2023 · Published · 🏆 Wiley Top Viewed Paper 2023

APE — Predicting equatorial plasma bubbles on the Swarm constellation

XGBoost Shapley Values ESA Swarm Ionosphere Space Weather

APE (AI Prediction of EPBs) is an XGBoost ensemble model that predicts the Ionospheric Bubble Index on ESA's Swarm constellation — and uses Shapley values to reveal which physical drivers matter most.

Paper (JGR Space Physics)

Overview

Equatorial Plasma Bubbles (EPBs) are plumes of low-density plasma that rise through the nighttime F-region ionosphere via the Generalized Rayleigh–Taylor instability. Inside a bubble, plasma density drops by orders of magnitude relative to the surrounding medium, scattering radio waves and causing GPS positioning errors, communication dropouts, and satellite navigation disruptions — particularly over equatorial and low-latitude regions.

Despite decades of study, EPBs remain difficult to predict: their occurrence depends on a complex mix of local time, season, solar flux, and geomagnetic activity, and many of these drivers interact nonlinearly. APE learns these interactions directly from eight years of Swarm data.

Simulated equatorial plasma bubbles — columns of severely depleted plasma rising through the dense F-region via the Generalized Rayleigh–Taylor instability. Yellow = high electron density (∼10⁸ cm⁻³); dark blue = depleted interior (∼10² cm⁻³). ESA Swarm (white track) detects each crossing as an IBI spike in the magnetometer and Langmuir probe.

Motivation

Existing EPB prediction approaches are largely climatological — they tell you where and when bubbles are most likely on average, but struggle with day-to-day variability. A model that learns directly from observations, and can explain its reasoning, is both scientifically valuable and practically useful for space weather operators.

APE outperforms linear regression and random forest baselines across every metric, and Shapley values reveal that F10.7 solar flux — not latitude — is the dominant driver of EPB occurrence.

Data

Training data comes from the three-spacecraft ESA Swarm constellation (Alpha, Bravo, Charlie), covering 2014–2022 at 1-second resolution. Each observation is transformed into a 6-dimensional feature vector:

MLT — magnetic local time (cyclic)
Latitude — geographic latitude
Longitude — geographic longitude (cyclic)
Day of year — season proxy (cyclic)
Kp — geomagnetic activity index
F10.7 — solar radio flux proxy for EUV

The target label is the IBI value (R² correlation between ΔNe and ΔB), treated as a continuous regression target. IBI > 0.5 = confirmed EPB. After binning and quality cuts: ~42 k samples, split 80/20 train/test.

Model

Three algorithms were benchmarked — standard linear regression, a random forest, and XGBoost. APE is the final XGBoost model, selected for its top performance and 3.8× faster training time over the random forest:

Algorithm: eXtreme Gradient Boosting (XGBoost), an ensemble of regression trees
Hyperparameters: 300 estimators, alpha = 0.1, subsample = 0.5, eta = 0.2
Tuning: GridSearchCV with 80/20 random stratified split

Cyclical features (MLT, longitude, day-of-year) are encoded as sine/cosine pairs to preserve their periodic structure.

Explainability

A key goal of this work was not just to predict EPBs but to understand why the model makes its predictions. APE uses Shapley values (SHAP) from game theory — treating each feature as a player and the IBI prediction as the pay-off — to attribute each prediction to its input features.

Key findings from the Shapley analysis:

F10.7 is the most important feature — solar activity drives EUV ionization which sets up the density gradient that enables the Rayleigh–Taylor instability.
Latitude is the least important — most confirmed EPBs occur within ±25° of the magnetic equator, so latitude provides little discrimination once that range is established.
EPBs peak in the American/Atlantic sector at 19–24 MLT, during equinox months, and are suppressed above Kp = 7.

Results

Evaluated on the 20% held-out test set — APE substantially outperforms both baselines:

Prediction Efficiency (PE): 0.96
Pearson R: 0.98
MAE: 0.05
RMSE: 0.08

Performance is consistent across MLT, latitude, longitude, season, and solar flux — with slightly elevated error at 18 and 3 MLT, corresponding to periods of low EPB activity and therefore less training signal. The model was also awarded the Wiley Top Viewed Paper of 2023 in JGR Space Physics.

What's next

Extending APE to forecast EPB onset (predictive, not nowcast) using real-time F10.7 and Kp.
Incorporating prompt penetration electric field (PPEF) and disturbance dynamo signatures to better handle storm-time EPB suppression and enhancement.
Multi-spacecraft constellation fusion — combining Swarm Alpha, Bravo, and Charlie observations to resolve longitudinal structure.