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Improving Solar EUV Irradiance Modeling with Differential Emission Measure Informed Spectra

This paper presents a hybrid modeling approach that integrates physics-informed differential emission measures with traditional proxy methods to significantly improve the accuracy of solar EUV irradiance predictions, particularly for high-temperature coronal lines during M- and X-class flares.

Original authors: Courtney L. Peck, Shah M. Bahauddin, Daniel B. Seaton, Janet L. Machol, Ed Thiemann, Mark Cheung

Published 2026-07-07

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CC BY 4.0

Original authors: Courtney L. Peck, Shah M. Bahauddin, Daniel B. Seaton, Janet L. Machol, Ed Thiemann, Mark Cheung

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Sun as a giant, complex orchestra. Sometimes it plays a steady, quiet melody (the "quiet sun"), and sometimes it hits a sudden, deafening crescendo (a solar flare). The music it plays is made of invisible light called Extreme Ultraviolet (EUV). This light is crucial because when it hits Earth, it acts like a cosmic wind, pushing against our satellites and messing up our GPS and radio signals.

The problem is that we don't have a perfect microphone to record this solar music all the time. Our instruments break, they miss certain notes, or they only listen to specific parts of the song. So, scientists have to guess what the missing music sounds like.

The Old Way: Guessing by Association
For a long time, scientists used a method called "proxy modeling." Think of this like trying to guess the temperature of a whole room by looking at just one thermometer in the corner. If that thermometer goes up, you assume the whole room is getting hotter.

This works okay when the room is stable. But when a solar flare hits, the "room" (the Sun's atmosphere) changes incredibly fast. The heat isn't uniform; it's a chaotic mix of cool gas and super-hot plasma. The old "one thermometer" method struggles here. It tries to guess the complex, hot notes of the flare based on simple, linear relationships, and it often gets the high-pitched, high-temperature notes wrong.

The New Way: A Hybrid Orchestra Conductor
This paper introduces a new, smarter way to fill in the missing music. The authors created a "hybrid model" that combines two different approaches:

The Physics Part (The Conductor): For the hot, chaotic parts of the Sun (the corona), they use a technique called Differential Emission Measure (DEM). Imagine this as a conductor who doesn't just look at one thermometer but listens to the entire orchestra to figure out exactly how many musicians are playing which notes at what volume. They use data from NASA's SDO satellite to map out the temperature of the solar gas. Then, they use a "recipe book" of physics (atomic databases) to calculate exactly what the light should look like based on that temperature map. This is great for capturing the sudden, intense heat of flares.
The Pattern Part (The Backup Singer): For the cooler, lower parts of the Sun (the chromosphere), the physics recipe is harder to apply because the gas is thick and opaque. Here, they stick to the old "proxy" method—using patterns and correlations from known measurements to fill in the gaps.

The Result: A Better Prediction
The researchers tested this new hybrid model against the old proxy-only model using real data from 2010 to 2013.

When the Sun was quiet: Both models did about the same job.
When the Sun flared: The new hybrid model was a clear winner. Because it used the "conductor" approach to understand the temperature of the flare, it could predict the intense, high-energy light much more accurately.

Specifically, for the hottest, most energetic parts of solar flares (the X-class and M-class flares), the new model reduced the prediction error by up to three times compared to the old method. It was able to capture the "sharp edges" of the flare that the old model smoothed over or missed entirely.

Why It Matters
The paper concludes that while we can't always have a perfect instrument recording every second of solar light, we can build a better "virtual instrument." By mixing the physical understanding of how hot gas behaves (DEM) with the pattern recognition of traditional methods (proxies), we get a much clearer picture of the Sun's energy output, especially when it's being most dangerous to our technology in space.

The authors note that this model works well but has limits: if the solar flare is so massive that it "blinds" the camera (saturates the sensor), the model can't see the full picture perfectly. However, for most events, this hybrid approach is a significant upgrade in accuracy.

Technical Summary: Improving Solar EUV Irradiance Modeling with Differential Emission Measure Informed Spectra

Problem Statement
Solar extreme ultraviolet (EUV) irradiance is a primary driver of space weather, influencing satellite drag, radio communications, and GPS accuracy. However, direct measurements of solar EUV irradiance are often intermittent and spectrally inhomogeneous due to instrument limitations and failures (e.g., the loss of the SDO/EVE MEGS-A channel in 2014). Consequently, models are required to fill spectral and temporal gaps. Existing models are predominantly empirical, relying on proxy-based methods that utilize linear correlations between observed emission lines and unobserved wavelengths. While effective under quiescent conditions, these proxy methods struggle to capture dynamic irradiance variations during solar flares. This failure stems from the relative infrequency of flares used to derive correlations and the steep temporal temperature gradients experienced during impulsive events, which often exceed the sampling capabilities of available proxies, particularly for high-temperature coronal plasma.

Methodology
The authors propose a hybrid modeling framework that integrates physics-informed forward modeling with traditional empirical proxy methods. The model is trained and tested using Level 1 data from the Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA) and Level 2B data from the EUV Variability Experiment (EVE), spanning May 2010 to July 2013.

The hybrid approach combines two distinct components as defined in Equation 5:

Proxy Component ( $I_{proxy}$ ): This term utilizes simulated GOES-R EXIS EUVS measurements (derived by convolving EVE and TIMED-SEE spectra with EUVS bandpasses) to capture optically-thick chromospheric and continuum emission. These inputs represent traditional proxy measurements.
DEM Component ( $I_{DEM}$ ): This term utilizes Differential Emission Measure (DEM) analysis to capture optically-thin coronal emission. Disk-integrated AIA images from six coronal channels are used to infer a global DEM. This DEM is then forward-modeled using the CHIANTI atomic database to generate a spectrally resolved irradiance estimate ( $I_{DEM}(\lambda)$ ).

The final model equation is a linear combination of the forward-modeled DEM spectra and the proxy measurements, with coefficients determined via multiple linear regression. The model is trained on a dataset split to include specific reserved test cases (quiet sun, active region, M-class, and X-class flares) to ensure unbiased evaluation of temporal generalization.

Key Contributions and Results
The study demonstrates that incorporating DEM-derived information significantly improves the accuracy of solar EUV irradiance modeling, particularly during flare events.

Performance During Flares: The hybrid model outperforms the proxy-only model across all flare classes (C, M, and X), with the most substantial gains observed during X-class flares. For high-temperature coronal lines (e.g., Fe XX at 13.3 nm, log T ≈ 6.97), the hybrid model reduces the mean absolute percentage error by a factor of approximately three compared to the proxy-only model during X-class flares (e.g., reducing error from ~18.7% to ~5.6%).
Temperature Dependence: The improvement is strongly correlated with formation temperature. For lines formed at high temperatures (log T > 6.7), the hybrid model maintains uniform error levels, whereas the proxy-only model exhibits systematically increasing errors toward hotter lines. Conversely, for cooler chromospheric and transition-region lines (log T < 5.5), both models perform similarly, as the hybrid model is dominated by the proxy component in these regimes where DEM assumptions for optically-thin plasma are less constraining.
Temporal Resolution: The hybrid model more accurately reproduces the temporal evolution and amplitude of irradiance during impulsive events. While both models smooth high-frequency noise (a characteristic of regression-based approaches), the hybrid model captures the peak emission of flares more faithfully than the proxy-only approach, which tends to underestimate peak intensities.
Limitations: The authors note that the hybrid model's performance can degrade during the rise and decay phases of X-class flares, potentially due to AIA detector saturation which limits the accuracy of DEM reconstruction. Additionally, during quiet sun conditions, the proxy-only model occasionally outperforms the hybrid approach for specific lines, likely due to increased uncertainty in DEM inversion when signal-to-noise ratios are low.

Significance
The paper concludes that neither proxy-based nor DEM-based approaches alone are sufficient for robust spectral reconstruction across all solar conditions. The hybrid framework provides a more complete and reliable representation of the solar EUV spectrum by leveraging the physical constraints of coronal thermodynamics (via DEMs) while retaining the empirical fidelity of proxies for optically-thick regions.

The authors assert that this approach offers a pathway to routine, physics-informed reconstructions of solar EUV spectra without reliance on continuous high-resolution spectrographs. By utilizing existing real-time observations (such as AIA or SUVI imaging and EUVS narrowband measurements), the framework can generate short-wavelength spectral irradiance estimates essential for space weather modeling and thermosphere-ionosphere studies. The work suggests that future operational implementations could utilize GOES-R SUVI and EXIS data to maintain these capabilities beyond the current SDO mission lifetime.

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