地-气耦合动力系统的研究

研究了一类地-气耦合系统的非线性模型,目的是创建一个地-气振子模型的非线性方程的渐近求解方法,利用变分迭代方法,构造了对应问题解的近似展开式。即首先引入一组泛函和计算出它们的变分,并算出Lagrange乘子,其次,决定变分迭代,最后得到原地-气振子模型非线性问题解的一致收敛的近似展开式。     

中国年降水气候振动的非线性动力学特征

从观测资料出发,利用反演方法,获得了描述我国17个站年降水气候振动的二阶非线性动力学方程组中的系数,并在无外源强迫的情况下对该非线性动力学方程组作了定性的分析,对17个站的年降水气候振动进行气候模拟试验。结果表明:我国大部分地区的年降水气候振动存在弱的非线性振动特征,17个站的年降水气候振动都可以看作是一个正阻尼的动力系统,在运动变化过程中,自身能量的变化dEdt<0,17个站年降水气候振动的固有频率的变化范围为0.6≤ω0≤1.417,其固有周期的变化范围为10.4≥T≥4.4年。从空间分布特征上可以看到,其固有周期的长短分布有明显的东西向特征。在17个站中,兰州、成都、重庆、南宁、福州、上海、温州地区的年降水气候振动是一个类似于具有渐软弹簧特性的非线性动力系统,而昆明、长春、哈尔滨、北京、广州、西安、厦门、长沙、南京、杭州地区的年降水气候振动是一个类似于具有渐硬弹簧特性的非线性动力系统,从其空间分布特征上看也有东西向特征。全国17个站年降水气候振动的动力系统都存在一个稳定的焦点,在无外源强迫作用时,各站的年降水气候振动将逐渐趋向于各自的稳定的焦点,但都不存在极限环。在仅考虑降水自身振动的情况下,利用我们反演得到的非线性动力学方程对年降水气候振动做模拟,位于内陆地区的模拟情况可以通过显著性水平检验,而靠近海洋的地区模拟效果没有内陆好。这一结果说明在降水气候振动中,靠近海洋地区的外源强迫影响作用比位于内陆地区大。     

湿大气方程组解的渐近性质

研究无穷维Ｈｉｌｂｅｒｔ空间中,湿大气运动系统解的长期行为,在导得了湿大气运动方程是Ｈｉｌｂｅｒｔ空间中一个非常特殊的算子方程之后,利用算子的性质讨论了全局吸收集和全局吸引子的存在性,揭示出系统解的渐近行为表现在吸引子的结构上及系统向非绝热加热的非线性适应过程。最后指出了几个简化方程组与原方程组在解的长期行为上的根本不同,从而给出长期天气或气候研究中简化方程组必须遵循的原则。     

一个自组织气候模型

本文选择全球平均地表温度#AT#a和全球平均云量#An#a为状态变量。通过对气候系统中物理过程的研究与在气候意义上的合理近似，得到行星反照率α和大气有效发射率ε与状态变量的参数化关系，它们给出了气候系统内部几个重要的反馈过程。利用这些结果，建立起一个云和辐射相互作用的零维的非线性气候模型。在Hopf分支点附近，得到极限环的解析解，它们同数值解吻合得相当好，由解析解得到振幅，周期和位相差与太阳常数和CO2的近似关系，依此可估计它们在气候振荡中的作用，尤其，我们发现CO2的增加除有增温效应外，还能使气候振荡的振幅增加，这个结果意味着CO2的增加可能导致自然灾害周期性地出现或加剧。     

CLIMATE CHANGE: LONG-TERM TRENDS AND SHORT-TERM OSCILLATIONS

Identifying the Northern Hemisphere (NH) temperature reconstruction and instrumental data for the past 1000 years shows that climate change in the last millennium includes long-term trends and various oscillations. Two long-term trends and the quasi-70-year oscillation were detected in the global temperature series for the last 140 years and the NH millennium series. One important feature was emphasized that temperature decreases slowly but it increases rapidly based on the analysis of different series. Benefits can be obtained of climate change from understanding various long-term trends and oscillations. Millennial temperature proxies from the natural climate system and time series of nonlinear model system are used in understanding the natural climate change and recognizing potential benefits by using the method of wavelet transform analysis. The results from numerical modeling show that major oscillations contained in numerical solutions on the interdecadal timescale are consistent with that of natural proxies. It seems that these oscillations in the climate change are not directly linked with the solar radiation as an external forcing. This investigation may conclude that the climate variability at the interdecadal timescale strongly depends on the internal nonlinear effects in the climate system.     

THE EFFECTS OF EXTERNAL FORCING,DISSIPATION AND NONLINEARITY ON THE SOLUTIONS OF ATMOSPHERIC EQUATIONS

Based on the primitive equations of the atmosphere,we study the effects of external forcing.dissipation and nonlinearity on the solutions of stationary motion and non-stationary motion.Theresults show that the asymptotic behavior of solutions of the forced dissipative nonlinear system isessentially different from that of the adiabatic non-dissipative system,the adiabatic dissipativesystem,the diabatic non-dissipative system and the diabatic dissipative linear system,and that thejoint action of external forcing,dissipation and nonlinearity is the source of multiple equilibria.From this we can conclude that the important actions of diabatic heating and dissipation must beconsidered in the models of the long-term weather and the climate.     

THE EFFECTS OF EXTERNAL FORCING,DISSIPATION AND NONLINEARITY ON THE SOLUTIONS OF ATMOSPHERIC EQUATIONS*

Based on the primitive equations of the atmosphere,we study the effects of external forcing.dissipation and nonlinearity on the solutions of stationary motion and non-stationary motion.The results show that the asymptotic behavior of solutions of the forced dissipative nonlinear system is essentially different from that of the adiabatic non-dissipative system,the adiabatic dissipative system,the diabatic non-dissipative system and the diabatic dissipative linear system,and that the joint action of external forcing,dissipation and nonlinearity is the source of multiple equilibria.From this we can conclude that the important actions of diabatic heating and dissipation must be considered in the models of the long-term weather and the climate.     

Bifurcation of Nonlinear Kelvin Wave-CISK with Conditional Heating in a Truncated Spectral Model:A Possible Mechanism of 30-60-Day Oscillation at the Equator

1.IntroductionSincethe40--50--dayoscillationinthetropicalPacificwasfirstfoundbyMaddenandJulian(1971,1972),ithaslongbeenanimportantresearchtopic.Inobservationalstudies,LauandChan(1985,1986),GhilandMo(1991)showedthattheintraseasonaloscillationsinthetro...     

太平洋年代际振荡的年代际预测方法

太平洋年代际振荡（PDO）是北太平洋海表温度年代际变率的主模态。由于太平洋年代际振荡对区域乃至全球气候的显著影响,其合理的预测结果可以带来多方面收益。然而,针对太平洋年代际振荡及其有关的海表温度的年代际预测,目前气候模式的预测水平还十分有限,因此,提出了一个新的增量方法。一系列的验证结果表明,增量方法可以有效预测太平洋年代际振荡,其中包括成功预测出其振荡的年代际转折。增量方法的预测过程主要包括3个步骤:（1）采用5 a滑动平均得到太平洋年代际振荡的年代际变率;（2）利用3 a增量形式的预测因子构建预测模型,预测3 a增量的太平洋年代际振荡（DI_PDO）;（3）将预测得到的DI_PDO加上3 a前的观测PDO,得到最后预测的PDO。增量方法亦可以应用到气候系统年代际内部变率的其他模态（如:北大西洋年代际振荡）和其他气候变量的年代际预测（如:海表温度）。      

Bifurcation of nonlinear Kelvin wave-CISK with conditional heating in a truncated spectral model: A possible mechanism of 30–60-day oscillation at the equator

In this paper, the nonlinear Kelvin wave equations with “positive-only” nonlinear (conditional) heating at the equator are reduced to a sixth-order nonlinear ordinary differential equation by using the Galerkin spectral truncated method. The stability analysis indicates that when the heating parameter increases, the supercritical pitchfork and Hopf bifurcations can occur for the prescribed three heating profiles. Numerical calculations are made with the help of the fourth-order Rung-Kutta method. It is found that the convec-tion heating-related Hopf bifurcation can lead to limit cycle and chaotic solutions. In a wide range of heat-ing parameter, the solutions possess 30-60-day periods, and are dominated by wavenumbers one and two, especially by wavenurnber-one. In addition, the zonal winds of the low-frequency solutions have a phase reversal between the upper and lower tropospheres. Thus, it appears that the convection heating-related Hopf bifurcation might be a possible mechanism of 30-60-day oscillation in the tropical atmosphere.