Abstract: Until now, past data are not utilized in numerical weather forecasting owing to the particular formulations, of the problemo It is pointed out in this paper that the condition for solution, formed by whole set of available meteorological data, is not competible to the general system of weather equations.Thus it is neccessary to study the best way of formulation of the problem using the available meteorological data as much as possible in the condition for solution, in order to obtain the optimum way of forecasting. Two possibilities are given. Firstly, it is shown that under certain condition, weather forecasting may be formulated as an evolution problem, in which the past data are utilized. Secondly, past data could also be partly utilized in an initial value problem in which the system of weather equations, with certain meteorological variables eliminated, contain higher order time derivatives. The significance of these formulations is discussed.