PREDICTABILITY, CHAOS & THE WEATHER

Ross Bannister

Data Assimilation Research Centre, University of Reading

Mechanics
Fluid dynamics
Meteorology
Thermodynamics
Mathematics
Computer Modelling

1. How is a Weather Forecast Made?

Picture (c) EUMETSAT

2. The Observation Network

SURFACE	SONDE
AIRCRAFT	SATWIND
SSMI	ATOVS

Above figures (c) Crown copyright, Met Office.

3. Why is a Weather Forecast Valuable?

Domestic

Do I take an umbrella? Shall I put the washing out to dry?

Leisure

Sporting events Caving, mountaineering Holidays

Agriculture

Frosts Weather related disease risk

Shipping

Storms Routing

Air flight

Routing (exploit tailwinds, avoid headwinds and turbulence) Fog

Road transport

Ice/fog/wind/precipitation Salt roads?

Rail

Snow ploughs

Power distribution

Weather forecast = demand forecast

Retail

Weather enforced demand (e.g. icecream/umbrellas/coats/etc.)

Defence

Plan training Strategic planning during conflict

Weather forecasts save the UK £1 billion annually

4. Forecast Failure

MeteoSat Image

(c) EUMETSAT

'Bad' forecast	'Better' forecast

(c) Crown copyright, Met Office

• "Lothar" was a deep low-pressure system which hit Northern France on Boxing Day 1999.
• 110 mph winds recorded in Paris.
• 100 people killed across Europe.
• 4000 trees uprooted in the Palace de Versailles (Paris) alone.
• Automated forecasting systems failed to forecast its severity.
• Observations were 'thrown away' as the computer assumed that they were 'wrong' ("quality control")!

5. Models and Predictability

Oxford English Dictionary: Model

• Something that accurately resembles something else.
• A simplified description of a system (often in mathematical terms) that is put forward as a basis for calculations, predictions, or further investigation.

F=ma

Moisture

Radiation

Surface

(c) Crown copyright, Met Office

The weather forecast model tries to predict the future state of the atmosphere using the laws of physics given the current state (i.e. the weather now).

• The more accurately we know the state of the atmosphere now, the better is our forecast, but ...
• The predictability barrier for the atmosphere is ~14 days.
• Many people would say that the atmosphere is chaotic.
• All measurements have errors.
• All models are wrong (but we hope that they are adequate).

6. What is CHAOS? - Simple Systems

Chaos:

• No periodic behaviour.
• Sensitivity to initial conditions.
• Chaotic motion is difficult or impossible to forecast.
• The motion 'looks' random.
• Non-linear.

NON-CHAOTIC	CHAOTIC
Simple pendulum	Double Pendulum
- Click here for demo. - Download .avi file of above	- Click here for demo. - Download .avi file of above
Slope	Pin-board

Can you think of any other chaotic systems?

7. Data Assimilation

In weather forecasting, data assimilation is a means of using current observations to prepare a forecast model.

Data assimilation is a non-trivial task: Observations are spread in space and time. There are "data voids" (esp. over oceans and in the upper troposphere and stratosphere). Many observations are 'indirect'. All observations have uncertainties.

The treatment should ideally be consistent with the laws of physics.

In the context of chaos theory: The better our knowledge of the state of the atmosphere now, the better the forecast quality.

9. Summary

• It is thought that the Earth's atmosphere forms a chaotic system.
  
  
• The definition of chaos here does not imply disorganisation (the system follows definite laws).
• In order to predict the future state of a chaotic system exactly, its current state must be known with zero uncertainty and the model must be perfect.
  
  
• The more that is known about the current state of the system, the better the forecast (but remember the predictability barrier).
• Information from observations are incorporated into a forecast model using the mathematical technique of data assimilation.