The development and initial tests of an atmospheric model based on a vertical coordinate with a smooth transition from terrain following to isentropic coordinates

1998 ◽  
Vol 15 (3) ◽  
pp. 283-299 ◽  
Author(s):  
D. R. Johnson ◽  
Zhuo jian Yuan
Keyword(s):  
Atmospheric Model ◽  
Smooth Transition ◽  
Vertical Coordinate ◽  
Model Based ◽  
Terrain Following ◽  
Isentropic Coordinates

Incorporating Condensational Heating into a Nonhydrostatic Atmospheric Model Based on a Hybrid Isentropic–Sigma Vertical Coordinate

2011 ◽  
Vol 139 (9) ◽  
pp. 2940-2954 ◽  
Author(s):  
Michael D. Toy
Keyword(s):  
Mass Flux ◽  
Deep Convection ◽  
Atmospheric Model ◽  
Atmospheric Models ◽  
Vertical Coordinate ◽  
Adiabatic Flow ◽  
Model Based ◽  
Terrain Following ◽  
Environmental Air ◽  
Isentropic Coordinates

Using isentropic coordinates in atmospheric models has the advantage of eliminating the cross-coordinate vertical mass flux for adiabatic flow, and virtually eliminating the associated numerical error in the vertical transport. This is a significant benefit since much of the flow in the atmosphere is approximately adiabatic. Nonadiabatic processes, such as condensational heating, result in a nonzero vertical velocity [Formula: see text] in isentropic coordinates. A method for incorporating condensational heating into a nonhydrostatic atmospheric model based on a hybrid isentropic–sigma vertical coordinate is presented. The model is tested with various 2D moist simulations and the results are compared with those using a traditional terrain-following, height-based sigma coordinate. With the hybrid coordinate, there are improvements in the representation of the developing cloud field in a mountain wave experiment. In a simulation of deep convection, the adaptive hybrid coordinate successfully simulates the turbulent nature of the convection, while maintaining the quasi-Lagrangian nature of the isentropic coordinate in the surrounding dry air. The vertical cross-coordinate mass flux is almost zero in the environmental air, as well as in the stratosphere above the convective tower.

A Supercell Storm Simulation Using a Nonhydrostatic Cloud-Resolving Model Based on a Hybrid Isentropic-Sigma Vertical Coordinate

2013 ◽  
Vol 141 (4) ◽  
pp. 1204-1215 ◽  
Author(s):  
Michael D. Toy
Keyword(s):  
Mass Flux ◽  
Potential Temperature ◽  
Three Dimensional ◽  
Vertical Motion ◽  
Implicit Time ◽  
Vertical Coordinate ◽  
Model Based ◽  
Supercell Storm ◽  
Coordinate Model ◽  
Isentropic Coordinates

Abstract A three-dimensional simulation of a supercell storm is performed with a nonhydrostatic model based on a hybrid isentropic-sigma vertical coordinate. The coordinate is a terrain-following, height-based coordinate near the surface that smoothly transitions to potential temperature with height. Using isentropic coordinates provides the advantage of having zero cross-coordinate vertical mass flux for adiabatic flow, which virtually eliminates the numerical error in the vertical transport. The model uses an adaptive grid algorithm by which the coordinate surfaces may deviate from their target isentropes to maintain a sufficiently smooth mesh, while allowing the turbulence and vertical motion associated with convection to develop. The storm simulated by the hybrid-coordinate model compares well with simulations by Eulerian-coordinate models, but with the key difference being that the cross-coordinate mass flux is significantly smaller in much of the domain with the hybrid-coordinate model. A semi-implicit time-differencing scheme for numerically stabilizing vertically propagating acoustic modes in isentropic coordinates is also presented in the paper.

scholarly journals Design of a Nonhydrostatic Atmospheric Model Based on a Generalized Vertical Coordinate

2009 ◽  
Vol 137 (7) ◽  
pp. 2305-2330 ◽  
Author(s):  
Michael D. Toy ◽  
David A. Randall
Keyword(s):  
Atmospheric Model ◽  
Static Stability ◽  
Vertical Coordinate ◽  
Adiabatic Flow ◽  
Pressure Drag ◽  
Model Based ◽  
Ale Methods ◽  
Coordinate Model ◽  
Atmospheric Motion ◽  
Limiting Case

The isentropic system of equations has particular advantages in the numerical modeling of weather and climate. These include the elimination of the vertical velocity in adiabatic flow, which simplifies the motion to a two-dimensional problem and greatly reduces the numerical errors associated with vertical advection. The mechanism for the vertical transfer of horizontal momentum is simply the pressure drag acting on isentropic coordinate surfaces under frictionless, adiabatic conditions. In addition, vertical resolution is enhanced in regions of high static stability, which leads to better resolution of features such as the tropopause. Negative static stability and isentropic overturning frequently occur in finescale atmospheric motion. This presents a challenge to nonhydrostatic modeling with the isentropic vertical coordinate. This paper presents a new nonhydrostatic atmospheric model based on a generalized vertical coordinate. The coordinate is specified in a manner similar to that of Konor and Arakawa, but “arbitrary Eulerian–Lagrangian” (ALE) methods are used to maintain coordinate monotonicity in regions of negative static stability and to return the coordinate surfaces to their isentropic “targets” in statically stable regions. The model is mass conserving and implements a vertical differencing scheme that satisfies two additional integral constraints for the limiting case of z coordinates. The hybrid vertical coordinate model is tested with mountain-wave experiments including a downslope windstorm with breaking gravity waves. The results show that the advantages of the isentropic coordinate are realized in the model with regard to vertical tracer and momentum transport. Also, the isentropic overturning associated with the wave breaking is successfully handled by the coordinate formulation.

The EPIC atmospheric model with an isentropic/terrain-following hybrid vertical coordinate

Icarus ◽  
2006 ◽  
Vol 182 (1) ◽  
pp. 259-273 ◽  
Author(s):  
Timothy E. Dowling ◽  
Mary E. Bradley ◽  
Edward Colón ◽  
John Kramer ◽  
Raymond P. LeBeau ◽  
...  
Keyword(s):  
Atmospheric Model ◽  
Vertical Coordinate ◽  
Terrain Following

scholarly journals A Generalization of the SLEVE Vertical Coordinate

2010 ◽  
Vol 138 (9) ◽  
pp. 3683-3689 ◽  
Author(s):  
Daniel Leuenberger ◽  
Marcel Koller ◽  
Oliver Fuhrer ◽  
Christoph Schär
Keyword(s):  
Atmospheric Model ◽  
Upper Atmosphere ◽  
Complex Topography ◽  
Uniform Thickness ◽  
Atmospheric Models ◽  
Vertical Coordinate ◽  
Numerical Errors ◽  
Computational Mesh ◽  
Terrain Following ◽  
New Formulation

Abstract Most atmospheric models use terrain-following coordinates, and it is well known that the associated deformation of the computational mesh leads to numerical inaccuracies. In a previous study, the authors proposed a new terrain-following coordinate formulation [the smooth level vertical (SLEVE) coordinate], which yields smooth vertical coordinate levels at mid and upper levels and thereby considerably reduces numerical errors in the simulation of flow past complex topography. In the current paper, a generalization of the SLEVE coordinate is presented by using a modified vertical decay of the topographic signature with height. The new formulation enables an almost uniform thickness of the lowermost computational layers, while preserving the fast transition to smooth levels in the mid and upper atmosphere. This allows for a more consistent and more stable coupling with planetary boundary layer schemes, while retaining the advantages over classic sigma coordinates at upper levels. The generalized SLEVE coordinate is implemented and successfully tested in real-case simulations using an operational nonhydrostatic atmospheric model.

scholarly journals Coordinates over Complex Terrain in Atmospheric Model

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
Wen-yih Sun
Keyword(s):  
Complex Terrain ◽  
Stokes Equations ◽  
Atmospheric Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vertical Coordinate ◽  
Curvilinear Coordinate ◽  
Terrain Following ◽  
Cartesian Coordinate ◽  
Energy And Momentum

In the terrain following coordinate, Gal-Chen and Somerville (1975) and other proposed a vertical coordinate  z*=(z-zb)/(zt-zb) and constant spatial intervals of dx* and  dy*along the other directions.  Because the variation of  and  was ignored, their coordinate does not really follow the terrain.  It fails to reproduce the divergence and curl over a complex terrain.  Aligning the coordinate with real terrain, the divergence and curl we obtained from the curvilinear coordinate are consistent with the Cartesian coordinate.  With a modification, the simulated total mass, energy, and momentum from the Navier-Stokes equations are conserved and in agreement with those calculated from Cartesian coordinate.

scholarly journals On the Progressive Attenuation of Finescale Orography Contributions to the Vertical Coordinate Surfaces within a Terrain-Following Coordinate System

2020 ◽  
Vol 148 (10) ◽  
pp. 4143-4158
Author(s):  
Syed Zahid Husain ◽  
Claude Girard ◽  
Leo Separovic ◽  
André Plante ◽  
Shawn Corvec
Keyword(s):  
Complex Terrain ◽  
Large Scale ◽  
Computational Cost ◽  
Vertical Motion ◽  
Atmospheric Model ◽  
Vertical Coordinate ◽  
Global Environmental ◽  
Terrain Following ◽  
Prediction Systems ◽  
Global Environmental Multiscale

AbstractA modified hybrid terrain-following vertical coordinate has recently been implemented within the Global Environmental Multiscale atmospheric model that introduces separately controlled height-dependent progressive decaying of the small- and large-scale orography contributions on the vertical coordinate surfaces. The new vertical coordinate allows for a faster decay of the finescale orography imprints on the coordinate surfaces with increasing height while relaxing the compression of the lowest model levels over complex terrain. A number of tests carried out—including experiments involving Environment and Climate Change Canada’s operational regional and global deterministic prediction systems—demonstrate that the new vertical coordinate effectively eliminates terrain-induced spurious generation and amplification of upper-air vertical motion and kinetic energy without increasing the computational cost. Results also show potential improvements in precipitation over complex terrain.

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