Reading 2 "Weather and Chaotic Systems" Scientists today have a very good understanding of the physical laws and mathematical equations that govern the behavior and motion of atoms in the air, oceans, and land. Why, then, do we have so much trouble predicting the weather For a long time, most scientists assumed that the difficulty of weather prediction would go away once we had enough weather stations to collect data from around the world and sufficiently powerful computers to deal with all the data. However, we now know that weather is fundamentally unpredictable on time scales longer than a few weeks. To understand why, we must look at the nature of scientific prediction. → Suppose you want to predict the location of a car on a road 1 minute from now. You need two basic pieces of information: where the car is now, and how fast it is moving. If the car is now passing Smith Road and heading north at 1 mile per minute, it will be 1 mile north of Smith Road in 1 minute. Now, suppose you want to predict the weather. Again, you need two basic types of information: (1) the current weather and (2) how weather changes from one moment to the next. You could attempt to predict the weather by creating a "model world." For example, you could overlay a globe of the Earth with graph paper and then specify the current temperature, pressure, cloud cover, and wind within each square. These are your starting points, or initial conditions. Next, you could input all the initial conditions into a computer, along with a set of equations (physical laws) that describe the processes that can change weather from one moment to the next. → Suppose the initial conditions represent the weather around the Earth at this very moment and you run your computer model to predict the weather for the next month in New York City. The model might tell you that tomorrow will be warm and sunny, with cooling during the next week and a major storm passing through a month from now. Now suppose you run the model again but make one minor change in the initial conditions—say, a small change in the wind speed somewhere over Brazil.For tomorrow’s weather, this slightly different initial condition will not change the weather prediction for New York City.But for next month’s weather, the two predictions may not agree at all!The disagreement between the two predictions arises because the laws governing weather can cause very tiny changes in initial conditions to be greatly magnified over time.This extreme sensitivity to initial conditions is sometimes called the butterfly effect: If initial conditions change by as much as the flap of a butterfly’s wings, the resulting prediction may be very different. → The butterfly effect is a hallmark of chaotic systems. Simple systems are described by linear equations in which, for example, increasing a cause produces a proportional increase in an effect. In contrast, chaotic systems are described by nonlinear equations, which allow for subtler and more intricate interactions. For example, the economy is nonlinear because a rise in interest rates does not automatically produce a corresponding change in consumer spending. Weather is nonlinear because a change in the wind speed in one location does not automatically produce a corresponding change in another location. Many (but not all) nonlinear systems exhibit chaotic behavior. → Despite their name, chaotic systems are not completely random. In fact, many chaotic systems have a kind of underlying order that explains the general features of their behavior even while details at any particular moment remain unpredictable. In a sense, many chaotic systems are "predictably unpredictable." Our understanding of chaotic systems is increasing at a tremendous rate, but much remains to be learned about them.
Reading 2 "Weather and Chaotic Systems"
Scientists today have a very good understanding of the physical laws and mathematical equations that govern the behavior and motion of atoms in the air, oceans, and land. Why, then, do we have so much trouble predicting the weather For a long time, most scientists assumed that the difficulty of weather prediction would go away once we had enough weather stations to collect data from around the world and sufficiently powerful computers to deal with all the data. However, we now know that weather is fundamentally unpredictable on time scales longer than a few weeks. To understand why, we must look at the nature of scientific prediction.
→ Suppose you want to predict the location of a car on a road 1 minute from now. You need two basic pieces of information: where the car is now, and how fast it is moving. If the car is now passing Smith Road and heading north at 1 mile per minute, it will be 1 mile north of Smith Road in 1 minute.
Now, suppose you want to predict the weather. Again, you need two basic types of information: (1) the current weather and (2) how weather changes from one moment to the next. You could attempt to predict the weather by creating a "model world." For example, you could overlay a globe of the Earth with graph paper and then specify the current temperature, pressure, cloud cover, and wind within each square. These are your starting points, or initial conditions. Next, you could input all the initial conditions into a computer, along with a set of equations (physical laws) that describe the processes that can change weather from one moment to the next.
→ Suppose the initial conditions represent the weather around the Earth at this very moment and you run your computer model to predict the weather for the next month in New York City. The model might tell you that tomorrow will be warm and sunny, with cooling during the next week and a major storm passing through a month from now. Now suppose you run the model again but make one minor change in the initial conditions—say, a small change in the wind speed somewhere over Brazil.For tomorrow’s weather, this slightly different initial condition will not change the weather prediction for New York City.But for next month’s weather, the two predictions may not agree at all!The disagreement between the two predictions arises because the laws governing weather can cause very tiny changes in initial conditions to be greatly magnified over time.This extreme sensitivity to initial conditions is sometimes called the butterfly effect: If initial conditions change by as much as the flap of a butterfly’s wings, the resulting prediction may be very different.
→ The butterfly effect is a hallmark of chaotic systems. Simple systems are described by linear equations in which, for example, increasing a cause produces a proportional increase in an effect. In contrast, chaotic systems are described by nonlinear equations, which allow for subtler and more intricate interactions. For example, the economy is nonlinear because a rise in interest rates does not automatically produce a corresponding change in consumer spending. Weather is nonlinear because a change in the wind speed in one location does not automatically produce a corresponding change in another location. Many (but not all) nonlinear systems exhibit chaotic behavior.
→ Despite their name, chaotic systems are not completely random. In fact, many chaotic systems have a kind of underlying order that explains the general features of their behavior even while details at any particular moment remain unpredictable. In a sense, many chaotic systems are "predictably unpredictable." Our understanding of chaotic systems is increasing at a tremendous rate, but much remains to be learned about them.
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