scholarly journals An orthogonal curvilinear terrain-following coordinate for atmospheric models

2013 ◽  
Vol 6 (4) ◽  
pp. 5801-5862
Author(s):  
Y. Li ◽  
B. Wang ◽  
D. Wang
Keyword(s):  
Momentum Equation ◽  
Gradient Force ◽  
Pressure Gradient Force ◽  
Atmospheric Models ◽  
Unified Framework ◽  
Terrain Following ◽  
Steep Terrain ◽  
Definition Of ◽  
Σ Coordinate ◽  
Basis Vectors

Abstract. We have designed an orthogonal curvilinear terrain-following coordinate (the orthogonal σ coordinate, or the OS coordinate) to overcome two well-known problems in the classic σ coordinate, namely, pressure gradient force (PGF) errors and advection errors. First, in the design of basis vectors, we rotate the basis vectors of the z coordinate in a particular way in order to reduce the PGF errors and add a special rotation parameter b to each rotation angel in order to reduce the advection errors. Second, the corresponding definition of each OS coordinate is solved through its basis vectors. Third, the scalar equations of the OS coordinate are solved by expanding the vector equation using the basis vectors. Since the computational form of PGF has only one term in each momentum equation of the OS coordinate, the PGF errors will be significantly reduced, according to Li et al. (2012). When a proper b is chosen, the σ levels over a steep terrain can be significantly smoothed, therefore alleviating the advection errors in the OS coordinate. This is demonstrated by a series of 2-D linear advection experiments under a unified framework.

scholarly journals An orthogonal terrain-following coordinate and its preliminary tests using 2-D idealized advection experiments

2014 ◽  
Vol 7 (4) ◽  
pp. 1767-1778 ◽  
Author(s):  
Y. Li ◽  
B. Wang ◽  
D. Wang ◽  
J. Li ◽  
L. Dong
Keyword(s):  
Rotation Angle ◽  
Computational Grids ◽  
Time Step ◽  
Numerical Errors ◽  
Terrain Following ◽  
Steep Terrain ◽  
Definition Of ◽  
Σ Coordinate ◽  
Basis Vectors ◽  
Better Than

Abstract. We have designed an orthogonal curvilinear terrain-following coordinate (the orthogonal σ coordinate, or the OS coordinate) to reduce the advection errors in the classic σ coordinate. First, we rotate the basis vectors of the z coordinate in a specific way in order to obtain the orthogonal, terrain-following basis vectors of the OS coordinate, and then add a rotation parameter b to each rotation angle to create the smoother vertical levels of the OS coordinate with increasing height. Second, we solve the corresponding definition of each OS coordinate through its basis vectors; and then solve the 3-D coordinate surfaces of the OS coordinate numerically, therefore the computational grids created by the OS coordinate are not exactly orthogonal and its orthogonality is dependent on the accuracy of a numerical method. Third, through choosing a proper b, we can significantly smooth the vertical levels of the OS coordinate over a steep terrain, and, more importantly, we can create the orthogonal, terrain-following computational grids in the vertical through the orthogonal basis vectors of the OS coordinate, which can reduce the advection errors better than the corresponding hybrid σ coordinate. However, the convergence of the grid lines in the OS coordinate over orography restricts the time step and increases the numerical errors. We demonstrate the advantages and the drawbacks of the OS coordinate relative to the hybrid σ coordinate using two sets of 2-D linear advection experiments.

A New Approach to Implement Sigma Coordinate in a Numerical Model

2012 ◽  
Vol 12 (4) ◽  
pp. 1033-1050 ◽  
Author(s):  
Yiyuan Li ◽  
Donghai Wang ◽  
Bin Wang
Keyword(s):  
Numerical Model ◽  
Atmospheric Model ◽  
New Method ◽  
Gradient Force ◽  
Pressure Gradient Force ◽  
Curvilinear Coordinate ◽  
Terrain Following ◽  
Cartesian Coordinate ◽  
Scalar Equations ◽  
Σ Coordinate

AbstractThis study shows a new way to implement terrain-following σ-coordinate in a numerical model, which does not lead to the well-known “pressure gradient force (PGF)” problem. First, the causes of the PGF problem are analyzed with existing methods that are categorized into two different types based on the causes. Then, the new method that bypasses the PGF problem all together is proposed. By comparing these three methods and analyzing the expression of the scalar gradient in a curvilinear coordinate system, this study finds out that only when using the covariant scalar equations of σ-coordinate will the PGF computational form have one term in each momentum component equation, thereby avoiding the PGF problem completely. A convenient way of implementing the covariant scalar equations of σ-coordinate in a numerical atmospheric model is illustrated, which is to set corresponding parameters in the scalar equations of the Cartesian coordinate. Finally, two idealized experiments manifest that the PGF calculated with the new method is more accurate than using the classic one. This method can be used for oceanic models as well, and needs to be tested in both the atmospheric and oceanic models.

scholarly journals Subsiding Shells around Shallow Cumulus Clouds

2008 ◽  
Vol 65 (3) ◽  
pp. 1003-1018 ◽  
Author(s):  
Thijs Heus ◽  
Harm J. J. Jonker
Keyword(s):  
Detailed Comparison ◽  
Momentum Equation ◽  
Gradient Force ◽  
Pressure Gradient Force ◽  
Cumulus Clouds ◽  
Responsible Mechanism ◽  
Lateral Mixing ◽  
Environmental Air ◽  
The Individual

Abstract In this study large-eddy simulations (LES) are used to gain more knowledge on the shell of subsiding air that is frequently observed around cumulus clouds. First, a detailed comparison between observational and numerical results is presented to better validate LES as a tool for studies of microscale phenomena. It is found that horizontal cloud profiles of vertical velocity, humidity, and temperature are in good agreement with observations. They show features similar to the observations, including the presence of the shell of descending air around the cloud. Second, the availability of the complete 3D dataset in LES has been exploited to examine the role of lateral mixing in the exchange of cloud and environmental air. The origin of the subsiding shell is examined by analyzing the individual terms of the vertical momentum equation. Buoyancy is found to be the driving force for this shell, and it is counteracted by the pressure-gradient force. This shows that evaporative cooling at the cloud edge, induced by lateral mixing of cloudy and environmental air, is the responsible mechanism behind the descending shell. For all clouds, and especially the smaller ones, the negative mass flux generated by the subsiding shell is significant. This suggests an important role for lateral mixing throughout the entire cloud layer. The role of the shell in these processes is further explored and described in a conceptual three-layer model of the cloud.

scholarly journals Comparison of Simulated Tropical Cyclone Intensity and Structures Using the WRF with Hydrostatic and Nonhydrostatic Dynamical Cores

Atmosphere ◽  
2018 ◽  
Vol 9 (12) ◽  
pp. 483 ◽  
Author(s):  
Fujun Qi ◽  
Jianfang Fei ◽  
Zhanhong Ma ◽  
Jinrong Chen ◽  
Xiaogang Huang ◽  
...  
Keyword(s):  
Pressure Gradient ◽  
Wrf Model ◽  
Vertical Motion ◽  
Radial Pressure ◽  
Momentum Equation ◽  
Gradient Force ◽  
Pressure Gradient Force ◽  
Dynamical Core ◽  
Budget Analysis ◽  
Perturbation Pressure

This study explored the influence of choosing a nonhydrostatic dynamical core or a hydrostatic dynamical core in the weather research and forecasting (WRF) model on the intensity and structure of simulated tropical cyclones (TCs). A comparison of cloud-resolving simulations using each core revealed significant differences in the TC simulations. In comparison with the nonhydrostatic simulation, the hydrostatic simulation produced a stronger and larger TC, associated with stronger convective activity. A budget analysis of the vertical momentum equation was conducted to investigate the underlying mechanisms. Although the hydrostatic dynamical core was used, the vertical motion was not in strict hydrostatic balance because of the existence of the vertical perturbation pressure gradient force, local buoyancy force, water loading, and sum of the Coriolis and diffusion effects. The contribution of the enhanced vertical perturbation pressure gradient force was found to be more important for stronger upward acceleration in the eyewall in the hydrostatic simulation than in the nonhydrostatic simulation. This is because it leads to intensified convection in the eyewall that releases more latent heat, which induces a larger low-level radial pressure gradient and inflow motion, and eventually leads to a stronger storm.

scholarly journals Hybrid σ–p Coordinate Choices for a Global Model

2009 ◽  
Vol 137 (1) ◽  
pp. 224-245 ◽  
Author(s):  
Stephen Eckermann
Keyword(s):  
Climate Models ◽  
Global Model ◽  
Implicit Time ◽  
Gradient Force ◽  
Pressure Gradient Force ◽  
Vertical Coordinate ◽  
Terrain Following ◽  
The Stability ◽  
Reference Pressure ◽  
The Impact

Abstract A methodology for choosing a hybrid σ–p (sigma–pressure) vertical coordinate of the Simmons–Strüfing form for a global model is presented. The method focuses on properties of the vertical derivative of the terrain-following coefficient, which affect the smoothness and shape of layer thickness profiles and determines the coordinate’s monotonicity over variable terrain. The method is applied to characterize and interrelate existing hybrid coordinate choices in NWP and climate models, then to design new coordinates with specific properties. Offline tests indicate that the new coordinates reduce stratospheric errors in models due to vertical truncation effects in the computation of the pressure gradient force over steep terrain. When implemented in a global model, the new coordinates significantly reduce vorticity and divergence errors at all altitudes in idealized simulations. In forecasting experiments with a global model, the new coordinates slightly reduce the stability of the semi-implicit time scheme. Resetting the reference pressure in the scheme to ∼800 hPa solves the problem for every coordinate except the Sangster–Arakawa–Lamb hybrid, which remains intrinsically less stable than the others. Impacts of different coordinates on forecast skill are neutral or weakly positive, with the new hybrid coordinates yielding slight improvements relative to earlier hybrid choices. This essentially neutral impact indirectly endorses the wide variety of hybrid coordinate choices currently used in NWP and climate models, with the proviso that these tests do not address the impact over longer time scales or on data assimilation.

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