An Integrated Hydrological–Hydrodynamic Model Based on GPU Acceleration for Catchment-Scale Rainfall Flood Simulation

Abstract

Extreme rainstorms are difficult to predict and often result in catchment-scale rainfall flooding, leading to substantial economic losses globally. Enhancing the numerical computational efficiency of flood models is essential for improving flood forecasting capabilities. This study presents an integrated hydrological–hydrodynamic model accelerated using GPU (Graphics Processing Unit) technology to perform high-efficiency and high-precision rainfall flood simulations at the catchment scale. The model couples hydrological and hydrodynamic processes by solving the fully two-dimensional shallow water equations (2D SWEs), incorporating GPU-accelerated parallel computing. The model achieves accelerated rainstorm flooding simulations through its implementation on GPUs with parallel computing technology, significantly enhancing its computational efficiency and maintaining its numerical stability. Validations are conducted using an idealized V-shaped catchment and an experimental benchmark, followed by application to a small catchment on the Chinese Loess Plateau. The computational experiments reveal a strong positive correlation between grid cell numbers and GPU acceleration efficiency. The results also demonstrate that the proposed model offers better computational accuracy and acceleration performance than the single-GPU model. This GPU-accelerated hydrological–hydrodynamic modeling framework enables rapid, high-fidelity rainfall flood simulations and provides critical support for timely and effective flood emergency decision making.

1. Introduction

Global climate change has significantly increased the frequency and intensity of extreme precipitation events, resulting in rising incidence and severity of flood disasters [1,2,3,4,5]. Flooding remains one of the most prevalent and devastating natural disasters worldwide, accounting for 44% of global disaster events between 2000 and 2019 [6,7,8]. Floods pose direct threats to human life and cause immense economic damage. Moreover, they can trigger secondary hazards such as flash floods, dam failures, landslides, and damage to critical infrastructure [9,10,11]. Low- and middle-income countries are especially vulnerable due to systemic deficiencies in disaster preparedness and infrastructure increasing their exposure to flood risks [12]. Enhancing flood early-warning systems is an effective means to mitigate economic loss and save lives [13]. Thus, the ability to efficiently forecast rainfall flooding and respond promptly is critical for effective risk management and decision making.

The numerical simulation method is a powerful technical means of modeling surface runoff and issuing flood warnings based on historical or synthetic rainfall scenarios [14,15]. Over the past decades, large-scale hydrological and hydrodynamic models have been widely used to simulate watersheds and urban flooding [16]. Compared to traditional hydrological or simplified models, hydrodynamic models based on the solution to shallow water equations can be better applied in the dynamics of flood simulations, producing higher accuracy [17]. The most common hydrodynamic models are primarily one-dimensional (1D) and two-dimensional (2D) [18]. Compared to 1D models, 2D hydrodynamic models require longer computation times and more data inputs but yield more accurate simulation results [19]. Many studies have demonstrated that 2D hydrodynamic models can effectively simulate flood characteristics such as the inundation extent, flow velocity, and water depth in complex terrain [20,21,22,23,24]. The rainstorm flooding process encompasses complete precipitation, infiltration, and runoff cycle mechanisms. Further research has demonstrated that the development of fully hydrodynamic models through coupling with hydrological processes enables accurate simulations of complex flood scenarios [25,26]. Therefore, implementing a fully coupled hydrological–hydrodynamic model not only improves the representation of flood dynamics but also enhances predictive capability for future floods.

The emergence of high-performance computing technologies, particularly GPU-accelerated computing, has dramatically increased the computational efficiency of flood simulations. However, the computational intensity inherent to the high-precision hydrodynamic modeling of surface flood inundation processes inevitably leads to compromised computational efficiency, particularly when resolving complex flow dynamics in high-resolution modeling scenarios [18]. Simulations of high-resolution, large-scale shallow water-flow problems have become feasible using GPUs.

GPU-based models can significantly accelerate the computing performance of flood simulations [27,28]; however, most existing 2D hydrodynamic models rely on a single GPU, which limits their scalability to large-domain simulations involving a large number of grid cells [26]. Integrating multiple GPUs for parallel computing into flood modeling frameworks offers a promising solution for the high-performance simulation of both urban and riverine flooding at large scales [29,30]. The multiple-GPU-accelerated hydrodynamic simulation method can enhance computational efficiency and accuracy for large-scale basin flood simulations, while providing robust technical support for flood risk assessments.

Despite progress in GPU-accelerated flood modeling, most existing applications focus on river channels or urban settings, while their implementation in gully catchment-scale flood simulation and forecasting remains unexplored. Therefore, this study proposes an integrated hydrological–hydrodynamic model implemented using multiple GPUs to carry out catchment-scale flood simulations in experimental and gully watersheds. This method can significantly enhance efficacy and save time in emergency decision making during serious flood events. In Section 2, the model framework and GPU-accelerated methods are introduced. In Section 3, the model is validated on an idealized V-catchment, an experimental catchment benchmark test, and a small catchment on the Chinese Loess Plateau to evaluate its accelerated computing performance. The conclusions are described in Section 4.

2. Materials and Methods

This section introduces the numerical methods and GPU-accelerated computing techniques used to implement the integrated hydrological–hydrodynamic model. The models require further testing and refinement (over 3 GPUs). The core computational work of this study was conducted on two identical GPUs, utilizing the CUDA/C++ programming language for high-performance parallel computing.

2.1. Numerical Method

The hydrological–hydrodynamic model is developed by integrating a two-dimensional hydrodynamic model with the Green–Ampt infiltration model to simulate catchment-scale rainfall flooding processes, improving upon the previous model [31]. Whereas previous research primarily employed an equivalent infiltration approach to represent drainage capacity in urban inundation modeling without a coupled infiltration model, this study employs a hydrological–hydrodynamic framework incorporating the Green–Ampt infiltration model, substantially improving the simulation of infiltration dynamics for all land uses across watershed scales. The model employs a finite volume method to solve the shallow water equations (SWEs), and the conservation form of the two-dimensional SWEs governing equation can be written as follows:

$${\displaystyle \frac{\partial \mathit{q}}{\partial t}}+{\displaystyle \frac{\partial \mathit{f}}{\partial x}}+{\displaystyle \frac{\partial \mathit{g}}{\partial y}}=\mathit{S}$$

(1)

where $\mathit{q}$ is the flow variable vector; $\mathit{f}$ and $\mathit{g}$ are the flux vectors in the x and y directions, respectively; and $\mathit{S}$ is the source vector. The vector terms of the governing equation can be expressed as follows:

$$\mathit{q}=\left[\begin{array}{l}h\\ q_x\\ q_y\end{array}\right], \mathit{f}=\left[\begin{array}{c}uh\\ u{q}_x+g{h}^2/2\\ u{q}_y\end{array}\right],\mathit{g}=\left[\begin{array}{c}vh\\ v{q}_x\\ v{q}_y+g{h}^2/2\end{array}\right]$$

(2)

$$\mathit{S}=\left[\begin{array}{c}i\\ -gh{\displaystyle \frac{\partial z_b}{\partial x}}-C_{f}u\sqrt{u^2+v^2}\\ -gh{\displaystyle \frac{\partial z_b}{\partial y}}-C_{f}v\sqrt{u^2+v^2}\end{array}\right]$$

(3)

where $q_x$ and $q_y$ are the unit-width discharges in the x and y directions, defined as $q_x=uh$ and $q_y=vh$; $z_b$ is the bed elevation; $h$ is the water depth; $u$ and $v$ are the velocity components in the two Cartesian directions; $C_f$ represents the bed roughness coefficient, defined as $C_f=g{n}^2/h^{1/3}$, where $g$, $h$, and n are the gravity acceleration, water depth, and Manning coefficient, respectively; and $i$ is the source and sink term representing rainfall and infiltration effects.

The infiltration formulation is incorporated into the model. The Green–Ampt infiltration model [32] is coupled into the source term Equation (3) and is applied to calculate the infiltration rate. The equation is as follows:

$$i(t)=k_s\left[1+{\displaystyle \frac{h+h_p}{z(t)}}\right]$$

(4)

where i(t) is the infiltration rate; k_s is the saturated hydraulic conductivity; h is the water depth over the surface; h_p is the suction head at the wetting front; and z(t) is the depth of the wetting front.

The Godunov-type finite volume scheme is implemented to solve governing Equation (1), as given in [33,34]. The equation is expressed in integral form as follows:

$${\displaystyle {\int }_{\Omega }\frac{\partial \mathit{q}}{\partial t}d}\Omega +{\displaystyle {\int }_{\Omega }\left(\frac{\partial \mathit{f}}{\partial x}+\frac{\partial \mathit{g}}{\partial y}\right)d\Omega }={\displaystyle {\int }_{\Omega }\mathit{S}d\Omega }$$

(5)

where $\Omega$ is the cell volume; and the source vector S contains the slope source S_b and friction source S_f; defined as S = S_b + S_f. The governing equations are solved using finite volume temporal discretization as follows:

$${{\displaystyle \mathrm{q}}}_i^{n+1}={{\displaystyle \mathrm{q}}}_i^n+{\displaystyle \frac{\Delta t}{\Omega }}\left({\displaystyle {\int }_{\Omega }\mathit{S}} d\Omega -{\displaystyle \sum _{k=1}^{nb}{F}_k}\left({\mathrm{q}}^n\right)\cdot n_k{l}_k\right)$$

(6)

where ${{\displaystyle \mathrm{q}}}_i^{n+1}$ is the updated flow of the i th cell in the next time step; k, l, and nb are the index, length, and number of edges of cell i, respectively; $F_k\left({\mathrm{q}}^n\right)$ is the flux vector normal to the cell i boundary; and $\Delta t$ is the time step.

Among the numerical solution methods, the method of applying the HLLC (Harten-Lax-van Leer-Contact) approximate Riemann solver [34] to calculate interfacial fluxes has demonstrated good performance in flood simulations. To enhance the spatial accuracy of the model’s numerical scheme, second-order spatial reconstruction is performed using the MUSCL (Monotone Upstream Scheme for Conservation Law) scheme proposed in [33]. To ensure numerical stability and high precision, the slope flux and splitting point implicit methods reported in [33,35] are applied to compute the bed slope and friction source terms. Additionally, the method proposed in [34] is adopted to solve the non-negative water depths and localized high-velocity flows, with good computational stability.

2.2. Accelerated Parallel Computing on GPUs

GPU acceleration is applied using explicit numerical schemes suitable for parallelization, as proved in [17,20,26]. Thus, the multi-GPU-accelerated parallel computing technique is applied in the model in this study to realize parallel simulations of rainfall, infiltration, and flow generation processes. A structured domain decomposition method is employed to distribute computational workloads across multiple GPUs. CUDA streams manage inter-device (GPU) communication for efficient data transfer. The two aforementioned approaches effectively address the challenges of data communication and exchange in multi-GPU computing, with the detailed computational processes described in our previous related study [31]. Firstly, the computational domain (M × N cells) is partitioned equally along the y direction into two subdomains (initially M/2 × N cells each), corresponding to the two utilized GPUs. To accurately handle flux calculations at the shared boundary between adjacent subdomains, where cells require data from neighboring cells residing on the other GPU, a one-cell-thick overlapping region is implemented. Then, the lower boundary of subdomain A (GPU 1) is extended by one row (1 × N cells) into the upper boundary region of subdomain B (GPU 2). This results in two final subdomains of size (M/2 + 1) × N cells each (Figure 1). These overlapping layers (gray areas in Figure 1) contain copies of the relevant boundary cells from the neighboring subdomain. This approach minimizes host-device memory transfers by allowing necessary inter-GPU data exchanges (specifically for these boundary cell values) to occur directly between devices, updating the overlapping layers prior to each computational step. This domain decomposition method is fundamental for facilitating efficient data exchange between GPU 1 and GPU 2, enabling effective multi-GPU parallel computation to enhance overall performance. All three cases employ the aforementioned domain decomposition method in this study.

Figure 2 shows the processes of implementing GPU-accelerated parallel computing for a full hydrodynamic model. The modeling procedure includes initializing parameters (e.g., rainfall, water depth), partitioning the domain based on the GPU number, synchronizing overlapping cells, and executing simulations in parallel. Firstly, the input parameters are initialized, including the water depth and level, rainfall, and infiltration. The computational domain is partitioned into the same subdomains equal in number to the GPUs, the values of the neighboring cells in the overlapping regions between adjacent subdomains are populated, and all variables are then asynchronously copied from the CPU to each GPU. The CUDA stream method is employed to enable data exchange for each GPU, including the runoff amount, water level, and flow velocity of the flood. Data exchange between GPUs occurs directly through these overlapping halo regions. Finally, after the computational tasks are completed, the simulation data from each GPU are copied back to the CPU for merging to obtain the complete simulation results.

The model was implemented in CUDA/C++ and tested using two identical NVIDIA GeForce GTX 1080 GPUs (NVIDIA Corporation, USA). In this study, two existing GPU cards (NVIDIA GeForce GTX 1080) with the same types (e.g., the same CUDA cores) were used to simulate the flood process and evaluate the model performance for all test cases. The single-GPU model was tested on a single-GPU card, and the multi-GPU model was tested on these two same GPU cards.

2.3. Assessment of Model Performance

Most studies have demonstrated that GPU-accelerated simulations are significantly faster than those only using a CPU. This study focuses on investigating the performance of multiple GPUs compared to a single GPU. The model’s performance is evaluated using three indicators. These metrics help compare single- and multi-GPU simulations in terms of both computational accuracy and efficiency. The Nash–Sutcliffe model efficiency coefficient (NSE) and root-mean-square error (RMSE) are employed to assess the simulation accuracy of the model, as reported in [36,37]. A comparative analysis is conducted using the relative error (RE) to evaluate the consistency of computational results from two different computing platforms, analyzing the simulation accuracy of single GPUs and multiple GPUs. The accelerated computing performance of the model is evaluated using the relative speedup (RS) ratio, as given in [31]. These assessment indices are defined as follows:

$$\mathrm{N}\mathrm{S}\mathrm{E}=1-{\displaystyle \frac{{\displaystyle {\sum }_1^{\mathrm{N}}{({\mathrm{q}}_{\mathrm{m}}^{\mathrm{n}}-{\mathrm{q}}_{\mathrm{o}}^{\mathrm{n}})}^2}}{{\displaystyle {\sum }_1^{\mathrm{N}}{({\mathrm{q}}_{\mathrm{m}}^{\mathrm{n}}-{\overline{\mathrm{q}}}_{\mathrm{o}})}^2}}}$$

(7)

where, $q_m^n$ and $q_o^n$ are the computed and observed flow at time step n, respectively; N is the total number of time steps; and ${\overline{q}}_o$ is the mean observed flow. An NSE value closer to 1 indicates higher reliability and simulation accuracy of the model.

$$RE={\displaystyle \frac{|S_{GPU\mathrm{s}}-S_m|}{S_m}}$$

(8)

where, $S_{GPU\mathrm{s}}$ and $S_m$ are the measured and multi-GPU-simulated inundation areas, respectively.

$$RS={\displaystyle \frac{t_{1GPU}}{t_{2GPUs}}}$$

(9)

where, $t_{ 1GPU}$ and $t_{2GPUs}$ are the computational time executed on a single GPU and 2 GPUs, respectively.

2.4. High-Resolution Data and Rainfall Input

The high-resolution DEM is vital for setting up the proposed model. An unmanned aerial vehicle (UAV) equipped with a multi-camera system and LiDAR (Light Detection and Ranging) was used to obtain high-resolution DEM and land-use image data, obtaining a spatial resolution of 2 m data in the gully catchment on the Chinese Loess Plateau. Using ArcGIS 10.3 software, we plotted the location map of the study area and distribution maps of the high-resolution DEM and land-use classification. The gully catchment was classified into eight land-use categories using the classification tool in ArcGIS. In this study, constant rainfall intensities were applied to an idealized V-shaped catchment, and artificial rainfall experiments were conducted. Rainfall events with return periods of 5, 20, and 50 years were designed for the gully catchment.

3. Results and Discussion

This section presents the results of model validation and performance testing on three benchmark scenarios: (1) an idealized V-shaped catchment; (2) an artificial rainfall experiment; and (3) a gully catchment on the Chinese Loess Plateau.

3.1. Simulation on Idealized V-Shape Catchment

The proposed model was used to carry out a rainfall–runoff simulation for an impermeable V-shaped idealized catchment with an approximated analytical solution. Some validated parameters were given in [17], including the rainfall and Manning coefficients of the channel and hillsides of the model input. The geometry of the V-shaped catchment is shown in Figure 3. The hillsides and channel within the watershed had dimensions of 1000 m × 800 m and 1000 m × 20 m, respectively. Thus, the validated parameters were used in this study. The channel and hillside slopes were set to 0.02 and 0.05, respectively. The Manning coefficients were assigned as 0.15 s/m^1/3 for the channel and 0.015 s/m^1/3 for the hillside. The simulations were performed at 1 m and 2 m resolutions, with 1.62 × 10⁶ and 4.05 × 10⁵ square cells, respectively. The simulation rainfall event maintained a constant intensity of 10.8 mm/h over a duration of 12,000 s.

The simulated depth results showed good agreement between the simulations on one GPU and two GPUs at 5 m terrain resolution, with a relative error of 0 between the two computed depths, indicating the higher accuracy of the model. The rainfall–runoff visual simulations for the whole catchment were executed on one GPU and two GPUs, as shown in Figure 4. The accelerated computing efficiency results of the different simulations are summarized in

Table 1. Accelerated computing efficiency results of the different simulations in the V-shaped catchment.

Resolution	Cell Number	Runtime (1 GPU)/h	Runtime (2 GPUs)/h	RS Ratio (Times)
1 m	1.62 × 106	1.43	0.91	1.57×
2 m	4.05 × 105	0.33	0.26	1.27×

, showing that the RS ratios were 1.27 and 1.57 times for the different simulations. The multi-GPU model had a higher RS ratio (1.57 times).

3.2. Simulation on Experimental Catchment Under Artificial Rainfall Platform

An experimental rainfall platform developed at Xi’an University of Technology (China) was used to assess the model’s accuracy in a controlled environment [38]. The experimental physical catchment model was designed based on the similarity theory from measured data of an actual road in Fengxi New City, Shaanxi Province, China. The experiment set up two simulation scenarios: LID (Low-Impact Development) and a traditional model with different surface patterns, showing the buildings, grasslands, roads, drainage channels, and runoff collecting tank (Figure 5). The traditional simulation scenario was selected to provide the data for the proposed model validation in this study, with an impervious simulated surface. Figure 6 shows a geometric graph of the simulated surface. The experimental platform had dimensions of 7 m × 3 m (length × width), while the watershed area of the traditional simulation scenario was 7 m × 1.65 m (length × width) and could be fully covered by the entire rainfall system, with a rainfall coverage area of 21 m². The whole surface comprised 48 two-layer rectangular acrylic plates uniformly distributed along both sides of the experimental platform, with the upper layer of each plate measuring 0.54 m × 0.33 m (length × width). The simulated longitudinal slope (i₁) and cross slope (i₂) of the catchment could be adjusted via a steel frame support system, with both the longitudinal and cross slopes set at 5° in this experiment. A rainfall intensity of 0.47 mm/min was adopted in the experimental design. The rainfall duration was set to 12 min, with a total simulation period of 20 min. Manning’s roughness coefficients were obtained from the empirical parameters of similar experiments in the literature. The fine cell resolution was 0.01 m for this catchment.

Figure 7 illustrates the observed and simulated runoff curve change processes for the traditional simulation scenario under the same longitudinal and cross slopes (5°), showing that the simulated runoff curve exhibits a similar change trend to the experimentally observed runoff variation. Meanwhile, the NSE value between the measured and simulated runoff under the traditional simulation scenario was calculated as 0.956, indicating that the result computed by the proposed model fits the measured value very well. The established model has high reliability and precision, as proved by it having the highest NSE value (near to 1).

To validate the computational acceleration performance of the proposed method, the simulation times executed on single GPUs and multiple GPUs were analyzed, as summarized in

Table 2. Evaluation of accelerated efficiency of traditional surface simulation scenario.

Cell Number/ Terrain Resolution	Execution Time on 1 GPU (h)	Execution Time on 2 GPUs (h)	Relative Speedup (RS) Ratio×
700 × 165 /0.01 m	0.63	0.59	1.1×

. The multi-GPU model had a smaller relative speedup ratio of 1.1 times compared to the single-GPU model, with approximately 1.16 × 10⁵ computing grid cells. The smaller relative speedup ratio may be attributed to the combined effects of a relatively small grid cell number (1.16 × 10⁵) and the higher-resolution terrain simulations (0.01 m) in the watershed, where complex flood-flow hydrodynamic processes could result in lower acceleration efficiency. However, although the acceleration efficiency appears to be lower under the current test conditions, the simulated results show that the proposed method retains measurable computational acceleration capabilities.

3.3. Simulation on Actual Gully Catchment on Chinese Loess Plateau

3.3.1. Model Parameters

The Wangmaogou catchment (110°20′26″–110°22′46″ E, 37°34′13″–37°36′03″ N) is located in the southeastern of Yulin City, Shaanxi Province, China, and has a total area of approximately 5.97 km² (Figure 8). Wangmaogou catchment is among China’s first experimental small watersheds to undergo treatment. The catchment exhibits elevations between 934 m and 1188 m. Its primary ditch is 3.75 km long with an average slope of 2.7% along the ditch bed. The rainy season is mainly concentrated from July to September. The watershed is characterized by a complex topography with densely distributed gullies on the Chinese Loess Plateau (CLP). The input datasets for the model contained a high-resolution DEM, observed and designed rainfall, land-use classifications with corresponding infiltration parameters, and Manning’s roughness coefficients. The observed rainfall event of 15 July 2012 was employed for the model validation. Designed precipitation events were used to test the model’s performance, with rainfall return periods of 5, 20, and 50 years. The high-resolution DEM data were obtained through unmanned aerial vehicle surveying, with a grid spatial resolution of 2 m (Figure 9a). The 5 m resolution data was calculated through spatial interpolation using ArcGIS. The domain was discretized into approximately 4.52 × 10⁵ (5 m) or 2.83 × 10⁶ (2 m) cells. The study area was classified into eight land-use categories, as presented in Figure 9b: water, orchard, forest, grass land, residential land, road, terrace land, and cropland. The infiltration and Manning coefficient values of the different land uses were assigned according to previous studies [21,39]. The duration of the simulated rainfall–runoff process was set to 14,400 s for all the different rainfall events, with return periods of 5, 20, and 50 a (Figure 9c).

3.3.2. Model Performance Assessment

To assess the model’s accuracy, the 15 July 2012 rainfall event was simulated in the Wangmaogou catchment. Figure 10 shows strong agreement between the simulated and observed hydrographs at the watershed outlet, with NSE and RMSE values of 0.78 and 0.87, respectively, indicating reliable simulation performance. The result also demonstrated that the model performed effectively in simulating flood processes in an actual gully basin. The proposed numerical simulation model was applied to simulate the rainfall flood processes in the Wangmaogou watershed, and the relative speedup (RS) ratios, obtained through runtime comparisons, were used to quantitatively analyze the computational efficiency of the model run on different computing platforms. The simulations were run at 5 m and 2 m terrain resolutions, with cell numbers of approximately 4.52 × 10⁵ and 2.83 × 10⁶, respectively. The simulation runtimes for the different scenarios are shown in

Table 3. A summary of accelerated computing efficiency in the gully catchment.

Grid Cell Resolution	Cell Number	Return Period (a)	Runtime on 1 GPU (s)	Runtime on 2 GPUs (s)	Acceleration Ratio Relative to Simulation Time
5 m	4.52 × 105	5	548	502	28.7
		20	623	568	25.4
		50	661	601	24.0
2 m	2.83 × 106	5	4606	2884	5.0
		20	5085	3266	4.4
		50	5611	3669	3.9

.

To further explore the speedup ratio of two GPUs relative to single-GPU computations, Figure 11 displays the RS ratios for two-GPU parallel computing at terrain resolutions of 5 m and 2 m, with computation cell numbers of approximately 4.52 × 10⁵ and 2.83 × 10⁶, respectively. For the 5 m resolution, the RS ratios range from 1.09 to 1.10, indicating a smaller RS ratio for the simulation at smaller grid-computational scales. However, at 2 m resolution, the RS improves significantly to between 1.53 and 1.60, confirming the benefits of two GPUs for processing large-scale and high-resolution flood simulations. Moreover, the model demonstrates 28.7-times acceleration compared to the simulation time (14,400 s) when running on two GPUs, which significantly enhances its early prediction capability for rainfall flood events. The results indicate that multiple-GPU computing exhibits greater acceleration ratios and superior computational performance in larger-catchment-scale flood simulations. In all, with a higher terrain resolution and a greater number of computational grid cells in the watershed, the acceleration efficiency in the flood simulation is more significant.

3.4. Discussion

The proposed hydrological–hydrodynamic model using multiple GPUs demonstrated high accuracy and speedup capability across a range of watershed scales, including the test cases of an experimental catchment and gully catchment. The model was also calibrated using the simulated and observed runoff (Figure 7 and Figure 10), with higher NSE values of 0.956 and 0.78, respectively. The GPU-based simulation significantly improved the computational speedup, and the performance gains were most evident in simulations with high-resolution grids and large computational domains [17,20,39]. The results show that the developed model enables robust and reliable simulations of stormwater processes, while also providing a foundational framework for the application of this numerical method to practical storm flood management simulations.

In addition, Figure 7 and Figure 10 show that the simulated peak flow rate exhibits a delay relative to observed data in two calibration curves. Physically-based hydrodynamic models commonly exhibit discrepancies like delayed peak flows (Figure 7 and Figure 10). Firstly, simplified 2D grid topography underestimating runoff velocity, and uniform Manning’s coefficients reducing flood wave speed. Uniform Manning’s roughness coefficients (typically assigned with limited field data) reduce simulated flood wave speed, contributing to peak time shifts. In this study, uniform Manning’s coefficients were applied across land uses. Secondly, initial and boundary conditions, including soil moisture and antecedent water storage, may not precisely reflect catchment states at the onset of the event. If initial saturation is underestimated, the onset of runoff generation is delayed, which can shift the timing of the hydrograph peak (as in Figure 10). Hortonian overland flow represents a fundamental runoff generation mechanism in arid and semi-arid regions of northern China. While hydrodynamic models employ mathematical frameworks to simulate hydrological processes across diverse climatic and geographical conditions, their application exhibits significant differences from the actual runoff generation patterns observed in Loess Plateau watersheds, where Hortonian mechanisms dominate. The studied Wangmaogou catchment is characterized by complex topography with densely distributed gullies on the Chinese Loess Plateau in this work.

This study systematically evaluated the accelerated parallel performance of flood simulations across watersheds of multiple scales, including an idealized V-shaped catchment, an experimental catchment, and an actual gully catchment. In comparative analyses of the rainstorm flood process simulations of the selected watersheds, the relative speedup ratio of multi-GPU parallel computing compared to single-GPU computation showed a positive correlation (Table 1, Table 2 and Table 3). The RS ratios were 1.27 and 1.57 times in the idealized V-shaped catchment, with 4.05 × 10⁵ and 1.62 × 10⁶ square cells, respectively. The RS ratio was 1.1 times in the experimental catchment, with 1.16 × 10⁵ square cells. The highest RS ratios were 1.1 and 1.6 times in the actual gully catchment on the Chinese Loess Plateau, with 4.52 × 10⁵ and 2.83 × 10⁶ square cells, respectively. It was found that as the number of computational grid cells increased, the acceleration performance obtained using two GPUs improved. As shown in Figure 11, flood simulations for the multiple rainfall scenario in the Wangmaogou watershed with 4.52 × 10⁵ grid cells and 2.83 × 10⁶ grid cells at a 5m terrain resolution indicated that higher numbers of grid cells resulted in higher relative speedup ratios for multi-GPU computing at the same terrain resolution. Rainfall flood simulations in small watersheds exhibited relatively low acceleration efficiency, with smaller speedup ratios. This shows that in smaller watersheds or those with low cell counts, speedup ratios remain modest. This is likely due to the limited workload distribution and high communication overhead across the GPUs. Topographic complexity also impacts computational stability and performance [31]. Thus, a multiple-GPU architecture is well suited for large-scale and high-resolution rainfall flood simulations.

In all, the approach of using GPU technology to speed up flood simulations is valuable and strongly needed in the field. It directly addresses the challenge of computational efficiency in high-precision flood modeling. Multi-GPU-based high-performance simulation methods have a distinct advantage in carrying out catchment simulations with a large number of grid cells. For large-scale rainstorm flood simulations, the multi-GPU approach can effectively overcome computational bottlenecks [26], enabling rapid simulations of areas with millions of computational cells. The proposed GPU-accelerated approach achieves critical gains in its response time, offering operational benefits for real-time flood prediction and emergency response planning.

4. Conclusions

This study introduced a GPU-accelerated integrated hydrological–hydrodynamic model for efficient rainfall flood simulation at the catchment scale. The model was tested on three different scenarios: an idealized V-shaped catchment, an experimental rainfall platform, and a real-world gully catchment in China. These tests showed that the model is reliable and accurate across various conditions. This method can help strengthen the accuracy and speed of rainfall flood prediction. The key conclusions can be summarized as follows:

• The model achieved high simulation accuracy, with NSE values of 0.956 and 0.78 in the experimental catchment and gully watershed, respectively. The proposed model indicated better simulation accuracy when validated against an experimental catchment under an artificial rainfall platform and an actual gully catchment on the Chinese Loess Plateau.
• Computational efficiency improved as the cell number in the computing domain increased, with RS ratios of up to 1.6 for two GPUs versus one GPU. Meanwhile, all simulations with a higher number of grid cells indicated a more significant advantage in accelerated computing performance for the established model in this study.
• The multiple-GPU implementation provided significant speedup over the single-GPU execution, particularly for large-scale and high-resolution rainfall flood simulations.

This study demonstrated that GPU-based modeling can address the computational challenges of simulating complex rainfall–runoff dynamics across diverse catchment types with a large number of grid cells. For practical large-scale watershed applications, the proposed approach proves to be better suited for enabling rapid and accurate flood forecasting. Therefore, this research provides a valuable tool for quick and accurate flood forecasting, which is crucial for making timely decisions during flood emergencies. While the core computational framework of this study achieved efficient parallelization on two identical GPUs, the models require further testing and refinement to achieve accelerated computation beyond three GPUs. Future work will implement deep learning methods for automated parameter calibration and develop asynchronous communication protocols to minimize inter-GPU data transfer latency within multiple GPUs.