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“Mathematicians save the planet” 24 May 2017 © University of Reading 2006 www.reading.ac.uk Who am I? • A levels: Maths, Further maths, Physics and Chemistry • BSc Physics degree University of Manchester • PHD Meteorology, University of Reading Dr Ellie Highwood 2 What is meteorology? 3 What is meteorology? Katrina nearing New Orleans 4 What is meteorology? 5 What is meteorology? IPCC 2007 report 6 What is meteorology? • Maths • Physics • Computer Science And increasingly • Chemistry • Engineering • Economics • Politics 7 How do we use maths? • To forecast the weather • To take the Earth’s temperature • To see why things are changing • To predict climate change • To predict air pollution 8 What kind of maths do we use? • Rates of change (e.g. temperature, ozone concentration, water vapour amount) DIFFERENTIATION / CALCULUS • Movement, forces etc MECHANICS • Cumulative amounts INTEGRATION/ CALCULUS • Risks and chances PROBABILITY • Proportions, hypotheses STATISTICS Plus obviously general arithmetic, algebra, trigonometry 9 YOU CAN LEARN ALL OF THESE IN AS and A2! And then do meteorology, maths or physics at university… 10 Forecasting the weather (and climate) • Take the best knowledge we have of the state of the atmosphere (and ocean) today – using as much real data as we can • Solve fundamental equations to predict what the atmosphere (and ocean) will look like tomorrow (or in 40 years) • You only need 6 types of equations to forecast weather and climate change 11 Forecast models are huge computer codes based on these equations. These govern: Air and water movement - winds in the atmosphere, currents in the ocean. Conduction, convection and radiation of heat Condensation and evaporation during the formation of clouds and raindrops Absorption of sunshine and emission of thermal radiation Take a deep breath and close your eyes 12 All the equations you ever need to forecast the weather Dr u uv tan 1 p uw 2 sin v 2 cos w Su Dt r r cos r Dr v u 2 tan 1 p vw 2 sin u Sv Dt r r r Dr w 1 p Dt r r g Dr Dr r u 0 S Dt Dt u 2 v2 r 2 cos u S w Dr mX S mX Dt p RT Don’t panic! If this freaks you out, you are normal! Close your eyes again…. 13 Or… How the west to east wind changes with time and place How the south to north wind changes with time and place How the ascent and descent in the atmosphere changes with time (and heating) We don’t lose or create mass We don’t lose or create entropy (order) Total mass of e.g. water remains constant The temperature of the atmosphere is related to its density and pressure 14 But… • We never actually solve these ourselves. They are simplified by making assumptions about the relative size of some bits and then a computer program calculates those terms that are left. • To do this we have to… 15 Put the world onto a grid Global weather 40 km Global climate 200km North Atlantic & European 12 km UK 4 km 16 Simplifying things to put on a grid • Finding a way to represent things that happen on very small scales to some AVERAGE effect on a whole model grid box. 17 Forecasting the weather…. 18 Probability in meteorology Modern weather forecasts are “probabalistic”. E.g. there is a 25% chance of rain tomorrow… Or, “the average temperature by 2090 to 2099 is likely (6690% certain) to be between 2.4 and 6.4 degrees higher than the average 1980 to 1990”, assuming the A1F – lots of fossil fuels – emissions scenario To do this we use “ensemble” forecasts 19 Ensemble weather prediction • ECMWF for Reading Sometimes there are tight plumes when the weather is more predictable – other times there is a big spread – this is when you might want to keep a close eye on the weather forecasts on TV. 20 So how can we predict 50 years time? • For short forecasts, initial conditions and chaos are more important • For long forecasts – the effects of chaos average out – but the model results can change a lot if we get the amount of carbon dioxide emitted slightly wrong • So we can predict the temperature change in 50 years time, even if we get the weather wrong tomorrow • BUT, this does mean that we can’t produce a UK weather forecast for Feb 7th 2050! 21 IPCC 2007 22 Mechanics in meteorology L 23 Statistics in meteorology • All about distributions… 24 Homework: How to describe the range of sizes of cloud droplets using just a yoghurt pot • Take one sealed, full, refrigerated yoghurt (doesn’t matter what size or flavour) • Remove from fridge • Open lid very carefully and peel back lid (it’s the lid we are interested in) • If there are droplets of condensation on the lid, start measuring and counting the drops. Count the number of very small, small, medium, large and very large drops. • Plot a bar chart 25 Distribution of droplet sizes in a cloud • For some reason, the drop sizes in condensation on a yoghurt lid have the same type of distribution as drops in a cloud…. 26 More statistics in meteorology 27 August 2003 28 29 Weather and climate is expensive Katrina alone $86 billion 30 Hot off the press: IPCC 2007 • “Most of the observed increase in globally averaged temperatures since the mid-20th century is very likely due to the observed increase in anthropogenic greenhouse gas concentrations. Discernible human influences now extend to other aspects of climate, including ocean warming, continental average temperatures, temperature extremes and wind patterns” 31 32 33 Mathematicians will be needed to: • Work on improving climate models and climate mitigation models • Work on economic models to improve the inputs to our climate models • As engineers to mitigate and adapt • As financiers (including insurance) Taking maths further than GCSE is the first step towards being able to help civilisation adapt to our changing environment. http://www.met.rdg.ac.uk 34