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 2040

2007 2005

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

summerwinterChange in

precipitation by the 2080s

winter summer

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

0.,Re

1. 2 uuPuuut

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

1 000 000 pieces of data

Scary slide ..

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

Du

Dt 2 f u

1

p g2u,

t

.(u)0,

CDT

DtRT

DDt

h2T Sh LP,

DqDt

q2q Sq P,

pRT.

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 …

1 000 000 000 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 Earth3. 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 it’s hard to stop: tipping point!!

I Ice Content

T Temperature

a Albedo

S Solar radiation

T 4 k (1 a)S,a a0 b0 I,dI

dt L T.

Black body radiation law

Albedo change

Melting ice

Here’s 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 can’t 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 2004

2. Better models of the weather

3. Better computers and better resolution (more cubes)