CN116842766B - Global TEC experience model based on space-time combination decomposition ionosphere anomaly - Google Patents
Global TEC experience model based on space-time combination decomposition ionosphere anomaly Download PDFInfo
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Abstract
The invention belongs to the technical field of ionosphere physics, and particularly relates to a global TEC experience model for decomposing ionosphere anomalies based on space-time combination, wherein the modeling comprises the following steps: s1, selecting data of the sun activity week as a modeling data set; s2, dividing the modeling data set into time periods; s3, dividing the modeling data set into grid points; s4, combining the time period in the S2 with the grid points in the S3 to form a space-time combination; s5, establishing an ionosphere experience sub-model of each space-time combination; s6, calculating parameters to be estimated in each sub-model through nonlinear least square fitting to form a single-point model set, and completing modeling to form the TEC empirical model. The invention solves the problem that model components of different abnormal phenomena can interfere with each other in the fitting process and are difficult to reconcile to a global model. The method can provide a new ionospheric delay correction method for GNSS single-frequency users, and has important reference significance for establishing and improving other new ionospheric experience models.
Description
Technical Field
The invention belongs to the technical field of ionosphere physics, and particularly relates to a global TEC experience model for decomposing ionosphere anomalies based on space-time combination.
Background
The global total electron content TEC is one of the important parameters in ionosphere physics and is widely used in the study of ionosphere delay and ionosphere space-time variation characteristics for correcting GNSS satellite signals.
The ionosphere contains a large number of free electrons and ions, and has a significant effect on the propagation of radio waves. The satellite signals of the global navigation satellite system (Global Navigation Satellite Systems, GNSS) are high frequency oscillating electromagnetic waves, which are severely disturbed or even interrupted when crossing the ionosphere. This effect, known as ionospheric delay, is the largest source of error for GNSS systems. The ionospheric delay is primarily dependent on the signal frequency and the total electron content TEC in the propagation path. When the signal frequency is known, TEC is the key to correcting ionospheric delay. Dual or multi-frequency users can use the observation data to make ionospheric-free delay combinations to cancel or attenuate the effects of ionosphere. Whereas single frequency users typically need to calculate TEC data using an ionospheric empirical model to correct for ionospheric delay. Therefore, the accuracy of the ionosphere empirical model is directly related to the accuracy and reliability of the positioning, navigation and time service results of the single frequency receiver, thereby affecting the application range of the GNSS single frequency receiver. Currently, different ionospheric empirical models are applied to GNSS systems to provide ionospheric delay correction for single frequency users.
Since 1998, ionospheric analysis centers of the international GNSS service (International GNSS Service, IGS) have continuously released global ionospheric map (Global Ionosphere Maps, GIMs) data products, up to now over a time span of 2 solar activity cycles. The long-term historical data provides a reliable database for building new global TEC empirical models. Global TEC empirical models built with GIMs TEC as background data developed rapidly over the last decade.
The existing ionosphere experience model adopts different methods (such as a nonlinear least square method, a neural network algorithm, a kriging interpolation method, an experience orthogonal function, a natural orthogonal function, a linear least square method, machine learning and the like) for modeling, and is generally composed of a series of function expressions describing the change rule of the ionosphere. However, global ionospheric empirical models built using GIMs as background data often have difficulty accurately expressing various ionospheric anomalies. Such as equatorial anomalies (Equatorial Ionization Anomaly, EIA), mid-latitude summer night anomalies (Mid-latitude Summer Nighttime Anomaly, MSNA), winter Anomalay (WA), night Winter anomalies (Nighttime Winter Anomaly, NWA), etc.
The regional and time-varying nature of ionospheric anomalies increases the complexity of the model, and model components of different anomalies interfere with each other during the fitting process, making it difficult to reconcile to the same global model. Thus, expressing various ionospheric anomaly phenomena in a global ionospheric empirical model is a challenging study. Existing global ionosphere models often fail to accurately express these anomalies.
To solve this problem, the present invention proposes the idea of decomposing ionospheric anomalies based on spatio-temporal combinations.
Disclosure of Invention
According to the defects in the prior art, the invention provides a global TEC empirical model for decomposing ionosphere anomalies based on space-time combination, and solves the problem that model components of different anomalies interfere with each other in a fitting process and are difficult to reconcile to a global model.
In order to achieve the above object, the present invention provides a global TEC empirical model for decomposing ionospheric anomalies based on spatio-temporal combinations, the modeling comprising the steps of:
s1, selecting TEC data of at least one solar active cycle as a modeling data set;
s2, dividing the modeling data set into time periods;
s3, dividing the modeling data set into grid points;
s4, combining the time period in the S2 with the grid points in the S3 to form a space-time combination;
s5, establishing an ionosphere experience sub-model of each space-time combination;
s6, calculating parameters to be estimated in each sub-model through nonlinear least square fitting to form a single-point model set, and completing modeling to form the TEC empirical model.
In the step S1, TEC data of IGS GIMs of a solar activity cycle are adopted as a modeling data set, and TEC data with Kp larger than 3 is removed, wherein Kp is the global geomagnetic activity overall level.
Preferably, the TEC data of IGS GIMs of 24 th solar activity cycle (2008 to 2018) is adopted as a modeling data set, and the TEC data based on multi-source data fusion or the TEC data of two solar activity cycles (more solar activity cycles can be selected) can be used for modeling, so that the model accuracy can be further improved.
In S2, TEC data in the modeling data set, the ascending phase and the descending phase of the solar activity cycle, the high solar activity level and the low solar activity level, the month and the day and night are divided to obtain 96 time periods of 2 multiplied by 12 multiplied by 2.
In the step S3, TEC data in the modeling data set is globally divided into 5183 grid points according to grid point positions of IGS GIMs data.
In S4, a total of 497568 space-time combinations of 96×5183 are formed based on 96 time periods and 5183 grid points.
In the step S5, the modeling process is as follows:
s51, establishing ionosphere experience submodels of each space-time combination:
；
wherein F is 1 Is a half-day scale change component, F 2 Is a single month scale change component, F 3 Is the component of TEC changing along with the solar activity level, and the input variables are year, year product day doy, world time ut and solar activity index F 10.7P ；
S52, determining a half-day scale change component F 1 Is represented by the expression:
；
wherein a is i And b i Is a parameter to be estimated; hod denotes a half-day period, i.e. hod =12; the 4 harmonics describe 1/2 day, 1/4 day, 1/6 day and 1/8 day changes of TEC, respectively, with p equal to 1.0, 1.5, 2.0 and 3.0, respectively; to ensure modeling continuity during night time periods, the range of local time is adjusted from 00:00-24:00LT to 06:00-30:00LT, and the symbol is marked as LTN; when 06 is less than or equal to LTN<At 18, considered daytime, dh=06; when 18 is less than or equal to LTN<At 30, considered night, dh=18;
s53, determining a single month scale change component F 2 Is a mathematical expression of (a):
；
wherein, c i And d i Is a parameter to be estimated; dom represents the month accumulation day, which is a month scale daily record method; the mv is dynamic and represents the total number of days of the corresponding month; the 4 harmonics describe month changes, 1/2 month changes, 1/3 month changes, and 1/4 month changes, respectively;
s54, determining a component F of TEC changing along with the solar activity level 3 Is represented by the expression:
；
wherein e, f and g are parameters to be estimated; will F 10.7P TEC data at 140sfu or less was used for one-time function fitting, where g= 0,F 3 Is a linear function; will F 10.7P >TEC data of 80sfu were used for quadratic function fitting when g.noteq. 0,F 3 Is a quadratic function; wherein 80sfu < F 10.7P TEC data less than or equal to 140sfu are public data, and participate in both primary function fitting and secondary function fitting.
In the step S6, parameters to be estimated in each sub-model in the step S5 are calculated through nonlinear least square fitting, so that ionosphere experience sub-models of each space-time combination are obtained, a single-point model set is obtained, and a TEC experience model is formed.
The algorithms involved in the modeling of the present invention may be executed by an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, the algorithms being implemented by the processor executing the program.
The invention has the beneficial effects that:
the invention provides an idea of decomposing ionosphere anomalies based on space-time combinations, which divides the world into a plurality of grid points and divides the time into a plurality of time periods to form different space-time combinations. At each grid point, the TEC is decomposed to a short time scale, retaining only the most basic time-varying features of regularity, thereby circumventing ionospheric anomalies.
According to the invention, IGS GIMs data of the solar activity cycle are taken as modeling data, split from the angles of time and space, corresponding sub-models are established, parameters to be estimated of all the sub-models are calculated by nonlinear least square fitting, a single-point model set is formed, and the internal coincidence precision and the external coincidence precision of the model set and the description capability of various ionosphere anomalies are evaluated. The method can provide a new ionospheric delay correction method for GNSS single-frequency users, and has important reference significance for establishing and improving other new ionospheric experience models. In addition, a special website is matched to realize the online running of the model set, and a convenient and quick online computing service is provided for a user.
The invention solves the problem that model components of different abnormal phenomena can interfere with each other in the fitting process and are difficult to reconcile to a global model. For example, dividing the solar activity cycle into a rising phase and a falling phase can circumvent hysteresis effects. Dividing the solar activity level into high/low states can distinguish ionospheric anomalies (such as winter anomalies, night winter anomalies, etc.) closely related to the solar activity level, and can also circumvent the "saturation" effect. Separating 12 months one by one can avoid season related anomalies (e.g., half-year anomalies, annual anomalies, etc.). Separating the day and night, combining with a single month, anomalies related to both day and night and seasons (e.g., mid-latitude summer night anomalies, winter anomalies, night winter anomalies, etc.) can be avoided.
Drawings
FIG. 1 is a graph of the 2003 to 2022 solar activity index F 10.7P A daily change curve of (2);
FIG. 2 is a modeling flow chart of the present invention;
FIG. 3 is an intra-compliance accuracy assessment in the verification process of the present invention;
fig. 4 is an external compliance assessment in the verification process of the present invention.
Detailed Description
Embodiments of the invention are further described below with reference to the accompanying drawings:
in this example, TEC data of IGS GIMs at 24 th solar week of activity (2008 to 2018) were selected as modeling data, and IGS GIMs at 2003 to 2007 and 2019 to 2022 were selected as test data.
IGS GIMs are: in 1998, IGS established an ionosphere work group aimed at providing a reliable joint global vertical total electron content map (felens, 2003). The product is formed by weighting and combining GIMs data of a plurality of ionosphere analysis centers, and has higher precision (Hernandez-Pawres et al 2009; li et al 2020). From 11.3.2002, the start and stop times of the data are 00:00UT and 24:00UT respectively, the time resolution is 2h, and 13 global ionospheric maps are obtained every day. Its latitude ranges from 87.5 ° S to 87.5 ° N, with an interval of 2.5 °, and its longitude ranges from 180 ° W to 180 ° E, with an interval of 5 °.
Solar extreme ultraviolet radiation (Extreme Ultraviolet, EUV) is the best parameter for studying the time-varying properties of solar radiation and the solar-ionospheric effect. However, empty-based EUV observations lack continuity and the observation history is short. Thus, in measuring solar activity levels, the solar activity index is commonly used to proxy EUV (Liu et al 2006). Due to F 10.7P With higher correlation coefficient with EUV, the invention adopts F 10.7P To describe the solar activity level (Lei et al, 2005). FIG. 1 is 2003 to 2022F 10.7P The daily profile of (in the figure the dashed line is the boundary between the rising and falling phases of the solar activity cycle). As can be seen from fig. 1, 2003 to 2007 are the 23 rd solar activity week descent phases; 2008-2018 are 24 th week of solar activity, wherein 2013, 7, 1 are demarcation points for ascending and descending phases; years 2019 to 2022 are the 25 th solar active cycle ascending phase.
The Kp index is generally used to describe the global level of geomagnetic activity. When Kp is greater than 3, it indicates that geomagnetic activity is strong. According to the invention, ionosphere modeling is performed during the quiet day of geomagnetic activity, so that TEC data with Kp more than 3 is removed. Table 1 shows the proportion of rejected data from 2008 to 2018. As can be seen from FIG. 1, the difference of the data quantity of the reject in different years is larger, the reject data proportion of the descending phase is relatively higher, and the maximum data quantity can reach 20%.
The TEC is decomposed from a long time scale to a short time scale, so that ionosphere anomalies can be avoided. For example, dividing the solar activity cycle into a rising phase and a falling phase can circumvent hysteresis effects. Dividing the solar activity level into high/low states can distinguish ionospheric anomalies (e.g., WA, NWA, etc.) that are closely related to the solar activity level, and can also circumvent the "saturation" effect. Separating 12 months one by one can avoid season related anomalies (e.g., half-year anomalies, annual anomalies, etc.). Separating the day and night, in combination with a single month, abnormalities associated with both the day and night and the season (e.g., MSNA, WA, NWA, etc.) can be circumvented.
Modeling flow as shown in fig. 2, the modeling data set is divided by "ascending and descending phases of the solar activity cycle (2)", "high solar activity level and low solar activity level (2)", "month (12)", and "day and night (2)", resulting in 2×2×12×2=96 time periods. On this basis, the global is divided into 5183 grid points along with the grid point positions of the IGS GIMs data. Based on 96 time periods and 5183 grid points, 96×5183 combinations are formed. And establishing ionosphere experience sub-models of each space-time combination, and calculating parameters to be estimated in each sub-model through nonlinear least square fitting to form a single-point model set.
Each space-time combination only retains the half-day scale change, the single-month scale change and the change with the solar activity level of the TEC. Thus, the functional expressions of the ionospheric empirical sub-models for each combination are the same.
The modeling flow is as follows:
s51, establishing ionosphere experience submodels of each space-time combination:
；
wherein F is 1 Is a half-day scale change component, F 2 Is a single month scale change component, F 3 Is the component of TEC changing along with the solar activity level, and the input variable is year year, yearling day doy, universal time ut and solar activity index F 10.7P ；
S52, determining a half-day scale change component F 1 Is represented by the expression:
；
wherein a is i And b i Is a parameter to be estimated; hod denotes a half-day period, i.e. hod =12; the 4 harmonics describe 1/2 day, 1/4 day, 1/6 day and 1/8 day changes of TEC, respectively, with p equal to 1.0, 1.5, 2.0 and 3.0, respectively; to ensure modeling continuity during night time periods, the range of local time is adjusted from 00:00-24:00LT to 06:00-30:00LT, and the symbol is marked as LTN; when 06 is less than or equal to LTN<At 18, considered daytime, dh=06; when 18 is less than or equal to LTN<At 30, considered night, dh=18;
s53, determining a single month scale change component F 2 Is a mathematical expression of (a):
；
wherein, c i And d i Is a parameter to be estimated; dom represents the month accumulation day, which is a month scale daily record method; the mv is dynamic and represents the total number of days of the corresponding month; the 4 harmonics describe the month change, 1/2 month change, 1/3 month change and 1/4 month change, respectively.
S54, determining a component F of TEC changing along with the solar activity level 3 Is represented by the expression:
；
wherein e, f and g are parameters to be estimated; will F 10.7P TEC data at 140sfu or less was used for one-time function fitting, where g= 0,F 3 Is a linear function; will F 10.7P >TEC data of 80sfu were used for quadratic function fitting when g.noteq. 0,F 3 Is a quadratic function; wherein 80sfu < F 10.7P TEC data less than or equal to 140sfu are public data, and participate in the first-order function fitting and the second-order function fittingAnd (5) fitting a secondary function.
To enhance TEC and F at low solar activity levels 10.7P Is a linear relationship of (1) while constraining TEC and F at high solar activity levels 10.7P Is a quadratic function of the solar activity middle section (80 sfu < F 10.7P TEC data of 140 sfu) are set as common data, both in the low solar activity phase (F 10.7P <80 sfu), again in the high solar activity phase (F10.7P)>140 Is reused 2 times (taking part in 2 times of fitting, and can better solve other model parameters, so that the model effect is better). Based on the classification method, F 10.7P TEC data at 140sfu or less was used for one-time function fitting, where g= 0,F 3 Is a linear function; will F 10.7P >TEC data of 80sfu were used for quadratic function fitting when g.noteq. 0,F 3 Is a quadratic function.
And when using the model, if the input solar activity index is less than 140sfu, using a linear function; if the input solar activity index is greater than 140sfu, then a quadratic function is used.
And calculating parameters to be estimated in each sub-model in the modeling flow through nonlinear least square fitting to obtain ionosphere experience sub-models of each space-time combination, thereby obtaining a single-point model set and forming a TEC experience model.
The verification process is as follows:
1. internal compliance accuracy assessment
The invention establishes a new global TEC experience model based on space-time combination decomposition ionosphere abnormity through the modeling process, and the model is called TECM-TS model for short.
TECU represents total electron content unit (total electron number unit) for representing the number of electrons, and 1TECU represents the 16 th power of 10 electrons.
The intra-compliance accuracy assessment of the TECM-TS model was performed using the IGS GIMs data from 2008 to 2018, and the results are shown in fig. 3. As can be seen from fig. 3, the model residual is-0.04 TECU, the median error is 2.56TECU, and the root mean square error is 2.56TECU. The model residuals fit a normal distribution, with about 94.11% model residuals between-5 TECU and 5TECU. Jakowski et al (2011) constructed an NTCM-GL model based on CODE GIMs data from 1998 to 2007 with a model residual of-0.3 TECU, a medium error of 7.5TECU, and a root mean square error of 7.5TECU. Mukhtarov al (2013 a) built a global ionospheric empirical model based on CODE GIMs data from 1999 to 2011, with model residuals of 0.003TECU, medium errors of 3.387TECU, root mean square errors of 3.387TECU. Feng et al (2022) established a TECM-MF model based on TEC fusion products from 2006 to 2020, with a model residual of 0TECU, a medium error of 3.9TECU, and a root mean square error of 3.9TECU. Overall, the TECM-TS model has better fitting ability to input data than the above three models.
2. External coincidence accuracy assessment
The present invention uses IGS GIMs data from 2003 to 2007 and 2019 to 2022 to evaluate the accuracy of the outer compliance of the TECM-TS model, as shown in fig. 4. As can be seen from fig. 4, the model residual is 0.74TECU, the medium error is 2.93TECU, the root mean square error is 3.03TECU. The model residuals fit a normal distribution. Overall, the TECM-TS model shows a better predictive power. However, TECM-TS model significantly overestimates TEC in the test year, which may be related to the division method of high and low solar activity levels. When the data volume is sufficient, the solar activity is divided into three solar activity levels of low, medium and high, and the model accuracy can be further improved.
In fig. 3 and 4, residual (residual) =tecm-TS-IGS GIMs.
3. Ionospheric anomaly description capability assessment
The anomaly description effect of the present invention is illustrated by comparing the TECM-TS model of the present invention with the IGS GIMs, IRI-2020 model (2020 edition of IRI International ionosphere reference model) and NTCM-GL model (global Neustrelitz TEC model, jakowski et al empirical climatology model).
1) Hysteresis effect
Huang et al (2019) suggested constructing a regression model using ionospheric parameters and a month average of EUV, avoiding seasonal variations in the introduction of ionosphere, to accurately evaluate hysteresis effects. The invention adopts the 24 th solar activity cycle as the research period, rising phase and falling phaseTEC and F for the four ionosphere models respectively 10.7P Linear regression was performed on the month average values of (a), and all four ionosphere models exhibited positive hysteresis effects (higher ionization level of the descending phase). The hysteresis effects of the IGS GIMs and TECM-TS models are comparable. The hysteresis effect of the IRI-2020 model is relatively small. The NTCM-GL model does not use hysteresis effect components, but also shows a certain hysteresis effect.
2) Equatorial abnormality
Some observations indicate that EIA presence varies daily with place, typically a large one around 14:00LT (Bagiya et al 2009; oryema et al 2016). According to the invention, the equatorial anomaly description capacity of four ionosphere models is reflected by calculating the TEC mean values of 14:00UT and 14:00LT in 2014, the equatorial anomalies of the IGS GIMs and the TECM-TS model are basically consistent, and the equatorial anomalies of the IRI-2020 model are relatively smaller. In addition, the 3 models can reflect the north-south asymmetry of the equatorial abnormality, and the TEC distribution is related to the corrected geomagnetic latitude. For the NTCM-GL model, TEC distribution is related to geomagnetic latitude, and equatorial abnormality cannot be represented.
3) Winter abnormality
The TEC changes in summer versus winter are generally compared to reflect winter anomalies. However, ignoring the difference in solar activity levels in summer versus winter can introduce errors in describing winter anomalies. Yasyukevich et al (2018) propose to study winter abnormalities using a linear regression method, as this method is able to calculate winter abnormality index at the same solar activity level. The present invention refers to this method for calculating a winter abnormality index as shown in the following formula.
；
Wherein WAI is winter abnormality index, TEC S And TEC (thermoelectric cooler) W TEC values in summer and winter, respectively, a, b, c, d are parameters to be estimated. At each grid point, TEC daytime maximum and F for summer and winter, respectively 10.7P Performing linear regression, and calculating parameters to be estimated by least square to obtain WAI calculation methodAnd (5) processing. At designation F 10.7P And then, calculating the winter abnormality index. If WAI is less than 1, then no winter anomalies exist; if WAI is greater than 1, then there is a winter anomaly, and the greater the WAI, the more significant the winter anomaly.
By separately aligning F 10.7P =100 sfu and F 10.7P The global distribution of winter abnormality index at =140 sfu was analyzed, and the IGS GIMs and TECM-TS models reflect winter abnormalities concentrated in north american regions, consistent with Yasyukevich et al (2018). Winter anomalies reflected by the IRI-2020 model are concentrated in north america, east siberia and australian. Furthermore, the IGS GIMs, TECM-TS and IRI-2020 models are capable of characterizing winter anomalies as solar activity levels increase, whereas the NTCM-GL models are not capable of reflecting winter anomalies.
4) Middle latitude summer night abnormality
Lin et al (2010) describe month-to-month changes in electron density at 300km in COSIC in 2007. The result shows that MSNA phenomenon of southern hemisphere appears in 10 months to 2 months of the next year, and is most remarkable in 12 months; MNSA phenomenon occurs in the northern hemisphere from 5 months to 8 months, most notably at 5 months and 6 months. The method calculates the TEC mean values of 22:00LT in the first and second days of 22 months of 06 and 22 days of 12 months of 2014 respectively so as to reflect the mid-latitude summer anomaly description capability of the four ionosphere models. MSNA phenomena occur mainly in eastern asia regions of the northern hemisphere, atlantic regions and wedelian regions of the southern hemisphere. The IGS GIMs, TECM-TS and IRI-2020 models are capable of describing MSNA, but the IRI-2020 model is relatively weak in describing, whereas the NTCM-GL model is not capable of exhibiting this anomaly.
In summary, the invention provides the idea of decomposing ionosphere anomalies based on space-time combination, and solves the problem that model components of different anomalies interfere with each other in the fitting process and are difficult to reconcile to a global model. IGS GIMs of 24 th solar activity weeks (2008 to 2018) are taken as modeling data sets, nonlinear least squares fitting is utilized to calculate parameters to be estimated of all sub-models (96×5183) to form a single-point model set TECM-TS, and the single-point model set TECM-TS can pass through websites [ ]) And providing a convenient and quick online computing service for users.
In the inner coincidence precision evaluation, the TECM-TS model shows good performance, the model residual error is-0.04 TECU, the middle error is 2.56TECU, the root mean square error is 2.56TECU, and the fitting capability of the model to input data is better than that of models such as NTCM-GL, TECM-MF and the like. In the external fitting precision evaluation, the model residual error of the TECM-TS is 0.74TECU, the middle error is 3.03TECU, the root mean square error is 2.93TECU, and the model shows better prediction capability. In terms of ionospheric anomaly description capability, the TECM-TS model is capable of accurately describing various ionospheric anomalies (hysteresis effects, equatorial anomalies, winter anomalies, and mid-latitude summer night anomalies), which are superior to IRI-2020 and NTCM-GL models.
In conclusion, the global TEC experience model set (TECM-TS model) constructed by the method has better precision and prediction capability in global ionosphere simulation, and has positive significance in overcoming the bottleneck of the existing ionosphere experience model. And, can use TEC data or TEC data of two sun activity week based on multisource data fusion to establish ionosphere experience model to simulate, in order to further improve the model precision. In general, the model can provide a new ionospheric delay correction method for GNSS single-frequency users, and has important reference significance for establishing and improving other new ionospheric experience models.
Claims (5)
1. A global TEC empirical model for decomposing ionospheric anomalies based on spatio-temporal combinations, characterized in that the modeling comprises the steps of:
s1, selecting TEC data of at least one solar active cycle as a modeling data set;
s2, dividing the modeling data set into time periods;
s3, dividing the modeling data set into grid points;
s4, combining the time period in the S2 with the grid points in the S3 to form a space-time combination;
s5, establishing an ionosphere experience sub-model of each space-time combination;
s6, calculating parameters to be estimated in each sub-model through nonlinear least square fitting to form a single-point model set, and completing modeling to form a TEC empirical model;
in the step S2, TEC data in the modeling data set are divided according to ascending and descending phases of the solar activity period, high solar activity level and low solar activity level, month and day and night to obtain 96 time periods of 2 multiplied by 12 multiplied by 2;
in the step S5, the modeling process is as follows:
s51, establishing ionosphere experience submodels of each space-time combination:
；
wherein F is 1 Is a half-day scale change component, F 2 Is a single month scale change component, F 3 Is the component of TEC changing along with the solar activity level, and the input variables are year, year product day doy, world time ut and solar activity index F 10.7P ；
S52, determining a half-day scale change component F 1 Is represented by the expression:
；
wherein a is i And b i Is a parameter to be estimated; hod denotes a half-day period, i.e. hod =12; the 4 harmonics describe 1/2 day, 1/4 day, 1/6 day and 1/8 day changes of TEC, respectively, with p equal to 1.0, 1.5, 2.0 and 3.0, respectively; to ensure modeling continuity during night time periods, the range of local time is adjusted from 00:00-24:00LT to 06:00-30:00LT, and the symbol is marked as LTN; when 06 is less than or equal to LTN<At 18, considered daytime, dh=06; when 18 is less than or equal to LTN<At 30, considered night, dh=18;
s53, determining a single month scale change component F 2 Is a mathematical expression of (a):
；
wherein, c i And d i Is a parameter to be estimated; dom represents the month accumulation day, which is a month scale daily record method; the mv is dynamic and represents the total number of days of the corresponding month; the 4 harmonics describe month changes, 1/2 month changes, 1/3 month changes, and 1/4 month changes, respectively;
s54, determining a component F of TEC changing along with the solar activity level 3 Is represented by the expression:
；
wherein e, f and g are parameters to be estimated; will F 10.7P TEC data at 140sfu or less was used for one-time function fitting, where g= 0,F 3 Is a linear function; will F 10.7P >TEC data of 80sfu were used for quadratic function fitting when g.noteq. 0,F 3 Is a quadratic function; wherein 80sfu < F 10.7P TEC data less than or equal to 140sfu are public data, and participate in both primary function fitting and secondary function fitting.
2. A global TEC empirical model for ionospheric anomalies based on spatiotemporal combinatorial decomposition according to claim 1, characterized in that: in the step S1, TEC data of IGS GIMs of a solar activity cycle are adopted as a modeling data set, and TEC data with Kp larger than 3 is removed, wherein Kp is the global geomagnetic activity overall level.
3. A global TEC empirical model for ionospheric anomalies based on spatiotemporal combinatorial decomposition according to claim 2, characterized in that: in the step S3, TEC data in the modeling data set is globally divided into 5183 grid points according to grid point positions of IGS GIMs data.
4. A global TEC empirical model for ionospheric anomalies based on spatiotemporal combinatorial decomposition according to claim 3, characterized in that: in S4, a total of 497568 space-time combinations of 96×5183 are formed based on 96 time periods and 5183 grid points.
5. A global TEC empirical model for ionospheric anomalies based on spatiotemporal combinatorial decomposition according to claim 1, characterized in that: in the step S6, parameters to be estimated in each sub-model in the step S5 are calculated through nonlinear least square fitting, so that ionosphere experience sub-models of each space-time combination are obtained, a single-point model set is obtained, and a TEC experience model is formed.
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