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Brazilian Butterflies: Chaos Theory and the Weather Forecast

You might wonder why RTE and Met Eireann can’t seem to accurately and consistently predict the weather. Sometimes, the weather report for a specific day says sunny but shifts the following day to cool with rain. We often hear predictions that this winter will be the worst on record, or that that summer will be the hottest. These predictions, however, must be taken with a grain of salt. Weather is unpredictable and any forecast beyond 10 days can be uncertain.  

Weather is an example of a Chaotic system. It is extremely hard to anticipate accurately, despite the fact that the Met Eireann has accurate historical weather data going back decades. It is something of a running joke both in Ireland and abroad that weather forecasts are more likely to be wrong than right. This inaccuracy is not down to incompetency on the part of the forecaster. Rather, uncertainty is built into the basic mathematical principles which underly how weather systems form and change over time.  

Modern meteorologists can predict atmospheric fluctuations in wind, temperature, pressure and humidity using various principles, statistical data and mathematical equations. In addition, meteorologists must pay attention to factors such as how water changing phase (for example, from water to steam) will affect the flow of energy. They also calculate earth’s rotation in space to draw conclusions about the weather. Even a minute change in the atmosphere can have a severe influence on the future climatic conditions.

Meteorology has improved rapidly over these last two decades. Present-day meteorologists use something called an ensemble forecast, meaning that various different forecasts are generated, giving the range of possible future weather conditions. Likewise, the use of Doppler radar to detect weather patterns are producing ever more efficient predictions. 

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This technology works by shooting sound waves into the sky then ‘listening’ for the results. If a storm is moving towards the instruments, the noise which returns will be of a higher frequency than the one which was sent out. If the storm is moving away, the frequency will be lower. This is due to the doppler effect; the same reason an ambulance siren will appear to be lower or higher-pitched depending on whether it is moving towards you or away from you. A computer converts the doppler information into images which show cloud coverage, precipitation, wind direction & speed. This technique has significantly improved forecast accuracy. 

Edward Norton Lorenz, an American theoretical meteorologist and mathematician who is now considered the father of Chaos theory, published an article in 1963 which first described the phenomenon that was later termed ‘The Butterfly Effect’. In 1961, Lorenz built a model which used differential equations representing temperature, pressure and wind to calculate the weather. One day he chose to repeat a few computations from a previous run and restarted the model calculations, changing one line of numbers in the initial conditions. After starting the simulation, Lorenz left to get a coffee.

When he returned, Lorenz was shocked by what the computer was telling him. In the second run, the system had generated a forecast which did not match with the data from the first, despite the two models being nearly identical. Thinking his machine was busted, Lorenz ran the model again and again, but each time got the same result. Lorenz found that the differences between the forecast in the first and second runs steadily increased over time, with all the initial values completely disappearing after a month. This was because the tiny changes he had made to the initial conditions had snowballed, ultimately altering the course of the entire weather system. 

This simple model exhibits ‘sensitive dependence on initial conditions’, also known as the butterfly effect. Can the flap of a butterfly’s wings in Brazil set off a tornado in Texas? It may sound ridiculous, but if we assume that a butterfly flaps its wings rapidly for several days, each time causing a miniscule change in the wind, then it’s conceivable that the cumulative effect could radically alter the trajectory of a tornado, hurricane or a thunderstorm over time. 

A common misinterpretation of the butterfly effect is that by purposely changing a small variable, you can force a tornado into existence. In reality, a butterfly flapping its wings could have a massive effect on the weather system, or it could have no effect at all. The problem is that it is next to impossible to tell which the case will be. Lorenz’s great achievement was highlighting our ignorance when it comes to weather systems. He showed us the complexity of Earth’s systems, and proved that nothing is too small to make a difference. 

 

Keerthana Dhanabal – Science Writer 

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