A global ionospheric f2 layer parameter modeling method based on machine learning and model constraints

Abstract

The application discloses a global ionospheric F2 layer parameter modeling method based on machine learning and model constraints, and comprises the following steps: step 1, obtaining and preprocessing of altimeter observation data; step 2, obtaining and preprocessing of occultation observation data; step 3, calculating NmF2 and hmF2 by using an international reference ionospheric model (IRI); step 4, calculating zonal wind field velocity and meridional wind field velocity by using a horizontal wind model (HWM); step 5, machine learning to construct a global NmF2 model; step 6, machine learning to construct a global hmF2 model; and step 7, evaluating the ionospheric F2 layer parameter model. The method disclosed by the application can provide model support for link design of a ground-air radio information system penetrating through an ionospheric environment.

Description

Technical Field

[0001] This invention belongs to the field of space environment situational awareness, and specifically relates to a method for modeling global ionospheric F2 layer parameters based on machine learning and model constraints. Background Technology

[0002] The ionosphere is a key space environment factor affecting radio systems such as communication, navigation, command and control, and remote sensing. Depending on altitude, the ionosphere can be divided into the D, E, and F layers. The F layer extends from approximately 140 to 600 km above the Earth and is divided into two layers, F1 and F2, during the day. The F2 layer has the highest electron density and significantly influences the propagation of high-frequency (HF) radio signals in the 10–35 MHz range. Establishing a global ionospheric F2 layer parameter model, particularly the peak density (NmF2) and peak height (hmF2), is of great practical value for improving the performance of radio systems traversing the ionosphere, such as shortwave communication, satellite navigation, telemetry, tracking, and command (TT&C) radars.

[0003] Currently, the amount of observational data available for the global ionosphere is increasing daily. The University of Massachusetts Lowell has established the Global Ionospheric Radio Observatory (GIRO), which provides autoscaling data from over 50 digital ionospheric altimeters worldwide. Meanwhile, since the establishment of the COSMIC constellation in 2006, the number of satellites using radio occultation for ionospheric exploration has also been steadily increasing. These ground-based and satellite-based systems provide a wealth of high-quality global ionospheric data, laying a crucial foundation for building global ionospheric models.

[0004] Machine learning guides computers to find patterns in big data, learn suitable models from massive amounts of data, and fit complex nonlinear functions. It is often used to predict or estimate other unknown data. With the improvement of computer performance and the continuous increase in data volume, machine learning has made great strides. However, machine learning algorithms lack inherent constraints on changes in ionospheric physics, which limits the improvement of model generalization ability. Combining machine learning with existing ionospheric models can further improve the reliability and modeling accuracy of machine learning algorithms.

[0005] The sun is the most important source of influence on ionospheric changes. Variations in solar radiation have a global impact on ionospheric changes, thus strongly controlling ionospheric behavior. Geomagnetic activity primarily affects the ionosphere by controlling the movement of charged particles; therefore, geomagnetism is another important source of influence. Coupled with the combined effects of neutral gas and ionized components, the temporal and spatial patterns of ionospheric variation are highly complex. A major challenge in ionospheric modeling is identifying the key control parameters of the F2 layer and using these parameters as inputs to construct an optimized mathematical model based on large-scale space-based and ground-based observational data. This model accurately describes the temporal and spatial variation characteristics of the F2 layer peak density (NmF2) and peak height (hmF2). Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a method for modeling global ionospheric F2 layer parameters based on machine learning and model constraints.

[0007] The present invention adopts the following technical solution:

[0008] An improved method for modeling global ionospheric F2 layer parameters based on machine learning and model constraints includes the following steps:

[0009] Step 1, Acquisition and preprocessing of altimeter observation data:

[0010] Step 11: Download the automatic interpretation data from the Global Ionospheric Radio Observatory's Ionospheric Digital Altimeter;

[0011] Step 12: Extract the altimeter's longitude and latitude coordinates, observation time, automatic interpretation confidence score, critical frequency foF2 of the F2 ionosphere, and peak height hmF2 of the F2 ionosphere from the automatically interpreted data.

[0012] Step 13: Delete vertical measurement data with an automatic confidence score below 75;

[0013] Step 14: Calculate the peak density NmF2 of the ionospheric F2 layer using foF2. The calculation method is as follows:

[0014] NmF2=foF2 2 / 80.62

[0015] Step 15: Output the ionospheric vertical measurement parameters processed in step 13 and store them in a text file. The ionospheric vertical measurement parameters include altimeter longitude, latitude coordinates, observation time, NmF2, and hmF2.

[0016] Step 2, Acquisition and Preprocessing of Occultation Observation Data:

[0017] Step 21: Download occultation electron density profile observation data;

[0018] Step 22: Extract observation time, latitude, longitude and altitude coordinates of the collision point, and ionospheric values from the electron density profile;

[0019] Step 23: Extract NmF2 and hmF2 from the electron density profile:

[0020] NmF2=max{Ne i ,i=1,2,...,n}

[0021] hmF2=h j (Ne j ==NmF2) j＝1,2,...n

[0022] In the above formula, max represents taking the maximum value, Ne is electron density, h is the altitude of the collision point, and n is the total number of sampling points contained in one occultation event;

[0023] Step 24: Reject electron density profiles where hmF2 is not within the altitude range of 150~450km;

[0024] Step 25: Reject electron density profiles where the slope S at altitudes of 490km and 420km is not within the interval of -9<S<-0.02:

[0025]

[0026] In the above formula, N e,490 represents the electron density at an altitude of 490km, and N e,420 represents the electron density at an altitude of 420km;

[0027] Step 26: Reject electron density profiles where the average deviation M between the electron density value of each point and the original value D is greater than 3:

[0028]

[0029] In the above formula, N represents the number of electron density samples;

[0030] Step 27: Reject electron density profiles where there exists electron density less than 0 above 110km;

[0031] Step 28: Output qualified occultation parameters and store them in a text file, wherein the occultation parameters include longitude and latitude coordinates of the collision point, observation time, NmF2 and hmF2;

[0032] Step 3: Calculate NmF2 and hmF2 using the international reference ionosphere model IRI:

[0033] Step 31: Input the altimeter coordinates, occultation collision point coordinates, observation time and sunspot number into the International Reference Ionospheric Model (IRI) to calculate NmF2 and hmF2 at the corresponding time and location;

[0034] Step 32: Output NmF2 and hmF2 calculated by the IRI model and store them in a text file;

[0035] Step 4: Calculate the zonal and meridional wind velocities using the horizontal wind field model HWM:

[0036] Step 41: Input the coordinates of the altimeter, the coordinates of the occultation collision point, the observation time, the number of sunspots, and the geomagnetic index into the horizontal wind field model, and calculate the zonal and meridional wind field velocities at the corresponding time and location.

[0037] Step 42: Output the zonal and meridional wind velocities calculated by the HWM model and store them in a text file;

[0038] Step 5: Machine learning to build a global NmF2 model:

[0039] Step 51: Select Year Day (DOY), Local Time (LT), and Geographic Latitude and Longitude Coordinates. Geomagnetic latitude Geographic longitude coordinates λ, sunspot number, F10.7 index, solar wind speed, geomagnetic Ap index, Kp index, and NmF2 calculated by the IRI model are used as training inputs.

[0040] Step 52, from geographical latitude coordinates Calculate geomagnetic latitude using longitude coordinates λ

[0041]

[0042] In the above formula: and These represent the latitude and longitude coordinates of the North Magnetic Pole, respectively.

[0043] Step 53: Normalize the annual day DOY and local time LT, and calculate their sine and cosine components respectively:

[0044]

[0045]

[0046]

[0047]

[0048] Step 54: Combine DOYs, DOYc, LTs, LTc, and geographic latitude coordinates. Geomagnetic latitude Geographic longitude coordinates λ, sunspot number R12, F10.7 index, solar wind speed SW, geomagnetic Ap index, Kp index, and NmF2 calculated by the IRI model are used as training inputs for machine learning, while the actual observed NmF2 values ​​from occultation and altimeters are used as outputs.

[0049] Step 55: Randomly select 70% of the NmF2 samples for training, 15% of the NmF2 samples for model testing, and 15% of the NmF2 samples for accuracy evaluation. Use the Random Forest (RF) algorithm for learning, set the number of leaves to 5, the forest size to 300, and use the bootstrap aggregation algorithm to train the learning network.

[0050] Step 56: Store the trained RF network in the computer for NmF2 calculation;

[0051] Step 6: Machine learning to build a global hmF2 model:

[0052] Step 61: Select Year Day (DOY), Local Time (LT), and Geographic Latitude and Longitude Coordinates. Geomagnetic latitude Geographic longitude coordinates λ, sunspot number, F10.7 index, solar wind speed, geomagnetic Dst index, Kp index, hmF2 calculated by the IRI model, and meridional wind speed Vz and zonal wind speed Vm calculated by the HWM model are used as training inputs.

[0053] Step 62, from geographical latitude coordinates Calculate geomagnetic latitude using longitude coordinates λ

[0054]

[0055] Step 63: Normalize the annual day DOY and local time LT according to the method in step 53, and calculate their sine and cosine components respectively.

[0056] Step 64: Combine DOYs, DOYc, LTs, LTc, and geographic latitude coordinates. Geomagnetic latitude Geographic longitude coordinates λ, sunspot number R12, F10.7 index, solar wind speed SW, geomagnetic Dst index, Kp index, hmF2 calculated by the IRI model, and meridional wind speed Vz and zonal wind speed Vm calculated by the HWM model are used as training inputs for machine learning, while the actual observed values ​​of hmF2 from occultation and altimeter are used as outputs.

[0057] Step 65: Randomly select 70% of the hmF2 samples for training, 15% of the hmF2 samples for model testing, and 15% of the hmF2 samples for accuracy evaluation. Use the Random Forest (RF) algorithm for learning, set the number of leaves to 5, the forest size to 350, and use the bootstrap aggregation algorithm to train the learning network.

[0058] Step 66: Wait for the learning network to finish training, then store the trained RF network in the computer for hmF2 calculation;

[0059] Step 7, Evaluation of the F2 layer parameter model of the ionosphere:

[0060] The root mean square error (RMSE), mean percentage error (MAPE), and correlation coefficient (ρ) were selected for model evaluation.

[0061] Calculate the root mean square error (RMSE) between the observed values ​​and the model predictions for NmF2 and hmF2, respectively, using the following formulas:

[0062]

[0063] In the above formula, m represents the total number of samples, and y obs Represents the observed values ​​of NmF2 and hmF2, y fore Represents the NmF2 and hmF2 predicted by the machine learning model, where i is the index number;

[0064] Calculate the mean percentage error (MAPE) between the observed values ​​and the model predictions for NmF2 and hmF2, respectively, using the following formulas:

[0065]

[0066] Calculate the correlation coefficient ρ of NmF2 and hmF2 respectively:

[0067]

[0068] In the above formula, This represents the mean of the observed values. This represents the mean of the model's predicted values.

[0069] The beneficial effects of this invention are:

[0070] The method disclosed in this invention, based on long-term observation data from the GIRO altimeter and GNSS occultation, uses machine learning combined with international reference ionospheric models and horizontal wind field models to model the temporal and spatial variations of global ionospheric F2 layer parameters, which can provide model support for the design of ground-to-air radio information system links traversing the ionospheric environment. Attached Figure Description

[0071] Figure 1This is a flowchart illustrating the method of the present invention;

[0072] Figure 2 This is a diagram showing the input and output settings of the machine learning algorithm during the modeling of the NmF2 ionosphere;

[0073] Figure 3 This is a diagram showing the input and output settings of the machine learning algorithm during the modeling of the ionosphere hmF2. Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0075] Example 1 discloses a method for modeling global ionospheric F2 layer parameters based on machine learning and model constraints, such as... Figure 1 As shown, it includes the following steps:

[0076] Step 1, Acquisition and preprocessing of altimeter observation data:

[0077] Step 11: Download the automatic interpretation data from the Global Ionospheric Radio Observatory (GIRO) digital altimeter. The download URL is http: / / giro.uml.edu / didbase / .

[0078] Step 12: Extract parameters from the automatic interpretation data, such as the altimeter's longitude and latitude coordinates, observation time, Autoscaling Confidence Score (ACS), critical frequency foF2 of the F2 ionosphere, and peak height hmF2 of the F2 ionosphere.

[0079] Step 13: Delete vertical measurement data with an automatic confidence score below 75;

[0080] Step 14: Calculate the peak density NmF2 of the ionospheric F2 layer using foF2. The calculation method is as follows:

[0081] NmF2=foF2 2 / 80.62

[0082] Step 15: Output the ionospheric vertical measurement parameters processed in step 13 and store them in a text file. The ionospheric vertical measurement parameters include altimeter longitude, latitude coordinates, observation time, NmF2, and hmF2.

[0083] Step 2, Acquisition and Preprocessing of Occultation Observation Data:

[0084] Step 21: download the ionospheric occultation electron density profile (IonPrf) observation data, the download website is cdaac-www.cosmic.ucar.edu;

[0085] Step 22: extract the observation time, latitude, longitude and height coordinates of the occultation tangent point, and ionospheric values from the electron density profile;

[0086] Step 23: extract NmF2 and hmF2 from the electron density profile:

[0087] NmF2=max{Ne i ,i=1,2,...,n}

[0088] hmF2=h j (Ne j ==NmF2) j＝1,2,...n

[0089] In the above formulas, max represents taking the maximum value, Ne is the electron density, h is the height of the tangent point, and n is the total number of sampling points contained in one occultation event;

[0090] Step 24: eliminate the electron density profiles where hmF2 is not within the height range of 150 to 450 km;

[0091] Step 25: eliminate the electron density profiles where the slope S at the heights of 490 km and 420 km is not within the interval of -9<S<-0.02:

[0092]

[0093] In the above formula, N e,490 represents the electron density at a height of 490 km, N e,420 represents the electron density at a height of 420 km, and the unit of electron density is el / cm 3 ;

[0094] Step 26: eliminate the electron density profiles where the average deviation M between the electron density value at each point and the original value is greater than 3: D

[0095]

[0096] In the above formula, N represents the number of electron density samples;

[0097] Step 27: eliminate the electron density profiles that have negative electron density values at heights above 110 km;

[0098] Step 28: output the qualified occultation parameters and store them in a text file, wherein the occultation parameters include the longitude and latitude coordinates of the tangent point, observation time, NmF2 and hmF2; ​

[0099] Step 3: Calculate NmF2 and hmF2 using the International Reference Ionospheric Model (IRI):

[0100] Step 31: Input parameters such as altimeter coordinates, occultation collision point coordinates, observation time, and sunspot number into the International Reference Ionospheric Model (IRI) to calculate NmF2 and hmF2 at the corresponding time and location;

[0101] Step 32: Output NmF2 and hmF2 calculated by the IRI model and store them in a text file;

[0102] Step 4: Calculate the zonal and meridional wind velocities using the Horizontal Wind Model (HWM):

[0103] Step 41: Input the coordinates of the altimeter, the coordinates of the occultation collision point, the observation time, the number of sunspots, the geomagnetic index and other parameters into the horizontal wind field model, and calculate the zonal wind field velocity and the meridional wind field velocity at the corresponding time and location.

[0104] Step 42: Output the zonal and meridional wind velocities calculated by the HWM model and store them in a text file;

[0105] Step 5: Machine learning to build a global NmF2 model:

[0106] Step 51: Select Year Day (DOY), Local Time (LT), and Geographic Latitude and Longitude Coordinates. Geomagnetic latitude Geographic longitude coordinates λ, sunspot number, F10.7 index, solar wind speed, geomagnetic Ap index, Kp index, and NmF2 calculated by the IRI model are used as training inputs.

[0107] Step 52, from geographical latitude coordinates Calculate geomagnetic latitude using longitude coordinates λ

[0108]

[0109] In the above formula: and These represent the latitude and longitude coordinates of the North Magnetic Pole, respectively. Since the geomagnetic poles change over time, these coordinates are not fixed constants and can be obtained using the International Geomagnetic Reference Field model (IGRF).

[0110] Step 53: Normalize the annual day DOY and local time LT, and calculate their sine and cosine components respectively:

[0111]

[0112]

[0113]

[0114]

[0115] Step 54, as follows Figure 2 As shown, DOYs, DOYc, LTs, LTc, and geographic latitude coordinates are included. Geomagnetic latitude Thirteen parameters, including geographic longitude coordinates λ, sunspot number R12, F10.7 index, solar wind speed SW, geomagnetic Ap index, Kp index, and NmF2 calculated by the IRI model, are used as training inputs for machine learning, while the actual observed NmF2 values ​​from occultation and altimeters are used as outputs.

[0116] Step 55: Randomly select 70% of the NmF2 samples for training, 15% of the NmF2 samples for model testing, and 15% of the NmF2 samples for accuracy evaluation. Use the Random Forest (RF) algorithm for learning, set the number of leaves to 5, the forest size to 300, and use the bootstrap aggregation algorithm to train the learning network.

[0117] Step 56: Store the trained RF network in the computer for NmF2 calculation;

[0118] Step 6: Machine learning to build a global hmF2 model:

[0119] Step 61: Select Year Day (DOY), Local Time (LT), and Geographic Latitude and Longitude Coordinates. Geomagnetic latitude The parameters such as geographic longitude coordinates λ, sunspot number, F10.7 index, solar wind speed, geomagnetic Dst index, Kp index, hmF2 calculated by the IRI model, and meridional wind speed Vz and zonal wind speed Vm calculated by the HWM model are used as training inputs.

[0120] Step 62, from geographical latitude coordinates Calculate geomagnetic latitude using longitude coordinates λ

[0121]

[0122] Step 63: Normalize the annual day DOY and local time LT according to the method in step 53, and calculate their sine and cosine components respectively.

[0123] Step 64, as follows Figure 3 As shown, DOYs, DOYc, LTs, LTc, and geographic latitude coordinates are included. Geomagnetic latitude The geographical longitude coordinates λ, sunspot number R12, F10.7 index, solar wind speed SW, geomagnetic Dst index, Kp index, hmF2 calculated by the IRI model, and meridional wind speed Vz and zonal wind speed Vm calculated by the HWM model are used as training inputs for machine learning, and the actual observed values ​​of hmF2 from occultation and altimeter are used as outputs.

[0124] Step 65: Randomly select 70% of the hmF2 samples for training, 15% of the hmF2 samples for model testing, and 15% of the hmF2 samples for accuracy evaluation. Use the Random Forest (RF) algorithm for learning, set the number of leaves to 5, the forest size to 350, and use the bootstrap aggregating algorithm to train the learning network.

[0125] Step 66: Wait for the learning network to finish training, then store the trained RF network in the computer for hmF2 calculation;

[0126] Step 7, Evaluation of the F2 layer parameter model of the ionosphere:

[0127] We select the root mean square error (RMSE), mean percentage error (MAPE), and correlation coefficient (ρ) for model evaluation; RMSE and MAPE reflect the estimation performance of the model, while ρ shows the correlation between the model's predicted values ​​and the actual observed values.

[0128] Calculate the root mean square error (RMSE) between the observed values ​​and the model predictions for NmF2 and hmF2, respectively, using the following formulas:

[0129]

[0130] In the above formula, m represents the total number of samples, and y obs Represents the observed values ​​of NmF2 and hmF2, y fore Represents the NmF2 and hmF2 predicted by the machine learning model, where i is the index number;

[0131] Calculate the mean percentage error (MAPE) between the observed values ​​and the model predictions for NmF2 and hmF2, respectively, using the following formulas:

[0132]

[0133] Calculate the correlation coefficient ρ of NmF2 and hmF2 respectively:

[0134]

[0135] In the above formula, This represents the mean of the observed values. This represents the mean of the model's predicted values.

[0136] Finally, the model accuracy evaluation results are output as the basis for model prediction error analysis.

Claims

1. A method for modeling global ionospheric F2 layer parameters based on machine learning and model constraints, characterized in that, Comprising the following steps: Step 1, acquisition and preprocessing of ionosonde observation data: Step 11, downloading automatically interpreted data of digital ionosondes from global ionospheric radio observatories; Step 12, extracting longitude and latitude coordinates of the ionosonde, observation time, automatic interpretation confidence score, ionospheric F2 layer critical frequency foF2 and ionospheric F2 layer peak height hmF2 from the automatically interpreted data; Step 13, deleting vertical ionospheric sounding data with an automatic interpretation confidence score lower than 75; Step 14, calculating the ionospheric F2 layer peak density NmF2 by using foF2, wherein the calculation method is as follows: NmF2=foF2 2 / 80.62 Step 15, outputting the ionospheric vertical sounding parameters processed in step 13 and storing them in a text file, wherein the ionospheric vertical sounding parameters include the longitude and latitude coordinates of the ionosonde, observation time, NmF2 and hmF2; Step 2, acquisition and preprocessing of occultation observation data: Step 21, downloading occultation electron density profile observation data; Step 22, extracting observation time, latitude and longitude of the tangent point, height coordinates and ionospheric values from the electron density profile; Step 23: extracting NmF2 and hmF2 from the electron density profile: NmF2=max{Ne i ,i=1,2,...,n} hmF2=h j (Ne j ==NmF2) j＝1,2,...n In the above formula, max represents obtaining the maximum value, Ne is the electron density, h is the tangent point height, and n is the total number of sampling points contained in one occultation event; Step 24: eliminating electron density profiles whose hmF2 is not within the height range of 150-450 km; Step 25: eliminating electron density profiles whose slope S at heights of 490 km and 420 km is not within the interval of -9<S<-0.02: In the above formula, N e,490 N represents the electron density at an altitude of 490 km. e,420 This represents the electron density at an altitude of 420 km; Step 26: Eliminate the average deviation M between the electron density value at each point and the original value. D Electron density profiles greater than 3: In the above formula, N represents the number of electron density samples; Step 27, eliminating electron density profiles that have values less than 0 above 110 km; Step 28, outputting qualified occultation parameters and storing them in a text file, wherein the occultation parameters include the longitude and latitude coordinates of the tangent point, observation time, NmF2 and hmF2; Step 3, calculating NmF2 and hmF2 by using the international reference ionosphere model IRI: Step 31, inputting ionosonde coordinates, occultation tangent point coordinates, observation time and sunspot number into the international reference ionosphere model IRI to calculate NmF2 and hmF2 at corresponding time and locations; Step 32, outputting NmF2 and hmF2 calculated by the IRI model and storing them in a text file; Step 4, calculating zonal wind velocity and meridional wind velocity by using the horizontal wind model HWM: Step 41, inputting ionosonde coordinates, occultation tangent point coordinates, observation time, sunspot number and geomagnetic index into the horizontal wind model to calculate zonal wind velocity and meridional wind velocity at corresponding time and locations; Step 42, outputting the zonal wind velocity and meridional wind velocity calculated by the HWM model and storing them in a text file; Step 5, constructing a global NmF2 model by machine learning: Step 51: Select Year Day (DOY), Local Time (LT), and Geographic Latitude and Longitude Coordinates. Geomagnetic latitude Geographic longitude coordinates λ, sunspot number, F10.7 index, solar wind speed, geomagnetic Ap index, Kp index, and NmF2 calculated by the IRI model are used as training inputs. Step 52, from geographical latitude coordinates Calculate geomagnetic latitude using longitude coordinates λ In the above formula: and These represent the latitude and longitude coordinates of the North Magnetic Pole, respectively. Step 53, performing normalization processing on day of year DOY and local time LT, and calculating their sine and cosine components respectively: Step 54: Combine DOYs, DOYc, LTs, LTc, and geographic latitude coordinates. Geomagnetic latitude Geographic longitude coordinates λ, sunspot number R12, F10.7 index, solar wind speed SW, geomagnetic Ap index, Kp index, and NmF2 calculated by the IRI model are used as training inputs for machine learning, while the actual observed NmF2 values ​​from occultation and altimeters are used as outputs. Step 55: Randomly select 70% of the NmF2 samples for training, 15% of the NmF2 samples for model testing, and 15% of the NmF2 samples for accuracy evaluation. Use the Random Forest (RF) algorithm for learning, set the number of leaves to 5, the forest size to 300, and use the bootstrap aggregation algorithm to train the learning network. Step 56: Store the trained RF network in the computer for NmF2 calculation; Step 6: Machine learning to build a global hmF2 model: Step 61: Select Year Day (DOY), Local Time (LT), and Geographic Latitude and Longitude Coordinates. Geomagnetic latitude Geographic longitude coordinates λ, sunspot number, F10.7 index, solar wind speed, geomagnetic Dst index, Kp index, hmF2 calculated by the IRI model, and meridional wind speed Vz and zonal wind speed Vm calculated by the HWM model are used as training inputs. Step 62, from geographical latitude coordinates Calculate geomagnetic latitude using longitude coordinates λ Step 63: Normalize the annual day DOY and local time LT according to the method in step 53, and calculate their sine and cosine components respectively. Step 64: Combine DOYs, DOYc, LTs, LTc, and geographic latitude coordinates. Geomagnetic latitude Geographic longitude coordinates λ, sunspot number R12, F10.7 index, solar wind speed SW, geomagnetic Dst index, Kp index, hmF2 calculated by the IRI model, and meridional wind speed Vz and zonal wind speed Vm calculated by the HWM model are used as training inputs for machine learning, while the actual observed values ​​of hmF2 from occultation and altimeter are used as outputs. Step 65: Randomly select 70% of the hmF2 samples for training, 15% of the hmF2 samples for model testing, and 15% of the hmF2 samples for accuracy evaluation. Use the Random Forest (RF) algorithm for learning, set the number of leaves to 5, the forest size to 350, and use the bootstrap aggregation algorithm to train the learning network. Step 66: Wait for the learning network to finish training, then store the trained RF network in the computer for hmF2 calculation; Step 7, Evaluation of the F2 layer parameter model of the ionosphere: The root mean square error (RMSE), mean percentage error (MAPE), and correlation coefficient (ρ) were selected for model evaluation. Calculate the root mean square error (RMSE) between the observed values ​​and the model predictions for NmF2 and hmF2, respectively, using the following formulas: In the above formula, m represents the total number of samples, and y obs Represents the observed values ​​of NmF2 and hmF2, y fore Represents the NmF2 and hmF2 predicted by the machine learning model, where i is the index number; Calculate the mean percentage error (MAPE) between the observed values ​​and the model predictions for NmF2 and hmF2, respectively, using the following formulas: Calculate the correlation coefficient ρ of NmF2 and hmF2 respectively: In the above formula, This represents the mean of the observed values. This represents the mean of the model's predicted values.

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