Layering Principles from One Approach to Isentropic Analysis and Modeling of the Atmosphere

Abstract:

Meteorologists often treat potential temperature (theta)—the temperature a parcel would have if moved adiabatically to the surface—as a vertical coordinate. The resulting layers (isentropes) are lagrangian-like. Bosart, in a 2002 tribute to Reed, writes “PV as a tracer [along isentropes] enabled Reed, Danielson … to adopt a Lagrangian perspective in studies of cyclogenesis and upper-level frontogenesis.” Bosart also mentions Shapiro’s work on clear-air turbulence and Bleck’s modeling: “Bleck ... simulated cyclogenesis using a simple model [on] surfaces of constant potential temperature.”

From the author’s work helping Bleck and Shapiro with isentropic analysis and modeling, the following principles are offered as potentially useful in defining reusable, consistent data layers across space and time in multiple domains.

Monotonicity— Layers reflect transformed coordinates, mappable to/from elevation, hence strictly monotonic across the geographic domain. I.e., layers cannot intersect. Bleck devised an invertible algorithm mapping pressure along soundings to a coordinate resembling potential temperature (departing only to maintain monotonicity). A collection of these (at one observing time) is a sampled representation of the transform between (lat, lon, elev) and (lat, lon, theta).

Suggested principle: Data layers possess, for a geographic sample set, invertible algorithms to map between elevation and a monotonic transform coordinate.

Intralayer Interpolation — The transformed coordinate may need evaluation at points not in the sample set. The Bleck/Shapiro work showed how easily monotonicity is violated when gridding sample data. This problem was solved via another transform: interpolation on the log of layer differences (i.e., thickness).

Suggested principle: Data layers possess a monotonicity-preserving algorithm to interpolate coordinate values to geographic points not in the sample set.

Representation— The Bleck/Shapiro work entailed no data sharing, so this suggestion is speculative.

Suggested principle: Layers are 2-D only superficially, so the OGC standard for representing them may be Web Coverage Service (WCS over netCDF). WCS embraces features as well as coverages and can represent higher dimensions. A WCS profile specific to layers may be required for true reusability.