Download Mathematicians save the planet!

“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