Brief communication: simple-INSYDE, development of a new tool for flood damage evaluation from an existing synthetic model

INSYDE is a multi-variable, synthetic model for flood damage assessment to dwellings. The analysis and use of this model highlighted some weaknesses, linked to its complexity, that can undermine its usability and correct implementation. This study proposes a simplified version of INSYDE which maintains its multi-variable and synthetic nature, but has simpler mathematical formulations permitting an easier use and a direct analysis of the relation between damage and its explanatory 10 variables.


INSYDE (IN-depth SYnthetic Model for Flood Damage Estimation,
) is a synthetic model for the estimation of flood damage to residential buildings at the micro scale (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 15 the model as the sum of 33 different components, referring to the costs of reparation, 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 discourage the implementation of the model and its use through other 20 platform such as GIS software. This study proposes an alternative version of the model, named simple-INSYDE, which aims at overcoming these limitations. Simple-INSYDE preserves the multi-variable nature of the model, but aggregates damage components in a smaller set of functions, which clearly describe the role of each explicative variable on 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 25 model are described in the following sections. https://doi.org/10.5194/nhess-2020-76 Preprint. Discussion started: 17 April 2020 c Author(s) 2020. CC BY 4.0 License.

Method
The first step to provide a simpler structure of the model was to aggregate the original damage functions into four components: 40 -Damage to basement: in case of flood, basement is assumed totally inundated and damage does not depend on water level.
-Damage to floor: in case of water level higher than the level of floor, the damage to floor is counted as independent from water level.
-Damage to storey: it considers damage to the elements over the floor (e.g., walls and plants) that depends on water 45 level.
-Damage to boiler: it depends on water level only if the basement is not present, otherwise, the boiler is considered located in the basement which is completely inundated.
In order to support model transferability (Merz et al., 2010), the simplified model computes damage in relative terms, as the ratio of the absolute damage to a reference value. The reference value is set as the cost of reconstruction of the storeys exposed 50 to the flood; cost of reconstruction is evaluated as the product of the replacement value RV [€/m 2 ] and the footprint area A of each storey [m 2 ]. Equation (1) represents the conceptual formula of the simplified model, where is the building damage in absolute term [€], in relative term, is the number of flood exposed storeys.
The second step was the choice of the independent variables to be included in the model, among those of the original INSYDE 55 (Table 1). The variables that were not included in simple-INSYDE were not effectively neglected, but implicitly assumed at the default values according to the assumptions made in INSYDE, for the geographical context and the flood type of interest (Wagenaar et al., 2016). Among the event feature variables, we preserved the water level, the duration of the flood and the presence of pollutants. Indeed, the sensitivity analysis performed in Dottori et al. (2016) highlighted that, in case of slow riverine flood events, water velocity and sediment load have a minor influence on damage, compared to the chosen variables. 60 The selection of the vulnerability variables followed different criteria. We considered the interfloor height and the basement height fixed at their default values because they do not vary significantly in Northern Italy. We kept the default value also for the ground floor level and the heating system variables (PD and PT), because information on them is difficult to retrieve, without a detailed field survey. The internal area, the external perimeter, the internal perimeter, the basement perimeter and  The interpolating functions were calibrated comparing the damage simulated by the simplified model and the original model, for a sample of 10000 buildings, whose features (i.e. input variables values) were randomly selected from probability 85 distributions assumed representative of Northern Italy (Table 2). In particular, for the footprint area, the finishing level, the building structure and the maintenance level, the distribution parameters were chosen on the bases of real estate data of Northern Italy. The comparison of the simulated damage by the original and the simplified model, 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 90 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 vary from 20% to exceed 1000% 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

Discussion
This study led to the main objective of developing a new tool for flood damage estimation to dwellings, which is based on a 100 sensible number of available input data, and allows investigating the relation between damage and its explanatory variables by means of a simple set of functions. For instance, Figure 1  Moreover, the study allowed to deeply investigate the behaviour of the original model and to highlight shortcomings that could be further improved in the future. For example, assumptions made in the model on building configuration, which limit its use to single housing units and not condominiums, is not directly reported in the paper of Dottori et al. (2016), but is important for a correct implementation of the model and a better understanding of estimation errors. 110 Compared to the original model, the simplified model requires fewer input variables, facilitating the model implementation, but impeding the control by the user on the variables that are implicitly considered. For this reason, Simple-INSYDE is less adaptable to contexts different from the calibration one than INSYDE. It is worth recalling that simple-INSYDE is addressed to evaluate damage in 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. 115 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, then, the simplification method can be implemented to obtain new functions with new coefficients. https://doi.org/10.5194/nhess-2020-76 Preprint. Discussion started: 17 April 2020 c Author(s) 2020. CC BY 4.0 License.