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.
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RC1: 'Comment on egusphere-2025-4297', Xavier Romão, 03 Nov 2025
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AC1: 'Reply on RC1', Chiara Arrighi, 13 Nov 2025
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We sincerely thank Prof. Xavier Romão for the careful reading of our manuscript and for the thoughtful and constructive comments provided. We highly appreciate the detailed feedback (Comments 1–14), 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 study’s 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. Romão 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
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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 RC1’s 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 ‘cultural heritage sites’, 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 ‘cultural heritage buildings’, 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 ‘buildings’ or clearly distinguishing the terms along the manuscript, when necessary.
- Lines 71–72: The statement “To 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.” 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 ‘location of openings’ and ‘location of artwork’. 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, ‘location’ 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 119–120, the phrase “only the internal non-structural components of the building (Custer et al., 2015)” 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 69–70) to reinforce the defined scope from the outset. This observation also corresponds with RC1’s comment regarding terminology: the expression ‘building envelope’ may be less precise in this context, and ‘interior finishes’ might more accurately convey the type of elements assessed.
- Lines 461–463: 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 486–493: 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 ‘current price lists’, 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
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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 reviewer’s 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 reviewer’s 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 reviewer’s 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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- 1
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 “the "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 items”, 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 “building's internal envelope”, which is a rather unusual terminology. Do they mean “interior finishes”? This unusual terminology should be replaced across the manuscript.
- 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.
- 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.
- In the assumptions of Section 2.3, the authors should include that material uniformity is assumed along the height of a given floodable floor.
- 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?
- In Section 2.4, explain the reasoning behind the seven levels of exposure heights that were considered for each asset. Why 7?
- In Section 2.4, additional clarification is necessary regarding Eq. (7). 𝑅𝐶k,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), 𝑅𝐶k,j should be a function of w. As it is, Eq. (7) only works if 𝑅𝐶k,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 “the affected area (or linear meters of damaged material) is quantified based on the building’s perimeter”, 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.
- 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.
- In the Conclusions the authors refer that one of their contributions is the “monetary assessment of direct total flood-related losses to CH”. This is a bold statement that implies a level of comprehensive loss/damage analysis that is not achieved. Even if the “other artworks” 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.