Stochastic dynamic prediction assumes the laws governing atmospheric behavior are entirely deterministic, but seeks solutions corresponding to probabilistic statements of the initial conditions, thus recognizing the impossibility of exact or sufficiently dense observations. The equation that must be solved is the continuity equation for probability. For practical reasons only approximate solutions to this equation are possible in general. Deterministic forecasts represent a very low order of approximation. More exact methods are developed and some of the attributes and advantages of stochastic dynamic predictions are illustrated by applying them to a low order set of dynamic equations.
Stochastic dynamic predictions have significantly smaller mean square errors than deterministic procedures, and also give specific information on the nature and extent of the uncertainty of the forecast. Also the range of time over which useful forecasts can be obtained is extended. However, they also require considerably more extensive calculations.
The question of analysis to obtain the initial stochastic statement of the atmospheric state is considered and one finds here too a promise of significant advantages over present deterministic methods. It is shown how the stochastic method can be used to assess the value of new or improved data by considering their influence on the decrease in the uncertainty of the forecast. Comparisons among physical-numerical models are also made more effectively by applying stochastic methods. Finally the implications of stochastic dynamic prediction on the question of predictability are briefly considered, with the conclusion that some earlier estimates have been too pessimistic.