**1. Introduction**

The issue of urban flood inundation has become a key global concern in recent years because of the regional impacts of climate change, which cause more frequent shortduration extreme storms [1]. The negative impacts of urban floods include the failure of city infrastructure, economic loss, the risk to life, etc. Inundation in urban areas is associated not only with the increase in the intensity and frequency of extreme rainfall, but also with impermeable surfaces and limited discharge capacity during heavy rainfall, as well as inappropriate artificial interventions that affect the intensity and magnitude of floods [2–4]. Analyses of the temporal characteristics of rainfall in Korea show a gradual increase in the intensity and frequency of extreme rainfall events. Therefore, the failure of the stormwater drainage system has become more frequent and severe. The metropolitan area of Seoul is vulnerable to urban flooding due to its high precipitation compared to other regions of Korea [5,6]. Recently, the potential for flood-resilient and sustainable redevelopment of Seoul was analyzed to propose city renovation strategies for resistance to flood disasters [7]. In Japan, urban flood vulnerability was quantified by analyzing the topographic characteristics of a fluvial area of the Kaki River in Nagaoka city to evaluate evacuation urgency during urban flooding [8]. Various studies have been conducted to accurately express the temporal distribution characteristics of input rainfall data used for urban flood simulation and analysis, including the Keifer and Chu method [9], the method suggested by Yen and Chow [10], the SCS curve method [11], the Huff method [12], etc.

**Citation:** Li, T.; Lee, G.; Kim, G. Case Study of Urban Flood Inundation—Impact of Temporal Variability in Rainfall Events. *Water* **2021**, *13*, 3438. https://doi.org/ 10.3390/w13233438

Academic Editor: Thomas M. Missimer

Received: 3 November 2021 Accepted: 1 December 2021 Published: 4 December 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

For example, the SCS curve method has been used in urban areas to predict the surface runoff from impervious areas and sediment yield in downstream areas [13]. In South Korea, there have been many studies on the distribution of Huff rainfall time; the Huff rainfall distribution is constructed so that the peak of the heavy rain can be placed in the desired time section. This tends to represent the time distribution of heavy rain relatively well; therefore, the Huff method was chosen in this study as the time distribution of rainfall was suitable for the applied rainfall–runoff model [14].

Many studies have been conducted on the assessment and management of urban flood inundation, using the Huff method to represent the time distribution of heavy storms. Yang et al. [15] modeled floods by coupling the 1D stormwater management model (SWMM) and the 2D flood inundation model (ECNU Flood-Urban) to analyze rainfall–runoff processes in an urban environment in the central business district of East Nanjing Road in downtown Shanghai. Bezak et al. [16] investigated the impact of the different design rainfall events of Huff curves on the combined 1D/2D hydraulic modeling results. Lee [17] proposed a support plan for the Huff rainfall distribution, impact-based, urban flooding forecast. The SWMM or FLO-2D models can be used to predict floods and pipeline drainage, or prepare flood hazard maps. Erena et al. [18] proposed local flood management strategies for 232 households located in flood-prone areas of Dire Dawa city, Ethiopia. Flood hazard mapping was used for different storm events. Luo et al. [19] used a calibrated flood inundation model to assess the influence of four extreme rainfall events on water depth and inundation area in the Hanoi Central Area, Vietnam. The research only focused on overland flooding caused by extreme rainfall, while little attention was paid to floods caused by failures of the drainage system. Vojtek et al. [20] investigated the sensitivity of flood areas, flood volume associated with model input parameters, and showed the importance of proper input parameter estimation in the flood simulation. GebreEgziabher et al. [21] coupled the one-dimensional SWMM model with the new flood inundation and recession model (FIRM) to model urban flood inundation and recession and the impact of manhole characteristics such as spatial extent and depth.

Urban floods are highly associated not only with future rainfall quantities, but also the time distribution characteristics of heavy storms, the antecedent rainfall conditions, the capacity of drainage networks, etc. Among all of these factors, the influence of the temporal patterns of extreme rainfall on the manhole overflow is one of the most important factors. Previous research has demonstrated that the impacts of the temporal characteristics of potential extreme rainfall events on the amount of urban flooding should be considered to enhance urban flood risk management systems. Nevertheless, previous studies have not thoroughly explored the impacts of the time distribution characteristics of extreme rainfall patterns on urban floods.

The temporal concentration level of storms and the storm peak occurrence quartile are the main time distribution characteristics of heavy storms associated with manhole overflow. In this study, the urban flood inundation impacts caused by the temporal concentration level of storms and the storm peak occurrence quartile were analyzed for a target drainage basin in Seoul, Korea. The total manhole overflow in the target urban drainage basin was calculated using the EPA-SWMM model for different rainfall scenarios. Rainfall scenarios reflecting the temporal characteristics of rainfall events were constructed using the Huff method. The impacts of the temporal concentration level were analyzed using nine different exceedance probabilities (10–90%) and the impacts of the temporal location of storm peak were analyzed using four different quartiles (1–4th quartile) for three different storm durations (1–3 h) and four different return periods (10, 50, 80, and 100-years). The two-dimensional inundation analysis of the overflow in each manhole was conducted using the FLO-2D model.
