A method for calculating low-water flow in river channels based on Manning's formula

Abstract

This invention discloses a method for calculating river flow during low water levels based on the Manning formula, comprising the following steps: S1, data collection and gridding processing; S2, calculation of water flow direction in cells; S3, calculation of water flow velocity in cells; S4, calculation of water exchange volume and water level in cells; S5, correction of water volume in cells; and S6, updating of water level information in cells. The advantages are: it proposes a method for calculating water flow that can solve the instability problem in calculating river flow during low water levels and simultaneously achieve two-dimensional spatial calculation. This method maintains the simplicity and practicality of one-dimensional hydrodynamic methods. While ensuring the efficiency and accuracy of water flow calculation, it solves the problem of the inapplicability or instability of previous hydrodynamic methods in shallow water depths and dry riverbeds, realizing water flow calculation for rivers during the low water season and providing technical support for engineering practices such as river replenishment scheduling during the low water season.

Description

Technical Field

[0001] This invention relates to the field of river hydrodynamics, and in particular to a method for calculating river low-water flow based on Manning's formula. Background Technology

[0002] With the impacts of human activities and global climate change, water replenishment scheduling during the dry season has become one of the most important tasks in watershed ecological management. Maximizing water conservation and scientifically and effectively allocating limited water resources to precisely meet the ecological water needs of the watershed is of practical significance, and this work is inseparable from the calculation of river flow during the dry season. Therefore, efficiently and accurately simulating the evolution of river flow during the dry season is a prerequisite for implementing water allocation and ecological protection in the watershed.

[0003] River flow simulation calculations currently fall into three main categories: empirical methods, hydrological methods, and hydrodynamic methods. Among them, empirical methods construct empirical models based on statistical correlation analysis, primarily linear systems; hydrological methods establish semi-empirical models of river flow evolution from the perspective of water balance principles and channel storage; and hydrodynamic methods mainly achieve numerical calculations of unsteady flow by solving the Saint-Venant equations. Empirical methods, similar to black-box models, have low data requirements and relatively low computational accuracy. They can be interpreted to some extent as theoretical solutions for moving waves and are mainly used in runoff generation and confluence calculations in hydrological models, rarely applied in watershed flood control and water replenishment scheduling. Hydrological methods are simplifications of hydrodynamic methods, requiring no topographic data and representing the difference form of moving wave equations. Their calculations are far less complex than dynamic wave solutions, but their accuracy is not superior, though they are widely used in river flood calculations. Hydrodynamic methods, by solving the complete Saint-Venant equations, obtain spatiotemporal distribution information of flow and water level, comprehensively reflecting the dynamic relationships between various hydraulic elements. Their calculation results better meet the accuracy requirements of water allocation during dry seasons. Nevertheless, during dry seasons, with low flow, low water levels, and even dry riverbeds, hydrodynamic methods often encounter numerical instability and iteration non-convergence. Even with shock wave capture techniques or slit methods, the frequent alternation of wet and dry periods cannot be resolved. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating river low-water flow based on Manning's formula, thereby solving the aforementioned problems existing in the prior art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for calculating low-water discharge in river channels based on Manning's formula includes the following steps:

[0007] S1. Data collection and gridding processing:

[0008] The collected or acquired river topographic data, riverbed infiltration data and model parameters are processed into grids to divide each river into multiple cells, and data input and parameter assignment are performed for each cell;

[0009] S2, Calculation of water flow direction in cell:

[0010] Based on the D8 algorithm, the slope between the current cell and its surrounding cells is calculated, and the direction represented by the maximum slope between the current cell and its eight adjacent cells is taken as the direction of the water flow in that cell.

[0011] S3, Cell flow velocity calculation:

[0012] Based on the water flow direction and corresponding gradient of the cell, the Manning formula is used to calculate the water flow velocity of the cell, and corrections are made for the case of rapid flow with high velocity.

[0013] S4. Calculation of water exchange volume and water level in cells:

[0014] Calculate the inflow and outflow of water in each cell and the leakage of water in each cell, which are included in the water exchange volume of each cell. Based on the obtained water exchange volume of each cell, calculate the water level of each cell using the principle of water balance.

[0015] S5, Cell Water Quantity Correction:

[0016] After the water level of all cells is calculated, the unbalanced water volume per unit area obtained by subtracting the outflow and infiltration volume from the inflow of each cell is used to correct the water balance of each cell one by one.

[0017] S6. Cell water level information update:

[0018] Update all cell water level information and proceed to the next water flow calculation period.

[0019] Preferably, step S1 specifically includes the following:

[0020] S11. Collect river topographic data and riverbed infiltration data, and determine model parameters based on river conditions;

[0021] S12. Perform grid-based processing on the river topography data, riverbed infiltration data, and model parameters. Divide the river into multiple square cells at a certain resolution, and input data and assign parameter values ​​to each cell.

[0022] Preferably, in step S12, the maximum number of rows in a cell is determined by the maximum width along the river, and the maximum number of columns in a cell is determined by the length of the river.

[0023] M = B MAX / DS (1)

[0024] N = Len / DS (2)

[0025] Where M is the maximum number of rows in the river network division cell; N is the maximum number of columns in the river network division cell; B MAX Len is the maximum channel width along the direction of water flow; DS is the channel length; and DS is the channel grid resolution, i.e., the side length of the cells.

[0026] Preferably, step S2 specifically includes the following:

[0027] S21. Using the center cell as the calculation object, encode the surrounding cells in sequence;

[0028] S22. Based on the water volume results of each cell calculated in the previous time period, calculate the slope between the current cell (i,j) in the i-th row and j-th column and the surrounding cells;

[0029] Slope(i,j)=dZ / DS (3)

[0030]

[0031] Where Z is the water level of the cell, and dZ is the water level difference between the center cell and the eight adjacent cells; the distance between cell (i,j) and its adjacent cells is related to the direction. For adjacent cells located directly above, to the left, to the right, or below cell (i,j), the distance between cell (i,j) and its adjacent cells is DS, and the slope calculation formula adopts equation (3); for adjacent cells located to the upper left, upper right, lower left, or lower right of cell (i,j), the distance between cell (i,j) and its adjacent cells is The slope calculation formula adopts equation (4);

[0032] S23. Based on the slope calculation results of cell (i,j), assuming that the water flow direction is unique within each calculation time step, the water flow direction of cell (i,j) is the direction represented by the maximum slope between that cell and its eight adjacent cells;

[0033] Aspect(i,j)=f(max Slope(i,j)) (5)

[0034] Where Aspect(i,j) is the code for the direction of water flow exchange between the calculated cell and the surrounding cells; f() is the code for the direction of water flow exchange indicated by the cell corresponding to the maximum slope.

[0035] Preferably, the water flow exchange direction code f() indicated by the cell corresponding to the maximum slope in step S23 is determined according to the following rules:

[0036] If maxSlope(i,j)≤0, then assign Aspect(i,j) as the current cell code value, indicating that the water does not flow out of the current cell;

[0037] If maxSlope(i,j)>0, and there is only one adjacent cell corresponding to the maximum slope, then assign Aspect(i,j) as the encoding value of the corresponding adjacent cell;

[0038] If maxSlope(i,j)>0, and there are two or more adjacent cells corresponding to the maximum slope, then assign the Aspect(i,j) code number in a clockwise direction.

[0039] Preferably, step S3 specifically includes the following:

[0040] S31. Calculate the water flow velocity in each cell using Manning's formula, based on the water flow direction and corresponding slope.

[0041]

[0042] Where v is the water flow velocity in the cell; n s is the Manning roughness coefficient; R is the hydraulic radius, approximately equal to the unit water depth;

[0043] S32. Based on the method of determining the flow state according to the Frod number, an upper limit threshold is set for the velocity to correct for the case of high-velocity rapid flow.

[0044]

[0045] Where g is the acceleration due to gravity; h(i,j) is the water depth in cell (i,j).

[0046] Preferably, step S4 specifically includes the following:

[0047] S41. Calculate the outflow volume of a cell based on the water flow velocity in the cell;

[0048] dw(i,j)=v·Δt·DS·h(i,j) (8)

[0049]

[0050] Where Δt is the length of the calculation period; dw(i,j) is the outflow of water from cell (i,j). When the flow direction is directly up, directly left, directly right, or directly down, dw(i,j) is calculated by formula (8). When the flow direction is directly up left, directly up right, directly down left, or directly down right, dw(i,j) is calculated by formula (9).

[0051] S42. Calculate the leakage volume of the cell based on the Horton flow formula;

[0052] Fp = [fc +(f0-f c )e -βt h(i,j) (10)

[0053] Where Fp is the leakage rate of the cell; f0 is the maximum infiltration rate when the riverbed is dry, which decreases to an approximately constant infiltration rate f as the infiltration process progresses. c The parameter β controls the rate of decrease in infiltration capacity; f0, f c And β are determined based on measured infiltration data;

[0054] S43. Based on the outflow and leakage of water in the cell, calculate the water level of the cell according to the principle of water balance.

[0055]

[0056] Where Z(t) and Z(t+Δt) are the cell water levels at the beginning and end of the calculation period, respectively; ∑dw′(i,j) is the amount of water flowing from adjacent cells into cell (i,j).

[0057] Preferably, step S5 specifically involves, after calculating the water level in all cells, using the following formula to perform water balance correction on each cell individually.

[0058] Z ‘ (t+Δt)=Z(t+Δt)+ΔZ (12)

[0059] Wherein, ΔZ is the unbalanced water volume per unit area obtained by subtracting outflow and infiltration from the inflow volume of each cell; Z ‘ (t+Δt) represents the water level after balance correction.

[0060] Preferably, step S6 specifically involves, after completing the calculation of water flow velocity and water level for all cells in the current time period, using the relevant calculation results as the initial values ​​for the next time period, and returning to step S2.

[0061] The beneficial effects of this invention are as follows: 1. The method for calculating river flow during low water levels provided by this invention solves the problem of instability in calculations under conditions of low water depth or dry riverbeds. On the one hand, the method maintains the simplicity and practicality of one-dimensional hydrodynamic methods, solving the problems of inapplicability or instability of previous hydrodynamic methods under conditions of low water depth and dry riverbeds while ensuring the efficiency and accuracy of flow calculations. On the other hand, the method can realize two-dimensional spatial calculations of river flow, which can more accurately characterize the spatial differences in lateral velocity and water level under conditions of low water depth in natural rivers. 2. The method of this invention achieves stable calculations of river flow during the dry season, providing technical support for engineering practices such as water replenishment scheduling and ecological protection in low-water rivers. 3. The method of this invention provides a new approach to flow calculation that balances calculation efficiency and accuracy, which can be extended to related similar engineering practices, especially problems such as water replenishment scheduling, ecological scheduling, and water resource management during the dry season. Attached Figure Description

[0062] Figure 1 This is a technical roadmap of the method in the embodiments of the present invention;

[0063] Figure 2 This is a schematic diagram of the model input data and parameter gridding processing in an embodiment of the present invention;

[0064] Figure 3 This is a schematic diagram of D8 grid encoding in an embodiment of the present invention;

[0065] Figure 4 This is a schematic diagram of river network grid unit division in an embodiment of the present invention;

[0066] Figure 5 This is the simulated water level distribution (m) of the river channel under the initial waterless state for 48 hours in this embodiment of the invention;

[0067] Figure 6 This is the distribution of river flow velocity (m / s) over 2 hours in the initial waterless state in this embodiment of the invention.

[0068] Figure 7 This is the distribution of river flow velocity (m / s) over 48 hours in the initial waterless state in this embodiment of the invention.

[0069] Figure 8 This is a simulation of different cross-sectional flow processes at an initial water depth of 0.02m in an embodiment of the present invention;

[0070] Figure 9 This is a simulation of different cross-sectional flow processes at an initial water depth of 0.05m in an embodiment of the present invention;

[0071] Figure 10 This is the flow velocity distribution (m / s) of the river channel over 2 hours under point source inflow and initial dry conditions in this embodiment of the invention. Detailed Implementation

[0072] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0073] Example 1

[0074] like Figure 1 As shown in this embodiment, a method for calculating low-water flow in river channels based on the Manning formula is provided, including the following steps:

[0075] I. Data Collection and Grid Processing:

[0076] The collected or acquired river topographic data, riverbed infiltration data, and model parameters are processed into a grid to divide each river channel into multiple cells, and data input and parameter assignment are performed for each cell.

[0077] Specifically, it includes the following:

[0078] 1. Collect river topographic data, riverbed infiltration data, etc., and determine model parameters (roughness coefficient) based on the riverbed conditions.

[0079] 2. The river channel topography data, riverbed infiltration data, and model parameters are processed into a grid, dividing the river channel into multiple square cells (i.e., square grids) at a certain resolution. Figure 2 As shown in the figure, data is input and parameter values ​​are assigned to each of the divided cells.

[0080] The maximum number of rows in a cell is determined by the maximum width of the river along its course, and the maximum number of columns in a cell is determined by the length of the river.

[0081] M = B MAX / DS (1)

[0082] N = Len / DS (2)

[0083] Where M is the maximum number of rows in the river network division cell; N is the maximum number of columns in the river network division cell; B MAX Len is the maximum channel width along the direction of water flow; DS is the channel length; and DS is the channel grid resolution, i.e., the side length of the cells.

[0084] II. Calculation of water flow direction in cells:

[0085] Based on the D8 algorithm, the slope between the current cell and its surrounding cells is calculated, and the direction represented by the maximum slope between the current cell and its eight adjacent cells is taken as the direction of the water flow in that cell.

[0086] Specifically, it includes the following:

[0087] 1. Using the center cell as the calculation object, encode the surrounding cells sequentially (e.g., ...). Figure 3 (As shown).

[0088] 2. Based on the water volume results of each cell calculated in the previous time period, calculate the gradient between the current cell (i,j) in the i-th row and j-th column and its surrounding cells;

[0089] Slope(i,j)=dZ / DS (3)

[0090]

[0091] Where Z is the water level of the cell, and dZ is the water level difference between the center cell and the eight adjacent cells; the distance between cell (i,j) and its adjacent cells is related to the direction, and for adjacent cells located directly above, to the left, to the right, or below cell (i,j)... Figure 3 The adjacent cells numbered 2, 4, 6, and 8 are given. The distance between cell (i,j) and its adjacent cells is DS. The slope calculation formula uses equation (3). For adjacent cells located in the upper left, upper right, lower left, and lower right directions of cell (i,j) (i.e., ... Figure 3 In the context of adjacent cells numbered 1, 3, 7, and 9, the distance between cell (i,j) and its adjacent cells is... The slope calculation formula adopts equation (4).

[0092] 3. Based on the slope calculation results of cell (i,j), assuming that the water flow direction is unique within each calculation time step, the water flow direction of cell (i,j) is the direction represented by the maximum slope between that cell and its eight adjacent cells;

[0093] Aspect(i,j)=f(max Slope(i,j)) (5)

[0094] Where Aspect(i,j) is the symbol for the direction of water flow exchange between the calculated cell and its surrounding cells (values ​​are shown in the appendix). Figure 3 (as shown); f() is the code for the direction of water flow exchange indicated by the cell corresponding to the maximum slope.

[0095] The code f() for the direction of water flow exchange indicated by the cell corresponding to the maximum slope is determined according to the following rules.

[0096] (i) If maxSlope(i,j)≤0, then assign Aspect(i,j) as the current cell's code value (i.e. Figure 3 (5) indicates that water is not flowing out of the current cell;

[0097] (ii) If maxSlope(i,j)>0, and only one adjacent cell corresponds to the maximum slope, then assign Aspect(i,j) as the encoding value of the corresponding adjacent cell (see appendix). Figure 3 (as shown);

[0098] (iii) If maxSlope(i,j)>0, and there are two or more adjacent cells corresponding to the maximum slope, then assign Aspect(i,j) code number in a clockwise direction (i.e. 1-2-3-6-9-8-7-4); for example, if cells with codes 2, 9, and 4 all correspond to the maximum slope, then Aspect(i,j) is assigned the value 2.

[0099] III. Calculation of water flow velocity in each cell:

[0100] Based on the water flow direction and corresponding gradient of the cell, the Manning formula is used to calculate the water flow velocity of the cell, and corrections are made for rapid flow with high velocity.

[0101] Specifically, it includes the following:

[0102] 1. Calculate the water flow velocity in each cell using Manning's formula, based on the water flow direction and corresponding gradient.

[0103]

[0104] Where v is the water flow velocity in the cell; n s R is the Manning roughness coefficient (abbreviated as roughness). The roughness values ​​for different riverbed types can be found using the Manning coefficient table; R is the hydraulic radius, which is approximately the unit water depth.

[0105] 2. The calculation formula for the water flow velocity calculated in the previous step is based on uniform flow. The Manning formula is effective for general dry water flow, but it needs to be modified for rapid flow with high velocity.

[0106] Therefore, based on the method of determining the flow state according to the Frod number, an upper limit threshold is set for the velocity to correct for the case of high-velocity rapid flow.

[0107]

[0108] Where g is the acceleration due to gravity; h(i,j) is the water depth in cell (i,j).

[0109] IV. Calculation of water exchange volume and water level in each cell:

[0110] Calculate the inflow and outflow of water in each cell and the leakage of water in each cell, which are included in the water exchange volume. Based on the obtained water exchange volume of each cell, calculate the water level of each cell using the principle of water balance.

[0111] Cell water exchange volume includes cell inflow and outflow volume and cell leakage volume.

[0112] Specifically, it includes the following:

[0113] 1. Calculate the outflow volume of a cell based on the water flow velocity in that cell;

[0114] dw(i,j)=v·Δt·DS·h(i,j) (8)

[0115]

[0116] Where Δt is the calculation period length; dw(i,j) is the outflow volume of cell (i,j). When the flow direction is directly up, directly left, directly right, or directly down (i.e., when the flow direction number is 2, 4, 6, or 8), dw(i,j) is calculated by formula (8). When the flow direction is directly up left, directly up right, directly down left, or directly down right (i.e., when the flow direction number is 1, 3, 7, or 9), dw(i,j) is calculated by formula (9).

[0117] 2. Calculate the leakage volume of the cell based on the Horton flow formula;

[0118] Fp = [f c +(f0-f c )e -βt h(i,j) (10)

[0119] Where Ep is the leakage volume of the cell; f0 is the maximum infiltration rate when the riverbed is dry, which decreases to an approximately constant infiltration rate f as the infiltration process progresses. c The parameter β controls the rate of decrease in infiltration capacity; f0, f c β is determined based on measured infiltration data.

[0120] 3. Based on the outflow and leakage of water from each cell, calculate the water level of the cell according to the principle of water balance;

[0121]

[0122] Where Z(t) and Z(t+Δt) are the cell water levels at the beginning and end of the calculation period, respectively; ∑dw′(i,j) is the amount of water flowing from adjacent cells into cell (i,j).

[0123] V. Cell Water Quantity Correction:

[0124] After the water level of all cells is calculated, the unbalanced water volume per unit area obtained by subtracting the outflow and infiltration volume from the inflow volume of each cell is used to correct the water balance of each cell one by one.

[0125] Specifically: After calculating the water level in all cells, use the following formula to perform a water balance correction on each cell individually.

[0126] Z'(t+Δt)=Z(t+Δt)+ΔZ (12)

[0127] Where ΔZ is the unbalanced water volume per unit area obtained by subtracting outflow and infiltration from the inflow of water into each cell; Z'(t+Δt) is the water level after balance correction.

[0128] VI. Cell water level information update:

[0129] Update all cell water level information and proceed to the next water flow calculation period.

[0130] Specifically: After completing the calculation of water flow velocity and water level for all cells in the current time period, use the relevant calculation results as the initial values ​​for the next time period and return to step S2.

[0131] Example 2

[0132] In this embodiment, the method of the present invention is implemented using a rectangular river channel that is 10 km long and 100 m wide as an example, as shown in the attached figure. Figure 4 As shown. The selected embodiment uses a non-constant small flow sequence input model (line source input, i.e., the flow velocity is the same in all cells at the boundary) for the river channel from upstream, considering three different initial water depth scenarios: dry riverbed, initial water depth of 0.02m, and initial water depth of 0.05m. The steps and benefit analysis of this embodiment are as follows:

[0133] 1. Based on the river channel topographic data, interpolate to generate river channel topographic grid cells with a resolution of 10m, as shown in the attached figure. Figure 4 As shown. All cells are assigned the same roughness coefficient of 0.02, the same initial water depth (0, 0.02m and 0.05m respectively), and the same infiltration coefficient (infiltration is not considered for now, all three coefficients are set to 0).

[0134] 2. Implement numerical calculations of water flow using Fortran programming, and output flow velocity and water level information, as shown in the attached document. Figure 5 and 6 As shown in the figure, the proposed method can calculate the flow field information under dry riverbed conditions, solving the problem that previous river hydrodynamic models could not be calculated when the initial riverbed was dry.

[0135] 3. Compare the calculation results of this embodiment with those of the traditional one-dimensional hydrodynamic method, and conduct a benefit analysis of the method, as shown in the appendix. Figure 7 and 8As shown in the figure, the proposed method can solve the problem of instability in calculations under low water conditions found in previous methods. The advantages of the proposed method become more pronounced as the initial water depth decreases. Furthermore, the comparison results in the attached figures also show that the proposed method is not inferior to one-dimensional hydrodynamic methods in terms of accuracy.

[0136] 4. In this embodiment, since the terrain and boundary conditions both satisfy the uniformity in the river width direction, the simulation results also exhibit one-dimensional characteristics. Nevertheless, the method can be used to analyze two-dimensional spatial results, as shown in the attached figure. Figure 9 The diagram shows the simulated velocity plane distribution under point source inflow conditions. (Based on the attached diagram...) Figure 9 As a result, the method proposed in this invention can reflect the spatial differences in the flow field under point source inflow conditions.

[0137] By adopting the above-disclosed technical solution of this invention, the following beneficial effects are obtained:

[0138] This invention provides a method for calculating river flow during low water levels based on the Manning formula. This method addresses the instability issues in calculations under conditions of low water depth or dry riverbeds. On one hand, the method maintains the simplicity and practicality of one-dimensional hydrodynamic methods, ensuring both efficiency and accuracy in flow calculations while resolving the inapplicability or instability of previous hydrodynamic methods under conditions of low water depth or dry riverbeds. On the other hand, the method enables two-dimensional spatial calculations of river flow, more accurately characterizing the spatial differences in lateral velocity and water level in natural river channels with low water depths. This invention achieves stable calculations of river flow during the dry season, providing technical support for engineering practices such as water replenishment scheduling and ecological protection during low water levels. This invention offers a new approach to flow calculation that balances computational efficiency and accuracy, and can be extended to similar engineering practices, particularly in issues such as water replenishment scheduling during the dry season, ecological scheduling, and water resource management.

[0139] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating low flow of a river channel based on Manning formula, characterized in that: Includes the following steps, S1. Data collection and gridding processing: The collected or acquired river topographic data, riverbed infiltration data and model parameters are processed into grids to divide each river into multiple cells, and data input and parameter assignment are performed for each cell; S2, Calculation of water flow direction in cell: Based on the D8 algorithm, the slope between the current cell and its surrounding cells is calculated, and the direction represented by the maximum slope between the current cell and its eight adjacent cells is taken as the direction of the water flow in that cell. S3, Cell flow velocity calculation: Based on the water flow direction and corresponding gradient of the cell, the Manning formula is used to calculate the water flow velocity of the cell, and corrections are made for the case of rapid flow with high velocity. S4. Calculation of water exchange volume and water level in cells: Calculate the inflow and outflow of water in each cell and the leakage of water in each cell, respectively, based on the obtained water exchange volume of each cell and the principle of water balance to calculate the water level of each cell. Step S4 specifically includes the following: S41. Calculate the outflow volume of a cell based on the water flow velocity in the cell; （8） （9） in, For the water flow velocity in the cell, For cells The water depth, To calculate the length of the time period; Cell The outflow volume, when the flow direction is directly upward, directly left, directly right, or directly downward, Calculated by formula (8), cell The distance between adjacent cells is When the flow direction is upper left, upper right, lower left, or lower right, Calculated by formula (9), cell The distance between adjacent cells is ; S42. Calculate the leakage volume of the cell based on the Horton flow formula; （10） in, This represents the amount of water leakage from the cell. The maximum infiltration rate occurs when the riverbed is dry, and decreases to an approximately constant infiltration rate as the infiltration process progresses. ;parameter It controls the rate at which the infiltration capacity decreases; , and Rated based on measured infiltration data; S43. Based on the outflow and leakage of water in the cell, calculate the water level of the cell according to the principle of water balance. （11） wherein, and are the water levels of the cell at the beginning and end of the calculation period, respectively; is the water volume flowing from the adjacent cell into the cell . S5, Cell Water Quantity Correction: After the water level of all cells is calculated, the unbalanced water volume per unit area obtained by subtracting the outflow and infiltration volume from the inflow volume of each cell is used to correct the water balance of each cell one by one. S6. Cell water level information update: Update all cell water level information and proceed to the next water flow calculation period.

2. The Manning formula-based river low flow calculation method according to claim 1, characterized in that: Step S1 specifically includes the following: S11. Collect river topographic data and riverbed infiltration data, and determine model parameters based on river conditions; S12. Perform grid-based processing on the river topography data, riverbed infiltration data, and model parameters. Divide the river into multiple square cells at a certain resolution, and input data and assign parameter values ​​to each cell.

3. The Manning formula-based river low flow computation method according to claim 2, characterized in that: In step S12, the maximum number of rows in a cell is determined by the maximum width of the river along its course, and the maximum number of columns in a cell is determined by the length of the river. （1） （2） in, The maximum number of rows in a cell for dividing a river network; The maximum number of columns to divide the river network into cells; The maximum width of the river channel along the direction of water flow; The length of the river channel; The resolution of the river channel grid is defined by the side length of each cell.

4. The Manning formula-based river low flow calculation method according to claim 3, characterized in that: Step S2 specifically includes the following: S21. Using the center cell as the calculation object, encode the surrounding cells in sequence; S22、According to the water amount result of each cell calculated in the last period, calculate the current first row, the first column cell Slope between the surrounding cells; （3） （4） in, For cell water level, The water level difference between the center cell and its eight adjacent cells; cell It depends on the distance and direction between adjacent cells, for cells located in Adjacent cells in the top, left, right, and bottom directions; cells The distance between adjacent cells is The slope calculation formula uses equation (3); for cells located in the cell Adjacent cells in the top left, top right, bottom left, and bottom right directions; cells The distance between adjacent cells is The slope calculation formula adopts equation (4); S23, Based on cell The gradient calculation results assume that the water flow direction is unique within each calculation time step, and the cell... The direction of water flow is the direction represented by the maximum slope between this cell and its eight adjacent cells; （5） in, This is a code indicating the direction of water flow exchange between the calculated cell and its surrounding cells; This is the code for the direction of water flow exchange indicated by the cell corresponding to the maximum slope.

5. The Manning formula-based river low flow computation method according to claim 4, characterized in that: The code indicating the direction of water flow exchange in the cell corresponding to the maximum slope in step S23. The following rules shall be used to determine this. If , then the current cell is assigned a value of , which indicates that the current cell has no outflow. If , and only one adjacent cell corresponds to the maximum slope, then the encoding value of is assigned to the corresponding adjacent cell; If , and there are two or more adjacent cells corresponding to the maximum value of the slope, then the code number is assigned in the clockwise direction.

6. The Manning formula-based river low flow computation method according to claim 5, characterized in that: Step S3 specifically includes the following: S31. Calculate the water flow velocity in each cell using Manning's formula, based on the water flow direction and corresponding gradient. （6） in, The water flow velocity in the cell; The roughness coefficient is Manning's coefficient. The hydraulic radius is approximately equal to the unit water depth. S32. Based on the method of determining the flow state according to the Frod number, a threshold limit is set for the velocity to correct for the case of high-velocity rapid flow. （7） in, It is the acceleration due to gravity; For cells The water depth.

7. The Manning formula based river low flow computation method of claim 1, wherein: Step S5 specifically involves, after calculating the water level in all cells, using the following formula to perform water balance correction on each cell individually. （12） wherein, is the unbalanced water quantity per unit area obtained by deducting the outflow and the amount of water infiltrated from the inflow of each cell; is the balanced corrected water level.

8. The Manning formula based river low flow computation method of claim 1, wherein: Step S6 specifically involves calculating the water flow velocity and water level for all cells in the current time period, using the relevant calculation results as the initial values ​​for the next time period, and then returning to step S2.

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