# A New Tool to Estimate Inundation Depths by Spatial Interpolation (RAPIDE): Design, Application and Impact on Quantitative Assessment of Flood Damages

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## Abstract

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## 1. Introduction

## 2. RAPIDE: RAPid GIS Tool for Inundation Depth Estimation

## 3. Case Study: 2002 Adda River Flood Event

^{3}/s, corresponding to a 100-year return period flood [25]. The river then overflowed, causing severe damages to residential buildings and commercial activities. This case study was considered as a validation test case for RAPIDE, as it was well documented in terms of both hazard and damage characteristics.

- Measured water levels at the ancient bridge of the town of Lodi;
- Observed water depths in more than 260 georeferenced points within the inundated area (Figure 3a), deriving from indications provided by municipal technicians and by citizens in the damage compensation forms, as well as from interpretation of photographs taken during or immediately after the event (these water depth measurements could be affected by average errors of about 20–30 cm, given the type and quality of the observations);
- Documented oil spills in some zones of the inundated area (Figure 3d);
- Observed losses for 271 residential buildings, deriving from damage compensation forms compiled by citizens, for a total of 3.77 M€ (as of year 2002).

## 4. Hazard Modelling of the 2002 Adda Flood

#### 4.1. 2D Hydraulic Model

^{3}/s and the entire hydrograph of the event [25], respectively.

^{2}. A computational grid with a resolution of 10 m was used in the model in order to reach a satisfactory compromise between computational time, model stability and accuracy.

- the average of the differences between simulated and observed water depths (AD);
- the absolute average of the differences between simulated and observed water depths (AAD);
- the Nash-Sutcliffe Efficiency (NSE) [27], defined as:$$NSE=1-\frac{{\displaystyle \sum _{i=1}^{n}{(W{D}_{{O}_{i}}-W{D}_{{S}_{i}})}^{2}}}{{\displaystyle \sum _{i=1}^{n}{(W{D}_{{O}_{i}}-\overline{W{D}_{Oi}})}^{2}}}$$
_{Oi}and WD_{Si}are, respectively, the observed and simulated water depth at location i, while $\overline{W{D}_{Oi}}$ is the mean observed water depth. The NSE may range between −∞ and 1 (goal value); - the flood area index (FAI) [28], defined as:$$FAI=\frac{{A}^{11}}{{A}^{11}+{A}^{01}+{A}^{10}}$$
^{11}, A^{01}and A^{10}respectively represent the numbers of pixels for which both simulation and observation indicate “wet”, simulation indicates “wet” and observation indicates “dry”, and simulation indicates “dry” and observation indicates “wet”. The FAI may range between 0 and 1 (goal value).

#### 4.2. RAPIDE Model

- the number of selected auxiliary lines (that is inversely proportional to the spacing between these lines): three scenarios with increasing mean spacing (from 450 m to 1.3 km, corresponding approximately to 3 and 10 times the Adda’s main channel width) were considered (i.e., ‘narrow’, ‘large’ and ‘very large spacing’ cases (Figure 5)); the last two configurations were obtained by deleting lines from the ‘narrow spacing’ case and without changing their positions;
- the use of a mask: the default condition for all the tested scenarios included the use of a polygon mask derived from the regional land-use map filtered for built-up areas (Figure 5d); the upstream and downstream boundaries of the inundated area (where it was known that water depth was not null) were masked as well; the ‘narrow spacing’ case was then tested also without the use of this mask;
- the resolution used for the discretization of the flood perimeter and auxiliary lines: in the RAPIDE toolbox the user can change the default values for the resolution of the discretization, equal to 25 m and 1 m for flood the perimeter and auxiliary lines, respectively; based on the ‘narrow spacing’ case, different conditions were tested, varying the resolution between 1 m and 50 m for the perimeter and up to 50 m for the lines;
- the location of the auxiliary lines: a total of 25 configurations were generated and tested; the number of possible configurations was mainly limited by the requirements of perpendicularity to the channel axis, non-intersection with other drawn lines, intersection with the flood perimeter in two points over the external boundary and physical meaning of the lines.

_{RAPIDE}) were compared to the benchmark one (WD

_{2D}) resulting from the 2D hydraulic model, by making a raster difference and then computing the cumulative density function of the differences (ΔWD = WD

_{RAPIDE}− WD

_{2D}). For each configuration of the sensitivity analysis, results are thus presented as maps depicting the differences between the water depths returned by RAPIDE and those simulated by the 2D model (ΔWD), and corresponding mean values and/or cumulative distribution functions of ΔWD. The mean absolute error (MAE) and the root mean squared error (RMSE) were also used as synthetic performance indicators.

_{RAPIDE}generally lower than WD

_{2D}in the upstream part of the domain and opposite relationship in the second half of the reach. The results do not change drastically when using in RAPIDE less auxiliary lines for the interpolation (Figure 6b,c), even though a general worsening of the performance is observed (Figure 6e, with median ΔWD of −0.07 m and −0.10 m; 90th percentile of the distributions: 0.56 m and 0.63 m; 10th percentile of the distributions: −0.43 m and −0.55 m for the ‘large’ and ‘very large spacing’ case, respectively). Calculated MAE and RMSE values increase from 0.28 m and 0.38 m (for the base case) to 0.38 m and 0.49 m (for the ‘very large spacing’ case).

## 5. Damage Modelling of the 2002 Adda Flood

- the geometric characteristics (i.e., footprint area, external perimeter, basement area, number of floors) and finishing level of the buildings were derived from cadastral data;
- the building type (i.e., apartment, semi-detached or detached house), level of maintenance and year of construction were assigned to different buildings, based on the urban development plan of the town of Lodi;
- the building material (i.e., reinforced concrete or masonry) was assigned considering the most frequent type observed in each census zone of Lodi, based on ISTAT data, as shown in [31].

## 6. Discussion and Recommendations

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**2002 Adda river flood in the town of Lodi: (

**a**) Observed flood footprint and location of observed water depths; (

**b**) Observed flood hydrograph at the ancient bridge (the hydrometer is depicted by the green point in panel a); (

**c**) Example of available aerial photographs taken during the event; (

**d**) Observed oil spill in a part of the inundated area.

**Figure 4.**Results of the 2D model for the 2002 Adda flood: (

**a**) Flood depth map, with indication of clusters considered in the calibration of the model; (

**b**) Distributions of water depths in the total inundated area and urban areas only.

**Figure 5.**Cases considered in a sensitivity analysis of RAPIDE results to the spacing between auxiliary lines and the use of a mask: (

**a**) ‘Narrow spacing’ case; (

**b**) ‘Large spacing’ case; (

**c**) ‘Very large spacing’ case; (

**d**) Mask for filtering interpolation points in urban areas.

**Figure 6.**Results for the sensitivity of RAPIDE results to line spacing and use of the mask. Maps of ΔWD for: (

**a**) ‘Narrow spacing’ (red); (

**b**) ‘Large spacing’ (blue); (

**c**) ‘Very large spacing’ (green); (

**d**) ‘Narrow spacing’ without a mask (red dotted); (

**e**) Cumulative density functions of ΔWD for the four cases.

**Figure 7.**Sensitivity of RAPIDE results to the discretization resolution of the flood perimeter and the auxiliary lines (‘Per’ and ‘XS’ in the legend, respectively). Cumulative density functions of ΔWD for the different resolutions considered.

**Figure 8.**Sensitivity analysis of RAPIDE results to the location of auxiliary lines: (

**a**) Water depth maps for the 25 tested configurations; (

**b**) ΔWD maps for 25 tested configurations; (

**c**) Water depth map for the ‘mean scenario’; (

**d**) Map of standard deviations of water depth for the ‘mean scenario’; (

**e**) ΔWD maps for the ‘mean scenario’; (

**f**) Cumulative density functions of ΔWD for the 25 considered configurations (green lines) and the ‘mean scenario’ (red line).

**Figure 9.**Results of damage modelling (loss data updated to year 2013). (

**a**) Cumulative density functions of simulated (green: 2D model; shades of blue: RAPIDE; red: ‘mean scenario’ of RAPIDE; yellow: mean damage calculated from RAPIDE scenarios) versus observed losses for the different tested hazard configurations. (

**b**) Boxplot of total damage calculated for the different configurations generated in the sensitivity analysis of RAPIDE (blue with yellow mean), together with the total damages for the other estimates.

Indicator | Cluster | ||||||||
---|---|---|---|---|---|---|---|---|---|

A | B | C | D | E | F | G | H | Average | |

AD (m) | 0.09 | −0.01 | 0.34 | 0.17 | −0.39 | −0.18 | −0.16 | −0.23 | −0.04 |

AAD (m) | 0.21 | 0.29 | 0.42 | 0.33 | 0.57 | 0.36 | 0.37 | 0.41 | 0.37 |

NSE | 0.24 | 0.42 | −1.03 | 0.39 | −0.04 | −0.19 | −0.11 | −0.31 | −0.18 |

**Table 2.**Hazard parameters considered in INSYDE, in the case of application of the results deriving from the 2D model and RAPIDE.

Hazard Parameter | 2D Model | RAPIDE |
---|---|---|

Water depth (h) | Water depth distribution as of output from 2D model | Water depth distribution as of output from RAPIDE |

Flow velocity (v) | Flow velocity distribution as of output from 2D model | Default value in INSYDE (0.5 m/s) |

Flood duration (d) | Default value in INSYDE (24 h) | |

Water quality (q) | As from documented observations during the event | |

Presence of sediment (s) | Default value in INSYDE (fine-grained sediment) |

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**MDPI and ACS Style**

Scorzini, A.R.; Radice, A.; Molinari, D.
A New Tool to Estimate Inundation Depths by Spatial Interpolation (RAPIDE): Design, Application and Impact on Quantitative Assessment of Flood Damages. *Water* **2018**, *10*, 1805.
https://doi.org/10.3390/w10121805

**AMA Style**

Scorzini AR, Radice A, Molinari D.
A New Tool to Estimate Inundation Depths by Spatial Interpolation (RAPIDE): Design, Application and Impact on Quantitative Assessment of Flood Damages. *Water*. 2018; 10(12):1805.
https://doi.org/10.3390/w10121805

**Chicago/Turabian Style**

Scorzini, Anna Rita, Alessio Radice, and Daniela Molinari.
2018. "A New Tool to Estimate Inundation Depths by Spatial Interpolation (RAPIDE): Design, Application and Impact on Quantitative Assessment of Flood Damages" *Water* 10, no. 12: 1805.
https://doi.org/10.3390/w10121805