Sloping Steps Eta Discretization

Choice of the vertical coordinate for NWP and climate models remains an unsettled subject. Following compelling results favoring the eta with step-topography discretization during the late eighties and the early to mid-nineties, difficulties the eta had with downslope windstorms became known. This, and Gallus and Klemp 2D experiments and arguments, led to a rather widespread view that the eta is "ill suited for high resolution prediction models". Thus, a number of recent development efforts, including several WRF (Weather Research and Forecasting Model) dynamical cores, are using sigma or sigma-like coordinates.

A number of recent results of the operational Eta suggests a reexamination of this view. Compared to its driver global model, GFS, the Eta is showing perhaps a surprising skill at extended forecast times, of 2 to 3.5 days, in spite of the advection of the less accurate lateral boundary data. In addition, compared to a higher resolution sigma system model, NMM, the Eta shows similar QPF skill in the eastern United States, with no major topography; but in the mountainous west, the Eta is doing better. GFS is achieving better scores than the Eta in the east, but in the west the Eta is doing better.

The difficulties the Eta had with strong downslope windstorms remain to be better understood. Explanation of the problem is offered. Refinement of the eta discretization, based on this explanation, is reported upon. It is shown that the refined, “sloping-steps” discretization removes the problem as it is illustrated by the Gallus-Klemp experiment. Discretization developed is an add-on to the traditional step-topography Eta code, and preserves the simplicity of the code. Thus, it may be an attractive alternative to shaved cells and/or partial step discretizations, in use in several other atmospheric models.