The relationship between nonconservative schemes and initial values of nonlinear evolution equations

For the nonconservative schemes of the nonlinear evolution equations, taking the one-dimensionalshallow water wave equation as an example, the necessary conditions of computational stability are given.Based on numerical tests, the relationship between the nonlinear computational stability and the construc-tion of difference schemes, as well as the form of initial values, is further discussed. It is proved throughboth theoretical analysis and numerical tests that if the construction of difference schemes is definite, thecomputational stability of nonconservative schemes is decided by the form of initial values.     

非线性发展方程的非守恒格式的计算稳定性问题

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.     

线性与非线性发展方程计算稳定性的比较分析

针对性与非线性发展方程的几种差分格式，以一维线性和非线性平流方程为例，对线性与非线笥发展方程差分格式的计算稳定性进行了比较分析，揭示了差分格式结构和初值形式与计算稳定性的关系。理论分析和数值试验证明，线性与非线性发展方程差分格式的计算稳定性在本质上是完全不同的。     

发展方程计算稳定性的比较分析

对线性与非线性发展方程的几种差分格式,以一维线性和非线性平流方程为例,对线性与非线性发展方程差分格式的计算稳定性进行了比较分析,揭示了差分格式结构和初值形式与非线性计算稳定性的关系。     

强迫耗散非线性发展方程准完全平方守恒格式的构造

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。     

非线性平流方程计算稳定性对初值的依赖性研究

对一维平流方程向前差格式的一个计算不稳定特例进行了讨论，给出了四个命题，并得出结论：在一定的条件下，可以对初值稍加改变，使其在x轴一侧分布而达到计算稳定，从而改进并修正了已有的相关结论。     

长时效的正压原始方程能量完全守恒(拟)谱模式

遵循误差反演补偿新计算原理,对正压原始方程传统气象全球拟谱模式方案进行了改造,构造了正压原始方程能量完全守恒全球拟增模式新计算方案,解决了正压原始方程的(非线性)计算稳定性问题和能量守恒整体性质保持问题,改进了相应正压原始方程传统气象全球拟谱模式方案的计算效能。新方案的数值试验表明:在计算实践上,新方案在解决能量守恒问题的同时,可解决(非线性)计算稳定性问题,并在一定条件下可解决非线性计算收敛性问题。进一步的比较数值试验还表明:在计算实践上,新方案具有在提高相应传统气象方案的计算精度,减少其计算量的同时,延长其计算时效,解决其中一类特定“气候漂移”问题方面的效用。本工作原理也适用于斜压原始方程情形。     

完全非内插半拉格朗日格式在一维 Burgers方程及二维浅水波方程上的应用

在作者过去提出的完全非内插半拉格朗日格式的基础上,针对半拉格朗日格式由于内插带来预报场人为的光滑性问题,进一步发展了这种计算格式,证明了此格式的计算稳定性。为检验这种新的计算格式的性能,在一维和二维问题上进行了应用。在一维问题中采用了一维无粘Burgers方程（方程中有突变点）;二维问题采用了浅水波方程,同时将这些计算结果与Ritchie方案及欧拉方案或一般半拉格朗日内插方案的计算结果进行了比较,发现新格式消除了内插和预报场的人为光滑,并且计算精度有一定程度的提高,这为以后将此格式推广到全球谱模式打下了基础。     

WRF模式物理参数化方案对一次局地大暴雨预报的影响研究

基于WRF(Weather Research and Forecasting)模式及其3Dvar(3-Dimentional Variational)资料同化系统,采用36、12、4 km嵌套网格进行快速更新循环同化和不同的微物理及积云对流参数化方案对比试验,对2011年5月8日鲁中一次局地大暴雨过程进行了研究。结果表明,快速更新循环同化地面观测资料是影响模式降水落区预报准确性的关键因素,不同的微物理和积云对流参数化方案主要影响降水强度预报。采用不同的微物理参数化方案和积云对流参数化方案进行降水预报对比试验表明,LIN方案和WSM6(WRF Single-Moment 6-class)微物理参数化方案对降水预报均较好,LIN方案降水预报较WSM6方案略强。4 km网格预报使用K-F (Kain-Fritsch)积云对流参数化方案或不使用积云对流参数化方案,预报的降水均较好。4 km网格使用旧的K-F积云对流参数化方案,预报的近地层大气风场偏弱,导致大气动力抬升作用偏弱,从而造成模式降水预报偏弱。     

The Impacts of Initial Perturbations on the Computational Stability of Nonlinear Evolution Equations

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.     

预报方程时变参数的一种新递推方案

针对经典递推算法的平稳性和初值敏感性问题，根据描述运动变化的一般性原理，导出一种新的递推算法，并将其引入到气候预报中。理论和实践证明，该方案成功地解决了经典递推算法存在的平稳性和初值敏感性问题。初步的预报应用结果也表明，该方案具有明显的优越性。     

A high-order compact scheme with square-conservativity

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A comparative study of the performance of various vertical discretization schemes

Summary Most finite-difference numerical weather prediction models employ vertical discretizations that are staggered, and are low-order (usually second-order) approximations for the important terms such as the derivation of the geopotential from the hydrostatic equation, and the calculation of the vertically integrated divergence. In a sigma-coordinate model the latter is used for computing both the surface pressure change and the vertical velocity. All of the above-mentioned variables can diminish the accuracy of the forecast if they are not calculated accurately, and can have an impact on related quantities such as precipitation.In this study various discretization schemes in the vertical are compared both in theory and in practice. Four different vertical grids are tested: one unstaggered and three staggered (including the widely-used Lorenz grid). The comparison is carried out by assessing the accuracy of the grids using vertical numerics that range from second-order up to sixth-order.The theoretical part of the study examines how faithfully each vertical grid reproduces the vertical modes of the governing equations linearized with a basic state atmosphere. The performance of the grids is evaluated for 2nd, 4th and 6th-order numerical schemes based on Lagrange polynomials, and for a 6th-ordercompact scheme.Our interpretation of the results of the theoretical study is as follows. The most important result is that the order of accuracy employed in the numerics seems to be more significant than the choice of vertical grid. There are differences between the grids at second-order, but these differences effectively vanish as the order of accuracy increases. The sixth-order schemes all produce very accurate results with the grids performing equally well, and with the compact scheme significantly outperforming the Lagrange scheme. A second major result is that for the number of levels typically used in current operational forecast models, second-order schemes (which are used almost universally) all appear to be relatively poor, for other than the lowest modes.The theoretical claims were confirmed in practice using a large number (100) of forecasts with the Australian Bureau of Meteorology Research Centre's operational model. By comparing test model forecasts using the four grids and the different orders of numerics with very high resolution control model forecasts, the results of the theoretical study seem to be corroborated.With 8 Figures     

LONG VALID TIME ENERGY PERFECT CONSERVATIVE FIDELITY SPECTRAL SCHEMES OF BAROTROPIC PRIMITIVE EQUATIONS

In accordance with a new compensation principle of discrete computations,the traditional meteo-rological global (pseudo-) spectral schemes of barotropic primitive equation (s) are transformed intoperfect energy conservative fidelity schemes,thus resolving the problems of both nonlinear computa-tional instability and incomplete energy conservation,and raising the computational efficiency of thetraditional schemes.As the numerical tests of the new schemes demonstrate,in solving the problem of energy conser-vation in operational computations,the new schemes can eliminate the (nonlinear) computational in-stability and,to some extent even the (nonlinear) computational diverging as found in the traditionalschemes,Further contrasts between new and traditional schemes also indicate that,in discrete opera-tional 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 com-putational“climate drift”,meanwhile increasing its computational accuracy and reducing its amount ofcomputation.The working principle of this paper is also applicable to the problem concerning baroclin-ic primitive equations.     

LONG VALID TIME ENERGY PERFECT CONSERVATIVE FIDELITY SPECTRAL SCHEMES OF BAROTROPIC PRIMITIVE EQUATIONS*

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.     

高阶正定守恒的中心约束多矩有限体积平流模式

采用新的均匀三点中心约束多矩有限体积方法（3-point Multi-moment Constrained finite-Volume scheme for Uniform Points with Center Constraints, MCV3_UPCC）,发展了一个三阶正定守恒的平流模式。三点多矩有限体积方法在单网格内定义等距的3个自由度,采用多矩约束条件并通过控制方程获得时间演变方程。新的三点中心约束多矩方法能在单网格内采用等距的3个点值及中心一阶、二阶导数作为约束条件进行空间4次多项式数值重构,获得3个自由度的时间演变方程;所构建的新数值方案具有三阶精度,边界通量连续性保证了其数值严格守恒。为了抑制该方法的非物理数值振荡,引入了边界保型限制器技术,它能够把数值解控制在既定物理场最小值（最小值为0时则保持数值正定）与最大值之间。数值试验表明新发展的三阶平流模式具有良好的计算精度,能够严格保持数值解的正定性和守恒性,同其他高精度平流模式相当,在实际大气模式水汽等平流输送应用中具备良好的发展潜力。      

WRF4.0模式陆气耦合对不同物理参数化方案的敏感性初探

模式的不同参数化方案会对模拟的天气和气候产生影响,但如何影响陆气耦合还不是很清楚。利用WRF 4.0模式设计了一组16种不同参数化方案组合的集合试验,对华北地区2013年夏季气候进行模拟。结果表明,不同积云对流参数化方案对模拟的降水平均态影响较大,其次是短波辐射方案,而微物理方案影响较小。进一步利用潜热通量(LH,Latent Heat flux)和土壤湿度(SM,Soil Moisture)、抬升凝结高度(LCL,Lifting Condensation Level)的相关系数R_(SM,LH)和R_(LH,LCL)表征陆气耦合过程,评估了陆气耦合对不同参数化方案的敏感性。模式模拟的R_(SM,LH)在不同区域随着平均降水、相对湿度的增加以及平均短波辐射的减少而减小,而R_(LH,LCL)的变化正好相反。它们内在的物理机制类似,与气候态的干湿变化密切相关,即随着土壤湿度趋于饱和,蒸散发过程逐渐受太阳辐射的限制,陆面对大气的影响减弱。另外,陆气耦合强度受积云对流方案、微物理方案和短波辐射方案的影响而产生差别,这与不同参数化方案模拟的气候态的不同密切相关,因此本研究对于WRF 4.0模式中参数化方案特别是积云对流方案的选择同样有着重要的指导意义。     

MCC降水过程集合预报不同物理过程扰动方案的对比试验研究

利用WRF模式,从模式的不确定性角度来构造中尺度的集合预报,重点对比分析了不同物理参数化方案、物理过程随机扰动方案、积云对流参数化敏感参数扰动方案对中尺度对流复合体降水集合预报的影响。试验结果表明:3种物理过程扰动方法都可以反映中尺度对流复合体降水预报的不确定性特征,其预报效果比控制预报好。物理过程随机扰动方案集合平均的降水落区及强度最接近实况,并且其降水的ETS评分要高于其他2种方案。从均方根误差与离散度的角度来看,3种方案中物理过程随机扰动的均方根误差要小于其他2种方案,而其离散度要大于其他2种方案,物理过程随机扰动方案要优于其他2种方案。     

不同云微物理方案对一次飑线过程模拟的影响

本文利用WRF(Weather Research and Forecasting)模式的不同云微物理方案对2009年6月14日发生在华东地区的一次飑线过程进行1 km的高分辨率模拟,探讨不同云微物理方案对飑线模拟的影响。结果表明:双参数方案的模拟效果总体上优于单参数方案,其中WDM6方案模拟效果最佳,能够较好的模拟出强对流回波区、层云区的主要特征。在单参数方案中以WSM6方案最优。Kessler和LIN方案模拟飑线的回波范围偏小,强度偏弱。进一步对比热力和动力场发现,WDM6方案模拟的冷池的面积最大,强度最强,气压最高,飑线前部的入流处风速最大。不同云微物理方案对微物理场的影响较明显,相比单参数方案,双参数方案模拟的水凝物混合比更高,且能够模拟粒子数浓度,更准确地描述了云中的各类粒子特征。     

雾与能见度数值预报诊断SW方案和FSL方案改进的研究及评估

为了提高雾与能见度的预报水平,对业务上常用的两种能见度诊断方案,即Stoelinga and Warner（SW）方案与Forecast Systems Laboratory（FSL）方案的改进进行预报试验,SW方案基于Gultepe方案考虑了液态水粒子数浓度对能见度的影响,FSL改进方案中利用了递减平均法对公式中用到的温度与露点温度进行订正,并用其重新计算公式中的相对湿度。基于山东省气象科学研究所逐时更新循环（hourly update cycle,HUC）业务模式输出结果,从2015—2016年选取10次雾天气过程,并详细分析了2015年11月13—14日这次雾天气过程的预报结果,比较了改进前后各方案对雾与能见度的预报效果,结果显示：在模式预报的雨水含量占总液态含水量比例较大的预报时效,改进后的SW方案对雾与能见度预报效果优于原始方案,在模式预报液态含水量接近0的预报时效,改进前后的SW方案对雾与能见度的预报效果相当;利用订正的温度与露点温度重新计算相对湿度,其平均绝对误差（mean absolute error,MAE）降低明显的预报时段,改进后的FSL方案对雾与能见度的预报效果大大提升。将两种改进后的方案相融合并进行预报试验,结果显示,综合对能见度与雾的预报效果,Combined Visibility（CVIS）方案要优于其他两种改进方案。