Predictability and Chaos

EPS and Probability Forecasting

Objectives of this session

Appreciate that NWP is not the complete answer

State reasons for uncertainties in weather prediction

Understand how the principle of chaos effects predictability of the atmosphere

Appreciate how ensemble forecasts help to account for chaos

Two 36-hour forecasts

Deterministic versus Probabilistic forecasts

Deterministic forecast - A forecast in which a single answer is given – It will snow this afternoon

– Temperatures will reach 4C today

Probabilistic forecast – A forecast in which a numerical estimate of the certainty of the forecast is given– 30% chance of a shower

Typical deterministic forecast chart

Why is there uncertainty in weather forecasting?

The variability of ‘local’ weather– Exactly where will a shower fall?

Analysis errors – NWP models sensitive to errors in initial

state

Systematic errors in NWP models– Assimilation, parametrization

Displacement

Time

Small differences here

Displacement

Time

Small differences here

BIG differences here

51 plots of height of a pressure level

Predictability

Errors in initial conditions have different effects

Why is the atmosphere predictable

on some occasions, not on others?

Chaos Theory !

Definition of Chaos

Dictionary Definition:Lack of form or systematic arrangement

Scientific Definition: Processes that are not random but look

random

– Random - toss a coin

– Chaotic - a pin ball machine

Edward Lorenz

1963 Massachusetts Institute of Technology

Used 3 equations in a simple model Truncating numbers produced

different results Introduced concept of “attractors” to

describe the state of dynamical systems

– certain states will never occur

A simple non-chaotic attractor

0

1

0

0

2

34

Why is the atmosphere chaotic?

Weather patterns are not totally random– e.g. seasonal variation is regular

… but they can appear so. Climate is the Attractor

– Set of patterns that have at least some chance of occurring

– Heat-wave in Arctic, snow in Sahara do not occur

The Lorenz Attractor

Predictable evolution

Predictable then unpredictable evolution

Implications of chaos theory

There is no one single solution to find There is a time limit beyond which

deterministic forecasts of daily weather become unpredictable

The outcome of all forecasts could be a set of probabilities

The predictability of the atmosphere will vary depending upon its initial state

NWP SYSTEM

ClimatologyClimatology

Predictability Predictability rangerange

The forecastThe forecast

Deterministic Deterministic solutionsolution

NWP SYSTEM

ClimatologyClimatology

Better model:Reduce the errorPredictability Predictability

rangerange

Deterministic Deterministic solutionsolution

NWP SYSTEM

ClimatologyClimatology

Run the model more:Explore the range

NWP SYSTEM

ClimatologyClimatology

BadBad day to be on duty:Lots of uncertainty

NWP SYSTEM

ClimatologyClimatology

GoodGood day to be on duty?

Coping with chaos: EPS

Ensemble forecasting at ECMWF: 51 forecasts run from similar initial

conditions

Use a lower resolution model (T399)

Used for guidance beyond 3-4 days

Generates a lot of data!

Ensemble: Postage Stamps T+120

Probability of surface wind > 10 m/s

EPS Plumes

EPSgram

Extreme Forecast Index

Interpreting Ensemble Data

The presentation of results is important Need to reduce the different solutions to something manageable

Clustering - grouping solutions that are similar

Probability forecasting

Clustering

Ensemble member

Cluster

Cluster mean

26/51=51% 9/51=17.5%

9/51=17.5% 7/51=14%

Deterministic versusprobabilistic forecasts

Deterministic forecast - A forecast in which a single answer is given – It will rain this afternoon

– Temperatures will reach 11 C today

Probabilistic forecast - Forecasts in which a numerical estimate of the certainty of the forecast is given– 30% chance of a shower

Conclusion