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1.
Abstract When a semi‐Lagrangian integration scheme was introduced into a global spectral model by Ritchie (1988), large errors developed in the neighbourhood of the poles. It took approximately 6 months of effort to diagnose the problem and find an appropriate correction. The method that was used to diagnose the source of error was quite tedious, but it was successful. Furthermore, it seems that this method could be used to diagnose other sources of error that occasionally show up in numerical integrations. For this reason, it was felt that this method should be described in a separate article. This is the main objective of the presentation that follows. An integration is carried out with the original version of the model and some results are presented in order to illustrate these errors. In order to identify their exact cause, the model is stripped down in two steps. At each step, some checks are made to ensure that the errors are stillpresent in the degraded version of the model. In the end, the remaining equations are sufficiently simple to ensure that the cause of the errors becomes obvious. The diagnosis immediately suggests some alternative computational designs. A modification that completely eliminates these errors is then proposed and tested. An integration with the modified spectral model is carried out and results are presented to show that the errors have disappeared. 相似文献
2.
T S Ledley 《Climate Dynamics》1987,2(2):91-100
A thermodynamic sea ice model that has been numerically structured to take time steps on the order of a week has been shown to be sensitive to time step size. This sensitivity was caused by the extrapolation of initial ice growth rates over the long time step. A new parameterization of new sea ice growth on open ocean and in leads that can be used over a large range of time step sizes (at least from 0.3 to 12 days) is described here. In this parameterization new sea ice growth is computed as a power law function of the initial energy deficit in the ocean. This power law takes into account the rapid reduction of the ice growth rate as the sea ice gets thicker, and therefore reduces sensitivity to time step size. Tests of this parameterization show that this method does a good job of simulating the rate of new ice growth when compared to data from Mawson, Antarctica, and is relatively insensitive to the length of the time step. 相似文献
3.
The Dynamical and Climate Tests of an Atmospheric General Circulation Model Using the Second-Order
Adams-Bashforth Method 
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下载免费PDF全文 The Asselin-Robert time filter used in the leapfrog scheme can degrade the accuracy of calculations. The second-order Adams-Bashforth method with the same accuracy as the leapfrog scheme is not subject to time splitting instability. A new semi-implicit atmospheric general circulation spectral model is developed on the basis of NCAR (National Center for Atmospheric Research) CAM3.0 (Community Atmosphere Model3.0). In this new model, the second-order Adams-Bashforth method is used as an alternative to the leapfrog scheme, and a Crank-Nicholson scheme is incorporated for the treatment of fast gravity modes. In this paper, the new model is tested by the Held-Suarez test and an idealized baroclinic wave test. Results of the Held-Suarez test show that the second-order Adams-Bashforth model has similar climate states to those of many other global models and it converges with resolutions. Based on the idealized baroclinic wave test, the capability of di?erent time di?erencing methods for keeping the initial steady-state are compared.This convinces a better ability of the second-order Adams-Bashforth method in maintaining the stability of the initial state. Furthermore, after the baroclinic wave is triggered through overlaying the steady-state initial conditions with the zonal perturbation, the second-order Adams-Bashforth method has an excellent property of convergence, and can represent the process of the baroclinic wave development much better than
the original scheme in CAM3.0. A long-term integration of the new model during the period of 1980-1999 is also carried out and compared with that of CAM3.0. It is found that due to the reduction of simulation errors of prognostic variables, the second-order Adams-Bashforth method also has a better simulation ability for the diagnostic variables, such as precipitation. 相似文献
4.
1 INTRODUCTIONIn global climate models belonging to the finitedifference calculation category, the equations aregenerally solved in normal spherical coordinates. Due tothe convergence of meridians towards the poles inspherical coordinates, the combination of thiscoordinate system and explicit finite-difference methodsleads to two problems. First, the pole itself is a point ofsingularity with direction undefined. Second, due to thedependence of the stability from finite-differencenumerics … 相似文献
5.
Motivated in part by the mathematical problems associated with the application of open boundary conditions to the hydrostatic primitive equations (PE), Browning et al. (1990, Dyn. Atmos. Oceans, 14: 303–332) proposed the use of the reduced system (RS) of equations to replace PE for oceanographic problems. The RS are essentially the Boussinesq equations (BO) with the non-hydrostatic terms in the vertical momentum equation multiplied by a constant δ2 ? 1. This artificially alters the physics (e.g. changing the intemal-inertial wave properties) to facilitate numerical integration, but the changes are assumed to have negligible effects on the dynamics of interest. We assess the accuracy and utility of the RS (following the guidelines for the choice of δ) by comparing numerical finite difference solutions of RS, PE and BO for initial-value problems involving three-dimensional instability of an ocean front and atmospheric frontal development in a two-dimensional Eady wave. Both explicit (BO, PE) and semi-implicit (BOSI, PESI) time-difference schemes are used for the Boussinesq and primitive equations. For RS, the same explicit scheme as for BO is used where δ ? 1 allows larger time steps than with the other explicit models. It is found that relative to BO solutions, the errors for RS are small but increase rapidly and monotonically with increasing δ (over a range consistent with the guidelines) and are greater than the errors for the other models. The use of BOSI allows time steps at least as large as those for RS and results in smaller errors than RS. For these problems, BOSI is the preferable model to replace PE. 相似文献
6.
With the development of numerical weather prediction technology,the traditional global hydrostatic models used in many countries of the world for operational weather forecasting and numerical simulations of general circulation have become more and more unfit for high-impact weather prediction.To address this,it is important to invest in the development of global nonhydrostatic models.Few existing nonhydrostatic global models use consistently the grid finite difference scheme for the primitive equations of dynamical cores,which can subsequently degrade the accuracy of the calculations.A new nonhydrostatic global spectral model,which utilizes the Eulerian spectral method,is developed here from NCAR Community Atmosphere Model 3.0(CAM3.0).Using Janjic's hydrostatic/nonhydrostatic method,a global nonhydrostatic spectral method for the primitive equations has been formulated and developed.In order to retain the integrity of the nonhydrostatic equations,the atmospheric curvature correction and eccentricity correction are considered. In this paper,the Held-Suarez idealized test and an idealized baroclinic wave test are first carried out,which shows that the nonhydrostatic global spectral model has similar climate states to the results of many other global models for long-term idealized integration,as well as better simulation ability for short-term idealized integration.Then,a real case experiment is conducted using the new dynamical core with the full physical parameterizations of subgrid-scale physical processes.The 10-day numerical integration indicates a decrease in systematic error and a better simulation of zonal wind,temperature,and 500-hPa height. 相似文献
7.
郑庆林 《Acta Meteorologica Sinica》1979,37(1):36-43
文中,非线性项的处理用了变维方法,纬向的“完全的谱方法”及经向的“准谱方法”,既有利于克服非线性不稳定,且能大大节省计算量及存储量,使之能在小型计算机上实现其程序设计。通过设计多个地形曲面的办法来考虑地形的作用。在时间差分格式中,将时间步长取成波数的函数,有利于节省计算量。这模式从一九七四年九月开始进行了较多个例的预报实验,其72小时以内的预报效果是比较好的。 相似文献
8.
The adjoint sensitivity related to explosive cyclogenesis in a conditionally unstable atmosphere is investigated in this study.The PSU/NCAR limited-area,nonhydrostatic primitive equation numerical model MM5 and its adjoint system are employed for numerical simulation and adjoint computation,respectively.To ensure the explosive development of a baroclinic wave,the forecast model is initialized with an idealized condition including an idealized two-dimensional baroclinic jet with a balanced three-dimensional moderateamplitude disturbance,derived from a potential vorticity inversion technique.Firstly,the validity period of the tangent linear model for this idealized baroclinic wave case is discussed,considering different initial moisture distributions and a dry condition.Secondly,the 48-h forecast surface pressure center and the vertical component of the relative vorticity of the cyclone are selected as the response functions for adjoint computation in a dry and moist environment,respectively.The preliminary results show that the validity of the tangent linear assumption for this idealized baroclinic wave case can extend to 48 h with intense moist convection,and the validity period can last even longer in the dry adjoint integration.Adjoint sensitivity analysis indicates that the rapid development of the idealized baroclinic wave is sensitive to the initial wind and temperature perturbations around the steering level in the upstream.Moreover,the moist adjoint sensitivity can capture a secondary high sensitivity center in the upper troposphere,which cannot be depicted in the dry adjoint run. 相似文献
9.
Comparison of different order Adams-Bashforth methods in an atmospheric general circulation model 下载免费PDF全文
下载免费PDF全文 The Asselin-Robert time filter used in the leapfrog scheme does degrade the accuracy of calculations. As an attractive alternative
to leapfrog time differencing, the second-order Adams-Bashforth method is not subject to time splitting instability and keeps
excellent calculation accuracy. A second-order Adams-Bashforth model has been developed, which represents better stability,
excellent convergence and improved simulation of prognostic variables. Based on these results, the higher-order Adams-Bashforth
methods are developed on the basis of NCAR (National Center for Atmospheric Research) CAM 3.1 (Community Atmosphere Model
3.1) and the characteristics of dynamical cores are analyzed in this paper. By using Lorenz nonlinear convective equations,
the filtered leapfrog scheme shows an excellent pattern for eliminating 2Δt wave solutions after 20 steps but represents less computational solution accuracy. The fourth-order Adams-Bashforth method
is closely converged to the exact solution and provides a reference against which other methods may be compared. Thus, the
Adams-Bashforth methods produce more accurate and convergent solution with differencing order increasing. The Held-Suarez
idealized test is carried out to demonstrate that all methods have similar climate states to the results of many other global
models for long-term integration. Besides, higher-order methods perform better in mass conservation and exhibit improvement
in simulating tropospheric westerly jets, which is likely equivalent to the advantages of increasing horizontal resolutions.
Based on the idealized baroclinic wave test, a better capability of the higher-order method in maintaining simulation stability
is convinced. Furthermore, after the baroclinic wave is triggered through overlaying the steady-state initial conditions with
the zonal perturbation, the higher-order method has a better ability in the simulation of baroclinic wave perturbation. 相似文献
10.
变分连续同化中优化步长的推导方法及数值试验 总被引：1，自引：0，他引：1
一个好的变分同化方法,必须考虑到预报模式具有误差,并对模式误差进行纠正.变分连续同化(VCA)通过在模式方程中引进一个修正项,连续地调整模式变量,从而达到以上目的.在变分连续同化的迭代过程中,优化步长的选取方法对于同化迭代是否收敛、收敛速度快慢与否都至关重要,文中推导了一种有效利用观测资料计算优化步长的新方法,并以大气运动方程中一维非线性平流波和二维惯性波为例,进行了四维变分资料同化数值试验.数值结果表明,VCA方法和计算优化步长的公式都是有效的. 相似文献
11.
纬向平均环流预报的系统性误差及其改进 总被引：8，自引：0，他引：8
大量的月预报实例分析表明,纬向平均环流(本指高度场纬向平均分量)存在明显的系统性预报误差,且在总误差中占有可观的份额。国内外其它模式也存在类似的现象。为克服这一困难,本尝试了“结合”(hybrid)的途径。应用重构相空间理论和非线性时空序列预测方法,在大量历史资料的基础上,构造了月尺度逐侯纬向平均高度场(零波分量)距平场的非线性预报模型。然后,将非线性预报和谱模式动力预报结合起来,即将非线性预报结果转化为模式需要的颅报量,再在模式积分过程中的每一步取代其相应部分,实施过程订正。初步试验结果表明,这种途样合效地减少了模式纬向环流的预报误差;特别是通过非线性波流相互作用,还改善了部分波动分量的预报。 相似文献
12.
The article is to report some results of numerical experiments on the error growth and the atmosphericpredictability Experiments with two-level global baroclinic primitive equation spectral model have mainresults as follows.The magnitude of initial errors directly affects the error growth,but its distributionform has little effect on the growth.The loss of predictability resulting from small-scale error is much greaterthan that from large-scale error.The small-scale error rapidly grows and is transferred to the large-scaleerror by interaction between different scale waves,which stimulates the growth of error for the whole systemOrographic forcing restrains planetary-scale error(wavenumbers 0—3)but enhances the small-scale error(wavenumbers 8 or greater).Hence,orographic effects on the error growth closely depend on the characteris-tic scale of initial errors,and there may be a critical wavenumber between 4 and 7.The error growth is great-er in Northern Hemisphere than in Southern Hemisphere if initial errors are the same.In the end we givesome discussions about model,initialization scheme,etc.,to improve model prediction. 相似文献
13.
Luo Zhexian 《Acta Meteorologica Sinica》1996,10(1):13-21
By using the linearized barotropic vorticity equation in polar coordinates the stability of perturbations on a large scale circular basic flow is transformed into a generalized eigenvalue problem,yielding the relationship between the growth rate of the amplitude of perturbations and the azimuthal wave number. Then, numerical experiments whose integration time is 60 model hours are performed in terms of a quasi-geostrophic barotropic model in Cartesian coordinates using the perturbation stream function field of unstable mode superimposed on a strong and weak circular basic flows as the initial fields. The experimental results reveal that the amplitudes of the initial perturbations in the model atmosphere grow with time. The amplitude of the perturbations superimposedon the strong circular basic flow grows quicker and forms a spiral-band-like structure. 相似文献
14.
The spatial propagation of meso- and small-scale errors in a Meiyu frontal heavy rainfall event,which occurred in eastern China during 4 -6 July 2003,is investigated by using the mesoscale numerical mo... 相似文献
15.
Operator splitting techniques are widely used in atmospheric modeling in order to reduce the cost of time integration and allow more flexibility by treating each operator separately. However, this is not error free and the magnitude of the error depends on whether the splitted operators commute or not and the magnitude of the splitting time step. In multiphase models, the gas and the aqueous phase chemistries are related through the gas-droplet mass transfer processes. In the present paper, we show that splitting the gas chemistry operator from the aqueous chemistry and mass transfer operator is not appropriate and leads to errors beyond the tolerated thresholds. Analytical expressions for the splitting errors are derived and numerical experiments are conducted. The LAMP chemical mechanism is employed. Time integration is performed with LSODE. 相似文献
16.
罗哲贤 《Acta Meteorologica Sinica》1996,(1)
By using the linearized barotropic vorticity equation in polar coordinates the stability of pertur-bations on a large scale circular basic flow is transformed into a generalized eigenvalue problem,yielding the relationship between the growth rate of the amplitude of perturbations and the az-imuthal wave number. Then, numerical experiments whose integration time is 60 model hours areperformed in terms of a quasi-geostrophic barotropic model in Cartesian coordinates using the per-turbation stream function field of unstable mode superimposed on a strong and weak circular basicflows as the initial fields. The experimental results reveal that the amplitudes of the initial pertur-bations in the model atmosphere grow with time. The amplitude of the perturbations superimposedon the strong circular basic flow grows quicker and forms a spiral-band-like structure. 相似文献
17.
从一般的谱展开方程出发，详细推导了误差增长方程。结果表明误差增长率主要由准确解的切线性方程所决定，扰动非线性平流作用不产生方差意义下的误差增长，而只起分配误差的作用。轨线不稳定是产生误差增长的根本原因。文中提出了计算轨线不稳定增长率的方法。这一方法也适合于时间演变状态不稳定问题的讨论，对Ｌｏｒｅｎｚ系统的轨线不稳定计算表明了理论分析的正确及其意义。 相似文献
18.
19.
In this paper,a numerical simulation of the geostrophic adjustment process with C-grid network is illustrated.A difference scheme which has the energy and potential vorticity conserving relation consistent with the differential equations is given,and the effect of some time difference schemes on dispersion of the gravity-inertia wave is discussed.An improved forward-backward time integration scheme is proposed for keeping the computational stability.The effect of various boundary conditions for a finite region model On the gravity-inertia wave is shown by some calculated results. 相似文献
20.
l.IntroductionWithhighlydevelopingofmodernscientifictechnologyandincessantupdatingoftheobservationalsystem,manykindsofnewsourcesofobservationaldataarereadilyobtained,suchassatellitedataandradardata.Ithasbeenacriticalproblemtopuzzleresearcherstoeffectivelyemploythesedatainnumericalcalculation.4DVARtechniquehasgraduallybeenaveryimportanttoolinthemainstreamofnumericalweatherprediction,becauseitisofstrongcapabilityofcombiningandextractingtheusefulinformationfromallkindsofobservationaldata.Thedat… 相似文献