# Hydrological and Hydraulic Flood Hazard Modeling in Poorly Gauged Catchments: An Analysis in Northern Italy

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

^{2}(Figure 1 and Table 1), about 40% of which is hilly and mountainous. The character of the river system is typically torrential, and not infrequently, in summer, the riverbeds are totally dry.

## 3. Hydrological Analysis

#### 3.1. Available Data

_{1}) and daily m(h

_{d}) maximum annual rainfall, equal to 24.1 mm and 65.9 mm, respectively (Table 2). These values may be of some interest if regionalization techniques at the outlet of contributing areas along the watercourses have to be adopted in the absence of reliable direct flow records.

^{1/3}s

^{−1}were assumed for the main channel and the floodplains, respectively, and a monomial function of the form Q = aℎ

^{𝑏}was fitted to the numerical stage–discharge relation computed at the gauging site (a = 5.579 m

^{3}

^{−b}s

^{−1}, and b = 2.267). From Figure 2, it can be observed that this numerical rating curve is in fairly good agreement with the 2009 official stage–discharge relationship. From the conversion of the recorded hydrographs using the interpolated stage–discharge relationship, the average value of the annual maximum series (AMS) of N flood peaks (N = 18 events) was evaluated, resulting in 94.8 m

^{3}s

^{−1}. It is good to keep this value in mind for considerations that will be made in the following.

#### 3.2. Peak Discharge Estimation

#### 3.2.1. Index Flood

_{mb}of the main branch, and the hourly rain value m(h

_{1}) are taken into consideration:

_{med}of the basin at the section of interest, and the pluvial average value relating to the daily rainfall m(h

_{d}):

_{1}) and m(h

_{d}). These values are in very good agreement with the corresponding values of 24.1 mm and 65.9 mm obtained from the rain sample introduced in Section 3.1.

^{3}s

^{−1}, evaluated in Section 3.1. As a precautionary choice, the maximum values provided by the regressive relations at the sections of interest, which correspond to the outcome of Equation (1), will be adopted (bolded in Table 3).

#### 3.2.2. Growth Factor

#### 3.3. Definition of the Design Hydrographs

#### 3.3.1. Flow Reduction Curve and Peak Position Ratio

_{D}(T):

_{D}(0 ≤ r

_{D}≤ 1) of the peak of the hydrographs in the same intervals (Figure 4). Some methodologies for identifying the reduction factor and peak position are available for instrumented river sections, where a series of historical floods has been recorded, and for which a reliable stage–discharge relationship is available. In the absence of the second condition, the reduction curve can be inferred, after appropriate processing, on the basis of the trend of the water stages instead of discharges. If water stages are also not available, as for the majority of non-instrumented river sections, some indirect methods still allow the estimation of the reduction factor and peak position through empirical regional relations, which express them as a function of some characteristics of the basin under consideration [51].

_{D}moving windows, it was then possible to extract N

_{D}samples with the size N for the value of the maximum annual average flow and (N

_{D}− 1) samples for the peak position ratio for the durations of interest (for the duration 0 the position of the peak is, in fact, not defined). The choice of the maximum window duration D

_{f}must derive from a preliminary examination of the characteristic durations of the most significant historical flood hydrographs. For the Chiavenna stream at the gauging site of Saliceto, durations from 0 to 96 h on an hourly basis were considered (D

_{f}= 96 h, N

_{D}= 97).

_{D}is a function of duration D and return period T, in many practical cases, it can be assumed independent of the latter. This is strictly true only if—neglecting the influence of the statistical moments higher than the second—the coefficient of variation $CV\left({\overline{Q}}_{D}\right)$ and the probability distribution type of ${\overline{Q}}_{D}$ can be considered independent of D. Under these assumptions, ε

_{D}becomes independent of T and reduces to the ratio of the averages of ${\overline{Q}}_{D}$ and ${Q}_{0}$:

^{2}) [54], like the one considered here, Equation (6) does not accurately fit the empirical reduction factor (Figure 5). It was, therefore, decided to adopt the following generalized form:

_{D}time series of observed peak position ratios are available for the Saliceto gauging station, one for each duration considered. For the purpose of the evaluation of the SDH, the average value of each series was calculated and the N

_{D}values thus achieved were interpolated with the expression:

_{D}(0) = 0.5 (Figure 7).

#### 3.3.2. Evaluation of the SDHs

#### 3.3.3. Water Stage Record Behavior

## 4. Hydraulic Analysis

#### 4.1. Numerical Model

#### 4.1.1. Hydraulic Model

#### 4.1.2. Bridge Modeling

#### 4.2. Model Setup

#### 4.2.1. DTM and Building Treatment

^{2}. A recent LiDAR survey provided a digital terrain model (DTM) with a resolution of 1 m × 1 m, which was converted to a raster map with a grid size of 2 m × 2 m, considered adequate for this test case. In the grid coarsening process, particular attention was paid to preserving the elevation of retaining structures along the streams and other thin linear topographic features in the domain. A further preprocessing of the DTM was necessary to restore the embankment crest elevations that were not correctly described due to the removal of the bank vegetation cover from the raw LiDAR data, and to integrate in the DTM the bathymetric portion of the riverbed not correctly detected due to the presence of water at the time of the survey.

#### 4.2.2. Mesh

^{4}= 16 m, was built. In order to model the flood propagation accurately, all the main waterways, urban areas, and road and rail communication routes were described with the highest resolution (Figure 13). Elsewhere, the spatial resolution is automatically relaxed by the preprocessing algorithm, as described in [37]. The calculation grid thus identified is made up of a total of 6.8 million cells.

#### 4.2.3. Domain Roughness

^{1/3}s

^{−1}was assumed based on local inspections, literature suggestions [65], and previous studies conducted by the authors concerning neighboring watersheds with similar characteristics [62]. Moreover, this value allowed the reproduction of, at best, the numerical rating curve previously obtained at Saliceto through 1D hydraulic modeling.

^{1/3}s

^{−1}[66,67,68,69]. For the low plain areas of Emilia-Romagna, indications can be obtained from the work by [34], where a Strickler’s coefficient equal to 20 m

^{1/3}s

^{−1}was calibrated to reproduce the well-known dynamics of the inundation caused by an embankment breach. Preliminary simulations of the present study indicated no significant differences in maximum water depths if values equal to 20 or 25 m

^{1/3}s

^{−1}were adopted outside the riverbeds, while flooding propagation times are slightly more influenced. As far as the time of arrival of the flooding is important in the emergency management phase during a real event, it is completely irrelevant for the identification of potentially floodable areas. In the absence of further information, it was, therefore, decided to adopt a uniform Strickler’s coefficient equal to 25 m

^{1/3}s

^{−1}over the whole domain.

#### 4.2.4. Boundary and Initial Conditions

^{3}s

^{−1}for the Chero, Chiavenna, and Riglio streams, respectively, was assumed as the initial condition.

## 5. Results

#### Bridges’ Conveyance

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Chiavenna watershed, (

**b**) location of the Po and Chiavenna basins in Italy, and (

**c**) river network in the urban area of Roveleto.

**Figure 9.**Water stages at the gauging stations of interest for two semesters in (

**a**) 2009 and (

**b**) 2016.

**Figure 13.**Multiresolution grid and main infrastructures present in the modeled domain; 2 m × 2 m cells in black, 4 m × 4 m cells in blue, 8 m × 8 m cells in green, and 16 m × 16 m cells in red.

**Figure 14.**Maximum water depths at Roveleto for T = 200 years: (

**a**) current condition; (

**b**) hypothetical scenario of absence of bridges.

**Figure 15.**Maximum water depths at Roveleto for T = 200 years: (

**a**) current condition; (

**b**) hypothetical scenario of absence of bridges.

**Table 1.**Watershed characteristics and mean annual rainfall for contributing areas at the gauging stations of interest for the period 1997–2018.

Watercourse | Gauging Station | Area, A (km ^{2}) | Main Branch Length, L_{mb} (km) | Average Altitude ^{1}, H_{med} (m) | Mean Annual Rainfall (mm) |
---|---|---|---|---|---|

Chero | Ciriano | 56 | 25 | 323 | 962 |

Chiavenna | Saliceto | 161 | 37 | 235 | 876 |

Riglio | Montanaro | 116 | 30 | 227 | 846 |

^{1}Above the gauging station.

Data Sample | Period | Size | 1-h Rainfall | Daily Rainfall | ||
---|---|---|---|---|---|---|

Mean (mm) | St. Dev. (mm) | Mean (mm) | St. Dev. (mm) | |||

Castellana Groppo | 1983–2001 | 19 | 24.3 | 11.2 | 66.9 | 14.5 |

Riglio | 2003–2018 | 16 | 23.9 | 9.5 | 64.6 | 17.0 |

Unique | 1983–2018 | 35 | 24.1 | 10.3 | 65.9 | 15.5 |

Watercourse | Gauging Station | Index Flood Equation (1) Q _{I1} (m ^{3} s^{−1}) | Index Flood Equation (2) Q _{I2} (m ^{3} s^{−1}) |
---|---|---|---|

Chero | Ciriano | 37 | 27 |

Chiavenna | Saliceto | 103 | 98 |

Riglio | Montanaro | 80 | 70 |

Watercourse | Gauging Station | Max. Index Flood Q_{I Max}(m ^{3} s^{−1}) | Peak Discharges | |||
---|---|---|---|---|---|---|

Q_{20}(m ^{3} s^{−1}) | Q_{50}(m ^{3} s^{−1}) | Q_{200}(m ^{3} s^{−1}) | Q_{500}(m ^{3} s^{−1}) | |||

Chero | Ciriano | 37 | 88 | 122 | 191 | 254 |

Chiavenna | Saliceto | 103 | 245 | 339 | 532 | 707 |

Riglio | Montanaro | 80 | 190 | 263 | 413 | 549 |

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Aureli, F.; Mignosa, P.; Prost, F.; Dazzi, S.
Hydrological and Hydraulic Flood Hazard Modeling in Poorly Gauged Catchments: An Analysis in Northern Italy. *Hydrology* **2021**, *8*, 149.
https://doi.org/10.3390/hydrology8040149

**AMA Style**

Aureli F, Mignosa P, Prost F, Dazzi S.
Hydrological and Hydraulic Flood Hazard Modeling in Poorly Gauged Catchments: An Analysis in Northern Italy. *Hydrology*. 2021; 8(4):149.
https://doi.org/10.3390/hydrology8040149

**Chicago/Turabian Style**

Aureli, Francesca, Paolo Mignosa, Federico Prost, and Susanna Dazzi.
2021. "Hydrological and Hydraulic Flood Hazard Modeling in Poorly Gauged Catchments: An Analysis in Northern Italy" *Hydrology* 8, no. 4: 149.
https://doi.org/10.3390/hydrology8040149