Comparison of Terrain-Following and Cut-Cell Grids Using a Nonhydrostatic Model

Hilary Weller,James Shaw

doi:10.1175/mwr-d-15-0226.1

Abstract

Abstract Terrain-following coordinates are widely used in operational models but the cut-cell method has been proposed as an alternative that can more accurately represent atmospheric dynamics over steep orography. Because the type of grid is usually chosen during model implementation, it becomes necessary to use different models to compare the accuracy of different grids. In contrast, here a C-grid finite-volume model enables a like-for-like comparison of terrain-following and cut-cell grids. A series of standard two-dimensional tests using idealized terrain are performed: tracer advection in a prescribed horizontal velocity field, a test starting from resting initial conditions, and orographically induced gravity waves described by nonhydrostatic dynamics. In addition, three new tests are formulated: a more challenging resting atmosphere case, and two new advection tests having a velocity field that is everywhere tangential to the terrain-following coordinate surfaces. These new tests present a challenge on cut-cell grids. The results of the advection tests demonstrate that accuracy depends primarily upon alignment of the flow with the grid rather than grid orthogonality. A resting atmosphere is well maintained on all grids. In the gravity waves test, results on all grids are in good agreement with existing results from the literature, although terrain-following velocity fields lead to errors on cut-cell grids. Because of semi-implicit time stepping and an upwind-biased, explicit advection scheme, there are no time step restrictions associated with small cut cells. In contradiction to other studies, no significant advantages of cut cells or smoothed coordinates are found.

Highlights

Representing orography accurately in numerical weather prediction systems is necessary to model downslope winds and local precipitation
We have presented a like-for-like comparison between terrain following and cut cell grids using a single model
Accuracy on the basic terrain following (BTF), smooth level vertical (SLEVE) and cut cell grids was evaluated in a series of two-dimensional tests

Summary

Introduction

Representing orography accurately in numerical weather prediction systems is necessary to model downslope winds and local precipitation. The technique proposed by Weller and Shahrokhi (2014) involved calculating pressure gradients in the direction aligned with the grid, ensuring curl-free pressure gradients and improving accuracy Despite their associated numerical errors, TF layers are in widespread operational use (Steppeler et al 2003). A comparison of TF and cut cells using real initial data by Steppeler et al (2013) found that five-day forecasts of precipitation and wind over Asia in January 1989 were more accurate in the cut cell model, this result was dependent on using an old version of a model Another alternative method is the eta coordinate, described by Mesinger et al (1988). This technique has the advantage that cells are not shortened in the direction of flow and so there should be no additional constraints on the advective Courant number

Models

Results

Conclusions