Tropospheric ozone is an important air pollutant, harmful to human health, agricultural crops and vegetation. It is the main precursor to the atmospheric oxidants which initiate the degradation of most reactive gases emitted to the atmosphere, and is an important greenhouse gas in its own right. As a consequence of this central role in atmospheric chemistry and air pollution, the capacity to understand, predict and manage tropospheric ozone levels is a key goal for atmospheric science research. This goal is hard to achieve, as ozone is a secondary pollutant, formed in the atmosphere from the complex oxidation of VOCs in the presence of NOx and sunlight, and the timescale of ozone production is such that a combination of in situ chemical processes, deposition and transport govern ozone levels. Uncertainties in all of these factors affect the accuracy of numerical models used to predict current and future ozone levels, and so hinder development of optimal air quality policies to mitigate ozone exposure. Here, we will address this problem by measuring the local chemical ozone production rate, and (for the first time) perform measurements of the response of the local atmospheric ozone production rate to NOx and VOC levels - directly determining the ozone production regime. We will achieve this aim by building upon an existing instrument for the measurement of atmospheric ozone production rates (funded through a NERC Technology Proof-of-Concept grant, and deployed in the recent ClearfLo "Clean Air for London" NERC Urban Atmospheric Science programme). In addition to directly measuring ozone production, by perturbing the ambient chemical conditions (for example, through addition of NOx or VOCs to the sampled airflow), and measuring the effect of this change upon the measured ozone production rate, the ozone control regime (extent of NOx vs VOC limitation) may be directly determined. Within this project, we will develop our existing ozone production instrument to include this capability, and validate the measurements, through comparison with ozone production from VOC oxidation in a large simulation chamber, and by measurement of the key oxidant OH radicals, and their precursors, within the system. We will then apply the instrument to compare the measured ozone production rates with those calculated using other observational and model approaches, and to characterise the ozone control regime, in two contrasting environments: In the outflow of a European megacity (at Weybourne Atmospheric Observatory, WAO, in the UK), and in a rural continental location (at Hohenpeissenberg, HPB, in southern Germany). At WAO, we will compare the measured ozone production rate with that calculated through co-located measurements of HO2 and RO2 radicals (using a newly developed approach to distinguish between these closely related species), and with that simulated using a constrained photochemical box model. We will compare the NOx-dependence of the ozone production rate with that predicted using indicator approaches, based upon observations of other chemical species. At HPB, we will focus upon the VOC-dependence of the ozone production rate, and assess the error in model predictions of ozone production, which arise from the presence of unmeasured VOCs. The project will develop and demonstrate a new measurement approach, and apply this to improve our understanding of a fundamental aspect of atmospheric chemical processing. Future applications have considerable potential both to support atmospheric science research, but also as an important air quality tool, alongside existing measurement and modelling approaches, to inform the most effective emission controls to reduce ozone production in a given location. In the context of global crop yield reductions arising from ozone exposure of 7 - 12 % (wheat), 6 - 16 % (soybean) and 3 - 4 % (rice), this is an important societal as well as scientific goal.

Our environment has a major influence on all aspects of human endeavour ranging from the mundane, such as deciding whether to cycle or take the bus to work, to the exceptional, such as coping with the ever more damaging effects of extreme natural phenomena (tropical storms, inundations, tsunamis, droughts, etc.). In addition, climate change is one of the most pressing challenges that confront humanity today. What was once viewed as something that might happen in the future is now part of daily life. Because most impacts of climate variability and change occur through extreme weather events and spells, the two issues of weather and climate are closely interlinked. We rely on science and technology to provide the means of managing the complex intricacies of the environment and to meet the pressing challenges of climate change. Mathematics plays a central role in this massive undertaking as it provides the fundamental basis of the theory and modelling of weather, oceans and climate. However the nature of the mathematical challenges is changing and the need for scientists trained in risk and uncertainty is growing rapidly. Meeting these needs can only be achieved by training an entirely new generation of scientists to meet the multi-faceted challenges, with all their complex inter-dependencies. These scientists will need extraordinarily broad training in several scientific areas, including geophysical fluid dynamics, scientific computing, statistics, data assimilation and partial differential equations. Above all, they must understand the mathematics that unifies them. The alignment of Imperial College's Mathematics Department and Grantham Institute for Climate Change with Reading University's Departments of Mathematics and Statistics and of Meteorology has put these two institutions into a unique position to offer a CDT focussing on the priority area: Mathematical Sciences for Weather, Ocean and Climate, as a 50-50 joint venture. We propose to bring together, as academic supervisors and stakeholders in the centre, more than 60 world-leading researchers with expertise in a wide spectrum of areas that comprise the mathematical foundation as well as the frontier application areas. The central aim of the proposal is to build a strong cohort of young scientists whose backgrounds will span the breadth of the mathematical sciences from statistics, PDEs and dynamical systems, scientific computing, data analysis, and stochastic processes including relevant application areas from weather, oceans and climate. These young scientists must also acquire problem-specific knowledge through an array of elective courses and supervisory expertise offered by the two institutions and the external partners. A core component of the cohort training will be a ten-week programme hosted by the Met Office in Exeter which will include lectures given by world-leading scientists and research internships with Met Office staff, tackling real-world projects by teamwork. Key partners to the proposed CDT include major international players in research and operational forecasting for weather, oceans, and climate, including the UK Met Office, the European Centre for Medium Range Weather Forecasts, the German DWD, the National Centre for Atmospheric Science and the National Centre for Earth Observation. The EPSRC contribution to the Centre will be heavily leveraged with institutional and external partners, whose financial commitments are estimated to cover 65% of the total costs. The proposal is also in alignment with the global initiative Mathematics of the Planet Earth 2013 which involves scientific societies, universities, institutes and organizations all over the world aiming to learn more about the challenges faced by our planet and to increase the research effort on these issues.

Global climate change threatens our future. Urgent societal action is demanded. However, crucial uncertainties regarding the future climate still need to be addressed. Extreme climate events are wreaking enormous environmental, societal, and economic tolls and they are becoming increasingly common and intense. The huge number of uncertainties related to our future climate combine with the sensitivity of the Earth's climate system to create extremely demanding challenges. Extending our understanding for deriving effective solutions demands interdisciplinary collaboration to determine the dominant factors in climate change. Currently, there is a lack of highly qualified mathematicians with the necessary training and experience to address the diverse problems and urgent challenges posed by climate change using computational and data-driven research. Our Centre for Doctoral Training (CDT) will train new cohorts of PhD students and build a scientific community to address the grand mathematical challenges raised by the significant levels of uncertainty in our future climate. The mission of our CDT will be to prepare graduates with strong mathematics, physics and engineering backgrounds to apply their skills in mathematical modelling, scientific computing, statistics and machine learning to key climate-related problems in oceanic, atmospheric and engineering contexts. By bringing together leading experts from Imperial College London, the University of Reading and the University of Southampton along with a wide range of external partners, our CDT will be uniquely placed to equip future mathematicians with the tools required to address global climate uncertainties. Our CDT will achieve its goals by developing the mathematics and its applications that are required to understand, better predict and, ultimately, respond to impending changes in the Earth's climate and the associated risks. A particular emphasis will be the creation of a vibrant environment to integrate strong cross-disciplinary engagement and collaboration, both within and between cohorts and disciplines, in advancing the range of scientific techniques, fundamental theories, approaches and applications. This will include engaging with academics, government organisations, industry and the public. As a result, the development of outstanding skills in mathematics and science communication will be a priority. The collaborative and peer-to-peer interactions will help develop the complementary techniques and approaches that will underpin essential technical research and innovation and will be coupled with exciting opportunities to discover and advance fundamental mathematics to provide practical solutions in climate science and beyond. Our CDT will act as a seed for growing the capability and capacity to inform decisions and efforts related to climate change on a rapid timescale. The technical focus of our CDT will be enhanced by activities to appreciate the social, political and economic dimensions of societal response to climate change. Furthermore, sustained efforts to mitigate and adapt to climate change will be required during the coming decades. For this reason, along with building a professional community of graduates, the CDT will invest in imaginative outreach programmes involving school pupils and undergraduates, building on opportunities through the institutions partnering with the CDT, including the Grantham Institute for Climate Change and the Environment, the National Oceanography Centre, the National Centre for Earth Observations, the UK Meteorological Office, the European Centre for Medium-Range Weather Forecasts, and the Natural History Museum.

Many of the clouds in the atmosphere contain ice particles. These ice particles play an important role in the climate system, because high-altitude cirrus clouds cover around 30% of the globe at any one time, and act to warm the planet. Ice particles are also important for the development of precipitation, and not only in cold polar climates: even in mid-latitudes (like the UK), over three quarters of the precipitation that falls originates as snowflakes aloft - it is just that most of it melts before arriving at the surface. Ice particles, both in clouds and in snowfall at the surface, precipitate. In other words, they are able to grow large enough to fall through the air. This has several implications. The most obvious of these is that the rate at which the particles fall out controls the transport of water vertically through the atmosphere and to the surface. More subtly, the movement of each ice particle through the air directly influences the rate at which the particle grows, evaporates and melts. For example, if the air is humid enough, water molecules will diffuse to the ice crystal's surface and deposit there, leading to growth. If the particle is stationary, this growth occurs steadily but slowly, because the growing ice crystal depletes the vapour around it, leading to a shallow gradient in the concentration of molecules. If the particle is falling, this growth can occur much faster, because the ice crystal is constantly falling into fresh, humid air, leading to steep concentration gradients. The quantitative details of exactly how fast an ice particle of a given size and shape falls, and how much the growth rates are enhanced by, is determined by the airflow around the ice particle, or its aerodynamics. Unfortunately, this is an area of cloud physics where our understanding is extremely limited. The aerodynamics of simple shapes like spheres, spheroids and discs is well studied. However it is clear from observation of natural ice particles that they are not simple in their geometry. Instead the particles are often complex and irregular in their shape. We have almost no high-quality data on the aerodynamics of such particles. As a result, even state-of-the-art microphysical models are forced to approximate the aerodynamical effects on ice processes as though these complex irregular particles were spheres or spheroids, hoping that this is an adequate approximation. To solve this problem, experimental data is needed for the aerodynamics of particles with the complex shapes that we observe in the atmosphere. The stumbling block is that making suitable observations of natural ice particles in free-fall is extremely challenging. In snowfall at the surface the particles are small, fragile, easily blown by the wind, and likely to melt or evaporate if not handled with great care. Direct sampling of falling particles in cirrus clouds is impossible. In neither case is it possible to directly determine the airflow around the particle or the influence of that flow on the microphysical process rates. In this project we overcome these problems with the use of analogues. Using 3D printing techniques we will create plastic particles with the same complex geometry as natural ice particles. By dropping the particles in tanks of liquids, and through air in the laboratory and a vertical wind tunnel, we can determine how the fall speed of the particles is controlled by their size and geometry. Exploiting recent developments in tomographic particle imaging velocimetry we can measure the airflow around the falling analogues. From this we can directly determine how the airflow enhances the particle growth, evaporation and melting rates.

This project, studying Convective Cloud Dynamics and Turbulence Interactions with Microphysical Processes and the Atmospheric Environment (CLOUDY TIME) will: (i) improve understanding of microphysics-turbulence interactions using a hierarchy of sub-km models and large-eddy simulations; (ii) evaluate the 3D representation of moist convective turbulence in sub-km and km-scale models, testing turbulence parametrization schemes including coupling with microphysics; (iii) improve understanding of model uncertainty due to representation of vertical profiles; and (iv) evaluate mesoscale processes that lead to cloud organisation to inform scale-aware convection parametrization schemes. The improved understanding and evaluation in CLOUDY TIME will be informed by novel measurements and observations planned for the UK summertime convection field campaign WesCon, which aims to observe many of the relevant turbulent processes, and their relation to the environment, for the first time. Convection leads to hazardous weather and is fundamental to the global atmospheric circulation. Modelling of convective storms is challenging due to the interaction of many processes which interact over a wide range of scales, from turbulence and microphysics, including precipitation formation, to the release of convective instability and evaporatively driven downdraughts and cold pools. The next generation of global weather and climate models will be run at km-scale grid lengths and will explicitly represent convective storms, but these models are highly sensitive to the sub-grid turbulence parametrization, even when run at finer resolutions with grid lengths less than 1 km. This sensitivity leads to biases in storm number, intensity and lifetime, and hence to errors in severe weather warnings and in the large-scale circulation. Conversely, errors on the large scale affect the timing and nature of convection, creating a complex web of interactions across scales. CLOUDY TIME aims to disentangle the controls on convection from the microscale, governed by parametrization, to the synoptic scale, governed by data assimilation and downscaling.