scholarly journals A New Hybrid Sigma-pressure Vertical Coordinate with Smoothed Coordinate Surfaces

2021 ◽  
Author(s):  
Suk-Jin Choi ◽  
Joseph B. Klemp
Keyword(s):  
Surface Pressure ◽  
Reference Surface ◽  
Rapid Decay ◽  
Vertical Coordinate ◽  
Terrain Following

AbstractAn alternative hybrid sigma-pressure terrain-following coordinate is presented here that provides smoother coordinate surfaces over terrain by allowing a more rapid decay of the influence of smaller-scale topographic structures with height. This is accomplished by first defining a reference surface pressure that includes the influence of the underlying topography. A smoothed version of this reference surface pressure is then created that represents the larger scale features of the topography, while the deviations from the smoothed profile contain the smaller-scale terrain structures. In the hybrid-sigma coordinate formulation presented here, the influences of these deviations in the reference surface pressure from their smoothed values are removed more rapidly with increasing height, thereby producing smoother coordinate surfaces. Testing this approach using several idealized simulations demonstrates a significant reduction in the artificial circulations compared to those arising with the basic sigma or the conventional hybrid sigma coordinate, confirming the beneficial aspects of the smoothed hybrid coordinate surfaces. The smoothed hybrid sigma-pressure coordinate proposed here provides flexibility in reducing the influence of the terrain on the coordinate surfaces and can be easily substituted for the basic hybrid sigma-pressure coordinate.

Two-way nesting ocean models with different vertical coordinates

2021 ◽  
Author(s):  
Jerome Chanut ◽  
James Harle ◽  
Tim Graham ◽  
Laurent Debreu
Keyword(s):  
Vertical Direction ◽  
Test Cases ◽  
Numerical Representation ◽  
Arbitrary Lagrangian Eulerian ◽  
Coordinate Systems ◽  
Vertical Coordinate ◽  
Terrain Following ◽  
New Feature ◽  
Polynomial Reconstruction ◽  
Horizontal Grid

<p>The NEMO platform possesses a versatile block-structured refinement capacity thanks to the AGRIF library. It is however restricted up to versions 4.0x, to the horizontal direction only. In the present work, we explain how we extended the nesting capabilities to the vertical direction, a feature which can appear, in some circumstances, as beneficial as refining the horizontal grid.</p><p>Doing so is not a new concept per se, except that we consider here the general case of child and parent grids with possibly different vertical coordinate systems, hence not logically defined from each other as in previous works. This enables connecting together for instance z (geopotential), s (terrain following) or eventually ALE (Arbitrary Lagrangian Eulerian) coordinate systems. In any cases, two-way exchanges are enabled, which is the other novel aspect tackled here.  </p><p>Considering the vertical nesting procedure itself, we describe the use of high order conservative and monotone polynomial reconstruction operators to remap from parent to child grids and vice versa. Test cases showing the feasibility of the approach are presented, with particular attention on the connection of s and z grids in the context of gravity flow modelling. This work can be considered as a preliminary step towards the application of the vertical nesting concept over major overflow regions in global realistic configurations. The numerical representation of these areas is indeed known to be particularly sensitive to the vertical coordinate formulation. More generally, this work illustrates the typical methodology from the development to the validation of a new feature in the NEMO model.</p>

A New Terrain-Following Vertical Coordinate Formulation for Atmospheric Prediction Models

2002 ◽  
Vol 130 (10) ◽  
pp. 2459-2480 ◽  
Author(s):  
Christoph Schär ◽  
Daniel Leuenberger ◽  
Oliver Fuhrer ◽  
Daniel Lüthi ◽  
Claude Girard
Keyword(s):  
Prediction Models ◽  
Vertical Coordinate ◽  
Terrain Following

scholarly journals Improvement of Mountain-Wave Turbulence Forecasts in NOAA’s Rapid Refresh (RAP) Model with the Hybrid Vertical Coordinate System

2019 ◽  
Vol 34 (3) ◽  
pp. 773-780 ◽  
Author(s):  
Jung-Hoon Kim ◽  
Robert D. Sharman ◽  
Stanley G. Benjamin ◽  
John M. Brown ◽  
Sang-Hun Park ◽  
...  
Keyword(s):  
North America ◽  
Coordinate System ◽  
Weather Prediction ◽  
Energy Dissipation Rate ◽  
Small Scale ◽  
False Alarms ◽  
Mountain Wave ◽  
Vertical Coordinate ◽  
Terrain Following ◽  
Scale Turbulence

Abstract Spurious mountain-wave features have been reported as false alarms of light-or-stronger numerical weather prediction (NWP)-based cruise level turbulence forecasts especially over the western mountainous region of North America. To reduce this problem, a hybrid sigma–pressure vertical coordinate system was implemented in NOAA’s operational Rapid Refresh model, version 4 (RAPv4), which has been running in parallel with the conventional terrain-following coordinate system of RAP version 3 (RAPv3). Direct comparison of vertical velocity |w| fields from the RAPv4 and RAPv3 models shows that the new RAPv4 model significantly reduces small-scale spurious vertical velocities induced by the conventional terrain-following coordinate system in the RAPv3. For aircraft-scale turbulence forecasts, |w| and |w|/Richardson number (|w|/Ri) derived from both the RAPv4 and RAPv3 models are converted into energy dissipation rate (EDR) estimates. Then, those EDR-scaled indices are evaluated using more than 1.2 million in situ EDR turbulence reports from commercial aircraft for 4 months (September–December 2017). Scores of the area under receiver operating characteristic curves for the |w|- and |w|/Ri-based EDR forecasts from the RAPv4 are 0.69 and 0.83, which is statistically significantly improved over the RAPv3 of 0.63 and 0.77, respectively. The new RAPv4 became operational on 12 July 2018 and provides better guidance for operational turbulence forecasting over North America.

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.

A Modified Dynamic Framework for the Atmospheric Spectral Model and Its Application

2008 ◽  
Vol 65 (7) ◽  
pp. 2235-2253 ◽  
Author(s):  
Tongwen Wu ◽  
Rucong Yu ◽  
Fang Zhang
Keyword(s):  
Difference Scheme ◽  
Surface Pressure ◽  
Atmospheric Temperature ◽  
Time Difference ◽  
Spectral Model ◽  
Implicit Time ◽  
Gradient Force ◽  
Reference Surface ◽  
Dynamic Framework ◽  
Simulated Climate

Abstract This paper describes a dynamic framework for an atmospheric general circulation spectral model in which a reference stratified atmospheric temperature and a reference surface pressure are introduced into the governing equations so as to improve the calculation of the pressure gradient force and gradients of surface pressure and temperature. The vertical profile of the reference atmospheric temperature approximately corresponds to that of the U.S. midlatitude standard atmosphere within the troposphere and stratosphere, and the reference surface pressure is a function of surface terrain geopotential and is close to the observed mean surface pressure. Prognostic variables for the temperature and surface pressure are replaced by their perturbations from the prescribed references. The numerical algorithms of the explicit time difference scheme for vorticity and the semi-implicit time difference scheme for divergence, perturbation temperature, and perturbation surface pressure equation are given in detail. The modified numerical framework is implemented in the Community Atmosphere Model version 3 (CAM3) developed at the National Center for Atmospheric Research (NCAR) to test its validation and impact on simulated climate. Both the original and the modified models are run with the same spectral resolution (T42), the same physical parameterizations, and the same boundary conditions corresponding to the observed monthly mean sea surface temperature and sea ice concentration from 1971 to 2000. This permits one to evaluate the performance of the new dynamic framework compared to the commonly used one. Results show that there is a general improvement for the simulated climate at regional and global scales, especially for temperature and wind.

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 Prediction of Clouds and Rain Using a z-Coordinate Nonhydrostatic Model

2006 ◽  
Vol 134 (12) ◽  
pp. 3625-3643 ◽  
Author(s):  
J. Steppeler ◽  
H. W. Bitzer ◽  
Z. Janjic ◽  
U. Schättler ◽  
P. Prohl ◽  
...  
Keyword(s):  
Numerical Models ◽  
Real Data ◽  
High Mountains ◽  
Grid Spacing ◽  
Physical Processes ◽  
Atmospheric Flow ◽  
Vertical Coordinate ◽  
The Earth ◽  
Systematic Improvement ◽  
Terrain Following

Abstract The most common option for numerical models of the atmosphere is to use model layers following the surface of the earth, using a terrain-following vertical coordinate. The present paper investigates the forecast of clouds and precipitation using the z-coordinate nonhydrostatic version of the Lokalmodell (LM-z). This model uses model layers that are parallel to the surface of the sphere and consequently intersect the orography. Physical processes are computed on a special grid, allowing adequate grid spacing even over high mountains. In other respects the model is identical to the nonhydrostatic terrain-following version of the LM, which in a number of European countries is used for operational mesoscale forecasting. The terrain-following version of the LM (LM-tf) is used for comparison with the forecasts of the LM-z. Terrain-following coordinates are accurate when the orography is shallow and smooth, while z-coordinate models need not satisfy this condition. Because the condition of smooth orography is rarely satisfied in reality, z-coordinate models should lead to a better representation of the atmospheric flow near mountains and consequently to a better representation of fog, low stratus, and precipitation. A number of real-data cases, computed with a grid spacing of 7 and 14 km, are investigated. A total of 39 real-data cases have been used to evaluate forecast scores. A rather systematic improvement of precipitation forecasts resulted in a substantial increase of threat scores. Furthermore, RMS verification against radiosondes showed an improvement of the 24-h forecast, both for wind and temperature. To investigate the possibility of flow separation at mountain tops, the flow in the lee of southern Italy was investigated.

A new vertical coordinate formulation to improve forecasts of fog and low stratus in high-resolution numerical weather prediction models

2021 ◽  
Author(s):  
Stephanie Westerhuis ◽  
Oliver Fuhrer
Keyword(s):  
High Resolution ◽  
Numerical Weather Prediction ◽  
Prediction Models ◽  
Positive Impact ◽  
Weather Prediction ◽  
Vertical Coordinate ◽  
Electrical Grid ◽  
Numerical Weather ◽  
Terrain Following ◽  
Numerical Weather Prediction Models

<p>Fog and low stratus pose a major challenge for numerical weather prediction (NWP) models. Despite high resolution in the horizontal (~1 km) and vertical (~20 m), operational NWP models often fail to accurately predict fog and low stratus. This is a major issue at airports which require visibility predictions, or for energy agencies estimating day-ahead input into the electrical grid from photovoltaic power.</p><p>Most studies dedicated to fog and low stratus forecasts have focused on the physical parameterisations or grid resolutions. We illustrate how horizontal advection at the cloud top of fog and low stratus in a grid with sloping vertical coordinates leads to spurious numerical diffusion and subsequent erroneous dissipation of the clouds. This cannot be prevented by employing a higher-order advection scheme. After all, the formulation of the terrain-following vertical coordinate plays a crucial role in regions which do not exhibit perfectly flat orography. We suggest a new vertical coordinate formulation which allows for a faster decay of the orographic signal with altitude and present its positive impact on fog and low stratus forecasts. Our experiments indicate that smoothing of the vertical coordinates at low altitudes is a crucial measure to prevent premature dissipation of fog and low stratus in high-resolution NWP models.</p>

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 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.

Sign in / Sign up

Export Citation Format

Share Document