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.

scholarly journals Staggered Vertical Discretization of the Canadian Environmental Multiscale (GEM) Model Using a Coordinate of the Log-Hydrostatic-Pressure Type

2014 ◽  
Vol 142 (3) ◽  
pp. 1183-1196 ◽  
Author(s):  
Claude Girard ◽  
André Plante ◽  
Michel Desgagné ◽  
Ron McTaggart-Cowan ◽  
Jean Côté ◽  
...  
Keyword(s):  
Hydrostatic Pressure ◽  
Solution Method ◽  
Time Integration ◽  
Atmospheric Model ◽  
Integration Scheme ◽  
Limited Area ◽  
Vertical Coordinate ◽  
Global Environmental ◽  
Time Integration Scheme ◽  
Global Environmental Multiscale

Abstract The Global Environmental Multiscale (GEM) model is the Canadian atmospheric model used for meteorological forecasting at all scales. A limited-area version now also exists. It is a gridpoint model with an implicit semi-Lagrangian iterative space–time integration scheme. In the “horizontal,” the equations are written in spherical coordinates with the traditional shallow atmosphere approximations and are discretized on an Arakawa C grid. In the “vertical,” the equations were originally defined using a hydrostatic-pressure coordinate and discretized on a regular (unstaggered) grid, a configuration found to be particularly susceptible to noise. Among the possible alternatives, the Charney–Phillips grid, with its unique characteristics, and, as the vertical coordinate, log-hydrostatic pressure are adopted. In this paper, an attempt is made to justify these two choices on theoretical grounds. The resulting equations and their vertical discretization are described and the solution method of what is forming the new dynamical core of GEM is presented, focusing on these two aspects.

An Evaluation of a Hybrid, Terrain-Following Vertical Coordinate in the WRF-Based RAP and HRRR Models

2020 ◽  
Vol 35 (3) ◽  
pp. 1081-1096 ◽  
Author(s):  
Jeffrey Beck ◽  
John Brown ◽  
Jimy Dudhia ◽  
David Gill ◽  
Tracy Hertneky ◽  
...  
Keyword(s):  
Complex Terrain ◽  
Wrf Model ◽  
Vertical Motion ◽  
Weather Research And Forecasting ◽  
Mountainous Terrain ◽  
Vertical Coordinate ◽  
Numerical Noise ◽  
Terrain Following ◽  
Model Equations ◽  
Real Time Simulations

Abstract A new hybrid, sigma-pressure vertical coordinate was recently added to the Weather Research and Forecasting (WRF) Model in an effort to reduce numerical noise in the model equations near complex terrain. Testing of this hybrid, terrain-following coordinate was undertaken in the WRF-based Rapid Refresh (RAP) and High-Resolution Rapid Refresh (HRRR) models to assess impacts on retrospective and real-time simulations. Initial cold-start simulations indicated that the majority of differences between the hybrid and traditional sigma coordinate were confined to regions downstream of mountainous terrain and focused in the upper levels. Week-long retrospective simulations generally resulted in small improvements for the RAP, and a neutral impact in the HRRR when the hybrid coordinate was used. However, one possibility is that the inclusion of data assimilation in the experiments may have minimized differences between the vertical coordinates. Finally, analysis of turbulence forecasts with the new hybrid coordinate indicate a significant reduction in spurious vertical motion over the full length of the Rocky Mountains. Overall, the results indicate a potential to improve forecast metrics through implementation of the hybrid coordinate, particularly at upper levels, and downstream of complex terrain.

scholarly journals A New Dynamical Core of the Global Environmental Multiscale (GEM) Model with a Height-Based Terrain-Following Vertical Coordinate

2019 ◽  
Vol 147 (7) ◽  
pp. 2555-2578 ◽  
Author(s):  
Syed Zahid Husain ◽  
Claude Girard ◽  
Abdessamad Qaddouri ◽  
André Plante
Keyword(s):  
Numerical Experiments ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dynamical Core ◽  
Vertical Coordinate ◽  
Solution Approach ◽  
Global Environmental ◽  
Wide Range ◽  
Terrain Following ◽  
Global Environmental Multiscale

Abstract A new dynamical core of Environment and Climate Change Canada’s Global Environmental Multiscale (GEM) atmospheric model is presented. Unlike the existing log-hydrostatic-pressure-type terrain-following vertical coordinate, the proposed core adopts a height-based approach. The move to a height-based vertical coordinate is motivated by its potential for improving model stability over steep terrain, which is expected to become more prevalent with the increasing demand for very high-resolution forecasting systems. A dynamical core with height-based vertical coordinate generally requires an iterative solution approach. In addition to a three-dimensional iterative solver, a simplified approach has been devised allowing the use of a direct solver for the new dynamical core that separates a three-dimensional elliptic boundary value problem into a set of two-dimensional independent Helmholtz problems. The issue of dynamics–physics coupling has also been studied, and incorporating the physics tendencies within the discretized dynamical equations is found to be the most acceptable approach for the height-based vertical coordinate. The new dynamical core is evaluated using numerical experiments that include two-dimensional nonhydrostatic theoretical cases as well as 25-km resolution global forecasts. For a wide range of horizontal grid resolutions—from a few meters to up to 25 km—the results from the direct solution approach are found to be equivalent to the iterative approach for the new dynamical core. Furthermore, results from the different numerical experiments confirm that the new height-based dynamical core is equivalent to the existing pressure-based core in terms of solution accuracy.

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.

A Higher-Order Closure Model with an Explicit PBL Top

2010 ◽  
Vol 67 (3) ◽  
pp. 834-850 ◽  
Author(s):  
Cara-Lyn Lappen ◽  
David Randall ◽  
Takanobu Yamaguchi
Keyword(s):  
Large Scale ◽  
Computational Cost ◽  
Higher Order ◽  
Entrainment Rate ◽  
Time Step ◽  
Vertical Coordinate ◽  
Second Moments ◽  
Scale Models ◽  
Vertical Grid ◽  
Flux Model

Abstract In 2001, the authors presented a higher-order mass-flux model called “assumed distributions with higher-order closure” (ADHOC 1), which represents the large eddies of the planetary boundary layer (PBL) in terms of an assumed joint distribution of the vertical velocity and scalars. In a subsequent version (ADHOC 2) the authors incorporated vertical momentum fluxes and second moments involving pressure perturbations into the framework. These versions of ADHOC, as well as all other higher-order closure models, are not suitable for use in large-scale models because of the high vertical and temporal resolution that is required. This high resolution is needed mainly because higher-order closure (HOC) models must resolve discontinuities at the PBL top, which can occur anywhere on a model’s Eulerian vertical grid. This paper reports the development of ADHOC 3, in which the computational cost of the model is reduced by introducing the PBL depth as an explicit prognostic variable. ADHOC 3 uses a stretched vertical coordinate that is attached to the PBL top. The discontinuous jumps at the PBL top are “hidden” in the layer edge that represents the PBL top. This new HOC model can use much coarser vertical resolution and a longer time step and is thus suitable for use in large-scale models. To predict the PBL depth, an entrainment parameterization is needed. In the development of the model, the authors have been led to a new view of the old problem of entrainment parameterization. The relatively detailed information available in the HOC model is used to parameterize the entrainment rate. The present approach thus borrows ideas from mixed-layer modeling to create a new, more economical type of HOC model that is better suited for use as a parameterization in large-scale models.

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 The CO5 configuration of the 7 km Atlantic Margin Model: Large scale biases and sensitivity to forcing, physics options and vertical resolution

2017 ◽  
Author(s):  
Enda O'Dea ◽  
Rachel Furner ◽  
Sarah Wakelin ◽  
John Siddorn ◽  
James While ◽  
...  
Keyword(s):  
Large Scale ◽  
Atmospheric Model ◽  
Coastal Ocean ◽  
Climate Projections ◽  
Vertical Resolution ◽  
Vertical Coordinate ◽  
North West ◽  
Sensitivity Tests ◽  
Ocean Forecasting ◽  
Atlantic Margin

Abstract. We describe the physical model component of the standard Coastal Ocean version 5 configuration (CO5) of the European North West Shelf (NWS). CO5 was developed jointly between the Met Office and the National Oceanography Centre. CO5 is designed with the seamless approach in mind, which allows for modeling of multiple timescales for a variety of applications from short-range ocean forecasting through to climate projections. The configuration constitutes the basis of the latest update to the ocean and data assimilation components of the Met Office's operational Forecast Ocean Assimilation Model (FOAM) for the NWS. A 30.5 year non-assimilating control hindcast of CO5 was integrated from January 1981 to June 2012. Sensitivity simulations were conducted with reference to the control run. The control run is compared against a previous non-assimilating Proudman Oceanographic Laboratory Coastal Ocean Modelling System (POLCOMS) hindcast of the NWS. The CO5 control hindcast is shown to have much reduced biases compared to POLCOMS. Emphasis in the system description is weighted to updates in CO5 over previous versions. Updates include an increase in vertical resolution, a new vertical coordinate stretching function, the replacement of climatological riverine sources with the pan-European hydrological model E-HYPE, a new Baltic boundary condition and switching from directly imposed atmospheric model boundary fluxes to calculating the fluxes within the model using bulk formula. Sensitivity tests of the updates are detailed with a view to attributing observed changes in the new system from the previous system and suggesting future directions of research to further improve the system.

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.

scholarly journals The CO5 configuration of the 7 km Atlantic Margin Model: large-scale biases and sensitivity to forcing, physics options and vertical resolution

2017 ◽  
Vol 10 (8) ◽  
pp. 2947-2969 ◽  
Author(s):  
Enda O'Dea ◽  
Rachel Furner ◽  
Sarah Wakelin ◽  
John Siddorn ◽  
James While ◽  
...  
Keyword(s):  
Large Scale ◽  
Atmospheric Model ◽  
Coastal Ocean ◽  
Climate Projections ◽  
Vertical Resolution ◽  
Vertical Coordinate ◽  
North West ◽  
Sensitivity Tests ◽  
Ocean Forecasting ◽  
Atlantic Margin

Abstract. We describe the physical model component of the standard Coastal Ocean version 5 configuration (CO5) of the European north-west shelf (NWS). CO5 was developed jointly between the Met Office and the National Oceanography Centre. CO5 is designed with the seamless approach in mind, which allows for modelling of multiple timescales for a variety of applications from short-range ocean forecasting to climate projections. The configuration constitutes the basis of the latest update to the ocean and data assimilation components of the Met Office's operational Forecast Ocean Assimilation Model (FOAM) for the NWS. A 30.5-year non-assimilating control hindcast of CO5 was integrated from January 1981 to June 2012. Sensitivity simulations were conducted with reference to the control run. The control run is compared against a previous non-assimilating Proudman Oceanographic Laboratory Coastal Ocean Modelling System (POLCOMS) hindcast of the NWS. The CO5 control hindcast is shown to have much reduced biases compared to POLCOMS. Emphasis in the system description is weighted to updates in CO5 over previous versions. Updates include an increase in vertical resolution, a new vertical coordinate stretching function, the replacement of climatological riverine sources with the pan-European hydrological model E-HYPE, a new Baltic boundary condition and switching from directly imposed atmospheric model boundary fluxes to calculating the fluxes within the model using a bulk formula. Sensitivity tests of the updates are detailed with a view toward attributing observed changes in the new system from the previous system and suggesting future directions of research to further improve the system.

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