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1.
Generalized Square Conservative Multistep Finite Difference Scheme Incorporating Historical Observations 
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下载免费PDF全文 In this paper,a multistep finite difference scheme has been proposed,whose coefficients are determined taking into consideration compatibility and generalized quadratic conservation,as well as incorporating historical observation data.The schemes have three advantages:high-order accuracy in time,generalized square conservation,and smart use of historical observations.Numerical tests based on the one-dimensional linear advection equations suggest that reasonable consideration of accuracy,square conservation,and inclusion of historical observations is critical for good performance of a finite difference scheme. 相似文献
2.
In this paper,a kind of explicit difference scheme to solve nonlinear evolution equations,perfectly keeping the square conservation by adjusting the time step interval,is constructed,from the comprehensive maintenance of the advantages of the implicit complete square conservative scheme and the explicit instantaneous square conservative scheme.The new schemes are based on the thought of adding a small dissipation,but it is different from the small dissipation method.The dissipative term used in the new schemes is not a simple artificial dissipative term,but a so-called(time) harmonious dissipative term that can compensate for the truncation errors from the dissociation of the time differential term.Therefore,the new schemes may have a high time precision and may acquire a satisfactory effect in numerical tests. 相似文献
3.
变步长显式完全平方守恒差分格式 总被引：8，自引：0，他引：8
综合隐式完全平方守恒差分格式和显式瞬时平方守恒差分格式的优点，针对一类非线性发展方程构造了一种通过自动调节时间步长来保持平方守恒性的显式差分格式。它基于加小耗散的思想，但又与小耗散法有所不同。本文取的耗散项不是一般的人工耗散，而是取能够弥补由于时间离散所产生的截断误差的所谓（时间）协调耗散。因此，该格式具有较高的时间精度。在数值试验中，该类格式可取得满意的效果。 相似文献
4.
一个压力坐标下的海洋环流模式 总被引：5，自引：0，他引：5
A new oceanic general circulation model in pressure coordinates is formulated. Since the bottom pressure changes with time, the vertical coordinate is actually a pressure-σ coordinate. The numerical solution of the model is based on an energy-conservation scheme of finite difference. The most important new feature of the model is that it is a truly compressible ocean model and it is free of the Boussinesq approxima tions. Thus, the new model is quite different from many existing models in the following ways: 1) the exact form of mass conservation, 2) the in-situ instantaneous pressure and the UNESCO equation of state to calculate density, 3) the in-situ density in the momentum equations, 4) finite difference schemes that conserve the total energy. Initial tests showed that the model code runs smoothly, and it is quite stable. The quasi-steady circulation patterns generated by the new model compare well with existing models, but the time evolution of the new model seems different from some existing models. Thus, the non-Boussinesq models may provide more accurate information for climate study and satellite observations. 相似文献
5.
强迫耗散非线性发展方程准完全平方守恒格式的构造 总被引：5，自引：0，他引：5
从描述大气和海洋运动的强迫耗散非线性发展方程出发，对强迫耗散非线性大气和海洋方程组显式差分格式的计算稳定性进行了分析，构造了一类强迫耗散性发展方程的显式准完全平方守恒差分格式，理论分析和数值试验证明，这类显式准完全平方守恒差分格式是计算稳定的．值得推广应用。 相似文献
6.
再论发展方程差分格式的构造和应用 总被引：40，自引：8，他引：32
【摘 要】本文把一大类大气、海洋方程归结为一种发展方程,具体构造了若干定时间步长的显式完全平方守恒差分格式。并证明在一定条件下,这类格式也具有能量守恒、“广义能量”守恒和“平均尺度”守恒的特性,它表明这类格式具有较好的计算稳定性和省时性。文中还探讨了显式平方守恒格式与隐式平方守恒格式之间的密切联系。最后给出了令人满意的用四波的R-H波作数值检验的结果。 相似文献
7.
基于计算准稳定的概念来分析强迫耗散非线性方程显式差分格式的计算稳定性，给出强迫耗散非线性大气方程组显示差分格式计算准稳定的判据，为设计强迫耗散非线性大气方程组计算稳定的显式差分格式提供了新的思路和理论依据。 相似文献
8.
钟青 《Acta Meteorologica Sinica》1999,(2)
In this paper,two formulation theorems of time-difference fidelity schemes for generalquadratic and cubic physical conservation laws are respectively constructed and proved,with earliermajor conserving time-discretized schemes given as special cases.These two theorems can providenew mathematical basis for solving basic formulation problems of more types of conservative time-discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelityschemes by combining existing instantly conserving space-discretized schemes.Besides.the twotheorems can also solve two large categories of problems about linear and nonlinear computationalinstability.The traditional global spectral-vertical finite-difference semi-implicit model for baroclinicprimitive equations is currently used in many countries in the world for operational weatherforecast and numerical simulations of general circulation.The present work,however,based onTheorem 2 formulated in this paper,develops and realizes a high-order total energy conservingsemi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model ofbaroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved forlong,whether in terms of theory or practice.The total energy conserving semi-implicit schemeformulated here is applicable to real data long-term numerical integration.The experiment of thirteen FGGE data 30-day numerical integration indicates that the newtype of total energy conserving semi-implicit fidelity scheme can surely modify the systematicdeviation of energy and mass conserving of the traditional scheme.It should be particularly notedthat,under the experiment conditions of the present work,the systematic errors induced by theviolation of physical laws of conservation in the time-discretized process regarding the traditionalscheme designs(called type Z errors for short)can contribute up to one-third of the totalsystematic root-mean-square(RMS)error at the end of second week of the integration and exceedone half of the total amount four weeks afterwards.In contrast,by realizing a total energyconserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors,roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reducedat the end of second week of the integration,and averagely more than one-third reduced at integraltime of four weeks afterwards.In addition,experiment results also reveal that,in a sense,theeffects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging. 相似文献
9.
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
10.
THE FORMULATION OF FIDELITY SCHEMES OF PHYSICAL CONSERVATION LAWS AND IMPROVEMENTS ON A TRADITIONAL SPECTRAL MODEL OF BAROCLINIC PRIMITIVE EQUATIONS FOR NUMERICAL PREDICTION* 下载免费PDF全文
下载免费PDF全文 Zhong Qing 《Acta Meteorologica Sinica》1999,13(2):226-248
In this paper,two formulation theorems of time-difference fidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,with earlier major conserving time-discretized schemes given as special cases.These two theorems can provide new mathematical basis for solving basic formulation problems of more types of conservative time-discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelity schemes by combining existing instantly conserving space-discretized schemes.Besides.the two theorems can also solve two large categories of problems about linear and nonlinear computational instability.The traditional global spectral-vertical finite-difference semi-implicit model for baroclinic primitive equations is currently used in many countries in the world for operational weather forecast and numerical simulations of general circulation.The present work,however,based on Theorem 2 formulated in this paper,develops and realizes a high-order total energy conserving semi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model of baroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved for long,whether in terms of theory or practice.The total energy conserving semi-implicit scheme formulated here is applicable to real data long-term numerical integration.The experiment of thirteen FGGE data 30-day numerical integration indicates that the new type of total energy conserving semi-implicit fidelity scheme can surely modify the systematic deviation of energy and mass conserving of the traditional scheme.It should be particularly noted that,under the experiment conditions of the present work,the systematic errors induced by the violation of physical laws of conservation in the time-discretized process regarding the traditional scheme designs(called type Z errors for short) can contribute up to one-third of the total systematic root-mean-square(RMS) error at the end of second week of the integration and exceed one half of the total amount four weeks afterwards.In contrast,by realizing a total energy conserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors,roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reduced at the end of second week of the integration,and averagely more than one-third reduced at integral time of four weeks afterwards.In addition,experiment results also reveal that,in a sense,the effects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging. 相似文献
11.
12.
不同模式误差方案在集合Kalman滤波土壤湿度同化中的比较试验 总被引：2，自引：2，他引：0
本文主要目的是探讨不同模式误差方案在土壤湿度同化中的性能。基于集合Kalman滤波同化方法和AVIM (Atmosphere-Vegetation Interaction Model) 陆面模式, 利用理想试验对膨胀因子方案 (Covariance Inflation, 简称CI)、 直接随机扰动方案 (Direct Random Disturbance, 简称DRD)、 误差源扰动方案 (Source Random Disturbance, 简称SRD) 等3种模式误差方案的同化效果进行了比较, 讨论了各方案在不同观测误差、 观测层数、 观测间隔情况下的同化性能。试验结果表明在观测误差估计完全准确的情况下, 3种方案都能获得较好的同化效果, 并且SRD方案相对于真值的均方根误差最小。当观测误差估计不准确时, SRD方案的同化效果仍能基本得以保持, 而CI和DRD方案则对观测误差估计更为敏感, 同化效果下降明显。当同化多层观测时, CI和DRD方案由于难以保持不同层观测之间的匹配关系, 同化结果反而变差, 而SRD方案能有效协调同化多层观测, 增加观测层后同化结果有了进一步的改善。当观测时间间隔较大时, CI和DRD方案的同化效果显著下降; 而SRD方案由于包含了一定的误差订正功能, 在观测稀疏时仍能保持较好的同化效果。 相似文献
13.
Existing simple but theoretically based clear-sky models for longwave down-welling radiation (LDRc) and cloud impact algorithms transforming them to all-sky radiation (LDR) are checked against locally calibrated empirical algorithms. They are evaluated for daylight hours based on measurements in regionally differing climates of Germany. The Prata clear-sky scheme is additionally tested with adjusted coefficients so that LDRc converges against a realistic emissivity for a completely dry atmosphere. This version is characterised by an improved modelled variance. Compared with locally calibrated schemes, bias and root mean square error (RMSE) of the more theoretical clear-sky schemes do not differ significantly and yield even better results at a mountain site. In contrast, the locally calibrated algorithms yield biases up to 9% and an increase in RMSE between 6% and 67%, if applied for other sites. For daylight hours, the cloud impact on LDR can be calculated via the ratio of observed to clear-sky global irradiation (CMFsol). With CMFsol, the Crawford and Duchon scheme reveals the lowest bias and a decrease in RMSE by 22% against the next best performing algorithms. Compared with synoptic cloud observations as input, the bias is reduced by 9 to 28 W m?2 and the scattering of the residuals decreases by 20% to 30%. Based on published results for also non-European sites, it is inferred that the more theoretically based LDRc schemes and cloud impact evaluated via CMFsol are universally applicable and perform at least in the order of magnitude of locally calibrated empirical algorithms. 相似文献
14.
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
15.
简要介绍中国科学院大气物理研究所七十多年来在理论与计算地球流体力学方面的若干研究及其新的进展.在理论地球流体力学方面,介绍了长波动力学及线性稳定性问题、弱非线性理论及行星波动力学以及用Arnold方法(能量-Casimir方法)研究大气和海洋中各种流体运动的非线性稳定性问题的成果.此外,对扰动演变、扰动和基流相互作用及热带大气动力学中的第二类不稳定条件(CISK)也作了简要的介绍.在计算地球流体力学方面,主要内容包括:用物理观点和数学分析相结合的方法阐述了造成计算紊乱和计算不稳定的机理,论证计算稳定性、算 相似文献
16.
LONG VALID TIME ENERGY PERFECT CONSERVATIVE FIDELITY SPECTRAL SCHEMES OF BAROTROPIC PRIMITIVE EQUATIONS* 下载免费PDF全文
下载免费PDF全文 Zhong Qing 《Acta Meteorologica Sinica》1995,9(3):313-324
In accordance with a new compensation principle of discrete computations,the traditional meteorological global (pseudo-) spectral schemes of barotropic primitive equation (s) are transformed into perfect energy conservative fidelity schemes,thus resolving the problems of both nonlinear computational instability and incomplete energy conservation,and raising the computational efficiency of the traditional schemes.As the numerical tests of the new schemes demonstrate,in solving the problem of energy conservation in operational computations,the new schemes can eliminate the (nonlinear) computational instability and,to some extent even the (nonlinear) computational diverging as found in the traditional schemes,Further contrasts between new and traditional schemes also indicate that,in discrete operational computations,the new scheme in the case of nondivergence is capable of prolonging the valid in-tegral time of the corresponding traditional scheme,and eliminating certain kind of systematical computational "climate drift",meanwhile increasing its computational accuracy and reducing its amount of computation.The working principle of this paper is also applicable to the problem concerning baroclinic primitive equations. 相似文献
17.
The Impacts of Initial Perturbations on the Computational Stability of Nonlinear Evolution Equations 下载免费PDF全文
下载免费PDF全文 The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations. 相似文献
18.
选取2014年4月发生的一次黄海近岸海雾个例,利用WRF(Weather Research and Forecasting)模式开展了集合预报试验研究。依据每个集合成员初始场中海平面气压、2 m温度、2 m水汽混合比与2 m相对湿度(relative humidity, RH)4个变量的均方根误差(root mean square error, RMSE)与RMSE集合平均值的相对大小,以剔除高于者而保留低于者的原则,设计了4种不同的初始场集合体择优方案,实施了一系列数值预报试验,比较了不同择优方案的集合预报效果。研究结果表明:(1)蒙特卡罗方法所生成的集合体中存在不少海雾预报效果较差的成员,这会降低集合预报效果,因此初始场择优十分必要;(2)以RH作为择优变量的择优方案(记为RH-RMSE方案),集合预报效果明显优于其他3种方案;(3)对比不择优集合预报,采用RH-RMSE方案的择优集合预报效果不仅节省了50%左右的计算时间,并且公正预兆评分(equitable threat score,ETS)改进率高达36%左右。本研究提出的RH-RMSE方案具有业务化应用前景。 相似文献
19.
针对非线性发展方程的非守恒格式,以一维浅水波方程为例,对非守恒格式的计算稳定性进行了研究分析,探讨了非线性发展方程的非守恒格式与初值的关系.理论分析和数值试验表明,在格式结构已经确定的情况下,非守恒格式的计算稳定性主要由初值的形式所决定. 相似文献