Analysis of Short-term Solar Activity Variability and Estimating the Timings of the Next Enhanced Bursts

Technical Summary: Analysis of Short-term Solar Activity Variability and Estimating the Timings of the Next Enhanced Bursts

Problem Statement
Solar activity exhibits variability across multiple timescales. While the decadal solar cycle (SC) is well-characterized, and daily flare/CME events are largely unpredictable on short timescales, a critical gap exists in forecasting intermediate-scale variability (weeks to months). The paper identifies "space weather seasons"—quasi-periodic enhanced activity bursts lasting 6–18 months—as a key driver of hazardous space weather (e.g., major flares and coronal mass ejections). Current operational forecasting focuses on either very short timescales (hours to days) or the decadal cycle amplitude, leaving intermediate bursts unaddressed. The authors note that while physical models (e.g., MHD shallow-water tachocline models and dynamo models) explain the existence of these quasi-annual periods via mechanisms like Tachocline Nonlinear Oscillations (TNOs), they lack the parameter precision to predict the specific timing, amplitude, and hemispheric sequence of individual bursts.

Methodology
The authors propose a novel hybrid forecasting strategy that integrates numerical, statistical, and machine learning techniques to predict these bursts using monthly smoothed sunspot number (SSN) data from 1878 to 2025. The methodology proceeds in three distinct steps:

1. Burst Detection and Characterization (Gaussian Fitting):

   • Hemispheric SSN data is smoothed using a 4-month Gaussian kernel to isolate subannual structures while filtering month-scale noise.
   • Enhanced bursts are defined as single-lobe enhancements lasting 6–18 months with a peak SSN $\ge$ 10.
   • A Gaussian profile with a linear background is fitted to identified bursts to extract key parameters: peak time, amplitude, Full Width at Half Maximum (FWHM), and duration.
   • Kernel Density Estimation (KDE) is used to analyze the statistical distributions of burst amplitudes and durations across the Northern and Southern Hemispheres and different SC phases.

2. Statistical Baseline Forecasting (SARIMA):

   • Separate Seasonal Autoregressive Integrated Moving Average (SARIMA) models are developed for the Northern and Southern Hemispheres to capture the underlying cyclic trends and seasonal patterns.
   • Model parameters are optimized using the Akaike Information Criterion (AIC).
   • Northern Hemisphere: The optimal model is SARIMA (3, 0, 5) $\times$ (2, 1, 0) with a 9-month seasonal period.
   • Southern Hemisphere: The optimal model is SARIMA (3, 0, 1) $\times$ (2, 1, 0) with a 10-month seasonal period.
   • To account for the post-peak decline of SC25, a multiplicative decay factor (20% reduction every 12 months) is applied to the baseline forecasts.

3. Machine Learning Burst Injection (Random Forest):

   • A Random Forest (RF) regression model is trained on a catalog of ~300 historical bursts to predict burst amplitude and duration.
   • Input features include lagged monthly SSNs (1–5 months prior to the burst) and a hemisphere indicator.
   • The RF model outputs predicted amplitudes and durations, which are then injected as asymmetric Gaussian envelopes onto the SARIMA baseline forecasts.

Key Results
The hybrid model successfully hindcasts and forecasts burst events for the current Solar Cycle 25 (SC25):

• Northern Hemisphere:
  • Hindcast (2024 Nov – 2025 May): The model identifies a burst peaking in March 2025 with an SSN of $\sim$70.
  • Forecast: A subsequent burst is predicted for December 2025 with a slightly lower amplitude of $\sim$60 SSN.
• Southern Hemisphere:
  • Behavior: Displays more complex behavior with multiple amplitudes. A main burst is identified starting in late 2024, peaking in March–April 2025 with a high amplitude of 130–140 SSN.
  • Forecast: A tertiary burst is predicted for January 2026 with an amplitude of $\sim$120 SSN.
• Total Disk:
  • The combined total SSN is forecast to peak at $\sim$205–210 in March–April 2025, followed by a plateau at $\sim$170–175 through late 2025 before a gradual decline.
• Model Performance:
  • The RF model achieves an $R^2$ score of 0.748 for amplitude prediction, with a Mean Absolute Error (MAE) of 12.60 SSN.
  • The SARIMA models show hemispheric asymmetry in optimal parameters, reflecting the Northern Hemisphere's more regular short-term fluctuations versus the Southern Hemisphere's punctuated, high-amplitude spikes.

Significance and Claims
The paper claims to address a "critical gap" in operational space-weather forecasting by providing lead times of weeks to months for "space weather seasons." The authors assert that their hybrid approach successfully translates the physically motivated concept of TNOs into a tractable, data-driven workflow.

Key contributions highlighted by the authors include:

• Hybrid Framework: The successful coupling of SARIMA baselines with machine learning-derived burst injections allows for the resolution of quasi-seasonal bursts (2–20 months) that traditional decadal forecasts miss.
• Hemispheric Asymmetry: The study explicitly models the distinct dynamical behaviors of the Northern and Southern Hemispheres, noting that the Southern Hemisphere dominates the total SSN activity in the current cycle.
• Uncertainty Quantification: The framework incorporates statistical confidence intervals (95% CI) for the SARIMA baseline and heuristic uncertainty estimates for the RF-predicted bursts, providing a probabilistic forecast product.
• Operational Utility: By predicting the timing and amplitude of these intermediate bursts, the method aims to provide sufficient lead time for society to prepare for the impacts of enhanced solar activity, distinct from the unpredictability of daily flare events.

The authors maintain that while physical models explain the mechanism of these bursts, their data-driven hybrid approach is currently the most effective method for predicting the specific occurrence and magnitude of these events.