Chaos: The enemy of seasonal forecasting! Richard Washington University of Oxford

DETERMINISTIC FORECAST Climate Model Initial conditions

DETERMINISTIC FORECAST Climate Model Initial conditions

DETERMINISTIC FORECAST Climate Model Initial conditions Realisation of weather will be different from observed After a few days…..

DETERMINISTIC FORECAST Climate Model Initial conditions BEWARE THE BUTTERFLY!

Climate Model

Initial conditions

Climate Model Initial conditions

ENSEMBLE FORECAST Climate Model Initial conditions

Very Low Skill Very High Skill

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 problem graphically……

y=2x+1 y=x 2 +1 Graphical solutions To simple equations

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

COLD & WETHOT & DRY

Evolution over 7 days……

COLD & WETHOT & DRY

Evolution over 7 days…… day 1: cold and wet 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: cold and wet COLD & WET HOT & DRY

Evolution over 7 days…… Sensitivity to initial conditions

Experiment A Evolution over 7 days……

COLD & WETHOT & DRY

Evolution over 7 days…… 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 B Evolution over 7 days……

COLD & WETHOT & DRY

Evolution over 7 days…… day 1: hot and dry day 2: cold and wet day 3: cold and wet day 4: cold and wet day 5: cold and wet day 6: cold and wet day 7: cold and wet

Experiment AExperiment B 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 day 1: hot and dry day 2: cold and wet day 3: cold and wet day 4: cold and wet day 5: cold and wet day 6: cold and wet day 7: cold and wet

COLD & WETHOT & DRY

Lorenz Attractor illustrates how the atmosphere: is sensitive to infenitismally small initial conditions 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 t1 t2 t3 t4 ? ? ?? ? ? ? ? ?? ??

Experimental Design- Pills and Patients t1 t2 t3 t4 RESULT????

Experimental Design- SST and Climate t1 t2 t3 t4 RESULT SST

Experiment 1Experiment 2

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Very Low Skill Very High Skill

What variance is common to each model run? What variance is unique to each model run? Forced Vs Free variance Forced Vs Free manifold Signal 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

Step 2: Estimate variance of ensemble means computed as variance of the ensemble mean from the mean of all the data

variance ensemble = variance due to forcing + 1/n variance due to internal variability Step 3: Estimate variance due to Forcing by SST

Actual Experiment UK Met Office Model: HADAM2A Forced with SST (GISST data set) 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 variance Forced Vs Free manifold Signal 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 ( ) : observations and modelling. Quarterly-Journal,-Royal-Meteorological- Society. 121(523), pp Palmer T.N 1998: Nonlinear dynamics and climate change, Bulletin of the American Met Society, 79, 7, Washington, R. 2000: Quantifying chaos in the atmosphere, Progress in Physical Geography.