In theory higher-order finite-differencing schemes provide higher accuracy in weather forecast models, and by the late 1980s several research and operational numerical models proved this to be the case in practice. As a result, the proposal to change the original design of the Nested Grid Model (NGM) with its Lax Wendroff scheme from second order finite differencing to fourth order was carefully explored starting in 1989. This was about four years after the NGM had been implemented under the leadership of Dr. Norman A. Phillips as the primary regional forecast model of the U.S. National Weather Service.

Linear analysis of the fourth order finite-differencing scheme indicates its instability with the Lax Wendroff procedure for long waves. When the NGM’s horizontal smoothing is taken into account in the stability analysis, however, the fourth order scheme is shown to be stable for all waves for small Courant number (such as less than 0.27, as the NGM has generally.)

A period of testing in the NGM, as discussed in Juang and Hoke (1992), demonstrated the fourth order scheme to be superior to the second order scheme in terms of the anomaly correlation, mean error, and root mean square error for all layers of the model. Thus, the fourth order scheme was implemented in the operational NGM on 11 December 1990, and continues in use in the model to this day. The elegant design of the code made the fourth order scheme easy to implement.

The experiences with the development of the NGM have significantly influenced the first author of this paper in his modeling work since then. For example, the design of the NCEP Regional Spectral Model (RSM) preprocessor with map projection is based on the NGM. The sigma coordinate used for the nonhydrostatic mesoscale spectral model as the hydrostatic coordinate embedded in the nonhydrostatic system is nothing but the NGM sigma coordinate. The concept of a common array name for carrying all prognostic variables in the NGM was incorporated into the data architecture of the newly developed NCEP flexible global model. Thus, in addition to the significant forecasting advances the NGM provided at the time, its legacy is also manifest in the subsequent and ongoing model development at NCEP.