, doi:10.1002/2016MS000822.

Related undergraduate subjects:

  • Applied mathematics
  • Atmospheric science
  • Engineering
  • Geophysics
  • Mathematics
  • Meteorology
  • Natural sciences
  • Physics