the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Oct 2025
Flood vulnerability models for damage assessment of artworks and cultural heritage buildings
Abstract. The assessment of flood-related losses to cultural heritage (CH) remains one of the most underexplored areas in flood risk management, largely due to the complexity of CH assets and their multiple, often intangible, values. In this study, extensive field data collection and archival research on artwork restoration costs were undertaken to support a synthetic approach for developing vulnerability models for both the building envelope and internal artworks across three primary CH asset types: places of worship, museums, and libraries. The methodology was applied to the historic city of Florence (Italy), enabling the derivation of mean and percentile vulnerability curves from a sample of 48 inspected CH buildings. For a 500-year flood scenario, estimated average losses amount to approximately €2.5 million for the building envelope and €3 million for artworks per asset, with total damages to CH in the city reaching approximately €550 million. While direct monetary loss estimates are subject to considerable uncertainty, the model results align well with available ex-post data, particularly for places of worship. These findings demonstrate that flood-related monetary losses to CH assets are far from negligible when compared to other damage categories, such as residential buildings, and therefore warrant increasing attention from the scientific and policy-making communities.
Competing interests: The contact author has declared that neither of the authors has any competing interests.
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RC1: 'Comment on egusphere-2025-4297', Xavier RomĆ£o, 03 Nov 2025
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AC1: 'Reply on RC1', Chiara Arrighi, 13 Nov 2025
We sincerely thank Prof. Xavier RomĆ£o for the careful reading of our manuscript and for the thoughtful and constructive comments provided. We highly appreciate the detailed feedback (Comments 1ā14), which has been extremely valuable in identifying aspects that require clarification and refinement to improve the methodological transparency and robustness of our work.
We will carefully consider and address all the points raised in a thoroughly revised version of the manuscript. In particular, we will clarify the methodological assumptions (e.g., the classification of artwork types, the definition of parameters, and the use of terminology), provide more detailed explanations of the equations and their practical implications, and expand the discussion of the studyās limitations and applicability.
We would also like to emphasize that this research represents an embryonic attempt to quantify monetary flood-related damage to cultural heritage assets (i.e., restoration costs) by integrating empirical post-event data and synthetic modeling approaches. Developing vulnerability functions for artworks and heritage buildings is a complex task, as the reviewer knows, constrained by data scarcity, heterogeneity of assets, and high uncertainty in damage mechanisms. We therefore acknowledge that several methodological and interpretive challenges remain, and in the revised version we will better highlight these limitations and the exploratory nature of the proposed framework, positioning it as a foundational step toward more comprehensive and validated future applications.
Once again, we thank Prof. RomĆ£o for his insightful and constructive suggestions, which will substantially contribute to improving the clarity, rigor, and impact of our manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-4297-AC1
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AC1: 'Reply on RC1', Chiara Arrighi, 13 Nov 2025
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RC2: 'Comment on egusphere-2025-4297', Anonymous Referee #2, 29 Nov 2025
Thank you for the opportunity to review this manuscript. I consider the work to present a valuable scientific contribution, particularly in its development of vulnerability functions that account for non-structural damage of cultural heritage buildings and artworks. The study appropriately addresses libraries/archives, museums, and places of worship, using synthetic modelling informed by data from past flood events, applied to 48 cultural heritage sites located in the historic centre of Florence. Additionally, the inclusion of repair cost estimations for flood-related losses to cultural heritage under a defined flood scenario enhances the practical relevance of the findings. I recommend the manuscript for publication. However, I also concur with the comments raised by Reviewer RC1, which align with several issues I detected during my evaluation. These points highlight aspects of the paper that are not entirely clear in their current form and could benefit from further explanation or reformulation to improve readability and methodological transparency. While I will outline specific comments from my review below, I emphasize that many of RC1ās observations reflect broader structural issues that, in my view, warrant careful attention and revision.
Specific comments:
- Lines 309 and 315: I suggest that the authors reconsider the terminology used in Section 4.1, as in this section refers to ācultural heritage sitesā, which is technically correct, as a cultural heritage building can be considered a site. However, throughout the paper, the application of the methodology is predominantly described in relation to ācultural heritage buildingsā, and this terminology appears more building-oriented in other sections. For clarity and uniformity, I recommend homogenizing the terminology across Section 4.1. using consistently the term ābuildingsā or clearly distinguishing the terms along the manuscript, when necessary.
- Lines 71ā72: The statement āTo the best of our knowledge, this is the first study to undertake a comprehensive analysis of restoration activities and their associated costs, enabling the quantification of direct economic losses.ā could benefit from rephrasing. As written, it presents a broad claim that may imply novelty across all hazard types. I suggest specifying that this assertion applies within the context of flood-related impacts, since comparable analyses may exist for other hazards, such as seismic vulnerability studies, even if the authors are unaware of them. Clarifying the hazard scope would prevent potential misunderstanding and strengthen the credibility of the claim.
- In Table 1, I suggest reconsidering the terminology used for ālocation of openingsā and ālocation of artworkā. As written, their meaning becomes clearer only after reading the subsequent explanation. To avoid ambiguity, I recommend adopting more explicit terminology in Table 1 that directly reflects the intended context. At first reading, ālocationā could be interpreted as referring to the room/spatial placement inside the building, or to vertical positioning (e.g., basement, ground floor, upper floors). Clarifying this distinction would guide the reader more intuitively and reduce potential misinterpretation when consulting the table.
- In Section 2.2, several parameters are assigned a value of 0. While this may appear self-explanatory, it could be helpful to include a brief note or general remark before presenting the equation to clarify that the value 0 is used in cases where certain factors are not applicable to specific cultural items. Providing this explanation upfront would prevent the reader from having to infer the reasoning and would improve transparency in the interpretation of the parameters.
In Lines 119ā120, the phrase āonly the internal non-structural components of the building (Custer et al., 2015)ā could benefit from further clarification. As currently written, the sentence may lead the reader to infer that structural damage may have occurred but was excluded from the analysis for the sake of simplicity. It is not clear whether structural damage was present but disregarded, or whether it simply lies outside the scope of the study. I suggest briefly specifying the rationale, either indicating that structural damage was not observed in the selected cases or clarifying that it was intentionally excluded because the objectives of the study focus solely on non-structural, interior components. This clarification could also be reflected in the introduction (Lines 69ā70) to reinforce the defined scope from the outset. This observation also corresponds with RC1ās comment regarding terminology: the expression ābuilding envelopeā may be less precise in this context, and āinterior finishesā might more accurately convey the type of elements assessed.
- Lines 461ā463: Here, it may be beneficial to mention the specific contents of the museums when discussing the three most affected institutions. While it is logical that libraries generally incur higher repair costs, in this case the costs appear closely linked to the type of contents they hold. For example, the results for the National Library and the University Library seem consistent with their holdings of paper-based materials and books, which are highly susceptible to water damage. However, for the Archaeological Museum, it would strengthen the discussion to briefly indicate the types of collections that contribute to their high ranking in artwork-related damages. Specifying the materials or artifacts affected would help the reader better understand the rationale behind.
Lines 486ā493: In line 490, the manuscript notes that the repair costs from the 1966 floods, as reported by conservators, were aligned with current price lists. I wonder whether this adjustment accounts for inflation, as also noted by RC1, or if other factors were considered when aligning historical costs with present-day values. Additionally, when referring to ācurrent price listsā, it would be helpful to clarify whether this refers to a standardized current list of material costs and labour rates for specialized conservators/restorers in Italy, and whether such a reference exists in a document or table that could be cited. If my interpretation is correct, the authors analysed the receipts from 1966 and updated the material and labour costs to present-day values. However, it is not clear whether there might be elements from the original receipts that are currently considered necessary for restoration (e.g., administrative and permit-related expenses required for the intervention), and whether those aspects were accounted for in the alignment process. If appropriate, I suggest refining the methodology description to improve transparency and reproducibility.
I hope my comments are clear and helpful in improving the clarity and readability of the manuscript. Should any point require further clarification, please do not hesitate to reach out.
Citation: https://doi.org/10.5194/egusphere-2025-4297-RC2 -
AC2: 'Reply on RC2', Chiara Arrighi, 09 Dec 2025
We sincerely thank the Anonymous Referee #2 for the positive evaluation of our manuscript and for recognizing the scientific and practical value of our contribution, particularly the development of vulnerability functions for cultural heritage buildings and artworks and the estimation of repair costs under a defined flood scenario. We also appreciate the reviewerās alignment with many of the observations raised by Reviewer RC1, and we are grateful for the additional clarifications and suggestions provided in this review.
We will carefully address each of the specific points raised in the revised manuscript. In particular, we will improve the consistency of terminology across sections, refine overly broad or ambiguous statements, clarify the meaning and use of parameters in the methodological framework, and expand explanations where additional context is needed, such as in the discussion of restoration cost data, the role of structural vs. non-structural components, and the interpretation of the results for the most affected institutions.
We acknowledge that several of the reviewerās comments highlight points that may hinder readability and methodological transparency in the current version of the manuscript. We agree with this assessment and will use the revision process to reorganize and clarify key sections to ensure smoother progression, clearer scope definition, and more intuitive presentation of concepts and terminology.
This study represents an embryonic and inherently challenging attempt to quantify flood-related losses for a wide variety of cultural heritage assets. The work is constrained by heterogeneity of materials, scarcity of detailed historical documentation, the need to harmonize data from different sources and periods, and the difficulty of translating restoration practices, highly specific and context-dependent, into a generalizable analytical framework. We appreciate the reviewerās recognition of these complexities, and in the revised version we will more explicitly articulate the limitations and exploratory nature of our approach. This will help situate our contribution as a foundational step toward more refined and validated methodologies in the future.
We once again thank the reviewer for the constructive comments, which will significantly improve the clarity, readability, and robustness of the revised manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-4297-AC2
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AC2: 'Reply on RC2', Chiara Arrighi, 09 Dec 2025
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RC3: 'Comment on egusphere-2025-4297', Anonymous Referee #3, 22 Feb 2026
This manuscript addresses a genuinely underexplored problem, the quantitative assessment of flood-induced damages to cultural heritage assets at city scale, and the development of detailed vulnerability models. Furthermore, the data collection effort is substantial. However, the manuscript requires significant revision before it can be considered for publication. The main concerns relate to: (i) inconsistent and not clear terminologies, (ii) insufficient justification of site selection, (iii) an overreaching objective statement relative to the actual analytical scope, (iv) extension to city-scale assessment.Ā
Inconsistent terminologies
The manuscript employs multiple terms (e.g. cultural heritage assets, cultural assets, cultural heritage sites, and cultural buildings) without definition or consistent application. The authors are encouraged to adopt a single term throughout; cultural heritage buildings and contents would align naturally with the two-component structure of the damage assessment (building fabric and artworks) and would be immediately interpretable.
Beyond this, several category-level terms require clarification. Libraries and archives are used interchangeably, yet they are institutionally distinct: libraries typically hold publicly accessible collections, while archives manage records under different access and conservation regimes. It is unclear whether this distinction is material to the vulnerability functions derived, and the authors should address it explicitly.
Places of worship is used throughout as a typological category without specification of the building types it encompasses. The category plausibly includes Catholic churches, oratories, monasteries, and baptisteries, which differ considerably in spatial configuration, artwork distribution, and flood exposure profile. A brief characterisation of the building types included is necessary, particularly given that vulnerability curves are aggregated at this category level.
Finally, building envelope defined by the authors as internal non-structural components (plaster finishes, flooring, and utility systems) is non-standard and likely to mislead readers familiar with the conventional use of the term to denote the external building shell. A clearer alternative, such as interior building fabric or non-structural interior components, should be adopted and defined at first use.
Site selection
The reduction from 175 classified CH sites to 48 inspected sites is stated but never justified (284ā285). For example (309) states that the analysed sites include places of worship, museums, and libraries. While (287-288) refers also to museums, places of worship, palaces, libraries, and archives. Based on these inconsistencies, the following questions must be addressed:
- Were the 48 sites selected based on flood exposure (i.e., falling within the modelled inundation zone)?
- Was selection driven by managerial availability, implying potential self-selection bias toward better-resourced, more prominent institutions?
- Is the sample proportionally representative of the 175 sites population by typology and footprint size?
- Were any sites excluded due to access restrictions or data insufficiency?
Without answers to these questions, the representativeness of the derived vulnerability curves is unknown, and the upscaling to the full city (Section 4.3) cannot be made (470-473). A dedicated paragraph addressing selection criteria and representativeness is essential, ideally with a statistical comparison of the sample versus the full population by typology distribution and/or building footprint area.
Objective and analytical scope
There is a significant mismatch between the stated objective and the actual analytical scope that must be addressed. The study frames its aim as developing vulnerability functions "at the city scale" (66) and evaluating "overall city-scale damage" (72), yet the methodology is applied to 48 selected buildings within the perimeter of Florence, not the city as a whole. The authors themselves acknowledge this implicitly by describing the sample as "selected buildings" (74). These two characterisations are irreconcilable without explicit clarification of what "city scale" is intended to mean in this context. The authors should either reframe the objective to reflect what the study actually delivers - a site-level synthetic vulnerability assessment applied to a sample of CH buildings within a historic urban core, with city-level aggregation presented as a secondary, exploratory estimate rather than a primary result - or provide a more detailed explanation, as the current formulation (66ā72) would benefit from substantial clarity improvements. Additionally, the claim that this is "the first study to undertake a comprehensive analysis of restoration activities and their associated costs" (71ā72) requires careful qualification: the analysis explicitly excludes several artwork categories for which archival data were insufficient, and validation is demonstrated only for places of worship, making the descriptor "comprehensive" difficult to sustain.
City-scale assessment
The extension of median volumetric damage (EUR 875/m3) to 127 non-inspected buildings, yielding an additional EUR 257 million and a city total of EUR 527 million (470ā474), is the most problematic step in the manuscript. The authors acknowledge that CH buildings are highly heterogeneous in spatial configuration, artwork distribution, and flood exposure, and that this heterogeneity is precisely what motivates individual site inspection rather than generalised damage functions. The extrapolation step effectively reverses this position by assuming that 127 non-inspected buildings are sufficiently comparable to the 48 inspected ones to warrant application of a single median damage metric. Moreover, there is an unresolved numerical discrepancy between "EUR 550 million" in the abstract and "EUR 527 million" in Section 4.3. These figures must be reconciled. The authors should either present the city-scale total as a rough-order-of-magnitude estimate with explicit uncertainty bounds, clearly separated from the validated site-level results, or relocate it entirely to a limitations and future work section.
Furthermone, other points to revise in the manuscript:
In the introduction section (42-45):
The paragraph introduces the Vecvagars (2006) value taxonomy to contextualise the scope of the damage assessment, but the conceptual link between the cited framework and the methodological approach actually adopted is not established. Specifically the taxonomy adopted in the Vecvagars (2006) refers to āextractive use valueā in terms of market-observed revenues generated by the asset, not restoration expenses following a damaging event. Restoration costs represent a measure of physical loss, not a direct proxy for market value. The authors should either clarify explicitly how their approach maps onto the cited framework, or replace this conceptual framing with a more appropriate theoretical grounding for cost-based damage assessment.
In the methodology section:
- Fig.1: Missing āRestoration cost for āenvelopeā - so the Figure should also include the integration of the Dottori et al. (2016) model.
- The survey forms from Molinari et al. (2014) and De Lucia et al. (2024) are cited as inspiration, but the degree of adaptation is unspecified (92-94). Clarify what was retained, modified (and why), or added for the CH-specific pre-event vulnerability survey context.
Overall, I believe that the manuscript is of great interest and it addresses relevant methodological gaps and so for this reason I hope my comments are contributing in improving the clarity of the presented work.
Citation: https://doi.org/10.5194/egusphere-2025-4297-RC3 -
AC3: 'Reply on RC3', Chiara Arrighi, 03 Mar 2026
Dear Reviewer #3,
We sincerely thank you for your thorough and constructive assessment of our manuscript. We greatly appreciate the time and care you have dedicated to reviewing our work, and we are encouraged by your recognition of the relevance of the research question and the value of the data collection effort.
We fully acknowledge the need for substantial revision and will carefully address all the points you have raised in the revised manuscript.
Regarding terminology, we agree that consistency and clarity are essential. We will adopt a single, clearly defined term throughout the manuscript and ensure that it aligns coherently with the two-components of the damage assessment and find a more appropriate and unambiguous expression and define it clearly at first use.
Concerning site selection, we recognize that the current manuscript does not sufficiently justify the reduction from 175 classified sites to the 48 inspected buildings. In the revised version, we will include a dedicated paragraph detailing the selection criteria, addressing flood exposure, accessibility constraints, managerial availability, and data completeness. We will also discuss the relationship between the inspected sample and the full population (e.g., typology distribution) to clarify representativeness and explicitly discuss potential sources of bias.
With respect to the objective and analytical scope, we appreciate your observation regarding the mismatch between the stated ācity-scaleā ambition and the effective scope of the analysis. In the revision, we will reframe the objective to reflect more accurately the site-level vulnerability assessment applied to a sample within the historic urban core. We will also qualify the claim of ācomprehensive analysisā to ensure it accurately reflects the categories included, the limitations of the archival data, and the scope of the validation exercise.
Regarding the city-scale extrapolation, we acknowledge your concerns about heterogeneity and the application of a single median volumetric damage value to non-inspected buildings. In the revised manuscript, we will clarify the assumptions underlying this step, reconcile the numerical discrepancy between the abstract and Section 4.3, and present the aggregated total strictly as a rough-order-of-magnitude estimate. Given the limited availability of quantitative studies on flood damage to cultural heritage, we believe that also orders of magnitude might help understand the contribution of this kind of loss in the overall computation of total losses.
We will also revise the additional specific points raised.
Overall, we are grateful for your detailed and thoughtful comments. They will substantially improve the clarity, transparency, and scientific robustness of the manuscript. We are committed to addressing each point carefully and systematically in the revised version.
Citation: https://doi.org/10.5194/egusphere-2025-4297-AC3
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2025-4297', Xavier RomĆ£o, 03 Nov 2025
The study provides an interesting study that addresses the quantification of flood-related damage to cultural heritage assets in Florence. In this approach, the authors develop vulnerability functions for cultural heritage buildings and artworks, combining empirical data with synthetic modelling. While the topic is relevant and timely to current debates on heritage resilience and disaster risk reduction, the following comments highlight a few points that should be addressed in a revised version of the manuscript to increase methodological clarity and robustness:
- In Section 2.1, the authors refer that āthe "content features" section of the survey focused primarily on the most common artwork types: panel or canvas paintings, frescoes, stone or wooden sculptures, and paper-based itemsā, and that everything else is assigned to other "Other artworks". Assuming the authors are proposing a general methodology that could be applied in other scenarios outside the one they are using to illustrate their proposal, this seems to be an arbitrary decision that should be clarified or better discussed, at least. If the authors consider that in their case study, damage to metal- or textile-based artworks are negligible, this should be said, but it should also be highlighted that the methodology can be applied to any type of material as long as data to characterize the cost-related factors are available. Addressing this issue needs to also consider what is written in Section 2.4 on this matter. Moreover, if the authors decided not to include these other artworks because there are no data available to quantify these cost-related factors, this must be made clear, and the topic must be revisited in the discussion section to highlight the limitations of the presented results.
- In Section 2.2, the authors use the term ābuilding's internal envelopeā, which is a rather unusual terminology. Do they mean āinterior finishesā? This unusual terminology should be replaced across the manuscript.Ā
- In Section 2.2, when introducing Eq. (1), it should be referred that it is for each artwork k or the kth artwork, for clarity (otherwise k remains undefined).
- In Section 2.2, the authors should clarify the practical use implications of their restoration cost assessment framework. From my understanding of the proposed framework, it is not supposed to be used based on the availability of an estimate of the physical damage to a given artwork. This issue comes from the fact that 1) it is difficult to predict the actual level of physical damage that will occur if an asset is exposed to a certain water level (namely due to some of the uncertain factors listed by the authors such as floodwater contamination, the amount of water the artwork was submerged in, the duration, etc.) and 2) it is also difficult to estimate the level of physical damage of the damaged assets for which the authors have the repair cost values. In light of these issues, the practical application of the proposed framework seems to establish the repair cost of a given asset by assessing the expected water level that can be reached in a flood at the location of the asset, and it then assigns minimum and maximum values of the repair cost (which accounts for the referred uncertain factors) to the asset in case the water level reaches it. If this interpretation is correct, it should be clearly described in the manuscript. If not, the authors should clearly describe how the repair cost is established based on physical damage.Ā
- In Section 2.3, line 175, the parameter for opening heights (ho,i) has an index i that is not defined. Note that, later, the letter i is used for the ith cultural heritage asset.Ā
- In the assumptions of Section 2.3, the authors should include that material uniformity is assumed along the height of a given floodable floor.Ā
- In Section 2.4, more details should be provided (to ensure replicability of the procedure that was used) about the statistical analysis that was carried out to determine the average surface area potentially exposed to floodwater. What is a statistically significant sample in this context? What were the artwork typologies that were selected? Paintings on canvas and painting on panels, or others? Can the data that was used actually be accessed thought the link that was provided?Ā
- In Section 2.4, explain the reasoning behind the seven levels of exposure heights that were considered for each asset. Why 7?Ā
- In Section 2.4, additional clarification is necessary regarding Eq. (7). š š¶k,j is said to be the maximum unit restoration cost for artworks and, for the case of large of large artworks, it is also said the cost depends on the water level w. This means that, in Eq. (7), š š¶k,j should be a function of w. As it is, Eq. (7) only works if š š¶k,j a restoration cost per meter or if w is a water level normalized by a maximum water level value, but this is not said. Similarly, the component associated with small-sized artworks does not seem to depend on the water level. As it is, the expressions just adds a constant value, which does not seem right. In addition, parameter P is also not clear. This parameter is said to be the perimeter of the cultural heritage asset in Eq. (2) but its use in Eq. (7) implies that all large artworks cover the entire perimeter of a given building, but what is said at the beginning of this section is that āthe affected area (or linear meters of damaged material) is quantified based on the buildingās perimeterā, which is not the same. Detailed clarifications of these issues need to be included in the revised version of the manuscript to help the reader understand the proposed approach.
- In Section 2.4, the role of the CRI (Eq. 9) is not clear. How is it expected to be used with the proposed methodology for developing vulnerability functions? It seems that its role is that of an uncertainty factor that provides extra information about the reliability of the predicted damage or vulnerability, but this is not clearly explained when the CRI is introduced. Moreover, the qualitative scale shown in Fig. 7 d) is not explained and justified.Ā
- In Section 3.2, clarify what criteria were used to select the 48 sites (among the 175) to which the proposed methodology was applied to.
- Regarding the costs reported in Section 4.1, it is assumed that they are corrected for inflation, but this should be said, nonetheless.
- Section 4.4 should discuss/refer a few aspects that underline the proposed application: the applicability of the proposed methodology relies on the availability of enough detailed post-disaster data to establish the repair cost components that are considered in the method. While this is something that should be clearly emphasized to highlight the importance of collecting and sharing such data. In cases where such data are not available, the authors should discuss how to proceed. What proxies or what approach could be used to determine these cost components? This is particularly important in order to clarify the scalability of the proposed methodology.Ā
- In the Conclusions the authors refer that one of their contributions is the āmonetary assessment of direct total flood-related losses to CHā. This is a bold statement that implies a level of comprehensive loss/damage analysis that is not achieved. Even if the āother artworksā are indeed negligible, what the authors achieve is an estimate of the quantifiable direct losses represented by the repair costs. These are not the total direct losses. For example, losses due to destroyed assets (i.e. irreparable) are not accounted for, as well as the loss in market value of assets that may have a market value. In light of this, this final statement should be rewritten accordingly.Citation: https://doi.org/10.5194/egusphere-2025-4297-RC1 -
AC1: 'Reply on RC1', Chiara Arrighi, 13 Nov 2025
We sincerely thank Prof. Xavier RomĆ£o for the careful reading of our manuscript and for the thoughtful and constructive comments provided. We highly appreciate the detailed feedback (Comments 1ā14), which has been extremely valuable in identifying aspects that require clarification and refinement to improve the methodological transparency and robustness of our work.
We will carefully consider and address all the points raised in a thoroughly revised version of the manuscript. In particular, we will clarify the methodological assumptions (e.g., the classification of artwork types, the definition of parameters, and the use of terminology), provide more detailed explanations of the equations and their practical implications, and expand the discussion of the studyās limitations and applicability.
We would also like to emphasize that this research represents an embryonic attempt to quantify monetary flood-related damage to cultural heritage assets (i.e., restoration costs) by integrating empirical post-event data and synthetic modeling approaches. Developing vulnerability functions for artworks and heritage buildings is a complex task, as the reviewer knows, constrained by data scarcity, heterogeneity of assets, and high uncertainty in damage mechanisms. We therefore acknowledge that several methodological and interpretive challenges remain, and in the revised version we will better highlight these limitations and the exploratory nature of the proposed framework, positioning it as a foundational step toward more comprehensive and validated future applications.
Once again, we thank Prof. RomĆ£o for his insightful and constructive suggestions, which will substantially contribute to improving the clarity, rigor, and impact of our manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-4297-AC1
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AC1: 'Reply on RC1', Chiara Arrighi, 13 Nov 2025
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RC2: 'Comment on egusphere-2025-4297', Anonymous Referee #2, 29 Nov 2025
Thank you for the opportunity to review this manuscript. I consider the work to present a valuable scientific contribution, particularly in its development of vulnerability functions that account for non-structural damage of cultural heritage buildings and artworks. The study appropriately addresses libraries/archives, museums, and places of worship, using synthetic modelling informed by data from past flood events, applied to 48 cultural heritage sites located in the historic centre of Florence. Additionally, the inclusion of repair cost estimations for flood-related losses to cultural heritage under a defined flood scenario enhances the practical relevance of the findings. I recommend the manuscript for publication. However, I also concur with the comments raised by Reviewer RC1, which align with several issues I detected during my evaluation. These points highlight aspects of the paper that are not entirely clear in their current form and could benefit from further explanation or reformulation to improve readability and methodological transparency. While I will outline specific comments from my review below, I emphasize that many of RC1ās observations reflect broader structural issues that, in my view, warrant careful attention and revision.
Specific comments:
- Lines 309 and 315: I suggest that the authors reconsider the terminology used in Section 4.1, as in this section refers to ācultural heritage sitesā, which is technically correct, as a cultural heritage building can be considered a site. However, throughout the paper, the application of the methodology is predominantly described in relation to ācultural heritage buildingsā, and this terminology appears more building-oriented in other sections. For clarity and uniformity, I recommend homogenizing the terminology across Section 4.1. using consistently the term ābuildingsā or clearly distinguishing the terms along the manuscript, when necessary.
- Lines 71ā72: The statement āTo the best of our knowledge, this is the first study to undertake a comprehensive analysis of restoration activities and their associated costs, enabling the quantification of direct economic losses.ā could benefit from rephrasing. As written, it presents a broad claim that may imply novelty across all hazard types. I suggest specifying that this assertion applies within the context of flood-related impacts, since comparable analyses may exist for other hazards, such as seismic vulnerability studies, even if the authors are unaware of them. Clarifying the hazard scope would prevent potential misunderstanding and strengthen the credibility of the claim.
- In Table 1, I suggest reconsidering the terminology used for ālocation of openingsā and ālocation of artworkā. As written, their meaning becomes clearer only after reading the subsequent explanation. To avoid ambiguity, I recommend adopting more explicit terminology in Table 1 that directly reflects the intended context. At first reading, ālocationā could be interpreted as referring to the room/spatial placement inside the building, or to vertical positioning (e.g., basement, ground floor, upper floors). Clarifying this distinction would guide the reader more intuitively and reduce potential misinterpretation when consulting the table.
- In Section 2.2, several parameters are assigned a value of 0. While this may appear self-explanatory, it could be helpful to include a brief note or general remark before presenting the equation to clarify that the value 0 is used in cases where certain factors are not applicable to specific cultural items. Providing this explanation upfront would prevent the reader from having to infer the reasoning and would improve transparency in the interpretation of the parameters.
In Lines 119ā120, the phrase āonly the internal non-structural components of the building (Custer et al., 2015)ā could benefit from further clarification. As currently written, the sentence may lead the reader to infer that structural damage may have occurred but was excluded from the analysis for the sake of simplicity. It is not clear whether structural damage was present but disregarded, or whether it simply lies outside the scope of the study. I suggest briefly specifying the rationale, either indicating that structural damage was not observed in the selected cases or clarifying that it was intentionally excluded because the objectives of the study focus solely on non-structural, interior components. This clarification could also be reflected in the introduction (Lines 69ā70) to reinforce the defined scope from the outset. This observation also corresponds with RC1ās comment regarding terminology: the expression ābuilding envelopeā may be less precise in this context, and āinterior finishesā might more accurately convey the type of elements assessed.
- Lines 461ā463: Here, it may be beneficial to mention the specific contents of the museums when discussing the three most affected institutions. While it is logical that libraries generally incur higher repair costs, in this case the costs appear closely linked to the type of contents they hold. For example, the results for the National Library and the University Library seem consistent with their holdings of paper-based materials and books, which are highly susceptible to water damage. However, for the Archaeological Museum, it would strengthen the discussion to briefly indicate the types of collections that contribute to their high ranking in artwork-related damages. Specifying the materials or artifacts affected would help the reader better understand the rationale behind.
Lines 486ā493: In line 490, the manuscript notes that the repair costs from the 1966 floods, as reported by conservators, were aligned with current price lists. I wonder whether this adjustment accounts for inflation, as also noted by RC1, or if other factors were considered when aligning historical costs with present-day values. Additionally, when referring to ācurrent price listsā, it would be helpful to clarify whether this refers to a standardized current list of material costs and labour rates for specialized conservators/restorers in Italy, and whether such a reference exists in a document or table that could be cited. If my interpretation is correct, the authors analysed the receipts from 1966 and updated the material and labour costs to present-day values. However, it is not clear whether there might be elements from the original receipts that are currently considered necessary for restoration (e.g., administrative and permit-related expenses required for the intervention), and whether those aspects were accounted for in the alignment process. If appropriate, I suggest refining the methodology description to improve transparency and reproducibility.
I hope my comments are clear and helpful in improving the clarity and readability of the manuscript. Should any point require further clarification, please do not hesitate to reach out.
Citation: https://doi.org/10.5194/egusphere-2025-4297-RC2 -
AC2: 'Reply on RC2', Chiara Arrighi, 09 Dec 2025
We sincerely thank the Anonymous Referee #2 for the positive evaluation of our manuscript and for recognizing the scientific and practical value of our contribution, particularly the development of vulnerability functions for cultural heritage buildings and artworks and the estimation of repair costs under a defined flood scenario. We also appreciate the reviewerās alignment with many of the observations raised by Reviewer RC1, and we are grateful for the additional clarifications and suggestions provided in this review.
We will carefully address each of the specific points raised in the revised manuscript. In particular, we will improve the consistency of terminology across sections, refine overly broad or ambiguous statements, clarify the meaning and use of parameters in the methodological framework, and expand explanations where additional context is needed, such as in the discussion of restoration cost data, the role of structural vs. non-structural components, and the interpretation of the results for the most affected institutions.
We acknowledge that several of the reviewerās comments highlight points that may hinder readability and methodological transparency in the current version of the manuscript. We agree with this assessment and will use the revision process to reorganize and clarify key sections to ensure smoother progression, clearer scope definition, and more intuitive presentation of concepts and terminology.
This study represents an embryonic and inherently challenging attempt to quantify flood-related losses for a wide variety of cultural heritage assets. The work is constrained by heterogeneity of materials, scarcity of detailed historical documentation, the need to harmonize data from different sources and periods, and the difficulty of translating restoration practices, highly specific and context-dependent, into a generalizable analytical framework. We appreciate the reviewerās recognition of these complexities, and in the revised version we will more explicitly articulate the limitations and exploratory nature of our approach. This will help situate our contribution as a foundational step toward more refined and validated methodologies in the future.
We once again thank the reviewer for the constructive comments, which will significantly improve the clarity, readability, and robustness of the revised manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-4297-AC2
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AC2: 'Reply on RC2', Chiara Arrighi, 09 Dec 2025
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RC3: 'Comment on egusphere-2025-4297', Anonymous Referee #3, 22 Feb 2026
This manuscript addresses a genuinely underexplored problem, the quantitative assessment of flood-induced damages to cultural heritage assets at city scale, and the development of detailed vulnerability models. Furthermore, the data collection effort is substantial. However, the manuscript requires significant revision before it can be considered for publication. The main concerns relate to: (i) inconsistent and not clear terminologies, (ii) insufficient justification of site selection, (iii) an overreaching objective statement relative to the actual analytical scope, (iv) extension to city-scale assessment.Ā
Inconsistent terminologies
The manuscript employs multiple terms (e.g. cultural heritage assets, cultural assets, cultural heritage sites, and cultural buildings) without definition or consistent application. The authors are encouraged to adopt a single term throughout; cultural heritage buildings and contents would align naturally with the two-component structure of the damage assessment (building fabric and artworks) and would be immediately interpretable.
Beyond this, several category-level terms require clarification. Libraries and archives are used interchangeably, yet they are institutionally distinct: libraries typically hold publicly accessible collections, while archives manage records under different access and conservation regimes. It is unclear whether this distinction is material to the vulnerability functions derived, and the authors should address it explicitly.
Places of worship is used throughout as a typological category without specification of the building types it encompasses. The category plausibly includes Catholic churches, oratories, monasteries, and baptisteries, which differ considerably in spatial configuration, artwork distribution, and flood exposure profile. A brief characterisation of the building types included is necessary, particularly given that vulnerability curves are aggregated at this category level.
Finally, building envelope defined by the authors as internal non-structural components (plaster finishes, flooring, and utility systems) is non-standard and likely to mislead readers familiar with the conventional use of the term to denote the external building shell. A clearer alternative, such as interior building fabric or non-structural interior components, should be adopted and defined at first use.
Site selection
The reduction from 175 classified CH sites to 48 inspected sites is stated but never justified (284ā285). For example (309) states that the analysed sites include places of worship, museums, and libraries. While (287-288) refers also to museums, places of worship, palaces, libraries, and archives. Based on these inconsistencies, the following questions must be addressed:
- Were the 48 sites selected based on flood exposure (i.e., falling within the modelled inundation zone)?
- Was selection driven by managerial availability, implying potential self-selection bias toward better-resourced, more prominent institutions?
- Is the sample proportionally representative of the 175 sites population by typology and footprint size?
- Were any sites excluded due to access restrictions or data insufficiency?
Without answers to these questions, the representativeness of the derived vulnerability curves is unknown, and the upscaling to the full city (Section 4.3) cannot be made (470-473). A dedicated paragraph addressing selection criteria and representativeness is essential, ideally with a statistical comparison of the sample versus the full population by typology distribution and/or building footprint area.
Objective and analytical scope
There is a significant mismatch between the stated objective and the actual analytical scope that must be addressed. The study frames its aim as developing vulnerability functions "at the city scale" (66) and evaluating "overall city-scale damage" (72), yet the methodology is applied to 48 selected buildings within the perimeter of Florence, not the city as a whole. The authors themselves acknowledge this implicitly by describing the sample as "selected buildings" (74). These two characterisations are irreconcilable without explicit clarification of what "city scale" is intended to mean in this context. The authors should either reframe the objective to reflect what the study actually delivers - a site-level synthetic vulnerability assessment applied to a sample of CH buildings within a historic urban core, with city-level aggregation presented as a secondary, exploratory estimate rather than a primary result - or provide a more detailed explanation, as the current formulation (66ā72) would benefit from substantial clarity improvements. Additionally, the claim that this is "the first study to undertake a comprehensive analysis of restoration activities and their associated costs" (71ā72) requires careful qualification: the analysis explicitly excludes several artwork categories for which archival data were insufficient, and validation is demonstrated only for places of worship, making the descriptor "comprehensive" difficult to sustain.
City-scale assessment
The extension of median volumetric damage (EUR 875/m3) to 127 non-inspected buildings, yielding an additional EUR 257 million and a city total of EUR 527 million (470ā474), is the most problematic step in the manuscript. The authors acknowledge that CH buildings are highly heterogeneous in spatial configuration, artwork distribution, and flood exposure, and that this heterogeneity is precisely what motivates individual site inspection rather than generalised damage functions. The extrapolation step effectively reverses this position by assuming that 127 non-inspected buildings are sufficiently comparable to the 48 inspected ones to warrant application of a single median damage metric. Moreover, there is an unresolved numerical discrepancy between "EUR 550 million" in the abstract and "EUR 527 million" in Section 4.3. These figures must be reconciled. The authors should either present the city-scale total as a rough-order-of-magnitude estimate with explicit uncertainty bounds, clearly separated from the validated site-level results, or relocate it entirely to a limitations and future work section.
Furthermone, other points to revise in the manuscript:
In the introduction section (42-45):
The paragraph introduces the Vecvagars (2006) value taxonomy to contextualise the scope of the damage assessment, but the conceptual link between the cited framework and the methodological approach actually adopted is not established. Specifically the taxonomy adopted in the Vecvagars (2006) refers to āextractive use valueā in terms of market-observed revenues generated by the asset, not restoration expenses following a damaging event. Restoration costs represent a measure of physical loss, not a direct proxy for market value. The authors should either clarify explicitly how their approach maps onto the cited framework, or replace this conceptual framing with a more appropriate theoretical grounding for cost-based damage assessment.
In the methodology section:
- Fig.1: Missing āRestoration cost for āenvelopeā - so the Figure should also include the integration of the Dottori et al. (2016) model.
- The survey forms from Molinari et al. (2014) and De Lucia et al. (2024) are cited as inspiration, but the degree of adaptation is unspecified (92-94). Clarify what was retained, modified (and why), or added for the CH-specific pre-event vulnerability survey context.
Overall, I believe that the manuscript is of great interest and it addresses relevant methodological gaps and so for this reason I hope my comments are contributing in improving the clarity of the presented work.
Citation: https://doi.org/10.5194/egusphere-2025-4297-RC3 -
AC3: 'Reply on RC3', Chiara Arrighi, 03 Mar 2026
Dear Reviewer #3,
We sincerely thank you for your thorough and constructive assessment of our manuscript. We greatly appreciate the time and care you have dedicated to reviewing our work, and we are encouraged by your recognition of the relevance of the research question and the value of the data collection effort.
We fully acknowledge the need for substantial revision and will carefully address all the points you have raised in the revised manuscript.
Regarding terminology, we agree that consistency and clarity are essential. We will adopt a single, clearly defined term throughout the manuscript and ensure that it aligns coherently with the two-components of the damage assessment and find a more appropriate and unambiguous expression and define it clearly at first use.
Concerning site selection, we recognize that the current manuscript does not sufficiently justify the reduction from 175 classified sites to the 48 inspected buildings. In the revised version, we will include a dedicated paragraph detailing the selection criteria, addressing flood exposure, accessibility constraints, managerial availability, and data completeness. We will also discuss the relationship between the inspected sample and the full population (e.g., typology distribution) to clarify representativeness and explicitly discuss potential sources of bias.
With respect to the objective and analytical scope, we appreciate your observation regarding the mismatch between the stated ācity-scaleā ambition and the effective scope of the analysis. In the revision, we will reframe the objective to reflect more accurately the site-level vulnerability assessment applied to a sample within the historic urban core. We will also qualify the claim of ācomprehensive analysisā to ensure it accurately reflects the categories included, the limitations of the archival data, and the scope of the validation exercise.
Regarding the city-scale extrapolation, we acknowledge your concerns about heterogeneity and the application of a single median volumetric damage value to non-inspected buildings. In the revised manuscript, we will clarify the assumptions underlying this step, reconcile the numerical discrepancy between the abstract and Section 4.3, and present the aggregated total strictly as a rough-order-of-magnitude estimate. Given the limited availability of quantitative studies on flood damage to cultural heritage, we believe that also orders of magnitude might help understand the contribution of this kind of loss in the overall computation of total losses.
We will also revise the additional specific points raised.
Overall, we are grateful for your detailed and thoughtful comments. They will substantially improve the clarity, transparency, and scientific robustness of the manuscript. We are committed to addressing each point carefully and systematically in the revised version.
Citation: https://doi.org/10.5194/egusphere-2025-4297-AC3
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Claudia De Lucia
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The study provides an interesting study that addresses the quantification of flood-related damage to cultural heritage assets in Florence. In this approach, the authors develop vulnerability functions for cultural heritage buildings and artworks, combining empirical data with synthetic modelling. While the topic is relevant and timely to current debates on heritage resilience and disaster risk reduction, the following comments highlight a few points that should be addressed in a revised version of the manuscript to increase methodological clarity and robustness:
- In Section 2.1, the authors refer that āthe "content features" section of the survey focused primarily on the most common artwork types: panel or canvas paintings, frescoes, stone or wooden sculptures, and paper-based itemsā, and that everything else is assigned to other "Other artworks". Assuming the authors are proposing a general methodology that could be applied in other scenarios outside the one they are using to illustrate their proposal, this seems to be an arbitrary decision that should be clarified or better discussed, at least. If the authors consider that in their case study, damage to metal- or textile-based artworks are negligible, this should be said, but it should also be highlighted that the methodology can be applied to any type of material as long as data to characterize the cost-related factors are available. Addressing this issue needs to also consider what is written in Section 2.4 on this matter. Moreover, if the authors decided not to include these other artworks because there are no data available to quantify these cost-related factors, this must be made clear, and the topic must be revisited in the discussion section to highlight the limitations of the presented results.
- In Section 2.2, the authors use the term ābuilding's internal envelopeā, which is a rather unusual terminology. Do they mean āinterior finishesā? This unusual terminology should be replaced across the manuscript.Ā
- In Section 2.2, when introducing Eq. (1), it should be referred that it is for each artwork k or the kth artwork, for clarity (otherwise k remains undefined).
- In Section 2.2, the authors should clarify the practical use implications of their restoration cost assessment framework. From my understanding of the proposed framework, it is not supposed to be used based on the availability of an estimate of the physical damage to a given artwork. This issue comes from the fact that 1) it is difficult to predict the actual level of physical damage that will occur if an asset is exposed to a certain water level (namely due to some of the uncertain factors listed by the authors such as floodwater contamination, the amount of water the artwork was submerged in, the duration, etc.) and 2) it is also difficult to estimate the level of physical damage of the damaged assets for which the authors have the repair cost values. In light of these issues, the practical application of the proposed framework seems to establish the repair cost of a given asset by assessing the expected water level that can be reached in a flood at the location of the asset, and it then assigns minimum and maximum values of the repair cost (which accounts for the referred uncertain factors) to the asset in case the water level reaches it. If this interpretation is correct, it should be clearly described in the manuscript. If not, the authors should clearly describe how the repair cost is established based on physical damage.Ā
- In Section 2.3, line 175, the parameter for opening heights (ho,i) has an index i that is not defined. Note that, later, the letter i is used for the ith cultural heritage asset.Ā
- In the assumptions of Section 2.3, the authors should include that material uniformity is assumed along the height of a given floodable floor.Ā
- In Section 2.4, more details should be provided (to ensure replicability of the procedure that was used) about the statistical analysis that was carried out to determine the average surface area potentially exposed to floodwater. What is a statistically significant sample in this context? What were the artwork typologies that were selected? Paintings on canvas and painting on panels, or others? Can the data that was used actually be accessed thought the link that was provided?Ā
- In Section 2.4, explain the reasoning behind the seven levels of exposure heights that were considered for each asset. Why 7?Ā
- In Section 2.4, additional clarification is necessary regarding Eq. (7). š š¶k,j is said to be the maximum unit restoration cost for artworks and, for the case of large of large artworks, it is also said the cost depends on the water level w. This means that, in Eq. (7), š š¶k,j should be a function of w. As it is, Eq. (7) only works if š š¶k,j a restoration cost per meter or if w is a water level normalized by a maximum water level value, but this is not said. Similarly, the component associated with small-sized artworks does not seem to depend on the water level. As it is, the expressions just adds a constant value, which does not seem right. In addition, parameter P is also not clear. This parameter is said to be the perimeter of the cultural heritage asset in Eq. (2) but its use in Eq. (7) implies that all large artworks cover the entire perimeter of a given building, but what is said at the beginning of this section is that āthe affected area (or linear meters of damaged material) is quantified based on the buildingās perimeterā, which is not the same. Detailed clarifications of these issues need to be included in the revised version of the manuscript to help the reader understand the proposed approach.
- In Section 2.4, the role of the CRI (Eq. 9) is not clear. How is it expected to be used with the proposed methodology for developing vulnerability functions? It seems that its role is that of an uncertainty factor that provides extra information about the reliability of the predicted damage or vulnerability, but this is not clearly explained when the CRI is introduced. Moreover, the qualitative scale shown in Fig. 7 d) is not explained and justified.Ā
- In Section 3.2, clarify what criteria were used to select the 48 sites (among the 175) to which the proposed methodology was applied to.
- Regarding the costs reported in Section 4.1, it is assumed that they are corrected for inflation, but this should be said, nonetheless.
- Section 4.4 should discuss/refer a few aspects that underline the proposed application: the applicability of the proposed methodology relies on the availability of enough detailed post-disaster data to establish the repair cost components that are considered in the method. While this is something that should be clearly emphasized to highlight the importance of collecting and sharing such data. In cases where such data are not available, the authors should discuss how to proceed. What proxies or what approach could be used to determine these cost components? This is particularly important in order to clarify the scalability of the proposed methodology.Ā
- In the Conclusions the authors refer that one of their contributions is the āmonetary assessment of direct total flood-related losses to CHā. This is a bold statement that implies a level of comprehensive loss/damage analysis that is not achieved. Even if the āother artworksā are indeed negligible, what the authors achieve is an estimate of the quantifiable direct losses represented by the repair costs. These are not the total direct losses. For example, losses due to destroyed assets (i.e. irreparable) are not accounted for, as well as the loss in market value of assets that may have a market value. In light of this, this final statement should be rewritten accordingly.