chaos: the enemy of seasonal forecasting! richard washington university of oxford...

Chaos:The enemy of seasonal

forecasting! Richard WashingtonUniversity of Oxford

[email protected]

DETERMINISTICFORECAST

Climate ModelInitial conditions



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Realisation of weather will be different from observed After a few days…..



BEWARE THE BUTTERFLY!

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ENSEMBLEFORECAST

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Sensitivity to initial conditions…….

How can we better understand this?

The Game of Pinball

Is the trajectory of the ball predictable?

Is the system predictable?

How long will the ball stay on the board?

How many seconds does it take for the ball to vanish?

The system is fixed: nothing changes from the release of one ball to the next….

The gradient of the board is the same

The strength of the magnets is the same

The position of the magnets is the same

So, why is the system unpredictable?

Only the initial position of the ball changes from one release to the next:

System is sensitive to initial conditions…….

The atmosphere in the mid latitudes never forgets the initial conditions

Understanding the problemgraphically……

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Graphical solutionsTo simple equations

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Take a system of 3 equationsSystem is simpler than the atmosphere….

COLD & WETHOT & DRY

Evolution over 7 days……

COLD & WETHOT & DRY

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• Evolution over 7 days……

• day 1: cold and wet

• day 2: hot and dry





• day 7: cold and wet COLD & WETHOT & DRY

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Evolution over 7 days……

Sensitivity to initial conditions

Experiment AEvolution over 7 days……

COLD & WETHOT & DRY

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• day 1: hot and dry • day 2 hot and dry• day 3: hot and dry• day 4: hot and dry• day 5: hot and dry• day 6: hot and dry• day 7: hot and dry

Experiment BEvolution over 7 days……

COLD & WETHOT & DRY

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Experiment A Experiment B















COLD & WETHOT & DRY

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Lorenz Attractor illustrates how the atmosphere:

• is sensitive to infenitismally small initial conditions.....7 days = hot and dry

• 7 days = cold and wet

• BUT Initial conditions A = B

• Weather/climate tends to modes or patterns of variability

How can we quantify this sensitivity to initial conditions?

How can we establish modes of atmospheric variability?

How chaotic is the atmosphere?

Experimental Design- Pills and Patients

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Experimental Design- Pills and Patients

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RESULT????

Experimental Design- SST and Climate

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RESULT

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Global SST

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Experiment 1 Experiment 2

Global SST

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MODEL




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Global SST

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Global SST MODEL

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MODEL




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Global SST

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MODEL

MODEL




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What variance is common to each model run?

What variance is unique to each model run?

Forced Vs Free varianceForced Vs Free manifoldSignal Vs Chaos

Simplest Case:Forced Vs Free Manifold

• single variable (rainfall)

• single model grid box

• Total Variance = forced variance + internal variability

Step 1: Estimate Internal Variability

computed as variance of each datum from its ensemble mean

N = number of years of forcing (92 years)n = number of experiments (6)

X = ensemble mean for ith year

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Step 2: Estimate variance of ensemble means

computed as variance of the ensemble mean from the mean of all the data

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variance ensemble = variance due to forcing + 1/n variance due to internal variability

2 2 21en SST

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Step 3: Estimate variance due to Forcing by SST

Actual Experiment

UK Met Office Model: HADAM2A

Forced with SST (GISST data set)

1904-1996

6 model runs = 6 twentieth centuries!

6 unique initial conditions

What variance is common to each model run?

What variance is unique to each model run?

Forced Vs Free varianceForced Vs Free manifoldSignal Vs Chaos

JFM % forced rainfall variance

JAS % forced rainfall variance

Chaos – the enemy of seasonal forecasting!

• Like many systems, the atmosphere is sensitive to initial conditions

• The same forcing due to SST can produce a different outcome if the starting conditions are different

• But the tropics is the least chaotic part of the atmosphere

• We can design methods to overcome the problem partially…e.g. ensemble forecasting

Readings

• Lorenz, E.N. 1995: The essence of chaos, UCL Press

• Rowell,-D.-P. et al 1995: Variability of summer rainfall over tropical north Africa (1906-92) : observations and modelling. Quarterly-Journal,-Royal-Meteorological-Society. 121(523), pp 669-704.

• Palmer T.N 1998: Nonlinear dynamics and climate change, Bulletin of the American Met Society, 79, 7, 1411-1423.

• Washington, R. 2000: Quantifying chaos in the atmosphere, Progress in Physical Geography.

chaos: the enemy of seasonal forecasting! richard washington university of oxford...

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enemy of seasonal forecasting