Mountainous river flow modulus dynamic simulation method

Abstract

This invention relates to the field of dynamic simulation of river flow modulus, and discloses a method for dynamic simulation of flow modulus in mountainous rivers. First, it acquires data on hydrological and meteorological elements, topographic river networks, soil properties, land cover, and glacier characteristics. Based on this data, it divides the river into sub-basins and contour zones, constructs a watershed hydrological model, and calculates the flow of each sub-basin along the main river channel. Based on satellite remote sensing data and the distribution location of the sub-basins along the main river channel, it calculates the average gradient of the sub-basins. Based on the flow and average gradient of each sub-basin along the main river channel, it calculates the flow modulus of all sub-basins along the river channel in the hydrological model under different seasons using the flow modulus calculation formula. This invention solves the problem in existing technologies where it is impossible to conduct on-site measurements of flow and gradient in mountainous rivers, thus making it impossible to draw dynamic flow modulus data for mountainous rivers.

Description

Technical Field

[0001] This invention relates to the field of dynamic simulation of river flow modulus, and more particularly to a method for dynamic simulation of river flow modulus in mountainous areas. Background Technology

[0002] Currently, a large number of studies on ecological flow theory are being conducted in China, revealing the regulatory role of water flow conditions (flow rate, etc.) in the maintenance of aquatic ecosystems. However, in mountain rivers, especially in rapid rivers with large drops, the influence of river channel characteristics (slope, etc.) on aquatic organisms cannot be ignored.

[0003] Due to its theoretical rigor (based on classical hydraulic equations) and parameter integration (coupling flow rate (Q-flow rate) and flow regime characteristics (i-gradient), the flow modulus has the potential value in characterizing the ecological state of rivers. Its mathematical framework, by integrating cross-sectional geometric properties and dynamic conditions, can avoid the morphological characterization defects of simple flow indicators (such as ignoring the driving force of river slope on the distribution of benthic organisms).

[0004] However, due to the rapid and treacherous flow patterns and steep banks of mountain rivers, it is extremely difficult to conduct on-site measurements of flow and gradient data (such as the Yarlung Tsangpo Grand Canyon section). Therefore, a dynamic simulation method for the flow modulus of mountain rivers is needed to reveal the spatiotemporal variation patterns of the flow modulus of mountain rivers, and thus characterize the dynamic response of the river's aquatic ecosystem. Summary of the Invention

[0005] The present invention aims to provide a dynamic simulation method for the flow modulus of mountain rivers, in order to solve the problem in the prior art that it is impossible to measure the flow and gradient in mountain rivers on-site, so as to make it impossible to draw dynamic flow modulus of mountain rivers.

[0006] To achieve the above objectives, the present invention provides the following method:

[0007] The present invention provides a method for dynamic simulation of the flow modulus of mountain rivers:

[0008] S1: Acquire hydrological and meteorological, topographic and river network, soil properties, land cover and glacier characteristic data, divide sub-basins and contour zones according to the data, construct a watershed hydrological model, and calculate the flow of each sub-basin through which the main river channel passes;

[0009] S2: Calculate the average gradient of the sub-basin based on satellite remote sensing data and the distribution location of the main river channel through the sub-basin;

[0010] S3: Based on the flow rate of each sub-basin along the main river channel and the average gradient of the sub-basin, calculate the flow modulus of all sub-basins along the river channel in the hydrological model under different seasons using the flow modulus calculation formula.

[0011] Preferably, the accuracy of the watershed hydrological model simulation is determined by comparing actual data from the survey sections of the main hydrological stations in the watershed.

[0012] Preferably, the flow rate of each sub-basin along the main channel is the inverted flow rate of each sub-basin along the main channel under the division of the watershed hydrological model.

[0013] Preferably, the simulation accuracy of the watershed hydrological model is measured by the Nash coefficient and the relative error value; when the Nash coefficient is greater than 0.7 and the absolute value of the relative error is less than 5%, the runoff process simulation results of the watershed hydrological model are considered reliable, and the Nash coefficient is... and relative error value The specific formula is as follows:

[0014]

[0015]

[0016] in, Represents the Nash coefficient. This represents the relative error value, where N represents the total number of days. and These represent the observed and simulated flow rates on day n, respectively. The average observed flow rate during this period. and These represent the observed and simulated runoff results for day n, respectively.

[0017] Preferably, the satellite remote sensing data is a high-resolution digital elevation model.

[0018] Preferably, the step of calculating the average gradient of the sub-basin based on satellite remote sensing data and the distribution location of the main river channel through the sub-basin includes: calculating the drop and length of the river channel in the sub-basin based on the satellite remote sensing data to obtain the average gradient of the sub-basin.

[0019] Preferably, the flow modulus calculation formula is obtained by rearranging terms of the open channel uniform flow rate formula; the open channel uniform flow rate formula is:

[0020] (Formula for flow rate of uniform flow)

[0021] Where Q is the flow rate, A is the cross-sectional area of ​​the water passage, v is the flow velocity, R is the hydraulic radius, i is the hydraulic gradient, and C is the Chezi coefficient;

[0022] The formula for calculating the flow modulus is:

[0023] .

[0024] Where K is the flow modulus.

[0025] Preferably, the flow modulus value is obtained by combining the flow modulus calculation formula with the inverted flow and the measured gradient.

[0026] Preferably, the inverted flow rate and the measured slope are obtained by setting the boundary of the fluid domain geometric model and creating an auxiliary surface using geometric topology to enclose the area enclosed by the terrain free surface, the auxiliary surface and the mountain land, forming a fluid domain geometric model for calculation.

[0027] The beneficial effects of this invention are as follows: This invention, by acquiring data on hydrological and meteorological factors, topographical river networks, soil properties, land cover, and glacier characteristics, divides the river basin into sub-basins and contour zones, constructs a watershed hydrological model, and calculates the flow of each sub-basin along the main river channel; based on a high-resolution digital elevation model and the distribution location of the sub-basins along the main river channel, it calculates the average gradient of the sub-basins; and based on the flow modulus calculation formula, it calculates the flow modulus of all sub-basins along the river channel in the hydrological model under different seasons. Currently, there are no relevant methods for dynamic simulation of river flow modulus. The dynamic simulation method for mountain river flow modulus based on hydrological models and satellite remote sensing data provided by this invention effectively solves the problem of not being able to conduct on-site measurement of flow and gradient in mountainous rivers, and provides an implementation path for dynamic simulation of river flow modulus in complex environments. Attached Figure Description

[0028] To more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0029] Figure 1 A flowchart illustrating a dynamic simulation method for the flow modulus of a mountain river provided in an embodiment of the present invention;

[0030] Figure 2 A terrain map of a steep and rugged canyon section in a mountainous area provided for an embodiment of the present invention;

[0031] Figure 3 This is a simulation diagram of the sub-basin division of a hydrological model for a canyon section in a mountainous area, provided in an embodiment of the present invention.

[0032] Figure 4 A schematic diagram of the monthly average flow at the runoff simulation calibration stations of Yangcun, Nuxia and Dexing hydrological stations, provided for embodiments of the present invention;

[0033] Figure 5A schematic diagram of the daily average flow at the runoff simulation calibration stations of Yangcun, Nuxia and Dexing hydrological stations, provided for embodiments of the present invention;

[0034] Figure 6 The slope distribution of the main areas of mountain rivers and the schematic diagram of wide valleys and canyon sections based on the slope distribution are provided for embodiments of the present invention.

[0035] Figure 7 A schematic diagram illustrating the spatiotemporal distribution differences of flow modulus calculated using hydrological models and satellite remote sensing data, provided for embodiments of the present invention.

[0036] Figure 8 This is a schematic diagram illustrating the time-distribution variation of the flow modulus provided in an embodiment of the present invention. Detailed Implementation

[0037] To enable those skilled in the art to better understand the present invention, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0038] The terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this invention are used to distinguish different objects, not to describe a specific order. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, apparatus, product, or end that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to these processes, methods, products, or ends.

[0039] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0040] Currently, a large number of studies on ecological flow theory are being conducted in China, revealing the regulatory role of water flow conditions (flow rate, etc.) in the maintenance of aquatic ecosystems. However, in mountain rivers, especially in rapid rivers with large drops, the influence of river channel characteristics (slope, etc.) on aquatic organisms cannot be ignored.

[0041] Due to its theoretical rigor (based on classical hydraulic equations) and parameter integration (coupling flow rate (Q-flow rate) and flow regime characteristics (i-gradient), the flow modulus has the potential value in characterizing the ecological state of rivers. Its mathematical framework, by integrating cross-sectional geometric properties and dynamic conditions, can avoid the morphological characterization defects of simple flow indicators (such as ignoring the driving force of river slope on the distribution of benthic organisms).

[0042] However, due to the rapid and treacherous flow patterns and steep banks of mountain rivers, it is extremely difficult to conduct on-site measurements of flow and gradient data (such as the Yarlung Tsangpo Grand Canyon section). Therefore, a dynamic simulation method for the flow modulus of mountain rivers is needed to reveal the spatiotemporal variation patterns of the flow modulus of mountain rivers, and thus characterize the dynamic response of the river's aquatic ecosystem.

[0043] The present invention aims to provide a dynamic simulation method for the flow modulus of mountain rivers, in order to solve the problem in the prior art that it is impossible to measure the flow and gradient in mountain rivers on-site, so as to make it impossible to draw dynamic flow modulus of mountain rivers.

[0044] like Figure 1 As shown in the figure, a specific embodiment of the present invention provides a method for dynamic simulation of the flow modulus of mountain rivers, including the following steps:

[0045] S1: Acquire data on hydrological and meteorological features, topography and river network, soil properties, land cover and glacier characteristics, divide sub-basins and contour zones based on the data, construct a watershed hydrological model, and calculate the flow of each sub-basin through which the main river channel passes.

[0046] In this embodiment of the invention, the accuracy of the watershed hydrological model simulation is determined by comparing actual data from the survey sections of the main hydrological stations in the watershed; the flow rate of each sub-basin along the main channel is the inverted flow rate of each sub-basin along the main channel under the watershed hydrological model; the simulation accuracy of the watershed hydrological model is measured by the Nash coefficient and the relative error value; when the Nash coefficient is greater than 0.7 and the absolute value of the relative error is less than 5%, the runoff process results simulated by the watershed hydrological model are considered reliable, and the Nash coefficient... and relative error value The specific formula is as follows:

[0047]

[0048]

[0049] in, Represents the Nash coefficient. This represents the relative error value, where N represents the total number of days. and These represent the observed and simulated flow rates on day n, respectively. The average observed flow rate during this period. and These represent the observed and simulated runoff results for day n, respectively.

[0050] S2: Calculate the average gradient of the sub-basin based on satellite remote sensing data and the distribution location of the main river channel through the sub-basin.

[0051] In this embodiment of the invention, the satellite remote sensing data is a high-resolution digital elevation model; the step of calculating the average gradient of the sub-basin based on the satellite remote sensing data and the distribution location of the main river channel through the sub-basin includes: calculating the drop and length of the river channel in the sub-basin based on the satellite remote sensing data to obtain the average gradient of the sub-basin.

[0052] S3: Based on the flow rate and average gradient of each sub-basin along the main channel, the flow modulus of all sub-basins along the channel in the hydrological model is calculated in different seasons using the flow modulus calculation formula.

[0053] In this embodiment of the invention, the formula for calculating the flow modulus is obtained by rearranging terms of the formula for uniform flow in an open channel; the formula for uniform flow in an open channel is:

[0054] (Formula for flow rate of uniform flow)

[0055] Where Q is the flow rate, A is the cross-sectional area of ​​the water passage, v is the flow velocity, R is the hydraulic radius, i is the hydraulic gradient, and C is the Chezi coefficient;

[0056] The formula for calculating the flow modulus is:

[0057] .

[0058] Wherein, K is the flow modulus; the flow modulus value is obtained by combining the flow modulus calculation formula with the inverted flow and the surveyed slope; the inverted flow and the surveyed slope are obtained by setting the boundary of the fluid domain geometric model and creating auxiliary surfaces using geometric topology, enclosing the area enclosed by the terrain free surface, the auxiliary surface and the mountain land, forming the fluid domain geometric model calculation. Specific Implementation

[0059] like Figure 2 As shown, the steep and rugged terrain of a mountain canyon section fully illustrates the difficulty of measuring river gradient and flow rate on the spot.

[0060] like Figure 3As shown, the hydrological model divides the watershed into sub-basins. The model simulation area is a mountainous watershed with a total area of ​​241,000 km². Based on the distribution of the watershed's river system, the watershed is divided into 10,234 sub-basins, which are further subdivided into several contour zones based on the topographic relief within the watershed. Sub-basins located in mountainous areas are divided into a maximum of 10 contour zones, while sub-basins in plain areas belong to the same contour zone. Thus, a total of 20,345 contour zones were identified in the watershed, which are the simulation calculation units of the model.

[0061] like Figure 4 , Figure 5 As shown, Yangcun, Nuxia, and Dexing hydrological stations were selected as calibration sites for the runoff simulation of the hydrological model. Simultaneously, 1980-1984 was designated as the warm-up period, 1985-2004 as the calibration period, and 2005-2024 as the validation period, to calibrate and validate the monthly runoff processes constructed by the watershed distributed hydrological model WEP-L. To evaluate the runoff simulation accuracy of the model downscaled to a daily scale, daily observed flow rates from available hydrological stations were used for validation. The Nash coefficient (NSE) and relative error (ReError) were used to measure the simulation accuracy of the distributed hydrological model. When the Nash coefficient was greater than 0.7 and the absolute value of the relative error was less than 5%, the runoff process simulation results of the watershed distributed hydrological model were considered reliable.

[0062] from Figure 4 The results show that the watershed hydrological model simulates the natural inflow processes (monthly scale) at key stations (Yangcun, Nuxia, and Dexing hydrological stations) from 1985 to 2024 relatively well. The Nash coefficients for all three stations are above 0.7 with relative errors less than 5% throughout the period. The lowest Nash coefficient was observed at Dexing (0.70), while the highest was at Nuxia (0.88), indicating a decrease in the accuracy of the simulated runoff process after the Great Bend, possibly due to errors in glacier and snowmelt simulations. The relative errors of runoff at all three stations fluctuated between -2.7% and 4.1% throughout the period, indicating high accuracy in simulating water inflow. During the calibration period, the Nash coefficient and relative error of Yangcun Hydrological Station were 0.79 and -0.7%, respectively; those of Nuxia Hydrological Station were 0.88 and 1.8%, respectively. During the verification period, the Nash coefficient and relative error of Yangcun Hydrological Station were 0.77 and 4.1%, respectively; those of Nuxia Hydrological Station were 0.85 and -2.7%, respectively; and those of Dexing Hydrological Station were 0.70 and 3.2%, respectively.

[0063] from Figure 5 The results show that the hydrological model maintains high simulation accuracy even after downscaling. Comparing the simulated daily runoff processes at the Nuxia hydrological station (2003-2013) with observed data, the Nash coefficient is greater than 0.7 and the relative error is less than 5%, with a Nash coefficient of 0.83 and a relative error of -3.0%. Furthermore, the accuracy of the simulations at the Yangcun and Dexing hydrological stations (2017-2024) is also acceptable.

[0064] In summary, the hydrological model demonstrates good results in simulating the natural inflow process of the watershed at the monthly scale, and it maintains high simulation accuracy even when scaled down to the daily scale, providing a solid foundation for further simulation of the spatiotemporal variation of the flow modulus.

[0065] like Figure 6 As shown, the gradient distribution of major mountain rivers and the differences between wide valley and canyon sections based on the gradient distribution are illustrated.

[0066] like Figure 7 , Figure 8 As shown, the spatiotemporal distribution of the flow modulus was calculated using hydrological models and satellite remote sensing data. Due to the continuous confluence process, the flow modulus gradually increases from upstream to downstream, but due to topographic relief, the flow modulus in wide valley sections is generally greater than that in canyon sections.

[0067] Due to topographic and geological tectonic activities, the flow modulus exhibits significant spatial differences. Figure 7 Based on multi-year averages, the flow modulus for the entire river section is at least 60 × 10⁻⁶. 3 m 3 / s or more (multi-year average modulus: 67.9 × 10 3 m 3 / s). Among them, the flow modulus of the wide valley section (ML-YSZ) is at least 100×10 3 m 3 / s or more (average gradient: 0.34‰; multi-year modulus mean: 105.5×10×10 3 m 3 / s), while the canyon section (below YSZ) is between 10 and 50 × 10. 3 m 3 Fluctuations within a range of / s (average gradient: 7.94‰; multi-year modulus mean: 23.8×10⁻⁶) 3 m 3 / s). As other tributaries flow in, the flow modulus of the canyon section (upstream of Dexing) increases, ranging from 20 to 100 × 10⁻⁶. 3 m 3 / s range (average gradient: 7.03‰; multi-year average modulus: 49.8×10 3 m 3 / s). In the downstream section where wide valleys and gorges intersect (below MT), as tributaries further converge, the flow modulus fluctuates from 50 to 200 × 10⁻⁶. 3 m 3 / s interval (average gradient: 2.23‰; multi-year average modulus: 92.8×10) 3 m 3 / s).

[0068] The seasonal evolution of hydrological processes is the main reason for the variability in the temporal distribution of flow modulus. Figure 8 ).

[0069] During the dry season (January to March), the flow modulus fluctuates between 0 and 100 × 10⁻⁶. 3 m 3 / s, of which the average value for the ML-YSZ river section is 19.5×10 3 m 3 / s, the average value of the river section below YSZ is 4.5×10 3 m 3 / s, the average value of the river section above Dexing is 10.3×10 3 m 3 / s, the average value for the river section below MT is 20.6×10 3 m 3 / s, the recommended control target value is 20×10 3 m 3 / s.

[0070] As the inflow further increases, the fluctuation range of the pre-flood season (April-June) flow modulus rises to 0 to 1200×10⁻⁶. 3 m 3 / s, of which the average value for the ML-YSZ river section is 56.6×10 3 m 3 / s, the average value of the river section below YSZ is 12.9×10 3 m 3 / s, the recommended control target value is 20×10 3 m 3 / s, the average value of the river section above Dexing is 49.6×10 3 m 3 / s, the average value for the river section below MT is 93.1×10 3 m 3 / s.

[0071] The fluctuation range of the flow modulus after the flood season (October-December) is consistent with that before the flood season, and the spatial difference in the flow modulus between these two periods is the most significant. Among them, the average value of the flow modulus in the ML-YSZ section after the flood season is 80.2×10. 3 m 3 / s, the average value of the river section below YSZ is 18.4×10 3 m 3 / s, the average value of the river section above Dexing is 31.8×10 3 m 3 / s, the average value for the river section below MT is 59.3×10 3 m 3 / s.

[0072] The large inflow during the flood season (July-September) significantly raises the lower limit of flow modulus fluctuation, from 0×10 3 m 3 / s increased to 20×10 3 m 3 / s, of which the average value for the ML-YSZ river section is 265.8×10 3 m 3 / s, the average value of the river section below YSZ is 59.4×10 3 m 3 / s, the average value of the river section above Dexing is 107.5×10 3 m 3 / s, the average value for the river section below MT is 198.1×10 3 m 3 / s.

[0073] The beneficial effects of this invention are as follows: This invention, by acquiring data on hydrological and meteorological factors, topographical river networks, soil properties, land cover, and glacier characteristics, divides the river basin into sub-basins and contour zones, constructs a watershed hydrological model, and calculates the flow of each sub-basin along the main river channel; based on a high-resolution digital elevation model and the distribution location of the sub-basins along the main river channel, it calculates the average gradient of the sub-basins; and based on the flow modulus calculation formula, it calculates the flow modulus of all sub-basins along the river channel in the hydrological model under different seasons. Currently, there are no relevant methods for dynamic simulation of river flow modulus. The dynamic simulation method for mountain river flow modulus based on hydrological models and satellite remote sensing data provided by this invention effectively solves the problem of not being able to conduct on-site measurement of flow and gradient in mountainous rivers, and provides an implementation path for dynamic simulation of river flow modulus in complex environments.

[0074] The above descriptions are merely embodiments of the present invention. Commonly known technical solutions or characteristics are not described in detail here. It should be noted that those skilled in the art can make various modifications and improvements without departing from the present invention, and these should also be considered within the scope of protection of the present invention. These modifications and improvements will not affect the effectiveness of the present invention or the practicality of the patent. The scope of protection claimed in this application should be determined by the content of its claims, and the specific embodiments described in the specification can be used to interpret the content of the claims.

Claims

1. A method for dynamic simulation of the flow modulus of mountain rivers, characterized in that, The method includes: S1: Acquire hydrological and meteorological, topographic and river network, soil properties, land cover and glacier characteristic data, divide sub-basins and contour zones according to the data, construct a watershed hydrological model, and calculate the flow of each sub-basin through which the main river channel passes; S2: Calculate the average gradient of the sub-basin based on satellite remote sensing data and the distribution location of the main river channel through the sub-basin; S3: Based on the flow rate of each sub-basin along the main river channel and the average gradient of the sub-basin, calculate the flow modulus of all sub-basins along the river channel in the hydrological model under different seasons using the flow modulus calculation formula.

2. The method for dynamic simulation of flow modulus in mountainous rivers according to claim 1, characterized in that: The accuracy of the watershed hydrological model simulation was determined by comparing the actual data from the survey sections of the main hydrological stations in the watershed.

3. The method for dynamic simulation of flow modulus in mountainous rivers according to claim 1, characterized in that: The flow rate of each sub-basin along the main channel is the inverted flow rate of each sub-basin along the main channel under the division of the watershed hydrological model.

4. The method for dynamic simulation of flow modulus in mountainous rivers according to claim 1, characterized in that: The accuracy of the watershed hydrological model simulation is measured by the Nash coefficient and the relative error value. When the Nash coefficient is greater than 0.7 and the absolute value of the relative error is less than 5%, the runoff process simulation results of the watershed hydrological model are considered reliable. and relative error value The specific formula is as follows: in, Represents the Nash coefficient. This represents the relative error value, where N represents the total number of days. and These represent the observed and simulated flow rates on day n, respectively. The average observed flow rate during this period. and These represent the observed and simulated runoff results for day n, respectively.

5. The method for dynamic simulation of flow modulus in mountainous rivers according to claim 1, characterized in that: The satellite remote sensing data is a high-resolution digital elevation model.

6. The method for dynamic simulation of flow modulus in mountainous rivers according to claim 1, characterized in that, The step of calculating the average gradient of the sub-basin channel based on satellite remote sensing data and the distribution location of the main river channel through the sub-basin includes: The drop and length of the river channel in the sub-basin are calculated based on the satellite remote sensing data to obtain the average gradient of the river channel in the sub-basin.

7. The method for dynamic simulation of flow modulus in mountainous rivers according to claim 1, characterized in that: The formula for calculating the flow modulus is obtained by rearranging terms of the formula for uniform flow in an open channel. The formula for the uniform flow rate of the open channel is: (Formula for flow rate of uniform flow) Where Q is the flow rate, A is the cross-sectional area of ​​the water passage, v is the flow velocity, R is the hydraulic radius, i is the hydraulic gradient, and C is the Chezi coefficient; The formula for calculating the flow modulus is: 。 Where K is the flow modulus.

8. The method for dynamic simulation of flow modulus in mountainous rivers according to claim 7, characterized in that: The flow modulus value is obtained by combining the flow modulus calculation formula with the inverted flow and the measured gradient.

9. The method for dynamic simulation of flow modulus in mountainous rivers according to claim 8, characterized in that: The inverted flow rate and measured gradient are obtained by setting the boundary of the fluid domain geometric model and creating auxiliary surfaces using geometric topology. The area enclosed by the free surface of the terrain, the auxiliary surface, and the mountainous land is closed, forming a fluid domain geometric model for calculation.

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