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REVIEW 4 major objections 6 minor 17 references

SITES: Solar Iterative Temperature Emission Solver for differential emission measure inversion of EUV observations

T0 review · 4 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read SITES recovers coronal temperature structure from EUV images using a simple iterative solver.

desk verdict A well-designed DEM solver with honest tests, but the printed Eq. 4 is wrong—the paper's own results cannot follow from the stated algorithm without a fix and released code. read the letter →

arxiv 1908.07773 v1 pith:OLD4SEBN submitted 2019-08-21 astro-ph.SR

Huw Morgan , James Pickering This is my paper · ORCID
classification astro-ph.SR
keywords differentialemissionmeasuresolarcoronaEUVimagingAIA/SDOtemperatureresponsefunctionsiterativeinversionfractionalopticallythinplasma
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Solar EUV images of the optically thin corona carry temperature information only indirectly: each channel mixes emission from many temperatures. This paper presents SITES, a differential emission measure (DEM) inversion that turns several EUV channel intensities into a temperature profile of the emitting plasma. The paper aims to show that a direct, weighted redistribution of observed intensities according to each channel's temperature response, refined by iterating on residuals, can recover model DEMs from synthetic AIA observations with accuracy comparable to established methods. It also shows the solver is fast enough for full-disk, long-duration datasets and introduces fractional emission measure maps that make temperature dominance in coronal structures visible at a glance.

What carries the argument

The core object is the relative temperature response $S_{ij} = w_i R_{ij} / (\sum_i w_i R_{ij})$, built from each channel's response function $R_{ij}$ weighted by measurement and calibration errors. Equation (4) converts observed intensities $I_i$ into an initial DEM by distributing each channel's intensity across temperature according to $R_{ij}$, combining channels through $S_{ij}$, and convolving with a narrow Gaussian in logarithmic temperature. The iteration then computes modelled intensities $M_i = \sum_j D_j R_{ij} \Delta T_j$, feeds the residual $I_i - M_i$ back through the same redistribution, and clips negative DEM values to zero, stopping when the weighted mean absolute residual falls below a threshold such as 4%. This iterative residual-correction loop, together with the single smoothing width, is what carries the whole argument.

What would settle it

A blind benchmark on synthetic AIA data spanning central temperatures from log T = 5.7 to 7.0 and widths from log T = 0.1 to 0.35, with Poisson noise added, would settle the accuracy claim: the central claim is wrong if SITES systematically shows input–output DEM correlations below 95% inside the region the paper marks as reliable, or if its measured residuals do not fall below the convergence threshold it reports.

Watch

Extended reading notes

Core claim

The central claim is that SITES reconstructs a DEM by first spreading each measured intensity across temperature in proportion to that channel's response function, combining the channels with inverse-noise weights, then repeatedly adding DEM corrections built from the residual intensities until the weighted residuals drop below a threshold. In tests on synthetic AIA observations, the recovered DEMs correlate at 95–98% with the input model across broad ranges of peak temperature and width, with median deviations around 12–26% for representative single- and double-Gaussian targets. The method is deliberately minimal: the only user-selected parameter is the width of a Gaussian smoothing kernel in logarithmic temperature, with positivity enforced by thresholding. The paper concedes two limits—very narrow DEM peaks are not well recovered at any temperature, and temperatures below about 0.5 MK are not reliable with AIA data—and argues these limits follow from the instrument's broad response functions rather than from the solver. On identical synthetic inputs, SITES matches or outperforms both a sparse-basis method and a Tikhonov-regularized method used as benchmarks, while running at roughly a thousand DEMs per second at the routinely used convergence threshold.

Load-bearing premise

The reconstruction inherits whatever bias lives in the AIA temperature response functions; if those functions are wrong, the iterative fitting cannot correct it, because the method only tries to match intensities computed with the same functions.

Editorial extensions

If this is right

  • Long time-series of AIA full-disk DEM maps become practical: at about 1,000 profiles per second, a full 4k disk can be processed in minutes to hours rather than days.
  • Multi-channel EUV instruments beyond AIA can use the same solver directly, provided their temperature response functions and error estimates are known.
  • The fractional emission measure visualization gives a standard, normalized way to compare which temperatures dominate in coronal holes, quiet Sun, and active region cores, independent of total emission.
  • The method's reliance on a single smoothing parameter makes it easier to reproduce and less dependent on analyst choices than methods with several tuning parameters.
  • Broad multithermal coronal structures are the natural target; narrow isothermal-like plasmas and sub-0.5 MK material should be interpreted with caution.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct extension is to feed SITES DEMs into rotational tomography: using multiple viewpoints would address the line-of-sight bias the paper notes for off-limb regions, and could also regularize narrow peaks.
  • The error bars from Equation (6) omit smoothing and iteration effects; the paper's own low-signal test shows underestimated uncertainty above ~2 MK, so users should treat those error bars as optimistic in faint regions.
  • The real 0.5 MK floor is a property of AIA's response functions, not of the algorithm; applying SITES to observations with stronger low-temperature sensitivity would likely push the useful range lower, a testable prediction.
  • Because the iteration is a residual-correction map with positivity clipping, it should be possible to prove convergence conditions, which might let future users choose thresholds automatically rather than by trial.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper presents SITES, an iterative differential emission measure (DEM) inversion method for AIA EUV observations. The method builds an initial DEM by backprojecting each channel's intensity across temperature according to the channel response, then iteratively updates the DEM using intensity residuals with positivity and smoothing constraints. The authors test SITES on synthetic DEMs (single and multi-Gaussian, with and without noise), measure its speed, compare it with the methods of Cheung et al. (2015) and Hannah & Kontar (2012), and apply it to full-disk AIA data. They also introduce a fractional emission measure (FEM) visualization. The central claims are that SITES is simple, fast (about 1000 DEMs per second), non-subjective apart from one smoothing parameter, and accurate for broad DEMs above ~0.5 MK, while performing poorly on narrow peaks and low-temperature DEMs.

Significance. If the method works as described, it is a useful addition to the DEM inversion toolbox: the synthetic validation is extensive, the authors explicitly characterize the failure modes (narrow peaks, temperatures below ~0.5 MK), and the uncertainty estimate is checked against Monte Carlo repetitions. The FEM visualization is a simple and effective idea for comparing temperature regimes across coronal structures. The speed and simplicity could make it practical for large AIA datasets. However, the central equation of the method as printed is not intensity-preserving, so the validation presented in Section 3 cannot be reproduced from the manuscript as written; this is a load-bearing issue that must be corrected before the results can be credited.

major comments (4)
  1. [Section 2, Eq. (4)] As printed, Eq. (4) cannot be the backprojection used in the paper. The per-channel term is I_i/(R_ij ΔT_j) times Σ_j (R_ij ΔT_j)^2, so for a single channel the forward-modeled intensity obtained by summing D_j R_ij ΔT_j over j is n_t I_i Σ_j (R_ij ΔT_j)^2, not I_i. The expression is also dimensionally inconsistent: it carries units of intensity times response, not DEM. The standard intensity-preserving backprojection would be I_i R_ij ΔT_j / Σ_j (R_ij ΔT_j)^2, with the sum in the denominator. Because no derivation or public code is provided, the text alone does not specify a valid, reproducible algorithm, and the convergence, timing, and comparison results in Section 3 cannot be traced to the stated equation. Please correct Eq. (4), provide a derivation, and state explicitly which expression was used in the synthetic tests.
  2. [Section 2, Eq. (6)] The quantity d_j defined in Eq. (6) is dimensionless: it is the square root of a weighted sum of squared relative errors (σ_i/I_i)^2 and ε_i^2. Yet it is presented as 'the final DEM uncertainty' and is compared in Figures 2, 9, and 10 to the absolute spread of DEMs, which has units cm^-5 K^-1. If d_j is intended as a relative uncertainty, this must be stated and the plotted error bars must be multiplied by the DEM value; if it is intended as an absolute error, the equation is incomplete. This issue directly affects the validation claim in Section 3.4 that the uncertainty estimate 'reflects well the true variation of the output DEMs.'
  3. [Sections 1 and 5] The claim that SITES is 'non-subjective' and that the smoothing kernel width is the only parameter affecting the result is overstated. The kernel width is chosen by trial and error with the criterion that it be minimal 'whilst still resulting in smooth DEMs', which is a subjective regularization choice. Moreover, Section 3.3 shows that the convergence threshold also affects both the fitted intensities and the output DEM (Figure 8a), so the convergence threshold is another parameter that influences the result. The non-subjectivity claim should be qualified to 'a single tunable regularization parameter plus a stopping criterion', and the dependence on the convergence threshold should be acknowledged in the summary.
  4. [Section 3.3] The text in Section 3.3 refers to a 'complex 3-Gaussian plus background' DEM, while the complex test in Section 3.2 is explicitly defined as two Gaussian peaks plus a constant background. This inconsistency makes it unclear which model was used for the speed and convergence-threshold tests. Please correct the description so that the number of Gaussians matches the actual test DEM.
minor comments (6)
  1. [Section 3.5] There is a typo: 'perofrmance' should be 'performance'.
  2. [Section 4.1] There is a typo: 'measurmeent' should be 'measurement'.
  3. [Section 2] The sentence following Eq. (4) says that integrating the individual DEMs over temperature would result in exactly the observed intensities; this statement is only true for the corrected form of the equation, not for the printed form. Please move this explanatory sentence next to the corrected equation.
  4. [General] The software is only available 'by email request to the authors'. For reproducibility, especially given the error in Eq. (4), please consider providing a version-controlled repository or a complete pseudocode listing that includes the exact update rule and convergence criterion.
  5. [Section 3.5] In the comparison with SMI, the plots show EM rather than DEM for the SMI output, and the text notes this in the caption; however, the y-axis labels are not visible in Figures 11a and 11b. Please ensure the figure axes make the EM/DEM distinction explicit.
  6. [Abstract] The abstract states 'about 1000 DEMs per second', but Section 3.3 reports this speed at a convergence threshold of 4%. The threshold dependence is shown in Figure 8b, so the abstract should either quote the speed with the associated threshold or mention that the speed is threshold-dependent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: SITES is benchmarked against externally defined model DEMs; no parameter is fitted to the test targets, and the only self-citations are contextual.

full rationale

The central inversion update (Eq. 4) and forward model (Eq. 5) are stated as independent definitions, and the method's adjustable smoothing kernel is explicitly a regularization choice: the paper says the width is found through trial and error with the criterion that the smoothing width is kept at a minimum 'whilst still resulting in smooth DEMs,' not by matching the benchmark DEMs. The Section 3 validation uses model DEMs defined by Eq. 7 and the two-Gaussian/background variants, compares the inversion to those targets through the independently defined correlation (Eq. 10) and deviation (Eq. 9), and compares SITES with the independent methods of Cheung et al. (2015) and Hannah & Kontar (2012) using identical response functions and synthetic measurements. The only self-citations (Morgan & Taroyan 2017 and Morgan & Druckmüller 2014) appear as background or image-processing context and do not carry the inversion argument. No fitted parameter is renamed as a prediction: the data-consistency residual is an iteration target, while the DEM-recovery claim is checked against externally constructed model DEMs, so the central results do not reduce to the method's own inputs.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The method introduces no new physical entities. Its free parameters are a smoothing kernel width chosen by trial and error and a convergence threshold chosen for practical use. The key axioms are the standard optically-thin, equilibrium assumptions and the accuracy of the AIA response functions, which are external inputs the paper does not independently verify.

free parameters (2)
  • Smoothing kernel width = 3.2 bins in logarithmic temperature
    The Gaussian smoothing kernel K has standard deviation 3.2 temperature bins over 43 bins spanning 0.07 to 20 MK. The authors state this value was found through trial and error, making it a subjective choice that affects the smoothness of the result.
  • Convergence threshold = 4% for real data (1% in tests)
    The iterative process stops when the weighted mean absolute residual ratio drops below this threshold. The paper tests thresholds from 1% to 32% and chooses 4% for real data as a balance of speed and accuracy, so the threshold is a user-selected parameter.
assumptions (4)
  • domain assumption The solar corona is optically thin in EUV, so measured intensities are line-of-sight integrals of the emission measure times temperature response.
    This is the basis for equation 5 and the entire inversion. It is standard in DEM analysis but is not proven in the paper.
  • domain assumption The AIA temperature response functions Rij, computed from CHIANTI atomic data and EVE calibration, are accurate.
    The paper uses response functions from Solarsoft without independent verification (Section 2). Any systematic error in these functions propagates directly into the DEM.
  • domain assumption The plasma is in thermal equilibrium with Maxwell-Boltzmann electron distributions, so the DEM formalism applies.
    The paper states 'using certain assumptions (e.g. Maxwell-Boltzmann distributions and thermal equilibrium)' in the introduction, and relies on CHIANTI line intensities calculated under these assumptions.
  • ad hoc to paper Positivity and smoothness are the only needed constraints to solve the underdetermined inversion.
    SITES imposes positivity by thresholding and smoothness via the Gaussian kernel. This is a modeling choice specific to this method, not derived from physics.

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Cite this review

Pith. "Pith review of SITES: Solar Iterative Temperature Emission Solver for differential emission measure inversion of EUV observations." pith.science (2026). https://pith.science/paper/OLD4SEBN

@misc{pith2026190807773,
  author       = {Pith},
  title        = {Pith review of: SITES: Solar Iterative Temperature Emission Solver for differential emission measure inversion of EUV observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OLD4SEBN}},
  note         = {Machine review of arXiv:1908.07773}
}
read the original abstract

Extreme UltraViolet (EUV) images of the optically-thin solar corona in multiple spectral channels give information on the emission as a function of temperature through differential emission measure (DEM) inversions. The aim of this paper is to describe, test, and apply a new DEM method named the Solar Iterative Temperature Emission Solver (SITES). The method creates an initial DEM estimate through a direct redistribution of observed intensities across temperatures according to the temperature response function of the measurement, and iteratively improves on this estimate through calculation of intensity residuals. It is simple in concept and implementation, is non-subjective in the sense that no prior constraints are placed on the solutions other than positivity and smoothness, and can process a thousand DEMs per second on a standard desktop computer. The resulting DEMs replicate model DEMs well in tests on Atmospheric Imaging Assembly (AIA) synthetic data. The same tests show that SITES performs less well on very narrow DEM peaks, and should not be used for temperature diagnostics below ~0.5MK in the case of AIA observations. The SITES accuracy of inversion compares well with two other established methods. A simple yet powerful new method to visualise DEM maps is introduced, based on a fractional emission measure (FEM). Applied to a set of AIA full-disk images, the SITES method and FEM visualisation show very effectively the dominance of certain temperature regimes in different large-scale coronal structures. The method can easily be adapted for any multi-channel observations of optically-thin plasma and, given its simplicity and efficiency, will facilitate the processing of large existing and future datasets.

Figures

Figures reproduced from arXiv: 1908.07773 by the authors.

Figure 1
Figure 1. (a) The temperature response of the seven AIA EUV channels, as given by the standard AIA calibration routines in Solarsoft, based on Chianti atomic data and normalised through cross-calibration with EVE data. This set is for date 2011/01/01. (b) The relative response as a function of temperature. At a given temperature, the relative responses sum to unity over all channels. It is convenient to include information on… view at source ↗
Figure 2
Figure 2. Comparing input (black) and output (red) DEM curves for the simple case of a single Gaussian in temperature (equation 7). The light red error bars show the uncertainty in the fitted DEM. The correlation c between the input and output DEM curves is defined as c = Pnt−1 j (Dj − D¯ j )(D0 j − D¯0 j ) qPnt−1 j (Dj − D¯ j ) 2 Pnt−1 j (D0 j − D¯0 j ) 2 (10) and is 98% for this simple test. Thus the position and width of t… view at source ↗
Figure 3
Figure 3. (a) Correlation c between input and SITES-inverted DEM profiles, (b) mean abso￾lute relative deviation TI between input measurement and output fitted measurement and (c) median absolute relative deviation TD of input and SITES-inverted DEM profiles. These are calculated for a range of centers and widths in logarithmic temperature of single-Gaussian DEM profiles. The dotted, dashed and dot-dashed lines in (a) show th… view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: Comparing input (black) and output (red) DEM curves for the complex case of two Gaussians in temperature and a constant background. The light red error bars show the uncertainty in the output DEM. peak at log T = 6.55. For the wide Gaussian profiles (solid lines), the …
Figure 5
Figure 5. Figure 5: DEM profiles formed from two Gaussians in logarithmic temperature plus a con￾stant background. The black lines are the input DEM, the red lines are the SITES DEM. The solid (dashed) lines are for wide (narrow) Gaussian profiles (0.35 and 0.1 in logarithmic temperature …
Figure 6
Figure 6. Figure 6: (a) Correlation c between input and SITES-inverted DEM profiles, (b) mean abso￾lute relative deviation TI between input measurement and output fitted measurement and (c) median absolute relative deviation TD of input and SITES-inverted DEM profiles. These are calculate…
Figure 7
Figure 7. Figure 7: As figure 6, but for the two narrow Gaussians. SOLA: ms.tex; 22 August 2019; 0:33; p. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: (a) The percentage median absolute relative deviation of the estimated DEM from the model DEM (crosses) and the relative measurement residuals (triangles) as a function of convergence threshold. These are calculated for a thousand DEMs, with the input measure￾ments var…
Figure 9
Figure 9. Figure 9: (a) Applying SITES a thousand times to noise-varying measurements gives a mean DEM (dotted line) and the standard deviation DEM (shaded area) at each temperature bin. The vertical error bars show the estimated error bars gained from equation 6, averaged over the thousa…
Figure 10
Figure 10. Figure 10: As figure 9, but for the very noisy case of a signal 10 times less intense. SOLA: ms.tex; 22 August 2019; 0:33; p. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_10.png]
Figure 11
Figure 11. Figure 11: Comparison of input target emission (black line), SITES (red line with error bars), Cheung et al (2015) (SMI, green lines) and Hannah & Kontar (2012) (blue line with error bars) for (a) the simple single Gaussian DEM of section 3.1 and (b) the multiple Gaussian DEM of…
Figure 12
Figure 12. Figure 12: (a) Correlation c between input and SITES-inverted DEM profiles, (b) mean abso￾lute relative deviation TI between input measurement and SITES output fitted measurement and (c) median absolute relative deviation TD of input and SITES-inverted DEM profiles. (d)-(f) Same…
Figure 13
Figure 13. Figure 13: As figure 12, but for the case of input data modulated by Poisson noise. These values show the mean calculated over 15 repetitions, with the intensity values varying randomly with an amplitude set by the Poisson uncertainty [PITH_FULL_IMAGE:figures/full_fig_p021_13.png]
Figure 14
Figure 14. Figure 14: A context image from 2015/01/01 03:00. All 7 AIA channels contribute to this composite, with the temperature response of each channel between 0.05 and 7.0MK specifying that channel’s contribution to the red, green and blue colour channels of the output images. The ima…
Figure 15
Figure 15. Figure 15: (a) An AIA 193 channel image from 2015/01/01 03:00. The dashed white line shows a heliocentric height of 1.45R , and the dashed red line shows a horizontal cut across the image. (b) The intensity along the dashed red line for the channel with the highest mean intensit…
Figure 16
Figure 16. Figure 16: Emission for four different temperatures as indicated in each panel. The field of view is curtailed to a maximum heliocentric distance of 1.15R . The color bars give EM in units of 1026cm−5 . is calculated from a DEM by F EMj = DEMj∆T P j DEMj∆T , (12) so the FEM in a…
Figure 17
Figure 17. Figure 17: Fractional emission (FEM) for four different temperatures as indicated in each panel. The field of view is curtailed to a maximum heliocentric distance of 1.15R . The color bars give FEM in %. The incentive for developing the method is to analyse large datasets, thus …

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