Maths, weather and climate. Chris Budd

Some scary climate facts which maths can tell us something about

Floods are more common Bees are vanishing In the UK, 55,000 homes and 6,000 businesses were flooded in 2007

The last twelve years have been the warmest on record 1998 was the hottest year ever recorded!!!!

Melting Arctic Summer sea ice in the Arctic has decreased by an area the size of Scotland every year and may vanish by

Summer ice coverage over the last 30 years Possible future projections

Things are predicted to get a lot worse!! Between a 2 and 5 degree increase by 2100

Temperature (°C) rise by the 2080s Climate Scenarios for the UK summer winter Change in precipitation by the 2080s wintersummer

How reliable are predictions of climate change? What does maths have to do with this? Everything.. Maths is the way that we understand both the weather and climate change

1. Weather forecasting

Q. What makes up the weather? Air Pressure p Air Velocity (u,v,w) Air Temperature T Air density Moisture q Same for the oceans + ice + salt All affected by: Solar radiation S Earths rotation f Gravity g Mountains, vegetation

How do we forecast the weather? 1. Make lots of observations of pressure, wind speed etc. 2. Write down differential equations which tell you how these variables are related 3. Solve the equations on a super computer 4. Constantly update the computer simulations with new data

Sources of observation pieces of data

Scary slide.. The basic equations linking all the variables were discovered by Euler and have been improved over many years The differential equations

Bad News … Equations are too hard to solve by hand Good News.. We can solve them on a computer 1.Divide the atmosphere up into many small cubes 2. Solve the equations on each cube 3. Put all the cubes together North Atlantic and Europe (NAE) UK

The smaller the cubes the better the forecast Modern forecast has cubes of size 1.5km over the UK and 25km over the Atlantic BUT the more cubes you use the longer it takes to do the sums! Typical forecast … things to calculate It takes one hour to forecast 24Hrs of weather 1.5km

Performance Improvements Improved by about a day per decade Andrew Lorenc

2. Predicting the climate

Climate is similar to weather and studied using the same equations solved on a supercomputer … but … Climate changes over years/centuries More things are involved: Greenhouse gases: water vapour, carbon dioxide, methane Carbon cycle Ice sheets Volcanos El Nino

1.Sunlight passes through the atmosphere 2. It warms the Earth 3. Infrared radiation (IR) is given off by the Earth 4. Most IR escapes to outer space and cools the Earth… 5....but some IR is trapped by gases in the air, thus reducing the cooling effect The greenhouse effect

Climate models are constantly improving Tested by being used to predict past climate change

Something to worry about Positive feedback can make the climate go out of control! 1. Hotter weather means more water vapour/methane means hotter weather 2. Ice reflects the sun Hotter weather melts the ice. Less sunlight reflected by the ice Weather gets hotter Once change starts its hard to stop: tipping point!!

I Ice Content T Temperature a Albedo S Solar radiation Black body radiation law Albedo change Melting ice Heres the maths of ice cover changes Black body radiation

Predicted sea ice Predicted sea level

Between a 2 and 5 degree increase by 2100

But can we be sure The Double Pendulum Motion can be Chaotic and unpredictable Even if we understand something we cant always predict it with certainty!!!!!!

Understand the climate system Monitor global and national climate Predict future change Attribute recent change to specific causes Climate prediction and research Uses climate models and mathematical equations to:

Improvements due to 1.Better data better linked to the calculations Satellite image from 1964 Satellite image from Better models of the weather 3. Better computers and better resolution (more cubes)