the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 Aug 2026
Beyond Spectral Smile: Comprehensive Imaging Spectrometer Wavelength Calibration from Atmospheric Features
Abstract. Accurate spectral calibration is essential for quantitative imaging spectroscopy, as even sub-nanometer wavelength errors can propagate into atmospheric correction and surface-property retrievals. Existing approaches for in-flight wavelength calibration typically assume simplified spectral parameterizations, limiting the complexity of wavelength variations that can be recovered from atmospheric absorption features. In this study, we investigate the information content of visible-to-shortwave infrared (VSWIR) observations for constraining instrument wavelength calibration using a Bayesian maximum a posteriori retrieval framework. Using nine high signal-to-noise EMIT (Earth Surface Mineral Dust Source Investigation) scenes acquired over spectrally homogeneous desert targets, we systematically evaluate spline-based wavelength calibration models with varying numbers and placements of spline knot points. Model performance is assessed using agreement with Zemax optical simulations, solution consistency across independent scenes, and leave-one-out cross-validation. All three evaluation criteria identify a four-knot spline representation as the optimal balance between model flexibility and stability, whereas more complex parameterizations exhibit increased sensitivity to knot placement and reduced reproducibility. Applying this optimal configuration independently across the detector array reveals coherent cross-track wavelength-dispersion variations that cannot be adequately represented by traditional uniform or simple spectral-smile corrections. Although the retrieved spatial variations are small—typically on the order of 1 % of a spectral channel width—they exhibit a structured saddle-shaped pattern that is consistent across scenes and indicative of genuine instrument behavior. These results demonstrate that atmospheric absorption features provide sufficient information to retrieve spatially varying wavelength calibration for modern VSWIR imaging spectrometers, supporting more accurate radiometric processing and motivating spatially resolved spectral calibration strategies for current and future spaceborne missions.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2026-4701', Anonymous Referee #1, 04 Sep 2026
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AC1: 'Reply on RC1', Mads Ahlebæk, 15 Oct 2026
L20 - In L4 this was expressed as 'visible-to-shortwave infrared'. Please, select just 1 way to express it.
We thank the reviewer for pointing out this consistency error, and we have corrected it.
L21 - There are more applications, such as gas retrievals. Please, rephrase as sth like 'a single instrument to address numerous applications such as...' or similar.
The phrasing has been been updated and now also include gas retrievals.
L26 - Any reference to back up this point?
We have added two references that backs our claim.
L36 - This sentence can be misleading because 'microns' can also be used to refer to the nomial central wavelength. Please, clarify that this is a mechanical movement.
The authors believe that the original wording already conveys that the micrometer-scale movements refer to physical displacements of the optical components. However, to make the optomechanical nature of these displacements more explicit, we have slightly revised the sentence accordingly.
L40 - 'based on' instead of 'with'?
This has been changed.
L40 - Do they only fit the atmosphere? and the surface? Please, clarify
We thank the reviewer for highlighting this ambiguity. The cited approaches do not fit atmospheric properties alone. Rather, atmospheric absorption features provide spectral references for estimating the instrument's wavelength positions and spectral response characteristics. The surface contribution to the measured radiance is also accounted for, although its treatment differs among methods. Specifically, Gao et al. (2004) assume a locally linear surface reflectance continuum, which is removed through continuum normalization before matching measured and modeled absorption features. Guanter et al. (2006) determine the wavelength shift by minimizing deviations between atmospherically corrected surface reflectance and its spectrally smoothed counterpart. Kuhlmann et al. (2016) jointly fit atmospheric absorber strengths, spectral calibration parameters, and a smooth albedo term representing surface reflectance and broadband atmospheric effects. Thus, surface reflectance is not neglected, but it is not necessarily retrieved independently in all approaches. We have revised the manuscript to explicitly clarify how the surface contribution is handled in these calibration methods.
L46 - and what about the distribution of sensitivity to the channel?
We thank the reviewer for the comment. In this study, the spectral response functions are assumed to be Gaussian, with their FWHM values retained from the initial instrument calibration. The retrieval focuses exclusively on adjustments to the channel center wavelengths, while the width and shape of the spectral response functions remain fixed. We have clarified this in both the Introduction and Methods sections.
* Wavelength dispersion is a term that is not well described here. Please, clarify the meaning of this term.
The term has been clarified as part of Reviewer 3, and also helps clarify some of Reviewer 1’s later comments.
By "wavelength-dispersions," we refer to the mapping between spectral channel position and center wavelength, including its variation across the focal plane array.
L51 - Where is this analysis coming from? Please, cite if there is a good reference that backs this up. If this is something that has been found and shown later in this work, please consider to leave it for the results/discussions/conclusion part.
We thank the reviewer for the comment. The statement refers to findings of the present study, which are demonstrated in the subsequent Results and Discussion sections, rather than findings from previous literature. We agree that these conclusions are more appropriately presented in those sections and have therefore revised the Introduction to focus on the objectives of the analysis rather than its outcomes.
2.1. - Please, consider to make some comments here about the central wavelength and FWHM values that are provided in EMIT acquisitions. The point of this study is to study variations in reference to this data.
We thank the reviewer for the suggestion. While the EMIT L1B products provide nominal center wavelengths and FWHM values, our study does not evaluate wavelength variations relative to the provided L1B wavelength assignments. Instead, we deliberately initialize the retrieval using a simplified wavelength grid and evaluate the recovered dispersion against the Zemax optical simulation. We have added a clarification in Section 2.1 and further specified this methodological distinction in Section 3.2.
L69 - I'm not sure whether the citations are well inserted. Please, review this sentence.
The citations has been reformatted to match the manuscript.
L73 – ‚spatially exensive‘ - Then, are these scenes covering a wider area in comparison to most acquisitions? Please, clarify
By "spatially extensive," we intended to describe the presence of large, relatively homogeneous surface areas within the selected scenes, rather than suggesting that the acquisitions cover a larger geographical extent than typical EMIT observations. We have revised the sentence to clarify this distinction.
L76 - One of my main concerns is that the instrument spectral calibration might be conditioned by the temperature, which could be dependent on the position in the orbit. What do you think of this effect and, if it's important, are the set of selected locations representative enough?
We thank the reviewer for this important comment. We agree that temperature-dependent optomechanical changes can influence the spectral calibration. However, EMIT operates under active thermal control, and instrument telemetry indicated that the spectrometer and detector temperatures were maintained within a narrow operating range during the selected acquisitions. Consequently, the observations represent comparable instrument thermal conditions, minimizing the potential influence of temperature-dependent calibration variations. The geographical diversity of the selected scenes is intentional. While surface temperatures and atmospheric conditions differ between acquisitions, the instrument calibration is expected to remain consistent. This allows us to assess whether the retrieved wavelength calibration is reproducible across independent scenes, rather than being influenced by scene-specific conditions. We acknowledge that the present dataset does not systematically sample different instrument thermal conditions or establish long-term calibration stability. We agree that repeated observations across different orbital conditions and years would be valuable for investigating potential temporal variability, although this falls outside the scope of the present study. We have clarified these considerations in the manuscript.
L76 - It'd be also interesting to analyze the same areas in different years in order to assess the temporal variability of the spectral calibration.
We thank the reviewer for pointing this out, and we agree this would be a natural next step for this analysis. This would be interesting for two reasons; 1. On a short timescale to validate the retrievals (with potentially different atmospheric configurations), and 2. Mapping out a potential trend in how the spectral calibration changes over time, both throughout the year but also from year to year.
L87 - So the instrument is internally thermally regulated? Therefore, my previous comment about the position of the satellite in the orbit is not valid? Moreover, please, cite the source from which you obtain this information.
We thank the reviewer for the comment. EMIT employs active thermal control, as described by Thompson et al. (2024), which reduces the influence of orbital temperature variations on the instrument's spectral calibration.
Figure 1. Are dunes and land changes such as those of Scene 5 breaking the homogeneity assumption?
We thank the reviewer for this observation. We agree that surface structures such as sand dunes, particularly those visible in Scene 5, introduce some degree of spatial heterogeneity. However, the scenes undergo substantial spatial averaging before the retrieval, both along-track and through bin-averaging in the cross-track direction. This reduces the influence of localized surface variations and improves the signal-to-noise ratio. While such averaging does not entirely eliminate surface heterogeneity, the consistency of the retrieved wavelength calibrations across the nine independent scenes suggests that these effects do not dominate the results. We have added a brief discussion of this potential limitation to the manuscript, beginning with "Another potential limitation arises from residual surface heterogeneity..."
L98 - Main concern: What about the striping effect? Making bins of 18 cross-track columns could in fact increase the dispersion. I think this is an important point. Please, clarify.
We thank the reviewer for raising this concern. We acknowledge that averaging adjacent detector columns may introduce spectral broadening if their wavelength-center positions differ, and that residual radiometric striping may not be entirely removed. However, previous on-orbit calibration measurements of EMIT indicate that wavelength-center variations across the focal plane array are predominantly smooth (Thompson et al., 2024, Fig. 5). We therefore expect the wavelength differences within each 18-column bin to be small, while the averaging improves the signal-to-noise ratio and preserves the larger-scale cross-track calibration variations investigated in this study. Nevertheless, we recognize that the averaging may suppress finer-scale spatial variations and introduce minor spectral broadening.
L100 - Where is this smooth function assumption coming from? Please, cite if needed.
The assumption of smoothly varying wavelength calibration across the focal plane array is motivated by previous on-orbit calibration measurements of EMIT, as presented by Thompson et al. (2024). In particular, their Figure 5 shows a predominantly smooth cross-track wavelength variation associated with spectral smile and detector rotation. This provides the basis for expecting relatively small wavelength differences between neighboring detector columns. We acknowledge, however, that finer-scale variations cannot be entirely excluded and have revised the sentence to clarify the basis and limitations of this assumption.
L121 - I don't think this is true. The elements in the state vector related to the surface are typically the coefficients of the polynomial that is used to characterize the surface. This would be much clearer if the forward model were expressed in a equation. Please, clarify.
We thank the reviewer for the comment. In the ISOFIT multicomponent surface model employed in this study, surface reflectance is represented by individual state-vector elements corresponding to the spectral channels, rather than polynomial coefficients. These reflectance values are constrained through a multivariate Gaussian prior, as described by Thompson et al. "Optimal estimation for imaging spectrometer atmospheric correction" (2018). Thus, the original example state vector is consistent with the retrieval framework used in our analysis. Nevertheless, we have revised the accompanying explanation to clarify the surface parameterization.
L122 - Wouldn't then this forward model only be valid for the 550 nm band? Please, clarify
We thank the reviewer for pointing out this ambiguity. The 550 nm wavelength refers only to the reference wavelength used to parameterize aerosol optical thickness, rather than the spectral range over which the forward model operates. The radiative transfer model accounts for the wavelength-dependent effects of aerosol absorption and scattering across the full VSWIR spectral range. We have clarified this distinction in the manuscript.
L125 - Please, if not explained later, explain here a more detailed explanation of the process: why are these wavelengths selected for the four-knots cubic spline parameterization? how do you introduce the spectal calibration parameters into the state vector and the forward model? Now you assume a smooth/continuous perturbation in reference to the initial calibration... why? Is this assumption taken in the across-track direction shifts, or in the shifts from a particular down-track bin, or both?
We thank the reviewer for this comment. We have expanded the paragraph to clarify the spline-based wavelength calibration approach. Additional information has also been added in both section 3 and 4 to help clarify this point.
Eq. 3 - This is the same equation as in Thompson et al., (2024) with the difference of the 1/2 factor, which can be removed since we are talking about a cost function that be minimized. Please, cite the formula correctly or just cite the reference and not inlcude the formula. On the other hand, I would also include the formulation of the forward model and see how you include the parameters to fit regarding the spectral calibration. Moreover, you included f(x) instead of F(x), which is how you formulated the forward model in a previous equation.
We thank the reviewer for these suggestions. We have removed the factors of 1/2 from the cost function, corrected the notation from f(x) to F(x), and included the appropriate reference to Thompson et al. (2024). Regarding the forward model, the underlying radiative transfer formulation is described in Thompson et al. (2018), while the spline-based spectral calibration approach is presented in Thompson et al. (2024). Rather than reproducing these established formulations, we refer to the original publications for further details. We have also expanded the description in Section 3.1 to clarify how the retrieved spline coefficients modify the channel center wavelengths used in the forward model.
* So far, I'm seeing lots of similarities with the work of Thompson et al., (2024).
L141 - Is the nominal the one provided from EMIT metadata? Please, clarify.
We thank the reviewer for pointing out this ambiguity. The initial center wavelengths used in the retrievals are not taken from the EMIT L1B metadata. Instead, a spectrally linear and spatially uniform wavelength grid is used to initialize the retrievals. We have clarified this distinction in the manuscript and replaced "nominal" with "initial" to avoid confusion.
L145 - I think that the previous selection of 4 knots from Thompson (2024) was the fact that the location of these 4 knots matchd the inflection points from the spectral dispersion. Which were the criteria followed here? Please, clarify.
We thank the reviewer for this comment. While the original four-knot configuration presented by Thompson et al. (2024) was motivated by the wavelength-dispersion relation predicted by the Zemax optical simulation, the present study systematically investigates the influence of both knot number and placement on retrieval performance. Specifically, four placement strategies were evaluated, including evenly spaced knots, two heuristic configurations, and the original On-Orbit configuration from Thompson et al. (2024). The first and last knots were fixed at the spectral extrema, while additional knot positions were varied to examine the sensitivity of the retrieval to the chosen parameterization. The objective was to determine whether the original optically motivated configuration remains optimal or whether alternative knot placements provide more accurate and stable wavelength calibration retrievals. We have clarified the selection criteria in Section 3.2, while the individual placement strategies and their evaluation are described in Section 4.1.
L151 - Please, extend the explanation regarding the role of Zemax optical simulations. It's not clear for me whether the Zemax simulations set up really reproduce the satellite-based acquisitions from the EMIT instrument.
We thank the reviewer for highlighting this ambiguity. The Zemax simulations do not aim to reproduce the individual satellite acquisitions or their measured radiance spectra. Instead, they model the optical dispersion of the EMIT instrument based on its optical design, providing a physically motivated prediction of the expected wavelength mapping across the detector. While the simulated dispersion may differ slightly from the actual on-orbit calibration due to optomechanical alignment differences, it provides a useful reference for evaluating the overall shape and curvature of the retrieved dispersion profiles. Importantly, agreement with Zemax is only one of three evaluation criteria employed in this study, alongside consistency across independent scenes and leave-one-out cross-validation. We have revised the manuscript to clarify the role of the Zemax simulations and their use as a reference rather than absolute ground truth.
L155. Main concern: Why in this way and not the other way around? i.e. uniform in spectral dimension and linear in spatial dimension. Moreover, how is the linearity established? I guess that the only way to understand this is knowing how the Forward model depends on these parameterization and how are the paremeters set as priors next to the a priori covariance. For the moment, this setup is not well described, which makes this work fail for reproducibility. Some details that are key for reproducibility are missing.
We thank the reviewer for raising these concerns. The retrievals were initialized using a spectrally linear and spatially uniform wavelength grid, reflecting the basic geometry of the imaging spectrometer, where spectral channels measure different wavelengths while the nominal wavelength mapping is shared across spatial positions. This simplified initialization deliberately excludes nonlinear spectral dispersion and cross-track wavelength variations, allowing these features to be recovered through the spline-based wavelength corrections. Regarding the retrieval configuration, all spline parameters (WLSPL_xxx) were initialized at zero, with bounds of [-7, 7], a prior mean of zero, a prior standard deviation of 100, and a scaling factor of one. The large prior standard deviation relative to the parameter bounds ensures that the retrieval is only weakly constrained by the prior, allowing the measured spectra to primarily determine the wavelength corrections. These settings were identical across all evaluated spline configurations, with only the number and spectral positions of the knots varying. We have expanded Section 3.2 to clarify the initialization, parameter constraints, and their role in the forward model, improving the reproducibility of the described methodology.
L159 - Using less than 2 knots something that is worth it? Or is it just set to test?
We thank the reviewer for the comment. No configurations with fewer than two knot points were evaluated. The two- and three-knot configurations were deliberately included as lower-complexity cases to assess the limitations of simpler wavelength-dispersion representations. For these configurations, piecewise-linear interpolation was employed, whereas configurations with four or more knots used cubic splines. We have revised the sentence to clarify this distinction and the motivation for including these configurations.
L173 - What do you mean with single retrieval configuration? Do you mean just 1 iteration in the inversion? Does this explain why they differ so much? Please, explain.
We thank the reviewer for pointing out this ambiguity. By "single retrieval configuration," we intended to indicate that the same spline configuration was applied independently to all nine scenes, rather than referring to a single iteration of the inversion process. The six-knot configuration with evenly distributed knot points was chosen solely to illustrate the intermediate retrieval results and has no particular significance compared with the other configurations evaluated in this study. The differences in atmospheric parameters reflect the varying conditions of the individual acquisitions, whereas the wavelength-calibration parameters remain comparatively consistent across scenes. The subsequent analysis systematically evaluates the full range of spline configurations. We have revised the manuscript to clarify the illustrative purpose of the figure and avoid implying that the selected configuration is of particular importance.
L180 - I do not agree. You cannot say that this indicates a reliable retrieval of the sensor parameters. You could say that the offsets are showing a similar shape, but their magnitude changes significantly. Does this mean that the instrument spectral dispersion changes importantly with time or the fit is not making a good job or the selection of number and location of knots is not really good? Please, clarify.
We thank the reviewer for this observation. We believe the original wording may have caused some ambiguity regarding the comparison being made. The relatively large differences in wavelength-offset magnitude between the six spline knot locations primarily reflect their different spectral positions and the deliberately simplified, spectrally linear initial wavelength grid. These differences should therefore not be interpreted as temporal variations in the instrument calibration. Our intended observation concerns the consistency between the nine independent scene retrievals at each individual knot location, where the retrieved wavelength offsets exhibit very similar magnitudes and cross-track patterns. This suggests good reproducibility across scenes, although the reliability of the retrieval is evaluated more systematically in the subsequent model-selection analysis. We have revised the manuscript to clarify this distinction and avoid overstating the conclusions drawn from this illustrative figure.
L185 - 44 sequences are tested. However, how are 2 and 3 knots strategies working for the Strat 1, Strat 2, and On-orbit if these start from 4 pre-defined knots? Please, clarify. Moreover, which are these heuristic choices and which is the difference between Strat 1 and Strat 2? More detail to really understand what the authors tested is needed.
This has been updated to give more specifics on both the heuristic choices and strategies used, and the specific rules used to place, both more and less, knot points in each sequence.
L193 - What does model selection mean? It's not clear. Vey confusing. Please, clarify.
We see and agree that the model selection terminology may lead to confusion, and have changed wording to improve clarity.
L195 - Summing the errors or combining the discrepamcy from retrieval and Zemax? It's not clear. Please, clarify.
We thank the reviewer for pointing out this ambiguity. For each knot arrangement, the spectral sampling interval profiles obtained independently from the nine scenes were first averaged to produce a representative profile. This scene-averaged profile was then compared with the corresponding Zemax simulation, as illustrated in Figure 3. Thus, discrepancies were not summed across individual scenes. We have clarified this procedure in the revised manuscript.
L195 - If you use Zemax as ~ground truth, why don't you just directly use the results from Zemax to set your calibration? I would prefer the calibration measured in laboratory as a reference to check consistency. Or at least, by-pass this and preserve your strategy by first checking that Zemax and laboratory results are consistent.
Figure 2. Which is the strategy followed in this specific example? Please, clarify. Moreover, ‚The suggested wavelength offsets of -1 to 2.5 nm are relatively large and reflect the simplifying assumption of a spectrally flat initial dispersion curve in the wavelength calibration.‘… This should be clearly included in the main text.
We thank the reviewer for these suggestions. The example shown in Figure 2 uses six spline knots with the evenly distributed knot placement strategy (Even). We have explicitly identified this strategy in both the main text and the revised figure caption. As clarified in the manuscript, this configuration serves solely to illustrate intermediate retrieval results and has no particular significance relative to the other configurations evaluated. We have also incorporated the explanation of the relatively large wavelength offsets into the main text. These offsets, ranging from approximately -1 to 2.5 nm, represent corrections relative to the deliberately simplified, spectrally linear and spatially uniform initial wavelength grid. Consequently, differences in offset magnitude between spectral knot locations primarily reflect the corrections needed to represent the nonlinear wavelength-dispersion relation, rather than variations in instrument calibration between scenes. We further clarify that the retrieved offsets exhibit similar magnitudes and cross-track patterns across the nine scenes at each corresponding knot location, with their reproducibility examined more systematically in the subsequent model-selection analysis.
L200 - This is the same spline formulation that considers the same location and number of knots used in the retrieval, right? If not, there might be a problem of consistency. Please, clarify.
We thank the reviewer for raising this question. We confirm that the wavelength-dispersion profiles analyzed in this study were reconstructed using the same number and spectral locations of knots, as well as the same interpolation formulation, as those employed in the corresponding ISOFIT retrievals.
L202 - In Figure 2, you clearly showed that there is quite large discrepancy among scenes. I'm not sure whether the methodology is stable enough to rely on these results and assume that all of them fluctuate around a true value.
We thank the reviewer for this comment. We have sharpened the description of Figure 2 to clarify that the wavelength-offset panels represent different spectral knot locations. The differences in offset magnitude between panels primarily reflect corrections to the simplified initial wavelength grid, rather than discrepancies between scenes. Inter-scene consistency should instead be assessed by comparing the curves within each individual panel, where broadly similar magnitudes and cross-track patterns are observed. The stability of the retrieved calibration is further assessed through the subsequent model-selection and cross-validation analyses.
L209 - Major concern: You talk about the first performance metric, but only the plots were shown, not the metric itself. Please, discard talking about this metric if it's not going to be used later. Moreover, I wonder why a range of number of knots is considered instead a single number of knots. Finally, the results aren't really capturing the spectral variability. In Thompson et al., (2024), this variability seems to be better captured, at least in comparison to the laboratory-measured spectral dispersion. Which is the added value of these experiments then? Please, clarify
L217 - Wasn't this already the point discussed in Thompson et al., (2024)? Moreover, results from this metric are not shown. For transparency's sake, I'd include some table / plot putting together all the information provided in the text.
We thank the reviewer for this comment. While Thompson et. al. (2024) introduced a four-knot spline parameterization motivated by the expected optical dispersion, the sensitivity of the retrieved calibration to alternative numbers and placements of knots was not systematically evaluated. Investigating this sensitivity is a central objective of the present study. We have clarified that the second assessment is qualitative rather than a numerical performance metric.
The results are presented in Figure 3, where the four placement strategies are compared for different numbers of knots. The close agreement between the four-knot solutions, contrasted with the increasingly divergent profiles obtained using eight and twelve knots, illustrates the sensitivity to knot placement. We have revised the accompanying text and figure caption to make this comparison and its interpretation more explicit. The subsequent leave-one-out cross-validation provides an additional, quantitative assessment supporting the four-knot selection.
L227 - How can you be sure that the chi-2 is only reflecting how good the spectral calibration is? It's true that that changes are related to the different model configurations, which totally depend on the the number and position of the knots. But, maybe the lower chi-2 comes from setting forward models that can better handle differences in reference to the measurement by any other reason? Please, explain more thoroughly why you can really isolate the dispersion offset as the only cause for the variation in chi-2. This is key for your results.
We thank the reviewer for these comments. We agree that the term "performance metric" was misleading, as the comparison with Zemax is presented primarily as a qualitative assessment. We have revised the terminology accordingly and clarified that the apparent agreement for arrangements employing four to eight knots does not, by itself, determine the preferred knot count. The subsequent assessments of sensitivity to knot placement and leave-one-out cross-validation support the selection of four knots.
We would also like to clarify that systematically varying the number and placement of knots is a central objective of this study. While Thompson et. al. (2024) adopted four knots based on the expected optical dispersion, the relative suitability of alternative parameterizations was not systematically investigated. Our experiments seek to establish whether this choice is supported by independent retrievals across different observing conditions.
Regarding the comparison with While Thompson et. al. (2024), our objective is not to demonstrate superior agreement with the laboratory-derived dispersion. Rather, the contribution is to evaluate the spline parameterization systematically and subsequently characterize the wavelength-dependent cross-track dispersion, extending beyond a conventional wavelength-shift representation. We have clarified these objectives and the interpretation of the results in the revised manuscript.
Figure 3. B-Spline? Please, clarify.
We thank the reviewer for pointing out this ambiguity. The term B-spline refers to the spline representation used to interpolate the retrieved wavelength-offset parameters. As clarified in the manuscript, piecewise-linear interpolation is employed for arrangements with two or three knots, while cubic spline interpolation is used for four or more knots, consistently with the modified ISOFIT implementation. We have revised the figure caption to explicitly distinguish the interpolation orders.
Figure 5. Then, this should be expressed with other symbol, not Delta_lambda
We thank the reviewer for pointing out this inconsistency. We have revised the figure labels, captions, and accompanying text to clearly distinguish the two quantities previously represented by the same symbol. Specifically, the quantity shown in Figure 3 has been redefined as the spectral sampling interval, while Figure 5 retains the wavelength offset notation ($\Delta\lambda$). This clarification resolves the ambiguity without changing the underlying analysis.
L244 - Main concern: Why does this pattern being reproduced but the numbers are totally changed? For instance, at wavelength ~1000 nm there is a difference of the order of 0.1 nm in Figure 3, but there is a large difference of 2.5 nm in this figure. This difference is too large and shows lack of consistency with previous results. Please, clarify.
We refer to the clarifications and response to the comment “Figure 5. Then, this should be expressed...”
L258 - Main concern: It's hard to believe this claiming under the inconsistencies I pointed out before. Hopefully, I'm missing several points that I currently don't see.
The authors hope that the clarifications throughout this review has helped you believe the results.
L268 - I don't think this is true. There are other points in which there is similar discrepancy.
We thank the reviewer for this observation. We agree that discrepancies relative to the Zemax simulation are not confined to the specified atmospheric absorption regions. We have revised the discussion to avoid overstating this relationship and to acknowledge that discrepancies also occur elsewhere in the spectrum.
L275 - Here you should repeat that Scene 6 is the one that is the one situated more temporally far away in reference to the other scenes. Moreover, quantitavely which were the differences in reference for Scene 6. In Figure 2, there is not significant difference. Please, clarify.
We thank the reviewer for this observation. We have clarified that Scene 6 was acquired considerably earlier than the other scenes. We also agree that Figure 2 does not provide sufficient evidence to establish a significant deviation in its retrieved wavelength offsets. As no dedicated quantitative assessment of temporal drift was performed, we have removed the statement identifying Scene 6 as supporting evidence of temporal variability. Instead, temporal changes are now discussed as a potential limitation of the analysis rather than a demonstrated effect.
Citation: https://doi.org/10.5194/egusphere-2026-4701-AC1
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AC1: 'Reply on RC1', Mads Ahlebæk, 15 Oct 2026
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RC2: 'Comment on egusphere-2026-4701', Anonymous Referee #2, 08 Sep 2026
This contribution presents an investigation on the use of Earth observations to constrain the spectral calibration of the instrument performing the observations. To this end, the method presented, already used in the EMIT mission, is applied to several selected EMIT scenes and systematically applied with different parametrizations of splines and analyzing the spatial variability of the results. The paper presents clearly the methodology and results and the outcome can help to improve the calibration of hyperspectral sensors in the future. For these reasons, I believe the paper can be accepted subject to some technical corrections and suggestions indicated below.
- Being applied to EMIT data and using very similar methodology as currently being used, one aspect which shall be more emphasized is what are the novel aspects introduced in this work. In my understanding it is the comprehensive study of the number of knot points in the splines and the different strategies and the use at different spatial locations. In section 4.2 the strategy and number of knots is reduced to values already in used in EMIT, so it is less clear what is the novelty.
-Another aspect that could be improved is the lack of reference to the Zemax package (there is reference to previous usage, though), which are an important part of the study and are mentioned several times along the paper. For the reader not familiar with this software package, it would be convenient to include a reference to a publication or online material describing this tool and if available also the accuracy of this type of simulations.
-There is probably some correlation between the fit parameters, for instance in figure 2 there are wiggles in AOT that match smaller wiggles visible in Knot Point 1600 or 2493, at least in some of the scenes. In addition, radiometric calibration (as mentioned in section 4.2), could have an important influenced on the results. Is an updated calibration the only mitigation measure?
-Sometimes there is a confusing use of \Delta \lambda which is wavelength dispersion in Figure 3-B, but later it is wavelength offset in Figure 5. I would suggest to address this to avoid confusions to the reader.
-Line 284 says "The 0.1% discrepancies....", but the text in the abstract, line 253 and line 311 explicitly mention 1%, is it a typo or is it a different quantity?
Citation: https://doi.org/10.5194/egusphere-2026-4701-RC2 -
AC2: 'Reply on RC2', Mads Ahlebæk, 15 Oct 2026
- Being applied to EMIT data and using very similar methodology as currently being used, one aspect which shall be more emphasized is what are the novel aspects introduced in this work. In my understanding it is the comprehensive study of the number of knot points in the splines and the different strategies and the use at different spatial locations. In section 4.2 the strategy and number of knots is reduced to values already in used in EMIT, so it is less clear what is the novelty.
We thank the reviewer for this observation. We agree that the scientific contributions of this study should be distinguished more clearly from those of \citet{thompson2024orbit}. We have strengthened the introduction to Section 4 to emphasize that the first contribution is a systematic evaluation of the number and spectral placement of spline knots, extending the original four-knot parameterization introduced by Thompson et al. (2024).
Although the four-knot On-Orbit arrangement is subsequently retained, this choice is supported by the sensitivity analysis and cross-validation rather than simply adopted from previous work. The contribution of Section 4.2 is to examine the wavelength-dependent cross-track calibration structure using the reconstructed wavelength-offset profiles, revealing spatial variations that are not fully described by a conventional spectral-smile representation. We have clarified this distinction in the revised manuscript.
-Another aspect that could be improved is the lack of reference to the Zemax package (there is reference to previous usage, though), which are an important part of the study and are mentioned several times along the paper. For the reader not familiar with this software package, it would be convenient to include a reference to a publication or online material describing this tool and if available also the accuracy of this type of simulations.
We thank the reviewer for this suggestion. We have added a reference to the Zemax OpticStudio documentation alongside the existing reference to the EMIT-specific optical simulations by Bradley et al. (2020). We have also clarified that these simulations provide a physically motivated reference based on the instrument's optical design, rather than an absolute ground truth. The accuracy of the simulated wavelength mapping depends on the fidelity of the underlying optical model, and the Zemax comparison is therefore considered alongside the other assessments when evaluating the spline parameterization.
-There is probably some correlation between the fit parameters, for instance in figure 2 there are wiggles in AOT that match smaller wiggles visible in Knot Point 1600 or 2493, at least in some of the scenes. In addition, radiometric calibration (as mentioned in section 4.2), could have an important influenced on the results. Is an updated calibration the only mitigation measure?
We thank the reviewer for these observations. We agree that correlations between retrieved atmospheric parameters and wavelength offsets may arise, as these parameters are estimated jointly within the inversion framework. The similarities in some cross-track patterns in Figure 2 may reflect such coupling, although they do not by themselves establish a quantitative correlation. We have clarified this potential limitation in the Discussion.
We also agree that radiometric calibration uncertainties can influence the retrieval results. The updated flat-field calibration mentioned in Section 4.2 mitigates the radiometric impact of the identified detector artifact but does not necessarily eliminate its influence on the wavelength-calibration retrieval. Additional approaches, such as excluding affected detector positions or further improving the radiometric calibration, could help mitigate these effects. We have expanded the discussion to acknowledge these limitations and possible mitigation measures.
-Sometimes there is a confusing use of \Delta \lambda which is wavelength dispersion in Figure 3-B, but later it is wavelength offset in Figure 5. I would suggest to address this to avoid confusions to the reader.
We thank the reviewer for identifying this ambiguity. We agree that the original notation did not sufficiently distinguish between the two quantities. We have revised the figure labels, captions, and accompanying text to consistently define the spectral sampling interval in Figure 3 as the wavelength separation between adjacent spectral channels, while retaining $\Delta\lambda$ for the wavelength offsets relative to the initial wavelength grid in Figure 5. These revisions clarify the physical interpretation of the results without affecting the underlying analysis.
-Line 284 says "The 0.1% discrepancies....", but the text in the abstract, line 253 and line 311 explicitly mention 1%, is it a typo or is it a different quantity?
We thank the reviewer for identifying this inconsistency. The value of 0.1% in the Discussion was a typographical error and has been corrected to 1%, consistent with the Abstract and Results. We have also clarified that this percentage refers to the spectral channel width rather than the absolute wavelength.
Citation: https://doi.org/10.5194/egusphere-2026-4701-AC2
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AC2: 'Reply on RC2', Mads Ahlebæk, 15 Oct 2026
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RC3: 'Comment on egusphere-2026-4701', A. Hueni, 09 Sep 2026
This study investigated the impact of the number of spline fitting knots as part of the ISOFIT atmospheric correction to optimise the wavelength calibration as part of the optimal estimation (OE), making the spectral calibration also spatially explicit.
It is a generally useful research, but the goal may need sharpening somewhat. The uninitiated reader may find that the ideal number of knots was already chosen in previous work (as noted by fellow reviewers). It should be pointed out that this study validates the originally chosen number of knots, thus, a seemingly obvious statement or conclusion only becomes so whence proven and stated clearly, as done in this work.
Line 165: while the a priori information for the OE remains the same for all simulation runs, it would still be interesting to know in which way the OE deviates when being given another dimension to optimise over. Hence, I would expect different results for BOA R, AOT and WV as a function of the different knot scenarios. It would be thus informative to see the variation in outputs produced by the different OE runs per scene (this also applies to FIg 6 where the result of a single knot simulation is show; adding here e.g. a standard deviation envelope or a min/max envelope showing the variability created by the different knot scenarios would be very helpful to understand the influence on the OE)
Figure 2: Not clear what the distance offset is; it is not mentioned in the text.
Line 211: "consistency of the model’s solution": it is not clear which of the model's solution have been assessed here. AOT? WV? BOA R? Estimated centre wavelengths? Estimated FWHM?
Figure 3: I suggest including here the nominal laboratory spectral calibration curve. This should help to understand the limitations of the pre-launch lab CAL (including the available spectral calibration tie points as function of the available laser wavelengths).
Generally, the dispersion curve is actually not really the wavelength dispersion itself (as I understand it), but the (presumably) first derivative of the wavelength dispersion (i.e. spectral sampling interval) plotted versus wavelength. Please ensure the reader understands this. Also, if plotted versus wavelength, please state against which wavelength you are plotting, as the wavelengths are being optimised as part of the study.Figure 5 left: These are the deltas in comparison to a uniform wavelength calibration. Please elaborate if this was the initial EMIT CAL (first order polynomial), or already the updated one (higher order), now part of the EMIT code base.
Line 197 & 279: Speaking of 'ground truth' is generally discouraged. Such a thing refers to the idea that a bit of the Earth surface represents the truth. In this case, a Zemax simulation is not that. Line 197 includes additionally a pleonasm: the true truth. I would refrain from using the word ground truth, unless it is a fully synthetic simulation where you control all variables. All real world measurements are uncertain.
Line 283: lab is a common acronym for laboratory; I suggest using the full word in publications
Citation: https://doi.org/10.5194/egusphere-2026-4701-RC3 -
AC3: 'Reply on RC3', Mads Ahlebæk, 15 Oct 2026
It is a generally useful research, but the goal may need sharpening somewhat. The uninitiated reader may find that the ideal number of knots was already chosen in previous work (as noted by fellow reviewers). It should be pointed out that this study validates the originally chosen number of knots, thus, a seemingly obvious statement or conclusion only becomes so whence proven and stated clearly, as done in this work.
We thank the reviewer for this constructive suggestion. We agree that an important contribution of this study is the systematic evaluation of the four-knot spline parameterization previously introduced by Thompson et al. (2024). While the original selection was motivated by the expected optical dispersion, the present work evaluates alternative knot numbers and placements using three complementary assessments. The results provide independent support for the suitability of the previously adopted four-knot representation. We have sharpened the study objectives and emphasized this contribution in the revised manuscript, alongside the subsequent characterization of wavelength-dependent cross-track calibration variations.
Line 165: while the a priori information for the OE remains the same for all simulation runs, it would still be interesting to know in which way the OE deviates when being given another dimension to optimise over. Hence, I would expect different results for BOA R, AOT and WV as a function of the different knot scenarios. It would be thus informative to see the variation in outputs produced by the different OE runs per scene (this also applies to FIg 6 where the result of a single knot simulation is show; adding here e.g. a standard deviation envelope or a min/max envelope showing the variability created by the different knot scenarios would be very helpful to understand the influence on the OE) We thank the reviewer for this interesting suggestion. We agree that varying the spline parameterization may also influence the jointly retrieved atmospheric and surface parameters, despite identical prior information. However, the primary objective of this study is to evaluate the suitability of different spline parameterizations for wavelength calibration. A systematic investigation of their influence on retrieved AOT, water vapor, and surface reflectance would be a valuable extension, but falls outside the scope of the present study.
Figure 2: Not clear what the distance offset is; it is not mentioned in the text.
We thank the reviewer for pointing out this ambiguity. The distance offset corresponds to the surface elevation offset described in Section 3.1, which accounts for differences between the retrieved and initially assumed surface elevation in the radiative transfer calculations. We have clarified this correspondence in the Figure 2 caption.
Line 211: "consistency of the model’s solution": it is not clear which of the model's solution have been assessed here. AOT? WV? BOA R? Estimated centre wavelengths? Estimated FWHM?
We thank the reviewer for pointing out this ambiguity. The consistency assessment refers specifically to the wavelength calibration, rather than the retrieved atmospheric or surface parameters. In particular, we examine how the spectral sampling interval profiles derived from the retrieved channel center wavelengths vary between different knot-placement strategies. We have revised the terminology in Section 4.1 to explicitly identify the quantities being compared.
Figure 3: I suggest including here the nominal laboratory spectral calibration curve. This should help to understand the limitations of the pre-launch lab CAL (including the available spectral calibration tie points as function of the available laser wavelengths).
We thank the reviewer for this suggestion. The pre-launch laboratory spectral calibration of EMIT, including its comparison with on-orbit measurements, is presented in Figure 3 of Thompson et al. (2024). The laboratory calibration was based on five reference lasers and the instrument optical model. We have added a description of this procedure and a reference to the published comparison in the revised manuscript. The present study focuses on evaluating alternative spline parameterizations using atmospheric absorption features, rather than reassessing the original laboratory calibration measurements.
Generally, the dispersion curve is actually not really the wavelength dispersion itself (as I understand it), but the (presumably) first derivative of the wavelength dispersion (i.e. spectral sampling interval) plotted versus wavelength. Please ensure the reader understands this. Also, if plotted versus wavelength, please state against which wavelength you are plotting, as the wavelengths are being optimised as part of the study.
We thank the reviewer for this important clarification. We agree that the curves in Figure 3 represent the spectral sampling interval, corresponding to the difference between adjacent channel center wavelengths, rather than the wavelength-dispersion relation itself. We have revised the figure labels, caption, and accompanying text to explicitly define this quantity and distinguish it from the retrieved wavelength offsets shown elsewhere in the manuscript. We have also clarified the wavelength reference used for the horizontal axis.
Figure 5 left: These are the deltas in comparison to a uniform wavelength calibration. Please elaborate if this was the initial EMIT CAL (first order polynomial), or already the updated one (higher order), now part of the EMIT code base.
We thank the reviewer for requesting this clarification. The wavelength offsets shown in Figure 5 are calculated relative to the deliberately simplified initial wavelength grid used in our retrievals, which is spectrally linear and spatially uniform. This reference is independent of both the original and updated operational EMIT wavelength calibrations. We have clarified this distinction in the figure caption to avoid confusion.
Line 197 & 279: Speaking of 'ground truth' is generally discouraged. Such a thing refers to the idea that a bit of the Earth surface represents the truth. In this case, a Zemax simulation is not that. Line 197 includes additionally a pleonasm: the true truth. I would refrain from using the word ground truth, unless it is a fully synthetic simulation where you control all variables. All real world measurements are uncertain.
We thank the reviewer for this observation and agree that the term "ground truth" is inappropriate in this context. We have removed this terminology throughout the manuscript and clarified that the Zemax simulation serves as a physically motivated reference rather than an exact representation of the instrument's on-orbit behavior.
Line 283: lab is a common acronym for laboratory; I suggest using the full word in publications
The acronym has been updated to using the full word as per your request. Thank you for pointing this out.
Citation: https://doi.org/10.5194/egusphere-2026-4701-AC3
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AC3: 'Reply on RC3', Mads Ahlebæk, 15 Oct 2026
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This study focuses on the EMIT spectral calibration, specially the spectral dispersion. The novelty of this work mainly yields in extending the calibration simultaneously to both the spectral and spatial dimensions, providing a more specific calibration that better accounts for non-uniformities from the instrument, which ultimately improves applications such as atmospheric absorption characterization. The study is therefore well motivated and the science community can really benefit from these findings.
The work seems to be strongly based on previous publications from David R. Thompson. So much so, that I needed to read Thompson et al., (2024) to better understand this work and I noticed great redundancy. Along the text, I found that some important details regarding the methodology and results description were missing, making diffficult to follow the narrative of the manuscript. Moreover, I found important inconsistencies in the results that make me doubt about how reliable are the methods used here, specially in the results from Figure 5. Hopefully, the authors can address all these concerns.
Comments
L20 - In L4 this was expressed as 'visible-to-shortwave infrared'. Please, select just 1 way to express it.
L21 - There are more applications, such as gas retrievals. Please, rephrase as sth like 'a single instrument to address numerous applications such as...' or similar.
L26 - Any reference to back up this point?
L36 - This sentence can be misleading because 'microns' can also be used to refer to the nomial central wavelength. Please, clarify that this is a mechanical movement.
L40 - 'based on' instead of 'with'?
L40 - Do they only fit the atmosphere? and the surface? Please, clarify
L46 - and what about the distribution of sensitivity to the channel?
* Wavelength dispersion is a term that is not well described here. Please, clarify the meaning of this term.
L51 - Where is this analysis coming from? Please, cite if there is a good reference that backs this up. If this is something that has been found and shown later in this work, please consider to leave it for the results/discussions/conclusion part.
2.1. - Please, consider to make some comments here about the central wavelength and FWHM values that are provided in EMIT acquisitions. The point of this study is to study variations in reference to this data.
L69 - I'm not sure whether the citations are well inserted. Please, review this sentence.
L73 – ‚spatially exensive‘ - Then, are these scenes covering a wider area in comparison to most acquisitions? Please, clarify
L76 - One of my main concerns is that the instrument spectral calibration might be conditioned by the temperature, which could be dependent on the position in the orbit. What do you think of this effect and, if it's important, are the set of selected locations representative enough?
L76 - It'd be also interesting to analyze the same areas in different years in order to assess the temporal variability of the spectral calibration.
L87 - So the instrument is internally thermally regulated? Therefore, my previous comment about the position of the satellite in the orbit is not valid? Moreover, please, cite the source from which you obtain this information.
Figure 1. Are dunes and land changes such as those of Scene 5 breaking the homogeneity assumption?
L98 - Main concern: What about the striping effect? Making bins of 18 cross-track columns could in fact increase the dispersion. I think this is an important point. Please, clarify.
L100 - Where is this smooth function assumption coming from? Please, cite if needed.
L121 - I don't think this is true. The elements in the state vector related to the surface are typically the coefficients of the polynomial that is used to characterize the surface. This would be much clearer if the forward model were expressed in a equation. Please, clarify.
L122 - Wouldn't then this forward model only be valid for the 550 nm band? Please, clarify
L125 - Please, if not explained later, explain here a more detailed explanation of the process: why are these wavelengths selected for the four-knots cubic spline parameterization? how do you introduce the spectal calibration parameters into the state vector and the forward model? Now you assume a smooth/continuous perturbation in reference to the initial calibration... why? Is this assumption taken in the across-track direction shifts, or in the shifts from a particular down-track bin, or both?
Eq. 3 - This is the same equation as in Thompson et al., (2024) with the difference of the 1/2 factor, which can be removed since we are talking about a cost function that be minimized. Please, cite the formula correctly or just cite the reference and not inlcude the formula. On the other hand, I would also include the formulation of the forward model and see how you include the parameters to fit regarding the spectral calibration. Moreover, you included f(x) instead of F(x), which is how you formulated the forward model in a previous equation.
* So far, I'm seeing lots of similarities with the work of Thompson et al., (2024).
L141 - Is the nominal the one provided from EMIT metadata? Please, clarify.
L145 - I think that the previous selection of 4 knots from Thompson (2024) was the fact that the location of these 4 knots matchd the inflection points from the spectral dispersion. Which were the criteria followed here? Please, clarify.
L151 - Please, extend the explanation regarding the role of Zemax optical simulations. It's not clear for me whether the Zemax simulations set up really reproduce the satellite-based acquisitions from the EMIT instrument.
L155. Main concern: Why in this way and not the other way around? i.e. uniform in spectral dimension and linear in spatial dimension. Moreover, how is the linearity established? I guess that the only way to understand this is knowing how the Forward model depends on these parameterization and how are the paremeters set as priors next to the a priori covariance. For the moment, this setup is not well described, which makes this work fail for reproducibility. Some details that are key for reproducibility are missing.
L159 - Using less than 2 knots something that is worth it? Or is it just set to test?
L173 - What do you mean with single retrieval configuration? Do you mean just 1 iteration in the inversion? Does this explain why they differ so much? Please, explain.
L180 - I do not agree. You cannot say that this indicates a reliable retrieval of the sensor parameters. You could say that the offsets are showing a similar shape, but their magnitude changes significantly. Does this mean that the instrument spectral dispersion changes importantly with time or the fit is not making a good job or the selection of number and location of knots is not really good? Please, clarify.
L185 - 44 sequences are tested. However, how are 2 and 3 knots strategies working for the Strat 1, Strat 2, and On-orbit if these start from 4 pre-defined knots? Please, clarify. Moreover, which are these heuristic choices and which is the difference between Strat 1 and Strat 2? More detail to really understand what the authors tested is needed.
L193 - What does model selection mean? It's not clear. Vey confusing. Please, clarify.
L195 - Summing the errors or combining the discrepamcy from retrieval and Zemax? It's not clear. Please, clarify.
L195 - If you use Zemax as ~ground truth, why don't you just directly use the results from Zemax to set your calibration? I would prefer the calibration measured in laboratory as a reference to check consistency. Or at least, by-pass this and preserve your strategy by first checking that Zemax and laboratory results are consistent.
Figure 2. Which is the strategy followed in this specific example? Please, clarify. Moreover, ‚The suggested wavelength offsets of -1 to 2.5 nm are relatively large and reflect the simplifying assumption of a spectrally flat initial dispersion curve in the wavelength calibration.‘… This should be clearly included in the main text.
L200 - This is the same spline formulation that considers the same location and number of knots used in the retrieval, right? If not, there might be a problem of consistency. Please, clarify.
L202 - In Figure 2, you clearly showed that there is quite large discrepancy among scenes. I'm not sure whether the methodology is stable enough to rely on these results and assume that all of them fluctuate around a true value.
L209 - Major concern: You talk about the first performance metric, but only the plots were shown, not the metric itself. Please, discard talking about this metric if it's not going to be used later. Moreover, I wonder why a range of number of knots is considered instead a single number of knots. Finally, the results aren't really capturing the spectral variability. In Thompson et al., (2024), this variability seems to be better captured, at least in comparison to the laboratory-measured spectral dispersion. Which is the added value of these experiments then? Please, clarify
L217 - Wasn't this already the point discussed in Thompson et al., (2024)? Moreover, results from this metric are not shown. For transparency's sake, I'd include some table / plot putting together all the information provided in the text.
L227 - How can you be sure that the chi-2 is only reflecting how good the spectral calibration is? It's true that that changes are related to the different model configurations, which totally depend on the the number and position of the knots. But, maybe the lower chi-2 comes from setting forward models that can better handle differences in reference to the measurement by any other reason? Please, explain more thoroughly why you can really isolate the dispersion offset as the only cause for the variation in chi-2. This is key for your results.
Figure 3. B-Spline? Please, clarify.
Figure 5. Then, this should be expressed with other symbol, not Delta_lambda
L244 - Main concern: Why does this pattern being reproduced but the numbers are totally changed? For instance, at wavelength ~1000 nm there is a difference of the order of 0.1 nm in Figure 3, but there is a large difference of 2.5 nm in this figure. This difference is too large and shows lack of consistency with previous results. Please, clarify.
L258 - Main concern: It's hard to believe this claiming under the inconsistencies I pointed out before. Hopefully, I'm missing several points that I currently don't see.
L268 - I don't think this is true. There are other points in which there is similar discrepancy.
L275 - Here you should repeat that Scene 6 is the one that is the one situated more temporally far away in reference to the other scenes. Moreover, quantitavely which were the differences in reference for Scene 6. In Figure 2, there is not significant difference. Please, clarify.