An extension of Smith's linear theory of orographic precipitation—a two layer approach

Full numerical models with sufficiently high resolution to resolve vital processes in orographic precipitation are often too computationally expensive - excluding accessibility for many users. Efficient and simplified models may be a good alternative. These models sometimes trade realism for simplicity, making them unsuitable for some applications.

In this work, a linear model of orographic precipitation (Smith and Barstad, 2004) with a single-layer approach, has been extended to include vertical layers. The methodology is based on vertically-integrated condensation forced by lifting, advection and transformation to hydro-meteors through microphysical delays. Instead of a single layer representing the whole atmosphere, the new method divides the vertical into layers. Now, an orographic precipitation system with snow aloft melting into rain below, may be represented by two layers. A wind shear with height can also be addressed by different winds at each level. The extended version will collapse into the single-layer version if no layered structure is applied.

In order to test the new approach, the atmosphere has been divided into two vertical layers with idealized flow over a Gaussian ridge of 500m height, and 30km half-width. The results are displayed in terms of i) condensation ratio (CR), the fraction of incoming moisture converted into condensate available for formation of hydrometeors, and ii) drying ratio (DR), defined as the fraction of incoming moisture removed as orographic precipitation. These measures give a good characteristic of the orographic precipitation system. DR and CR have been calculated for various cloud delays and interface heights (separating the two layers). Results from these analyses and comparisons with single-layer theory for various constructions will be presented.

The new approach allows mitigation of the well-known problem of over-excessive drying on the lee sides. The new approach shows a good fit to full numerical model results over the crest and on the lee side.

The new approach enables users to apply a more realistic simple model in simulating orographic precipitation. It requires more vertical information (meting layer height, stability and wind information) than the old theory. However, this is often available from sonde and reanalysis data.