the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
LIME: Lunar Irradiance Model of ESA, a new tool for the absolute radiometric calibration using the Moon
Sarah Taylor
África Barreto
Stefan Adriaensen
Alberto Berjón
Agnieska Bialek
Ramiro González
Emma Woolliams
Marc Bouvet
Abstract. Absolute calibration of Earth observation sensors is key to ensuring long term stability and interoperability, essential for long term global climate records and forecasts. The Moon provides a photometrically stable calibration source, within the range of the Earth radiometric levels and is free from atmospheric interference. However, to use this ideal calibration source one must model the variation of its disk integrated irradiance resulting from changes in SunEarthMoon geometries. LIME, the Lunar Irradiance Model of the European Space Agency, is a new lunar irradiance model developed from groundbased observations acquired using a lunar photometer operating from the Izaña Atmospheric Observatory and Teide Peak, located in Tenerife, Spain. Nightly topofatmosphere irradiance is determined using the Langley plot method and each observation is traceable to the international system of units (SI), through the photometer calibration performed at the National Physical Laboratory. Approximately 590 lunar observations acquired between March 2018 and December 2022 currently contribute to the model parameter derivation, which builds on the widelyused ROLO (Robotic Lunar Observatory) model analytical formulation. This paper presents the strategy used to derive LIME model parameters: the characterisation of the lunar photometer, the derivation of nightly top of atmosphere lunar irradiance and a description of the model parameter derivation, along with the associated metrologicallyrigorous uncertainty. The model output has been compared to PROBAV, Pleiades, Sentinel 3B as well as to the VITO implementation of the ROLO model. Initial results indicate that LIME predicts 3 %–5 % higher disk integrated lunar irradiance than the ROLO model for the visible and nearinfrared channels. The model output has an expanded (k = 2) radiometric uncertainty of ∼2 % at the lunar photometer wavelengths, and it is expected that planned observations until at least 2024 further constrain the model parameters in subsequent updates.
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Carlos Toledano et al.
Status: final response (author comments only)

RC1: 'Comment on egusphere20231539', Anonymous Referee #1, 03 Aug 2023
 general comments
This paper outlines very well the strategy used to develop a lunar irradiance model from new groundbased measurements obtained from a high altitude location, as a need shown from literature overview to develop an SItraceable absolute irradiance model of the Moon.
LIME, the Lunar Irradiance Model of the European Space Agency, is a new lunar irradiance model developed from groundbased observations acquired using a lunar photometer operating from the Izaña Atmospheric Observatory and Teide Peak, perfect sites for such measurements. A key attribute of the LIME model is a rigorous uncertainty analysis and the ambitious target of a sub2% uncertainty in the resultant model as it is finally proved by this study.
This new model is expected to play an important role on EO radiometric calibration, which can be validated using radiometrically stable natural targets, like the lunar disk irradiance. With this information, Earth Observation measurements can be radiometrically linked to all past, present and future sensors having performed similar measurements.
Strategy for extraterrestrial Moon irradiance retrieval is described and easy to follow., along with the calibration. The linearity of the measurements with CIMEL photometer is tested. Also the thermal sensitivity of the instrument and the irradiance responsivity of each lunar photometer spectral channel were assessed. Rigorous uncertainty analysis of the calibration was performed, sources of uncertainty for individual lunar observations were correctly identified and assessed.
The LIME model as derived from the lunar irradiance measurements from the Cimel photometer is fully described. LIME basically improves ROLO model by using an independent set of Ccoefficients for each spectral band of the model, calculated using different steps in the procedure (Figure 8 in the article).
A reflectance spectrum of the Moon is used to increase the model spectral resolution.
The LIME model outputs have been compared with the satellite spectral imagers PROBAV and PLEIADESHR1B but considering the limitations of such comparisons. Procedure nicely and clear described and also represented in Figure 11
The manuscript is overall well written and addresses globally relevant issues.
 specific comments
This paper is a response to a need related to the calibration of Earth observation sensors (to ensure the continuity of longterm and global climate records) and especially important for satellite sensors, calibrated prior to launch because their susceptibility to degradation in space.
I think the authors should add a short paragraph in the conclusions related to availability of LIME to be used by other interested parties.
 technical corrections
 You are using VITO in the abstract Please consider to write the name of the Institute here in parenthesis
 Line 465 equation 15 please use subscript for 3 and 4 of the coefficients “p3” and “p4”
 Figure 8 please change Pico Teide with the English versionPeak Teide 
 Line 519 (page 25) please write “six values of S...” instead of “6 values of S...”
 Equation no.20 (page 33) Please make the correction: for fitting coefficient “a4” 4 should be subscript
 In Figure 14 for a better visualisation in the graph the authors should consider black color for 440 nm or 1020 nm (since now it could be difficult to distinguish between the two)
Citation: https://doi.org/10.5194/egusphere20231539RC1 
RC2: 'Comment on egusphere20231539', Thomas Stone, 11 Aug 2023
This paper is a welcome contribution to the field of lunar calibration. The LIME project represents a significant effort toward producing a more accurate model for the exoatmospheric lunar irradiance, and there has been a need to consolidate the documentation on LIME development. This paper covers the topic comprehensively, with including uncertainty analyses for each component of the model development. There are a few technical points that should be explained more fully, noted in specific comments below. The manuscript is well written and is recommended for publication.
Specific Comments
Section 2.3
A more uptodate accounting of the uncertainty in the ROLO model is given in the reference Stone et al. 2020, cited elsewhere in this manuscript. But it generally aligns with the 510% value quoted here, so this is a very minor issue.Section 3.5
It would be informative to have values for: 1) the typical duration of the Langley acquisition period, 2) the typical lunar phase change during this period (i.e. quantify "minute changes"), and 3) the numerical range of the correction A(t_ref,lambda)/A(t,lambda).
Section 4.1
It would be informative to have typical DN values expected for Full Moon and for 90 degrees phase, to see where the lunar measurements fall on the linearity factor plots in Fig.4.
Section 4.2
The much larger temperature sensitivity for the Si 1020 channel suggests using the InGaAs 1020 channel  are there other considerations that led to the choice to use the Si channel, despite the potential added uncertainty?
Section 4.4
Units should be given for the calibration coefficients, preferably in Table 4 but alternatively in the text.
Section 5.1
The text seems to imply that the CAELIS software conducts the uncertainty analysis described in section 5.3  is that correct, or is this analysis done offline from CAELIS? How are the "statistical indicators of the fit quality" used?
Section 5.3.1
What is the relation between count signal D(lambda,t) and V^m(lambda,t) used in the Langley plots and converted to irradiance through the calibration coefficient, as in Eq.10?
Please provide the method used to compute the lunar zenith angle (theta) using the SPICE tools, as mentioned in section 5.1. Kasten and Young (1989) state: "substantial errors will be incurred if unrefracted elevations are used" when applying their Eq.3, from which Eq.14 here is derived (see also the Technical Correction below). This potential source of uncertainty in theta propagates into an uncertainty in the airmass values m, and the assumption that uncertainty associated with airmass is negligible might not be valid if refraction is not taken into account for specifying the zenith angle.
Presumably the choice to restrict the airmass range to 25 is also driven by the time required to collect the Langley data, to limit the effects of variability in the atmosphere.
Section 5.3.2
What is the "expected chi^2" value? What was the rationale for choosing this value?
The uncertainties in the Langley plot intercept u(ln[V_0]) are critical, since the V_0 quantities from the fits ultimately are used for deriving the model coefficients in section 6.2, and the uncertainties in V_0 are central to the model uncertainty analysis in section 6.3. The quoted uncertainties u(ln[V_0]) in Figs.6 and 7 seem unreasonably small for fitted parameter uncertainties (specifically, the intercept) derived from these linear regressions, given the range of airmass and the extrapolation to zero airmass. But these parameter uncertainty values can't be checked without having access to the Langley datasets. This reviewer is willing to run checks on these fit results if the authors would provide the data for Figs.6 and 7, with including the measurement uncertainties.
Section 6.2
This section is missing a description of how the geometry variables g, Phi, theta and phi are computed for each data point.
For the nonlinear part of the fitting to determine the p coefficients, how is the degeneracy of the d_1 and d_2 terms handled? The form of these two terms is identical in Eq.15.
Section 6.3
This section is very important, because it presents the method used to derive the uncertainty in the LIME outputs. More detail here would be helpful, as suggested in the following:
Presumably the values in Table 9 are used to specify the variances of the Probability Distribution Functions (PDFs) for S_lambda and C; this is not mentioned in the text. How are these table values related to the instrument calibration uncertainties given in section 4.4, Tables 3 and 4? Is the PDF for random errors R_i,lambda constructed from the individual measurement errors, or is it an analytic function (such as a Gaussian) with characteristic parameters specified by the collective results given in section 5.3.2 and Table 8?
Additional details are needed to explain the statement: "These [1000] model outputs are then used to determine the uncertainty associated with the model, by considering the uncertainty associated with each of the parameters and the covariance between them." How are the uncertainties in the (18) model parameters combined to give the uncertainty distributions for the full model for each band? Presumably the latter are the distributions from which the confidence intervals shown in Fig.9 are derived, which are considered specifications of the uncertainty in the LIME outputs.
Lastly, it would informative to see values for the mean absolute residuals of the full dataset, between the TOA irradiance measurements and the corresponding LIME outputs. These are an indicator of the relative accuracy of the model, and they would provide a useful comparison to the results from the Monte Carlo analysis.
Section 6.4
It would be informative to see in Fig.10 the model outputs for the 6 Cimel bands and the smoothed lunar reflectance spectrum for an example measurement.
What is the form of the regression that is solved using least absolute deviation?
Section 6.5.4
In the lunar calibration field, the common usage of "GIRO" means "GSICS Implementation of ROLO", i.e. the lunar model software built by EUMETSAT and validated against the USGS ROLO model. It is confusing to refer to the VITO implementation of the ROLO model as GIRO.
It would be worth mentioning that the 3% to 5% differences between the irradiances predicted by ROLO/GIRO and LIME are within the range of uncertainties quoted for the two models.
The LIME documents on the CEOS calval portal at URL provided were not accessible on 10 August 2023  the site gives the message: "Error: You do not have the required permissions."
Section 7
With due respect for the authors' discretion as to the paper's contents, may I suggest to consider removing this section. This topic could support a separate paper, the text indicates that the study is incomplete, and the material on irradiance measurements, modeling, and uncertainties makes a very substantial paper on its own.
Technical Corrections
Section 5.3.1: m(Theta) before Eq.12 should be lower case theta.
The form of Eq.14 is incorrect as written  the constants from Kasten and Young (1989) have been incorrectly converted from degree to radian measure.
Section 6.3: several instances of misprinted "ith observation"
Section 8: this section might actually start with the current second paragraph  the first paragraph appears to be mistakenly present.
Citation: https://doi.org/10.5194/egusphere20231539RC2
Carlos Toledano et al.
Carlos Toledano et al.
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