El Niño prediction and predictability

El Niño-Southern Oscillation (ENSO) is by far the most energetic, and at present also the most predictable, short-term fluctuation in the Earth’s climate system, though the limits of its predictability are still a subject of considerable debate. As a result of over two-decades of intensive observational, theoretical and modeling efforts, ENSO’s basic dynamics is now well understood and its prediction has become a routine practice at application centers all over the world. The predictability of ENSO largely stems from the ocean–atmosphere interaction in the tropical Pacific and the low-dimensional nature of this coupled system. Present ENSO forecast models, in spite of their vast differences in complexity, exhibit comparable predictive skills, which seem to have hit a plateau at moderate level. However, mounting evidence suggests that there is still room for improvement. In particular, better model initialization and data assimilation, better simulation of surface heat and freshwater fluxes, and better representation of the relevant processes outside of the tropical Pacific, could all lead to improved ENSO forecasts.     

Properties of a simple bilinear stochastic model: Estimation and predictability

We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear predictability (non-zero three-point correlation). It can thus be considered as a paradigm for testing the existence of a possible nonlinear predictability in a given time series. We present a rather exhaustive study of the process, including its ability to produce fat-tailed distributions from Gaussian innovations, the unstable characteristics of the inversion of the key nonlinear parameters and of the two initial conditions necessary for the implementation of a prediction scheme and an analysis of the associated super-exponential sensitivity of the inversion of the innovations in the presence of a large impulse. Our study emphasizes the conditions under which a degree of predictability can be achieved and describe a number of different attempts, which overall illuminates the properties of the process. In conclusion, notwithstanding its remarkable simplicity, the bilinear stochastic process exhibits remarkably rich and complex behavior, which makes it a serious candidate for the modeling of financial time series among others.     

Nonlinear analysis of irregular animal vocalizations

Animal vocalizations range from almost periodic vocal-fold vibration to completely atonal turbulent noise. Between these two extremes, a variety of nonlinear dynamics such as limit cycles, subharmonics, biphonation, and chaotic episodes have been recently observed. These observations imply possible functional roles of nonlinear dynamics in animal acoustic communication. Nonlinear dynamics may also provide insight into the degree to which detailed features of vocalizations are under close neural control, as opposed to more directly reflecting biomechanical properties of the vibrating vocal folds themselves. So far, nonlinear dynamical structures of animal voices have been mainly studied with spectrograms. In this study, the deterministic versus stochastic (DVS) prediction technique was used to quantify the amount of nonlinearity in three animal vocalizations: macaque screams, piglet screams, and dog barks. Results showed that in vocalizations with pronounced harmonic components (adult macaque screams, certain piglet screams, and dog barks), deterministic nonlinear prediction was clearly more powerful than stochastic linear prediction. The difference, termed low-dimensional nonlinearity measure (LNM), indicates the presence of a low-dimensional attractor. In highly irregular signals such as juvenile macaque screams, piglet screams, and some dog barks, the detectable amount of nonlinearity was comparatively small. Analyzing 120 samples of dog barks, it was further shown that the harmonic-to-noise ratio (HNR) was positively correlated with LNM. It is concluded that nonlinear analysis is primarily useful in animal vocalizations with strong harmonic components (including subharmonics and biphonation) or low-dimensional chaos.     

Stochastic climate dynamics: Random attractors and time-dependent invariant measures

This article attempts a unification of the two approaches that have dominated theoretical climate dynamics since its inception in the 1960s: the nonlinear deterministic and the linear stochastic one. This unification, via the theory of random dynamical systems (RDS), allows one to consider the detailed geometric structure of the random attractors associated with nonlinear, stochastically perturbed systems. We report on high-resolution numerical studies of two idealized models of fundamental interest for climate dynamics. The first of the two is a stochastically forced version of the classical Lorenz model. The second one is a low-dimensional, nonlinear stochastic model of the El Niño-Southern Oscillation (ENSO). These studies provide a good approximation of the two models’ global random attractors, as well as of the time-dependent invariant measures supported by these attractors; the latter are shown to have an intuitive physical interpretation as random versions of Sinaï-Ruelle-Bowen (SRB) measures.     

基于EMD方法的非线性/非平稳时间序列的气候预测研究

目前，大多数统计预测模型均假设时间序列或观测数据是线性和平稳的。然而，自然界的观测资料是非线性和非平稳的，通常很难用这些数学模型预测它们。本文针对这一问题提出了一个新的预测方案，即首先利用经验模态分解方法将非线性/非平稳时间序列平稳化，得到一系列本征模函数(IMF)；其次用均生函数模型预测各IMF分量；最后以所有IMF的预测值为新样本对源序列作最优子集回归模型的拟合及预测。结果表明每个IMF，尤其是特征IMF(即特征层次)比源序列有更高的可预测性。该方案为气候预测开辟了一条新的有效途径。     

逆磁效应对交换模湍流产生的带状流的影响

运用并扩展了Guzdar等人提出的一种简单的低维模型, 讨论了交换模湍流中的非线性逆磁效应对带状流产生的影响,通过对非线性演化方程的数值计算,得到如下结论：逆磁效应能抑制通常的（雷诺胁强驱动的）极化非线性效应,由此导致带状流的阻尼. 关键词： 托卡马克等离子体 交换模湍流 带状流 逆磁效应     

混沌系统可预报期限随初始误差变化规律研究

利用非线性误差增长理论计算了Logistic映射和Lorenz系统可预报期限随初始误差的变化,发现Logistic映射等简单混沌系统的可预报期限与初始误差的对数存在线性关系.在非线性误差增长理论的框架下,理论分析表明,平均误差增长达到一定值时,误差增长进入明显的非线性增长阶段,最终达到饱和;对于一个确定的混沌系统,在控制参数固定的情况下误差增长的饱和值也是固定的,因此可预报期限只依赖于初始误差. 在可预报期限与初始误差对数存在的线性函数关系式中,线性系数与最大Lyapunov指数有关,在已知混沌系统的最大 关键词： 非线性局部Lyapunov指数 可预报期限 初始误差 混沌系统     

Asymptotic solution for a class of sea-air oscillator model for El Nin^～o-southern oscillation

The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.     

Signatures of deterministic chaos in radar sea clutter and ocean surface winds

Several time series of wind components and X-band Doppler radar signals, gathered concurrently over a approximately 0.01 km(2) area of the ocean surface, were examined for evidence of a low-dimensional dynamical attractor with the Grassburger-Procaccia algorithm. Only the vertically polarized radar reflectivity and the horizontal surface wind speed time series suggested the presence of such an attractor. The correlation dimension for these two observables appeared to be nearly the same. This suggested a working hypothesis that the dynamical behavior of both the vertically polarized radar reflectivity and the horizontal surface winds are controlled by a single low-dimensional dynamical system. The hypothesis was further examined by predicting winds from radar reflectivity, using a neural network deterministic model, and comparing the prediction performance with that of the SEASAT statistical algorithm for retrieving surface winds from radar backscatter. It was found that the deterministic model did, in fact, achieve a higher prediction correlation coefficient for a limited time period. (c) 1995 American Institute of Physics.     

声波在有裂纹的固体中的非经典非线性传播

固体材料的无损检测是一个非常重要的课题,带裂纹的固体材料显示非经典非线性声学现象,本文对此现象进行了实验和理论研究。从实验上一维观察到此现象,发现奇次谐波振幅与基波振幅呈平方关系,与理论预计基本吻合;理论上从二维的角度数值模拟了声波在有损耗的带裂纹的固体中的声传播,并讨论了经典非线性和非经典非线性对声传播的影响,发现裂纹的贡献主要体现在非经典非线性上。分析了样品中裂纹的宽度和位置与非线性声参数的关系,在靠近样品中心的两个对称区域以及距离声源较近点,非线性声参数对样品的破损较为敏感,而在中央和距声源最远端敏感性较低;随着裂纹宽度的扩大,非线性声参数也开始变大,但在破损区域蔓延到棒边缘之前,有下降的趋势。      

A nonlinear correlation measure for multivariable data set

The paper states that the mutual information carried by the rank sequences that are obtained from the original two sequences is a good measure of nonlinear correlation. Based on that, the nonlinear correlation information entropy (NCIE) is proposed for measuring the general relationship of a multivariable data set. NCIE uses a number in the closed interval [0, 1] to indicate the nonlinear correlation degree of the concerned multivariable data set, with 0 and 1 denotes the weakest and the strongest relationship, respectively. Data sets generated from an autoregressive model, a nonlinear chaotic Lorenz system, and a logistic function as known correlation sequences are analyzed using the proposed NCIE. The results testify the suitableness and correctness of the proposed concepts as nonlinear correlation measure.     

基于延伸期可预报性的集合预报方法和数值试验

集合预报是考虑初始条件和模式不确定性的有效途径. 结合延伸期可预报性特征,对具有不同特性的可预报分量和随机分量采用不同的集合预报方案和策略,发展了一种基于延伸期可预报性的集合预报新方法(PBEP).该方法以延伸期数值预报模式为平台,对可预报分量采用多个模式误差订正方案,从考虑模式不确定性的角度进行集合;而对随机分量则利用历史资料从气候概率的角度给出集合概率分布,避免模式误差对随机分量概率分布的影响.试验结果表明,相比于国家气候中心的业务动力延伸集合预报系统,该集合预报方法对全球各区域环流预报技巧均有提高,对不同空间尺度的波也有不同程度的改进,显示出潜在的业务应用前景.     

粗糙接触界面超声非线性效应的概率模型

提出描述粗糙接触界面超声非线性效应的概率模型,利用分段均匀概率函数描述粗糙接触界面劲度系数变化,结合表面粗糙峰的几何分布特征,得到界面粗糙度和两侧表面相对运动对声波的非线性调制作用。实验观测了铝合金材料的粗糙接触界面的高次谐波现象和阈值现象,进一步分析了归一化非线性参数与界面加载压力、粗糙度之间的关系。实验测量结果与概率模型的理论预测一致,证明了该模型的正确性,为利用超声非线性效应评价粗糙接触界面提供了理论依据。      

The homotopic mapping method for sea-air oscillator model of interdecadal climate fluctuations

The E1 Nifio/La Nifia Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a coupled system of sea-air oscillator model is studied. The aim is to create an asymptotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the method of homotopic mapping, the approximate solution of corresponding problem is studied. It is proven from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.     

Influence of optical nonlinearity on combining efficiency in ultrashort pulse fiber laser coherent combining system

The influence of optical nonlinearity on combining efficiency in ultrashort pulse fiber laser coherent combining system is investigated theoretically and experimentally. In the theoretical work, a new theoretical algorithm is presented for the coherent combining efficiency, which can be used to quantify the spectral coherence decay induced by optical nonlinearity imbalance between the sub-beams. The spectral information of the sub-beam is obtained by numerically solving the nonlinear Schrödinger equation (NLSE) in this algorithm to ensure an accurate prediction. In the experimental work, the coherent combining of two all-fiber picosecond lasers is achieved, and the influence of imbalanced optical nonlinearity on the combining efficiency is studied, which agrees with the theoretical prediction. This paper reveals the physical mechanism for the influence of optical nonlinearity on the combining efficiency, which is valuable for the coherent combining of ultrashort pulse fiber laser beams.     

Experimental model validation for a nonlinear energy harvester incorporating a bump stop

In some practical applications, cantilever beam piezoelectric energy harvesters are subjected to large amplitude base excitations which induce nonlinear behaviour in the harvester that affects their performance. In this paper, a cantilever piezoelectric energy harvester model is developed which takes account of geometric nonlinearity arising through the inextensible beam condition and material nonlinearity arising in the piezoelectric layers of the harvester. The model is validated against experimental measurements for different base accelerations and load resistances, and an investigation into the nonlinear behaviour indicates that nonlinear softening is caused predominantly by material nonlinearity. To reduce the beam amplitude and the resulting bending stress in the cantilever harvester, a bump stop is incorporated into the harvester design and the influence of the bump stop is modelled. Comparisons of theoretical predictions with experimental measurements indicate that taking account of the nonlinear behaviour improves the prediction significantly in some cases. Parameter studies are also conducted to investigate how the stop location and initial gap size between the harvester and stop affect the performance of the nonlinear energy harvester.     

Surrogate analysis for detecting nonlinear dynamics in normal vowels.

Normal vowels are known to have irregularities in the pitch-to-pitch variation which is quite important for speech signals to be perceived as natural human sound. Such pitch-to-pitch variation of vowels is studied in the light of nonlinear dynamics. For the analysis, five normal vowels recorded from three male and two female subjects are exploited, where the vowel signals are shown to have normal levels of the pitch-to-pitch variation. First, by the false nearest-neighbor analysis, nonlinear dynamics of the vowels are shown to be well analyzed by using a relatively low-dimensional reconstructing dimension of 4 < or = d < or = 7. Then, we further studied nonlinear dynamics of the vowels by spike-and-wave surrogate analysis. The results imply that there exists nonlinear dynamical correlation between one pitch-waveform pattern to another in the vowel signals. On the basis of the analysis results, applicability of the nonlinear prediction technique to vowel synthesis is discussed.     

基于季节气候可预报分量的相似误差订正方法和数值实验

基于由历史相似信息对模式预报误差进行预报的思路,发展了一种针对季节气候可预报分量的相似误差订正新方法（FACEPC）,目的是识别模式预报结果中对初值相对不够敏感的可预报分量,将其作为对象进行历史相似选取和误差订正.该方法被应用到国家气候中心业务季节预报模式实验中,对不同区域给出有针对性的相似选取指标和预报方案.25年的交叉检验结果表明,夏季降水和环流的预报技巧评分相对于系统误差订正有明显提高,在发生中等及以上强度ENSO事件年和可预报分量贡献较大地区的预报技巧提高更为显著.特别是中国区域降水和关键区环流的 关键词： 短期气候预测 相似误差订正 可预报分量     

Multidimensional semi-gap solitons in a periodic potential

The existence, stability and other dynamical properties of a new type of multi-dimensional (2D or 3D) solitons supported by a transverse low-dimensional (1D or 2D, respectively) periodic potential in the nonlinear Schr?dinger equation with the self-defocusing cubic nonlinearity are studied. The equation describes propagation of light in a medium with normal group-velocity dispersion (GVD). Strictly speaking, solitons cannot exist in the model, as its spectrum does not support a true bandgap. Nevertheless, the variational approximation (VA) and numerical computations reveal stable solutions that seem as completely localized ones, an explanation to which is given. The solutions are of the gap-soliton type in the transverse direction(s), in which the periodic potential acts in combination with the diffraction and self-defocusing nonlinearity. Simultaneously, in the longitudinal (temporal) direction these are ordinary solitons, supported by the balance of the normal GVD and defocusing nonlinearity. Stability of the solitons is predicted by the VA, and corroborated by direct simulations.     

错位光纤干涉激光谱结合BP神经网络的温度传感研究

在分析不同温度时单模错位光纤干涉光谱对应波长的条件下,搭建三层BP神经网络模型对温度传感进行研究,解决了常规光纤测温系统复杂和精度不高的问题。对建立的网络模型参数进行探讨,将采集的激光波长与对应的温度数据,经BP神经网络训练,对比得到最佳网络结构,达到在训练完成的网络输入层输入激光波长值时,便可在输出层得到对应的温度预测值。结果证明,实验输出的预测温度值与实际温度值之间表现出明显的相关性,即预测值能够逼近实测值。温度校正和预测相关系数分别达到0.999 61和0.979 27,校正标准误差与预测标准误差分别为0.017 5和0.144 0,得到预测集的平均相对误差为0.17%,剩余预测误差RPD可达到5.258 3,RPD大于3.0,说明定标效果良好,所建模型可用于实际的检测。另外,将该算法用于了带校正的双耦合结构单模错位光纤测温系统中,结果表明BP神经网络方法能够较好的处理错位光纤测温系统中激光光谱数据和温度之间的非线性关系,预测温度值与实测温度值之间的相关度为0.996 58,得到预测温度值与实际温度值之间平均相对误差为0.63%,从而提高了光纤测温传感器的精度和稳定性,同时也验证了该算法在光纤传感上的可行性,也为错位光纤的压力、曲率等其他物理量传感的精确测量提供了新思路。