# A Simple GIS-Based Model for Urban Rainstorm Inundation Simulation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Model Development

#### 2.1.1. SCS Runoff Model

_{a}is the initial rainfall loss (unit: mm); F is the real retention (post-loss) (unit: mm); S is the potential retention capacity (the upper limit of the post-loss) (unit: mm); Q is the surface runoff depth (unit: mm); and λ is the dimensionless initial loss coefficient, which mainly depends on local geographic and climatic factors and generally ranges from 0 to 0.4 [40,41]. When plugged in, the classic rainfall runoff equation is obtained with only one parameter to solve, and it is assumed that there is no surface runoff when the initial loss is small:

#### 2.1.2. Combining the Surface Runoff Model and Drainage Model

^{2}); Area is the total area of the sub-catchment (unit: m

^{2}); and ${CN}_{i}$ is the CN value of land use type i in Table 1.

^{n}, where 1, 4, 16, 64 means a perpendicular direction flow, and 2, 8, 32, 128 means an oblique direction flow.

^{2}); Δd is the hydraulic slope; P is the pipeline length (unit: m); Δh is the elevation difference between the upper and lower ends of the pipeline (unit: m); and $C$ is the Chezy coefficient (unit: m

^{0.5}/s), estimated with the Manning equation determined by the pipeline material.

^{3}/s), is expressed as:

- Data input module. Provide spatial data input, including rainfall pattern editing, land use classification, sub-catchment division, and pipe network connectivity editing.
- SCS rainfall-runoff module. Provide surface runoff calculation based on the raster grid, the Thiessen partition of a sub-catchment, and calculation of $\overline{CN}$ for each sub-catchment.
- Surface flow module. Extract hydrological parameters, such as the elevation, slope, aspect, and flow direction. Simulate surface runoff by calculating the flow path, flow speed, and the maximum weighted distance to the manhole for each sub-catchment.
- Drainage flow module. Establish the feature database of the directed pipe-network with spatial topological relationships. Build the attribute database with attributes, such as pipe caliber, material, elevation, and so on, and relate the attribute database to the feature database.

#### 2.2. Model Application

#### 2.2.1. Study Area

^{2}, i.e., 2.9 km long from east to west and 2.7 km wide from north to south (Figure 2). The average population density in this district is very high, up to 40,000 per km

^{2}. The district is committed to establishing a high-quality residential area, high-grade central business district, and an international commercial area [55]. However, due to the low land elevation and high building density, waterlogging disasters occur frequently during the rainy season. Therefore, it is meaningful to study the risks of rainstorm-waterlogging in the area.

#### 2.2.2. Data Used

^{2}; the semi-physical hydraulic model was established in each sub-catchment.

_{p}is the rainstorm intensity (unit: mm/min); Te is the return period (unit: year); and t is the precipitation duration (unit: min).

^{2}).

## 3. Results

#### 3.1. Model Performance and Validation

#### 3.2. Urban Surface Flooding

^{3}/min) after 11 min, but rainfall runoff continuously flows into low-lying areas. After the 60th minute, waterlogging disappears gradually due to the stop of the precipitation, but the drainage and infiltration continues. The detailed changes of flood receding, and drainage processes are shown in Figure 7 and Figure 8.

#### 3.3. Drainage Discharge

^{2}was still retained; while under the Poisson-pattern rainfall, the flooding area was reduced significantly within 80 min, but 0.05 km

^{2}was still retained. At this stage, the flooding of Poisson-pattern rainfall is more serious than that of normal-pattern because Poisson-pattern rain tends to cause larger waterlogging instantaneously with high-intensity precipitation at the beginning. Furthermore, manholes are not necessarily located at the lowest point of the sub-catchment, and as a result, some flooding of the low-lying area can only be removed by infiltration and evaporation.

## 4. Discussion

^{2}when the DTM resolution was coarsened from 2 to 10 and 20 m, respectively. Moreover, some small rainwater retaining facilities, such as depression structures, and some micro-reliefs of artificial structures, such as road shoulders, will also influence the urban flooding propagation. Therefore, a high-quality DEM with reasonable resolution is important to reduce the uncertainty of modeling, which significantly reduces simulation times while providing reasonable simulation results for planning purposes.

^{2}, which primarily consists of sub-catchments where the area is large. Taking sub-catchment ID1615 as an example, the required safety drainage for pipeline ID2289 is 2.7 m

^{3}/min under a 3-year return period and 20-min rainfall duration; however, the actual drainage capacity is only 1.8 m

^{3}/min, which is 0.9 m

^{3}/min lower than the requirement. Therefore, it is hypothesized that inadequate drainage capacity is the main cause of urban waterlogging during heavy rainstorms.

^{3}/min by 18%, 22%, 20%, and 16%, respectively. The safety qualification rate increased from the original 82% of the total sub-catchments to 88%, 91%, 92%, and 91%, respectively. Therefore, it was demonstrated that the safety qualification rate increases significantly with the increase of the pipeline diameter. However, both the safety qualification rate and average drainage capacity are slightly reduced after a 20% increase of diameter, which may be due to the neck effect of some of the restrictive pipelines (pipe diameter less than 0.5 m accounts for 23% in the study area). Thus, the detection of the restrictive pipelines and then increasing their diameters is key to improvements of the overall drainage efficiency in old town rebuilding. Moreover, the flooding caused by Poisson-pattern rainfall is more serious than that of normal-pattern because Poisson-pattern rainfall will result in excessive rainfall immediately at the beginning, and the drainage capacity is limited to discharge severe waterlogging. Therefore, in addition to the drainage system, other low-impact development measures, such as increasing the concave green land, should also be included as comprehensive measures to treat the waterlogging caused by heavy precipitations.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Conceptual model of the urban hydrological process showing the water balance of rainfall (P), runoff (Q), and pipe network flow (Se), where retention (F), primary rainfall loss (${I}_{a}$), and evaporation (E) compose the water losses.

**Figure 5.**Simulated maximum flooding depth and reported flooding streets during Typhoon Matsa in 2005.

**Figure 6.**Flooding depths and their changes over time for (

**a**) the first 1 min, (

**b**) the first 20 min, (

**c**) the first 40 min, and (

**d**) the first 60 min under a 20-year return period rainfall scenario.

**Figure 7.**Maximum flooding depth distribution under the return periods of (

**a**) 2a, (

**b**) 5a, (

**c**) 10a, and (

**d**) 20a for a 60-min rainfall duration and Poisson-precipitation-pattern rain.

**Figure 8.**A comparison of the rainfall runoff–drainage flow–flooding area change under Poisson-pattern and normal-pattern rainfall with an intensity defined as a 3-year return period and a 20-min duration.

Land Use Classification | Soil Permeability | ||||
---|---|---|---|---|---|

A | B | C | D | ||

Residential land (R) | 77 | 85 | 90 | 92 | |

Commercial land (B) | 88 | 91 | 93 | 95 | |

Industrial land (M) | 86 | 89 | 91 | 93 | |

Public facilities (A) | 85 | 89 | 92 | 95 | |

Square land (G) | Green space (G1) | 30 | 55 | 74 | 80 |

Squares (G2) | 80 | 90 | 95 | 98 | |

Other land (G3) | 67 | 76 | 80 | 87 | |

Water surface (E) | 100 | 100 | 100 | 100 | |

Road (R) | 85 | 89 | 95 | 97 |

Pipeline Length | Pipeline Diameter | ||||||||
---|---|---|---|---|---|---|---|---|---|

Length (m) | 10–20 | 20–30 | 30–50 | 50–100 | >100 | Diameter Range: 0.2–3.6 m | |||

Diameter (m) | ≤0.5 | 0.6–1 | >1 | ||||||

Number | 738 | 835 | 1054 | 221 | 24 | Percentage (%) | 23 | 58 | 19 |

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## Share and Cite

**MDPI and ACS Style**

Meng, X.; Zhang, M.; Wen, J.; Du, S.; Xu, H.; Wang, L.; Yang, Y.
A Simple GIS-Based Model for Urban Rainstorm Inundation Simulation. *Sustainability* **2019**, *11*, 2830.
https://doi.org/10.3390/su11102830

**AMA Style**

Meng X, Zhang M, Wen J, Du S, Xu H, Wang L, Yang Y.
A Simple GIS-Based Model for Urban Rainstorm Inundation Simulation. *Sustainability*. 2019; 11(10):2830.
https://doi.org/10.3390/su11102830

**Chicago/Turabian Style**

Meng, Xianhong, Min Zhang, Jiahong Wen, Shiqiang Du, Hui Xu, Luyang Wang, and Yan Yang.
2019. "A Simple GIS-Based Model for Urban Rainstorm Inundation Simulation" *Sustainability* 11, no. 10: 2830.
https://doi.org/10.3390/su11102830