Lorenz is the MIT atmospheric science researcher whose work led to the development of the idea of chaos in physical systems. In meteorology, one of the important implications is that small differences in the initial conditions of the atmosphere can lead to big differences in the weather that results only a few days later. These differences can be too small to detect.
All weather forecasts begin with observations of what the weather is doing all over the world.
These observations are then fed into super computers that use mathematical models of the atmosphere to make predictions. In the United States, these computers are operated by the National Weather Service. The links below will tell you more about how all of this is done. Basics of forecasting The University of Illinois' Online Meteorology section on weather forecasting is the best way to begin understanding the topic. This site's projects and activities section gives teachers and students good ideas for learning more about weather and forecasting.