Improving climate and weather forecasting models have come from particular mathematical as well as scientific and technological advances. One can identify some of the mathematical problems which need solving to make the next steps in improving these models. I would point to internal ocean dynamics, increasing extreme precipitation events, and longer periods of atmospheric blocking that cause extended periods of heat, drought and cold. Mathematics needs to continue to show how approximate data and models can be used for rapid on-line and interactive warning and advice systems for communities exposed to extreme natural hazards. Finally, perhaps the scientific and mathematical communities can do a better job of explaining in the public sphere the more certain and less certain aspects of climate and natural hazards, and the methodologies (eg statistical or reductionist). But they should listen to the public debate, not least in parliament, and constructively engage with the relevant information and by correcting mistakes; neither of which happens much at present.

This talk will follow a welcome introduction and is part of the UK Launch of Mathematics of Planet Earth 2013. More info @ www.newton.ac.uk/events/2013/mpe/