Chaos Theory is a result of solving differential equations. When you solve these equations, you still need a set of starting conditions. In a chaotic system, a very similar set of starting conditions can result in very different results.
If you remember from basic school maths, when you integrate 2x you get x^2 plus a constant. This constant is an initial starting condition.
Example 1: A non-chaotic system - an accelerating car
If two cars accelerate at a uniform rates, but one starts at 40mph and one at 41mph, the results will be fairly similar.
Example 2: An analogy of a chaotic system - marbles on a hill
Think of a marble on top of a uniform frictionless hill. If you drop two marbles almost at the very top of the hill, one will go in a completely different direction to another.
Weather has a set of chaotic non-linear differential equations. The reason forecasting is difficult is that the errors in initial measurement will results in a very different result after many iterations. If we had perfect measurements of the state of the atmosphere, and infinitely powerful computers forecasting could be almost perfect.
Chaotic systems are still totally deterministic, but the further into the future you try to predict them, the more accurate an initial observation you need.
If you remember from basic school maths, when you integrate 2x you get x^2 plus a constant. This constant is an initial starting condition.
Example 1: A non-chaotic system - an accelerating car
If two cars accelerate at a uniform rates, but one starts at 40mph and one at 41mph, the results will be fairly similar.
Example 2: An analogy of a chaotic system - marbles on a hill
Think of a marble on top of a uniform frictionless hill. If you drop two marbles almost at the very top of the hill, one will go in a completely different direction to another.
Weather has a set of chaotic non-linear differential equations. The reason forecasting is difficult is that the errors in initial measurement will results in a very different result after many iterations. If we had perfect measurements of the state of the atmosphere, and infinitely powerful computers forecasting could be almost perfect.
Chaotic systems are still totally deterministic, but the further into the future you try to predict them, the more accurate an initial observation you need.
