Two-dimensional storm flood simulation method and device based on hydrological and hydrodynamic coupling

Abstract

The embodiment of the present disclosure provides a two-dimensional storm flood simulation method and device based on hydrological and hydrodynamic coupling, relates to the technical field of intelligent water conservancy and flood simulation, and in particular to a high-precision and high-performance numerical simulation method suitable for small watershed storm floods. The method comprises the following steps: discretizing a region to be analyzed into a plurality of calculation units, and configuring the calculation units with a physical property field including runoff parameters; determining the rainfall rate of the calculation units changing with time based on the rainfall data of the region to be analyzed; determining the cumulative rainfall and the cumulative runoff of the calculation units based on the rainfall rate and the runoff parameters, and determining the net rainfall rate of the calculation units based on the cumulative rainfall and the cumulative runoff; and performing confluence calculation by taking the net rainfall rate as a source term to simulate the flood evolution process of the region to be analyzed.

Description

Technical Field

[0001] The embodiments disclosed herein relate to the field of smart water conservancy and flood simulation technology, and particularly to a two-dimensional rainstorm and flash flood simulation method and a two-dimensional rainstorm and flash flood simulation device based on hydro-hydrodynamic coupling. The two-dimensional rainstorm and flash flood simulation method and device based on hydro-hydrodynamic coupling can be used for real-time early warning and forecasting of rainstorms and flash floods in small watersheds. Background Technology

[0002] Floods can be understood as a natural phenomenon in which the volume of water in rivers, lakes, oceans, and other bodies of water exceeds their carrying capacity, leading to overflowing or abnormally rising water levels. As a common natural disaster, floods are characterized by their suddenness, destructiveness, and difficulty in prediction. Flood simulation technology is an important tool supporting flood disaster prevention, risk assessment, and the construction of digital twin watersheds.

[0003] Taking flash floods caused by torrential rain as an example, flash floods are sudden floods triggered by torrential rain and occurring in mountainous areas. They are characterized by rapid formation, high flow velocity, suddenness, great destructiveness, and small spatial scale. Flash floods usually occur in small and medium-sized watersheds with limited catchment areas. The flood peak can form within tens of minutes to several hours after rainfall. Because they occur in mountainous areas with steep slopes, the water flow velocity is fast and the scouring force is strong. They are often accompanied by secondary disasters such as debris flows and landslides, making them difficult to predict accurately and requiring short warning times.

[0004] Therefore, a method for simulating rainstorms and flash floods that can balance high accuracy, high efficiency, and simple calculation is needed to meet the requirements of precision and timeliness in flood simulation. Summary of the Invention

[0005] The embodiments of this disclosure provide a two-dimensional rainstorm and flash flood simulation method and apparatus based on hydrodynamic coupling, which can at least partially solve the above-mentioned problems or other problems in the art. The embodiments of this disclosure can be used for real-time early warning and forecasting of rainstorms and flash floods in small watersheds.

[0006] According to a first aspect of this disclosure, a two-dimensional storm flash flood simulation method based on hydrodynamic coupling is provided. The method includes: discretizing the region to be analyzed into multiple computational units and configuring a physical attribute field including runoff generation parameters for each computational unit; determining the rainfall rate of each computational unit over time based on rainfall data of the region to be analyzed; determining the cumulative rainfall and cumulative runoff of each computational unit based on the rainfall rate and runoff generation parameters, and determining the net rainfall rate of each computational unit based on the cumulative rainfall and cumulative runoff; and performing runoff calculation using the net rainfall rate as a source term to simulate the flood evolution process of the region to be analyzed.

[0007] In some embodiments of this disclosure, determining the cumulative rainfall and cumulative runoff of a computing unit based on rainfall rate and runoff parameters includes: determining the cumulative rainfall based on rainfall rate on a time-step basis; and determining the cumulative runoff based on cumulative rainfall and runoff parameters on a time-step basis.

[0008] In some embodiments of this disclosure, determining the net rainfall rate of a calculation unit based on cumulative rainfall and cumulative runoff includes: determining the net rainfall rate of the calculation unit step by step based on cumulative rainfall and cumulative runoff.

[0009] In some embodiments of this disclosure, determining the net rainfall rate of a calculation unit step by step, based on cumulative rainfall and cumulative runoff, includes: determining the cumulative rainfall loss of the calculation unit step by step, based on cumulative rainfall and cumulative runoff; determining the rainfall loss rate of the calculation unit step by step, based on the rate of change of the cumulative rainfall loss; and determining the net rainfall rate step by step, based on the rainfall rate and the rainfall loss rate.

[0010] In some embodiments of this disclosure, net rainfall rate is used as a source term for confluence calculation to simulate the flood evolution process of the area to be analyzed. This includes: performing confluence calculation on a time-step basis using net rainfall rate as a source term to simulate the flood evolution process of the area to be analyzed, wherein the simulation results of the flood evolution process include at least one of the flood inundation range, water depth, flow velocity, and flow rate process curve.

[0011] In some embodiments of this disclosure, net rainfall rate is used as a source term for confluence calculation to simulate the flood evolution process of the area to be analyzed. This includes: using net rainfall rate as a source term and performing confluence calculation based on hydrodynamic control equations to simulate the flood evolution process of the area to be analyzed, wherein the hydrodynamic control equations include two-dimensional shallow water equations.

[0012] In some embodiments of this disclosure, the method further includes using a graphics processor to perform at least one of the following steps in parallel: determining the cumulative rainfall and cumulative runoff of the computing unit based on the rainfall rate and runoff parameters, and determining the net rainfall rate of the computing unit based on the cumulative rainfall and cumulative runoff; and performing runoff calculations using the net rainfall rate as a source term to simulate the flood evolution process of the area to be analyzed.

[0013] In some embodiments of this disclosure, determining the rainfall rate of the calculation unit over time based on rainfall data of the area to be analyzed includes: determining the rainfall rate based on the rainfall data of the area to be analyzed using a spatial interpolation method, wherein the rainfall data of the area to be analyzed includes at least one of measured rainfall data from rain gauge stations located in the area to be analyzed and forecast rainfall data.

[0014] In some embodiments of this disclosure, the region to be analyzed is discretized into multiple computing units, and a physical attribute field including flow generation parameters is configured for each computing unit. This includes: discretizing the region to be analyzed into multiple computing units, and using geospatial data of the region to be analyzed to configure a physical attribute field for each computing unit. The physical attribute field also includes a water-blocking parameter used to characterize the ability of the computing unit to obstruct water flow. The method further includes: in response to information in the geospatial data indicating the presence of a water-blocking structure, correcting the water-blocking parameter of the computing unit where the water-blocking structure is located based on the information of the water-blocking structure.

[0015] According to a second aspect of this disclosure, a two-dimensional storm flash flood simulation device based on hydrodynamic coupling is provided. The device includes: a geographic data processing unit configured to discretize the area to be analyzed into multiple computational units and configure a physical attribute field including runoff generation parameters for the computational units; a rainfall processing unit configured to determine the rainfall rate of the computational units over time based on rainfall data of the area to be analyzed; a runoff generation calculation unit configured to determine the cumulative rainfall and cumulative runoff of the computational units based on the rainfall rate and runoff generation parameters, and to determine the net rainfall rate of the computational units based on the cumulative rainfall and cumulative runoff; and a runoff calculation unit configured to perform runoff calculation using the net rainfall rate as a source term to simulate the flood evolution process of the area to be analyzed.

[0016] In some embodiments of this disclosure, the runoff calculation unit is further configured to: determine cumulative rainfall on a time-step basis based on rainfall rate; and determine cumulative runoff on a time-step basis based on cumulative rainfall and runoff parameters.

[0017] In some embodiments of this disclosure, the runoff calculation unit is further configured to: determine the net rainfall rate of the calculation unit step by step, based on the cumulative rainfall and cumulative runoff.

[0018] In some embodiments of this disclosure, the runoff calculation unit is further configured to: determine, step by step, the cumulative rainfall loss of the calculation unit based on the cumulative rainfall and the cumulative runoff; determine, step by step, the rainfall loss rate of the calculation unit based on the rate of change of the cumulative rainfall loss; and determine, step by step, the net rainfall rate based on the rainfall rate and the rainfall loss rate.

[0019] In some embodiments of this disclosure, the confluence calculation unit is further configured to: perform confluence calculation step by step, taking net rainfall rate as the source term, to simulate the flood evolution process of the area to be analyzed, wherein the simulation results of the flood evolution process include at least one of the flood inundation range, water depth, flow velocity, and flow rate process curve.

[0020] In some embodiments of this disclosure, the runoff calculation unit is further configured to: use net rainfall rate as a source term and perform runoff calculation based on hydrodynamic control equations to simulate the flood evolution process of the area to be analyzed, wherein the hydrodynamic control equations include two-dimensional shallow water equations.

[0021] In some embodiments of this disclosure, at least one of the flow generation calculation unit and the flow merging calculation unit is implemented as a graphics processor. In some embodiments of this disclosure, the rainfall processing unit is further configured to determine the rainfall rate based on rainfall data of the region to be analyzed using a spatial interpolation method, wherein the rainfall data of the region to be analyzed includes at least one of measured rainfall data from rain gauge stations located in the region to be analyzed and forecast rainfall data.

[0022] In some embodiments of this disclosure, the geographic data processing unit is further configured to: discretize the area to be analyzed into multiple computing units, and configure physical attribute fields for the multiple computing units using geospatial data of the area to be analyzed, wherein the physical attribute fields also include water-blocking parameters for characterizing the ability of the computing units to obstruct water flow, and the geographic data processing unit is further configured to: in response to information in the geospatial data indicating the presence of water-blocking structures, correct the water-blocking parameters of the computing units where the water-blocking structures are located based on the information of the water-blocking structures.

[0023] The two-dimensional storm flash flood simulation method and apparatus based on hydrodynamic coupling provided by the embodiments of this disclosure achieves spatially distributed processing of runoff calculation by discretizing the area to be analyzed into multiple calculation units and configuring runoff generation parameters for the calculation units. This helps to improve the spatial resolution of runoff simulation and reduce local runoff estimation bias caused by the use of lumped parameters. Based on the runoff generation parameters and the rainfall rate that changes over time, the cumulative rainfall and cumulative runoff of the calculation units are determined, enabling the runoff calculation to reflect the cumulative effect of the rainfall process in the calculation units. Compared with the runoff estimation method based solely on the total rainfall, this can reduce the calculation bias of net rainfall rate caused by ignoring the spatiotemporal distribution characteristics of the rainfall process, which helps to improve the accuracy of runoff simulation. The net rainfall rate is directly added to the runoff calculation as a source term, realizing the coupling of runoff calculation and runoff calculation, which is beneficial to improving the coherence and accuracy of flood evolution simulation. In addition, by integrating the runoff calculation results into the runoff calculation in the form of source terms, the additional data conversion or interpolation steps between runoff calculation and runoff calculation are reduced, which helps to simplify the calculation process and improve the overall simulation efficiency.

[0024] This scheme, based on the independent configuration of runoff generation parameters by computing units and the determination of net rainfall rate step by step, can effectively adapt to the characteristics of large topographic relief and strong spatial heterogeneity of runoff generation, and is especially suitable for areas with complex geometries such as mountainous watersheds.

[0025] It should be understood that the description in this section is not intended to identify key or important features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description.

[0026] Other features and aspects of this disclosure will become clear from the following detailed description of exemplary embodiments with reference to the accompanying drawings. Attached Figure Description

[0027] Other features, objects, and advantages of this disclosure will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 This is a flowchart of a two-dimensional rainstorm and flash flood simulation method based on hydrodynamic coupling provided by an exemplary embodiment of this disclosure; Figure 2 This is a flowchart illustrating the determination of the net rainfall rate of the calculation unit according to an exemplary embodiment of this disclosure; and Figure 3 This is a block diagram of a two-dimensional rainstorm and flash flood simulation device based on hydrodynamic coupling, provided according to an exemplary embodiment of this disclosure. Detailed Implementation

[0028] The various exemplary embodiments, features, and aspects of this disclosure will now be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings denote elements that have the same or similar functions. Although various aspects of the embodiments are shown in the drawings, they are not necessarily drawn to scale unless specifically indicated otherwise.

[0029] The term “exemplary” as used herein means “serving as an example, implementation method, or illustration.” Any implementation method described herein as “exemplary” is not necessarily to be construed as superior to or better than other implementation methods.

[0030] Furthermore, to better illustrate this disclosure, numerous specific details are set forth in the following detailed description. Those skilled in the art will understand that this disclosure can be practiced without certain specific details. In some instances, systems, means, components, and circuits well known to those skilled in the art have not been described in detail in order to highlight the main points of this disclosure.

[0031] Floods, as common natural disasters, are characterized by their suddenness, destructiveness, and difficulty in prediction. Flood simulation technology is an important tool for supporting flood disaster prevention, risk assessment, and the construction of digital twin watersheds.

[0032] Flood simulation can employ either hydrological or hydrodynamic models. Hydrological models can output runoff generation results and are characterized by rapid modeling and high efficiency. Hydrodynamic models can simulate the flood evolution process and output flow field information such as water depth and velocity. However, hydrological models can only output cross-sectional flow processes and cannot provide details of the spatial distribution of flood inundation, while hydrodynamic models have a relatively large computational burden, require external input of runoff generation results, and often ignore or simplify the rainfall-runoff conversion process, resulting in low model reliability.

[0033] Therefore, in some implementation schemes, to compensate for the shortcomings of both models, a coupling approach between hydrological and hydrodynamic models can be used to simulate flooding processes. For example, the hydrological model's calculation results can be used as boundary conditions for the hydrodynamic model to achieve unidirectional coupling between the two models. Alternatively, the hydrological model can be dynamically coupled to a one-dimensional hydrodynamic model, and then coupled to a two-dimensional hydrodynamic model, achieving indirect coupling between the hydrological and two-dimensional hydrodynamic models. However, in the unidirectional coupling method, the hydrological and hydrodynamic models are difficult to synchronize in time, resulting in significant errors in the simulation results. In the indirect coupling method, there is a lack of a direct dynamic coupling mechanism between the hydrological model and the two-dimensional hydrodynamic model, making it difficult for the simulation results to accurately reflect the actual flood development process. Furthermore, the treatment of rainfall infiltration losses can be incorporated into the governing equations of the hydrodynamic model; however, this implementation scheme has high computational costs and is difficult to meet real-time emergency response needs.

[0034] To address at least the aforementioned issues, this disclosure provides a two-dimensional storm flash flood simulation method and apparatus based on hydrodynamic coupling. By discretizing the area to be analyzed into multiple computational units and configuring runoff generation parameters for each unit, spatially distributed processing of runoff generation calculation is achieved. This helps improve the spatial resolution of runoff generation simulation and reduces local runoff estimation bias caused by the use of lumped parameters. Based on the runoff generation parameters and the rainfall rate that varies over time, the cumulative rainfall and cumulative runoff of each computational unit are determined, enabling the runoff generation calculation to reflect the cumulative effect of the rainfall process within the computational unit. Compared to runoff generation estimation methods based solely on total rainfall, this reduces the bias in net rainfall rate calculation caused by ignoring the spatiotemporal distribution characteristics of the rainfall process, thus improving the accuracy of runoff generation simulation. By directly incorporating the net rainfall rate as a source term into the runoff calculation, the coupling of runoff generation and runoff calculation is achieved, which is beneficial for improving the coherence and accuracy of flood evolution simulation. Furthermore, by integrating the runoff generation calculation results into the runoff calculation as source terms, the additional data conversion or interpolation steps between runoff generation and runoff calculations are reduced, which helps simplify the calculation process and improve the overall simulation efficiency.

[0035] This scheme, based on the independent configuration of runoff generation parameters by computing units and the determination of net rainfall rate step by step, can effectively adapt to the characteristics of large topographic relief and strong spatial heterogeneity of runoff generation, and is especially suitable for areas with complex geometries such as mountainous watersheds.

[0036] Some embodiments of this disclosure provide a two-dimensional rainstorm and flash flood simulation method based on hydrodynamic coupling. Figure 1 This is a flowchart of a two-dimensional rainstorm and flash flood simulation method 1000 based on hydrodynamic coupling, provided according to an exemplary embodiment of this disclosure.

[0037] like Figure 1 As shown, the two-dimensional rainstorm and flash flood simulation method 1000 based on hydrodynamic coupling includes: Step S1: Discretize the region to be analyzed into multiple computational units, and configure the computational units with physical property fields including flow generation parameters.

[0038] Step S2: Based on the rainfall data of the area to be analyzed, determine the rainfall rate of the calculation unit over time.

[0039] Step S3: Based on the rainfall rate and runoff parameters, determine the cumulative rainfall and cumulative runoff of the calculation unit, and based on the cumulative rainfall and cumulative runoff, determine the net rainfall rate of the calculation unit.

[0040] Step S4: Use net rainfall rate as the source term for runoff calculation to simulate the flood evolution process of the area to be analyzed.

[0041] Specifically, runoff generation can be understood as the process by which rainfall, after deducting losses such as infiltration and evaporation, forms surface runoff. In step S1, the continuous geographic space is divided into a finite number of discrete computational units, and runoff generation parameters are independently configured for each computational unit. These parameters characterize the computational unit's ability to convert rainfall into runoff. Exemplarily, runoff generation parameters can be determined by factors such as land use type and soil type. In different hydrological models or application scenarios, runoff generation parameters can be implemented as different specific parameters. For example, in some embodiments of this disclosure, runoff generation parameters may include the Curve Number (CN value), etc. In other embodiments of this disclosure, runoff generation parameters may include the runoff coefficient, infiltration capacity parameters, etc. It should be noted that the above examples are merely illustrations, and this disclosure does not limit the specific implementation of runoff generation parameters, as long as they can characterize the computational unit's ability to convert rainfall into runoff.

[0042] In the field of flood simulation, discretizing continuous geographic space into computational units is fundamental to numerical calculations. In step S1, the area to be analyzed is divided into computational units, and there are various options for the division method and unit type.

[0043] For example, the computational units may include structured grids and unstructured grids. Structured grids may have regular topological relationships, with each computational unit arranged in an orderly manner, facilitating program design and data access, and exhibiting high computational efficiency in flood simulation within regular regions. Unstructured grids, on the other hand, have irregular connections between computational units, allowing for better fitting of complex terrain boundaries, and are particularly suitable for geometrically complex regions such as mountainous watersheds. In some embodiments of this disclosure, to simplify data management and computational logic, the region to be analyzed can be discretized into multiple structured grids.

[0044] The size of the computational cells affects the accuracy and computational cost of flood simulation. Using smaller computational cells, or higher-resolution grids, means denser cell distribution, which helps improve the spatial resolution of runoff generation simulation and more finely characterize the spatial distribution features of runoff generation parameters. Conversely, using larger computational cells, or lower-resolution grids, reduces the number of computational cells, thus reducing computational cost. Therefore, high-resolution grids can be used in areas with dramatic topographic changes, such as narrow channels, while low-resolution grids can be used in flat areas, to improve computational efficiency while maintaining the accuracy of flood simulation.

[0045] Step S1 discretizes the area to be analyzed into multiple computational units and configures runoff generation parameters for each unit, enabling runoff generation calculations to be performed in a spatially distributed manner. Compared to the lumped approach that treats the entire watershed as a single-parameter homogeneous region, this method can reflect the spatial differences in runoff generation capacity between different computational units due to factors such as land use and soil type. This helps improve the spatial resolution of runoff generation simulation and reduces estimation bias caused by averaging runoff generation capacity in local areas using lumped parameters.

[0046] Rainfall data can originate from measured data at rain gauge stations or from precipitation forecast data generated by Numerical Weather Prediction (NWP) methods (i.e., numerical precipitation forecast data). Essentially, it is a record of rainfall obtained by sampling at discrete times at finite discrete locations such as rain gauge stations. Numerical weather prediction is a method that, based on actual atmospheric conditions and under certain initial and boundary conditions, uses large-scale computers to perform numerical calculations to solve a set of fluid dynamics and thermodynamics equations describing weather evolution, predicting atmospheric motion and weather phenomena over a future period. For example, numerical precipitation forecast data can be gridded forecast field data, which can correspond to discrete computational units, thus directly serving as the rainfall input for each computational unit. It should be noted that the above examples are merely illustrations, and this disclosure does not limit the specific source or form of rainfall data, as long as it can provide the rainfall rate changing over time for each computational unit in the area to be analyzed.

[0047] In step S2, discrete rainfall data can be mapped to each computing unit using spatial interpolation methods, and converted into rainfall rates that vary over time, yielding the water depth falling onto the computing unit per unit time. By determining the rainfall rate that varies over time for each computing unit, runoff generation calculation can obtain the rainfall intensity input for each time step. Compared to simplified methods that only use total rainfall or constant rainfall intensity, this approach reflects the impact of rainfall intensity fluctuations over time on the runoff generation process, such as the effects of peak rainfall and intermittent rainfall, providing temporally continuous input data for determining subsequent cumulative rainfall.

[0048] Cumulative rainfall can be understood as the total rainfall from the start of rainfall to the current moment. In actual numerical simulations, continuous time is divided into a series of consecutive time intervals, each of which can have a predetermined length. Within each time interval, the rainfall rate can be considered a constant value. Cumulative rainfall is the sum of the rainfall from the initial time interval to the current time interval. Cumulative runoff can be understood as the corresponding cumulative runoff depth calculated based on cumulative rainfall and runoff generation parameters.

[0049] Based on the cumulative rainfall and cumulative runoff of a calculation unit, the net rainfall rate of that calculation unit can be determined. The net rainfall rate of a calculation unit can be understood as the rate at which water actually enters the surface and participates in runoff within the current time interval. Therefore, the net rainfall rate of a calculation unit enables the runoff calculation results to dynamically respond to changes in rainfall intensity over time within the calculation unit.

[0050] The determination of the aforementioned cumulative rainfall, cumulative runoff, and net rainfall rate was performed independently for each calculation unit. By performing these calculations independently on each calculation unit, the spatial differences in runoff generation capacity caused by factors such as land use and soil type between different calculation units can be reflected. This helps to improve the spatial resolution of runoff generation simulation and reduce estimation bias caused by averaging runoff generation capacity in local areas using lumped parameters.

[0051] Rainfall rates are determined using spatial interpolation methods based on measured and / or forecasted rainfall data from rain gauge stations, enabling the simulation scheme to access real-time or forecasted rainfall for flood early warning. It should be noted that the above description of time discretization is merely for ease of understanding the technical solution of this disclosure; this disclosure does not limit the specific length of the time interval or the time discretization method.

[0052] The runoff confluence calculation simulates the process of runoff flowing, converging, and evolving downstream on the land surface. The source term can be understood as an additional term in the governing equations upon which the runoff confluence calculation is based, used to represent external inputs or source-sink effects. In step S4, the net rainfall rate of each calculation unit obtained from the runoff generation calculation is input as a source term into the runoff confluence calculation, allowing the increased runoff volume in each calculation unit within each time interval to directly participate in the solution of the runoff confluence equation. It should be noted that the above description of the time interval is consistent with the aforementioned explanation of time discretization; this disclosure does not limit the specific length of the time interval.

[0053] By directly incorporating the net rainfall rate of each computational unit as a source term into the runoff calculation, direct coupling between runoff generation and runoff calculation is achieved, or in other words, direct dynamic coupling between the hydrological model and the two-dimensional hydrodynamic model. The net rainfall rate of each computational unit is independently determined based on its own runoff generation parameters and rainfall rate. These net rainfall rates collectively constitute the source term input for the runoff calculation. This allows runoff generation results to participate in flood evolution simulation in real time at each time interval, maintaining synchronization between runoff generation and runoff on the time scale. This helps improve the coherence and accuracy of flood evolution simulation and reduces the time mismatch problems that might be introduced by using runoff generation results as independent boundary condition inputs. Furthermore, since the net rainfall rate is directly incorporated into the runoff equation as a source term, the need for additional data conversion or spatial interpolation between runoff generation and runoff calculations is reduced, simplifying the computational process, improving overall simulation efficiency, and achieving integrated runoff generation and runoff simulation.

[0054] In summary, by discretizing the region to be analyzed into multiple computational units and configuring runoff generation parameters for each unit, spatially distributed processing of runoff generation calculations is achieved. This helps improve the spatial resolution of runoff generation simulations and reduces local runoff estimation bias caused by the use of lumped parameters. Based on runoff generation parameters and rainfall rates that change over time, the cumulative rainfall and cumulative runoff of each computational unit are determined, enabling runoff generation calculations to reflect the cumulative effect of rainfall processes within the computational units. Compared to runoff generation estimation methods based solely on total rainfall, this reduces the bias in net rainfall rate calculations caused by ignoring the spatiotemporal distribution characteristics of rainfall processes, thus improving the accuracy of runoff generation simulations. Integrating net rainfall rate directly into the runoff calculations as a source term achieves coupling between runoff generation and runoff calculations, which is beneficial for improving the coherence and accuracy of flood evolution simulations. Furthermore, by incorporating the runoff generation calculation results into the runoff calculations as source terms, the need for additional data conversion or interpolation between runoff generation and runoff calculations is reduced, simplifying the calculation process and improving overall simulation efficiency.

[0055] In other words, the implementation of this disclosure discretizes the area to be analyzed into multiple computing units and configures runoff generation parameters. Based on the rainfall rate that changes over time, the cumulative rainfall and cumulative runoff are determined to obtain the net rainfall rate. Then, the net rainfall rate is used as the source term for runoff calculation. This enables spatially distributed processing of runoff generation calculation, improves simulation accuracy and efficiency, and is especially suitable for small watersheds in mountainous areas.

[0056] Step S1 In some embodiments of this disclosure, step S1, discretizing the area to be analyzed into multiple computational units and configuring a physical attribute field including runoff generation parameters for the computational units, may include: discretizing the area to be analyzed into multiple computational units and configuring a physical attribute field for the multiple computational units using geospatial data of the area to be analyzed. Optionally, the geospatial data may include a digital elevation model (DEM), land use types, soil types, and river cross-section measurement data, etc.

[0057] Optionally, the resolution of a digital elevation model (DEM) can be understood as the level of detail in the terrain it represents. The resolution of the DEM can be selected based on the terrain characteristics of the area to be analyzed. In areas with dramatic terrain changes, a higher resolution DEM is preferable to accurately depict terrain details; in relatively flat areas, a lower resolution DEM can be used to reduce the amount of data, thereby achieving a balance between simulation accuracy and computational efficiency.

[0058] Based on the above data, structured and unstructured grids can be generated, and each structured or unstructured grid can serve as a computational unit. The computational unit can be configured with runoff generation parameters. For example, runoff generation parameters may include at least one of the following: number of runoff curves, runoff coefficient, infiltration capacity parameter, etc.

[0059] Optionally, the physical property field may also include water-blocking parameters characterizing the ability of the computational unit to impede water flow. Alternatively, the computational unit may be configured with water-blocking parameters such as the Manning coefficient (commonly denoted by n). Furthermore, the computational unit may be configured with parameter fields such as topographic elevation. In some embodiments of this disclosure, the computational unit may be configured with only a small number of physical property fields, including runoff generation parameters and water-blocking parameters, thus reducing the number of parameters involved in the entire flood simulation scheme. For example, runoff generation parameters may be represented by the number of runoff curves, and water-blocking parameters by the Manning coefficient. Both the number of runoff curves and the Manning coefficient have clear physical meanings and mature calibration methods, making them easy to calibrate using measured data or empirical values. This parameter simplicity reduces the difficulty of parameter calibration when applying flood simulation schemes to different watersheds, facilitating the rapid deployment and widespread application of flood simulation schemes.

[0060] In other words, the area to be analyzed is discretized into computational units, and geospatial data is used to configure physical attribute fields for the computational units, so that parameters such as runoff generation and water blocking parameters can reflect the spatial distribution characteristics of actual topography and land use, thereby improving the fidelity of the model.

[0061] Building upon this, the two-dimensional storm flash flood simulation method 1000 based on hydrological-hydrodynamic coupling may further include: responding to information in geospatial data indicating the presence of water-blocking structures, and correcting the water-blocking parameters of the computational unit where the water-blocking structure is located based on the information of the water-blocking structure. In other words, when information about water-blocking structures exists in the geospatial data, the water-blocking parameters (such as the Manning coefficient) of the computational unit where the water-blocking structure is located are corrected based on this information, effectively simulating the flood-blocking effects of bridges, culverts, etc., without increasing the complexity of geometric modeling.

[0062] Specifically, geospatial data can include the location and geometric attributes of water-blocking structures such as bridges, culverts, and embankments. Using this information, the computational units occupied by the water-blocking structures can be identified, and the water-blocking effect can be represented by increasing water-blocking parameters within those units.

[0063] For example, for bridges, one or more computational units can be identified, and the backwater and obstruction effects of piers and superstructure on water flow can be simulated by increasing the Manning coefficient of these units. The magnitude of the increase in the Manning coefficient can be pre-set based on information about the water-blocking structures or calculated using empirical formulas. This information may include pier density, beam bottom clearance, etc. This correction method can effectively reflect the impact of water-blocking structures on flood evolution without increasing the complexity of geometric modeling, and reduces the computational overhead of finely depicting the geometry of the structures.

[0064] Furthermore, the topography on both banks of the river can be locally refined based on measured river cross-section data, making the river topography more closely resemble the actual cross-sectional shape. For example, digital elevation model data, land use data, soil type data, and river cross-section measurement data of the study area are collected to generate calculation cells and assign runoff curve numbers and Manning coefficients to these cells. Then, the topography on both banks of the river is locally refined based on the measured cross-section data, and the Manning coefficient is increased for the calculation cells at the bridge locations.

[0065] Therefore, by discretizing the area to be analyzed into multiple computational units and configuring runoff generation parameters for each unit, runoff generation calculation can be performed in a spatially distributed manner. Compared to the lumped approach that treats the entire watershed as a single-parameter uniform region, this approach can reflect the spatial differences in runoff generation capacity between different computational units due to factors such as land use and soil type. It is particularly suitable for small watersheds in mountainous areas with complex topography and can effectively handle the impact of water-blocking structures such as bridges on flood evolution.

[0066] Furthermore, smaller computational units can be used in areas with dramatic topographical changes, such as narrow channels, while larger units can be used in flat areas. This improves the accuracy and efficiency of flood simulation while enhancing the applicability of the flood simulation scheme, making it particularly suitable for simulating flash floods in small mountain watersheds. Additionally, by utilizing information about water-blocking structures, such as their location and geometric properties, the computational units occupied by these structures can be identified. The water-blocking effect can then be represented by increasing the water-blocking parameters within these units, further enhancing the applicability of the flood simulation scheme.

[0067] Step S2 In some embodiments of this disclosure, step S2, which determines the rainfall rate of the calculation unit over time based on the rainfall data of the area to be analyzed, may include: determining the rainfall rate based on the rainfall data of the area to be analyzed using a spatial interpolation method, wherein the rainfall data of the area to be analyzed includes at least one of measured rainfall data from rain gauge stations located in the area to be analyzed and forecast rainfall data.

[0068] For example, rainfall data is typically provided in the form of discrete-time sampling, such as hourly rainfall records. Here, "hourly" means that the time interval between two consecutive samples is one hour. Within the time discretization framework described above, this time interval is a basic unit of time, within which the rainfall rate can be approximated as a constant value. Therefore, the average rainfall rate within this time interval can be determined by converting the hourly rainfall to a unit.

[0069] Multiple rain gauge stations in the area to be analyzed are spatially discrete. Spatial interpolation methods are used to extrapolate rainfall data from finite discrete locations to each computational unit. As an option, spatial interpolation methods may include the Thiessen polygon method, the inverse distance weighting method, and the Kriging method. The Thiessen polygon method, also known as the nearest neighbor interpolation method, assigns each computational unit the rainfall rate from the nearest rain gauge station. The inverse distance weighting method uses a weighted average based on the distance between each rain gauge station and the computational unit, with closer stations receiving greater weight. The Kriging method provides the optimal unbiased estimate based on spatial autocorrelation characteristics. It should be noted that the above examples are merely illustrations, and this disclosure does not limit the specific form of the spatial interpolation method, as long as it can map discrete rainfall data to each computational unit.

[0070] Through the above processing, the calculation unit can obtain the corresponding rainfall rate in each time interval. Since hourly rainfall may fluctuate, the rainfall rate can change over time. This provides a dynamically changing rainfall intensity input that matches the time interval for runoff calculation, thus laying the foundation for the accurate determination of subsequent cumulative rainfall. Compared to the simplified approach of using only the total amount of a single rainfall event or assuming a constant rainfall intensity, the embodiments of this disclosure can reflect the impact of rainfall intensity fluctuations over time (e.g., peak rainfall, intermittent rainfall) on the runoff process, helping to improve the accuracy of runoff simulation.

[0071] Furthermore, rainfall data can originate from measured data at rain gauge stations or from precipitation forecast data generated by numerical weather prediction methods. For example, numerical precipitation forecast data can be gridded forecast field data, which can correspond to discretized computational units, thus directly serving as the rainfall input for each computational unit. Therefore, the flood simulation scheme provided by the embodiments of this disclosure can be used for flood early warning. In addition, the flood simulation scheme provided by the embodiments of this disclosure can be modularly designed to facilitate coupling with other functional modules. For example, coupling with a water quality simulation module can analyze pollutant transport and diffusion during floods, and coupling with a sediment transport module can simulate soil erosion and sediment transport caused by flash floods, thereby expanding its application scenarios in integrated watershed management.

[0072] Step S3 In some embodiments of this disclosure, determining the cumulative rainfall and cumulative runoff of the calculation unit based on the rainfall rate and runoff parameters in step S3 may include: determining the cumulative rainfall based on the rainfall rate on a time-step basis; and determining the cumulative runoff based on the cumulative rainfall and runoff parameters on a time-step basis.

[0073] In addition, determining the net rainfall rate of the calculation unit based on the cumulative rainfall and cumulative runoff in step S3 may include: determining the net rainfall rate of the calculation unit step by step based on the cumulative rainfall and cumulative runoff.

[0074] In some embodiments of this disclosure, step S3 further defines the method for determining the cumulative rainfall, cumulative runoff, and net rainfall rate step-by-step. A "time step" discretizes a continuous rainfall process into multiple consecutive time segments, each with a predetermined duration. Embodiments of this disclosure do not restrict whether the lengths of each time step are equal. One option is to use a fixed time step with equal intervals; another option is to use a variable time step strategy based on changes in rainfall intensity or computational accuracy requirements. For example, a shorter time step can be used during periods of drastic rainfall intensity changes to capture details, while a longer time step can be used during periods of calm to reduce computational load. As long as the simulation process can proceed sequentially in discrete time order and the rainfall rate can be approximated as constant within each time step, it falls within the scope of step-by-step simulation defined by this disclosure. This flexibility allows the two-dimensional storm flash flood simulation method 1000 based on hydrological-hydrodynamic coupling to adapt to different computational resources and accuracy requirements, enhancing its applicability in different application scenarios.

[0075] By updating the cumulative rainfall of the computational unit step-by-step, the cumulative rainfall can accurately reflect the cumulative effect of rainfall intensity fluctuations over time, rather than relying solely on the total amount of a single rainfall event. Based on this, the cumulative runoff is determined step-by-step using this cumulative rainfall and the computational unit's own runoff generation parameters, conforming to the fundamental law of nonlinear growth of runoff with cumulative rainfall. Furthermore, determining the net rainfall rate step-by-step allows the net rainfall rate to dynamically respond to real-time changes in rainfall intensity within a time step. Compared to estimating runoff generation solely based on the total amount of a single rainfall event or assuming a constant rainfall intensity, this method reduces the calculation bias of the net rainfall rate caused by neglecting the temporal distribution characteristics of the rainfall process, thus contributing to improved accuracy in runoff generation simulation.

[0076] Since the determination of cumulative rainfall, cumulative runoff, and net rainfall rate is performed independently for each calculation unit, and the runoff generation parameters can differ between different calculation units (e.g., due to variations in land use and soil type), this implementation method can precisely characterize the distribution features of runoff generation capacity in space and dynamically respond to changes in rainfall processes in time, achieving refined simulation in both spatial and temporal dimensions. This spatiotemporal integrated processing approach makes the flood simulation scheme provided by the embodiments of this disclosure particularly suitable for simulating flash floods in mountainous small watersheds with complex terrain and strong spatial heterogeneity of runoff generation.

[0077] In other words, the cumulative rainfall is determined step-by-step based on the rainfall rate, and the cumulative runoff is determined step-by-step based on the cumulative rainfall and runoff parameters. This allows the runoff calculation to reflect the cumulative effect of the rainfall process and reduces the calculation bias of the net rainfall rate. In addition, the net rainfall rate is determined step-by-step based on the cumulative rainfall and cumulative runoff, enabling the net rainfall rate to dynamically respond to real-time changes in rainfall intensity, further improving the accuracy of runoff simulation.

[0078] In some embodiments of this disclosure, the execution of step S3 requires time loop control. First, parameters such as start time, end time, result output interval, and CFL number (Courant-Friedrichs-Lewy condition, used to control computational stability) can be set according to the flood simulation requirements, and the initial water depth and flow velocity of each computational unit are set to zero. Then, a time loop is entered, and the following operations are performed within each time step: reading the rainfall rate of the current time step. Based on the runoff generation parameters (e.g., number of runoff curves) of the calculation unit and the current cumulative rainfall, the net rainfall rate is determined according to the runoff generation calculation method. .

[0079] For example, runoff generation calculation can employ the runoff curve number method: The cumulative runoff volume is calculated based on the cumulative rainfall and the number of runoff curves, thus obtaining the cumulative loss. The loss rate for the current time step is then calculated from the changes in cumulative loss over adjacent time steps. Finally, the net rainfall rate *r* is obtained by subtracting the loss rate from the rainfall rate. After each time step calculation is completed, it is determined whether a preset output interval has been reached. In response to reaching the preset output interval, the results such as the current inundation range, water depth, and flow velocity are saved. This cycle is repeated until the simulation ends, ultimately outputting the complete simulation results of the flood evolution process. The specific implementation of the runoff curve number method in runoff generation calculation will be further described in detail in step S4 below.

[0080] Figure 2 This is a flowchart of determining the net rainfall rate of a calculation unit according to an exemplary embodiment of the present disclosure.

[0081] For example, such as Figure 2 As shown, in step S3, determining the net rainfall rate of the calculation unit based on cumulative rainfall and cumulative runoff may include: Step S3-1: Time step by time, based on the cumulative rainfall and cumulative runoff of the calculation unit, determine the cumulative rainfall loss of the calculation unit.

[0082] Step S3-2: Time step by time, determine the rainfall loss rate of the calculation unit based on the rate of change of the cumulative rainfall loss of the calculation unit.

[0083] Step S3-3: Time step by time, determine the net rainfall rate of the computing unit based on the rainfall rate and rainfall loss rate of the computing unit.

[0084] Specifically, based on the runoff curve number method, the relationship between the cumulative runoff Q and the cumulative rainfall P of a single rainfall event can be expressed by formulas (1) and (2): (1) (2) Where P is the rainfall (mm) of the calculation unit; Q is the surface runoff depth (mm) generated by the calculation unit; S is the potential maximum water storage capacity (mm) of the calculation unit; λ is the initial loss coefficient, dimensionless, which can be taken as 0.2; CN is the number of runoff curves of the calculation unit, dimensionless.

[0085] Alternatively, the rainfall loss of the calculation unit can be determined by formula (3): (3) in, The rainfall loss (mm) is calculated for the unit. The cumulative rainfall (mm) for the calculation unit; The cumulative runoff (mm) for the calculation unit.

[0086] Within the current time step, the rainfall loss rate of the computational unit can be determined by formula (4): (4) in, for t ~( t+Δt The rainfall loss rate (mm / s) of the calculation unit within the time period; From the start of time to t+Δt The cumulative rainfall loss (mm) of the time unit is calculated. From the start of time to t The cumulative rainfall loss (mm) of the time unit is calculated. The time step is the length of the time step, or the time interval between two adjacent calculations. In the embodiments of this disclosure, "time step by time" refers to... Using time as the basic unit, calculations proceed sequentially in chronological order. Each time step corresponds to a unit of length... The time interval is such that the rainfall rate can be considered a constant value within each time interval.

[0087] In each time step, the net rainfall rate of the computational unit can be determined by formula (5): (5) in, fort ~( t+Δt The rainfall rate of the calculation unit within the time period; for t ~( t+Δt The rainfall loss rate (mm / s) of the calculation unit within the time period; for t ~( t+Δt The net rainfall rate (mm / s) of the calculation unit within the time period.

[0088] Based on the aforementioned steps S3-1, S3-2, and S3-3, the implementation method of this disclosure determines the cumulative rainfall loss, rainfall loss rate, and net rainfall rate step by step, enabling runoff calculation to dynamically track real-time changes in losses such as infiltration and depression filling during rainfall. Specifically, within each time step, the cumulative rainfall loss is calculated based on the current cumulative rainfall and cumulative runoff, reflecting the total loss from the start of rainfall to the current moment; the rainfall loss rate for the current time step is determined by the rate of change of the cumulative loss in adjacent time steps, reflecting the dynamic process of infiltration capacity gradually decreasing as soil saturation; the net rainfall rate is obtained by subtracting the rainfall loss rate from the rainfall rate for the current time step, which is the rate at which water actually enters the surface and participates in runoff in the current time step. Since the cumulative rainfall and cumulative runoff are updated at each time step, the net rainfall rate can respond in real time to changes in rainfall intensity, thereby avoiding the bias caused by using a fixed loss rate or relying solely on total rainfall to estimate runoff. Through iterative calculations at each time step, the runoff generation results can be updated synchronously with subsequent runoff calculations on the same time scale, providing accurate and dynamic source term inputs for flood evolution simulation, which helps to improve the accuracy and reliability of the overall simulation.

[0089] In other words, by determining the cumulative rainfall loss step by step, determining the rainfall loss rate based on its rate of change, and then determining the net rainfall rate based on the rainfall rate and the rainfall loss rate, it is possible to dynamically track the real-time changes in losses such as infiltration and depression filling, and avoid the errors caused by fixed loss rates.

[0090] Step S4 In some embodiments of this disclosure, step S4, which uses net rainfall rate as a source term to perform confluence calculation to simulate the flood evolution process of the area to be analyzed, may include: performing confluence calculation on a time-step basis using net rainfall rate as a source term to simulate the flood evolution process of the area to be analyzed, wherein the simulation results of the flood evolution process include at least one of the flood inundation range, water depth, flow velocity, and flow rate process curve.

[0091] Alternatively, net rainfall rate can be used as the source term, and runoff calculations can be performed based on the hydrodynamic governing equations to simulate the flood evolution process in the area under analysis. These hydrodynamic governing equations include two-dimensional shallow-water equations. Using net rainfall rate as the source term and performing runoff calculations based on hydrodynamic governing equations containing two-dimensional shallow-water equations achieves direct coupling between runoff generation and runoff at the governing equation level, reducing data conversion steps and simplifying the calculation process.

[0092] For example, the following coupled process can be performed on each computing unit at each time step: reading the rainfall rate at the current time step. Based on cumulative rainfall and cumulative runoff Calculate the net rainfall rate at the current time step. Net rainfall rate The water depth and velocity are added as source terms to the hydrodynamic control equations to obtain updated values ​​for each computational unit. The cumulative rainfall P(t+Δt) and cumulative runoff Q(t+Δt) are updated, and the process proceeds to the next time step. During the time loop, the current inundation extent, water depth, and velocity are saved upon reaching a preset output interval. After the simulation concludes, all result files are output, including a map of the maximum inundation extent, a peak water depth map, and the outlet cross-sectional flow process curve.

[0093] By directly incorporating the net rainfall rate of each computational unit as a source term into the runoff calculation at each time step, the above method achieves time-step coupling between runoff generation and runoff at each computational unit level, enabling the runoff generation results of each computational unit to participate in the flood evolution simulation of that computational unit in real time.

[0094] Net rainfall rate is directly embedded as a source term in the two-dimensional hydrodynamic governing equations and participates in the equation solution, thus achieving direct coupling between runoff generation and confluence at the governing equation level. Since runoff generation and confluence are synchronized on the time scale, the potential time mismatch problem introduced by using runoff results as independent boundary conditions is reduced. Net rainfall rate is directly integrated into the confluence equation as a source term, eliminating the need for additional data conversion or spatial interpolation between runoff generation and confluence calculations, which helps simplify the computational process and improve overall simulation efficiency. The output results, including the maximum flood inundation area map, peak water depth map, and outlet section flow process line, provide intuitive and quantitative data support for flood disaster prevention and risk assessment.

[0095] Specifically, the following section will use the two-dimensional shallow water equation based on a Cartesian uniform grid as an example to describe the time-step coupling of runoff generation and confluence at each computational unit level, where the governing equation in vector form can be expressed as formula (6): (6) Among them, Let be a vector containing unknowns. and It is the flux vector in the x and y directions. These are the source term vectors representing runoff, bottom slope, and friction, respectively. , and The values ​​are time and two Cartesian coordinates, respectively.

[0096] The expressions for each vector in formula (6) are as follows: (7) in, For water level, Because of the water depth, For the terrain, and These represent the flow velocities in the x and y directions, respectively. It is the acceleration due to gravity. As a net rain spot source, , The bed friction force obtained using Manning's formula (8) is: (8) in, For water density, It is the acceleration due to gravity. This is the Manning coefficient. Because of the water depth, and These represent the flow velocities in the x and y directions, respectively. For example, in a rainstorm and flash flood simulation, these parameters... The value can be taken from the standard water density.

[0097] Optionally, the numerical solution employs the Godunov scheme (one of the basic schemes of the finite volume method) to discretize the two-dimensional shallow water equation; the time discretization employs the MUSCL-Hancock (Monotonic Upwind Scheme for Conservation Laws-Hancock, a prediction-correction method) prediction-correction method, which enables the calculation to have high numerical accuracy in both time and space, and can more accurately capture the water flow characteristics in the process of flood evolution. (9) Among them, subscript i and j These are the grid indices in the x and y directions, respectively; superscript n This is the number of the time step; For time steps. and These are the dimensions of the computational cells along the x and y directions, respectively; , , and The interface flux between adjacent computing units can include the mass of water flowing through the interface and the flow rate of water flowing through the interface.

[0098] As an alternative, the interface flux between adjacent computational units can be solved using the HLLC (Harten-Lax-van LeerContact approximate Riemann solver) approximate Riemann solver; the bottom slope term can be solved using the hydrostatic reconstruction method to ensure that the water depth is non-negative; the friction term can be handled using a point implicit scheme to avoid rigidity problems at shallow water depths, and the adaptive time step can be controlled using CFL conditions.

[0099] In the finite volume method, each computational cell shares a common interface with its adjacent cells. Interface flux is the physical quantity transferred through this interface per unit time. For two-dimensional shallow water equations, these interface fluxes can include both the mass and flow rate of water passing through the interface. Interface flux characterizes the rate of exchange of water volume and momentum between adjacent computational cells, ensuring the conservation of mass and momentum in the analyzed region. An approximate Riemannian solver can handle discontinuities in the flow state at the interfaces of adjacent computational cells. Thus, flood evolution simulations can still obtain stable and accurate interface flux calculations even in scenarios with drastic flow changes (e.g., dam breaks, overtopping, and rapids on steep mountain slopes), significantly improving the overall reliability and accuracy of the simulation.

[0100] In the above specific implementation method, the net rainfall rate The simulation uses the input term as the source term to calculate the confluence, solves the two-dimensional shallow water equation, and updates the water depth and velocity of each calculation unit. Intermediate results such as the inundation range, water depth, and velocity at the current moment can be saved during the simulation at the preset output interval. After the simulation ends, all result files are output, including a map of the maximum inundation range, a peak water depth map, and an outlet cross-sectional flow process line. Therefore, the flood simulation scheme provided by the embodiments of this disclosure can effectively simulate flood processes such as flash floods in small watersheds in mountainous areas, outputting rich spatial hydraulic information and providing technical support for flood control and disaster reduction. It should be noted that the specific form of the above output results is only an example, and this disclosure does not limit the content and format of the output results, as long as they can reflect the simulation results of the flood evolution process.

[0101] In other words, by using net rainfall rate as a source term for runoff calculation at each time step, the simulation results include at least one of the following: inundation range, water depth, flow velocity, and flow rate process line. This allows runoff generation and runoff to be updated synchronously in time, improving the coherence and information richness of the flood evolution process.

[0102] Alternatively, the two-dimensional storm flash flood simulation method 1000 based on hydrodynamic coupling may further include using a Graphics Processing Unit (GPU) to execute at least one of steps S3 and S4 in parallel. In other words, in at least one embodiment described above, a GPU may be used to determine the cumulative rainfall and cumulative runoff of the computing unit based on rainfall rate and runoff parameters, and to determine the net rainfall rate of the computing unit based on the cumulative rainfall and cumulative runoff; or, a GPU may be used to perform runoff calculations using the net rainfall rate as a source term to simulate the flood evolution process of the area to be analyzed; or, a GPU may be used to determine the cumulative rainfall and cumulative runoff of the computing unit based on rainfall rate and runoff parameters, and to determine the net rainfall rate of the computing unit based on the cumulative rainfall and cumulative runoff, and to perform runoff calculations using the net rainfall rate as a source term to simulate the flood evolution process of the area to be analyzed.

[0103] Specifically, when using GPUs for parallel execution, each computational unit obtained after discretizing the region to be analyzed can be mapped to a single thread of the GPU, such as a CUDA (Compute Unified Device Architecture) thread. Multiple threads of the GPU can independently execute the streaming computation and / or merging computation of each computational unit. Since the streaming computation between each computational unit is independent of each other, and the data exchange between adjacent computational units in the merging computation can be efficiently completed through the GPU's shared memory or global memory, the GPU can significantly reduce the computation time of each time step under large-scale computational units.

[0104] For example, in a small mountainous watershed containing millions of computing units, GPUs can simulate a flood process lasting tens of hours within hours. This parallel processing approach allows the flood simulation scheme to meet the timeliness requirements of emergency response while maintaining high spatial resolution, thereby enhancing the practicality and deployability of the flood simulation scheme in actual flood control and disaster reduction. It should be noted that the above description of the specific GPU implementation is merely an example, and this disclosure does not limit the parallel computing hardware and programming model used, as long as it can achieve parallel execution of flow generation and / or flow merging calculations on multiple computing units.

[0105] In other words, by using GPUs to perform parallel streaming and / or merging calculations, and mapping each computing unit to an independent thread, the simulation time under large-scale computing units is significantly reduced, meeting the timeliness requirements of emergency response.

[0106] Therefore, according to at least one embodiment of this disclosure, by discretizing the region to be analyzed into multiple computing units and configuring runoff generation parameters for the computing units, spatially distributed processing of runoff generation calculation is achieved, which helps to improve the spatial resolution of runoff generation simulation and reduce local runoff generation estimation bias caused by the use of lumped parameters. Based on the runoff generation parameters and the rainfall rate that changes over time, the cumulative rainfall and cumulative runoff of the computing units are determined, so that the runoff generation calculation can reflect the cumulative effect of the rainfall process in the computing units. Compared with the runoff generation estimation method based only on the total rainfall, this can reduce the net rainfall rate calculation bias caused by ignoring the spatiotemporal distribution characteristics of the rainfall process, which helps to improve the accuracy of runoff generation simulation. The net rainfall rate is directly added to the runoff calculation as a source term, realizing the coupling of runoff generation calculation and runoff calculation, which is beneficial to improving the coherence and accuracy of flood evolution simulation. In addition, by integrating the runoff generation calculation results into the runoff calculation in the form of source terms, the additional data conversion or interpolation steps between runoff generation calculation and runoff calculation are reduced, which helps to simplify the calculation process and improve the overall simulation efficiency.

[0107] Furthermore, the above-mentioned scheme, which is based on the independent configuration of runoff generation parameters by computing units and the determination of net rainfall rate step by step, can effectively adapt to the characteristics of large topographic relief and strong spatial heterogeneity of runoff generation, and is especially suitable for areas with complex geometries such as mountainous watersheds.

[0108] Some embodiments of this disclosure provide a two-dimensional rainstorm and flash flood simulation device based on hydrodynamic coupling. Figure 3 This is a block diagram of a two-dimensional rainstorm and flash flood simulation device 2000 based on hydrodynamic coupling, provided according to an exemplary embodiment of this disclosure.

[0109] like Figure 3 As shown, the two-dimensional rainstorm and flash flood simulation device 2000 based on hydrodynamic coupling provided by the embodiments of this disclosure may include: a geographic data processing unit 100, a rainfall processing unit 200, a runoff generation calculation unit 300, and a runoff calculation unit 400. The geographic data processing unit 100 is configured to discretize the area to be analyzed into multiple calculation units and configure a physical attribute field including runoff generation parameters for each calculation unit. The rainfall processing unit 200 is configured to determine the rainfall rate of the calculation unit over time based on the rainfall data of the area to be analyzed. The runoff generation calculation unit 300 is configured to determine the cumulative rainfall and cumulative runoff of the calculation unit based on the rainfall rate and runoff generation parameters, and to determine the net rainfall rate of the calculation unit based on the cumulative rainfall and cumulative runoff. The runoff calculation unit 400 is configured to perform runoff calculation using the net rainfall rate as a source term to simulate the flood evolution process of the area to be analyzed.

[0110] Runoff can be understood as the process by which rainfall, after deducting losses such as infiltration and evaporation, forms surface runoff. The geographic data processing unit 100 divides a continuous geographic space into a finite number of discrete computational units and independently configures runoff parameters for each computational unit. These runoff parameters characterize the computational unit's ability to convert rainfall into runoff. For example, runoff parameters can be determined by factors such as land use type and soil type. In different hydrological models or application scenarios, runoff parameters can be implemented as different specific parameters. For instance, in some embodiments of this disclosure, runoff parameters may include the number of runoff curves. In other embodiments of this disclosure, runoff parameters may include runoff coefficients, infiltration capacity parameters, etc. It should be noted that the above examples are merely illustrations, and this disclosure does not limit the specific implementation of runoff parameters, as long as they can characterize the computational unit's ability to convert rainfall into runoff.

[0111] In the field of flood simulation, discretizing continuous geographic space into computational units is fundamental to numerical calculations. The geographic data processing unit 100 divides the area to be analyzed into computational units, and there are various options for the division method and unit type.

[0112] For example, the computational units may include structured grids and unstructured grids. Structured grids may have regular topological relationships, with each computational unit arranged in an orderly manner, facilitating program design and data access, and exhibiting high computational efficiency in flood simulation within regular regions. Unstructured grids, on the other hand, have irregular connections between computational units, allowing for better fitting of complex terrain boundaries, and are particularly suitable for geometrically complex regions such as mountainous watersheds. In some embodiments of this disclosure, to simplify data management and computational logic, the region to be analyzed can be discretized into multiple structured grids.

[0113] The size of the computational cells affects the accuracy and computational cost of flood simulation. Using smaller computational cells, or higher-resolution grids, means denser cell distribution, which helps improve the spatial resolution of runoff generation simulation and more finely characterize the spatial distribution features of runoff generation parameters. Conversely, using larger computational cells, or lower-resolution grids, reduces the number of computational cells, thus reducing computational cost. Therefore, high-resolution grids can be used in areas with dramatic topographic changes, such as narrow channels, while low-resolution grids can be used in flat areas, to improve computational efficiency while maintaining the accuracy of flood simulation.

[0114] In some embodiments of this disclosure, the geographic data processing unit 100 may further be configured to: discretize the area to be analyzed into multiple computing units, and configure physical attribute fields for the multiple computing units using geospatial data of the area to be analyzed. Furthermore, the physical attribute fields may also include water-blocking parameters characterizing the ability of the computing units to impede water flow. The geographic data processing unit 100 may also be configured to: in response to information in the geospatial data indicating the presence of water-blocking structures, correct the water-blocking parameters of the computing unit where the water-blocking structure is located based on the information about the water-blocking structure.

[0115] Optionally, geospatial data may include digital elevation models, land use types, soil types, and river cross-section measurement data. Structured and unstructured grids can be generated based on the geospatial data, and each structured or unstructured grid can serve as a computational unit. Computational units can be configured with runoff generation parameters. For example, runoff generation parameters may include at least one of the following: number of runoff curves, runoff coefficient, infiltration capacity parameter, etc.

[0116] Optionally, the physical property field may also include water-blocking parameters characterizing the ability of the computational unit to impede water flow. Alternatively, the computational unit may be configured with water-blocking parameters such as the Manning coefficient. Furthermore, the computational unit may be configured with parameter fields such as topographic elevation. In some embodiments of this disclosure, the computational unit may be configured with only a small number of physical property fields, including runoff generation parameters and water-blocking parameters, thus reducing the number of parameters involved in the entire flood simulation scheme. For example, runoff generation parameters may be represented by the number of runoff curves, and water-blocking parameters may be represented by the Manning coefficient. Both the number of runoff curves and the Manning coefficient have clear physical meanings and mature calibration methods, making them easy to calibrate using measured data or empirical values. This parameter simplicity reduces the difficulty of parameter calibration when applying flood simulation schemes to different watersheds, facilitating the rapid deployment and widespread application of flood simulation schemes.

[0117] Optionally, by utilizing information about water-blocking structures, such as their location and geometric properties, the computational units occupied by these structures can be identified, and the water-blocking effect can be represented by increasing water-blocking parameters within each unit. For example, for bridges, one or more computational units can be identified, and the backwater and obstruction effects of the piers and superstructure on the water flow can be simulated by increasing the Manning coefficient of these units. The magnitude of the increase in the Manning coefficient can be pre-set based on information about the water-blocking structures or calculated using empirical formulas. This information may include pier density, beam bottom clearance, etc. This correction method effectively reflects the impact of water-blocking structures on flood evolution without increasing the complexity of geometric modeling, reducing the computational overhead associated with meticulously depicting the geometric shape of the structures. By representing the water-blocking effect through increasing water-blocking parameters, the applicability of the flood simulation scheme is further enhanced.

[0118] In some embodiments of this disclosure, the rainfall processing unit 200 may also be configured to determine the rainfall rate based on rainfall data of the area to be analyzed using a spatial interpolation method, wherein the rainfall data of the area to be analyzed includes at least one of measured rainfall data from rain gauge stations located in the area to be analyzed and forecast rainfall data.

[0119] Rainfall data can originate from measured data at rain gauge stations or from precipitation forecast data generated by numerical weather prediction methods. Essentially, it is a record of rainfall obtained by sampling at discrete times at finite discrete locations such as rain gauge stations. For example, numerical precipitation forecast data can be gridded forecast field data, which can correspond to discrete computational units, thus directly serving as the rainfall input for each computational unit. It should be noted that the above examples are merely illustrations, and this disclosure does not limit the specific source or form of rainfall data, as long as it can provide the rainfall rate changing over time for each computational unit in the area to be analyzed.

[0120] Rainfall data can be derived from measured data at rain gauge stations or from precipitation forecast data generated by numerical weather prediction methods. Therefore, the flood simulation scheme provided by the embodiments of this disclosure can be used for flood early warning. Furthermore, the flood simulation scheme provided by the embodiments of this disclosure can be modularly designed to facilitate coupling with other functional modules. For example, coupling with a water quality simulation module can analyze pollutant transport and diffusion during floods, and coupling with a sediment transport module can simulate soil erosion and sediment transport caused by flash floods, thereby expanding its application scenarios in integrated watershed management.

[0121] Rainfall processing unit 200 can map discrete rainfall data to each computing unit through spatial interpolation methods, and convert it into rainfall rates that vary with time, thus obtaining the water depth falling onto the computing unit per unit time. By determining the rainfall rate that varies with time for each computing unit, runoff generation calculation can obtain the rainfall intensity input for each time step. Compared to simplified processing methods that only use total rainfall or constant rainfall intensity, it can reflect the impact of rainfall intensity fluctuations over time on the runoff generation process, such as the impact of peak rainfall and intermittent rainfall, providing temporally continuous input data for determining subsequent cumulative rainfall.

[0122] In some embodiments of this disclosure, the runoff calculation unit 300 may also be configured to: determine cumulative rainfall based on rainfall rate on a time-step basis; and determine cumulative runoff based on cumulative rainfall and runoff parameters on a time-step basis. Furthermore, in some embodiments of this disclosure, the runoff calculation unit 300 may also be configured to: determine the net rainfall rate of the calculation unit on a time-step basis based on cumulative rainfall and cumulative runoff.

[0123] A "time step" discretizes a continuous rainfall process into multiple consecutive time segments, each with a predetermined duration. The embodiments of this disclosure do not restrict whether the lengths of the time steps are equal. One option is to use a fixed time step with equal intervals; another option is to employ a variable time step strategy based on changes in rainfall intensity or computational accuracy requirements. For example, a shorter time step can be used during periods of drastic rainfall intensity changes to capture details, while a longer time step can be used during periods of calm to reduce computational load. As long as the simulation process can proceed sequentially in discrete time order and the rainfall rate can be approximated as constant within each time step, it falls within the time-step category defined by this disclosure. This flexibility allows flood simulation schemes to adapt to different computational resources and accuracy requirements, enhancing their applicability in various application scenarios.

[0124] By updating the cumulative rainfall of the computational unit step-by-step, the cumulative rainfall can accurately reflect the cumulative effect of rainfall intensity fluctuations over time, rather than relying solely on the total amount of a single rainfall event. Based on this, the cumulative runoff is determined step-by-step using this cumulative rainfall and the computational unit's own runoff generation parameters, conforming to the fundamental law of nonlinear growth of runoff with cumulative rainfall. Furthermore, determining the net rainfall rate step-by-step allows the net rainfall rate to dynamically respond to real-time changes in rainfall intensity within a time step. Compared to estimating runoff generation solely based on the total amount of a single rainfall event or assuming a constant rainfall intensity, this method reduces the calculation bias of the net rainfall rate caused by neglecting the temporal distribution characteristics of the rainfall process, thus contributing to improved accuracy in runoff generation simulation.

[0125] Since the determination of cumulative rainfall, cumulative runoff, and net rainfall rate is performed independently for each calculation unit, and the runoff generation parameters can differ between different calculation units (e.g., due to variations in land use and soil type), this implementation method can precisely characterize the distribution features of runoff generation capacity in space and dynamically respond to changes in rainfall processes in time, achieving refined simulation in both spatial and temporal dimensions. This spatiotemporal integrated processing approach makes the flood simulation scheme provided by the embodiments of this disclosure particularly suitable for simulating flash floods in mountainous small watersheds with complex terrain and strong spatial heterogeneity of runoff generation.

[0126] Alternatively, the runoff calculation unit 300 can also be configured to: determine the cumulative rainfall loss of the calculation unit step by step based on the cumulative rainfall and cumulative runoff; determine the rainfall loss rate of the calculation unit step by step based on the rate of change of the cumulative rainfall loss; and determine the net rainfall rate step by step based on the rainfall rate and the rainfall loss rate.

[0127] Because cumulative rainfall and cumulative runoff are updated at each time step, the net rainfall rate can respond in real time to changes in rainfall intensity, thus avoiding the biases caused by using a fixed loss rate or relying solely on total rainfall to estimate runoff generation. Through iterative calculations at each time step, the runoff generation results can be updated synchronously with subsequent runoff calculations on the same time scale, providing accurate and dynamic source term inputs for flood evolution simulation, which helps improve the overall accuracy and reliability of the simulation.

[0128] In some embodiments of this disclosure, the runoff calculation unit 400 may also be configured to perform runoff calculations step-by-step, using net rainfall rate as a source term, to simulate the flood evolution process of the area to be analyzed. The simulation results of the flood evolution process include at least one of the flood inundation extent, water depth, flow velocity, and flow rate hydrograph. In this embodiment, runoff generation calculation can be synchronized with runoff calculation in time. Within each time step, runoff generation results are entered into the runoff calculation in real time, updating water depth and flow velocity, thereby reducing simulation errors caused by the mismatch between runoff generation and runoff timescales. This synchronization helps improve the coherence and accuracy of the flood evolution process, making the simulation results closer to the dynamic development process of actual floods.

[0129] In addition, in some embodiments of this disclosure, the runoff calculation unit 400 can also be configured to: use net rainfall rate as a source term and perform runoff calculation based on the hydrodynamic control equations to simulate the flood evolution process of the area to be analyzed, wherein the hydrodynamic control equations include two-dimensional shallow water equations. In this embodiment, the net rainfall rate is directly embedded as a source term into the two-dimensional hydrodynamic control equations and participates in the equation solution, thereby achieving direct coupling between runoff generation and runoff at the control equation level. Since runoff generation and runoff are synchronized on the time scale, the time mismatch problem that may be introduced by using runoff generation results as independent boundary condition inputs is reduced. The net rainfall rate is directly integrated into the runoff equation in the form of a source term, eliminating the need for additional data conversion or spatial interpolation between runoff generation and runoff calculations, which helps to simplify the calculation process and improve the overall simulation efficiency. The information in the output results, such as the maximum flood inundation range map, peak water depth map, and outlet section flow process line, can provide intuitive and quantitative data support for flood disaster prevention and risk assessment.

[0130] In some embodiments of this disclosure, at least one of the flow generation computing unit 300 and the flow merging computing unit 400 can be implemented as a GPU. When using GPU parallel execution, each computing unit obtained after discretizing the region to be analyzed can be mapped to a single thread of the GPU. Multiple threads of the GPU can independently execute the flow generation computing and / or flow merging computing of each computing unit. Since the flow generation computing between each computing unit is independent of each other, and the data exchange between adjacent computing units in the flow merging computing can be efficiently completed through the shared memory or global memory of the GPU, the GPU can significantly reduce the computing time of each time step under large-scale computing units.

[0131] This parallel processing approach enables the flood simulation scheme to meet the computational timeliness requirements of emergency response while maintaining high spatial resolution, thereby enhancing the practicality and deployability of the flood simulation scheme in actual flood control and disaster reduction. It should be noted that the above description of the specific GPU implementation is merely an example, and this disclosure does not limit the parallel computing hardware and programming model used, as long as it can achieve parallel execution of flow generation and / or flow merging calculations on multiple computing units.

[0132] Therefore, according to at least one embodiment of this disclosure, by discretizing the region to be analyzed into multiple computing units and configuring runoff generation parameters for the computing units, spatially distributed processing of runoff generation calculation is achieved, which helps to improve the spatial resolution of runoff generation simulation and reduce local runoff generation estimation bias caused by the use of lumped parameters. Based on the runoff generation parameters and the rainfall rate that changes over time, the cumulative rainfall and cumulative runoff of the computing units are determined, so that the runoff generation calculation can reflect the cumulative effect of the rainfall process in the computing units. Compared with the runoff generation estimation method based only on the total rainfall, this can reduce the net rainfall rate calculation bias caused by ignoring the spatiotemporal distribution characteristics of the rainfall process, which helps to improve the accuracy of runoff generation simulation. The net rainfall rate is directly added to the runoff calculation as a source term, realizing the coupling of runoff generation calculation and runoff calculation, which is beneficial to improving the coherence and accuracy of flood evolution simulation. In addition, by integrating the runoff generation calculation results into the runoff calculation in the form of source terms, the additional data conversion or interpolation steps between runoff generation calculation and runoff calculation are reduced, which helps to simplify the calculation process and improve the overall simulation efficiency.

[0133] Furthermore, the above-mentioned scheme, which is based on the independent configuration of runoff generation parameters by computing units and the determination of net rainfall rate step by step, can effectively adapt to the characteristics of large topographic relief and strong spatial heterogeneity of runoff generation, and is especially suitable for areas with complex geometries such as mountainous watersheds.

[0134] Various embodiments of this disclosure have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical applications, or technological improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

[0135] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this disclosure can be achieved, and this is not limited herein.

[0136] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A two-dimensional simulation method for flash floods caused by rainstorms based on hydrodynamic coupling, characterized in that, The method includes: The region to be analyzed is discretized into multiple computational units, and the computational units are configured with physical property fields including flow generation parameters; Based on the rainfall data of the area to be analyzed, the rainfall rate of the calculation unit over time is determined; Based on the rainfall rate and the runoff parameters, the cumulative rainfall and cumulative runoff of the calculation unit are determined, and based on the cumulative rainfall and cumulative runoff, the net rainfall rate of the calculation unit is determined; and The net rainfall rate is used as a source term for runoff calculation to simulate the flood evolution process of the area to be analyzed.

2. The method according to claim 1, wherein, Determining the cumulative rainfall and cumulative runoff of the calculation unit based on the rainfall rate and the runoff parameters includes: On a time-step basis, the cumulative rainfall is determined based on the rainfall rate; and At each time step, the cumulative runoff is determined based on the cumulative rainfall and the runoff parameters.

3. The method according to claim 1, wherein, Determining the net rainfall rate of the calculation unit based on the cumulative rainfall and the cumulative runoff includes: The net rainfall rate of the calculation unit is determined step by step based on the cumulative rainfall and the cumulative runoff.

4. The method according to claim 3, wherein, The step-by-step determination of the net rainfall rate of the calculation unit based on the cumulative rainfall and the cumulative runoff includes: For each time step, the cumulative rainfall loss of the calculation unit is determined based on the cumulative rainfall and the cumulative runoff. For each time step, based on the rate of change of the cumulative rainfall loss, the rainfall loss rate of the calculation unit is determined; and At each of the stated time steps, the net rainfall rate is determined based on the rainfall rate and the rainfall loss rate.

5. The method according to claim 1, wherein, The step of using the net rainfall rate as a source term for runoff calculation to simulate the flood evolution process of the area to be analyzed includes: At each time step, the net rainfall rate is used as a source term for runoff calculation to simulate the flood evolution process of the area to be analyzed. The simulation results of the flood evolution process include at least one of the following: flood inundation range, water depth, flow velocity, and flow rate process curve.

6. The method according to claim 1 or 5, wherein, The step of using the net rainfall rate as a source term for runoff calculation to simulate the flood evolution process of the area to be analyzed includes: The net rainfall rate is used as the source term, and the runoff calculation is performed based on the hydrodynamic control equations to simulate the flood evolution process of the area to be analyzed. The hydrodynamic control equations include two-dimensional shallow water equations.

7. The method according to claim 1, wherein, The method further includes performing at least one of the following steps in parallel using a graphics processor: Based on the rainfall rate and the runoff parameters, the cumulative rainfall and cumulative runoff of the calculation unit are determined, and based on the cumulative rainfall and cumulative runoff, the net rainfall rate of the calculation unit is determined. The net rainfall rate is used as a source term for runoff calculation to simulate the flood evolution process of the area to be analyzed.

8. The method according to claim 1, wherein, The determination of the rainfall rate over time by the calculation unit based on the rainfall data of the area to be analyzed includes: The rainfall rate is determined based on rainfall data from the region to be analyzed using spatial interpolation methods. The rainfall data for the area to be analyzed includes at least one of the measured rainfall data from rain gauge stations located in the area to be analyzed and the forecast rainfall data.

9. The method according to claim 1, wherein, The step of discretizing the region to be analyzed into multiple computational units and configuring a physical property field including flow generation parameters for the computational units includes: The region to be analyzed is discretized into multiple computing units, and the physical attribute field is configured for the multiple computing units using the geospatial data of the region to be analyzed. The physical property field further includes water-blocking parameters characterizing the ability of the computing unit to impede water flow, and the method further includes: In response to information indicating the presence of a water-blocking structure in the geospatial data, the water-blocking parameters of the computing unit containing the water-blocking structure are corrected based on the information of the water-blocking structure.

10. A two-dimensional rainstorm and flash flood simulation device based on hydrodynamic coupling, characterized in that, The device includes: The geographic data processing unit is configured to discretize the area to be analyzed into multiple computing units and configure a physical attribute field including runoff parameters for the computing units; A rainfall processing unit is configured to determine the rainfall rate that the calculation unit changes over time based on rainfall data of the area to be analyzed. A runoff calculation unit is configured to determine the cumulative rainfall and cumulative runoff volume of the calculation unit based on the rainfall rate and the runoff parameters, and to determine the net rainfall rate of the calculation unit based on the cumulative rainfall and the cumulative runoff volume; and The runoff calculation unit is configured to perform runoff calculations using the net rainfall rate as a source term to simulate the flood evolution process of the area to be analyzed.

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