Solar Seed

Geometry-controlled mutual information reveals temperature-ordered coupling in the solar atmosphere

TL;DR: Open-access reference implementation for geometry-controlled mutual information analysis of SDO/AIA EUV channels. Includes paper, code, and reproducible pipelines demonstrating temperature-ordered coupling in the solar atmosphere.

Abstract

Understanding how different thermal layers of the solar atmosphere are coupled is central to solar physics and space-weather prediction. While correlations between extreme-ultraviolet (EUV) channels are well known, disentangling genuine physical coupling from geometric and statistical confounders remains challenging.

We introduce a geometry-controlled mutual information framework to quantify multichannel coupling in SDO/AIA data. By systematically removing disk geometry, radial intensity statistics, and coarse azimuthal structure through a hierarchy of null models, we isolate a residual local coupling component.

Applying this method to seven EUV channels spanning chromospheric to flare temperatures, we find that neighboring temperature channels exhibit significantly stronger local coupling than thermally distant pairs. This temperature-ordered structure is stable over time, survives time-shift and alignment controls, and is spatially localized to active regions.

During major flares, this organization undergoes regime switching: coupling hierarchies break down, the system collapses onto a low-dimensional manifold, and post-flare hysteresis leaves lasting imprints on coronal structure.

Key Results

Metric	Value	Interpretation
MI Ratio	30.8% ± 0.7%	~31% of MI survives geometry removal
ΔMI_sector	0.17 bits	Local structure coupling
Z-Score	1252 ± 146	p < 10⁻¹⁰⁰ (highly significant)
Time-shift control	>95% reduction	Confirms temporal coherence

Temperature-Ordered Coupling

Strongest local coupling between thermally adjacent layers:

193-211 Å (1.2-2.0 MK): ΔMI_sector = 0.73 bits
171-193 Å (0.6-1.2 MK): ΔMI_sector = 0.39 bits

Chromospheric (304 Å) and flare channels (94, 131 Å) show weaker, activity-dependent coupling.

State-Space Dynamics

Regime	Participation Ratio	Volume	Entropy
Quiet	5.37	1.7×10⁵	1.88 bits
Active	4.85	4,139	1.78 bits
Flare	3.11	486	1.34 bits

Key finding: Flares contract the state space (0.58× dimensionality, 360× volume reduction), channeling dynamics through fewer degrees of freedom.

Cross-Instrument Validation (STEREO-A/EUVI)

180° cross-hemisphere validation establishes temperature-ordered coupling as an intrinsic organizational principle:

Instrument	Separation	Rank Correlation
SDO/AIA vs STEREO-A/EUVI	180°	90.6%

Absolute amplitudes differ (ratio 0.48–0.76) due to instrumental calibration
Ranking preserved: coronal pairs strongest, chromospheric coupling weakest
Independent of viewing geometry, active region population, or instrument

Regime-Switching & Hysteresis

Operator difference: ‖A_F − A_N‖ = 2.90 (distinct flare dynamics)
Early warning: Residual r(t) exceeds threshold before X-ray peak
Hysteresis: ‖A_NF − A_FN‖ = 4.93 (irreversible transition)
Post-flare shift: System occupies new attractor (+108% in I₅)

Visualizations

Figure 1 — Effect of Geometric Normalization

Global mutual information (MI) between AIA EUV channels before and after geometric normalization. Left: MI on original images; Right: MI on residual images after radial profile normalization. Approximately 70% of apparent MI is removed, while a stable residual component remains.

Figure 2 — Spatial Distribution

Spatial maps of mutual information between 193 Å and 211 Å channels on an 8×8 grid. Left: Original MI showing strong limb bias. Right: Residual MI after geometric normalization. Stars indicate top residual MI cells, corresponding to active regions.

Figure 3 — Null Model Decomposition

Mutual information values under progressively restrictive null models: global shuffle (destroys all structure), ring shuffle (preserves radial statistics), sector shuffle (preserves coarse geometry). The difference ΔMI_sector quantifies local coupling beyond geometry. Error bars indicate standard deviation over time.

Figure 4 — Coupling Matrix

Geometry-controlled local coupling matrix (ΔMI_sector) for seven AIA EUV channels. Channels ordered by characteristic formation temperature. Stronger coupling is observed between thermally adjacent channels, consistent with magnetically mediated interactions between neighboring layers.

Figure 5 — Flare Event Analysis

Geometry-controlled coupling during an X9.0 solar flare (2024-10-03). Time evolution of the local coupling metric ΔMI_sector for selected EUV channel pairs across pre-flare, flare, and post-flare phases (left). The flare peak is marked by the dashed line. Contrary to a naive expectation of uniformly increased coupling during extreme activity, most channel pairs exhibit reduced coupling during the flare peak. Percentage changes from pre-flare to flare conditions are shown on the right. Only a small subset of thermally adjacent channels (e.g. 171–211 Å) shows enhanced coupling, indicating selective reorganization rather than global amplification of multichannel structure.

Figure 6 — Regime-Switching Dynamics

Regime-switching dynamics of the solar state vector during an X-class flare. (A) Residual r(t) quantifying deviations from quiet-regime operator—exceeds threshold prior to X-ray peak. (B) Difference between flare and quiet transition operators. (C) Eigenvalue spectrum showing fast–slow manifold separation. (D) State-space trajectory demonstrating hysteresis and post-flare attractor shift.

Figure 7 — Network Phase Transitions

Network-level phase transitions during X1.9 flare. (A) Number of significant coupling pairs over time. (B) Network density and clustering coefficient. (C) Phase-space trajectory showing pronounced hysteresis. (D) Rate of change highlighting collapse and reconnection timing.

Figure 8 — Redundancy Structure

Redundancy and functional clustering. (A) Correlation matrix of coupling strengths. (B) Hierarchical clustering identifying four functional groups. (C) Stability backbone of persistent channel pairs. (D) Network of redundant coupling relationships.

Figure 9 — State Space Contraction

State-space contraction during flares. (A) PCA projection showing quiet (green), active (orange), flare (red) regimes. (B) Participation ratio by regime. (C) Volume contraction (>100×). (D) Entropy reduction indicating constraint rather than chaos.

Figure 10 — Antipodal Validation (STEREO)

Time-synchronized antipodal validation of thermal coupling hierarchy. (a) Opposition geometry (2011-02-06): STEREO-A views far hemisphere, SDO/AIA views near hemisphere. (b) Temperature-ordered coupling for three pair types. (c) Scatter comparison showing ρ = 0.906 rank agreement despite amplitude differences (×0.48–0.76). (d) Rank preservation across instruments confirms intrinsic organizational principle.

Flare Analysis

Analysis of the X9.0 flare (October 3, 2024) reveals a key insight: extreme events reduce coupling rather than increasing it.

Phase	n	94Å Intensity	ΔMI_sector (94-131)
Pre-Flare	13	5.4	0.098 bits
Flare	4	4.1	0.073 bits
Post-Flare	13	4.3	0.022 bits

Key Changes During Flare:

Pair	Change	Interpretation
171-211 Å	+19.4%	Exception: enhanced coronal coupling
193-211 Å	−29.4%	Coronal organization breakdown
94-131 Å	−25.1%	Flare channel decoupling
335-131 Å	−47.2%	Hot plasma disruption

Interpretation: Reduced coupling during flares does not contradict physical expectations—it reflects the breakdown of coherent multichannel organization during rapid magnetic reconfiguration. The metric measures structural organization, not activity intensity.

Implications

Space-Weather Forecasting

The operator residual r(t) provides an early-warning indicator that precedes conventional X-ray flare signatures, detecting destabilization before large-scale energy release.

Physical Modeling

Solar flares are regime switches, not perturbations. Models must account for distinct dynamical laws in quiet vs. eruptive states.

Structural Memory

Post-flare hysteresis demonstrates that eruptive events leave lasting imprints on coronal organization—the system does not return to its pre-flare configuration.

Reduced-Order Modeling

State-space contraction during flares (PR 5.37→3.11) enables low-dimensional models that capture eruptive dynamics with fewer degrees of freedom.

Methods

Hierarchy of Null Models

MI_global < MI_ring < MI_sector < MI_original
    ↓          ↓          ↓           ↓
  noise    radial    azimuthal     local

Component	Calculation	Meaning
Radial	MI_ring − MI_global	Disk geometry
Azimuthal	MI_sector − MI_ring	Coarse angular structure
Local	MI_original − MI_sector	Genuine spatial coupling

Mutual Information

I(X;Y) = Σ p(x,y) log₂ [p(x,y) / p(x)p(y)]

Estimated via histogram discretization (64 bins), reported in bits.

Geometric Normalization

Per-frame radial mean profile removal:

R(r,θ) = I(r,θ) / ⟨I(r)⟩

Instruments & Channels

SDO/AIA (Primary)

Wavelength	Temperature	Region
304 Å	0.05 MK	Chromosphere
171 Å	0.6 MK	Quiet Corona
193 Å	1.2 MK	Corona
211 Å	2.0 MK	Active Regions
335 Å	2.5 MK	Hot Active Regions
94 Å	6.3 MK	Flares
131 Å	10 MK	Flares

STEREO-A/EUVI (Validation)

Wavelength	AIA Equivalent	Temperature
304 Å	304 Å	0.05 MK
171 Å	171 Å	0.6 MK
195 Å	193 Å	1.2 MK
284 Å	211 Å	2.0 MK

Installation

git clone https://github.com/lubeschanin/solar-seed.git
cd solar-seed
uv sync

# For real solar data (SDO/AIA, STEREO)
uv sync --extra sunpy

Quick Start (Interactive CLI)

The easiest way to use Solar Seed is through the interactive menu:

# Linux / macOS
./solar-seed

# Windows
solar-seed.bat

This opens a user-friendly menu:

  ╭─────────────────────────────────────────────╮
  │  🌞 SOLAR SEED 🌱                           │
  │  Mutual Information Analysis of the Sun     │
  ╰─────────────────────────────────────────────╯

  [1]  Quick Test (synthetic data, ~2 min)
  [2]  Multi-Channel Analysis (21 wavelength pairs)
  [3]  Rotation Analysis (segment-based, scalable)
  [4]  Flare Analysis (X9.0 Event)
  [5]  Render Sun Images (download + visualize)
  [6]  Early Warning System (real-time monitoring)
  [7]  Reports (daily/weekly summary, precursor stats)
  [8]  Status: Check running analysis
  [9]  View Results
  [q]  Quit

Features:

Segment-Based Analysis: Each day analyzed independently, scalable to 100+ days
Checkpoint/Resume: Long analyses save progress automatically
Auto-Push: Git push segments for cross-system resume (--auto-push)
Timezone Support: Enter local times with automatic UTC conversion
Mirror Fallback: Automatic failover to backup data sources (ROB, SDAC, CfA)

Usage (Command Line)

# Hypothesis test with controls
uv run python -m solar_seed.hypothesis_test --spatial --controls

# Reproducible run with reports
uv run python -m solar_seed.real_run --hours 6 --synthetic

# Multi-channel analysis (7 channels, 21 pairs)
uv run python -m solar_seed.multichannel --hours 24

# With real AIA data
uv run python -m solar_seed.multichannel --real --hours 1 --start "2024-01-15T12:00:00"

# Final analyses
uv run python -m solar_seed.final_analysis

# Segment-based rotation analysis (recommended, scalable)
uv run python -m solar_seed.final_analysis --segments --start 2025-12-01 --end 2025-12-27
uv run python -m solar_seed.final_analysis --segment 2025-12-15  # Single day
uv run python -m solar_seed.final_analysis --aggregate           # Combine segments
uv run python -m solar_seed.final_analysis --convert-checkpoint  # Convert legacy data

# Legacy rotation analysis (monolithic, with checkpoint)
uv run python -m solar_seed.final_analysis --rotation --start "2024-01-01"

# Flare analysis (X9.0 event)
uv run python -m solar_seed.flare_analysis --real

# Render sun images (with timezone support)
uv run python -m solar_seed.render_sun --date "08.03.2012" --time "14:00" --timezone Europe/Berlin

# Generate figures
uv run python -m solar_seed.visualize --output figures/

# STEREO cross-instrument validation
uv run python scripts/stereo_sync_native.py

Early Warning System

Real-time space weather monitoring with ΔMI coupling analysis:

# Set your location (one-time setup)
uv run python scripts/early_warning.py location          # Interactive
uv run python scripts/early_warning.py location berlin   # Direct

# Minimal alert view (operators)
uv run python scripts/early_warning.py check -m

# Full scientific dashboard
uv run python scripts/early_warning.py check -c

# With STEREO-A advance warning (~3.9 days ahead)
uv run python scripts/early_warning.py check -c -s

# Continuous monitoring (5-minute interval)
uv run python scripts/early_warning.py monitor -c -i 300

# Database statistics & correlations
uv run python scripts/early_warning.py stats
uv run python scripts/early_warning.py correlations

Commands:

Command	Description
`check`	🔍 Single status check (use `-m` for minimal, `-c` for coupling)
`monitor`	📡 Continuous monitoring with periodic updates
`location`	📍 Set/show your location for personal relevance
`stats`	📊 Show database statistics
`correlations`	📈 Show coupling-flare correlations

Options:

Option	Short	Description
`--coupling`	`-c`	Include SDO/AIA coupling analysis
`--stereo`	`-s`	Include STEREO-A EUVI (~3.9 days ahead)
`--minimal`	`-m`	Minimal alert view (only actionable info)
`--location`	`-l`	Show personal relevance (or use `location` command)
`--interval`	`-i`	Monitoring interval in seconds (default: 60)
`--no-db`		Disable database storage

Display Modes:

Mode	Command	Shows
Minimal	`check -m`	193-211 status, trend, CLEAR/CAUTION/BREAK
Full	`check -c`	All channels, Anomaly levels, Phase, GOES, Solar Wind
Personal	`check -m -l berlin`	+ Day/night status, radio/GPS risk

Anomaly Level (Statistical):

NORMAL: |z| < 2σ
ELEVATED: 2-4σ
STRONG: 4-7σ
EXTREME: > 7σ

Phase (Interpretive):

Phase	Icon	Meaning	Trigger
`BASELINE`	🟢	Thermal & structural quiet	GOES quiet, \|z\| < 3
`ELEVATED-QUIET`	🟢	Structurally active but stable	\|z\| > 3, stable trends
`POST-EVENT`	🟣	Non-flaring but reorganizing	GOES quiet, \|z\| > 5
`RECOVERY`	🟡	Decaying activity	GOES falling
`PRE-FLARE`	⚠️	Destabilization detected	Negative z + GOES rising
`ACTIVE`	🔴	Ongoing energy release	GOES M/X-class

Parallel Classification: The system runs two classifiers in parallel for empirical validation:

GOES-only: Traditional flux-based (current operational standard)
ΔMI-integrated: Experimental coupling-based (may detect events GOES misses)

Divergences are logged to the database for correlation analysis with subsequent flares.

Personal Relevance:

Day side: Radio/GPS effects affect you NOW (~8 min latency)
Night side: Only geomagnetic effects (15-48h latency)
Aurora possible at high latitudes when Kp ≥ 7

Data Sources:

GOES X-ray flux (NOAA SWPC) — flare classification
DSCOVR solar wind plasma & magnetic field (L1 point)
SDO/AIA multichannel coupling — pre-flare detection
STEREO-A EUVI (51° ahead) — 2-4 day advance warning
NOAA Space Weather Alerts

Control Tests

Test	Purpose	Result
C1: Time-Shift	Temporal decoupling	>95% MI reduction
C2: Ring/Sector	Shuffle hierarchy	Confirmed
C3: PSF/Blur	Resolution sensitivity	<20% at σ=1px
C4: Co-Alignment	Registration check	Peak at (0,0)

Output

results/
├── real_run/
│   ├── timeseries.csv          # MI time series
│   ├── controls_summary.json   # C1-C4 results
│   ├── run_metadata.json       # Run configuration
│   └── spatial_maps.txt        # MI maps + hotspots
├── multichannel/
│   ├── coupling_matrices.txt   # 7×7 coupling matrix
│   ├── coupling_matrices.json  # Machine-readable
│   ├── pair_results.csv        # All 21 pairs ranked
│   └── temperature_coupling.txt
├── multichannel_real/          # Same structure, real AIA data
├── flare/
│   ├── flare_analysis.txt      # X9.0 flare phase comparison
│   └── flare_analysis.json
├── rotation/
│   ├── segments/               # Segment-based analysis (recommended)
│   │   ├── 2025-12-01.json     # Day 1 raw data + stats
│   │   ├── 2025-12-02.json     # Day 2 ...
│   │   └── ...
│   ├── rotation_analysis.txt   # Aggregated results
│   ├── rotation_analysis.json
│   ├── coupling_evolution.csv  # Time series for all pairs
│   └── checkpoint.json         # Legacy checkpoint (optional)
├── final/
│   ├── timescale_comparison.txt
│   ├── timescale_comparison.json
│   ├── activity_conditioning.txt
│   └── activity_conditioning.json
├── stereo/
│   ├── stereo_validation_2011-02-06.json      # STEREO-A/EUVI validation
│   └── stereo_validation_2011-02-06_native.json  # Native resolution
├── state_space_analysis.json   # Dimensionality metrics by regime
├── redundancy_analysis.json    # Channel redundancy structure
└── hypothesis_test_results.json

figures/
├── figure1_geometric_normalization.png
├── figure2_spatial_distribution.png
├── figure3_null_model_decomposition.png
├── figure4_coupling_matrix.png
├── figure5_flare_phases.png
├── figure6_operator_dynamics.png
├── figure6_stereo_validation.png          # Cross-instrument validation
├── figure7_phase_transitions.png
├── figure8_redundancy_structure.png
└── figure9_state_space.png

scripts/
├── early_warning.py            # Real-time space weather CLI (Typer + Rich)
├── figure9_state_space.py      # State-space visualization
├── stereo_prototype.py         # STEREO-A/EUVI cross-validation
├── stereo_sync_native.py       # Native resolution STEREO analysis
└── generate_pdf.py             # PDF generation from PAPER.md

Project Structure

src/solar_seed/
├── cli.py               # Interactive CLI menu
├── render_sun.py        # Sun image rendering with timezone
├── mutual_info.py       # MI computation (pure NumPy)
├── null_model.py        # Shuffle-based null models
├── radial_profile.py    # Radial profile subtraction
├── spatial_analysis.py  # Spatial MI maps
├── control_tests.py     # C1-C4 + sector shuffle
├── real_run.py          # Reproducible pipeline
├── hypothesis_test.py   # Main test runner
├── collector.py         # Time series collector
├── multichannel.py      # 7-channel coupling matrix, AIA loading
├── flare_analysis.py    # X9.0 flare event analysis
├── final_analysis.py    # Timescale + activity + rotation
├── visualize.py         # Publication figures
├── data_loader.py       # Data loading utilities
├── monitoring/          # Early warning system components
│   ├── db.py            # SQLite monitoring database
│   ├── coupling.py      # CouplingMonitor with baselines
│   ├── detection.py     # Break detection & classification
│   ├── formatting.py    # Rich terminal output
│   ├── validation.py    # Data quality gates
│   └── constants.py     # Thresholds (MIN_MI, MIN_ROI_STD)
└── data_sources/        # Data loading modules
    ├── aia.py           # SDO/AIA full-res via VSO
    ├── synoptic.py      # AIA synoptic (1k, direct JSOC)
    └── stereo.py        # STEREO-A/EUVI loader

Limitations

MI quantifies dependence, not causality
Histogram MI introduces finite-sample bias (mitigated by null-model comparisons)
Radial normalization assumes approximate radial symmetry
ΔMI_sector does not identify mechanisms; additional diagnostics required

Data Sources

NASA SDO/AIA: https://sdo.gsfc.nasa.gov/
STEREO-A/EUVI: https://stereo.gsfc.nasa.gov/
AIA Level 1.5: Via SunPy/aiapy
ML Dataset: https://registry.opendata.aws/sdoml-fdl/

Citation

If you use this work, please cite:

Geometry-controlled mutual information reveals temperature-ordered coupling in the solar atmosphere (2025) https://github.com/lubeschanin/solar-seed

@software{solar_seed_2025,
  author = {Lubeschanin},
  title = {Solar Seed: Geometry-controlled mutual information analysis of SDO/AIA},
  year = {2025},
  url = {https://github.com/lubeschanin/solar-seed}
}

License

GNU General Public License v3.0

Careful separation of geometric, statistical, and local contributions is essential for interpreting multichannel dependencies.

Name		Name	Last commit message	Last commit date
Latest commit History 380 Commits
docs		docs
figures		figures
results		results
scripts		scripts
src/solar_seed		src/solar_seed
tests		tests
.gitignore		.gitignore
LICENSE		LICENSE
PAPER.md		PAPER.md
README.md		README.md
pyproject.toml		pyproject.toml
solar-seed		solar-seed
solar-seed.bat		solar-seed.bat
uv.lock		uv.lock

Folders and files

Latest commit

History

Repository files navigation

Solar Seed

Abstract

Key Results

Temperature-Ordered Coupling

State-Space Dynamics

Cross-Instrument Validation (STEREO-A/EUVI)

Regime-Switching & Hysteresis

Visualizations

Figure 1 — Effect of Geometric Normalization

Figure 2 — Spatial Distribution

Figure 3 — Null Model Decomposition

Figure 4 — Coupling Matrix

Figure 5 — Flare Event Analysis

Figure 6 — Regime-Switching Dynamics

Figure 7 — Network Phase Transitions

Figure 8 — Redundancy Structure

Figure 9 — State Space Contraction

Figure 10 — Antipodal Validation (STEREO)

Flare Analysis

Implications

Space-Weather Forecasting

Physical Modeling

Structural Memory

Reduced-Order Modeling

Methods

Hierarchy of Null Models

Mutual Information

Geometric Normalization

Instruments & Channels

SDO/AIA (Primary)

STEREO-A/EUVI (Validation)

Installation

Quick Start (Interactive CLI)

Usage (Command Line)

Early Warning System

Control Tests

Output

Project Structure

Limitations

Data Sources

Citation

License

About

Topics

Resources

License

Uh oh!

Stars

Watchers

Forks

Releases 1

Packages 0

Uh oh!

Contributors

Uh oh!

Languages

Packages