Performance of the cut‐cell method of representing orography in idealized simulations

Abstract

Several tests of a model with a cut-cell representation of orography are presented: a resting atmosphere test, advection across a hill and a warm rising bubble over hills with different gradients. The tests are compared with results from terrain-following models. Results indicate that errors associated with terrain-following coordinates are reduced, in some cases greatly reduced, with the cut-cell approach. In a resting atmosphere, the cut-cell approach does not generate flow around an isolated hill however steep the terrain. Relative errors in a rising bubble test are an order of magnitude smaller than terrain-following simulations.

Curl-Free Pressure Gradients over Orography in a Solution of the Fully Compressible Euler Equations with Implicit Treatment of Acoustic and Gravity Waves

“…To test the model in nonlinear flow regimes and to further test the representation of orography, we use the rising bubble test case of Bryan and Fritsch (2002), modified by Good et al (2013) so that the bubble is rising over orography. This tests the representation of the nonhydrostatic buoyancy and pressure gradient terms on distorted grids such as those associated with terrainfollowing layers.…”

“…To eliminate errors associated with sloping coordinate surfaces, cut cells can be used adjacent to the orography (Adcroft et al 1997;Bonaventura 2000;Steppeler et al 2002;Good et al 2013) so that horizontal grid layers intersect with the orography. However, it is difficult to maintain the resolution of the boundary layer at mountain peaks with cut cells and nonorthogonal distortions will still exist between-cut and non-cut cells next to the ground, meaning that pressure gradients will still not be curl free.…”

Advection errors in an orthogonal terrain‐following coordinate: idealized 2‐D experiments using steep terrains

“…The most popular and successful one is the hybrid terrain-following coordinate (the HTF-coordinate; Arakawa and Lamb, 1977;Simmons and Burridge, 1981;Simmons and Strüfing, 1983;Schär et al, 2002;Klemp, 2011;Li et al, 2011), which has the smoothed vertical layers over steep terrain. An innovative method called cut-cell method featured with the orthogonal Cartesian grids above terrain and irregular grids near the terrain has been introduced to overcome the problem of non-orthogonal grids in the vertical (Adcroft et al, 1997;Yamazaki and Satomura, 2010;Lock et al, 2012;Adcroft, 2013;Steppeler et al, 2013;Good et al, 2014).…”

A Conserved Topographical Representation Scheme Using a Thin-Wall Approximation in Z-Coordinates

“…Although it is simple and straightforward, the nonorthogonality of this approach induces large numerical errors near steep slopes and causes numerical instability for steep topography (Sundqvist 1976). Good et al (2014) demonstrated the undesirable influence of its nonorthogonality using idealized test cases. With realistic forecasting cases, the property of the terrain-following approach was considerably sensitive for precipitation or temperature, particularly near high mountains (Steppeler et al 2006(Steppeler et al , 2011(Steppeler et al , 2013.…”

“…A cut-cell approach with z-coordinates, which has recently been investigated (e.g., Adcroft 2013; Adcroft et al 1997;Good et al 2014;Lock et al 2012;Steppeler et al 2002Steppeler et al , 2006Steppeler et al , 2011Steppeler et al , 2013Walko and Avissar 2008;Yamszaki and Satomura 2010;Yamazaki et al 2016), is that topography is approximated using pricewise linear or bilinear functions. Although topography can be more accurately represented, the method requires complex boundary conditions for the pressure or the velocities on topographical surface.…”