However, the new values are lower and therefore the previous values are retained. Iw values computed after the second iteration left and at the end of the iteration process right. For the third iteration, the reference cell would now be c ; however, the Iw values computed for adjacent cells b, e, f are all lower than previous values, and therefore are discarded.
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The same happens for the following iteration steps considering cells b and j. Instead, the Iw value computed using cell e is higher than previous value for cell b , and therefore the value is updated. Finally, cell a is not reached by flow because the Iw value on adjacent cells b , e is not high enough to generate a positive value. Since all cells with positive Iw values have been considered, computations are stopped and the final grid of Iw values is shown in Figure 4. The most straightforward application of Iw is to consider a simple flood scenario with one localized hazard source.
Possible examples are a localized dyke failure, or a section of a riverbank being overtopped. In this case, a reference water depth can be used as boundary condition to compute the spatial distribution of Iw over the area of interest. Such an application is similar to standard applications of flood inundation models, and in this case, the algorithm will provide a map of Iw values similar to a map of maximum water depths.
However, the application of Iw can be further expanded. In this area, we consider different flood scenarios, originated by the same hazard source, but with a different hydraulic boundary condition, e. Moreover, the relation between Iw values and flooded area can be expressed as a curve for each scenario and plotted in the same graph for different scenarios. Figure 5 shows a conceptual scheme for this approach, which is useful to provide, at a glance, a comparison of flood prone areas in each scenario.
Conceptual scheme of the derivation of I w curves. In order to investigate the relationship between damage and hazard variables for the study area, it is possible to apply the Iw index as a measure of hazard. The true potential of the Iw calculation algorithm lies with its applicability to complex flood scenarios extremely efficiently in terms of computational effort, which enables the possibility of performing areal vulnerability analyses over very large regions in short amounts of time, as further described in Complex flood scenarios subsection.
A different approach to the use of Iw consists of analysing the flood susceptibility and vulnerability of a study area potentially prone to different, complex hazard sources, for instance a flood plain protected by dykes and surrounded by one or more watercourses. In such a case, a flooding could potentially originate at any point of the flood defences, and for different hydraulic conditions in the rivers. As previously mentioned, the application of standard 2D hydrodynamic models to combine all the possible hazard combinations would be complex and computationally demanding.
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On the contrary, the iterative algorithm of Iw can easily handle linear sources of hazard at the same time, since only the maximum values of Iw are used in the computation. Using the algorithm in such a way allows for an effortless quantification of the maximum flood intensity indexes in the study area.
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Different scenarios can be analysed, for instance considering the water levels related to a specific flood return period. In case of an area bounded by more than one water course, each scenario can consider a different combination of boundary conditions in the rivers concerned Figure 7. This approach allows not only the quantification of the maximum flood intensity indexes in the area which are the maximum Iw values for each cell from all the runs , but also to relate the index with its probability of occurrence, considering the number of sources that can originate it in relation to all the potential sources along the river reach.
This enables the effective quantification of the flood susceptibility of the area and the generation of the respective susceptibility curves and maps. Both sites have been affected by severe flood events in recent years caused by dyke failures. The location of test sites is shown in Figure 8. The first test area is located at approximately 30 km northeast of the city of Bologna, next to the river Reno Figure 8.
The site is mainly used for agriculture, with sparsely distributed farm buildings and the small village of Malalbergo. The area of interest is entirely bounded by road embankments and dykes, and crossed by a motorway embankment.
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A drainage network composed by field tile drains and a main drain is also located in the site, as shown in Figure 9. The total extent is approximately 8 km 2. Detail of test area 1, with the location of the Reno River, the drain and the motorway and railway embankments. A breach on the right levee of the Reno River caused the flooding of the test site in November The flood event has been studied in previous research works Dottori, ; Hailemariam et al. These authors collected a comprehensive set of topographic data including embankments and drainage network and observations of flood extent and depth, which were used for the application and evaluation of the 2D hydrodynamic model CA2D.
Therefore, this case is used to test whether the flood intensity index values can be considered as a reliable proxy of water depths, by comparing Iw values against both observations and results from the CA2D model. The second test site has a total extent of around km 2 and is located northeast of the city of Modena Figure 8. It is a lowland agricultural area with several small towns, villages and sparsely distributed farm buildings. As in Area 1, a complex drainage network is present in the site. The test site was affected by flooding on January due to a dyke breach along the River Secchia.
For this event, topographic information and flood footprints at different time steps have been collected; however, the level of detail is not as high as for area 1, since embankments and the drainage network could not be integrated in spite of their influence on flooding processes.
Therefore, the case is used as a conceptual exercise for producing maximum vulnerability maps, as well as a benchmark for testing Iw performance in large areas. The performance of the Flood Intensity Index in test area 1 is evaluated through a sensitivity analysis of the parameter space, following the usual approach applied for flood hazard models Dottori, The reference water level over the source point H source has been set equal to the average water depth 0.
The flood extent computed through Iw is compared against observed maximum flood extent using the performance indexes P1, P2 proposed in Hunter et al. Iw values in correspondence of high water marks are evaluated using absolute and relative root mean square error RMSE. In order to derive areal susceptibility and vulnerability curves for test site 1, the flood event of has been considered together with two additional, higher magnitude flood scenarios. The scenario is indicated as S1. The functions are derived from a database of existing studies for several European Countries, and classify asset values into five damage classes: residential, commercial, industrial, roads and agriculture.
Although the damage model has been successfully tested in two case studies in Germany and England Jongman et al. Therefore, the present application should be regarded as a conceptual exercise, as a detailed validation would be beyond the scope of this paper. The curves derived for the test case are described in Susceptibility and areal vulnerability graphs.
To analyse the flood susceptibility of the study area 2, the Iw index has been computed considering the two embankments bounding the area Figure 6 as linear, continuous hazard sources that is, every grid cell on these borders is considered as a source cell. The dike breach occurred in has been taken as reference to define the magnitude of the flood scenarios: in each source cell, the reference water level has been defined as the local bottom elevation of the embankment, plus the average water depth computed from the reconstructed breach hydrograph 1.
Given the comparable discharge of the rivers Secchia and Panaro, the same reference depth has been used. In practice, such a schematization implies a uniform failure probability of the defence structures, since no information on geometrical and geotechnical conditions of the embankments is available.
The curves derived for the test case are described in Maximum Flood Intensity Index maps. As can be seen from the graphs, it is not possible to find a calibration that maximizes the index performance against both the observed data types. Although such errors are not negligible, they are relatively close to the results of CA2D model obtained by Dottori Using the optimum calibration for the model parameters, the author reported an RMSE on observed depths of 32 cm, and a value of P2 index of 0.
Figures 13 and 14 show a visual comparison of results for CA2D and Iw in terms of flood extent. In addition, the same author observed some incoherencies between high water marks and observed flood extent, meaning that observed data sets are also affected by errors.
Map of CA2D maximum water depths roughness values: 0. Figure 15 shows the Iw curves Iw values against cumulated area for the three flood scenarios considered. As can be seen, the areal curves can be used to characterize at a glance the flood susceptibility in each scenario, allowing for quick comparisons. Also, the highest values of Iw more than 1. Figure 16 reports the areal vulnerability curves reference water depth H ref on the breach point versus total damage for the three flood scenarios.
It is interesting to note how the damage shows a marked increase from scenario S1 to S2, despite a limited increase in flood extent from 5. This is due to the fact that in scenario 1 most of the village of Malalbergo is not reached by flooding, while it happens for scenario 2. The map of Iw values obtained considering multiple linear sources has been normalized and classified, and is shown in Figure Isotope numbers should precede the symbols, e. Figures and Tables Authors are requested to include at least 2 and a maximum of 8 figures or tables to illustrate their work.
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