The paper presents a methodology to evaluate uncertainties in spectral UV irradiance measurements by Brewer spectroradiometers. The methodology considers most of the possible sources of uncertainty and has been applied on several instruments. In this respect, the study is innovative and useful for the uncertainty evaluation of the global Brewer network. However, it is alarming that the evaluation for one spectrum takes so long (8 hours), making the method impractical for evaluating large numbers of spectra.

The presentation is generally clear, but there are several places where clarifications are needed. See specific comments below.

The language can certainly be improved. There are many typographical, syntax and grammar errors that can easily be corrected by careful reading. In my Technical Comments section below I have listed a few, but there are many more.

Therefore, my recommendation is that the paper would be suitable for publication in ACP, after addressing by comments below.

Specific comments:

27: The difference between single and double monochromators is mainly due to stray light and not due to dark signal. I suggest deleting "and dark count".

29-30: How the “irradiance of the calibration lamp” is involved in the uncertainty? I think you mean the uncertainty associated with the reference lamp calibration, therefore I suggest replacing "irradiance" with "uncertainty". The same applies to lines 418 and 618.

153-155: I am not sure what you mean here: First you say that some uncertainties are considered int eh analysis and then that you prefer to ignore them. Please clarify.

157: Replace "counts" with "signal". It is better to use “signal” when you are referring generally to what is measured. This applies, for example, also to lines 159 and 160 and elsewhere.

157: What do you mean by unprocessed? To what does this differ from (1)? My understanding after reading the next sections is that this category refers to uncertainties related to absolute irradiance, specifically to wavelength shifts, angular response and temperature dependence. All three affect the absolute irradiance rather than the raw (or unprocessed) irradiance.

202: Does “40” refers to all dark signal measurements (which I think is too low) or to measurements at each temperature? Please specify.

242, 245, 477: To which period do these drifts refer?

251: Since the spectral range is defined from short to long wavelengths, the irradiance is increasing rather than declining. You could cope with it more easily by saying "marked variability".

269: It appears that not all uncertainties were considered for all instruments. You might consider summarizing in a table the types of uncertainties considered in each instrument.

333-335: Why were spectra corrected for shifts only if they were measured at SZAs<90°?

I think the second sentence complicates the discussion. You can simply say: "Only spectra recorded at SZA's smaller than 90° were used in this study."

359: What about cloudy conditions? Other sources of uncertainty are also involved. Maybe you could discuss briefly what happens under cloudy conditions.

371: Good agreement cannot be assessed by this figure. If ratios were shown against one instrument (e.g., the QASUME or the average / median of all instruments) the level of agreement would have been more evident.

378: I am not sure if Figure 2 is necessary. It is expected that the standard uncertainty will increase with wavelength and solar elevation since the irradiance increases. In contrast Figure 3 is more meaningful to discuss.

393: Better say, at the end of the sentence: "... and some Brewers showed almost no SZA dependency, as shown later in Figure 4".

406: In fact, half of the 10 Brewers considered show some SZA dependency and half are not; so, I wouldn't say "most Brewers".

416: In this section, a table summarizing the ranges of uncertainties due to different factors together with the combined uncertainty would be useful.

417-418: The relative contribution to the combined uncertainty is based (or at least it is shown in Figure 5) by the two example spectra. I think it would be more representative to show average contributions from a larger number of spectra recorded for several days in a narrow range of SZAs.

424: You might consider including a table with individual and total uncertainties for each of the Brewers considered.

452: How your results on Dead Time compare with those derived by Fountoulakis et al., 2016? https://amt.copernicus.org/articles/9/1799/2016/

506: Caption of Fig. 7: This figure shows the relative standard uncertainty (not the combined). Please correct the axis title and caption.

517-525: Although the contents of this paragraph are correct, they are not very relevant to the topic of the paper. The authors have already published a work on the TCO uncertainties using the same methodology.

556-562: I am afraid that the uncertainty in quantifying the effects of UV radiation on materials is much higher than the uncertainty in UV measurements.

581-586: Note that photolysis frequencies are estimated from actinic flux measurements which are not measured by Brewer spectroradiometers. However, generally speaking, the estimation of uncertainties of relevant instruments can benefit from this study.

591: In the conclusions section, I suggest discussing the uncertainties against those reported in previous studies. Does this study show significantly different results from the uncertainties in spectral UV irradiance usually quoted in the literature?

623: Apart from the need to monitor the wavelength shifts, it is essential to reduce them through accurate determination of the instrument’s wavelength scale and frequent wavelength calibrations.

Technical comments:

30: Rephrase to "measured UV irradiance decreases, the dark signal"

99: Replace "using" with "by"

177: Please rephrase to: "These values are deemed reliable as they were derived by analyzing data from over 20 single Brewers."

191: replace "was" with "is"

289: Insert “by” before “integrating”

294: Replace “diffuser error” with “diffuse error”

295: “derived for inhomogeneous sky radiance distribution”

377: Replace “displaying” with “display”

445: Delete “those of”

456: Replace “as SZAs decrease” with “at small SZAs”

603: Replace “depended on the wavelength and SZA, increasing as wavelength rose and SZA declined.” with “increases with increasing wavelength and decreasing SZA”.

604: Replace “tripled” with “are triple”

624: Replace "committed in” with “associated with”

Anonymous review of the manuscript by Gonzalez et al., entitled "Evaluation of the uncertainty of the spectral UV irradiance

measured by double- and single-monochromator Brewer spectroradiometers".

General comments:

The manuscript describes the evaluation of uncertainties of spectral UV irradiance measured by two types of Brewer spectroradiometers. The evaluation is done using measurements from an intercomparison campaign. I think the study and the results are very important for the scientific community, as they are among the first to use the MCM technique to account for the propagation of uncertainties of Brewers. The sensitivity test is used to distinguish the impact of each uncertainty component, which is also a very interesting result and can help the scientific community to improve the quality of measurements. However, I think some issues need to be clarified before the manuscript can be published: There are already WMO-GAW guidelines for quality control (QC) and quality assurance (QA) of UV measurements, which are WMO-GAW Reports No. 146 (Webb et al., 2003, Quality assurance in monitoring Solar UV radiation: the state of the art) and No. 126 (Webb et al., 1998, Guideliness for site quality control of UV monitoring). I think you should discuss more in the Introduction how your study reflects the guidelines of these reports and refer to the "deductive" and "inductive" methods for QA introduced in Webb et al., 2003. You should also refer more closely to Webb et al., 1998. In addition, I think you should consider showing and discussing your uncertainty estimate and the results of the intercomparison campaign. You have the ideal setup of having the QASUME intercomparison results from the El Arenosillo campaign. Thus, you could compare the results of your "deductive" method with the results of the "inductive" method.

Another concern is the uncertainty associated with cosine correction. I don't understand why you get such higher uncertainties in measurements that are cosine corrected compared to those that are not. Shouldn't it be the other way around? If the cosine correction is in the range of 5 to 10%, then the measurements missing that correction should be at least that far off and have higher uncertainties? And, as mentioned in the specific comments, please include the information of which part of the cosine correction (angular response characterization, dir/diff ratio determination...?) has the largest uncertainty. Maybe I missed something: please explain this more clearly.

Then comes the transfer of the irradiance scale from an accredited lab to the instrument itself (which is basically the spectral response determination). There are uncertainties in the transfer, which you've described well, but it's unclear how you've accounted for them in your analysis. I wonder if when you do the lamp calibration (transfer of the irradiance scale), you also have to take into account the uncertainties in the Brewer irradiance measurements, don't you (in addition to the distance from the lamp: levelling, dead time, noise, etc....)?

And about stability, changes in response over time: I think you should discuss this as an additional source of uncertainty for long-term monitoring. Not for newly calibrated instruments. And add a time specification. That you assume for example a 1-3% drift in response per year. The drift is really instrument-dependent and depends on modifications/maintenance/upgrades of each instrument. As stated in Webb et al. 1998, "Each time the calibration is checked or changed, the data gathered between the two calibration times has an unceratinty which depends on the difference between the two calibrations, and it is these uncertainties which should be used for this calculation".   

Specific comments:

line 157: Please specify in which section you describe which of the three uncertainty sources. Check that you make clear in text what do you mean by the three different uncertainty sources.

lines 168-169:  "However, deriving the uncertainty of this method for the Brewers under study is difficult, as it would use the information from only five wavelengths (from 290 to 292 nm)." -> I don't see your point. Uncertainty related to this approach could also be determined, e.g., compared to the QASUME. I think this sentence should be rethought.

line 229: "Brewer #150, on the other hand, has an additional source of uncertainty since the position of its diffuser’s reference plane needs to be determined as well (González et al., 2023)"-> I don't understand the sentence, as the previous sentence describes as distance 500+-0.6mm, which is less than the "standard" one of 500+-1mm explained earlier.

line 230:"Regarding the uncertainties of the irradiances of the reference lamps, there is no need to determine them since all lamps used during the campaign had been previously calibrated in different standard laboratories." -> I suggest skipping this sentence or rephrasing it.

line 255: Please add a short sentence describing the idea of SHICRIVM wavelength shift detection.

line 260: "Furthermore, there is a second contribution to the wavelength misalignment, the precision of the micrometre, i.e. the system setting the wavelengths measured by a Brewer spectroradiometer". -> yes, it contributes to the wavelength misalignment, but the impact is seen in the wavelength shift recorded by SHICRIVM. Please rephrase.

Figure 6: I think you should also include the uncertainty related to stray light, even if the double monochromators are known to have less stray light than single ones.

Section 3.2 UV model -> Is it really a model? Couldn't the Chapter be called "UV processing algorithm"?

line 465: What about the wavelength dependency of the distance-related uncertainty? The irradiance of the calibration lamp is wavelength-dependent, isn't it? So the effect of the distance measurement error is wavelength-dependent, too?

Line 475 and 4.2.7. Radiometric stability

I think you should report the uncertainties at the moment of a fresh calibration. If I understand right, you assume some drift in the spectral responsivity of the Brewer, which is based on measurements over several years. The instruments drift at a different speed, and the spectral response is strongly dependent on instrumental modifications.

Section 4.2.10 Cosine correction

What is the reason for the high uncertainty related to cosine correction? Is it due to the uncertainty in angular response characterization or the DIR/DIFF ratio or something else? Please include this information in the text.

line 520: But the Brewer ozone processing is not based on UV measurements you describe in this study. I don't see the point of this paragraph.

line 534: Do you mean combined uncertainty?

line 573: For global radiation?

line 582: I refer to my earlier comment that, at least for the Brewer, the ozone is not calculated using the UV irradiances which you describe in this manuscript.

line 585: I don't see the connection between your work and the last sentence of this paragraph.

GENERAL COMMENTS

The study by González et al. builds upon previous work by the same authors (https://doi.org/10.1029/2023JD039500), extending the methodology applied to Brewer #150 to a broader set of Brewer spectrophotometers participating in an RBCC-E campaign. The authors discuss various factors influencing the uncertainty in spectral UV measurements and estimate the overall uncertainty using a Monte Carlo approach. A notable limitation, however, is that approximately half of the instruments were not fully characterized, for instance lacking angular response measurements. An additional contribution beyond the 2023 study is the inclusion of stray light effects, addressed here using a method originally developed for direct-sun observations and never demonstrated to work on global UV irradiance.

The general topic is of high relevance to both the Brewer user community and the broader scientific community, particularly in the context of long-term UV trend detection related to ozone variability and climate change. Nevertheless, the manuscript contains several inaccuracies and errors concerning the description of the Brewer instrument. Furthermore, the methodology is presented in a confusing manner, frequently confounding systematic effects with the uncertainties introduced by their corrections. The improper distinction between systematic and random effects appears to result in absurd outcomes, for example, an estimated uncertainty in the UV Index of only 0.28–0.53%, which is significantly lower than the stated calibration uncertainty of the irradiance standard lamps used for Brewer calibration.

I strongly recommend against publication of the manuscript in its current form, as it risks disseminating incorrect and potentially misleading information to the user community.

SPECIFIC COMMENTS

1. Scope of the paper

The scope and applicability of the results remain unclear. For instance, it appears that the calculated uncertainties pertain to measurements performed during the RBCC-E campaign. However, a long-term drift in Brewer responsivity of 3 % is then mentioned: clarification is needed on whether this drift refers to a time span that includes or exceeds the duration of the campaign. Additionally, it is not clear whether the stray light correction method described in the manuscript was actually implemented during the campaign, or if the cosine correction was actually applied to the data described in the campaign report.

2. Inaccuracies and errors in the description of the Brewer spectrophotometer

• Line 97: Global spectral UV radiation reaches the foreoptics after two prism reflections (UV-B prism and zenith prism), not one
• Lines 97–98: Filter Wheel #3 is typically set to the open position
• Line 98: Filter wheels are mechanical components used to position optical elements, but are not optical elements themselves
• Line 105: MkIV Brewers use the third diffraction order for UV measurements. The diffraction grating has 1200 lines per *mm*, not 1800 lines per *nm* as stated
• Line 108: The correct specification is 3600 lines per *mm*, not *nm*
• Line 108: According to the diffraction equation, identical diffraction angles for a given wavelength occur with 1200 lines/mm in third order and 3600 lines/mm in first order
• Line 116: The Brewer slit function is better described as trapezoidal, not triangular (e.g., https://acp.copernicus.org/articles/14/1635/2014/)
• Line 208: The statement “using the DT tests, this constant is frequently checked and updated when necessary” is misleading, especially after the claim that the dead time value is stored in the B-files. This could wrongly imply real-time updates. Furthermore, DT test results are highly sensitive to the intensity of the standard lamp (SL), making their use as an uncertainty estimate questionable. In practice, the dead time is more reliably verified through ozone direct-sun (DS) comparisons during calibration audits
• Line 263: Many modern Brewers are now equipped with heaters, thus minimizing internal temperature fluctuations
• Lines 465–466: A more accurate phrasing would be: “The instrument is calibrated using the standard lamps with the input optics positioned at zenith.”

3. Treatment of stray light

The application of the algorithm proposed by Savastiouk et al. (2023) to spectral UV irradiance measurements raises several concerns. According to their paper, this method was specifically developed for direct-sun observations conducted at a fixed grating position and was not validated for use at other wavelengths or for measurements requiring grating movement, such as those involved in spectral UV irradiance scans. Additionally, spectral UV irradiance measurements are not performed simultaneously across wavelengths, further complicating the applicability of the method to this context.

The validity of applying this correction approach should be demonstrated, ideally through comparisons of corrected UV spectra from single-monochromator instruments with measurements from reference instruments with negligible stray light effects. Alternatively, the uncertainty introduced by the application of this stray light "model" should be explicitly quantified, in addition to the two uncertainty sources discussed in lines 181–182.

The manuscript states that “deriving the uncertainty of this [the 5-wavelength] method for the Brewers under study is difficult, as it would use the information from only five wavelengths.” However, it remains unclear what correction method, if any, was actually employed during the RBCC-E campaign. Moreover, the statement regarding the difficulty of the 5-wavelength approach is vague. The authors should clarify what specific challenges prevent its application and provide justification for the selected correction method.

4. Treatment of systematic error sources

4a. Ambiguity in use of terminology

According to the Guide to the Expression of Uncertainty in Measurement (GUM), all known systematic error sources must be corrected prior to uncertainty estimation, with the residual uncertainty from those corrections included in the total uncertainty budget. This methodological framework is not clearly articulated in the manuscript, particularly in the methodology section, and the terminology used throughout the manuscript often conflates systematic errors with uncertainty contributions.

For example, lines 26–28 state: “For wavelengths below 300 nm, the differences between single- and double-monochromator Brewers increase, due to stray light and dark counts. For example, at 295 nm, the relative uncertainties of single Brewers range between 11–14% while double Brewers have uncertainties of 4–7%.” This wording implies that stray light is itself a source of uncertainty, rather than a systematic (albeit variable) error that should be corrected. A similar ambiguity is present in lines 449–450: “the contribution of stray light increases rapidly as wavelength decreases.” It is unclear whether this refers to the increasing magnitude of the stray light error or to the uncertainty associated with correcting it. The same confusion is evident in the discussion of cosine correction.

The authors should explicitly distinguish between systematic effects (which must be corrected) and the uncertainties associated with those corrections.

4b. Effectiveness of corrections

To justify the inclusion of systematic error corrections, the authors must demonstrate that these corrections lead to improved measurement accuracy. This could be done by presenting plots showing the relative (%) differences between corrected spectra and a reference standard (e.g., QASUME). Such comparisons would help assess the effectiveness of the applied stray light and cosine corrections. The residual discrepancies should then be discussed in the context of the total uncertainty budget.

4c. Missing information for some Brewers

Only five Brewer instruments were characterized for their angular response, yet cosine correction is an essential component of systematic error treatment. Given this limitation, the authors should consider restricting their analysis to only those instruments for which a full angular characterization was performed.

4d. Uncertainty in cosine correction

The uncertainty associated with the direct-to-global ratio (DIR/GLO) has not been addressed in the manuscript. This is a significant omission, as this uncertainty can be non-negligible, particularly under overcast or mixed sky conditions. By excluding it, the analysis is effectively constrained to clear-sky scenarios. This limitation should be explicitly acknowledged and clearly stated in the discussion.

4e. Uncertainty in wavelength alignment

Section 4.2.8 addresses wavelength alignment uncertainty, but the proposed treatment is incomplete. The wavelength shifts should first be minimized through the application of an improved dispersion equation, after which any residual shifts can be analyzed to assess temporal variability. Ignoring this step may overestimate the uncertainty or fail to correct for avoidable errors.

4f. Separation of systematic and random error sources

There appears to be a fundamental issue in how error sources are classified and treated. It seems that all sources of error were handled as random, without distinguishing between random and systematic effects. This approach leads to implausible outcomes, such as the claim that the UV Index can be determined with an uncertainty (0.28–0.53%) lower than that of the irradiance calibration lamps themselves (line 538). The authors should clearly explain how systematic and random error sources were identified and subsequently treated in the uncertainty analysis.

5. Calibration and measurements

In standard practice, the uncertainty budget for UV irradiance measurements is assessed in two distinct phases: one for the calibration process and one for actual solar measurements (e.g., Bernhard and Seckmeyer, 1999). This distinction is important because calibration is itself a measurement procedure and shares several uncertainty sources with field measurements. Typically, the uncertainty associated with the calibration is propagated and added to the overall uncertainty of the spectral UV irradiance. Given that the authors employed a Monte Carlo method, it would be expected that the analysis reflects this two-phase approach, explicitly separating and then combining the calibration and measurement uncertainties. This methodological structure appears to be missing from the current work.

6. Bibliographic references

The bibliography omits several relevant studies related to uncertainty analysis in Brewer spectrophotometer measurements. Notably, valuable insights can be found not only in works addressing UV irradiance, but also in studies focused on trace gas retrieval and aerosol optical depth (AOD) measurements using the Brewer in direct-sun mode. These references often include rigorous uncertainty analyses that could enhance the methodology of this study. The authors should broaden the literature review to incorporate these contributions.

7. Section 5

Section 5 could be significantly shortened or removed entirely. Much of the content is either self-evident or repetitive of points that belong more appropriately in the Introduction.

TECHNICAL REMARKS

• The terminology used for the Brewer instrument should be standardized throughout the manuscript. The correct and commonly accepted term is “Brewer spectrophotometer“. The inconsistent use of terms such as “spectroradiometer“ or “spectrometer“ is confusing. If the authors want to emphasize the Brewer's capability to measure global irradiance, the more general term Brewer “instrument“ may be appropriate in that context.
• Line 25: Please note that only a limited number of steps in the algorithm are non-linear, and these are likely to represent minor contributors to the total uncertainty.
• Line 30: The statement that stray light depends simply or solely on UV intensity is inaccurate.
• Line 57: The phrase “is trying” is outdated as the COST Action Eubrewnet has concluded. Please revise to reflect the current status.
• Line 60: Appropriate bibliographic references on the “well-established QA for UV measurements“ must be included.
• Line 61: Please clarify whether the intended meaning is ozone, UV irradiance, or both.
• Line 96: It should be explicitly stated that a diffuser is used as the global entrance optic for irradiance measurements.
• Line 99: Please include an explanation that the diffraction grating is rotated during UV spectral scans. Also, provide a description of Filter Wheel #3 (FW#3) for MkIV Brewers.
• Table 1: The column listing operator names should be omitted. Rather, the characteristics of the diffuser used with each Brewer would be more relevant to the technical discussion.
• Line 110: The cosine error can be mitigated through appropriate correction methods, as discussed in Section 3.1.3.
• Line 129: Clarify how the angular response characterization was conducted for the two additional Brewers.
• Line 131: Replace “dawn” with “sun rise”.
• Lines 141–142: The names of instrument operators should be moved to the Acknowledgements section.
• Line 149: Please provide a proper citation or link to the Eubrewnet guidelines referenced.
• Lines 154–155: The rationale for completely ignoring certain uncertainty sources is not adequately justified. It is unclear whether this was actually done and, if so, on what basis.
• Line 177: The statement that the coefficients are "deemed reliable" is misleading. The two coefficients referenced were derived for ozone and SO2 retrievals in direct sun mode, not for spectral UV irradiance. Their applicability to spectral UV measurements should be justified.
• Lines 201–202: All Brewer measurements, not only global UV scans, collect dark count data. Therefore, the authors could have considered a much larger dataset, potentially an order of magnitude more observations per day.
• Line 215: Please specify which laboratories or types of labs are being referred to.
• Line 219: The text should elaborate on the effect of the current uncertainty.
• Line 229: Clarify how the reference plane issue for Brewer #150 was resolved.
• Line 242: The statement referencing a “3%” drift lacks a time frame. Please specify the period over which this drift was observed.
• Lines 252–253: The wavelength dependency of the stated effect should be included. Please indicate the specific wavelength used in this calculation.
• Lines 271–272: A formula should be included to clarify the described temperature dependence. Specify whether the linear relationship applies to raw count rates or their logarithms.
• Line 273: According to Eq. 9, the irradiance is divided by 1 + C(T – T_ref), not simply by the correction factor C.
• Line 285: Avoid using the same variable name (C) for both the temperature and cosine corrections.
• Lines 360–364: Describe how systematic error sources were treated for the Brewer instruments that lacked a full calibration.
• Line 372: A plot comparing the ratios between instruments should be included. These ratios should then be compared with the corresponding percentage uncertainties to assess the consistency of the results.
• Line 377: The sentence "the uncertainty increases as wavelength grows and SZA decreases" is highly misleading. While the absolute uncertainty may increase, the relative (%) uncertainty generally decreases.
• Figure 3 and Line 402: The fluctuations observed in the data from Brewers #158 and #151 should be discussed. If these variations are attributable to an outdated or inaccurate dispersion function, then why this function was not updated prior to the analysis?
• Line 461: Clarify whether the term “error” or “uncertainty” is intended here. Also, please verify the stated values using the inverse square law.
• Lines 518–520: The statement is misleading. Total ozone column (TOC) is typically derived from direct-sun observations, not from spectral UV irradiance measurements.
• Lines 542–549: Ozone is only one of several atmospheric factors that influence long-term changes in UV irradiance. Other contributors can also introduce significant variability and trends.
• Line 622: Calibration should be conducted more frequently than once per year. Critically, it should be stated explicitly that the calibration lamps themselves must be periodically recalibrated, and up-to-date certificates must be used.
• Lines 622–623: The cosine error should be characterized and corrected systematically. If uncorrected, replacing the diffuser could introduce a step-change in the time series data, undermining the consistency of long-term measurements.