21层大气环流模式IAP AGCM-Ⅲ的设计及气候数值模拟Ⅰ.动力框架

设计了IAP(Institute of Atmospheric Physics, Chinese Academy of Sciences) AGCM-III,对其动力框架作说明和检验,时间积分采用改进的非线性迭代法.用Rossby-Haurwitz 波对框架进行了波型检验、能量检验和波速检验.结果表明,非线性迭代3次的时间积分方案具有较好的稳定性,能够有效地抑制短波,同时对长波的歪曲较小,且时间积分步长可放得较大;该框架能够较长时间地保持Rossby-Haurwitz 4波波型,在积分过程中能够较高精度地保持总有效能量守恒;模式计算的Rossby-Haurwitz波速为每天西传15个经度,这与理伦值很接近.     

特定外源下的非线性Rossby椭圆余弦波和孤立波

本文讨论了在特定外源的条件下正压无辐散大气中存在的非线性Rossby椭圆余弦波和孤立波解,并求出了非线性波动的波速公式及其振幅与其它波参数间的诊断关系.证明了当不考虑外源时非线性波动的波速公式在振幅趋于零时即退化为通常的线性化的Rossby长波公式.     

论Rossby波在东、西风带中传播与频散Ⅱ——球面Rossby波方程与诊断分析

从球坐标(Spherical coordinate)非地转、正压水平无辐散大气运动微扰方程出发,推导出球面Rossby波方程,证明球面Rossby波的物理机制仍然是绝对涡度守恒与卢效应,但基本气流以涡度形式参与了卢效应。因球面Rossby波偏微分方程不存在经向-纬向传播的"双向简谐波(传统Rossby波)"解,则将它做经向-纬向求导分离,从而得到关于球面经向风扰动的二阶偏微分方程及与之相应的仅作纬向传播的简谐波解,但待解的二阶偏微分方程不归于数理方程中的任何特殊函数,即证明不存在以连带Legendre函数为通解的Haurwitz波。采用传统Rossby波两个通解,当作球面Rossby波两类特解,做诊断分析表明,传统Rossby波正确反映球面Rossby波的(β-平面近似)"线性部分",但球面Rossby波及其纬向波速和群速都带有地球曲率性,并且存在奇点,其中,球面谐波扰动Rossby波仍然保持槽与脊纬向对称性,但"正弦扰动"与"余弦扰动"Rossby波有一定差别,而球面指数扰动Rossby波槽与脊不具备纬向对称性,后者可以解释东、西风带槽与脊一般为纬向非对称,还可以解释台风的纬向非对称结构。     

一个大气环流模式差分格式的检验

本文用两种工具对我们设计的一个大气环流模式及其差分格式作了较为严格的检验。首先,我们用检验球面模式的传统工具Rossby-Haurwitz波对简化的正压模式进行了检验,其效果与欧洲中心的结果极为一致。其次,我们发展了检验斜压初始方程模式的工具——非线性Haurwitz波,并对环流模式的框架部分作了检验,取得了令人满意的结果。     

非线性Rossby波动特征的进一步探讨

在一定的假定下,利用自然坐标系对正压非线性Rossby波的特征作了进一步探讨,指出控制Rossby波动过程的本质方程是摆型方程及类似于Sine—Gordon方程的关系式,得到了波动过程中复杂的质点振动轨迹和非线性振荡的周期;给出了定常Rossby波的几种复杂流型,证明了非线性Rossby波的位相传播和能量传播是沿着流线进行的。这些结果对深入认识大气内部动力过程和解释某些观测现象具有一定意义。     

IAP AGCM-4动力框架的积分方案及模式检验

以灵活性跳点格式和时间分解算法为重点, 介绍了IAP (中国科学院大气物理研究所) AGCM-4的动力框架, 并用R-H (Rossby-Haurwitz) 波和Held-Suarez方案对框架进行了检验。结果表明: 高纬灵活性跳点格式很好地保持了普通跳点格式的各种性质, 未产生计算紊乱现象, 可在一定程度上增大时间步长, 在未采用滤波处理时增大时间步长的效果更为显著; 时间分解算法, 即将平流过程与适应过程分开计算, 二者都采用3次非线性迭代积分方案, 在N=5和N=10 (N为平流过程时间步长与适应过程时间步长的比值) 的情况下, 可分别节省CPU时间10.7%和19.9%; R－H波检验表明, 在积分的前80天, 框架较好地保持了R－H 4波的波形, 总有效能量仅衰减0.1%, 从第80天开始, 风场波形开始变形和破碎, 对应的动能和总能量也开始急剧衰减, 至第365天, 总有效能量衰减约8%, 此时, 风场和高度场亦变得较平直。经分析, 第80天R－H波破碎的主要原因是平流项的计算误差使R－H波失稳, 而其后的高度场和风场的变平直是典型的旋转适应机制; Held－Suarez方案检验也证明该框架是可靠的。     

非线性正压Rossby波及其稳定性

本文应用常微分方程的稳定性理论和几何理论,从非线性正压涡度方程出发,讨论了一类非线性正压Rossby波的存在性和稳定性。结果表明:对于无耗散系统Rossby波的存在和稳定要求基本气流绝对涡度的经向梯度与波速,基本气流之差为反号,即:且V=0时初始涡度不为零。最后给出两种情况下波的解析解表达式。     

旋转正压大气中的非线性Schrödinger方程和大气阻塞

本文利用WKB方法导出了旋转正压大气中的非线性Rossby波所满足的立方Schrödinger方程,指出在1≤m≤2的情况下,非线性Schrödinger方程具有包络孤立波解,同时我们还对大气中的包络Rossby孤立波的流场进行了计算,结果得到了阻塞高压和切断低压等结构,并且这些阻塞系统能够维持五天以上。     

旋转正压大气中的非线性Schrödinger方程和大气阻塞

本文利用WKB方法导出了旋转正压大气中的非线性Rossby波所满足的立方Schrödinger方程,指出在1≤m≤2的情况下,非线性Schrödinger方程具有包络孤立波解,同时我们还对大气中的包络Rossby孤立波的流场进行了计算,结果得到了阻塞高压和切断低压等结构,并且这些阻塞系统能够维持五天以上。     

非线性正压Rossby波的精确解

本文从半地转近似下的正压大气运动方程组出发,导出了非线性正压Rossby波所精确满足的KdV方程,求得了椭圆余弦波解和孤立波解,并讨论了非线性波动的波速公式及其振幅与其它波参数间的关系。同时指出,在对大气模式进行数学简化时必须尽可能保证原模式所具有的一些守恒关系,否则有可能使原问题的解受到歪曲。     

GRAPES模式动力框架的长期积分特征

通过考虑动量表面拖曳并利用牛顿松弛方法将温度松弛到纬向对称的温度场, 对GRAPES模式的动力框架进行了长期时间积分试验。通过统计分析其积分结果表明:GRAPES模式的动力框架可以模拟出大气环流的基本特征; 随着分辨率的提高, GRAPES模式动力框架的模拟结果显示出收敛的特性; 虽然GRAPES模式动力框架采用的是能量不守衡的半隐式半拉格朗日时间积分方案, 但长期时间积分试验表明其能量基本保持稳定。这些结果显示使用GRAPES模式动力框架作大气环流和气候研究的大气动力框架是可行的, 同时也为进一步改进GRAPES模式动力框架提供了线索和依据。     

回溯时间积分格式的有效性研究

采月正压准地转模式作为动力核,用Rossby-Haurwitz波函数作为理想场,同时使用回溯时间积分格式和普通中央差格式进行数值试验.结果表明,在短时积分的情况下,回溯格式能减小数值解误差1～2个量级,而且它对时间步长的增大不敏感.因此使用回溯格式可以减少积分计算量,延长积分时效.     

GRAPES模式中三维科氏力计算及其效果评估

作为一种连续可压缩流体,大气具有分层流体特性,其状态变化可由牛顿第二定律、热力学第一定律、连续方程和理想大气状态方程组成的偏微分方程组描述。为了更加精细地描述GRAPES全球模式的动力过程,使模式大气更接近真实大气,在全球非静力模式GRAPES中考虑三维科氏力作用,通过重新构建半隐式半拉格朗日求解大气动力方程组的亥姆霍兹方程系数,在不改变求解方案的前提下实现对GRAPES模式动力过程的更新。然后采用在静力平衡基础上建立的三维大气理想试验对新的动力过程进行数值试验,检验其计算效果和数值稳定性。结果显示,考虑三维科氏力的模式动力框架计算稳定,提高了三维标量和矢量场的计算精度,在水平1°×1°分辨率模式中,平衡流试验第15天计算结果标量场Π'的l₁和l₂误差分别为0.00023和0.0004,而三维矢量场 V 的l₁和l₂误差分别为0.002和0.003,均较原模式误差小一个数量级。在罗斯贝-豪威兹波、地形罗斯贝波和斜压波试验中,新框架均表现出很高的计算稳定性和良好的计算效果。      

Oscillatory Rossby Solitary Waves in the Atmosphere

The linear Rossby wave frequency expression is expanded at higher accuracy based on the scale difference char?acteristics of atmospheric long waves in the and directions. That the nature of the waves represented by the expan?sion is identical to that of the original ones is demonstrated both in phase velocity and wave energy dispersion speed , followed by the derivation of the nonlinear expression describing atmospheric long wave behaviors with the associated approximate analytic solution obtained. Then, for the first time atmospheric’ oscillatory Rossby solitary wave’ with its dispersion relation is obtained by numerical calculation with the aid of physical parameters of the real atmosphere. The solitary wave is found to be very close to such longwave systems as blocking highs and cut-off de?pressions in the actual atmosphere.     

Comparison of different order Adams-Bashforth methods in an atmospheric general circulation model

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.     

非线性迭代时间积分方案在IAP AGCM-II中的实施及其模拟结果

将非线性迭代时间积分方案用于大气环流模式 IAP AGCM-II中, 并用 Rossby-Hauwitz波进行了检验, 结果表明, 该方案能长期稳定的积分。此外, 还将采用该方案的模式(其中物理过程不变)和原 IAP AGCM-II模式作了模拟结果的比较, 以考察其效果; 发现采用该方案模式对降水尤其是东亚地区降水的模拟能力较原模式有所提高。     

THE FORMULATION OF FIDELITY SCHEMES OF PHYSICAL CONSERVATION LAWS AND IMPROVEMENTS ON A TRADITIONAL SPECTRAL MODEL OF BAROCLINIC PRIMITIVE EQUATIONS FOR NUMERICAL PREDICTION*

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.