A stacked machine learning model for the vertical total electron content forecasting

We design four Artificial Neural Network (ANN) models, namely a Multilayer Perceptron (MLP), a Convolutional Neural Network (CNN), an Extreme Learning Machine network (ELM) and an ensemble model based on stacking (STACKED) to forecast the ionospheric vertical Total Electron Content (vTEC) from 1 to 24 hours in advance on a single station at mid latitude. The time series used, spanning from January 2006 to December 2018, includes vTEC, provided by the Global Navigation Satellite System (GNSS) receiver at Tsukuba (TSKB), Japan (36.06o N, 140.05o E) and suitable external drivers selected among several helio-geophysical parameters. The selection of appropriate external drivers is made by rating their relevance on the vTEC at forecasting timescales (from 1 to 24 hours). The process, based on eleven machine learning models, highlights that the most important external drivers are: the 10.7 cm Solar Flux (F10.7), the magnitude BT of the Interplanetary Magnetic Field (IMF), and the Auroral Electrojet (AE) index. The forecasting performance of the four models (MLP, CNN, ELM, STACKED) is then analysed. The analysis relies on three statistical metrics to compare actual and forecasted vTEC: the coefficient of determination (R2 ), the Mean Absolute Error (MAE), and the Root Mean Squared Error (RMSE). Additionally, descriptive statistics are presented using box and whisker plots. The four ANN models show a quite satisfactory capability to forecast vTEC when applied to the test dataset which represents 10% of the available data from 2006 to 2018. Furthermore, by conducting a Wilcoxon signed rank test, it is shown that statistically significant improvements are achieved by the STACKED model with regard to MLP, CNN and ELM. On average, by analysing the forecasted (from 1 to 24 hours in advance) vs the actual vTEC, the STACKED model achieves R2 ¼ 0:816; RMSE ¼ 0:426 TECu, and MAE ¼ 0:296 TECu (1 TECunit ¼ 1016 electrons/m2) whilst MLP, CNN and ELM show respectively R2 ¼ 0:808; 0:812; 0:803; RMSE ¼ 0:436 TECu, 0:431 TECu, 0:441 TECu and MAE ¼ 0:304 TECu, 0:299 TECu, 0:312 TECu