Estimating the role of local evaporation in precipitation for a two-dimensional region

Budyko's model for estimating the contributions of locally evaporated and advected moisture to regional precipitation is extended to two dimensions. It is shown that a simple extension by analogy of the one-dimensional Budyko's formula to a two-dimensional region is inconsistent unless the flow in the region is parallel and uniform. The correct extension based on the two-dimensional equations of conservation of water vapor in the region leads to a generalization of Budyko's formula that includes a correction factor depending on the atmospheric flow structure. A general procedure for calculating the correction factor for a given atmospheric flow field is presented. Calculations of the correction factor for specific flow structures show that the deviations of the flow from the rectilinear structure can significantly affect the degree to which the local evaporation contributes to precipitation.