Maths, weather and climate Chris Budd
Mar 28, 2015
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)