地球化学景观吸引子的发现及其意义

勘查地球化学对异常评价的最大不确定性源于对地球化学景观特性的认识不够。我们应用构造相空间的方法分析了浙江儒岙幅（1:5万）水系沉积物测量的Ag含量数据，揭示了地球化学景观是具有低维吸引子（DZ≈2．9）的混饨系统。这一发现将对勘查地球化学中采样密度的选择、地球化学场模拟、异常评价等根本性问题产生重大影响。     

FURTHER STUDY ON THE PROPERTIES OF OPERATORS OF ATMOSPHERIC EQUATIONS AND THE EXISTENCE OF ATTRACTOR

The equivalent operator equation is derived from the full primitive nonlinear equations of theatmospheric motion and the properties and physical senses of the operators are studied.In theinfinite dimensional Hilbert space,the global asymptotic behavior of the atmosphere system withthe non-stationary external forcing is studied under the assumption of the bounded externalforcing.The existence theorems of the global absorbing set and the global attractor are obtained.Thus,the conclusions deduced from the large-scale atmosphere(Li and Chou 1996 a;1996 b)areextended to the general atmosphere.     

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.     

气候噪声和气候系统的分维

根据相空间嵌入定理，按照Grassberger和Procaccia提出的计算分数维的方法，利用近百年来南、北半球地面气温资料，估算了气候吸引子的分数维，计算结果表明:气候吸引子的分数维南半球为3.3～3.7，北半球为3.2～3.7。它提供了气候吸引子的自相似结构的基本信息，表明模似气候系统最少需要4个独立变量。另外，还讨论了气候噪声对估算维数的影响。     

基于混沌吸引子的复杂农业系统预测模型研究

农业生产是自然再生产和经济再生产有机结合的过程，农业系统是高度耦合了自然生态、社会经济系统等的复杂大系统，具有非线性和耗散性特征。复杂农业系统要素非线性作用所表现的系统行为形成农业系统的整个演化轨迹。从长期演化来看，由于系统内部自组织作用、系统协同和外部随机扰动的作用使得农业系统出现混沌现象，故复杂系统具有长期不可预测性。本文根据复杂农业系统的预测规范，重构复杂农业系统相空间，建立了基于“混沌吸引子”的非线性混沌动力学预测模型，并以成都的相关数据进行分析验证。     

The Relationship between Deterministic and Ensemble Mean Forecast Errors Revealed by Global and Local Attractor Radii

It has been demonstrated that ensemble mean forecasts, in the context of the sample mean, have higher forecasting skill than deterministic(or single) forecasts. However, few studies have focused on quantifying the relationship between their forecast errors, especially in individual prediction cases. Clarification of the characteristics of deterministic and ensemble mean forecasts from the perspective of attractors of dynamical systems has also rarely been involved. In this paper, two attractor statistics—namely, the global and local attractor radii(GAR and LAR, respectively)—are applied to reveal the relationship between deterministic and ensemble mean forecast errors. The practical forecast experiments are implemented in a perfect model scenario with the Lorenz96 model as the numerical results for verification. The sample mean errors of deterministic and ensemble mean forecasts can be expressed by GAR and LAR, respectively, and their ratio is found to approach2~(1/2) with lead time. Meanwhile, the LAR can provide the expected ratio of the ensemble mean and deterministic forecast errors in individual cases.     

磁层顶等离子体中的混沌现象

本文研究了磁层顶等离子体的一个基本模型,得到了一新的非线性常微分方程组.数值分析表明,在一定的磁Reynolds数范围内,系统呈现混沌行为,相轨道趋向于奇异吸引子.     

大气动力学方程组的定性理论及其应用

基于完整的湿大气动力学方程组,利用无穷维动力系统的新理论和新方法,系统讨论了强迫耗散的非线性大气系统的定性理论及其应用。将完整的强迫耗散非线性湿大气动力学方程组化为Hilbert空间中一个等价的算子方程,研究了算子的性质及其物理意义,在此基础上得到湿大气系统全局吸引子的存在性定理,揭示出系统向外源的非线性适应特征,并把结果推广到有地形动力作用和非定常外源强迫的情形。同时探讨了大气方程组惯性流形的存在,大气多平衡态产生的根源以及强迫、耗散和非线性对系统解的渐近行为的影响。在理论结果的基础上,提出强迫耗散的非线性动力系统中存在三类时间边界层、方程组简化准则、分解算法的算子约束原则以及支撑吸引子基底的少数自由度的构造方法,探讨了理论在非线性发展方程差分格式的设计和计算稳定性分析、多平衡态的数值分析、数值模式延伸预报的改进、短期气候预测以及一类中尺度系统分析与预测中的应用,指出描述长期过程动力学模式的必备条件,给出初值与模式相协调的合理解释。最后,对今后的研究方向作了展望。     

吕宋海峡内波吸引子的三维数值模拟

Internal waves propagate along wave beams that are inclined with respect to the horizontal plane. It is conjectured that the internal waves generated in the Luzon Strait may be confined between the double ridges in the strait and concentrate to a closed trajectory, the so-called internal wave attractor, due to the reflection of wave beams from the lateral boundaries, sea surface and bottom. This work carried out two experiments using a three dimensional non-hydrostatic general circulation model, MITgcm, to investigate the possibility that the ridges in the Luzon Strait allows for internal wave attractors. Baroclinic current in both of the experiments demonstrate the forming of ring-like patterns in some section around 20° and 21°N, indicating that the development of the internal wave attractors are allowed in the Luzon Strait. The different resolutions and initial conditions in the two experiments also reveal that the internal-wave-attractor phenomenon is robust in this region.