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This paper proposes an extension of a linear theory of orographic precipitation (OP). In the original theory, cloud water is produced by forced lifting over mountains, moderated by airflow dynamics. Controlled by a time delay tc, the cloud water converts into hydrometeors, which drift and fall out as precipitation. This drift is controlled by another time delay tf. The new extension proposed here introduces vertical layers, limited to two in this study. In this way, a more realistic vertical structure is permitted. Wind and stability may change with height and different microphysical properties may be assigned to the layers. For instance, a long fallout delay in the upper layer may represent snow that, after falling through a melting layer, turns into rain that has a short delay in the lower model layer. The sensitivity to microphysical delay and wind speed has been addressed for various interface heights separating the two layers. This layered approach allows adjustment of the water vapor influx and truncation of dry descent above a crest line, which, in the context of the existing linear theory, otherwise could cancel cloud water in lower layers. The introduction of layers requires more information in the vertical, but this may be derived, to some extent, from surface information.

An Extension of Smith’s Linear Theory of Orographic Precipitation: Introduction of Vertical Layers*