Based on a review of the literature as well as on our own modelling experience, we propose the methodological framework presented in Table . It is presented in the form of questions that are as many conditions to be respected for the development of process-based models from a capitalisation perspective. We detail the conditions of each axis in Sect.  to .

reviewed 47 flood damage models (process based or data driven) in order to create a basis for harmonisation and benchmarking. One of their main conclusions is that this requires profound insight into the model structures, mechanisms and underlying assumptions. In the following, we highlight which assumptions need to be made explicit.

Flood damage is usually classified into four types: direct tangible (e.g. physical damage due to contact with water), indirect tangible (e.g. loss of production and income), direct intangible (e.g. loss of life) and indirect intangible . To evaluate the flood effects on economic activities, defining the limits of the system considered is crucial to distinguish between direct and indirect damage since the flood impacts not only the property directly affected. As an example, in agricultural assets, identified damage induced at the farm scale due to the links between farm plots and buildings. shows the importance of interactions betweens farms and the cooperative at a winery cooperative scale and the consequences on flood damage estimation. Therefore, a clear definition of the boundaries and components of the system under consideration is necessary in order to avoid errors of double counted or uncounted damage. This refers to condition EA1 in Table .

Then, process-based models try to reflect physical or biophysical processes that occur in the considered system and which generate flood impacts. These processes are numerous, depend on the component of the system considered and may depend on different flood parameters . Explicit assumptions regarding which processes are considered as well as which components of the system and which flood parameters are involved are essential in process-based models . Condition EA2 (Table ) is developed in sub-conditions that help to detail how the biophysical processes due to a flood in the considered system are taken into account.

Finally, flood damage results in an interaction between the flood impacts and human behaviour . At the end, evaluating the damage in monetary terms requires knowledge of the repair and restoration choices made by the people affected and their costs. In data-driven modelling, these choices are implicitly included in the damage data collected. In process-based models, the property damage avoided technique is used . The repair choices and their costs are hypothetical and fed with expert knowledge. As a consequence, explicit assumptions on the decision rules considered are also critical to properly describe a process-based damage model. This refers to condition EA3 (Table ).

Although the research community has put a lot of effort into improving flood damage models, point to the lack of validation and identify three modalities for the validation of flood damage models, which are (i) the comparison with observed data, (ii) the comparison with other models, (iii) the use of expert judgement. In the methodological framework (Table ), condition V1 questions the possibility to compare the outputs with observed damage data and condition V2 to compare the models between them. However, for all sectors, and especially for the agricultural one, a lack of data to fully implement the first modality is commonly observed. In addition, sinistrality data should be considered with caution as they may only represent part of the damage that one wishes to compare. The insurance coverage of the different types of damage, in particular in agriculture, is not complete. As for the second one, a lot of work is being done to compare the different existing models in order to have a better idea of the uncertainties. However, the difficulties encountered are often related to the lack of explicit assumptions used in the approaches and modelling choices, which brings us back to the importance of properly addressing axis 1 of our methodological framework. The third modality is a validation related to the operationality and use of the model. We state that two perspectives should be distinguished: (i) adequacy with the stakeholders' expectations (condition V3), which is related to the use of the model in practice (V4), (ii) validation with the experts involved in the modelling process (V5). As for the second point, few experiences and methods have been found. Let us mention the experience of , who discussed with experts the data collected for the construction of damage functions in buildings. The methodology for validating the models with experts remains to be consolidated. Based on our own experience, we detail in condition V5, the sub-conditions which seem to us necessary for the validation by the experts involved in the modelling process in the following steps: (i) discussion of the modelling assumptions about processes and recovery actions, (ii) discussion of the monetisation values; (iii) discussion of the outputs.

Although some research exists on updating flood hazard models, for example by integrating climate change , the update of flood damage models remains minimally investigated but is necessary . Updatability is defined as the possibility of updating and should be understood as the anticipation in the modelling process of the possibility of updating the calibration data of the model. This notion is different from the update, which corresponds to updating the model outputs. It can be achieved through the updatability of the source data or through simplified methods of actualisation of the outputs. The update when it is addressed, concerns the values enabling the monetisation as, for example in the last version of the multi-coloured handbook . In general, the databases used are rarely made explicit and even less so the vintages. It is therefore important to verify whether the types of data and their sources are made explicit (condition U1, Table ), whether the database vintages used are specified (condition U2) and whether the databases are tracked over time (condition U3).

Transferring the flood damage model is a challenging issue . As we dealt with updating in Sect. , we focus here on transfer in space and on improvements of the model. Improving modelling techniques to transfer data-driven flood damage models has been widely explored . However, the transfer of process-based model is very challenging mainly because it requires in-depth understanding of the origin, calibration, assumptions and field of application, which brings us back again to the central issue of explicit modelling assumptions (Sect. ). Although process-based modelling approaches seem to be the most promising in terms of transferability, the lack of explicit assumptions hinders this and the models developed remain context-specific . For example, for the development of AGRIDE-c , floodam.agri was partially transferred. In particular, the yield loss coefficients were directly used after discussions with local experts. However, the part concerning the validation by experts remains poorly detailed in and . We are not sure that all the central assumptions of floodam.agri, namely biophysical processes and farmers' decisions, were sufficiently detailed in to enable transferability. Condition T1 (Table ) checks whether the adaptation, improvement or transfer conditions have been taken into account and described at the time of the model design. Condition T2 refers to the effective transfer of the model.

In France, since 2011, it has been mandatory for local flood risk managers to conduct cost–benefit analysis (CBA) of their flood management projects to make them eligible for financial support from the State. Meanwhile, as support, the French ministry in charge of the environment proposed a methodology to fulfil CBA . A working group of engineers and researchers of which we were part was charged with developing damage functions usable at a national scale. The idea was that the consulting firms in charge of the realisation of CBA for local flood risk managers could use these resources whatever the context. Two strategies were possible: reuse and adapt damage functions to the French context or develop our own functions. For the agricultural sector, among existing process-based models, the AGDAM model developed by the and the model developed by the FHRC stood out as being the most advanced. The possibility of adapting AGDAM or the FHRC damage functions was investigated. However, a review of the literature revealed that no existing damage function could meet the operational needs. Indeed, the ministry needed ready-to-use French National Damage Functions (i) that cover the vast majority of French agricultural crops and that were compatible with the databases used to locate them (Graphical Plot Register, GPR, which is the French Land Parcel Identification System, LPIS, connected to the Common Agricultural Policy), (ii) that are applicable at a national scale but can be adjusted to local specificities if needed (specific culture, selling price, etc.) and (iii) that are updatable, i.e. based on values from identified databases that can be tracked over time as far as possible. Then, the option selected was to develop our own damage functions. As in other countries, the lack of sinistrality data quickly led us to choose process-based models based on expert knowledge. In this paper, we focus on the floodam.agri model that we developed and that was used to produce the national damage functions. However, ready-to-use national flood damage functions have been developed for the residential sector, public infrastructures, agricultural sector, and commercial and industrial sectors. They are all available online (https://www.ecologie.gouv.fr/levaluation-economique-des-projets-gestion-des-risques, last access: 13 October 2022). In practice, since 2013, over 200 flood management projects have been analysed by CBA using this method and flood damage functions.

The floodam.agri model includes generic parts and can produce damage functions at different scales, depending on the calibration. We illustrate in this paper the use of floodam.agri to produce damage functions at the national scale. This methodology has followed seven stages (Fig. ).

First, the conceptual framework was established. A crop category is broken down into elementary components and for each component, the damage is estimated based on the biophysical processes at work due to the flood and the actions carried out by farmers after the flood.

Second, to inform the conceptual framework, 30 individual surveys (Fig. ) with agricultural experts working in regional technical institutes were carried out. They usually had expertise at the level of a crop family that encompasses several categories (Appendix , Table ). Some had expertise in several families of crops. Among the experts, six were specialists in grain and oleaginous crops, eight in vegetable crops, four in vines, three in fruit trees, and eight in meadows and feeding crops. The experts worked in geographical areas where crops had been impacted by at least once flood since 2005. We focused on five areas that differ in terms of hydrological and agricultural contexts: two Mediterranean areas, an area composed of alluvial plains and mountains, an oceanic area, and a rural area composed of plains and plateaus.

A questionnaire was designed (Supplement 1) to conduct semi-structured interviews that lasted about 1 h. It was structured in two parts in order to collect information (i) on the impacts on farm components and (ii) on the consequences for farmers' practices. Prior to every interview, production cycles in terms of physiological stages and agricultural work calendar were established based on the literature, for the categories of crop corresponding to the expert interviewed. This information was presented and discussed with the experts too.

Third, floodam.agri implementation can be summarised as shown in Fig. . The crops for which damage can be estimated with floodam.agri are defined in a three-level classification (Appendix , Table ). All the crops that belong to the same category are associated with a similar vulnerability to floods, but can differ in terms of their other characteristics (yield, selling price, crop calendar, intermediate consumption). For each component, based on the interviews, the sensitivity to flooding is modelled, i.e. a proportion of loss or level of deterioration of a component is associated with flood parameters; for example for the crop component, the sensitivity determines a loss of yield in percent of the standard yield. Decision rules associate behaviours with the proportion of loss or level of deterioration of a component. The floodam.agri model was implemented using R language.

Fourth, floodam.agri must be calibrated with data such as agricultural calendars, yields, and sales prices to produce flood damage functions. The level of data specification should be appropriate for the scale at which the damage functions are to be produced. For the national damage functions, we used data at the national level.

Fifth, a validation was carried out through focus groups bringing together the experts consulted in individual interviews for each crop family. This step occurred on average 1 year after the first interview. In total, five focus group were organised (see Sect. ).

Sixth, based on focus group discussions, some corrections were made.

Seventh, the process resulted in ready-to-use flood damage functions. To produce them, two more steps (3 and 4 in Fig. ) were achieved: (3) adapting the damage functions to fit the typology used to locate the crops (GPR), (4) adapting the resolution of the functions to fit the available data that pertain to flood parameters. The ranges of values considered for each parameter in floodam.agri and the grouping choices for the period of occurrence and flood duration categories chosen for ready-to-use damage functions are specified in Appendix  (respectively Tables –). In addition for the national application, to manage rotations if necessary on the application territory, we proposed to create a mixed function. For example, if the 3-year rotation is wheat, wheat, rape, the weight assigned to the wheat function is 2/3 and the weight assigned to rape is 1/3.

Ready-to-use national damage functions were produced for 15 of the 28 sorts of crop of the GPR typology (Supplement 2). These 15 sorts accounted for 89 % of agricultural areas located in flood-prone areas in metropolitan France in 2010, according to the GPR database. They indicate the estimated expected value of damage in euros by hectare, depending on the water depth, submersion duration, season of occurrence of the flood, and flow speed. The maximum expected damage is the lowest by hectare for sunflower crops (EUR 1611) and the highest for arboriculture and orchards (EUR 93 549) (Table ).

For illustrative purpose, Fig.  shows the damage function of the arboriculture. How the hazard parameters were aggregated to produce these graphical outputs is specified in Appendix . The damage increases with the flow speed, the submersion duration and the water depth. It is generally the highest in spring and the lowest in winter.

The threshold effects in the relationship between the damage and the water depth correspond to the water depths at which new types of plant organs are reached by water (e.g. leaves, fruits).

In this section, the methodological framework (Table ) is used to describe the validation process implemented for floodam.agri.

In this section, the methodological framework (Table ) is used to describe the updatability of floodam.agri.

In this section, the methodological framework (Table ) is used to describe the conditions on transferability.

The proposed framework clarifies the components, interactions and decision entities that are or are not considered in the damage assessment model. In economic systems, added value is produced on spatial entities (plots in the agricultural case) and depends on production factors (material, labour, input) and decision rules. In the case of agriculture, the added value increases on the plots and is then stored and transformed in other spatial entities on or off the farm. show the importance of these interactions for avoiding over- and underestimation in damage assessment. Because of the complexity of these mechanisms of localisation of added value in a production chain, the FHRC recommends, in an operational way, not to take into account the indirect effects . However, making the limits of the modelled system explicit remains fundamental in the classification of damage between direct and indirect effects. The larger the system considered, the more it will include effects that could be considered indirect. Developing models that locate and characterise interactions between several components in the field is time consuming. Depending on operational needs, this approach may be required (resilience analysis of a sector affected by a project) or not (large-scale damage assessment on all the issues).

From the modelling experience presented in this article around floodam.agri, the proposed framework concerning the explicitation of assumptions appears to us to be effective for two main reasons. Firstly, the explanation of the assumptions facilitated the collection of information from the experts. Indeed, we found that the logic we proposed to deconstruct the biophysical processes and the decisions made by farmers was consistent with the cognitive approach of damage assessment of the experts. In this sense, the application of the framework reduces the uncertainties surrounding the collection of expert knowledge. Secondly, the explicitness of the assumptions appears to be a necessary condition for the implementation of the other axes, namely validation, updatability and transferability. For example, it is essential to know which processes have been taken into account in determining yield losses. Studies carried out in the context of drainage may only take into account processes such as root asphyxiation, which will be predominant, but in the case of floods with significant velocity effects, it is essential to integrate also the processes of uprooting or laying down. This effort to clarify assumptions is also necessary for capitalisation.

The proposed framework allows for a clear improvement in the validation methodology with experts involved in the modelling process. However, we are aware of the need to consolidate this aspect. Two avenues are usually identified: first, the comparison of model results with each other; second, the comparison with claims data . A third avenue is to consider the geographical transfer of models as an opportunity to capitalise on expert knowledge by involving new experts and being able to clearly present the modelling assumptions to them. We consider that the clarification of the assumptions is a prerequisite for both avenues and the framework presented here is a step towards the possibility of comparing models with each other. We have made a first proposal in Table  based on the existing literature. This should not be considered a result but a discussion support to facilitate exchanges on methods with a view to capitalisation. Concerning the collection of ex post damage data, in particular for the agricultural sector, this is a real challenge that requires a long-term effort. Some interesting initiatives are to be highlighted such as, for example the validation carried out by or . The modelling effort we have carried out to develop floodam.agri has highlighted the importance of acquiring knowledge both on biophysical and human processes in order to be able to assess damage in economic terms. This implies that the data to be collected post-flood in order to validate a model such as floodam.agri must be of different nature, ranging from biophysical impacts (yield loss, mortality of plant material, soil erosion, etc.) to monetary damage, including the chain of behaviours of recovery and continuation of crop management sequence. But this type of post-flood data collection is very time consuming. Most of the time, in large-scale events, the primary objective will be to obtain an overall damage assessment fairly quickly and not to carry out a detailed characterisation of the damage formation processes. In this case, it could be used to estimate damage in monetary terms from hazard parameters. It could also be used to estimate damage in monetary terms from partial post-flood data collection such as yield losses, which corresponds to the practice of the insurance system in France. This type of use would provide a more complete picture of the damage on the basis of the current modelling assumptions, but would not validate or only partially validate the estimated values. On the contrary, such a characterisation makes sense for small-scale events for which, however, various levels of impact can be encountered on an individual scale. In this case, the collection of data allows for validation. For this, the implementation of observatories is an interesting approach.

The proposed methodological framework requires the specification of all the data used, their source and their vintage. This makes it possible to consider updating the models produced for a given context over time. This is the case for the damage functions produced thanks to floodam.agri. This effort allows us to consider the transfer by comparison of existing databases from one context to another. A difficulty persists for data that are not tracked over time, and in this case we recommend either updating the data on the basis of expert opinions or using a discount rate whose value must be specified.

Transferability needs to be anticipated right from the design stage. We are convinced that process-based models have generic parts that can be transposed and specified in other contexts. The methodological framework has proven useful to describe these aspects and their specification. In particular, we propose a reflection with experts on the basis of vegetative cycles rather than on a monthly basis as was done by for the evaluation of yield losses due to flash floods in Greece. We believe that this approach has two major advantages. First, discussing biophysical impacts (yield and plant material losses), and decisions to continue cultivation, with experts on this basis fits better with their cognitive approach and reduce uncertainty in data collection. Second, it makes it possible to transfer this method to other contexts, by calibrating vegetative cycles of crops.

The proposed methodological framework also provides a basis for future improvements. In this sense, the explicitness of the assumptions (biophysical processes, decision rules) should not be fixed but should be fed. This suggests the possibility of pooling efforts at an international scale. The tracks of improvement which we consider be a priority concern taking into account (i) other biophysical processes, (ii) agricultural buildings, (iii) breeding systems and (iv) adaptations of the trajectories of farms to floods.

Some biophysical processes such as pollution, salinisation or degradation of soil quality remain scarcely studied and should be consolidated.

For agricultural buildings, a similar approach by breaking down the basic components of the farm building (structure, equipment, input) could be conducted using the model floodam.building . It will then be necessary to specify the sensitivity and reparation costs of these components with experts. The challenge remains to determine the location associated with the use and technical orientation of buildings, which is not specified in existing databases in France.

Regarding livestock systems, the work carried out by the FHRC is a solid base that should be consolidated by addressing the issue of delayed effects related to the loss of animals as has been integrated through the loss of plant material for crops.

Finally, an important challenge remains to take into account the adaptive capacities of farmers in the long term. Collecting data from agricultural experts who have witnessed flooding on a large number of farms allows us to model a standard behaviour. However, we are aware that this average view does not reflect the diversity of individual vulnerability situations at the farm level. Thus, at the individual scale, decisions, especially those concerning long-term issues such as replanting, will depend on individual parameters such as investment dynamics, the age of the farm manager, the farm's trajectory etc. While it would be possible to assess the economic relevance of certain measures in terms of damage avoided using floodam.agri (e.g. assessment of the damage avoided by establishing a grassland in place of a vineyard), the determinants of these adaptation decisions are much more complex at the level of individuals and in particular farms. Understanding the internal and external determinants of adaptation implementation would require a different approach and investigation at the individual level .