Abstract
With the increasing frequency of extreme convective weather, the spatial–temporal variability of rainfall becomes more diversified. As a result of the insufficient quality of rainfall monitoring data in mountainous areas, the flash flood simulation usually does not consider the effect of the rainfall center location. In this work, the GPU Accelerated Surface Water Flow and Associated Transport hydrodynamic model is used to simulate the flash flood discharge process. The effect of the rainfall center location and the basin scale on the discharge process were analyzed based on simulated data. The results show that when the rainfall center is in the upstream and midstream basins, because of gravitational potential energy conversion, the total flood volume and the flood peak discharge increase to 2–10 times, and the peak time of flash flood caused by 100 mm rainfall amount can be advanced by up to 3,000 s compared to the 20 mm rainfall amount condition. The peak discharge and the delay of peak time increase with the increase of rain peak coefficient. In addition, the increase of the basin area enhances the effect of the rainfall center location. This work is helpful to quantify the effect of the rainfall center location, which can clarify the uncertainty of flash flood simulation caused by not considering the rainfall center factor.
HIGHLIGHTS
When the rainfall center is in the upstream and midstream basins, the total flood volume and the peak discharge increase to about 2–10 times, the flood peak time can be advanced by 3,000 s.
The flood peak discharge increases with the increase of the rain peak coefficient, while the delay of the flood peak time is longer.
The increase of the basin area enhances the effect of the rainfall center location on flash flood.
INTRODUCTION
Flash flood is caused by heavy rainfall in the mountainous area, which is characterized by its suddenness, wide-ranging danger, and difficulty in prediction (Ahmadalipour & Moradkhani 2019). In Europe, 40% of flood-related deaths between 1950 and 2006 were attributed to flash flood (Barredo 2007). In the United States, flash flood is the deadliest type of flood event (Alipour et al. 2020). Furthermore, 82% of the casualties from flood disasters in China between 2010 and 2016 were caused by flash flood (Liu et al. 2018b). Unfortunately, with an increase in the heavy precipitation event, future flash flood incidents may become more frequent (Alipour et al. 2020). Under the influence of global climate change, the uneven temporal–spatial distribution of extreme rainfall events is on the rise, which will seriously affect flash flood processes (Chen et al. 2020). As the temporal–spatial variability of rainfall becomes more complex, the accuracy of flash flood simulation methods that do not consider the rainfall center location will be compromised.
The temporal–spatial structure of rainfall has a significant impact on the hydrological response of flood (Zhu et al. 2018). In recent years, many researchers have studied the temporal–spatial characteristics of rainfall and their influence on flash flood. Llasat et al. (2014) analyzed flash floods in the northwest Mediterranean and concluded that flash flood is triggered by intense, short-duration, and localized rainfall with convective characteristics. Emmanuel et al. (2015) developed rainfall spatial variability indices to detect the influence of rainfall spatial variability on the hydrological response. Silvestro et al. (2016) studied the impact of rainfall spatial distribution on flood discharge. Wright et al. (2020) developed a method for flood frequency analysis, considering rainfall variability. The impact of rainfall on flash flood is complex and related to the basin area, and it may be influenced by other terrain factors such as soil moisture and slope (Crow et al. 2017; Rogger et al. 2017). Zhou et al. (2021) found that the spatial heterogeneity of land use complicates the transformation of rainfall into flood. Grillakis et al. (2016) demonstrated that accurate soil moisture estimation can improve flood simulations. Besides, the relative importance of rainfall temporal and spatial characteristics is also a crucial research focus. Yang et al. (2016) found that in flood simulations, the temporal resolution of rainfall data is more important than spatial resolution. It is worth noting that most of the conclusions regarding the impact of rainfall temporal–spatial heterogeneity on flash flood is based on a relatively limited basin and rainfall event data. Limited monitoring data cannot provide detailed information about how the spatial–temporal distribution characteristics of rainfall affect flash flood. Flash flood results from complex interactions between spatiotemporal heterogeneity rainfall events, non-uniform surface features, and river network distribution, making conclusions drawn from specific basins and rainfall events somewhat specific (Zhu et al. 2018). In a basin, due to significant variations in morphological parameters across different regions, such as river width and length, bifurcation ratio, river density, elevation changes, basin perimeter, and area, the contribution of each local area to triggering floods differs (Oborie & Rowland 2023). This creates the need for more morphometric statistical analysis to understand the relationship between rainfall and flash flood under complex basin conditions. Furthermore, the relationship between rainfall and floods is basin scale-dependent (Zhou et al. 2021). However, there has been relatively little research focused on a small basin scale, and the impact of basin size on flash flood processes with different rainfall center locations still requires further investigation (Peleg et al. 2017).
High-quality rainfall information is crucial for the accurate simulation of flood (Wright et al. 2014). Measuring rainfall at individual locations using rain gauges is straightforward and has been widely used by researchers for decades, significantly advancing the study of rainfall-induced flood. However, as flood results from the combination of extreme rainfall events across a basin rather than at single points, the limitation of rain gauge has become increasingly apparent as flood modeling efforts progress (Wright 2018). The establishment of the dense rain gauge network can effectively monitor the temporal–spatial characteristics of rainfall. Nevertheless, the complex terrain of the mountainous basin makes it challenging to provide a reasonable and comprehensive rain gauge coverage. Additionally, the installation of advanced weather radars comes with high costs, making it unaffordable for many regions (Novák et al. 2021). With the advancement of satellite remote sensing technology, new methods have been introduced for rainfall prediction, showing excellent performance in large-scale and long-term rainfall prediction. However, the prediction accuracy for sudden rainfall events in local mountainous areas is relatively low (Wang & Wang 2022; Gultepe 2023). This underscores the need for a deeper understanding of the mechanisms through which rainfall temporal–spatial heterogeneity affects flash flood and for incorporating these effects fully into models to improve flash flood prediction (Saharia et al. 2021). Today, due to the efficiency and capabilities of Artificial Intelligence (AI) technology, various AI computational algorithms such as artificial neural networks, binary logistic regression, and entropy weights method have been widely applied to address water-related issues (Samadi et al. 2021; Borjalilu & Bozorgi-Amiri 2022; Dinh et al. 2022). Fayaz et al. (2022) proposed that a rainfall prediction algorithm based on the adaptive linear M5 model tree was proposed and demonstrated good predictive performance in the study area. However, these AI algorithms employ ‘black-box’ methods to provide results, where users can only analyze input and output values without understanding the internal workings of the algorithms, leading to decreased reliability and confidence in prediction. Additionally, issues such as low generalization ability, local minima, and overfitting may affect the stability of AI algorithms (Samadi et al. 2020). Currently, numerous hydrological models are applied in the numerical simulation of flash flood, such as the Hydrologic Engineering Center's-Hydrologic Modeling System (HEC-HMS) and the Variable Infiltration Capacity (VIC) model. These hydrological models offer high computational efficiency and are fairly accurate in simulating flood processes (Hu & Song 2018). However, the high-computational efficiency of the hydrological model is achieved by simplifying hydrological processes and setting numerous conceptual parameters, resulting in less than perfect simulation performance. It is necessary to use a more accurate model for simulation, and the hydrodynamic model coupled with hydrological processes, which simulate the flood progression process based on the laws of fluid dynamics, can address this issue. With rapid advancements in computer technology, the computational burden no longer hampers the widespread application of the hydrodynamic model (Ming et al. 2020). It can effectively capture the influence of micro-topography on runoff.
Therefore, the lack of sufficient high-resolution rainfall data and the hydrodynamic model that has high-computational efficiency and accuracy poses the greatest obstacles to constructing the simulation model that investigate the impact of spatiotemporal changes in heavy rainfall on flash flood. This study utilizes the Graphics Processing Unit (GPU) Accelerated Surface Water Flow and Associated Transport (GAST) hydrodynamic model, which employs GPU acceleration technology and is based on solving the shallow water equations to simulate high-precision flash flood processes. And by constructing high-resolution rainfall data with different characteristics, the study analyzes the impact of the rainfall center location on flash flood processes in the small basin. Furthermore, the study examines variations in flash flood processes resulting from the combined effects of the basin scale and the rainfall center location.
METHODOLOGY
The GAST model






Evaluation indicator








EXPERIMENTAL DESIGN
Basin data
Location and terrain data of the basin: (a) location; (b) DEM; and (c) land use.
Location and terrain data of the basin: (a) location; (b) DEM; and (c) land use.
Topographic features of the V-shaped basin can be altered by changing parameters, such as slope and area. Three V-shaped basins were used in this work to investigate the effect of the basin area on the study results. The parameters of each V-shaped basin are shown in Table 1. V1 is the prototype of the V-shaped basin. The area size of V2 is larger than V1, and the area size of V3 is larger than V2. These three terrains were used in this work to investigate the impacts of the area size of the basin on the flash flood process.
The parameters of different V-shaped ideal basins
. | S1 . | S2 . | LC (m) . | LO (m) . | W (m) . | D (m) . |
---|---|---|---|---|---|---|
V1 | 0.01 | 0.01 | 1,000 | 800 | 20 | 20 |
V2 | 0.01 | 0.01 | 5,000 | 4,000 | 100 | 100 |
V3 | 0.01 | 0.01 | 10,000 | 8,000 | 200 | 200 |
. | S1 . | S2 . | LC (m) . | LO (m) . | W (m) . | D (m) . |
---|---|---|---|---|---|---|
V1 | 0.01 | 0.01 | 1,000 | 800 | 20 | 20 |
V2 | 0.01 | 0.01 | 5,000 | 4,000 | 100 | 100 |
V3 | 0.01 | 0.01 | 10,000 | 8,000 | 200 | 200 |
Rainfall data
Rainfall amount distribution of the three rainfall center scenarios: (a) upstream basin; (b) midstream basin; and (c) downstream basin.
Rainfall amount distribution of the three rainfall center scenarios: (a) upstream basin; (b) midstream basin; and (c) downstream basin.
The second step is to design the temporal distribution of rainfall. The Chicago rainfall pattern can be used to describe the short-duration rainfall process in the study area, which is usually generated rainfall data with 2 h duration (Li et al. 2018). Ochoa-Rodriguez et al. (2015) identified that the optimal temporal resolution applicable to the simulation is 5 min. Therefore, the rainstorm temporal resolution is 5 min, and the duration is 2 h in this work.
There are four types of rainfall center locations (including uniform-distributed rainfall), three types of rain peak coefficients, and five types of rainfall amount. The total number of simulated cases is 4 × 3 × 5 = 60. The simulated scenarios are shown in Table 2.
Rainfall simulated scenarios with different rainfall center locations and other rainfall factors
Scenario number . | Accumulative rainfall . | Rain peak coefficient . | Rainfall center location . |
---|---|---|---|
1 | 20 | r = 0.2 | Upstream basin |
2 | 20 | r = 0.2 | Midstream basin |
3 | 20 | r = 0.2 | Downstream basin |
··· | ··· | ··· | ··· |
11 | 20 | r = 0.5 | Uniform distributed |
12 | 20 | r = 0.8 | Uniform distributed |
··· | ··· | ··· | ··· |
24 | 40 | r = 0.8 | Uniform distributed |
··· | ··· | ··· | ··· |
60 | 100 | r = 0.8 | Uniform distributed |
Scenario number . | Accumulative rainfall . | Rain peak coefficient . | Rainfall center location . |
---|---|---|---|
1 | 20 | r = 0.2 | Upstream basin |
2 | 20 | r = 0.2 | Midstream basin |
3 | 20 | r = 0.2 | Downstream basin |
··· | ··· | ··· | ··· |
11 | 20 | r = 0.5 | Uniform distributed |
12 | 20 | r = 0.8 | Uniform distributed |
··· | ··· | ··· | ··· |
24 | 40 | r = 0.8 | Uniform distributed |
··· | ··· | ··· | ··· |
60 | 100 | r = 0.8 | Uniform distributed |
RESULTS AND DISCUSSION
Model validation
The rainfall data and water level data used for model validation were obtained from the Qingshui hydrological station. The rainfall data for model validation is from May 9, 2012 and June 6, 2013. According to the government's 2021 Soil Moisture Briefing in Liuyang City, Hunan Province, the soil type in the Baogaisi basin is red loam. However, since the soil texture varies from place to place, the values of each soil parameter were determined by considering the parameter values already used in the reference study conducted in this area for research (Liu et al. 2018a). The soil-saturated hydraulic values in the river channel and the hillside are 0.333 and 0.100 mm/min, respectively. The river of the Baogaisi basin is an intermittent river. When no rainfall occurs, the river is usually water-free and the soil at the river bottom is exposed, so the soil infiltration of the river channel needs to be considered. The wetting front suctions are 50 and 20 mm, respectively. The Manning coefficients are 0.02 and 0.2, respectively.
Detailed information on the GAST model validation for the V-shaped basin has been presented in the literature (Hou et al. 2018). The NSE of simulated runoff data and analytical solution for the hillside is 0.99 and for the river channel is 0.98. This shows that the simulation of this model is accurate and can reproduce the runoff process of the V-shaped basin well. In this work, the same GAST model was used to simulate the flash flood discharge process in terrain V1, terrain V2, and terrain V3.
Influence of the rainfall center location on the flash flood process
Flood discharge process of the outlet under different rainfall spatial distributions.
Flood discharge process of the outlet under different rainfall spatial distributions.
Discharge process at the outlet with different rainfall amounts (r = 0.5): (a) rainfall center at the upstream; (b) rainfall center at the midstream; and (c) rainfall center at the downstream.
Discharge process at the outlet with different rainfall amounts (r = 0.5): (a) rainfall center at the upstream; (b) rainfall center at the midstream; and (c) rainfall center at the downstream.
Through the comparison of the discharge process shown in Figure 8, when the rainfall amount is 20 mm, the rainfall center location has the greatest influence on the outlet discharge process. When the rainfall amount reaches 100 mm, the rainfall center location has the least influence. It can be concluded that with the increase of rainfall amount, the effect of the rainfall center location on the flash flood process gradually decreases. The reduction of the flood peak time is the greatest when the rainfall center is in the downstream. However, the reduction of the flood peak time is similar both when the rainfall center is in the upstream and midstream basins and when it is smaller than when the rainfall center is in the downstream. In the simulated cases, both the total flood volume and the flood peak discharge increased by 2–10 times, and the flood peak time can be advanced by 0–3,000 s.
Deviation index E of the discharge process under different rain peak coefficients
Rain peak coefficient . | 0.2 . | 0.5 . | 0.8 . | |
---|---|---|---|---|
The rainfall center location | Upstream basin | 0.288 | 0.232 | 0.167 |
Midstream basin | 0.340 | 0.013 | 0.041 | |
Downstream basin | 0.618 | 0.504 | 0.503 |
Rain peak coefficient . | 0.2 . | 0.5 . | 0.8 . | |
---|---|---|---|---|
The rainfall center location | Upstream basin | 0.288 | 0.232 | 0.167 |
Midstream basin | 0.340 | 0.013 | 0.041 | |
Downstream basin | 0.618 | 0.504 | 0.503 |
Flash flood discharge process with different rain peak coefficients (40 mm): (a) rainfall center at the upstream; (b) rainfall center at the midstream; and (c) rainfall center at the downstream.
Flash flood discharge process with different rain peak coefficients (40 mm): (a) rainfall center at the upstream; (b) rainfall center at the midstream; and (c) rainfall center at the downstream.
Flow velocity map at the flood peak time (40 mm, r = 0.5). (a) Rainfall center at the upstream; (b) rainfall center at the midstream; and (c) rainfall center at the downstream.
Flow velocity map at the flood peak time (40 mm, r = 0.5). (a) Rainfall center at the upstream; (b) rainfall center at the midstream; and (c) rainfall center at the downstream.
Impact of basin area size on the flash flood process with different rainfall center locations
The change of flood peak discharge under different rainfall center locations at different basin areas.
The change of flood peak discharge under different rainfall center locations at different basin areas.
In addition to the basin-scale parameters mentioned above, other morphological parameters also exert a significant influence on flood response (Oborie & Rowland 2023). Mountainous micro-topography is recognized as an important influential factor in the flash flood generation, because it affects flow-generating processes and streamflow situation (Borga et al. 2010). Therefore, in the ideal basin, the influence caused by the spatial and temporal variability of rainstorms can directly impact streamflow without being affected by micro-topography. In real-world basins, the simulation results are affected by the surface micro-topography, which is consistent with the findings of the existing research (Braud et al. 2014). The steep slopes in small catchments over complex mountainous terrains lead to rapid runoff yield and the concentration of moisture, with sudden and sharp rises and drops in water depth, which contribute to the rapid development of flash flood disasters (He et al. 2018). The influence of longitudinal and transverse slopes on flood processes under different rainfall conditions also needs to be further studied in the future. Longitudinal slope can directly affect the flood process within the river channel by altering the channel gradient, while transverse slope, by changing the slopes on either side of the hills, influences the runoff process indirectly and affects the flood processes at the basin outlet.
CONCLUSIONS
In this paper, the effect of the rainfall center location on the flash flood process at the small basin scale is investigated by using the GAST hydrodynamic model to simulate different flash flood processess under different rainfall center locations. Based on the results and discussion made, the following conclusions are drawn.
When the rainfall center is in the upstream and midstream basins, the total flood volume and the flood peak discharge can increase up to 2–10 times due to gravitational potential energy conversion. The flood peak time can be advanced by up to 3,000 s. This uncertainty should be considered in flood warning systems, with appropriate deviation ranges for flood peak arrival time.
As the rainfall peak coefficient increases, the flood peak discharge rises and the flood peak time delays. Emergency management should simulate different rainfall peak scenarios, considering different flood peak time for rational flood planning.
The basin area amplifies the rainfall center's impact on flash flood. This effect is enhanced most significantly when the rainfall center is in the upstream basin, followed by the midstream and downstream basins. Therefore, emergency plans should account for the rainfall center location, lowering critical rainfall thresholds when it is in upstream.
This work quantitatively analyzes the variation in the flash flood discharge process with different rainfall center locations and clarifies its mechanisms. However, in this work, some characteristic information of rainfall was not considered, such as the spatial resolution of rainfall data (Lobligeois et al. 2014), different rainfall durations (Wei et al. 2019), and the temporal resolution of rainfall data (Wei et al. 2019). Changes in these factors may influence the conclusions drawn above, which requires further research.
ACKNOWLEDGEMENTS
This work is partly supported by the National Natural Science Foundation of China (Grant Nos. 52079106 and 52009104); the Sino-German Mobility Programme (Grant No. M-0427); Key Science and Technology Projects of Power China (DJ-ZDXM-2022-41); Major Company-Level Science and Technology Projects of Northwest Engineering Corporation Limited, Power China (XBY-ZDKJ-2022-9); Key R&D Program of Shannxi of China Key Technology and Industrialization of Sustainable Management of Flood Disaster (2023GXLH-042).
DATA AVAILABILITY STATEMENT
Data cannot be made publicly available; readers should contact the corresponding author for details.
CONFLICT OF INTEREST
The authors declare there is no conflict.