Q. J. zyxwvutsrqpo R. Mereorol. zyxwvutsr SOC. zyxwvutsrqponm (1996), 122, pp. 495-513 A non-hydrostatic version zyxwv of the NMC’s regional Eta model By WILLIAM A. CALLUS Jr. and MIODRAC RAN(?I@ National Meteorological Center, USA (Received 25 March 1994; revised 12 June 1995) SUMMARY A non-hydrostatic version of the regional Eta model used operationally at the National Meteorological Center (NMC) has been developed by implementing the ideas of Juang (1992) and Laprise (1992), who independently recommended a hydrostatically based, vertical coordinate for a fully compressible set of equations. The grid-point model dynamics is based on perturbation equations in the rpvertical coordinate; the base state may be taken from the operational NMC model, and thus updated with time. Thc non-hydrostatic model uses a stepwise treatment of terrain present in the operational version, eliminating the pressure-gradient-term error associated with sigma-coordinate models over steep topography. The compressible equations are written in a form that allows conservation of energy in a horizontally closed domain with appropriate advective schemes. A two-dimensional version of the model, without parametrizations of physical processes, has been used successfully to simulate ascending warm bubbles and collapsing cold bubbles at high resolutions. KEYWORDS: Convective-scale simulations Non-hydrostatic perturbation model Numerical weather prediction Step orography 1. INTRODUCTION Most numerical models of the atmosphere that are run operationally for forecasting purposes use the hydrostatic approximation and a pressure-related coordinate system. There are only a few exceptions, such as the non-hydrostatic model of the Meteorological Office (e.g. Golding 1990, 1992), used during the early 1990s. The major reason for using the hydrostatic approximation is computational economy. The hydrostatic approximation eliminates vertically propagating sound waves, which may impose a severe linear stability condition since the vertical resolution in the models is typically much higher than the horizontal. In addition, non-hydrostatic models require the solution of either two more prognostic equations (typically for pressure and vertical velocity), or an elliptic equation if the anelastic approximation of Ogura and Phillips (1962) is made. Application of the hydrostatic approximation may be well justified for the horizontal resolutions of 100 km in the 1980s and 40 km in the early 1990s. With a rapid evolution of computing technology and implementation of massively parallel computers in forecasting applications, it is only reasonable to expect that a goal of running a regional model at a resolution of 5 to 10 km may be attainable in the near future. There is probably general agreement that, with these horizontal resolutions, the hydrostatic models should be replaced by non-hydrostatic ones. A difference between the hydrostatic and non-hydrostatic atmosphere, according to Eckart’s (1960) linear analysis of atmospheric waves, concerns the dispersive behaviour of gravity waves. There is a range of high wave-numbers that cannot be described adequately within the hydrostatic approximation. As the frequency of these gravity waves approaches the Brunt-Vaisala frequency, some of the energy must be transferred to vertical kinetic energy, and this process is excluded in the hydrostatic approximation. With horizontal res- olutions that may resolve convective scales, the characteristic strong vertical flows cannot appear unless the non-hydrostatic effects are properly incorporated into the forecasting model. Early non-hydrostatic models have been used mainly for studying small-scale phe- nomena (e.g. Klemp and Wilhelmson 1978; Cotton and Tripoli 1978; Wilhelmson and zy * Corresponding author: National Meteorological Center, UCAR Visiting Research Program, W/NMC2, Room 204, 5200 Auth Road, Camp Springs, MD 20746, USA. 495