The Eta slope adjustment, contender for an optimal steepening in a piecewise-linear scheme? Comparison tests

"Attractive features of a fairly simple linear advection scheme are pointed out: the scheme is stable within the CFL condition, conservative, monotonic, and does not falsely amplify extrema during the advection process. It is a piecewise-linear scheme, with an iterative adjustment of slopes within the grid zones, aiming for what may be the most desirable shape within the piecewise-linear framework. Thus, in addition to the features listed, the scheme is "strictly monotonic", the term we suggest to denote that not only will monotonicity be preserved following a time step, but that the piecewise-linear representation prior to the actual transport within the time step is also monotonic. The scheme has been used for some time for the vertical advection of moisture variables in the Eta Model"--Summary, paragraph 1. Fedor Mesinger and Dusan Jovic. "3 September, 2002." System requirements: Adobe Acrobat Reader. Includes bibliographical references (page 28-29). 2002 NWS (National Weather Service) NCEP (National Centers for Environmental Prediction) Library Public Domain 2285