INSYDE (IN-depth SYnthetic Model for Flood Damage Estimation; Dottori et al., 2016) is a synthetic model for the estimation of flood damage to residential buildings at the microscale (i.e. building level), developed and tested in Italian case studies (Amadio et al., 2019; Molinari and Scorzini, 2017; Molinari et al., 2020). The monetary damage to a dwelling is computed in the model as the sum of 33 different components, referring to the costs of repair, removal, and replacement of the damaged elements, which are functions of several damage explicative variables, related both to the hazard and to the vulnerability of the affected item (Table 1). Since the same explicative variable may directly or indirectly influence more than one damage component, it is difficult to understand the weight that each explicative variable has on the overall damage estimate. Moreover, the complex and articulate structure of INSYDE could dissuade less expert users from using the model and discourage its implementation with platform and calculation tools other than the original one. This study proposes an alternative version of the model, named simple-INSYDE, which aims at overcoming these limitations. Simple-INSYDE preserves the multivariable nature of the model but aggregates damage components in a smaller set of functions, which clearly describe the role of each explicative variable in the total damage figure and can be easily implemented, even by non-expert users. Such functions are calibrated for low-velocity floods, with building characteristics typical of Northern Italy. The method and the assumptions implemented to obtain the simplified version of the model are described in the following sections.

The first step to provide a simpler structure of the model was to aggregate the original damage functions into four components.

Damage to basement. In the case of a flood, the basement is assumed totally inundated and damage does not depend on water level.

The last step was the development of the simplified functions. For the four damage components, a set of reference values was defined for each variable that influences the component under investigation, e.g. A=100 m2 and FL = low. Then, damage to each component was calculated by varying the value of one variable at a time (e.g. f(A) or f(FL)) and keeping the others at their reference value. The resulting functions are simple interpolating functions suitable for representing the role of each variable in the estimation of a specific damage component: for variables that assume only two values, such as BS or FL, the only identification of multiplicative coefficients was required, for variables with a wide range of values, such as d or A, the functions that approximate the role of the variables in the final damage figure are more complex. Then, the interpolating functions were calibrated comparing the damage simulated by the simplified model and the original model for a sample of 10 000 buildings, whose features (i.e. input variables values) were partly randomly selected from probability distributions assumed representative of Northern Italy (Table 2) and partly set at default values. In particular, the parameters of the probability distributions were chosen on the basis of data supplied by Istat (the Italian National Institute of Statistics), the real estate market observatory of the revenue agency (Agenzia delle Entrate), and some provincial databases that refer to built environment in the regions Emilia Romagna, Lombardy, Piemonte, and Veneto.

The final result of the process is expressed by Eqs. (2)–(5), which represent the simple-INSYDE model. 2dbasement=f(Abasem)f(du)→f(Abasem)=0.02+0.35Abasemf(du)=1+0.3arctan⁡(du-36)3dstorey=f(h)f(A)f(LM,du)f(BS)f(FL)f(q)→f(h)=(0.17h-0.02h2)f(A)=(0.2+7A)f(LM,du)=1+0.15⋅arctan⁡(du-36)ifLMlow0.8+0.2⋅arctan⁡(du-36)ifLMhighf(BS)=1.35,ifBSmasonry1,elsewheref(FL)=1.5,ifFLhigh1,elsewheref(q)=1.2,ifq=1,presenceofpollutants1,elsewhere4dfloor=f(h,FL)=0.04,ifh>0andFLhigh0,elsewhere5dboiler=f(Abasem,h)=0.015,ifAbasem≠0orAbasem=0andh>1.6m0,elsewhere Here the units of measure of the variables are square metres for the area (A), hours for duration (du), and metres for water depth (h).

The comparison of the simulated damage by the original and the simplified models, showed a mean relative error equal to 0.24, with a ratio to the mean absolute damage equal to 1.07. The application of the model INSYDE in real case studies (Dottori et al., 2016; Molinari and Scorzini, 2017; Amadio et al., 2019; Molinari et al., 2020) showed good performance of the model, with a mean ratio between the total damage simulated and the observed damage equal to 1.26. On the other hand, literature shows that the performance of flood damage models can be affected by high uncertainty, with relative errors varying from 20 % to over 1000 % (Scorzini and Frank, 2017; Thieken et al., 2008). Thus, we consider that the additional error caused by the use of simple-INSYDE is acceptable and that the estimation of the overall damage is comparable with that supplied by INSYDE.

This study led to the main objective of developing a new tool for flood damage estimation to dwellings from the simplification of the model INSYDE. The new model is based on a sensible number of available input data and allows investigation of the relation between damage and its explanatory variables by means of a simple set of functions. For instance, Fig. 1 shows the relative damage computed by simple-INSYDE as a function of water depth, for the different damage components of the model. The figure highlights that the storey component gives the biggest contribution to the damage and it is the only one depending on water level. The other components are independent of water level and have a lower weight on the final damage figure; still, they assume a non-negligible role, especially in the case of shallow waters.

Moreover, the study allowed the deep investigation of the behaviour of the original model and highlighting of shortcomings that could be further improved upon in the future. For example, assumptions made in the model on building configuration, which limit its use to single housing units and not condominiums, are not directly reported in the paper of Dottori et al. (2016), but it is important for a correct implementation of the model and a better understanding of estimation errors.

The study demonstrates that the use of a simplified model, which is consistent with the assumption of the original one, can lead to comparable results and does not considerably decrease the accuracy of the damage forecast.

Compared to the original model, the simplified model requires fewer input variables, facilitating the model implementation, but hampering the control on the variables that are implicitly considered. For this reason, simple-INSYDE is less adaptable to contexts different from the calibration one than INSYDE. In this regard, it is worth recalling that simple-INSYDE is addressed to evaluate damage in the case of low-velocity floods and built environments typical of Northern Italy. It is recommended not to use it for other types of inundation (Kreibich and Dimitrova, 2010) or for other types of building and/or geographical contexts. In these cases, the derivation of new interpolating functions from INSYDE, with the process described in this study, is suggested; to this aim, the original model needs be adapted to the context of interest, by modifying the default values of the variables and the unit prices of the building components and then by implementing the simplification method to obtain new functions with new coefficients.

It is worth noting that the method proposed in this study for the derivation of the model is not limited to INSYDE but can also be repeated and developed for other multivariable models to obtain alternative, simpler, and more explicit versions.