As a common boundary layer that distinctly separates the regions of high-density plasmasphere and low-density plasmatrough, the plasmapause is essential to comprehend the dynamics and variability of the inner magnetosphere. Using the machine learning framework PyTorch and high-quality Van Allen Probes data set, we develop a neural network model to predict the global dynamic variation of the plasmapause location, along with the identification of 6,537 plasmapause crossing events during the period from 2012 to 2017. To avoid the overfitting and optimize the model generalization, 5,493 events during the period from September 2012 to December 2015 are adopted for division into the training set and validation set in terms of the 10-fold cross-validation method, and the remaining 1,044 events are used as the test set. The model parameterized by only AE or Kp index can reproduce the plasmapause locations similar to those modeled using all five considered solar wind and geomagnetic parameters. Model evaluation on the test set indicates that our neural network model is capable of predicting the plasmapause location with the lowest RMSE. Our model can also produce a smooth magnetic local time variation of the plasmapause location with good accuracy, which can be incorporated into global radiation belt simulations and space weather forecasts under a variety of geomagnetic conditions.
A neural network model is constructed based on Van Allen Probes observations to predict the dynamic plasmapause location
The model parameterized by AE or Kp without inclusion of other parameters shows good accuracy to predict the plasmapause location
Our neural network model is capable of predicting the global plasmapause location with low RMSE
The plasmasphere, which is full of cold and dense plasma (electrons ∼1 eV with density ∼102–104 cm−3), plays an important role in modulating the fluxes of energetic particles in the Earth's ring current and radiation belts (e.g., Cao et al., 2017; Darrouzet et al., 2009; Fu et al., 2020; Gu et al., 2011, 2012, 2020; Hua et al., 2019; Kozyra et al., 1995; Lemaire & Gringauz, 1998; Ni et al., 2013; Orr & Webb, 1975; Sandel et al., 2003; Takahashi & Anderson, 1992; Webb & Orr, 1975; Yi et al., 2021; Zhou et al., 2020). The plasmasphere strongly influences the plasma properties of the inner magnetosphere by wave-particle interactions (e.g., Fu et al., 2016; Gary et al., 1994; Hua et al., 2020a; Ni et al., 2017, 2014; Thorne & Horne, 1992; Wilson et al., 1992; Xiang et al., 2018; Young et al., 1981), and contributes to assessing the low-latitude boundary layer and plasma sheet (e.g., Cao et al., 2016; Elphic et al., 1997). The outer boundary of the plasmasphere is called “plasmapause,” which is often defined as a transition region in which the plasma density drops dramatically by at least half an order of magnitude in a short distance of 0.5 RE (RE is Earth's radii) (e.g., Carpenter & Anderson, 1992; Moldwin et al., 2002). The position of the plasmapause (Lpp) is usually balanced by the convection electric field outside the plasmasphere and the corotation electric field inside the plasmasphere. The variation of Lpp responds considerably to the changes of solar wind forcing and geomagnetic activity (e.g., Goldstein et al., 2003; Liu et al., 2015). Because the plasmapause is related to the plasmasphere, the ring current, and the radiation belts in the inner magnetosphere, where the wave-particle interactions inside and outside the plasmapause are quite different due to the sharp change in plasma density, the prediction of the plasmapause location becomes very important for magnetospheric research (e.g., Hua et al., 2020b; Khoo et al., 2018, 2019; Ma et al., 2020; Ni et al., 2015; Summers et al., 2008; Xiang et al., 2020; Zhang et al., 2018, 2019).
In the past three decades, several statistics-based empirical models using satellite observations have been developed to study the dynamic variations of the plasmasphere and to predict the plasmapause location. Below we review briefly some important empirical models in this regard.
Carpenter and Anderson (1992) (hereafter referred to as CA-1992) proposed a functional Kp-based empirical model to specify the plasmapause location, i.e., Lpp = 5.6–0.46Kpmax, where Kpmax is the maximum Kp in the preceding 24 h. By defining the plasmapause as the position where the plasma number density drops by a factor of 5 or more within ΔL < 0.5, this model was developed for magnetic local time (MLT) = 00–15 based on the plasmapause crossing events obtained from the International Sun-Earth Explorer (ISEE 1) data
Based on the Combined Release and Radiation Effects Satellite (CRRES) measurements in 1990–1991, Moldwin et al. (2002) (hereafter referred to as MOL-2002) followed the same plasmapause definition of CA-1992 and put forward a Kp-dependent plasmapause model with Lpp = (5.39 ± 0.072) − (0.382 ± 0.019) Kpmax, where Kpmax is the maximum Kp in the preceding 12 h. Using the same database, O'Brien and Moldwin (2003) (hereafter referred to as OBM-2003) developed an MLT-dependent plasmapause model below
The plasmapause locations extracted from the Imager for Magnetosphere-to-Aurora Global Exploration (IMAGE) extreme ultraviolet (EUV) imager data were used by Larsen et al. (2007) to construct the first solar wind-driven plasmapause model (hereafter referred to as LAR-2007) without considering the MLT dependence. The LAR-2007 model is a function of interplanetary magnetic field (IMF) BZ component with a shift time of 155 min, and of (where VSW is the solar wind speed, B is the IMF magnitude, and θc is the IMF clock angle) with a shift time of 275 min, i.e.,
Cho et al. (2015) (hereafter referred to as CHO-2015) developed a new model of Lpp as a fit function of VSW, BZ, and AE based on the plasmapause crossings from the Time History of Events and Macroscale Interactions during Substorms (THEMIS) during the ascending phase of Solar Cycle 24
Plasmapause crossing events measured from the Waves of High frequency and Sounder for Probing of Electron density by Relaxation (WHISPER) on Cluster were used by Verbanac et al. (2015) (hereafter referred to as VER-2015) to establish a plasmapause location model as a function of BZ, VSWBZ, dΦmp/dt, Dst, Ap, and AE in three MLT sectors (i.e., 01–07, 07–16, and 16-01)
Liu et al. (2015) (hereafter referred to as LIU-2015) used the THEMIS data to further construct an MLT-dependent Lpp model with the input parameters of SYM-H, AL, AU, AE, and Kp. Their database identified a plasmapause crossing by requiring that the plasma density changes by a factor of 5 (or more) within and that the spacecraft potential changes at least 1.5 V during the crossing
He et al. (2017) proposed a new solar wind-driven global dynamic plasmapause (NSW-GDP) model using VSW, BZ, SYM-H, AE and including the MLT dependence. Their database comes from the study of Zhang et al. (2017) with 48,899 plasmapause crossing events from 18 satellites during a very long period of 1977–2015
Those models above are mostly developed as functions of solar wind and/or geomagnetic parameters with/without the MLT dependence, in terms of certain fitting methods based on the statistics of satellite observations. Because the plasmapause varies significantly with changes of the solar wind and geomagnetic activity, a time-dependent model of the plasmapause, including its MLT dependence, is required for a variety of magnetospheric physics studies and magnetospheric dynamic simulations. However, in-situ satellite observations cannot provide this important information of the plasmapause location due to the limited spatiotemporal coverage of satellites in space. Regarding the empirical plasmapause models mentioned above, they use the parameter values at one specific time stamp as inputs to evaluate the plasmapause location, thereby possibly missing some underlying connection of the plasmapause evolution in a specific time period. Recently, the machine learning technique has emerged into its golden age with considerable developments of algorithms, tools, and high-speed computers (Camporeale et al., 2018). A number of models in the field of space physics and space weather have been established based on the machine learning technique and produced good performance (e.g., Bortnik et al., 2016; Chu et al., 2017a, 2017b; Pires de Lima et al., 2020; Shprits et al., 2019; Zhelavskaya et al., 2016, 2017, 2019). Thus, in this study, we attempt to establish a machine learning model of the plasmapause location in terms of a neural network, aiming to predict the global distribution of the plasmapause location and its temporal evolution with good accuracy.
The outline of this paper is arranged as follows. In Section 2, we introduce the adopted instrumentation and data sets, the criteria that we use to distinguish a plasmapause crossing event, and the adopted back propagation neural network method with the selection of input parameters. Section 3 presents our neural network model results using either single or multiple input parameters, and examines the model performance. Finally, we make the conclusions in Section 4.
2 Data Sets and Methodology
In this study, we use the solar wind parameters (VSW, BZ) and geomagnetic parameters (Kp, Dst, and AE indices) to predict plasmapause locations. These five parameters have good relations with the Lpp, according to previous studies (e.g., He et al., 2017; Liu et al., 2015; Moldwin et al., 2002). The time series of these parameter values with 1 h resolution are obtained from OMNIWeb (http://omniweb.gsfc.nasa.gov/). The background electron densities are evaluated from the upper hybrid resonance frequencies measured by the High-frequency Receiver of the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) instrument (Kletzing et al., 2013; Kurth et al., 2015) onboard the Van Allen Probes (VAP) (Mauk et al., 2012). For this study, we adopt the VAP Level-4 plasma density data during the period from September 2012 to December 2017.
2.2 Determination of Plasmapause Crossings
The plasmapause positions measured by Van Allen Probes are used to develop the plasmapause model and to test the accuracy of the model prediction. As widely adopted in previous studies (e.g., Liu & Liu, 2014; Liu et al., 2015; Moldwin et al., 2002), we define the plasmapause where the value of background electron density drops/increases by a factor ≥5 within 0.5 L. Using this criterion, we further determine the satellite position with the sharpest density gradient to represent the plasmapause location during a plasmapause crossing event. For reliability, we only consider the cases of one plasmapause crossing determined in each inbound and outbound satellite trajectory.
Applying the above identification criterion to Van Allen Probes measurements, we finally register 6,537 plasmapause crossing events during the period from September 2012 to December 2017. The plasmapause crossing events without valid solar wind parameters are removed to generate a robust database.
2.3 Statistics of the Plasmapause Crossing Events
Figure 2 displays the global distribution of the plasmapause locations and the sample points of VAP as a function of MLT and L. For the 2-D distribution of the plasmapause crossing events shown in Figure 2a, it is clear that the plasmapause crossing is most likely to occur around L = 4–5, consistent with the frequent observations of the plasmasphere boundary at this region. It is also indicated that VAP crossed the plasmapause with the largest number of events on the midnight-to-dawn side (i.e., 00–05 MLT) and the smallest number of events on the postnoon-to-dusk side (i.e., 14–19 MLT). The global distribution of the VAP sample points is shown in Figure 2b. Evidently, the satellite trajectories cover all MLT sectors at L < 6 with similar sample numbers, indicating that the preferential plasmapause location at L ∼ 4–5 on the midnight-to-dawn side is not a result of the orbit configuration but a phenomenon fact.
To understand the underlying relationship between the plasmapause location and geomagnetic activity, we perform a detailed analysis of the magnitudes of the three geomagnetic indices (Kp, AE, and Dst) corresponding to the identified plasmapause crossing events. Specifically, we determine the maximum/minimum values of the three geomagnetic indices in the preceding 24-h and 72-h periods of each crossing event, respectively, and scatter plot them in a color-coded manner in the (L, MLT)-coordinate, the results of which are presented in Figure 3. During the preceding 24 h of the plasmapause crossings, Figures 3a, 3c, and 3e indicate that when the plasmapause becomes closer to the Earth, enhanced geomagnetic activities are required to compress the magnetosphere, as represented by the increase of the maximum values of Kp and AE and the decrease of the minimum value of Dst. However, this trend is not as evident for the trend in the preceding 72 h. Figures 3b, 3d, and 3f show that the plasmapause locations are scattered over a wide range of L shell for large values of maximum Kp, maximum AE, and minimum Dst during the preceding 72 h. This indicates that the plasmapause location is more closely correlated with the indices in the preceding 24 h than 72 h. The results of Figure 3 also show that only using the maximum/minimum values of these indices to predict the plasmapause location may possibly miss some underlying evolution of the plasmapause in a specific time period. For example, for the maximum Kp = 2, Lpp can vary largely between L = 4–6. Therefore, in this study, we use the neural network to process a large amount of input information and establish a plasmapause prediction model in terms of an optimal input-output mapper.
2.4 Neural Network and Input Selection
For neural networks, these input data need to be normalized to their minimum/maximum values at the beginning. We use the Min-Max scaler from the Python scikit-learn library (https://scikit-learn.org/stable/, see also Pedregosa et al., 2011).
3 Model Results and Performance Validation
Following the methodology described above, we establish the single-parameter and multiple-parameter neural network models to predict Lpp with the MLT dependence. The time delay for each single-parameter model follows the results of Figure 5 (43, 42, 36, 7, and 6 time delay for AE, Kp, BZ, VSW, and Dst, respectively), and the inputs of the multiparameter model adopt the time delay combination of these five parameters with the best performance. Detailed comparisons between the observed plasmapause locations (Lpp-OBS) and the prediction model results (Lpp-MOD) using the test set are shown in Figure 6. Each panel illustrates the color-coded occurrence probabilities (the ratio between the crossing event number in each 0.1 × 0.1 L bin and the total crossing event number of the test set) as a function of Lpp-OBS (x axis) and Lpp-MOD (y axis). In each panel, the blue solid line represents a perfect match between the observations and the model results, the yellow dashed line represents that the model prediction results are within ±0.5 L differences with the observations, and the red solid line represents ±2.0 L differences. The numbers at the right-bottom side of each panel are RMSE values (black color) and CC (correlation coefficients, red color) between the Lpp-OBS and Lpp-MOD. For the single-parameter models (Figures 6a–6e), using the AE or Kp indices as inputs tend to obtain better performance (RMSE = 0.7 and 0.73, respectively). Furthermore, the performance of the single-parameter model using the AE or Kp indices as inputs only are comparable to the performance of the multiparameter model (Figure 6f). These results suggest that AE and Kp index are good parameters for predicting plasmapause location. Moreover, Figures 6d and 6e show that the Lpp-MOD is scattered over a much narrower L shell range than Lpp-OBS when modeled using only AE or only Dst index. This means that using multiparameter, the trend of Lpp-MOD lies better with Lpp-OBS, with the range of Lpp-MOD wider than the range of Lpp-MOD when only using AE or Dst.
To investigate the MLT dependences of the model performance, we calculate the RMSE values and standard deviations between Lpp-OBS and Lpp-MOD in our test set from six plasmapause prediction models in different MLT ranges and show the results in Figure 7. The red, black, gold, purple, blue, green curves indicate our ANN AE model, CA-1992 model, MOL-2002 Kp model, OBM-2003 models (Kp, AE, and Dst), respectively. It should be noted that CA-1992 and MOL-2002 models do not have MLT dependences. Thus, the same plasmapause positions are used in different MLT ranges for the two models. Generally, the ANN AE model introduced in this study (red curves) has the lowest RMSE values and standard deviations in all MLT ranges. These comparison results suggest that the ANN plasmapause models built in this study have better performance than previous empirical plasmapause models.
4 Discussions and Conclusions
In this study, we develop an Lpp prediction model with MLT dependences based on the ANN technique. The results suggest that only using the AE or Kp indices as inputs can yield good predictions of plasmapause positions. Our neural network model is capable of predicting the global plasmapause location and simulating the evolution of the plasmapause with low RMSE.
In our ANN model, only solar wind and geomagnetic parameters are used as inputs. Basically, the current plasmapause positions are also related to previous plasmapause locations since the change of the plasmapause location is continuous. Adding the previous plasmapause locations as inputs in our model is a potential method to address this issue and improve model performance. However, the orbit period of VAP is around 9 h, which is too long to get continuous measurements of plasmapause locations. Generally, one VAP satellite samples the plasmapause in every ∼4.5 h and two VAP satellites can sample the plasmapause in every 2–3 h. In addition, some other satellites can be used to measure the plasmapause positions, like MMS, ERG, and THEMIS. Using all these satellite measurements, it is likely to find approximately continuous measurements of plasmapause locations during some periods. Therefore, it is interesting to build a new plasmapause prediction model based on measurements during these special periods, which is left for further study.
This study aims to obtain a model that can predict plasmapause location and we only focus on the data set obtained from VAP. However, the currently largest available plasmapause location database is compiled based on observations from 18 satellites from 1977 to 2015 (Zhang et al., 2017). To examine the reliability of our developed ANN model, we display our AE model performance on their database only including VAP observations in Figure 8a and the whole database in Figure 8b, respectively. Clearly, for the observed plasmapause locations in the VAP's scope ∼L = 3–6, our model can reproduce the evolution of the plasmapause and accurately predict the plasmapause location (RMSE = 0.59 with CC = 0.87). However, our model has weak predictive ability on the plasmapause locations beyond VAP's scope (RMSE = 2.10 with CC = 0.67). In addition, to evaluate the performance more precisely with multisatellites databases, our ANN model needs further improvements. For example, when we obtain the whole database to test our model in Figure 8b, we could use a classification machine learning model to judge whether the plasmapause is at L < ∼5.5 or at L > ∼5.5 during all conditions. After the classification, we can model the plasmapause location only for the category that the modeled plasmapause is at L < ∼5.5. For the observed plasmapause at L > ∼5.5, we can first compare the categorization results, i.e., whether the neural network model can correctly predict the times when the observed plasmapause is at L > ∼5.5. Then we can compare the performance for the times when the plasmapause is at L < ∼5.5. This approach will be applied in our future study.
Although previous studies (e.g., Cho et al., 2015; Larsen et al., 2017; O'Brien & Moldwin, 2003) demonstrate that solar wind parameters and geomagnetic indices both have strong correlation with the plasmapause, the prediction results using geomagnetic indices seem better than the results using solar wind parameters (Verbanac et al., 2015). The underlying reasons are still unsolved.
This work was supported by the National Natural Science Foundation of China (Grant 42025404, 41974186, 41904144, 41904143, 41674163), the B-type Strategic Priority Program of the Chinese Academy of Sciences (Grant XDB41000000), the pre-research projects on Civil Aerospace Technologies (Grant D020303, D020308, D020104) funded by the China National Space Administration, the National Key R&D Program of China (2018YFC1407303), and the China Postdoctoral Science Foundation Project (Grant 2019M662700). Song Fu thanks Xiangning Chu for constructive discussions. We also acknowledge the Van Allen Probes mission, particularly the ECT and EMFISIS team, for providing particle and wave data.
Data Availability Statement
The background electron density data from the EMFISIS instrument were obtained from http://emfisis.physics.uiowa.edu/data/index. The solar wind parameters and geomagnetic indices were obtained from the online OMNIWeb (http://omniweb.gsfc.nasa.gov/). Our crossing events data and model could be found in https://figshare.com/articles/dataset/Prediction_of_Dynamic_Plasmapause_Location_using_a_Neural_Network/13181171.
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