A backpropagation Neural Network Model to Predict the Plasmapause Location

Background

The discovery of the Earth’s radiation belts by Explorer 1 in 1958 was a major milestone in geophysics and astronomy, which marked the birth of magnetospheric physics. Owing to continuous accumulations of the high-resolution wave and particle measurements from multiple satellite missions in geospace and the development of the state-of-art modeling during the Van Allen Probe Era, significant advances have been made in understanding the dynamic properties of the energetic electrons and the underlying physical mechanisms in the radiation belts. Wave-particle interactions play a fundamental role in the dynamic variability of Earth’s donut-shaped radiation belts that are highly populated by magnetically trapped energetic particles and characteristically separated by the slot devoid of high energetic electrons. The boundary of the plasmasphere, i.e., the plasmapause [Moldwin et al., 2002] separates the cold and dense plasma and sparse one is of great significance in construction of radiation belt models, as the plasma density strongly influences the electron dynamics under the impact of wave-particle interactions. The location of this important boundary strongly depends on geomagnetic activities, which can be compressed down to very low region during strong storm or substorm activities [Carpenter and Anderson, 1992; Goldstein et al., 2014; Liu X. and Liu W., 2014]. We usually use SYM-H and AE indices to indicate the magnitude of the storm and substorm activities. Since the dynamics of the solar wind play an important role in driving geomagnetic activities, I also consider solar wind velocity in the model predication.

The goal of this project is to build a machine learning model to predict the location of plasmapause (Lpp) based on 2-year Van Allen Probe measurements. This is a regression problem. Firstly, the random forest regressor model is constructed to determine the feature importance of each inputs. Then I select the most important feature to construct a supervised backpropagation neutral network model (Model 1) using only SYM-H index, which is further compared with a neutral network model (Model 2) using AE, SYM-H, and solar wind velocity. Furthermore, since the plasmapause location is strongly related to the preceding SYM-H index, I use the preceding 6 hrs of the SYM-H index as the input to build Model 3. The comparison of the performance of these three models indicates that only using SYM-H index as the input, the ANN model can provide reasonable prediction of the plasmapause location.

Dataset

The HFR data (https://emfisis.physics.uiowa.edu/Flight/RBSP-A/L2/)), electron density data (https://emfisis.physics.uiowa.edu/Flight/RBSP-A/L4/)), and the satellite position data (https://rbsp-ect.newmexicoconsortium.org/data_pub/rbspa/MagEphem/definitive/) from Van Allen Probe A from 2016–01–01 to 2017–12–31 are adopted to build the dataset for the Lpp by following the criteria:

(1). If ECH waves are observed, the satellite is outside the plasmapause, otherwise the satellite is inside the plasmasphere.

(2). The plasmapause location is further confirmed by the sharp density variation by 5 times within 0.5 L.

The geomagnetic indices including AE and SYM-H, and the solar wind velocity (Vsw) data at 5 min cadence are publicly available from https://omniweb.gsfc.nasa.gov/ow.html. There are 5410 samples of identified Lpp based on the criteria above using 2-year data. The identified Lpp together with the related geomagnetic indices are provided in the format of a csv file. It is worth noting that the reason that I use two year data is that the measurements from Van Allen Probe can cover the full MLT and L-shell regions during 2-year interval.

Figure 1 shows the distributions of the identified Lpp color-coded by different indices: (a) AE, (b) AE* (Maximum AE in the preceding 6 hrs), © SYM-H, (d) SYM-H* (Minimum SYM-H in the preceding 6 hrs), (e) Vsw, and (e) Vsw* (Maximum Vsw in the preceding 6 hrs). By comparing the left to the right column, the plasmapause location has a better correlation with the history of the geomagnetic indices rather than the present ones, which can be attributed to that it takes time for the plasmapause to evolve under the impact of geomagnetic storms. Besides, the plasmapause location are compressed to lower L-shells under more disturbed geomagnetic conditions, i.e., increasing AE and solar wind velocity, and decreasing SYM-H.

Figure 1. Distributions of identified plasmapause location (Lpp) with respect to different indices.

Methods

Firstly, the random forest regressor “DecisionTreeRegressor” from sklearn with maximum depth of 5 is implemented to determine which index is most important for the prediction of plasmapause location. The dataset is split into training and testing sets using “train_test_split”, with the testing set having 25% of the total samples. Figure 2 shows the feature importance of different indices, demonstrating that the minimum SYM-H in the preceding 6 hrs is most important to the prediction. Moreover, this feature importance can help us understand the driver of the evolution of the plasmapause location, which indicates that the geomagnetic storm fundamentally influences the topology of the plasmapause.

Figure 2. Feature importance based on random forest regressor.

Since the dataset is relatively large for this regression problem, I decided to use neural network model to predict the plasmapause location. I tried three ways to construct the backpropagation neural network model based on “MLPRegressor” from sklearn. The detailed information for these three models is listed in the Table 1.

Table 1. Inputs for the backpropagation neural network models

Model Validation and Application

The dataset is separated into the training (75%) and testing (25%) sets. First, I used the training set to develop the model, and then I use the testing set to validate the model. Figure 3 presents the comparison of the predicted and observed plasmapause locations for these three models using testing set. By only using minimum SYM-H in the preceding 6 hrs, Model 1 can predict the plasmapause location with a reasonable error of RMSE = 0.825. However, the predicted Lpp strongly deviates from the observed Lpp at L < 3.0 and L > 5.0. Still, it is amazing that only use SYM-H* can predict Lpp in a reasonable range. Comparing the regression lines from Model 1 and Model 2, we can see that Model 2 have a much better performance in the prediction of Lpp, with the RMSE = 0.704. Therefore, the plasmapause location not only strongly depends on geomagnetic storms, but also substorm activities and solar wind dynamics might play an important role in plasmapause evolution.

Both Model 1 and Model 2 either use the present or the maximum values of the geomagnetic indices during the preceding 6 hrs as input, but the evolution of the Lpp also is related to the history of these geomagnetic indices. Therefore, I use the SYM-H in the preceding 6 hrs with a cadence of 5 min (73 features) as input to build the Model 3. By comparing the results from Model 1 and Model 3, the predictions are significantly improved, indicating that only use the SYM-H* is not enough to represent the history of the evolution of geomagnetic conditions. By comparing the results from Model 2 and Model 3, they are surprisingly very similar, which demonstrates that only including the history of SYM-H index in the ANN model can successfully predict the location of plasmapause. Therefore, the conclusion from Model 3 is opposite to the Model 2 that SYM-H dominantly determines the plasmapause location, while AE and Vsw indices play a minor role in the prediction.

Figure 3. The comparison of the predicted and observed plasmapause locations for the three models. The RMSE of each model is shown below.

Summary

The comparison of the performance of these three models indicates that SYM-H dominantly determine the plasmapause location, while AE and Vsw indices play a minor role in the prediction. In other words, the topology of the plasmasphere is most significantly affected by geomagnetic storm activities. There are still limitations in the present study due to a time limit. I only use 2-year measurements from Van Allen Probe A during 2016–2017. However, there are more data from 2012.9–2020.7 during Van Allen Probe Era, which can be included in the future study. With more samples, the model prediction can have better performance. Nevertheless, the current model can provide reasonable prediction of the plasmapause location by using only the history of SYM-H index, which can be adopted in the future radiation belt models.

References

Carpenter, D. L., and R. R. Anderson, An ISEE/whistler model of equatorial electron density in the magnetosphere, J. Geophys. Res., 97, 1097, 1992.

Goldstein, J., Pascuale, S. De, Kletzing, C., Kurth, W., Genestreti, K. J., Skoug, R. M., Larsen, B. A., Kistler, L. M., Mouikis, C., and Spence, H. (2014), Simulation of Van Allen Probes plasmapause encounters, J. Geophys. Res. Space Physics, 119, 7464– 7484, doi:10.1002/2014JA020252.

Liu, X., Liu, W. A new plasmapause location model based on THEMIS observations. Sci. China Earth Sci. 57, 2552–2557 (2014). https://doi.org/10.1007/s11430-014-4844-1

Moldwin, M. B., Downward, L., Rassoul, H. K., Amin, R., and Anderson, R. R., A new model of the location of the plasmapause: CRRES results, J. Geophys. Res., 107( A11), 1339, doi:10.1029/2001JA009211, 2002.