# Quantifying the Uncertainty Related to Climate Change in the Assessment of Urban Flooding—A Case Study

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Case Study and Dataset

^{2}, consisting of about 45.5% of impervious areas and 54.5% of pervious areas. The impervious area is mainly concentrated in the central part of the catchment being characterized by the urban city centre. The 92% of the constructed area is concentrated in the city center (4.7 km

^{2}); the remaining 8% is due to rural buildings and infrastructures around the center. The urban catchment is drained by a combined sewer system designed in HDPE (high-density polyethylene), considering a return period of 10 years. The design is rather new, and the network was completely redesigned in 2002 and rebuilt between 2004 and 2005. The total pipe length is approximately 74 km (considering only the main and secondary pipes, so neglecting service connections and pipes with a diameter smaller than 200 mm). As the present paper is focused on flooding only, the main pipes were simulated having diameters higher than 500 mm, being 23% of the total length (around 17 km). The concentration time of the considered urban catchment is about 2.1 hours. The DDF curve used for design purposes was evaluated by means of univariate statistical analysis of the annual maxima series recorded at the Piazza Armerina rain gauge during the 1956–2008 period.

#### 2.2. Estimation of DDF Curve Parameters in Climate Change Scenarios

_{T}is the rainfall depth at the specified return period T, duration d, and a

_{T}and n

_{T}are parameters. According to previous studies, the annual maxima rainfall trends occurring in Sicily are because of variations of the a

_{T}parameter [25,26]. By means of the Bayesian procedure described in detail by Liuzzo et al. [23] the a

_{T}parameter of Equation (1) was estimated for some future scenarios.

_{T}parameter of the DDF curve in the presence of an annual maxima rainfall trend. Specifically, the procedure was applied to incorporate, in the DDF curve parameters, the effect of the statistically significant trends of annual maximum rainfall of 1-hour duration. The methodology can be briefly summarized as follows:

- From the original dataset, several continuous sub-datasets with different ending years and lengths were extracted. Specifically, starting from a minimum of 15 years, the length of each sub-dataset was increased by one, up to a maximum of 35 years. This choice was based on the evidence that an intensification of the hydrological cycle occurred in the last 30–35 years [27]. Moreover, this assumption is furtherly supported by the evidence of a statistically significant increase of the average annual rainfall during the last 30 years in Sicily [28];
- The a
_{T}parameter was estimated for each of the above-mentioned sub-datasets; - The likelihood function was used to evaluate the 95th, 50th, and 5th percentiles of each a
_{T}series.

_{T}variability in time, a linear regression of the a

_{T}percentiles was performed considering the last 30 years of the series.

_{T}parameter, and the width of these bands provides a quantification of the uncertainty in the a

_{T}appraisal.

_{T}parameter values for the short-term projections to 2025 and 2050. Figure 2 shows the flow chart of the entire procedure applied in this study.

_{T}in 2010. The a

_{T}parameters were evaluated using the generalized extreme value (GEV) distribution for four return periods T: 2, 5, 10, and 20 years.

#### 2.3. The Hydraulic Model: FLO-2D

_{fx}and S

_{fy}are the friction slope components according to Manning’s equation of the x-axis and y-axis direction, respectively; S

_{bx}and S

_{by}are the bed slope of the x-axis and the y-axis directions, respectively; and g is the gravity acceleration (m/s

^{2}).

^{2}, and it was discretized with 2.8 million squared cells 2 m × 2 m. In the area, different values of roughness were attributed: Rural and agricultural area were assumed to have roughness equal to 0.041 in the Manning scale; gardens and parks were assumed to have roughness equal to 0.032; while roads, pavements, roofs were assumed to have roughness equal to 0.017. The layout of the simulated urban drainage system is shown in Figure 1b.

## 3. Results

#### 3.1. DDF Curves Parameters

_{T}percentiles showed an increasing trend for each of the considered return periods (Figure 3). The linear regression of the 95th and 5th percentile series delineated the upper and lower limits of the uncertainty bands related to the a

_{T}assessment.

_{T}50th percentiles were affected by a quick increase in the last 30 years; nevertheless, the uncertainty bands, delimited by the 95th and the 5th percentiles, were divergent, meaning that the bandwidth was wider for the last years of the examined period compared to the earlier years of the series. This behavior is more emphasized for T equal to 10 and 20 years (Figure 3c,d, respectively) and can be attributed to the higher variability of the 95th percentiles. Specifically, an abrupt change of the 95th percentile can be observed in 1990. The divergence of the 95th and 5th linear regression lines indicates that the uncertainty related to climate change in the assessment of the a

_{T}parameter increases over time. Therefore, medium- and long-term future projections will be affected by an increasing level of uncertainty.

_{T}values for the current climate conditions, the 2010 scenario, and for two future short-term projections to 2025 and 2050. Table 1 summarizes the values of the a

_{T}parameters for each scenario and return period. In the examined scenarios, variations due to climate change of the scaling exponent n

_{T}in Equation (1) were neglected [23].

_{T}values in the 2010 and the 2025 scenarios. Specifically, the highest increase of a

_{T}is assessed in the 2025 scenario for T = 5 years. As regards the 2050 scenario, the a

_{T}increase varies between 21% and 28%, with the highest increase for T = 2 years. These increases are comparable to those assessed for the 5th percentiles, whereas the 95th percentiles show slightly higher increases (up to 30% for the 2050 scenario).

_{T}parameters in Table 1 were used to calculate the design storm provided as input of the FLO-2D hydraulic simulations. These simulations were performed considering all the a

_{T}percentiles for each return period and scenario (36 simulations).

#### 3.2. Maps of Maximum Flow Depths

_{T}. For T equal to 2, 5, and 10 years (Figure 4a–c, respectively), flooded areas have a small extension, and the flow depth does not exceed 0.3 m. For T equal to 20 years (Figure 4d), flooded areas are distributed over the whole urban catchment area, and in some locations, maximum flow depths are up to 0.8 m. The percentage of the flooded areas in the urban catchment ranges from 0.17% (for T = 2 years) to 5.48% (for T = 20 years).

_{T}parameters (Table 1). However, for all the examined return periods, hydraulic simulations were also carried out using the design storm obtained using the DDF curves with 95th and the 5th percentiles of the a

_{T}parameters. Results were reported in maps, and the flooded areas were calculated. Assessing the extension of the flooded areas also using the 95th and the 5th percentiles of the a

_{T}parameter allowed quantifying the uncertainty related to the estimations illustrated in Figure 4, Figure 5 and Figure 6. Specifically, the maps obtained with the 95th and the 5th percentiles of a

_{T}identified the upper and lower limit of the flooded areas, respectively. Basically, the application of the Bayesian procedure for the assessment of the design storms allowed defining a potential range of variation for the flooded areas in climate change scenarios.

_{T}percentile. The analysis of these results shows that in the 2010 scenario, for T equal to 2 and 5 years, there are no substantial differences between the flooded areas, and the range of variations identified with the percentiles of a

_{T}is very small. This behavior is also observed for the 2025 and the 2050 scenarios, but only when T is equal to 2 years. The uncertainty related to the assessment of flooded areas is increasing with the increase of the return period. Therefore, the uncertainty is minimum for every scenario with T equal to 2 years, while it is maximum for the 2050 scenario when T is equal to 20 years. In this case, there is a difference of 0.54 km

^{2}in the flooded areas assessed with the 95th and the 5th percentiles of the aT parameter.

## 4. Discussion

_{T}parameter for short-term scenarios. In order to obtain more reliable future estimation, the calculation of a

_{T}needs to be updated by including any new available data to the original dataset. The addition of new data can affect the detected trend in terms of direction and magnitude. If the procedure were to be applied without the updating of the original dataset, the linear extrapolation approach would lead to an unreliable unlimited rainfall increase.

## 5. Conclusions

_{T}parameter of the DDF curves in some climate change scenarios. These curves were used as input of the FLO-2D model to evaluate and quantify the effects of extreme rainfall variations on urban flooding in Piazza Armerina, a small town located in Southern Italy. In this area, the annual maximum rainfall increased during the 1956–2008 period. The parameters of the DDF curves were updated to take into account this positive trend in two short-term climate projection at 2025 and 2050. The implications of the rainfall increase on the performance of the urban drainage system of Piazza Armerina were investigated, comparing the maximum flow depths and the flooded areas assessed for the current climate conditions (scenario 2010) with those of the 2025 and 2050 scenarios. The analysis was performed considering the design storm of the 2-, 5-, 10-, and 20-year return period. A total of 36 hydraulic simulations were carried out. Results showed that the effect of the rainfall trend is more significant for the flooding related to events with 10- and 20-year return periods. The application of the Bayesian procedure for the assessment of the DDF curve parameters allowed quantifying the uncertainty due to rainfall change related to the definition of the design storm and, consequently, the identification of the flooded areas in the examined urban catchment.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**(

**a**) Orthoimage of the area of study; (

**b**) location of the urban drainage main pipes in the area of study.

**Figure 3.**The 95th, 50th, and 5th percentiles of the aT parameter and linear regressions for different return periods T: (

**a**) 2 years; (

**b**) 5 years; (

**c**) 10 years; and (

**d**) 20 years.

**Figure 4.**Maximum flow depth for the 2010 scenario: (

**a**) T = 2 years; (

**b**) T = 5 years; (

**c**) T = 10 years; and (

**d**) T = 20 years.

**Figure 5.**Maximum flow depth for the 2025 scenario: (

**a**) T = 2 years; (

**b**) T = 5 years; (

**c**) T = 10 years; and (

**d**) T = 20 years.

**Figure 6.**Maximum flow depth for the 2050 scenario: (

**a**) T = 2 years; (

**b**) T = 5 years; (

**c**) T = 10 years; and (

**d**) T = 20 years.

**Figure 7.**Detail of a flooded urban area in Piazza Armerina for T = 20 years: (

**a**) 2010 scenario; (

**b**) 2025 scenario; and (

**c**) 2050 scenario.

**Figure 8.**Percentage of flooded areas for each range of maximum flow depths (m): (

**a**) T = 2 years; (

**b**) T = 5 years; (

**c**) T = 10 years; and (

**d**) T = 20 years.

**Table 1.**Parameters n

_{T}and a

_{T}of depth–duration–frequency (DDF) curves for each scenario and return period T.

T (Years) | Scenario | n_{T} | a_{T} (mm) | ||
---|---|---|---|---|---|

95th Percentile | 50th Percentile | 5th Percentile | |||

2 | 2010 | 0.27 | 30.5 | 28.3 | 27.0 |

2025 | 0.27 | 34.0 | 31.3 | 29.7 | |

2050 | 0.27 | 39.7 | 36.2 | 34.1 | |

5 | 2010 | 0.32 | 41.7 | 38.4 | 37.0 |

2025 | 0.32 | 45.5 | 41.4 | 39.7 | |

2050 | 0.32 | 51.9 | 46.4 | 44.4 | |

10 | 2010 | 0.29 | 52.9 | 48.3 | 45.6 |

2025 | 0.29 | 58.1 | 52.2 | 48.5 | |

2050 | 0.29 | 66.6 | 58.8 | 53.2 | |

20 | 2010 | 0.29 | 68.0 | 61.1 | 56.3 |

2025 | 0.29 | 76.0 | 67.0 | 59.7 | |

2050 | 0.29 | 89.2 | 76.8 | 65.4 |

Scenario | Return Period (Years) | Flooded Area (km^{2}) | ||
---|---|---|---|---|

95th Percentile | 50th Percentile | 5th Percentile | ||

2010 | 2 | 0.020 | 0.019 | 0.018 |

5 | 0.042 | 0.021 | 0.020 | |

10 | 0.274 | 0.034 | 0.025 | |

20 | 0.788 | 0.603 | 0.441 | |

2025 | 2 | 0.021 | 0.020 | 0.019 |

5 | 0.164 | 0.029 | 0.024 | |

10 | 0.507 | 0.243 | 0.094 | |

20 | 0.788 | 0.764 | 0.556 | |

2050 | 2 | 0.023 | 0.022 | 0.021 |

5 | 0.472 | 0.225 | 0.111 | |

10 | 0.750 | 0.523 | 0.276 | |

20 | 1.258 | 0.970 | 0.719 |

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**MDPI and ACS Style**

Liuzzo, L.; Freni, G. Quantifying the Uncertainty Related to Climate Change in the Assessment of Urban Flooding—A Case Study. *Water* **2019**, *11*, 2072.
https://doi.org/10.3390/w11102072

**AMA Style**

Liuzzo L, Freni G. Quantifying the Uncertainty Related to Climate Change in the Assessment of Urban Flooding—A Case Study. *Water*. 2019; 11(10):2072.
https://doi.org/10.3390/w11102072

**Chicago/Turabian Style**

Liuzzo, Lorena, and Gabriele Freni. 2019. "Quantifying the Uncertainty Related to Climate Change in the Assessment of Urban Flooding—A Case Study" *Water* 11, no. 10: 2072.
https://doi.org/10.3390/w11102072