CN116738159B - A global ionospheric space weather response extraction method based on complex network - Google Patents

Abstract

The invention discloses a global ionospheric space weather response extraction method based on a complex network, which belongs to the field of space physics intelligent data processing. This method preprocesses and meshes the time series data of the total electron content of the ionosphere, and uses the Pearson correlation method Calculate the connection strength between nodes, use a greedy algorithm to obtain the homogeneity area of the ionosphere, construct a regional node network and extract its corresponding feature variables, calculate the degree distribution and clustering coefficient statistical characteristics of the nodes formed in the area and visualize them , analyze and extract the response characteristics of complex networks to magnetic storm events and solar activity in different periods. The present invention proposes a visual analysis method for ionospheric complex network big data, which can better reflect the spatiotemporal disturbances and anomalies of the total electron content of the ionosphere under space weather. The constructed network can efficiently and accurately describe the ionospheric space weather. Spatial correlation mechanisms and response characteristics.

Description

A global ionospheric space weather response extraction method based on complex network

Technical field

The invention belongs to the field of space physics intelligent data processing, and specifically relates to a global ionospheric space weather response extraction method based on complex networks, especially complex network modeling and visual analysis of long-scale time series data.

Background technique

As humans gradually enter the information age, satellite communications and satellite navigation systems have been widely used in all aspects of military and civilian use, becoming indispensable tools for human life. At the 2018 annual meeting of the China Association for Science and Technology, a number of major engineering and technical issues and scientific issues were listed as priority research objects, and issues related to the accurate extraction, analysis, and forecasting of space weather are one of them.

With the development of artificial intelligence technology represented by deep learning, its application in the evolution process of space physics, especially the causal coupling mechanism and prediction of space physics, has gradually become a research hotspot. In the existing technology, research on the evolution of the total electron content of the ionosphere can rely on long short-term memory networks or generative adversarial networks. Related methods can better extract the spatiotemporal variation characteristics of the ionosphere. However, the spatiotemporal evolution of the global ionosphere The mechanism is regarded as a complex system. The spatial interaction relationship between the total electron content of the ionosphere in different regions and its changing rules are affected by space weather, which is still a blind spot in related fields of research.

Complex network is the main research method for the evolution of complex systems at different scales. With the in-depth exploration of complex network technology, its application in geophysical complex systems has become a hot and difficult research topic. The German Max Planck Institute and the Chinese Academy of Sciences Atmospheric Research Scholars from the Institute of Physics, Sun Yat-sen University and other institutions have taken the lead in constructing a complex network model of surface temperature and applied it to the prediction of ENSO and the analysis of extreme weather events. Related research is highly inspiring. As the main component of the upper atmosphere, the ionosphere's spatio-temporal evolution is also one of the complex systems in the geophysics discipline. Therefore, inspired by previous studies, the complex network method was introduced into the study of the spatial correlation of the total electron content of the ionosphere and its distribution in space. Global and local scale changes in weather are a new technical approach to solve the problems described in the present invention.

The dynamic characteristics of the ionosphere have an important impact on changes in global satellite communications. Using complex network theory to study the dynamic changes and functional structure of the ionosphere can find its influencing factors and help researchers better understand the causes of space weather phenomena. Therefore, by extracting and analyzing the global ionospheric space weather response characteristics, we can better grasp the dynamic change trend of the earth's ionosphere, which is helpful for monitoring and researching the global ionospheric spatiotemporal evolution situation, and providing a basis for predicting the ionosphere. Provide effective support for space weather response.

Contents of the invention

In order to overcome the shortcomings of the existing technology, the present invention provides a global ionospheric space weather response extraction method based on a complex network. This method preprocesses and meshes the time series data of the total electron content of the ionosphere, and uses the Pearson correlation method Calculate the connection strength between nodes, use a greedy algorithm to obtain the homogeneity area of the ionosphere, construct a regional node network and extract its corresponding feature variables, calculate the degree distribution and clustering coefficient statistical characteristics of the nodes formed in the area and visualize them . The present invention can reflect the fluctuation of ionospheric data under space weather, and the constructed network can efficiently and accurately extract the response characteristics of the ionosphere to space weather, providing effective technical support for improving ionospheric prediction.

In order to achieve the above objects, the present invention adopts the following technical solutions:

A global ionospheric space weather response extraction method based on complex networks includes the following steps:

Step 1) Preprocess the original data and construct a three-dimensional array of total electron content in the ionosphere. Interpolate the constructed three-dimensional array of total electron content in the ionosphere into grid points around the world. The grid points are regarded as the total electron content in the ionosphere. For the nodes of the network, extract the time series of the total electron content of the ionosphere at the nodes;

Step 2) Construct a local homogeneous region of the ionospheric total electron content network:

Use a greedy algorithm to group the nodes of the preprocessed ionospheric total electron content network into global geographical areas to construct a local homogeneous area of the ionospheric total electron content network over the time series length; for any arbitrary ionospheric total electron content network two nodes and/> , combine the two nodes/> and/> The Pearson correlation coefficient between , its calculation formula is as follows:

(1)

in, For the first/> Linear ionospheric time series data of nodes,/> is the total number of nodes in the total electron content network of the ionosphere, adopted in global latitude and longitude/> The value at resolution is/> ,/> is the selected time length;

Step 3) Perform node modeling of the local homogeneous region of the ionospheric total electron content network;

Step 4) Use the degree distribution and clustering coefficient statistical characteristics of the nodes in the local homogeneous area of the ionospheric total electron content network to calculate the structural characteristics of the ionospheric total electron content network, thereby extracting the characteristics of the ionospheric total electron content network under different space weather. Response characteristics and spatial correlation properties between different regions. The beneficial effects of the present invention are:

This invention uses a greedy algorithm to construct a local homogeneous area of the ionospheric network, fits the ionospheric observation data, can restore the fluctuations of the total electron content changes in the ionosphere reflected in the time series data to the maximum extent, and uses model parameters to express the three-dimensional ionosphere The total electron content data solves the problem that the complex network model constructed using only the Pearson correlation method can only calculate time series data, while retaining the spatial correlation characteristics between different regions.

Compared with traditional ionospheric analysis methods, this invention can more accurately describe the spatial structure and characteristics of the total electron content of the ionosphere based on complex network theory, study the dynamic changes and refined response structure of the total electron content of the ionosphere, and find its influencing factors. This helps researchers better understand the global multi-scale response mechanism of ionospheric space weather. In addition, the network constructed by the present invention can efficiently and accurately extract the space weather response characteristics of the total electron content of the ionosphere, thereby realizing the analysis of the response characteristics of the ionospheric space weather on a global scale, and providing a basis for improving the analysis of the total electron content of the ionosphere under space weather. Space-time prediction provides effective technical support. Therefore, the method of the present invention has broad application prospects and can be used in the fields of research on the physical mechanism of ionospheric space and ionospheric space weather monitoring and prediction.

Description of the drawings

Figure 1 is a flow chart for the implementation of a complex network-based global ionospheric space weather response extraction method of the present invention;

Figure 2(a) shows the visualization result of node intensity distribution in the local homogeneous area of the ionospheric complex network under a magnetic storm event;

Figure 2(b) shows the visualization result of node intensity distribution in the local homogeneous area of the ionospheric complex network under a magnetic calm event;

Figure 3 is a visualization result of the probability density distribution of the connection strength between real data and randomized data nodes;

Figure 4(a) shows the visualization results of the distribution of topological characteristics of the ionospheric complex network under magnetic storm events;

Figure 4(b) shows the visualization results of the distribution of topological characteristics of the ionospheric complex network under magnetic calm events.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that the described embodiments are only intended to facilitate the understanding of the present invention and do not serve any limiting purpose.

According to the embodiment of the present invention, a global ionospheric space weather response extraction method based on complex network is proposed. The total electron content data of the ionosphere is modeled through complex network theory and visually analyzed. The process is shown in Figure 1. Now, The total electron content data of the ionosphere from 2008 to 2019 is used as input to introduce the main steps of complex network modeling. The specific process is as follows:

Step 1. Perform data preprocessing:

Download the original data of global ionospheric total electron content distribution from 2008 to 2019 provided by the International GNSS Service Organization. The original data has resolution of two-hour interval data, and the original data of the total electron content grid of the ionosphere is constructed as/> three-dimensional array. Furthermore, when the resolution of both longitude and latitude is/> The original data is mapped to the new data space, thereby dividing the world into 90×180 grids; then, the original ionospheric total electron content distribution data is used to obtain the ionosphere corresponding to the new mapping space time, longitude and latitude The total electron content value, where the grid points in the new mapped space are regarded as the original nodes of the ionospheric network. Furthermore, the constructed three-dimensional array of total electron content in the ionosphere is interpolated into global grid points. The grid points are regarded as nodes of the total electron content network in the ionosphere, and the time series of total electron content in the ionosphere at the nodes are extracted.

The grid area of any area in the world is described by the spherical trigonometry formula. The implementation method is to convert the given longitude and latitude into radians, and obtain the area composed of the longitude and latitude arc length through differentiation, and finally obtain the corresponding area on the earth through three-dimensional projection. area, the calculation formula is as follows:

(1)

in, To form the first/> area of a locally homogeneous region,/> The radius of the earth is 6378.1km, Indicates the latitude and longitude coordinates of the first network node in the area,/> Indicates the latitude and longitude coordinates of the last network node in the area.

Step 2. Construct a local homogeneous region of the total electron content network of the ionosphere:

The greedy algorithm is used to group the nodes of the preprocessed ionospheric total electron content network in global geographical areas to construct a homogeneous area of the ionospheric total electron content network in the time series length. The greedy algorithm can select the local optimal area, Effectively achieve local area homogenization; for any two nodes in the ionospheric total electron content network and/> , record the Pearson correlation coefficient between two nodes as/> , its calculation formula is as follows:

(2)

in, For the first/> Linear ionospheric time series data of nodes,/> is the total number of nodes in the total electron content network of the ionosphere,/> is the selected time length.

When the Pearson correlation coefficient between nodes Exceeds area threshold/> When , these nodes are regarded as homogeneous nodes, and a greedy algorithm is used to continuously find adjacent areas whose average Pearson correlation coefficient is greater than the regional threshold, and merge to form a local homogeneous area. The formed local homogeneous area is recorded as A; each local The number of nodes contained in a homogeneous region is at least two, and there is a connecting link between any two nodes in the same local homogeneous region.

area threshold It is defined as the average of the positive correlation values of all grid nodes, so the local homogeneous area also needs to satisfy that the average correlation of all grid nodes in the area is greater than the regional threshold/> , expressed as the following formula:

(3)

in, Represented in a locally homogeneous region/> Pearson correlation coefficient between two nodes.

area threshold in/> is significant at the level of unilateral/> Inspection confirmed:

(4)

in, is the number of original nodes in this homogeneous area.

Step 3. Model the network area nodes of the total electron content of the ionosphere:

Nodes in a local homogeneous area can be regarded as connected by links, so any node i shares a weighted connection with other nodes in the network. This local homogeneity is extracted by calculating the time series of each node in the local homogeneous area. The characteristic variables of the nodes in the qualitative area are summed up with the weighted cumulative sum of all grids in the area according to the square root of their geographical area to obtain the ionospheric total electron content network. The sum of area-weighted time series of local homogeneous regions/> , can be expressed as the following formula:

(5)

in, is the /> in the local homogeneous region Linear ionospheric time series data of nodes,/> For the first/> The corresponding area of nodes on the global grid,/> To form the first/> a locally homogeneous region.

There is a time correlation in the changes in node connection strength in the time series network, so the nonlinear synchronization method is used to construct the link edges under different local homogeneous areas of the ionospheric total electron content complex network; the connection strength of nodes between local homogeneous areas is the The absolute value of the time covariance between area-weighted time series of locally homogeneous regions, for any length of time , the connection strength between area nodes i and j/> It can be expressed as the following formula:

(6)

in, Indicates averaging the accumulated time series data of nodes in a certain area, and the connection strength/> Depends on the statistical interdependence that exists between two regional nodes,/> is the number of original nodes in the homogeneous area,/> is the selected time length.

In the established network model of total electron content in the ionosphere, regional nodes The node strength of is defined as the sum of the connection strengths of all links associated with it, which is recorded as/> , can be expressed as the following formula:

(7)

The coordinates of a regional node are the average coordinates of all nodes in the region.

In order to intuitively see the impact of different space weather on the complex network of the ionosphere, the present invention combines two types of space weather: the largest magnetic storm event in 2015, a year of high solar activity, that is, March 17, and the magnetic calm period of 2018, a year of low solar activity. The regional nodes and edges of the complex network are drawn on the map, and the results are shown in Figure 2(a) and Figure 2(b). It can be found from Figure 2(a) and Figure 2(b) that there are more isolated nodes in mid- and high-latitude areas and poor connectivity, while nodes in low-latitude areas have strong correlation and better connectivity. At the same time, when a geomagnetic storm occurs, the dominant nodes of the complex network are concentrated near the equator, while during the calm period, the dominant nodes of the complex network are distributed in mid- and low-latitudes, and the node strength of the complex network near the equator during the geomagnetic storm is significantly greater than during the calm period. This is It shows that geomagnetic events will increase the intensity and correlation of nodes near the equator, thereby increasing the number of dominant nodes near the equator. During the quiet period, the total electron content of the ionosphere changes more slowly, and the distribution range of dominant nodes is wider.

Step 4. Extract the network structure characteristics of the total electron content of the ionosphere under different space weather:

After the ionosphere total electron content network model is established, the structural characteristics of the network are described using the statistical characteristics of node degree distribution and clustering coefficient in complex network theory.

The degree of a node in a complex network refers to the number of nodes directly connected to the node. And the node threshold can directly obtain the degree of area node i/> , the formula is as follows:

(8)

in, Indicates whether nodes i and j are connected, if/> If it is 0, it means that the two nodes are connected to each other, if/> If it is 1, it means that the two nodes are not connected to each other,/> is the number of original nodes in this homogeneous area.

Node thresholds need to be set as the basis for whether nodes are connected, and the confidence level is determined by randomizing the ionospheric time series. node threshold/> , if the connection strength of a pair of nodes/> Above node threshold/> , then the two nodes are considered to be directly connected, otherwise they are considered not to be directly connected, from which the node/> can be obtained to/> degree, use The function is expressed as follows:

(9)

in, is the step function coefficient.

Shuffle means randomizing the ionospheric time series of each node, that is, disrupting the order of the time series of each node and rearranging it. The randomization process can break the spatial dependence of each node. Given in conjunction with Figure 3 Significance test of correlation coefficient, final selection based on probability density distribution/> as node threshold.

The number of nodes directly connected to node i is the degree of the node , the actual number of connected edges/> with the maximum possible number of edges/> The ratio between them is defined as the clustering coefficient of the node/> , the formula is as follows:

(10)

In order to intuitively see the impact of different space weather on the complex network of the ionosphere, the present invention combines two types of space weather: the largest magnetic storm event in 2015, a year of high solar activity, that is, March 17, and the magnetic calm period of 2018, a year of low solar activity. The distribution of topological characteristics of the complex network in the lower ionosphere is plotted on the map. The results are shown in Figure 4(a) and Figure 4(b). The left side represents the degree distribution of the nodes in the network, and the right side represents the clustering coefficient of the nodes in the network. It can be found from Figure 4(a) and Figure 4(b) that when a magnetic storm occurs, the degree and clustering coefficient of the network are higher in low latitudes, and the distribution corresponds to the geomagnetic lines, while the degree and clustering coefficient of the network in high latitudes are higher. The class coefficient is low. When it is in the quiet period, the distribution of degree and clustering coefficient of the network is more uniform, and the difference in latitude is small. The results show that geomagnetic storms will significantly enhance the strength of dominant nodes in low latitudes, causing network connectivity and aggregation in low latitudes to increase. However, the impact on node connectivity in mid- and high-latitudes requires further study. At the same time, the Atlantic regional degree and clustering coefficient are the highest when a geomagnetic storm occurs. This is because the equatorial ionization anomaly area in the Americas was most severely affected when a geomagnetic storm occurred in 2015, causing the connection strength between nodes in the network in the region to rise sharply. , the connectivity between nodes is enhanced. The above results verify that by analyzing the structural characteristics of the ionospheric complex network and the parameter changes of node attributes under space weather such as magnetic storm events, the response characteristics of the ionospheric network and the spatial correlation characteristics between different regions can be effectively extracted.

The above are only specific embodiments of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included in the scope of the present invention. within the scope of protection.

Claims (6)

1. The global ionosphere space weather response extraction method based on the complex network is characterized by comprising the following steps of:

step 1) preprocessing original data, constructing a three-dimensional array of total electronic content of an ionized layer, interpolating the constructed three-dimensional array of total electronic content of the ionized layer into grid points of the world, regarding the grid points as nodes of a network of total electronic content of the ionized layer, and extracting a time sequence of total electronic content of the ionized layer on the nodes;

step 2) constructing a local homogeneous region of an ionosphere total electron content network:

grouping the nodes of the preprocessed ionized layer total electron content network on a global geographic area by using a greedy algorithm, and constructing a local homogeneous area of the ionized layer total electron content network on a time sequence length; for any two nodes in the ionosphere total electron content networkAnd->Two nodes ∈>And->The Pearson phase relationship between them is recorded as +.>The calculation formula is as follows:

(1)

wherein,is->Linear ionospheric timing data of individual nodes, +.>For the total node number in the ionosphere total electron content network, adopting +.>The resolution is +.>，/>For the selected length of time;

step 3) carrying out node modeling of a local homogeneous region of the ionosphere total electron content network;

any node within a locally homogeneous regionSharing a weighted connection with other nodes in the ionosphere total electron content network, extracting the characteristic variable of the nodes in the local homogeneous region by calculating the time sequence of each node in the local homogeneous region, and weighting and accumulating all grids of the local homogeneous region according to the square root of the geographical areaCalculating sum to obtain the first part of the ionosphere total electron content network>Sum of local homogeneous region area weighted time series +.>Expressed by the following formula:

(5)

wherein,is the +.>Linear ionospheric timing data of individual nodes, +.>Is->Area of the individual node on the global grid, < >>To form->A plurality of localized homogeneous regions;

constructing link edges under different local homogeneous areas of the ionosphere total electron content network by adopting a nonlinear synchronization method; the connection strength of nodes between local homogeneous regions, i.e. the absolute value of the time covariance between two local homogeneous region area weighted time series, for any length of timeRegional nodes i andj is the connection strength between j->Expressed by the following formula:

(6)

wherein,mean the accumulated time sequence data of a certain area node, and the connection strength is +.>Depending on the statistical interdependence existing between two regional nodes ++>For the number of local homogeneous region nodes in the region, < > N->For the selected length of time;

in the ionospheric total electron content network, the node strength of a regional node i is defined as the sum of the connection strengths of all the chain-sides associated therewith, and is noted asExpressed by the following formula:

(7)

the coordinates of the nodes in the local homogeneous region are the average value of the coordinates of all the nodes in the region;

step 4) calculating structural characteristics of the ionosphere total electron content network by utilizing the degree distribution and the clustering coefficient statistical characteristics of nodes of the local homogeneous region of the ionosphere total electron content network, so as to extract response characteristics of the ionosphere total electron content network under different spatial weather and spatial correlation characteristics among different regions;

the degree of a node refers to the number of nodes directly connected with the node through the connection strengthAnd the node threshold directly gets the degree +.>The formula is as follows:

(8)

wherein,representing node->And->Whether or not to connect, if->A value of 0 indicates that the two nodes are connected to each other, if +.>A1 indicates that the two nodes are not connected to each other, < >>The number of nodes in the local homogeneous region;

the number of nodes directly connected with node i, namely the degree of the nodesActual number of edges>And the maximum possible edge numberThe ratio between them is defined as the clustering coefficient of the node +.>The formula is as follows:

(9)

extracting response characteristics of the ionosphere network by calculating parameter changes of structural characteristics and node attributes of the total electronic content network of the ionosphere constructed under the spatial weather; the spatial weather includes a magnetic storm event.

2. The method for extracting global ionospheric spatial weather response of a complex network according to claim 1, wherein: the step 1) comprises the following steps: using global ionosphere total electron content distribution map as original data, projecting the original data asConstructing a three-dimensional array of ionosphere total electron content, wherein +.>The dimension of time is represented as such,is related to the time update frequency of the original data,/->Sample number representing global latitude, +.>A sample number representing a global longitude range;global longitude and latitude are adopted +.>Resolution sampling to set global grid pointsAnd->The values of (2) are 90 and 180 respectively, and the total grid number is +.>And each.

3. The method for extracting global ionospheric spatial weather response of a complex network according to claim 2, wherein: in the step 1), the grid area of any region of the world is described by a spherical trigonometry formula, the implementation method is that given longitude and latitude are converted into radian, the longitude and latitude arc length composition area is obtained through differentiation, and finally the area of the region corresponding to the earth is obtained through three-dimensional projection, and the calculation formula is as follows:

(2)

wherein,to form->Area of the local homogeneous region->For the earth radius>Representing the longitude and latitude coordinates of the first node of the area,/->Representing the latitude and longitude coordinates of the last node of the area.

4. The method for extracting global ionospheric spatial weather response of a complex network according to claim 1, wherein: in the step 2), when two nodes are presentAnd->Pearson correlation coefficient between->When the area threshold is exceeded, two nodes +.>And->Considered as homogeneous node and continuously searching the average pearson correlation coefficient ++>Greater than the region threshold->Combining the adjacent regions to form a local homogeneous region, and marking the formed local homogeneous region as A; the number of the nodes contained in each local homogeneous region is at least two, and any two nodes in the same local homogeneous region have one communication link.

5. The method for extracting global ionospheric spatial weather response of a complex network according to claim 4, wherein: in the step 2), the region threshold valueDefined as the average of the positive correlation values of all nodes, the average correlation coefficient of all nodes in the local homogeneous region should be greater than the region threshold +.>Expressed by the following formula:

(3)

wherein,is indicated in the local homogeneous region->Two nodes inside->And->Pearson correlation coefficient of (b);

region thresholdIs significant at the level of 95%, by one side +.>And (3) checking and determining:

(4)

wherein,is the number of local homogeneous region nodes.

6. The method for extracting global ionospheric spatial weather response of a complex network according to claim 1, wherein: in the step 4), the confidence level is determined to be the ionosphere time sequence by randomizing the ionosphere time sequenceNode threshold of->If the connection strength of a pair of nodes +.>Above node threshold +.>The two nodes are considered to be directly connected, otherwise they are not, thus obtaining the degree of nodes i to j, using +.>The function is expressed as follows:

(10)

wherein,is a step function coefficient.