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1.
Nonlinear ensemble prediction of chaotic daily rainfall 总被引：3，自引：0，他引：3
The significance of treating rainfall as a chaotic system instead of a stochastic system for a better understanding of the underlying dynamics has been taken up by various studies recently. However, an important limitation of all these approaches is the dependence on a single method for identifying the chaotic nature and the parameters involved. Many of these approaches aim at only analyzing the chaotic nature and not its prediction. In the present study, an attempt is made to identify chaos using various techniques and prediction is also done by generating ensembles in order to quantify the uncertainty involved. Daily rainfall data of three regions with contrasting characteristics (mainly in the spatial area covered), Malaprabha, Mahanadi and All-India for the period 1955–2000 are used for the study. Auto-correlation and mutual information methods are used to determine the delay time for the phase space reconstruction. Optimum embedding dimension is determined using correlation dimension, false nearest neighbour algorithm and also nonlinear prediction methods. The low embedding dimensions obtained from these methods indicate the existence of low dimensional chaos in the three rainfall series. Correlation dimension method is done on the phase randomized and first derivative of the data series to check whether the saturation of the dimension is due to the inherent linear correlation structure or due to low dimensional dynamics. Positive Lyapunov exponents obtained prove the exponential divergence of the trajectories and hence the unpredictability. Surrogate data test is also done to further confirm the nonlinear structure of the rainfall series. A range of plausible parameters is used for generating an ensemble of predictions of rainfall for each year separately for the period 1996–2000 using the data till the preceding year. For analyzing the sensitiveness to initial conditions, predictions are done from two different months in a year viz., from the beginning of January and June. The reasonably good predictions obtained indicate the efficiency of the nonlinear prediction method for predicting the rainfall series. Also, the rank probability skill score and the rank histograms show that the ensembles generated are reliable with a good spread and skill. A comparison of results of the three regions indicates that although they are chaotic in nature, the spatial averaging over a large area can increase the dimension and improve the predictability, thus destroying the chaotic nature. 相似文献
2.
地球系统模拟和混沌时间序列 总被引：18，自引：0，他引：18
地球系统是非线性的系统.为了模拟地球系统,我们就必须了解非线性科学的最新进展.本文从非线性科学角度论述了地球系统模拟中的几个关键问题,如尺度是分层次的,不同尺度之间存在着相似性及标度律,同时也存在差异性及非均匀性.为此还介绍了一些概念:吸引子、分维、信息和熵等.最后本文还说明如何从地球系统中所观测到的时间序列取得地球系统模拟所需要的信息. 相似文献
3.
Based on the body strain observation data at Liyang and Xuzhou stations, the Correlation Dimension D2 and the second-order Renyi entropy K2 of the attractor are calculated and studied. In addition, a new method of evaluating the longest predictable time of precursor attractor is advanced under the condition of a certain anomalous criterion rule. The conclusion indicates that the body strain precursor attractor is one of the chaotic attractors and it has some determinate change rules such as the dimension declines before an earthquake and the number of the independent factors on which the variation of the system depends is within the range of 5 - 12. The conclusion also indicates that the longest evaluated predictable time of the body strain attractor is 213 days at the Liyang station and 342 days at the Xuzhou station. It is clear that this research can be of great reference value for recognizing the nonlinear behavior of precursor attractors and for evaluating the predictability of different precursor 相似文献
4.
引入非线性动力学理论和混沌时间序列分析方法考察强震地面运动加速度时程的非线性特征。首先采用功率谱分析法、主成份分析法和Cao方法定性判断地震动加速度时程具有混沌特性,然后应用混沌时间序列分析方法定量计算了30条地震动加速度时程的三个非线性特征参数。计算表明,这些地震动时程的关联维数为2．0～4．0的分数维,Kolmogorov熵K2为大于零的有限正值,最大Lyapunov指数在o～i．0之间。结果说明,强震地面运动具有混沌特性,地震动的高度不规则和复杂性是地震过程强非线性的反映。 相似文献
5.
李强 《地震学报(英文版)》2000,13(4):434-439
IntroductionThere are some problems we often meet when we work for earthquake forecasting with theobservational data of earthquake precursor observation. Such items as the deformation of earth'scrust, underground fluid, geoelectricity and so on. These problems include that the ceasing workof the observational apparatus because of malfunction or accident in case of emergent ewthquakesituation will lose some imperative information and make it more difficult to evaluate futUreearthquake situation… 相似文献
6.
人工神经网络是用来模拟人脑智能特点和结构的一种模型,具有很强的非线性映射功能．把它引用到地震前兆观测数据的分析处理中,可为前兆观测更好地服务于地震分析预报开辟出一条新路,也是对人工神经网络方法应用的推广．本文分析了时间序列的可预测性,给出了用人工神经网络预测地震前兆混沌时间序列的方法,并以江宁台和徐州台SQ 型地倾斜仪观测及溧阳台体应变观测的时间序列为例,对其作了预测和处理．结果表明:用该方法处理达到的精度能满足实际工作的需要,因而该方法在今后的实际地震分析预报工作中具有重要应用价值． 相似文献
7.
In this paper we outlined the chaotic attractor of the precursory field evolution of the seismogenic system and its fractal
dimension of the precursory time and space distribution. We developed the calculative method of reconstruction complex system
dynamics from single time series and analysed the descent dimension phenomena of the precursory distribution before large
earthquakes. We also showed the time-space synthesis method constructed complex system dynamics by many stations or many methodes
in the seismogenic system consists of large area tectonic network. This method can describe the self-organization behavior
of the system more accurately and get rid of the uncertainty and randomness caused by single station or single method. As
an example, we calculated the chaotic attractor of the precursory field evolution and the fractal dimension of the precursory
time and space distribution and its change tendencies before large earthquakes in Beijing-Tianjing area.
The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 463–469, 1993. 相似文献
8.
《Advances in water resources》1999,23(3):253-260
The standing debate over whether hydrological systems are deterministic or stochastic has been taken to a new level by controversial applications of chaos mathematics. This paper reviews the procedure, constraints, and past usage of a popular chaos time series analysis method, correlation integral analysis, in hydrology and adds a new analysis of daily streamflow from a pristine watershed. Significant problems with the use of correlation integral analysis (CIA) were found to include a continued reliance on the original algorithm even though it was corrected subsequently and failure to consider the physics underlying mathematical results. The new analysis of daily streamflow reported here found no attractor with D⩽5. Phase randomization of the Fourier Transform of streamflow was used to provide a better stochastic surrogate than an Autoregressive Moving Average (ARMA) model or gaussian noise for distinguishing between chaotic and stochastic dynamics. 相似文献
9.
10.
Nonlinear and multifractal approaches of the geomagnetic field 总被引：2，自引：0，他引：2
L. Hongre P. Sailhac M. Alexandrescu J. Dubois 《Physics of the Earth and Planetary Interiors》1999,110(3-4):157-190
Recent nonlinear dynamics techniques have been developed to analyse chaotic time series data. We first summarize the procedure which gives an appropriate reconstruction of the unknown dynamics from scalar measurements in a pseudophase space. It permits, firstly, the representation of the trajectories of the dynamical system—they define an attractor when the system is dissipative—by preserving its topological properties. We then present the invariant measures and ergodic quantities such as the multifractal spectrum and Lyapunov exponents which can be estimated on the reconstructed attractor. The multifractal analysis provides us with a characterization of the scaling energy of the process whereas the Lyapunov exponent gives another statistical measure of the stability of the dynamics. The estimation of these quantities was tested on synthetic data. The nonlinear and multifractal analyses were finally applied to the hourly mean values of the magnetic field recorded at the Eskdalemuir (ESK) observatory over 79 years (692,520 data measurements for each component). The estimations of a 5-dimensional pseudo-phase space and a positive Lyapunov exponent confirm the possibility of low-dimensional deterministic chaos in the magnetic field observations at ESK observatory. The correlation between the solar activity (the Wolf number), the unstable nature of the magnetic field, and the singularity spectrum points out the forcing of the solar cycles on the dynamics of the magnetic field at ESK observatory. 相似文献
11.
The onset of Alfvén intermittent chaos in space plasmas is studied by numerically solving the derivative non-linear Schrödinger equation (DNLS) under the assumption of stationary Alfvén waves. We describe how the Alfvénic fluctuations of the magnetic field can evolve from periodic to chaotic behavior through a sequence of bifurcations as the plasma dissipation is varied. The collision of a chaotic attractor with an unstable periodic orbit leads to the generation of strongly chaotic behavior, in an event known as interior crisis. We also show that in the DNLS equation, chaotic attractors coexist with nonattracting chaotic sets responsible for transient chaotic behaviors. After the interior crisis point, a wide chaotic attractor can be decomposed into two coupled nonattracting chaotic sets, resulting in intermittent chaotic time series. Understanding transient chaos is a key to understand intermittency in space plasmas. 相似文献
12.
I. R. Stakhovsky 《Izvestiya Physics of the Solid Earth》2016,52(5):740-753
The attractor is reconstructed from the time series of the information entropy of the seismic kinetics process. It is shown that the seismic kinetics process is governed by three order parameters and is characterized by a strange attractor in the three-dimensional phase space. The Dq-spectrum of the multifractal measure induced by the attractor, which describes the topological structure of the latter, is obtained. The monofractal dimension of the attractor is Dq(0) = 2.31…, and the correlation dimension is Dq(2) = 2.16…. The estimate of the largest Lyapunov exponent of the attractor λ1 = 0.331…. The positive signature of the largest Lyapunov exponent suggests that the attractor is chaotic and the behavior of the phase trajectory is unpredictable. 相似文献
13.
Signatures of low-dimensional chaos in hourly water level measurements at coastal site of Mariupol,Ukraine 总被引：2，自引：2，他引：0
V. Khokhlov A. Glushkov N. Loboda N. Serbov K. Zhurbenko 《Stochastic Environmental Research and Risk Assessment (SERRA)》2008,22(6):777-787
Variations of water levels in ports and estuaries are important for ship guidance and navigation and are influenced by a variety
of factors. The hourly data that was collected from the coastal site at the Port of Mariupol, Ukraine during January–December
2005 were analysed with an objective to reveal features of chaotic behaviour. The concepts and methods of chaos theory (average
mutual information, correlation dimension, false nearest neighbours, Lyapunov exponents) were applied. The manifestation of
low-dimensional chaos was found in the time series. The possibility of nonlinear prediction was concluded. 相似文献
14.
Accurate simulation and prediction of the dynamic behaviour of a river discharge over any time interval is essential for good watershed management. It is difficult to capture the high‐frequency characteristics of a river discharge using traditional time series linear and nonlinear model approaches. Therefore, this study developed a wavelet‐neural network (WNN) hybrid modelling approach for the predication of river discharge using monthly time series data. A discrete wavelet multiresolution method was employed to decompose the time series data of river discharge into sub‐series with low (approximation) and high (details) frequency, and these sub‐series were then used as input data for the artificial neural network (ANN). WNN models with different wavelet decomposition levels were employed to predict river discharge 48 months ahead of time. Comparison of results from the WNN models with those of the ANN models alone indicated that WNN models performed a more accurate prediction. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
15.
Abstract A trial is made to explore the applicability of chaos analysis outside the commonly reported analysis of a single chaotic time series. Two cross-correlated streamflows, the Little River and the Reed Creek, Virginia, USA, are analysed with regard to the chaotic behaviour. Segments of missing data are assumed in one of the time series and estimated using the other complete time series. Linear regression and artificial neural network models are employed. Two experiments are conducted in the analysis: (a) fitting one global model and (b) fitting multiple local models. Each local model is in the direct vicinity of the missing data. A nonlinear noise reduction method is used to reduce the noise in both time series and the two experiments are repeated. It is found that using multiple local models to estimate the missing data is superior to fitting one global model with regard to the mean squared error and the mean relative error of the estimated values. This result is attributed to the chaotic behaviour of the streamflows under consideration. 相似文献
16.
Rahman Khatibi Mohammad Ali Ghorbani Mohammad Taghi Aalami Kasim Kocak Oleg Makarynskyy Dina Makarynska Mahdi Aalinezhad 《Ocean Dynamics》2011,61(11):1797-1807
Water level forecasting using recorded time series can provide a local modelling capability to facilitate local proactive
management practices. To this end, hourly sea water level time series are investigated. The records collected at the Hillarys
Boat Harbour, Western Australia, are investigated over the period of 2000 and 2002. Two modelling techniques are employed:
low-dimensional dynamic model, known as the deterministic chaos theory, and genetic programming, GP. The phase space, which
describes the evolution of the behaviour of a nonlinear system in time, was reconstructed using the delay-embedding theorem
suggested by Takens. The presence of chaotic signals in the data was identified by the phase space reconstruction and correlation
dimension methods, and also the predictability into the future was calculated by the largest Lyapunov exponent to be 437 h
or 18 days into the future. The intercomparison of results of the local prediction and GP models shows that for this site-specific
dataset, the local prediction model has a slight edge over GP. However, rather than recommending one technique over another,
the paper promotes a pluralistic modelling culture, whereby different techniques should be tested to gain a specific insight
from each of the models. This would enable a consensus to be drawn from a set of results rather than ignoring the individual
insights provided by each model. 相似文献
17.
18.
Long‐term river meandering as a part of chaotic dynamics? A contribution from mathematical modelling
In the present contribution we focus our attention on the possible signatures of a chaotic behaviour or a self‐organized criticality state triggered in river meandering dynamics by repeated occurrence of cutoff processes. The analysis is carried out examining, through some robust nonlinear methodologies inferred from time series analysis, both the spatial series of local curvatures and the time series of long‐term channel sinuosity. Temporal distribution of cutoff inter‐arrivals is also investigated. The analyzed data have been obtained by using a suitable physics‐based simulation model for river meandering able to reproduce reasonably the features of real rivers. The results are consistent and show that, at least from a modelling point of view, no evidence of chaotic determinism or self‐organized criticality is detectable in the investigated meandering dynamics. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
19.
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. 相似文献
20.
Different time series were constructed from the data set containing all the seismic events recorded by the Parkfield network between 1969 and 1987. These series were analyzed to determine whether there exists an attractor in the phase space of the dynamical system characterizing seismic activity and to tentatively establish its dimension. The study has yielded ambiguous results. For all the time series analyzed, the dimension of the attractor appears higher than 12 and the correlation function of the seismic time series is undistinguishable from that of a series of random numbers of the same length. The lack of difference between the scaling parameters of two series suggests that, for all practical purposes, the seismic time series cannot be discriminated from a random series. 相似文献