An ESMF unified nonhydrostatic model for a broad range of spatial and temporal scales

A unified nonhydrostatic model (UMO) for a broad range of spatial and temporal scales is being developed within the Earth System Modeling Framework (ESMF) at the National Centers for Environmental Prediction (NCEP). The UMO follows the general modeling philosophy of the earlier NCEP WRF Nonhydrostatic Mesoscale Model (NMM) grid-point dynamical core. However, the unified model has been reformulated for the Arakawa B grid in the (rotated) longitude-latitude coordinate system.

The dynamical core of the model was discretized following the so called mimetic approach introduced by Arakawa. The “isotropic” horizontal differencing employed in the model conserves a variety of basic and derived dynamical and quadratic quantities and preserves some important properties of differential operators. Among these, the conservation of energy and enstrophy improves the accuracy of the nonlinear dynamics of the model on all scales. In the vertical, the hybrid pressure-sigma coordinate is used. The forward-backward scheme is used for horizontally propagating fast waves, and an implicit scheme is applied for vertically propagating sound waves. The Adams-Bashforth scheme is employed for non-split horizontal advection of the basic dynamical variables and for the Coriolis force. In order to eliminate stability problems due to thin vertical layers, the Crank-Nicholson scheme is used to compute the contributions of the vertical advection. Despite the complexity of the formulation, the computational efficiency of the model has been significantly higher than the computational efficiency of most other nonhydrostatic models.

The nonhydrostatic component of the model dynamics is introduced through an add–on module that can be turned on or off. The extra computational cost of the nonhydrostatic dynamics is low, or nonexistent if the nonhydrostatic extension is switched off at coarser resolutions.

“Across the pole” polar boundary conditions are specified in the global limit. The polar filter selectively reduces tendencies of the wave components of the basic dynamical variables that would otherwise propagate faster in the zonal direction than the fastest wave propagating in the meridional direction. In regional applications the rotated longitude-latitude system is used. With the Equator of the rotated system running through the middle of the integration domain, more uniform grid distances are obtained.

A variety of WRF physical parameterizations have been coupled to the model. This variety is expected to be further extended in the future.

The model code has been parallelized and it scales well. Estimates indicate that the model can be competitive in computational efficiency with other global and regional models. The high computational efficiency of the model promises the possibility of application of nonhydrostatic dynamics on the global scale when single digit resolutions become affordable.

The results of the preliminary testing and evaluation of the model have been encouraging. Examples illustrating the performance of the model on various scales will be discussed.