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Green computing is the current research hotspot; adapting the professional computing model to the low-power ARM architecture processor is a research trend. This article constructs a hydrological–hydrodynamic model by choosing SWMM and TELEMAC-2D as submodules, taking stormwater grates and inspection wells as water flow exchange nodes. The container technology was selected to couple the model on the ARM architecture processor, and the adapted coupling model is named the ARM hydrological–hydrodynamic model (AHM). To verify the reasonableness and accuracy of the model, taking the inner harbor of Macao Peninsula as the study area, a numerical simulation study on the evolution of waterlogging was carried out in various scenarios. The analysis showed that the maximum flow velocity was concentrated in the streets with low topography in the city center, and the areas of standing water were distributed in a point-like manner. Risk distribution maps during different storm recurrence periods were also constructed. Finally, the direct economic losses caused by Typhoon Mangkhut were calculated based on the model results and compared with the statistical values, with an error of only 2.3%, and the direct flooding losses in the inner harbor area under different rainfall scenarios were derived accordingly.

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  • A coupled urban hydrology and hydrodynamics model was constructed and adapted to a low-power ARM processor.

  • Numerical simulation studies on the evolution of waterlogging in Macao were carried out under various scenarios.

  • Risk distribution maps for the inner harbor area under different rainfall return periods were prepared, and flood-prone points were noted.

  • Predicting and projecting the direct loss of waterlogging in the inner harbor area under different rainfall scenarios.

ARM architecture processor, flood losses, green computing, hydrological and hydrodynamic modelling, urban flooding
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With the rapid urbanization process and global climate change, the extreme precipitation characteristics of urban areas have changed significantly, and intense rainstorms occur frequently, causing huge socioeconomic and life and property losses (Zhang et al. 2014; Alabbad et al. 2023; Li et al. 2023). Numerical simulation is an important method to study the formation mechanism and evolution law of urban flooding, through which the simulation can restore the rainfall, water conditions, and disaster-affected process of burdensome rainfall events and provide theoretical and technological references for the construction of urban flood prevention and disaster mitigation system (Zhou et al. 2012; Zang et al. 2020; Xu & Ye 2021; Luo et al. 2022; Alipour et al. 2023). It is worth mentioning that urban waterlogging is a real-world problem. Using different hydrological models to solve water problems will help achieve the UN's sustainable development goals and ensure that urban development is inclusive, safe, resilient, and sustainable (Mohammadi et al. 2024).

Urban areas are densely populated and property intensive. Once waterlogging occurs, it will cause huge losses. The construction of an urban waterlogging model can effectively reduce waterlogging losses. However, the irregular distribution of streets and buildings in urban areas results in very complex surface runoff. One-dimensional (1D) flow models cannot accurately describe the changes in subsurface water flow and the distribution of waterlogged areas, and two-dimensional (2D) surface flow models must be applied. At the same time, urban floods are usually discharged through streams that outlet from the source catchment, so the influence of urban drainage systems on surface runoff is significant (Bazin et al. 2014). However, early simplified models did not reflect the presence of subsurface drainage systems or the drainage systems are modeled as unidirectional (Ellis et al. 1982), which means that the drainage system does not allow water to return to the surface even when it exceeds its capacity. In extreme rainfall events, surface runoff is dominant, and simplified models also have high accuracy. However, the drainage system's presence in most cases will significantly impact the flooding simulation. Therefore, a large number of scholars have made an in-depth investigation into the construction of a 1D–2D coupled model. Leandro et al. (2009) adopted the concept of dual drainage, constructed a 1D/1D model and a 1D/2D model, and compared them, pointing out the problems that should be paid attention to in establishing the coupled model and the calibration. Seyoum et al. (2012) coupled the stormwater channel model SWMM5 and a 2D noninertial slope flow model in a two-dimensional coupled model. The inertial slope flow model is used to simulate the interaction between the sewerage system and the urban floodplain, and the ability model to simulate flooding was demonstrated through two case studies. Subsequently, Yu & Huang (2015) proposed a coupled one-dimensional (1D) and two-dimensional (2D) numerical model for the free-surface flow. Practical applications show that the model can accurately and effectively simulate the free-surface flow. To predict the extent of flood inundation more accurately, Leandro & Martins (2016) proposed a method to link the 2D overland flow model with the storm sewer model SWMM5 to achieve bidirectional interaction between the two models during simulation. Wu et al. (2017) established a two-dimensional hydrodynamic inundation model based on SWMM and LISFLOOD-FP models, revealing urban inundation's evolution under different storms, sea level rise, and subsidence scenarios. Zeng et al. (2019) and Chen et al. (2021) used SWMM as a one-dimensional computing module, combined with other two-dimensional computing modules to construct a coupled model of urban waterlogging, achieving high computational accuracy.

After years of research, many excellent coupled models for urban flooding have been developed. However, almost all of them are based on the X86 architecture processor. The X86 instruction set adopts the complex instruction set computer architecture, which makes the X86 processor costly to design and manufacture and is prone to design flaws and loopholes. The complexity of the instruction set also leads to lower efficiency, higher power consumption, and less flexibility in executing instructions, which can be limited in application scenarios such as embedded systems, mobile devices, and Internet-of-Things (IoT) devices (Blem et al. 2013; Kaiser et al. 2023). As the scale of cloud computing and cloud data centers continues to expand, large-scale, high-accuracy simulation of urban flooding is also gradually shifted to cloud computing platforms, and with it comes enormous energy consumption. In contrast, the Advanced RISC Machines (ARM) architecture has advantages such as high performance and low power consumption and is rapidly becoming the first choice for green computing. ARM architecture processors use a reduced instruction set computer (RISC) processor with a relatively small number of instructions that can be combined to achieve complex calculations and operations, increasing the speed at which instructions run and minimizing power consumption. Aroca & Gonalves (2012) compared parameters such as power consumption, CPU load, temperature, and floating point performance of applications on X86 and ARM computer architecture servers, showing that ARM-based servers are a good choice for green data centers. Yokoyama et al. (2019) analyzed the ARM architecture processors' improvement capabilities and the history of developing energy-efficient processors. They concluded that ARM would be a viable solution for tens of billions of power walls. Rico et al. (2017) have also tested the performance of supercomputers and high-performance computing applications (CP2K, GROMACS, NAMD, VASP, etc.) based on ARM instruction set compatible architecture processors. The results of the experiments show that ARM-based processors can provide performance levels that are competitive with the existing state-of-the-art X86 products, and ARM-based server CPUs optimized for High Performance Computing (HPC) can match the performance of comparable X86-based server CPUs. ARM-based servers optimized for HPC can match the performance of best-in-class CPUs while offering attractive price and performance advantages. To achieve the coupled model, ARM architecture adaptation needs to address the main compatibility issues so that the computing software can meet the functional requirements of professional computing but also needs to consider giving full play to the advantages of the ARM architecture of low power consumption while ensuring that the adapted model does not affect the host and other applications. Compared with x86 architecture, some ARM processors still have some limitations in performance. Especially when dealing with large amounts of data and complex calculations, it may not be able to compete with high-end x86 processors. However, with the development of technology and the improvement of the ecosystem, the limitations of ARM processors are gradually decreasing. Therefore, adapting the constructed coupling model to ARM architecture processing is also the highlight of this article (Blake et al. 2021; Jin et al. 2022).

In the simulation calculation of urban waterlogging, there are some limitations in the use of the hydrological model or hydrodynamic model alone. Hydrological models are usually used to predict rainwater runoff processes and lack a detailed description of urban characteristics, such as buildings, roads, and drainage systems. The hydrological models are usually based on natural processes while ignoring the impact of human drainage systems, which may lead to inaccurate predictions in urban waterlogging simulations. The limitation of the hydrodynamic model is that it requires a lot of computing resources and time, especially in the simulation of urban waterlogging; it is necessary to consider the large-scale complex urban terrain and water flow path. To reduce the amount of calculation, the hydrodynamic model may need to parameterize or simplify the urban characteristics, which may lead to a decrease in the accuracy of the simulation results.

Combining the aforementioned analyses, a coupled urban ARM hydrological–hydrodynamic model (AHM) is constructed in this article. The hydrological method simulates the rainfall production process, the slope confluence and surface inundation process are simulated by the two-dimensional hydrodynamic method, and the river and pipe network flow is simulated by the one-dimensional hydrodynamic method. The two models are synchronized to perform the computation and achieve the real-time exchange of computational data to carry out the bidirectional coupled simulation. To achieve the goal of green computing, the coupled model and its dependencies are packaged into a mirror file using container technology to make it adaptable to the ARM architecture. Taking the inner harbor of the Macao Peninsula as an example, numerical simulation studies on the evolution of waterlogging in the inner harbor area of Macao under various scenarios are carried out to analyze the weaknesses and significant problems in the prevention and control of waterlogging in the Macao area, to classify the risk level of the Macao area by combining the characteristics of the disaster-carrying body and the characteristics of the distribution of the GDP, to form the distribution map of the risk of the disaster, and to predict and deduce the direct loss of the flooding in the inner harbor area under different rainfall scenarios.

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The model in this article adopts the concept of dual drainage, with rain grates and catchment wells as nodes, to establish the link between the urban surface and the drainage network, and the construction of hydrological–hydrodynamic coupling model can improve the accuracy of urban flooding simulation, to effectively prevent and respond to urban flooding events. The current models that can realize one-dimensional and two-dimensional coupled simulation include MIKE 21, MIKE URBAN, InfoWorks ICM, etc. However, most are commercial paid software, while free, open-source research models are relatively scarce. Therefore, this study uses the open-source software SWMM and TELEMAC-2D as submodules to construct a coupled urban hydrological and hydrodynamic model.

SWMM model

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One-dimensional hydrodynamic models are used to simulate water flow in urban drainage systems, rivers, and channels, including SWMM (Storm et al. Model), HEC-RAS (Hydrologic Engineering Center's River Analysis System), InfoWorks (Integrated Catchment Modeling), ICM (integrated catchment modeling), and so on. Among them, the SWMM model is adopted as the one-dimensional hydrodynamic module of the model due to its good stability and applicability, and the open-source code is conducive to the secondary development of the model, so the hydrological–hydrodynamic coupled model adopts the EXTRAN module of SWMM.

The EXTRAN module provides the equations in three forms: diffusion, kinematic, and power wave, and its power waveform is generally used, i.e., to solve the complete set of St. Venant equations (Equations (1) and (2)):
(1)
(2)
In Equations (1) and (2), x is the distance (m); t is the time (s); A is the over-water cross-sectional area (m2); Q is flow (m3/s); H is the head (m); g is the gravitational acceleration (m2/s); Sf is the friction ratio drop, i.e., the pressure drop caused by the friction between the fluid and the pipe wall, which can be calculated by using Equation (3):
(3)
Associative Equations (1) and (2) lead to Equation (4):
(4)

A one-dimensional hydrodynamic simulation of the governing equations based on the assumptions of the ‘pipe-node’ mechanism and the power wave equation is constructed, and due to the difficulty of obtaining an analytical solution of the equations, the EXTRAN module of SWMM uses a numerical solution method to solve the equations.

TELEMAC-2D model

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TELEMAC software can construct 1D, 2D, and 3D hydrodynamic models to address wave propagation, water quality pollution, surface hydrology, sediment transport, and other issues. The 2D hydrodynamic module (TELEMAC-2D) has been widely used to simulate hydrodynamic processes in rivers, estuaries, coasts, and floodplains with good results (Pinel et al. 2019), and the code is open source and can be developed for secondary use. The TELEMAC-2D module adopts the SCS method to perform the rainfall production flow calculations for the simulation. This method is an empirical model developed in the United States based on rainfall and runoff data from small watersheds, which is suitable for analyzing the flow processes in small watersheds and is widely used in hydrological problems related to small watersheds. The model is well developed, easy to compute, and has shown good simulation results in studying data-poor regions.

The Soil Conservation Service (SCS) hydrologic model has a simple structure and adopts a comprehensive parameter CN (curve number) value to describe the flow-producing capacity of different types of subsurface, which is a dimensionless parameter. The main influencing factors include soil type, land use type, hydrological terrain conditions, and pre-existing soil water content conditions. The method is based on the principle of water balance and certain assumptions to get the expression of the relationship between rainfall and runoff:
(5)
(6)
where P is the total rainfall; Q is the surface runoff; λ is the initial loss rate of rainfall; and S is the maximum possible water storage capacity. The initial loss rate λ is usually taken as 0.2 according to the experience of the US Department of Agriculture. However, due to the soil and climate differences in different watersheds, using a uniform value of λ cannot meet the needs of other watersheds. The calculation of the relevant scholars showed that λ is taken as 0.05, and the simulation effect will be better. Therefore, the model generally adopts 0.05 as the initial loss rate.

Coupling model

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The one-dimensional hydrodynamic module used for the coupled hydrological–hydrodynamic model is SWMM5.1, and the two-dimensional hydrodynamic module is the v7p2r3 version of the TELEMAC-2D module. Vertical nodal coupling is used for water exchange, and the basic weir flow and orifice flow equations are used to calculate overflow and return flows. The equations are as follows.

Calculation formula of the node overflow flow:
(7)
Return flow calculation formula of node:
(8)
where is the overflow flow of the flow point; is the return flow of the node (⁠⁠), which represents the flow exchange between the pipe network and the surface; is the orifice outflow coefficient; is the weir flow coefficient; is the area of the exchange node between the surface and the pipe network (⁠⁠); the area of the corresponding rainwater wellhead in this study; ω is the width of the crest of the weir (⁠⁠), in this study, the perimeter of the corresponding rainwater wellhead; is the node water level of one-dimensional pipe network; is a two-dimensional surface water level; and is the surface elevation. The subscript n is the node number. The specific explanation is that assuming that the node water level is H1D and the surface grid water level corresponding to the node is H2D; when H1D > H2D, the water flow in the pipe network system overflows through the node to the surface flow; when H1D < H2D time, the water flow from the surface to the underground drainage network; and when H1D = H2D and the node water level is lower than the surface elevation, the exchange of water flow does not occur (Chen et al. 2018).
Call two calculation models through the Python, and start TELEMAC-2D and SWMM. The two models calculate the surface and pipe network flow data according to the initial data, create data processing and data exchange channel, and carry out one- or two-dimensional data exchange. The data exchanged in the coupling model are then written into the file, and the number of coupling calculation steps is increased by 1. At this time, the two models are in the waiting stage. Suppose the number of calculation steps reaches the set number of steps. In that case, the TELEMAC-2D and SWMM models are exited, the coupling calculation is finished, or the coupling calculation is continued, and the calculation flow is shown in Figure 1.
Figure 1
Flow of coupled model calculation.
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Flow of coupled model calculation.

Figure 1
Flow of coupled model calculation.
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Flow of coupled model calculation.

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ARM hydrodynamic model

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Container technology, also known as container virtualization, can package the coupling model and its runtime environment into independent container images, enabling them to run on different hardware platforms and operating systems. It is a sandbox that does not depend on any language, framework, or system, and each container is independent (Wu et al. 2022). Compared with other mainstream virtualization technologies, such as Kernel-based Virtual Machine (KVM) and VMware, the coupling model within the container runs directly on the host machine's kernel. There is no kernel of its own within the container nor virtualization of the hardware, so the container starts faster and occupies a smaller volume than a virtual machine (Yi et al. 2018). Containers also provide perfect isolation, protecting the security and dependencies of the coupled model and using containers as a security boundary to protect the host and other software. Docker is the most popular container technology, through which the code, dependent libraries, environment variables, and configuration files of the coupling model can be packaged into image components, which can solve the problems in adapting the coupling model ARM architecture. Figure 2 shows how Docker containers work. The Docker engine can run multiple containers in a separate, isolated application environment. Each container runs its application and has access to its file system, system libraries, etc. (Dong et al. 2023), thus eliminating the dependency on the underlying architecture and enabling the adaptation of the coupled model ARM architecture.
Figure 2
The schematic of the Docker container.
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The schematic of the Docker container.

Figure 2
The schematic of the Docker container.
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The schematic of the Docker container.

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In this study, Docker cross-platform construction image technology is adopted to build a Docker container image with a hydrological–hydrodynamic coupling model as the core, and the coupled model is adapted. The TELEMAC-2D and SWMM source codes are compiled, and the runtime environment is set up in the Dockerfile to build a container image containing the coupled model and the related runtime environment to run independently on the ARM architecture processing. The hardware and software test environments and adaptation conditions used in this study are presented in Table 1.

Table 1

Adaptation conditions

CategoryProjectRequirement
Hardware Server TaiShan 200 
CPU Kunpeng 920 
Network Card TM210 
Software Operating System Centos7.6 
CategoryProjectRequirement
Hardware Server TaiShan 200 
CPU Kunpeng 920 
Network Card TM210 
Software Operating System Centos7.6 
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Dockerfile is a text file used to build a Docker image, which consists of one command and a parameter needed to build the image. The construction of a Docker image is a top-down process, as shown in Figure 3, and the execution of each command is a layered construction process. The image construction process is as follows: First, select a base image as the basis for new image construction; execute the first Dockerfile command to modify the container generated by the base image, add environment variables and necessary libraries to run the software; and then execute an operation similar to ‘docker commit’ to commit the changed container to a new image. Then execute a ‘docker commit’ operation to commit the changed container to a new image layer; finally, take the new image as the base image and run a new container to continue executing the following command. Each command in the Dockerfile is executed this way until all commands have been executed. The coupled model image is constructed through the Dockerfile file, which summarizes the whole image, containing all the environment variable configurations of the constructed model, the installation of software dependencies, and the instructions for downloading and installing the software (Xu 2021). In this article, Docker version 23.0.1 is used to build the coupled model image in layers.
Figure 3
Image building schematic.
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Image building schematic.

Figure 3
Image building schematic.
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Image building schematic.

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Selection of study area

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Macao is a typical monsoon climate with tropical climate characteristics. The average annual precipitation is 1986.4 mm, and the seasonal distribution of regional rainfall is uneven. The average rainfall in the rainy season from April to September is 1,666.6 mm, accounting for 84% of the total annual rainfall. The inner Harbor area has a low topography in the western part of the Macau Peninsula. More than 70% of the terrain is below 6 m in height and is Macau's political, economic, and cultural center, with a concentrated population. The large proportion of floor area leads to an increase in the impermeable area. At the same time, the internal streets in the western part of the Macao Peninsula are dominated by the combined flow system, which has a low drainage standard. Whenever there is heavy rainfall, the rainwater cannot be discharged through the drainage system and flows on the road surface to the low-lying areas, which are highly susceptible to flooding. Among them, the most severe flooding disasters are found in the Causeway Bay, Nei Hong Kong, and Taishan districts of the Macao Peninsula, as shown in Figure 4, cited from the Geophysical and Meteorological Bureau (GMB). In summary, based on the topography and geomorphology and the investigation of the flooding situation in Macao since 2000, the independent sub-watershed in the western part of Macao Peninsula, which has the highest concentration of flooding disasters, is selected as the study area (with an area of 4.06 km2) along the watershed. The extent of the study area is shown in Figure 5.
Figure 4
Location of historical flooding occurrences.
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Location of historical flooding occurrences.

Figure 4
Location of historical flooding occurrences.
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Location of historical flooding occurrences.

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Figure 5
Schematic of the study area.
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Schematic of the study area.

Figure 5
Schematic of the study area.
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Schematic of the study area.

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Computational model construction

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ArcGIS is used to preprocess the pipeline network data, Digital Elevation Model (DEM) data land use data in the study area, and the pipeline network is calibrated to obtain 5,080 pipelines, 5,017 inspection wells, and 68 drainage outlets. The specific pipe distribution is shown in Figure 6.
Figure 6
Distribution of the 1D pipeline model.
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Distribution of the 1D pipeline model.

Figure 6
Distribution of the 1D pipeline model.
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Distribution of the 1D pipeline model.

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In this study, to consider the study area's water-blocking effect, the building elevation is superimposed on the original DEM data. To ensure the continuity of the building contour, this study adopts the way of dividing the grid for the noninterpolated value-taking method, the grid resolution is 3 m irregular triangular mesh, and the processed mesh has a total of 497,498 mesh nodes and 989,313 triangular meshes.

Different soil types have different infiltration rates and water retention capacities (CN values), which directly affect rainwater's infiltration and runoff process. Due to the small study area, the hydrological grouping of soil is only C and D. The different land use CN values of each soil type are taken as shown in Table 2. The type was obtained from the Macao Cadastral Bureau. The CN value was comprehensively considered by referring to the CN value table of the TR-55 manual of the United States Soil Protection Bureau and the research of relevant scholars, combined with soil types and land use classification (Cronshey et al. 1985; Liu et al. 2019).

Table 2

Soil type hydrological grouping CN values

CNCD
Green space 71 80 
Roads 94 98 
Buildings 96 98 
Mountain 79 84 
Water 100 100 
Other 88 92 
CNCD
Green space 71 80 
Roads 94 98 
Buildings 96 98 
Mountain 79 84 
Water 100 100 
Other 88 92 
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In the simulation of urban waterlogging, the surface roughness directly affects the velocity and path of water flow. The roughness values (MN) are selected based on land use, and the specific values of related studies are taken, as shown in Table 3. At the same time, the geographic elevation of the model is used to determine the path and aggregation point of the water flow, which helps accurately predict the flood-inundated area and the water flow path. Since the topography of the study area is high in the east and low in the west, and the western part is coastal, the western part of the study area is set as an open boundary to allow free outflow. The eastern part, adjacent to the land, is set as a closed boundary to consider its water-blocking effect. The model roughness (MN), soil hydrological grouping (CN), and model geographic elevation (ELE) are shown in Figures 7–9.
Table 3

Manning's coefficient for different land use types

Land use typeManning's coefficient
Green space 0.15 
Roads 0.012 
Buildings 0.012 
Mountain 0.4 
Water 0.015 
Other 0.05 
Land use typeManning's coefficient
Green space 0.15 
Roads 0.012 
Buildings 0.012 
Mountain 0.4 
Water 0.015 
Other 0.05 
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Figure 7
Model roughness.
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Model roughness.

Figure 7
Model roughness.
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Model roughness.

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Figure 8
Soil hydrological grouping.
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Soil hydrological grouping.

Figure 8
Soil hydrological grouping.
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Soil hydrological grouping.

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Figure 9
Model geographic elevation (m).
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Model geographic elevation (m).

Figure 9
Model geographic elevation (m).
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Model geographic elevation (m).

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AHM validation

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The rainfall of Typhoon Mangosteen from 5:00 to 24:00 on 16 September 2018 is selected for AHM validation. Figure 10 shows the rainfall process. The calculation time of the model is consistent with the rainfall duration, which is 20 h. Figure 11 shows the simulation results of the total amount of waterlogging and the area (>0.1 m) in Macao under the influence of Typhoon Mangkhut. This is consistent with the changes in rainfall and justifies the coupled model. The changes in the depth of waterlogging at the Kang Kung Temple and Lower Ring rainfall stations are selected for comparison with the simulation results. The Nash efficiency coefficients are 0.91 and 0.87, respectively, as shown in Figure 12(a) and 12(b), which verified the accuracy of the constructed model and showed that the constructed model can simulate the waterlogging event in Macao.
Figure 10
Rainfall in Typhoon Mangkhut.
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Rainfall in Typhoon Mangkhut.

Figure 10
Rainfall in Typhoon Mangkhut.
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Rainfall in Typhoon Mangkhut.

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Figure 11
Total rainfall water accumulation/water accumulation area of Typhoon Mangkhut.
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Total rainfall water accumulation/water accumulation area of Typhoon Mangkhut.

Figure 11
Total rainfall water accumulation/water accumulation area of Typhoon Mangkhut.
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Total rainfall water accumulation/water accumulation area of Typhoon Mangkhut.

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Figure 12
Model validation: (a) Kang Kung Temple and (b) lower ring.
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Model validation: (a) Kang Kung Temple and (b) lower ring.

Figure 12
Model validation: (a) Kang Kung Temple and (b) lower ring.
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Model validation: (a) Kang Kung Temple and (b) lower ring.

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In this study, different recurrence periods of rainfall of 2a, 5a, 10a, 20a, 50a, and 100a (a is the average inter-annual return period, and the unit is year) are fitted according to the rainfall equations for the Macao area with a rainfall duration of 120 min (the rain peak coefficient is 0.4), as shown in Figure 13. The total amount of standing water, inundation depth, inundation area, inundation time, and flow velocity of the Macau area for different recurrence periods of rainfall are calculated by the coupled model.
Figure 13
Rainfall in different return periods.
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Rainfall in different return periods.

Figure 13
Rainfall in different return periods.
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Rainfall in different return periods.

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The design rainfall intensity expression for the Macau area is expressed as follows:
(9)
where I is the rainfall intensity (mm/h), a and b are the parameters in Table 4, and t is the rainfall duration (min).
Table 4

Design rainfall parameter values

Return periodab
2 390.29 −0.457 
5 412.82 −0.499 
10 434.72 −0.388 
20 457.88 −0.372 
50 490.78 −0.357 
100 516.25 −0.347 
Return periodab
2 390.29 −0.457 
5 412.82 −0.499 
10 434.72 −0.388 
20 457.88 −0.372 
50 490.78 −0.357 
100 516.25 −0.347 
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The changes in the total amount of standing water for different recurrence periods of rainfall are shown in Figure 14, which shows that the changes in the total amount of standing water are consistent with the rainfall pattern. The rate of change of the total amount of standing water is consistent with the increase in the intensity of the rainfall with a gradual increase in the rate of growth before 50 min, the total amount of standing water shows a trend of slow increase beyond the 50-min node, and the total amount of standing water reaches its maximum value at the end of the 120-min rainfall as well. The change in the total amount of waterlogging further verifies the model's reasonableness and the simulation results' accuracy. The maximum amount of waterlogging is reached at the end of the rainfall, which means that the rainfall of 1 in 2 years has exceeded the capacity of the drainage system of the Macao region, and waterlogging will be formed inside the city. The total amount of standing water grows most rapidly in the first half of the rainfall, which means that the prevention of internal flooding should be highly efficient, and dynamic monitoring should be done to predict before the rainfall intensity reaches the maximum to give a timely warning. Otherwise, it will result in a significant loss of waterlogging, which proves the necessity of constructing the dynamic assessment model of flooding.
Figure 14
Change of water accumulation.
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Change of water accumulation.

Figure 14
Change of water accumulation.
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Change of water accumulation.

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Flood risk assessment

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The main factors contributing to flood damage are indicators such as flood velocity and depth of standing water. Under extremely heavy rainfall conditions, there is a high risk of street flooding currents, significantly affecting the flow of vehicles and people traveling to and from the area. Therefore, this article analyzes the street flow velocity data for the inner harbor area of the Macau Peninsula under different design storm conditions and the depth of standing water in the study area.

The first is the flow velocity of water in the streets. When the flow velocity is large enough, the impact of flood water on buildings and the instability of people or objects caused by the water flow are essential factors causing disasters. 2a, 5a, and 10a rainfall flow velocity of 0.6–0.9 m/s is mainly concentrated in the coastal neighborhoods. This phenomenon is attributed to the low topography of the coastal area, and the water that exceeds the drainage pipe is discharged from the streets. In the event of rainfall of this intensity, attention should be paid to early warning forecasts and timely drainage measures in coastal areas. The maximum flow velocities of 20a, 50a, and 100a rainfall reached more than 1.0 m/s, and most of them are concentrated in the lower topographic streets in the city's center, as shown in Figure 15. The main reason for this is that some parts of the central neighborhoods in Macao are low-lying, and when heavy rainfall occurs, water will form in the city. The rainfall from the higher-lying areas converges to the central neighborhoods, resulting in large flow velocities in the central streets. When the flow velocity exceeds 0.5 m/s in areas with dense buildings, it is a hazardous area and can cause enormous flood damage. The changes in road water accumulation and flow velocity will affect the rescue efficiency and indirectly increase the flooding losses in Macao. This part of the study can provide theoretical references for rational planning rescue routes and reducing flooding-induced losses.
Figure 15
Road flow velocities in the study area (m/s).
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Road flow velocities in the study area (m/s).

Figure 15
Road flow velocities in the study area (m/s).
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Road flow velocities in the study area (m/s).

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The second is the depth of standing water, which, when it reaches a certain depth, can submerge buildings, roads, and means of transport, causing severe flooding. The simulation results show that all rainfall flooding areas are the same, showing a point-like distribution in the study area and coinciding with the historical frequent flooding locations shown in Figure 4. This means that this part of the area faces the most significant risk of flooding, with the maximum depth of water for a 1 in 100-year rainfall even exceeding 5.0 m (Figure 16), which would result in substantial economic losses, as well as significant risks to passing vehicles and pedestrians.
Figure 16
Depth of inundation in the study area (m).
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Depth of inundation in the study area (m).

Figure 16
Depth of inundation in the study area (m).
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Depth of inundation in the study area (m).

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The maximum depth of waterlogging is more than 5.0 m, taking the rainfall of a 1-in-100-year event as an example and counting the areas of waterlogging at different levels of waterlogging. The area of waterlogged areas with a depth of water exceeding 0.1 m is 8.1 × 10−2km2, which accounted for 1.9% of the area of the study area. The area with water depth exceeding 1.0 m is only 6.81 × 10−4km2, which is only 0.068% of the study area, as shown in Figure 17. The aforementioned analyses show that the central depth is between 0.1 and 0.5 m despite the wide distribution of waterlogged areas. The areas with water depths exceeding 0.5 m are small, but the depths of waterlogged areas are generally deeper. The relevant departments should do an excellent job of monitoring and early warning of the critical areas to reduce the risk of waterlogging and losses.
Figure 17
Different submerged water depth area.
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Different submerged water depth area.

Figure 17
Different submerged water depth area.
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Different submerged water depth area.

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Flooded areas in different recurrence periods are analyzed. The water accumulation areas with different return periods are superimposed and the overlapping areas are screened out, and flooding points larger than 1.0 m are marked and labeled in the study area. Red (water depth greater than 3.0 m), green (water depth greater than 2.0 m), and blue (water depth greater than 1.0 m) were marked, respectively, according to the different water depths. Figure 18 shows the distribution of flooded areas with waterlogging depths greater than 1.0 m for different return periods, which will serve as critical areas for monitoring the risk of flooding in the Macao region and provide a reference for flood management.
Figure 18
Water distribution area.
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Water distribution area.

Figure 18
Water distribution area.
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Water distribution area.

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Risk level distribution

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Defining the area with a waterlogging depth greater than 0.1 m as the area where flooding occurs, the area with a waterlogging depth greater than 0.1 m for different recurrence periods of rainfall is calculated, as shown in Figure 19. When the rainfall intensity exceeds once in 10 years, the inundation area increases significantly, and the duration is about 3 h. This indicates that the drainage pipes in Macao have limited drainage capacity, and rainfall more than once in 10 years will cause extensive inundation. The waterlogged area would be drained quickly after 2 h of rainfall, and the waterlogging area reduction would start to slow down after 2 h. The main reason for this is that, on the one hand, a large amount of rainfall causes the drainage network to be filled with stagnant water, and the drainage capacity is insufficient to remove the stagnant water quickly. To improve this situation, it is necessary to increase the number of drainage pipes in Macao, to increase the drainage capacity per unit of time, and to enable the stagnant water to be discharged quickly. Another reason is the influence of storm surges, where rainfall increases the tide level in the coastal areas, making it impossible to discharge the water at the outlets of the pipelines. The primary measure to solve this problem is the construction of tide gates, which reduces the influence of storm surges in coastal areas.
Figure 19
Waterlogging area in different return periods.
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Waterlogging area in different return periods.

Figure 19
Waterlogging area in different return periods.
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Waterlogging area in different return periods.

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Based on the model calculation results, the study area is divided into several levels and plotted into a visual risk zoning map, which can provide a scientific basis for the decision-making of the flood control and drainage departments. Considering the data accuracy, scale size, and data distribution characteristics, the risk zoning classes selected for this study are divided into six levels, as shown in Table 5. These are low risk (<0.1 m), medium to low risk (0.1–0.3 m), medium risk (0.3–0.5 m), medium to high risk (0.5–1.0 m), high risk (1.0–1.5 m), and very high risk (>1.5 m).

Table 5

Flood risk classification

Degree123456
Risk Low Medium–low Medium Medium–high High Very high 
Water depth <0.1 m 0.1–0.3 m 0.3–0.5 m 0.5–1.0 m 1.0–1.5 m >1.5 m 
Degree123456
Risk Low Medium–low Medium Medium–high High Very high 
Water depth <0.1 m 0.1–0.3 m 0.3–0.5 m 0.5–1.0 m 1.0–1.5 m >1.5 m 
View Large

The maximum submerged water depth of each area was obtained by superimposing the submerged water depth data and industry distribution data in Macao. According to the risk level classification in Table 5, all land areas were divided into different risk levels, and the distribution map of waterlogging risk level in different return periods in the study area was formed (Figure 20). At the same time, the proportion of the area of the medium-risk area (water depth greater than 0.3 m) in the total study area in different recurrence periods was analyzed, as shown in Figure 21. The results show that with the increase in rainfall return period, the area above the medium-risk area of once in 2 years and once in 5 years accounts for 0.0051 and 0.0062% of the total area of the study area, and the medium-risk area in the rainfall intensity above the once in 10 years rainfall accounts for more than 0.015%, which is more than three times that of the once in 5 years rainfall. This is consistent with the performance of waterlogging areas in different recurrence periods in Figure 17, that is, when the rainfall intensity exceeds once in 10 years, it exceeds the drainage capacity of Macao, and the risk of waterlogging increases significantly.
Figure 20
Risk classification.
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Risk classification.

Figure 20
Risk classification.
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Risk classification.

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Figure 21
Proportion of medium risk.
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Proportion of medium risk.

Figure 21
Proportion of medium risk.
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Proportion of medium risk.

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Waterlogging solutions

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According to the analysis of the model calculation results, the relevant measures taken include engineering and nonengineering measures to reduce the risk of waterlogging in Macao. The engineering measures include optimizing and upgrading the drainage system in the waterlogging area, accelerating the discharge of rainwater and reducing the occurrence of waterlogging. It also includes building, expanding, or transforming water conservancy projects; reasonably setting rainwater collection ponds, green spaces, and wetlands; and increasing city's ability to resist waterlogging risks; nonengineering measures include establishing a sound meteorological monitoring and flood warning system, timely monitoring of weather changes and water conditions, and issuing early warning information to the public to take countermeasures. It also includes establishing and improving the emergency management mechanism, emergency rescue ability, and personnel training level to ensure they can quickly and effectively respond to and rescue during waterlogging disasters.

Calculation of flood losses

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The loss of economic activity is an essential indicator of flood damage assessment and an important target of flood damage. Due to the difficulty in obtaining data on the distribution of urban economic industries in the selected study area, the total GDP of the study area is distributed by population. It accounts for about 65% of the total economy of the Macao region. Concerning the distribution of land use types in 2021 in Figure 22 (http://data.ess.tsinghua.edu.cn/) and the share of each industry in the GDP of Macao (Table 6), the GDP is distributed by the share of industry in the GDP. Figure 23 shows the distribution of the average GDP value (MOP million/km2) in the study area, where the average value of GDP is multiplied by the proportion of land area occupied by each industry. As shown in Figure 24, the total amount of GDP per site is obtained.
Table 6

Statistics on Macao's main economic indicators (MOP million)

GDPProportion (%)GDPProportion (%)
Manufacturing 2,053 0.8 Insurance and Pension Funds 10,171 4.1 
Electricity, water and gas production and supply 2,772 1.1 Real Estate 32,201 13.1 
Construction 14,230 5.8 Rental and Business Services 11,375 4.6 
Wholesale and retail trade 21,555 8.8 Public Administration 19,830 8.1 
Hospitality 7,211 2.9 Education 9,123 3.7 
Catering 3,923 1.6 Healthcare & Social Welfare 7,458 3.0 
Transport, storage and communications 6,660 2.7 Gaming and Gaming Intermediation 63,420 25.8 
Banking 25,732 11.3 Other services 6,158 2.5 
GDPProportion (%)GDPProportion (%)
Manufacturing 2,053 0.8 Insurance and Pension Funds 10,171 4.1 
Electricity, water and gas production and supply 2,772 1.1 Real Estate 32,201 13.1 
Construction 14,230 5.8 Rental and Business Services 11,375 4.6 
Wholesale and retail trade 21,555 8.8 Public Administration 19,830 8.1 
Hospitality 7,211 2.9 Education 9,123 3.7 
Catering 3,923 1.6 Healthcare & Social Welfare 7,458 3.0 
Transport, storage and communications 6,660 2.7 Gaming and Gaming Intermediation 63,420 25.8 
Banking 25,732 11.3 Other services 6,158 2.5 
View Large
Figure 22
Urban land use types.
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Urban land use types.

Figure 22
Urban land use types.
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Urban land use types.

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Figure 23
Average GDP data (MOP million).
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Average GDP data (MOP million).

Figure 23
Average GDP data (MOP million).
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Average GDP data (MOP million).

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Figure 24
GDP data spatial spread results (MOP million).
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GDP data spatial spread results (MOP million).

Figure 24
GDP data spatial spread results (MOP million).
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GDP data spatial spread results (MOP million).

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Direct economic losses are calculated using the loss rate method. Lv et al. (2021) determined the relationship between the depth of inundation and the loss rate for different land use types. Based on the cumulative inundation depth combined with the disaster damage curves of different land use types under different inundation depths can be calculated to obtain the corresponding loss amount. The Macao region is mainly dominated by commercial land use, residential land use, industrial land use, and public service land use. Table 7 shows the data obtained based on the flood loss rate function for the four land types.

Table 7

Vulnerability functions to storm flooding for different land use types

Land use typeDepth of inundation (m)
< 0.10.1–0.30.3–0.50.5–1.01.0–1.51.5–2.02.0–3.0> 3.0
Commercial 0.009 0.020 0.05 0.09 0..15 0.20 0.26 0.28 
Residential 0.008 0.015 0.04 0.08 0.14 0.18 0.24 0.27 
Industrial 0.006 0.012 0.03 0.06 0.11 0.17 0.21 0.25 
Public services 0.005 0.010 0.02 0.05 0.10 0.16 0.20 0.24 
Land use typeDepth of inundation (m)
< 0.10.1–0.30.3–0.50.5–1.01.0–1.51.5–2.02.0–3.0> 3.0
Commercial 0.009 0.020 0.05 0.09 0..15 0.20 0.26 0.28 
Residential 0.008 0.015 0.04 0.08 0.14 0.18 0.24 0.27 
Industrial 0.006 0.012 0.03 0.06 0.11 0.17 0.21 0.25 
Public services 0.005 0.010 0.02 0.05 0.10 0.16 0.20 0.24 
View Large

According to the different land use types, the GDP is reasonably distributed, the GDP data are gridded, and the specific loss value of the flood disaster can be calculated by combining the grid data of the inundation depth in the study area with the disaster damage curve. In this study, the spatial distribution of the depth of inundation simulated by AHM is superimposed on the spatial distribution data of GDP to find the direct economic losses at different moments. First, the direct economic loss caused by typhoon Mangosteen in Macau is calculated based on the constructed model using typhoon Mangosteen as an example. The direct economic losses caused by Typhoon Mangosteen are summarized in Table 8.

Table 8

Typhoon Typhoon Mangkhut economic losses in Macao region

Estimated projectsDirect losses (MOP billion)
(a) Wholesale, retail and foodstuffs 2.49 
(b) Construction 0.94 
(c) Hospitality 1.12 
(d) Finance 0.19 
(e) Gaming – 
(f) Other industries 0.10 
(g) Residential and vehicle 0.03 
(h) Public facilities and government departments 0.30 
Total 5.17 
Estimated projectsDirect losses (MOP billion)
(a) Wholesale, retail and foodstuffs 2.49 
(b) Construction 0.94 
(c) Hospitality 1.12 
(d) Finance 0.19 
(e) Gaming – 
(f) Other industries 0.10 
(g) Residential and vehicle 0.03 
(h) Public facilities and government departments 0.30 
Total 5.17 
View Large

The moment of maximum water accumulation (13 h) is selected for direct flooding loss calculation, and the mean GDP number is assigned to the calculation grid based on the distribution of different industries and the total value of GDP per unit area in 2018, with a maximum calculation grid area of 9 m2, then superimposed on the depth of water accumulation in each grid of the calculation area, and the loss calculation is carried out based on the flooding loss rate function for different land use types. The direct economic loss at the moment of maximum waterlogging for the rainfall of Typhoon Mangkhut is calculated to be MOP 344 million. Since the total GDP value of the study area accounts for 65% of the total GDP of the Macao region, the direct economic loss caused by typhoon Mangosteen to the study area is MOP 336 million. The error between the results calculated by this model and the statistical value of the Macao region is 2.3%.

To predict and extrapolate the direct losses due to waterlogging in the inner harbor area under different rainfall scenarios, the direct economic losses are calculated for the year 2021 for rainfalls of 2a, 5a, 10a, 20a, 50a, and 100a, for example. Figure 25 shows that the direct loss due to flooding increases with the increase of the return period, and the economic loss for the once in 100 years event is MOP 247 million, which is 2.7 times the once in 2 years rainfall. The variation of the maximum flooding losses shows that the direct economic losses from flooding increase significantly for rainstorms exceeding the once in 10-year period, compared to the once in 2 years and once in 5-year periods, which is related to the fact that the standard of the drainage system in the Macao area is primarily the once in 2-year period.
Figure 25
Maximum waterlogging loss under different rainfalls.
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Maximum waterlogging loss under different rainfalls.

Figure 25
Maximum waterlogging loss under different rainfalls.
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Maximum waterlogging loss under different rainfalls.

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To analyze the variation of inundation losses during rainfall, rainfalls of different recurrence periods are analyzed. One scenario is selected every 10 min, and the depth of inundation and the GDP of the area under study are superimposed to obtain the change curve of rainfall inundation losses, as shown in Figure 26. From the trend of direct economic losses, before the end of the rainfall, the trend of direct economic losses is more in line with the trend of the design storm intensity, and the rate of increase of direct economic losses is getting faster before the peak rainfall intensity. The rainfall intensity reaches a peak value. When the rainfall intensity peaks, the direct economic loss reaches a more significant value. After the rainfall intensity decreases, the direct economic loss also grows slowly. At the end of the rainfall, the loss reaches its maximum value, consistent with when the maximum value of the amount of water and the waterlogged area occurs. After 4 h, the slow decline in direct economic losses is because the rainfall exceeded the drainage capacity of the Macao area, and the water within the city could not be removed in time, resulting in a more extended period of inundation in some areas. After the end of the rainfall, the water in the higher terrain areas flowed to the lower terrain areas, causing the water depth in some areas to increase rather than decrease. Based on the distribution of land use types in the Macau area, the areas with lower topography are also commercial and residential agglomeration areas, so the direct economic loss has no decreasing trend for a more extended period. The direct economic losses given in this study are only a reference value. Whether the government and the community are adequately prepared for flooding and the construction of various flood control measures will significantly impact the direct economic losses. Due to Macao's limited area and highly developed economy, the type of land use remains the same. Combined with the change in GDP, the flooding loss in Macao can be deduced in different years according to this article's change rule of flooding loss.
Figure 26
Variation of waterlogging loss under different rainfalls.
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Variation of waterlogging loss under different rainfalls.

Figure 26
Variation of waterlogging loss under different rainfalls.
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Variation of waterlogging loss under different rainfalls.

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To achieve the purpose of green computing, a coupled urban hydrological–hydrodynamic model is constructed, and the coupled model is adapted to the ARM architecture processor (AHM). To verify the rationality of the model and the accuracy of the results, the inner harbor of Macao Peninsula is taken as the study area, and the evolution of flooding in the inner harbor area of Macao is analyzed based on the AHM model under different rainfall scenarios. The following conclusions are drawn:

  • (1)

    The AHM can perform urban flooding calculations on the ARM architecture processor, and the results show that the rainfall pattern of the change of the total amount of standing water in different rainfall recurrence periods is consistent. The measured water depth changes and simulation results of Kang Kung Temple and Lower Ring rainfall stations are compared, and the Nash efficiency coefficients are 0.91 and 0.87, respectively, which indicates that the AHM has reasonableness and accuracy. From the calculation results, we can obtain the flow velocity trends, water depth, waterlogged area, and volume during the rainfall recurrence period, which provides technical support for constructing the dynamic assessment model of waterlogging.

  • (2)

    The rainfall velocities of 2a, 5a, and 10a ranged from 0.6 to 0.9 m/s and are mainly concentrated in the coastal neighborhoods. In contrast, the maximum velocities of 20a, 50a, and 100a reached more than 1.0 m/s, and most are concentrated in the low-lying streets in the city center. The changes in road water accumulation and flow velocity will affect rescue efficiency and indirectly increase the flood damage in Macao. In this article, the distribution maps of road flow velocity and water accumulation can provide theoretical references for rational planning rescue routes in the inner harbor area and reducing flood damage.

  • (3)

    The waterlogging in the study area is distributed pointwise, with water depths ranging from 0.1 to 0.5 m in most centers. The area of flooded points with a water depth of more than 1.0 m is 6.81 × 10−4km2, which is only 0.068% of the study area. In this study, the inundation points are also screened, and those with inundation water depths exceeding 1.0 m are marked and labeled. The inundation water depth data are also overlaid with the industry distribution data in Macau to form a map of the distribution of flooding risk levels in the study area. The results show that when the rainfall intensity exceeds once in 10 years, the drainage capacity of the Macao area is well overloaded and the risk of flooding increases significantly.

  • (4)

    Taking Typhoon Mangkhut as an example, the specific damage value of Mangosteen is calculated to be MOP 344 million by combining the grid data of inundation depth and the disaster damage curve of the study area. The error with the statistical value for the Macau area is 2.3%. To analyze the changes in inundation loss during rainfall, it provides a reference for the direct economic loss of inundation in the Macao region. Rainfalls of different recurrence periods are analyzed, and one scenario is selected every 10 min to obtain the change curve of inundation direct loss of internal flooding. Meanwhile, combined with the change in GDP, the flooding loss of Macau in different years can be deduced according to the change rule of inundation loss in this article.

The AHM in this article only applies to serial computing, and improving the AHM to enable parallel computing and GPU-accelerated computing is the current direction of model improvement. At the same time, the coupled model can be adapted to ARM architecture to improve its computational performance. However, the specific performance enhancement value needs to be further studied and evaluated, which will be the focus of the subsequent research.

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This work was supported by Chinese National Key Research and Development Program (No. 2022YFE0205200 & 2022YFC3090600), the National Natural Science Foundation of China (No. 52192671), IWHR Research & Development Support Program (WR110145B0022022), the Research Fund of the State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin (No. SKL2022TS11), and the Open Research Fund of Key Laboratory of River Basin Digital Twinning of Ministry of Water Resources.

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Haijia Zhang: conceptualization, validation, formal analysis, investigation, and writing – original draft; Jiahong Liu: conceptualization, software, writing – review and editing, and resources; Chao Mei: conceptualization, writing – review and editing, and resources; Lirong Dong: conceptualization, writing – review and editing, and project administration. Tianxu Song: conceptualization, writing – review and editing, and project administration.

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Data cannot be made publicly available; readers should contact the corresponding author for details.

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The authors declare there is no conflict.

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