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.

scholarly journals A harmonized multi-time difference scheme and its stability

2005 ◽  
Vol 54 (7) ◽  
pp. 3465
Author(s):  
Zhang Li-Xin ◽  
Qian Wei-Hong ◽  
Gao Xin-Quan ◽  
Chou Ji-Fan
Keyword(s):  
Difference Scheme ◽  
Time Difference

An Explicit Time-Difference Scheme with an Adams–Bashforth Predictor and a Trapezoidal Corrector

2012 ◽  
Vol 140 (1) ◽  
pp. 307-322 ◽  
Author(s):  
Sajal K. Kar
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Numerical Models ◽  
Time Difference ◽  
Von Neumann ◽  
Fully Implicit ◽  
Implicit Schemes ◽  
Spatial Dimensions ◽  
Von Neumann Stability ◽  
Predictor Corrector

Abstract A new predictor-corrector time-difference scheme that employs a second-order Adams–Bashforth scheme for the predictor and a trapezoidal scheme for the corrector is introduced. The von Neumann stability properties of the proposed Adams–Bashforth trapezoidal scheme are determined for the oscillation and friction equations. Effectiveness of the scheme is demonstrated through a number of time integrations using finite-difference numerical models of varying complexities in one and two spatial dimensions. The proposed scheme has useful implications for the fully implicit schemes currently employed in some semi-Lagrangian models of the atmosphere.

scholarly journals Numerical experiments on a harmonized multi-time difference scheme

2006 ◽  
Vol 55 (4) ◽  
pp. 2099
Author(s):  
Zhang Li-Xin ◽  
Gao Xin-Quan ◽  
Li Jian-Ping
Keyword(s):  
Difference Scheme ◽  
Numerical Experiments ◽  
Time Difference

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.

scholarly journals A Dynamical Core with Double Fourier Series: Comparison with the Spherical Harmonics Method

2006 ◽  
Vol 134 (4) ◽  
pp. 1299-1315 ◽  
Author(s):  
Hyeong-Bin Cheong
Keyword(s):  
Fourier Series ◽  
Helmholtz Equation ◽  
Gravity Wave ◽  
Spherical Harmonics ◽  
Surface Pressure ◽  
Double Fourier Series ◽  
Implicit Time ◽  
Dynamical Core ◽  
Fourier Filtering

Abstract A dynamical core of a general circulation model with the spectral method using double Fourier series (DFS) as basis functions is presented. The model uses the hydrostatic balance approximation and sigma coordinate system in the vertical direction and includes no topography. The model atmosphere is divided into 25 layers with equal sigma depths. Prognostic equations for the vorticity, divergence, temperature, and logarithmic surface pressure are solved by the DFS spectral-transform method with the Fourier filtering at middle and high latitudes. A semi-implicit time-stepping procedure, which deals with the eigendecomposition and inversion of the 3D Helmholtz equation associated with the gravity wave terms, is incorporated for the gravity wave–related terms. The DFS model is tested in terms of the solution of the 3D Helmholtz equation, balanced initial state, developing baroclinic waves, and short- and long-term Held–Suarez–Williamson simulations for T42, T62, T84, and T106 resolutions. It is found that the DFS model is stable and accurate and produces almost the same results as the spherical harmonics method (SHM). The normalized difference (i.e., L2 norm error) measured from the results of highest-resolution SHM-T106 showed a desirable convergence of the DFS solution with the resolution. The convergence property, however, varies with the test case and prognostic variables. The total mass (or global integrated surface pressure) is conserved to a good approximation in the long-term simulations. Computing on the high-performance computer NEC SX-5 (parallel-vector architecture) indicated that DFS is more efficient than the SHM and the efficiency increases with the resolution, for example, by factors of 2.09 and 7.68 for T212 and T1022, respectively.

scholarly journals On the Computation of the Mountain Torque from Gridded Global Datasets

2008 ◽  
Vol 136 (10) ◽  
pp. 4005-4009 ◽  
Author(s):  
Huei-Ping Huang ◽  
Klaus M. Weickmann
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Spectral Method ◽  
Surface Pressure ◽  
Finite Difference Scheme ◽  
Difference Schemes ◽  
Finite Difference Schemes ◽  
Axial Component ◽  
Practical Applications ◽  
Benchmark Calculation

This note evaluates the numerical schemes used for computing the axial component of the mountain torque from gridded global surface pressure and topography datasets. It is shown that the two formulas of the mountain torque based on (i) an integral of the product of the surface pressure and the gradient of topography, and (ii) an integral of the product of the topography and the surface pressure gradient, should produce identical results if a centered even-ordered finite-difference scheme or the spectral method is used to evaluate the integrand. Noncentered finite-difference schemes are not recommended not only because they produce extremely large errors but also because they produce different results for the two formulas. When compared with the benchmark calculation using the spectral method, it is found that the centered fourth-order finite-difference scheme is an efficient and generally accurate approximation for practical applications. Using the data from NCEP–NCAR reanalysis, the finite-difference schemes generally underestimate the global mountain torque compared to the benchmark. This negative error is interpreted as due to the asymmetry in the distribution of surface pressure and in the steepness of the topography between the western and eastern slopes of the mountains.

Numerical Analysis on Aerodynamic Characteristics of Truck

2012 ◽  
Vol 590 ◽  
pp. 337-340
Author(s):  
Hai Tao Bao
Keyword(s):  
Difference Scheme ◽  
Aerodynamic Drag ◽  
Length Change ◽  
Aerodynamic Characteristics ◽  
Implicit Time ◽  
Dissipation Term ◽  
Time Integral ◽  
Integral Scheme ◽  
Volume Method ◽  
Scheme Analysis

Computational Fluid Dynamics (CFD) is used for the investigation of the aerodynamic characteristics of the truck. The gap between the truck and the container of the heavy truck on its aerodynamic characteristics were simulated by using equations and dynamic mesh method. The finite volume method is used to discrete the governing equations, the second-order up wind difference scheme is adopted for the convection term and the centric difference scheme for the dissipation term. The discretion of time is carried out by a full-implicit time integral scheme. Analysis of the simulated flow fields and the change pattern of the aerodynamic drag under different gap length demonstrate that when the gap length change and the aerodynamic characteristics change. This paper provides a theoretical reference for the development of truck products determining the gap distance between the truck and the container.

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