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...     

Topographically forced three-wave quasi-esonant and non-resonant interactions among barotropic rossby waves on an infinnite beta-plane

In this paper, we first apply the assumption h = εh′ of topographic variation (h is the nondimensional topographic height and is a small parameter) to obtain nonlinear equations describing three-wave quasi-resonant and non-resonant interactions among Rossby waves for zonal wavenumbers 1—3 over a wavenumber-two bottom topography (WTBT). Some numerical calculations are made with the fourt-order Rung-Kutta Scheme. It is found that for the case without topographic forcing, the period of three-wave quasi-resonance (TWQR) is found to be independent of the zonal basic westerly wind, but dependent on the meridional wavenumber and the initial amplitudes. For the fixed initial data, when the frequency mismatch is smaller and the meridional wavelength is moderate, its period will belong to the 30–60-day period band. However, when the wavenumber-two topography is included, the periods of the forced quasi-resonant Rossby waves are also found to be strongly dependent on the setting of the zonal basic westerly wind. Under the same conditions, only when the zonal basic westerly wind reaches a moderate extent, intraseasonal oscillations in the 30–60-day period band can be found for zonal wavenumbers 1–3. On the other hand, if three Rossby waves considered have the same meridional wavenumber, three-wave non-resonant interaction over a WTBT can occur in this case. When the WTBT vanishes, the amplitudes of these Rossby waves are conserved. But in the presence of a WTBT, the three Rossby waves oscillate with the identical period. The period, over a moderate range of the zonal basic westerly wind, is in the intraseasonal, 30–60-Day range.     

应用非线性振荡理论研究云南局地气温的演变规律

将描述局地气温变化的非线性振荡方程应用到云南省17个测站局地气温演变研究中,根据各测站1958年1月—2000年12月逐旬气温距平资料和反演理论获得具体描述各测站局地气温变化的非线性振荡方程。以经典非线性振荡理论为依据,研究了云南省17个测站的局地气温演变规律。结果表明,云南局地气温系统是弱的非线性系统;其演变的固有周期大致在6～10旬之间;在无外源强迫的条件下,云南局地气温振幅随时间增加总是衰减;考虑外源强迫的作用后,云南局地气温系统在其演变过程中只随外源强迫的振荡而振荡。应用反演获得的描述各测站局地气温变化的有外源强迫非线性振荡方程做出未来云南局地气温演变趋势预报,其平均预报准确率约为78．9％。说明该模型具有良好的预报能力和预报稳定性。     

Chaos of a simple coupled system generated by interaction and external forcing

Summary ?This paper is concerned with the chaotic behavior of a coupled system consisting of two components, one representing the atmosphere and the other representing the ocean. The system is expressed as a highly truncated spectral model and for each component, the spectral model is similar to that of Lorenz (1963). Interactions between the two components are permitted, which lead to the temporal variation of surface temperature and hence that of a critical model parameter (the Rayleigh number). The emphasis of the paper is placed upon the chaotic behavior arising from the interactions between the two components and from periodic external forcing. Numerical tests are carried out to show that through interactions, the chaotic behavior of one component may result in chaos of the other even if the latter is otherwise stationary or periodic. It is shown that chaos may also occur if the system is forced periodically at certain frequencies. This study indicates that a new mechanism for chaos exists for coupled systems which are subject not only to internal fluid dynamic nonlinear interactions, but also to interactions between different components and external forcing. Received July 24, 2001; revised March 25, 2002     

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.     

A STUDY ON PHYSICAL MECHANISM OF INTERANNUAL VARIATIONS OF LARGE-SCALE FLOW PATTERNS*

The thermal forcings of annual and interannual periodic variations are introduced into the barotropic vorticity equation,by using low order spectral model of the equation,more than 40 numerical experiments whose integration time is larger than 100 model years are performed in order to investigate variations of large-scale flow patterns arising from both external interannual thermal forcing and internal dynamical processes.In certain parametric range,when the frequency of the forcing term with interannual period equals to the frequency which is created by the internal dynamical processes alone,the amplitude of interannual variations of flow patterns increases obviously,and the period becomes double.In other parametric range,the amplitude of interannual variations of flow patterns shows abrupt changes and other nonlinear behavior,along with gradual changes of interannual forcing parameters.     

Overturning and wind-driven circulation in a low-order ocean–atmosphere model

A low-order ocean–atmosphere model is presented which combines coupling through heat exchange at the interface and wind stress forcing. The coupling terms are derived from the boundary conditions and the forcing terms of the constituents. Both the ocean and the atmosphere model are based on Galerkin truncations of the basic fluid dynamical equations. Hence, the coupled model can readily be extended to include more physics and more detail. The model presented here is the simplest of a hierarchy of low-order ocean–atmosphere models. The behaviour of the coupled model is investigated by means of geometric singular perturbation theory and bifurcation analysis. Two ways are found in which the slow time scales can play a role in the coupled dynamics. In the first scenario, a limit cycle on the overturning time scale is created. The associated oscillatory behaviour is governed by internal ocean dynamics. In the second scenario, intermittent behaviour occurs between periodic and chaotic regimes in parameter space.     

A study of the climatic regimes of the Pleistocene using a stochastic resonance model

A global energy balance model employing the stochastic resonance mechanism, previously used to explain the climatic variability of the late Pleistocene, has now been extended to account for the climatic variations over the full Pleistocene. The possibility that extremely long-term changes (of the order of millions of years) in the boundary conditions of the climate system have altered the response of the Pleistocene climate to the external orbital forcing has been investigated. It is shown that, by slowly changing the only free parameter of the model, the system can undergo a pitchfork bifurcation. The bifurcation point separates a linear regime (identified with the early Pleistocene climate) from a strongly nonlinear regime (the late Pleistocene) where the stochastic resonance mechanism produces rapid and symmetric transitions between the two stable steady states of the system. The main differences in the dynamic features of the two regimes are the change in amplitude of the oscillations, the relative importance of the stochastic forcing, the change in shape of the probability distribution, and the corresponding change in the power centered around the 100000 year cycle: in qualitative agreement with the observed geological record. With the introduction of the external orbital forcing, now spectrally complete and included without requiring any additional hypothesis, the model reproduces the previous results, namely the good correlation with the isotopic record, the appearance of the dominant spectral peaks, as well as the redness of the power spectrum. In particular, it is shown that the orbital forcing in eccentricity acts as a pacemaker of the major glacial cycles of the late Pleistocene through the mechanism of stochastic resonance. A stochastic sensitivity analysis is then applied to validate the significance of the results and to investigate the predictability of the climate system over the time-scales of the orbital cycles.     

大尺度流型年际变化可能机制的研究

本文将年变周期和非年变周期热力强迫项引进正压涡度方程,用方程的截谱形式实施了几十组时间长度为100年的数值积分,研究了非年变周期热力强迫和大气内部动力过程共同激发的大尺度流型的年际变化问题。在一定的参数集合,当非年变外源强迫的振荡周期与大气内部动力过程单独激发出来的振荡的周期相同时,流型年际振动的振幅明显加大,振动的周期则为倍化。在另外的参数集合,随着非年变强迫参数的渐变,流型年际变化的幅度显示出清楚的突变以及其它富有非线性特色的行为。     

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.     

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 the atmospheric motion and the properties and physical senses of the operators are studied.In the infinite dimensional Hilbert space,the global asymptotic behavior of the atmosphere system with the non-stationary external forcing is studied under the assumption of the bounded external forcing.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 1996a;1996b) are extended to the general atmosphere.     

Four-wave resonance in a forced-dissipative barotropic atmosphere

Summary This paper investigates four-wave resonance dynamics containing Ekman friction and diabatic heating. A general nonlinear low-frequency-period (LFP) solution is derived by a new time transformation from the equation of quasigeostrophic vorticity for the forced-dissipative barotropical atmosphere. The solution shows that the friction tends to prolong the LFP and the heating tends to shorten it. For a given time interval, because the effect of the friction exceeds that of the heating it is responsible for the LFP lengthening and v.v. The fact that frictional impact may be either stronger or weaker for a particular period of time leads to a longer or shorter LFP, suggesting a chaotic state of atmospheric motion. For statistical averaging on a long-term basis, however, the effects of both types are in balance so that the LFP is more or less fixed, thereby providing a new kind of physical mechanism for the predictability of climate on monthly/seasonal timescales. Furthermore, the extra-tropical quasi biweekly and 30–50 days oscillations are related to external forcing, and free Rossby wave quasi-resonance, respectively. For the first time it is found that the Ekman friction is able to excite explosive instability in a barotropical atmosphere. These results will be of use to the improvement of the two conclusions reported in Craik (1985).Project supported by the National Natural Science Foundation of China.     

大气随机动力学与可预报性

偶然性与必然性过程及其相互转化是世界事物变化复杂性的根源。根据布朗运动统计理论,提出了分子热运动是不稳定流体中湍流形成之源,由此形成不同宏观尺度的随机运动是大气运动固有的属性。观测事实表明,太阳辐射作为决定大气运动与变化的主要因子,它的变化具有随机性,是大气的随机强迫因子,它对气候变化具有决定性影响。地-气相互作用是一个时变的非线性相互反馈的耦合过程,形成了下边界对大气复杂的随机强迫作用,其界面交换耦合随机动力学模式尚待建立。由于大气过程固有的随机性以及随机的外强迫耦合作用,大气确定性预报的时效是有界的,它决定于预报对象的不确定性及其空间尺度与时间尺度,以及预报时效内的大气不确定性。由此,客观存在着大气过程的报不准关系。     

On long range dependence in global surface temperature series

Long Range Dependence (LRD) scaling behavior has been argued to characterize long-term surface temperature time series. LRD is typically measured by the so-called “Hurst” coefficient, “H”. Using synthetic temperature time series generated by a simple climate model with known physics, I demonstrate that the values of H obtained for observational temperature time series can be understood in terms of the linear response to past estimated natural and anthropogenic external radiative forcing combined with the effects of random white noise weather forcing. The precise value of H is seen to depend on the particular noise realization. The overall distribution obtained over an ensemble of noise realizations is seen to be a function of the relative amplitude of external forcing and internal stochastic variability and additionally in climate “proxy” records, the amount of non-climatic noise present. There is no obvious reason to appeal to more exotic physics for an explanation of the apparent scaling behavior in observed temperature data.     

The structure and propagation of stationary planetary wave packet in the barotropic atmosphere

Monthly or seasonally mean anomalies of large-scale atmospheric circulation are better represented by wave packets or their combination. Both qualitative and quantitative analyses of equations of wave packet dynamics, which are obtained by the use of WKB approximation, are very helpful for the understanding of structure, formation and propagation of stationary and quasi-stationary planetary wave packet patterns in the atmosphere. Indeed, these equations of wave packet dynamics can be directly solved by the method of characteristic lines, and the results can be simply and clearly interpreted by physical laws. In this paper, a quasi-geostrophic barotropic model is taken for simplicity, and the wave packets superimposed on several ideal profiles of the basic current and excited by some ideal forcings are investigated in order to make comparison of the accuracy of calculation with the analytical solution. It is revealed that (a) the rays of stationary planetary wave packet do not coincide with but go away from the great circle with significant difference if the shear of the basic zonal flow is not too small; (b) being superimposed on a westerly jet flow with positive shear (Uλ/y>0), the stationary wave packets excited by low-latitudinal forcing are first intensified during their northeastward propagation in the Northern Hemisphere, then reach their maximum of amplitude at some critical latitude, and after that weaken again; (c) the connected line of extremes (the positive and negative centres) of wave packet does not coincide with but crosses the ray by an angle, the larger the scale of external forcing, the larger the angle; and (d) the whole pattern of a trapped stationary wave packet is complicated by the interference between the incident and reflected waves.     

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.     

热带扰源对不同基流作用的数值试验

本文采用非线性浅水方程谱模式,通过数值试验,分析了热带定常涡源对不同基流的动力作用。由试验结果看到,当基流有经向分布或为均一西风时,热带扰动的影响是全球性的。它能激发大约3对波动,这些波动主要沿“大圆路径”传播,对中高纬的环流形势有重要影响。当基流为静止大气或全球东风时,热带外强迫力只能在其附近激发很弱的扰动。      

青藏铁路沿线地面气温演变的非线性振荡规律研究

将描述局地气温变化的非线性振荡方程应用到青藏铁路沿线9个测站(安多、当雄、托托河、班戈、格尔木、那曲、西宁、拉萨及五道梁)局地年气温演变研究中，根据各测站1966—1997年逐年年气温距平资料和反演理论获得具体描述各测站局地气温的非线性振荡方程。在不考虑外源强迫项的情况下，以经典非线性力学理论为依据，研究青藏铁路沿线9个测站的气温演变规律。结果表明，青藏铁路沿线9个测站局地气温系统是明显的非线性系统，其演变周期大致在3～6年之间，气温振幅随时间增加而衰减。其平均预报准确率为75．4％，有较好的预报能力。