Certain unusual configurations of data can serve as the basis for precise weather forecasts, even though the exact causal mechanisms are not understood.

Most significant gains in the accuracy of the relevant mathematical models are accompanied by clear gains in the precision of weather forecasts.

Mathematical models of the meteorological aftermath of such catastrophic events as volcanic eruptions are beginning to be constructed.

Modern weather forecasts for as much as a full day ahead are broadly correct about 80 percent of the time.

Meteorologists readily concede that the accurate mathematical model they are talking about is not now in their power to construct.