Theoretical Probabilities of Predicted Occurrences and Amounts of Precipitation

Abstract

In a statistical-dynamical study of the atmosphere, the dependent variables of the dynamic equations constitute the continuous coordinates of a phase space in which an ensemble of possible states develops with time, according to the equations. However, the prediction of precipitation requires upward, not downward, winds and saturated, not unsaturated, air. These dichotomous features introduce first-order discontinuities in the dynamics at the time of condensation. It is shown that these discontinuities do not prevent the continuous transformation of a model ensemble with time, so that theoretical probabilities of atmospheric states are still possible both before and after precipitation begins. By means of the probability calculus, a model is developed to predict a theoretical probability of precipitation occurrence. Examples are given to illustrate these methods.