相域中电离层TEC参数的分析、建模与预测
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摘要
电离层电子浓度总含量TEC是最为重要的电离层参数之一。由于采用卫星探测技术,TEC探测空间范围广阔,时间连续不断,因而在电离层物理和电离层电波传播研究中日益重要起来。无论是基础理论方面还是工程应用方面,TEC的探测与研究都极具价值。在基础理论研究中,与其他电离层参数一样,TEC受到太阳活动、磁层、大气中性风等各种因素的显著影响,具有复杂的和不同尺度的空间分布与时间变化。对其所做的深入研究,可揭示电离层的基本物理过程的规律,帮助了解电离层和磁层,电离层和中高层大气层之间的相互耦合与相互作用。在工程应用方面,TEC的大小和分布变化直接影响在其中传播的电磁波的特性,影响无线电通信、导航、测量等人类空间活动。通过对TEC参数的分析、建模和预报,可大大增强对空间资源开发利用的效率,例如,利用TEC的现报和预报进行电离层电波传播的修正,可极大提高卫星定位导航的精度。
对电离层TEC参数的研究,特别是在数据分析、建模和预测等三个重要方面的研究已有多年历史,并积累了大量的成果。必须指出,现有的关于TEC参数的分析、建模和预测工作,大部分都是在真实的物理空间进行,虽然结果直观,应用方便,但难以深入揭示发生在TEC参数变化中的复杂过程,例如不同过程之间的非线性相互作用。根据不同的研究目的,采用不同的相空间分析方法,将可克服简单的物理空间分析中的不足,是揭示TEC参数的非线性过程等复杂现象的一种行之有效的方法。
本文利用混沌等相空间的分析方法,着重研究TEC参数的数据分析、建模和预测等三个重要环节的内容。本文的主要工作和结果如下:
(1)在TEC时间序列的相空间特性分析中,揭示出电离层TEC中的行星波特征和混沌现象特性。
采用小波分析和混沌相空间分析两种法,对1996-2004年期间,经度为120oE,纬度从-40o到60o子午线上的电离层TEC观测数据进行了相空间特性分析。
首先,通过小波变换的方法,从原始时间信号中分离出TEC中存在着周期不同的行星波波谱。发现不同的周期行星波的出现频率和振幅的比率分布很有规律;同时,不同的周期的行星波的振幅也随季节和纬度变化。必须指出,这些变化规律和人们对行星波的现有认识基本一致,表明大气行星波可能通过每种机理耦合到电离层F2区。
其次,通过混沌相空间分析方法,获得了电离层TEC参数的关联维数、李雅普诺夫指数等混沌特征参量。实际计算表明,在指定经纬度的TEC时序数据中存在混沌特性,其关联维数在2.7661 ~ 5.0334之间,李雅普诺夫指数在0.0007 ~ 0.7554之间。关联维数和李雅普诺夫指数比较典型的值出现在磁赤道上空的,分别为3.6092和0.3369,确定TEC存在混沌现象。
上述结果表明了利用小波分析法和混沌分析法对TEC数据进行分析,可成功地揭示出直接物理空间分析时难以得到的一些电离层重要物理过程的特性。
(2)探讨了基于混沌相空间理论的TEC参数建模问题,引入相空间TEC参数的几何预测模型,并创立了相空间TEC参数的解析预测模型。
首先,我们引入“加权一阶局域法”作为TEC参数建模问题中的相空间几何预测模型。时间序列的相空间几何预测模型有全域法、局域法、加权零阶局域法、加权一阶局域法、基本李雅普诺夫指数的时间序列预测方法,及基于神经网络的时间序列预测方法等。其中加权一阶局域法是较有效和较精确的方法。因此,“加权一阶局域法”成为电离层TEC参数相空间几何预测模型的首选。
其次,我们建立了电离层TEC参数的相空间解析预测模型。该模型从一组相空间中理想的偏微分控制方程出发,用相矢量为变量,导出其离散形式,再通过变换到实际的物理空间,得到最后要的电离层TEC参数的相空间解析预测模型。该模型能将需要预测的某一时间点上的TEC值用这一时间点之前N个时间点上的TEC值表示出来。该模型不仅可单步预测,还可实现多步预测。
(3)分别利用上述TEC参数的几何和解析预测模型,对实际的电离层TEC参数的观测值进行了预测。
首先,采用了“加权一阶局域法”这一混沌相空间几何法,对TEC时间序列进行了预测。要预测的地点选在120oE磁赤道上空,具体预测的时间是2004年年底的最后500个小时和2500个小时,预测时间点分别为1000和5000。根据这一地点的李雅普诺夫指数,算出理论上有效预测点数为144个。在这个范围内进行了有效的预测,对最后1000点做预测时,标准差为8.3123 TECU,相关系数0.8664;对最后5000点做预测时,标准差为7.6438 TECU,相关系数为0.9172。
其次,采用混沌相空间解析法对TEC时间序列进行了预测。要预测的地点同样选在120oE磁赤道上空,预测的时间是2007年1月。当预测点取第48点和144点时(相当于1-3天),标准差分别为6.1063和7.4431 TECU,相关系数分别为0.81594和0.73501。
上述预测结果表明,我们采用的几何与解析预测模型,均能对电离层TEC参数进行较好地预测。对预测误差分析表明,预测点在1-144之间误差相对较小,标准差范围约为7.4431-8.3123TECU之间,相关系数范围约为0.73501-0.9172之间。
总之,本文的研究工作和成果丰富了对电离层TEC进行研究的途径和方法。对TEC采用相空间方法分析及新分析,不仅可获得TEC在相空间中的特性,更重要的是在通过这些特性加深对TEC参数所反应的电离层基本物理过程特性的理解。本文提出得相空间几何预测模型和相空间解析预测模型,提供了两种TEC参数的有效预测工具。本文运用这些模型,基于电离层TEC参数的实际观测值进行的预报研究,具有精度较高,稳定性较好等突出优点,可望在实际的电离层环境的现报与预报中推广使用。
Total Electron Content (TEC) is one of the most important ionospheric parameters. As ground-based GPS-TEC network provides a powerful tool to monitor ionospherie continuously in a wide range, GPS-TEC is playing an important role in the research of ionospheric physics and the theory of radio wave propagation. It is valuable in the fields of both theory and engineering. Based on the previous investigation, TEC is influenced by sun activities, magnetic fields, atmospheric winds, and so on. As the same with others ionospheric parameters, TEC’s change is also complex in both space and time. The study of TEC reveals the rules of ionospheric-physics processing, and helps us to know the relations between ionosphere and magnetic field, ionosphere and atmosphere. In engineering application, the values of TEC influence the radio wave propagation directly, and influence the human activities just like radio-communication, navigation, measurement and so on. Through the data-analysis, modeling and predicting of TEC, we can obtain space-resource more efficiently. For example, we can increase precision of satellite navigation.
It has been many years since TEC was studied, especially in data-analysis, modeling and predicting, and large numbers of fruits are accumulated. It must be pointed out that most of works about the analysis, modeling and predicting of TEC are dealed with in real physics-space, and this method is directly and convenient in use, but not able to open out the complex process in the changes of TEC parameter deeply, for example, the nonlinear reciprocity between varied processes. According to different research purposes, the varied analysis methods in phase-space are adopted and these will be effective methods to open out complex phenomena just like the nonlinear processes and so on.
The phase-space analysis like chaos was applied to study TEC analysis, TEC modeling and TEC predicting in this paper. The results of our work are followed:
(1) Analysesing the property of TEC time series in phase space to open out the property of planetary wave-type oscillations (PWTO) and chaos existed in ionospheric TEC.
Using the two methods of wavelet-analysis and chaos-analysis, we analyses the TEC data, during year 1996-2004,at longitude 120oE, and latitude from -40o to 60o to attain their phase-space properties.
At the first, using the method of wavelet-analysis, we separate the spectrum of varied-periodic PWTO from the original temporal signal existed in TEC time series. It is found that the appeared rates and amplitudes of varied-periodic PWTO are distributed quite follow some certain law. At the same time, the amplitudes of varied-periodic PWTO are changed by seasons and latitude. It must be pointed out that these laws are in accord with people’s knowledge to PWTO today. This says that planetary waves (PW) are coupled with ionospheric F2 by some mechanism.
Secondly, using the method of chaos-analysis, we get the values of the correlation dimension and the Lyapunov exponent of TEC. By fact calculating, it says that the chaotic properties exist in some certain TEC time series and its correlation dimensions are between 2.6592 ~ 5.0334 , its Lyapunov exponents are between 0.0007 ~ 0.7554. The typical correlation dimension and the typical Lyapunov exponent, appeared over magnet equator, are 3.6092 and 0.3369 separately on. These make sure that TEC time series have chaotic property.
Follow these results, It says that, using wavelet-analysis and chaos-analysis to analyses TEC data, we can get the characteristic of some important processes of ionospheric physics which are difficult to be got in real physics-space..
(2) This paper discusses the modeling problem based on chaotic phase-space theory. Phase-space geometry predicting model is introduced and phase-space analytic predicting model is created.
At the first, we introduce one-rank local-region method (ORLRM) to be the model of TEC parameter as geometry predicting model in phase-space. There are many geometry predicting models in phase-space, such as globe-region method, local-region method, zero-rank local-region method, one-rank local-region method, Lyapunov exponent method, NN method and so on. Here, the method, whose precise is the most high, is one-rank local-region method.
Secondly, we set up an phase-space analytic predicting model. This model, based on a perfect group of partial differential equations, taking phase vectors as variables, is educed as a discrete one and, at last, is changed into real physics-space. It can express the TEC value in some future time point using the TEC values of N time points before the time we predict at. It can predict not only one step, but also multiple steps.
(3) This paper used two models, geometry one and analysis one, to predict real TEC time series detected.
At the first, we use weighted one-rank local-region forecasting model, a kind of geometry ones, to predict the TEC time series. The place we predict is chosen at 120oE over magnet equator, and the time we predict is the time points, 500 hours and 2500 hours, or 1000 time points and 5000 time points, that before the bottom of 2004 year. According to the Lyapunov exponent in this area, we reckon the efficient time points are 144 in theory. In this score, our prediction is successful. To 1000 time points, its standard deviation is 8.3123 TECU and the correlation coefficient is about 0.8664. To 5000 points, its standard deviation is 7.6438 TECU and the correlation coefficient is about 0.9172.
Secondly, we use chaos phase-space analysis forecasting model to predict the TEC time series. The place we predict is chosen at 120oE over magnet equator, and the time we predict is in January 1997. Its standard deviation is 6.1063~7.4431 TECU and Its correlation coefficient is 0.81594~0.73501 when the prediction step is 48 and 144 point (equal 1~3 day).
It says that, we can take the models, geometry model and analysis model, to predict ionospheric TEC parameter preferably. Error analysis shows that, if predicted point is between 1- 144, the error is less. Its standard deviation is between 7.4431 and 8.3123 TECU and the correlation coefficient is between 0.73501 and 0.9172.
In conclusion, this investigation provides us with a new method to study TEC of ionosphere. We can not only obtain the characters of TEC, but also enrich our understanding on the ionospheric physics by analyzing in phase-space. Two methods to forecast TEC including phase-space geometry predicting model and phase-space analytic predicting model are put forward. Based on these models, the practical TEC can be predicted with high precision and good stability by our test. We suggest that these models can be used in ionospheric weather nowcast and forecast.
对电离层TEC参数的研究,特别是在数据分析、建模和预测等三个重要方面的研究已有多年历史,并积累了大量的成果。必须指出,现有的关于TEC参数的分析、建模和预测工作,大部分都是在真实的物理空间进行,虽然结果直观,应用方便,但难以深入揭示发生在TEC参数变化中的复杂过程,例如不同过程之间的非线性相互作用。根据不同的研究目的,采用不同的相空间分析方法,将可克服简单的物理空间分析中的不足,是揭示TEC参数的非线性过程等复杂现象的一种行之有效的方法。
本文利用混沌等相空间的分析方法,着重研究TEC参数的数据分析、建模和预测等三个重要环节的内容。本文的主要工作和结果如下:
(1)在TEC时间序列的相空间特性分析中,揭示出电离层TEC中的行星波特征和混沌现象特性。
采用小波分析和混沌相空间分析两种法,对1996-2004年期间,经度为120oE,纬度从-40o到60o子午线上的电离层TEC观测数据进行了相空间特性分析。
首先,通过小波变换的方法,从原始时间信号中分离出TEC中存在着周期不同的行星波波谱。发现不同的周期行星波的出现频率和振幅的比率分布很有规律;同时,不同的周期的行星波的振幅也随季节和纬度变化。必须指出,这些变化规律和人们对行星波的现有认识基本一致,表明大气行星波可能通过每种机理耦合到电离层F2区。
其次,通过混沌相空间分析方法,获得了电离层TEC参数的关联维数、李雅普诺夫指数等混沌特征参量。实际计算表明,在指定经纬度的TEC时序数据中存在混沌特性,其关联维数在2.7661 ~ 5.0334之间,李雅普诺夫指数在0.0007 ~ 0.7554之间。关联维数和李雅普诺夫指数比较典型的值出现在磁赤道上空的,分别为3.6092和0.3369,确定TEC存在混沌现象。
上述结果表明了利用小波分析法和混沌分析法对TEC数据进行分析,可成功地揭示出直接物理空间分析时难以得到的一些电离层重要物理过程的特性。
(2)探讨了基于混沌相空间理论的TEC参数建模问题,引入相空间TEC参数的几何预测模型,并创立了相空间TEC参数的解析预测模型。
首先,我们引入“加权一阶局域法”作为TEC参数建模问题中的相空间几何预测模型。时间序列的相空间几何预测模型有全域法、局域法、加权零阶局域法、加权一阶局域法、基本李雅普诺夫指数的时间序列预测方法,及基于神经网络的时间序列预测方法等。其中加权一阶局域法是较有效和较精确的方法。因此,“加权一阶局域法”成为电离层TEC参数相空间几何预测模型的首选。
其次,我们建立了电离层TEC参数的相空间解析预测模型。该模型从一组相空间中理想的偏微分控制方程出发,用相矢量为变量,导出其离散形式,再通过变换到实际的物理空间,得到最后要的电离层TEC参数的相空间解析预测模型。该模型能将需要预测的某一时间点上的TEC值用这一时间点之前N个时间点上的TEC值表示出来。该模型不仅可单步预测,还可实现多步预测。
(3)分别利用上述TEC参数的几何和解析预测模型,对实际的电离层TEC参数的观测值进行了预测。
首先,采用了“加权一阶局域法”这一混沌相空间几何法,对TEC时间序列进行了预测。要预测的地点选在120oE磁赤道上空,具体预测的时间是2004年年底的最后500个小时和2500个小时,预测时间点分别为1000和5000。根据这一地点的李雅普诺夫指数,算出理论上有效预测点数为144个。在这个范围内进行了有效的预测,对最后1000点做预测时,标准差为8.3123 TECU,相关系数0.8664;对最后5000点做预测时,标准差为7.6438 TECU,相关系数为0.9172。
其次,采用混沌相空间解析法对TEC时间序列进行了预测。要预测的地点同样选在120oE磁赤道上空,预测的时间是2007年1月。当预测点取第48点和144点时(相当于1-3天),标准差分别为6.1063和7.4431 TECU,相关系数分别为0.81594和0.73501。
上述预测结果表明,我们采用的几何与解析预测模型,均能对电离层TEC参数进行较好地预测。对预测误差分析表明,预测点在1-144之间误差相对较小,标准差范围约为7.4431-8.3123TECU之间,相关系数范围约为0.73501-0.9172之间。
总之,本文的研究工作和成果丰富了对电离层TEC进行研究的途径和方法。对TEC采用相空间方法分析及新分析,不仅可获得TEC在相空间中的特性,更重要的是在通过这些特性加深对TEC参数所反应的电离层基本物理过程特性的理解。本文提出得相空间几何预测模型和相空间解析预测模型,提供了两种TEC参数的有效预测工具。本文运用这些模型,基于电离层TEC参数的实际观测值进行的预报研究,具有精度较高,稳定性较好等突出优点,可望在实际的电离层环境的现报与预报中推广使用。
Total Electron Content (TEC) is one of the most important ionospheric parameters. As ground-based GPS-TEC network provides a powerful tool to monitor ionospherie continuously in a wide range, GPS-TEC is playing an important role in the research of ionospheric physics and the theory of radio wave propagation. It is valuable in the fields of both theory and engineering. Based on the previous investigation, TEC is influenced by sun activities, magnetic fields, atmospheric winds, and so on. As the same with others ionospheric parameters, TEC’s change is also complex in both space and time. The study of TEC reveals the rules of ionospheric-physics processing, and helps us to know the relations between ionosphere and magnetic field, ionosphere and atmosphere. In engineering application, the values of TEC influence the radio wave propagation directly, and influence the human activities just like radio-communication, navigation, measurement and so on. Through the data-analysis, modeling and predicting of TEC, we can obtain space-resource more efficiently. For example, we can increase precision of satellite navigation.
It has been many years since TEC was studied, especially in data-analysis, modeling and predicting, and large numbers of fruits are accumulated. It must be pointed out that most of works about the analysis, modeling and predicting of TEC are dealed with in real physics-space, and this method is directly and convenient in use, but not able to open out the complex process in the changes of TEC parameter deeply, for example, the nonlinear reciprocity between varied processes. According to different research purposes, the varied analysis methods in phase-space are adopted and these will be effective methods to open out complex phenomena just like the nonlinear processes and so on.
The phase-space analysis like chaos was applied to study TEC analysis, TEC modeling and TEC predicting in this paper. The results of our work are followed:
(1) Analysesing the property of TEC time series in phase space to open out the property of planetary wave-type oscillations (PWTO) and chaos existed in ionospheric TEC.
Using the two methods of wavelet-analysis and chaos-analysis, we analyses the TEC data, during year 1996-2004,at longitude 120oE, and latitude from -40o to 60o to attain their phase-space properties.
At the first, using the method of wavelet-analysis, we separate the spectrum of varied-periodic PWTO from the original temporal signal existed in TEC time series. It is found that the appeared rates and amplitudes of varied-periodic PWTO are distributed quite follow some certain law. At the same time, the amplitudes of varied-periodic PWTO are changed by seasons and latitude. It must be pointed out that these laws are in accord with people’s knowledge to PWTO today. This says that planetary waves (PW) are coupled with ionospheric F2 by some mechanism.
Secondly, using the method of chaos-analysis, we get the values of the correlation dimension and the Lyapunov exponent of TEC. By fact calculating, it says that the chaotic properties exist in some certain TEC time series and its correlation dimensions are between 2.6592 ~ 5.0334 , its Lyapunov exponents are between 0.0007 ~ 0.7554. The typical correlation dimension and the typical Lyapunov exponent, appeared over magnet equator, are 3.6092 and 0.3369 separately on. These make sure that TEC time series have chaotic property.
Follow these results, It says that, using wavelet-analysis and chaos-analysis to analyses TEC data, we can get the characteristic of some important processes of ionospheric physics which are difficult to be got in real physics-space..
(2) This paper discusses the modeling problem based on chaotic phase-space theory. Phase-space geometry predicting model is introduced and phase-space analytic predicting model is created.
At the first, we introduce one-rank local-region method (ORLRM) to be the model of TEC parameter as geometry predicting model in phase-space. There are many geometry predicting models in phase-space, such as globe-region method, local-region method, zero-rank local-region method, one-rank local-region method, Lyapunov exponent method, NN method and so on. Here, the method, whose precise is the most high, is one-rank local-region method.
Secondly, we set up an phase-space analytic predicting model. This model, based on a perfect group of partial differential equations, taking phase vectors as variables, is educed as a discrete one and, at last, is changed into real physics-space. It can express the TEC value in some future time point using the TEC values of N time points before the time we predict at. It can predict not only one step, but also multiple steps.
(3) This paper used two models, geometry one and analysis one, to predict real TEC time series detected.
At the first, we use weighted one-rank local-region forecasting model, a kind of geometry ones, to predict the TEC time series. The place we predict is chosen at 120oE over magnet equator, and the time we predict is the time points, 500 hours and 2500 hours, or 1000 time points and 5000 time points, that before the bottom of 2004 year. According to the Lyapunov exponent in this area, we reckon the efficient time points are 144 in theory. In this score, our prediction is successful. To 1000 time points, its standard deviation is 8.3123 TECU and the correlation coefficient is about 0.8664. To 5000 points, its standard deviation is 7.6438 TECU and the correlation coefficient is about 0.9172.
Secondly, we use chaos phase-space analysis forecasting model to predict the TEC time series. The place we predict is chosen at 120oE over magnet equator, and the time we predict is in January 1997. Its standard deviation is 6.1063~7.4431 TECU and Its correlation coefficient is 0.81594~0.73501 when the prediction step is 48 and 144 point (equal 1~3 day).
It says that, we can take the models, geometry model and analysis model, to predict ionospheric TEC parameter preferably. Error analysis shows that, if predicted point is between 1- 144, the error is less. Its standard deviation is between 7.4431 and 8.3123 TECU and the correlation coefficient is between 0.73501 and 0.9172.
In conclusion, this investigation provides us with a new method to study TEC of ionosphere. We can not only obtain the characters of TEC, but also enrich our understanding on the ionospheric physics by analyzing in phase-space. Two methods to forecast TEC including phase-space geometry predicting model and phase-space analytic predicting model are put forward. Based on these models, the practical TEC can be predicted with high precision and good stability by our test. We suggest that these models can be used in ionospheric weather nowcast and forecast.
引文
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