Chaos Theory and Meteorological Predictions

Introduction

Nonlinear systems can exhibit apparent disorder (randomness) even when future behaviors are well defined by initial conditions and external factors are eliminated. When such situations occur, systems exhibit deterministic chaos or, simply, chaos. For instance, the back-and-forth motion of a pendulum may appear to be steady but, in reality, it is a disordered system guided by chaos theory. Where the ball lands on a roulette wheel may appear to be random but, again, it depends on initial conditions and external influences. It, too, is a chaotic system. Any system that changes a large amount with only a small modification is especially sensitive on its initial conditions. These systems have a basis in chaos theory.

Scientists involved with chaos theory attempt to examine, describe, and quantify complex and unpredictable dynamics of systems that are sensitive to their initial conditions but follow mathematic laws—even though their outward appearance appears random. Meteorology, and the prediction of weather and climate, is a classic example of such an unpredictable (chaotic) system.

Historical Background and Scientific Foundations

Chaos in a system was discovered by American mathematician and meteorologist Edward Lorenz (1917-) during research performed at Massachusetts Institute of Technology in the United States. In the late 1950s and early 1960s, Lorenz modeled the weather using twelve differential equations. He wanted to save time on one occasion and started the program in the middle, rather than at its initial conditions, and stored computer data to three decimals rather than the usual six. Instead of getting an expected close approximation to his result, Lorenz got a very different answer. His 1962 paper “Deterministic Nonperiodic Flow” is considered the beginning of chaos theory.

Lorenz rationalized that a small change in the initial conditions can drastically change the long-term behavior of a meteorological system. He called this phenomenon the “butterfly effect.” In its extreme case, Lorenz contended it was possible for the flapping of butterfly wings to cause a massive storm a half world away. His 1972 paper “Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas?” originated the term. Based on his results, Lorenz stated that it is impossible to predict the weather accurately.

The meteorological processes and forecasting of weather and climate, along with various other natural systems, are subject to the second law of thermodynamics, which states that entropy (disorder) of an isolated system not in equilibrium will increase in entropy over time. Ultimately, the ability to predict meteorological events is tied with chaos theory.

Impacts and Issues

Even though Lorenz contended it was impossible to accurately predict meteorological events, when computers were invented their ability to handle massive amounts of variables changed that impossibility to, at least, a possibility. Meteorologists in the twenty-first century attempt to predict weather and climate using complicated mathematical equations that model the behavior of Earth's atmosphere. They would also like to be able to estimate global climate changes caused by human activities.

WORDS TO KNOW

DETERMINISTIC: Able to occur in only one way: determined by the laws of nature. In contrast to stochastic, random, or chaotic processes, which are inherently difficult to forecast even when the physical laws governing them are well understood.

DIFFERENTIAL EQUATION: In mathematics, any equation in which one or more derivatives (rates of change) of a variable appear along with the variable itself. Differential equations are needed to describe many physical processes in engineering, physics, and other sciences, and are essential to climate modeling.

EL NIÑO: A warming of the surface waters of the eastern equatorial Pacific that occurs at irregular intervals of 2 to 7 years, usually lasting 1 to 2 years. Along the west coast of South America, southerly winds promote the upwelling of cold, nutrient-rich water that sustains large fish populations, that sustain abundant sea birds, whose droppings support the fertilizer industry. Near the end of each calendar year, a warm current of nutrient-poor tropical water replaces the cold, nutrient-rich surface water. Because this condition often occurs around Christmas, it was named El Niño (Spanish for boy child, referring to the Christ child). In most years the warming lasts only a few weeks or a month, after which the weather patterns return to normal and fishing improves. However, when El Niño conditions last for many months, more extensive ocean warming occurs and economic results can be disastrous. El Niño has been linked to wetter, colder winters in the United States; drier, hotter summers in South America and Europe; and drought in Africa.

ENTROPY: Measure of the disorder of a system.

METEOROLOGY: The science that deals with Earth's atmosphere and its phenomena and with weather and weather forecasting.

NONLINEAR SYSTEM: Physical system in which changes are not always additive or smooth. Climate is a nonlinear system composed of numerous nonlinear subsystems: abrupt climate change occurs at tipping points where the nonlinearity of the system causes drastic change in response to a small additional change in conditions.

The atmosphere itself and individual weather systems are difficult to predict. For instance, because the atmosphere is chaotic, a weather forecast for a 10-day period has little validity by the tenth day and sizeable errors can be noticed after only a few days. However, larger weather systems can be characterized from historical records by knowing initial conditions in the atmosphere. To determine these initial conditions, a large number of initial, but not identical, states are collected. There are about 10 different systems (or regimes) that define weather variability in the northern hemisphere. For instance, the dynamics of ocean water and the atmosphere can raise the water temperature in the Pacific Ocean by about 7°F (4°C), which sometimes causes an El Niño event.

Thus, the meteorologist's goal is not to predict one specific climatic event. Instead, it is to determine the general chance for minor changes in climate (well within average variability of weather from year to year) versus the chance for major changes in climate (which may result in drastic weather changes not experienced in normal climates). Chaos theory allows for the prediction of long-term meteorological events such as global warming and the greenhouse effect.

Modern weather prediction can work when meteorologists gather large amounts of data from accurate sensing devices on Earth and in space about past and current weather and use complicated computer programs to estimate future weather.

However, it is unwise to make premature predictions about meteorological events. Because of chaos theory, it is difficult to calculate the weather with perfect accuracy since meteorology is a chaotic system controlled by an infinite number of variables. Any inaccuracies in the initial conditions, big or small, will have dramatic consequences on the final outcome. These inaccuracies can include defective weather satellites, restrictions of only making approximate measurements, and myriad other reasons.

To succeed over chaos theory, infinitely precise measurements must be done on infinitely accurate computers. In reality, this is impossible. Totally accurate predictions of weather and climate are not possible due to chaos theory. However, scientists will continue to improve on their analyses of weather forecasting with regards to general patterns and forecasts.

See Also Climate Change; El Ninño and La Ninña; Global Warming; Greenhouse Effect; Meteorology.

BIBLIOGRAPHY

Books

The Chaos Avant-garde: Memories of the Early Days of Chaos Theory, edited by Ralph Abraham and Ueda Yoshisuke. River Edge, NJ: World Scientific, 2000.

Danielson, Eric William. Meteorology. Boston: McGraw-Hill, 2003.

Environmental Modelling and Prediction, edited by Gongbing Peng, Lance M. Leslie, and Yaping Shao. New York: Springer, 2002.

Hirsch, Morris W. Differential Equations, Dynamical Systems, and an Introduction to Chaos. Boston: Academic Press, 2004.

Peitgen, Heinz-Otto. Chaos and Fractals: New Frontiers of Science. New York: Springer, 2004.