A method for estimating spatial distribution of slope flow velocity based on terrain and vegetation characteristics

Abstract

The present invention discloses a method for estimating the spatial distribution of slope flow velocity based on terrain and vegetation characteristics, which mainly includes the following steps: calculating the slope and runoff accumulation value of each grid unit in the watershed based on digital elevation data; calculating the average flow velocity factor of the watershed in combination with the average slope and watershed area of ​​the watershed; estimating the spatial distribution of roughness in the watershed based on vegetation coverage type data; estimating the spatial distribution of slope flow velocity based on slope, roughness and average flow velocity factor. This method mainly uses remote sensing observation data such as watershed digital elevation model and vegetation coverage type. The data source is stable and reliable. The functional relationship between variables in the method is clear, which is conducive to the computer automation execution of the estimation of the spatial distribution of slope flow velocity. At the same time, the digital watershed technology is used to simplify the extraction steps to ensure the objectivity and rationality of the results, which is conducive to the promotion and application of distributed hydrological models and the in-depth development of digital hydrology research.

Description

Technical Field

[0001] The invention belongs to the field of hydrological technology, and in particular relates to a method for estimating the spatial distribution of slope flow velocity based on terrain and vegetation characteristics. Background Art

[0002] With the development of remote sensing, geographic information, and digital watershed technologies, distributed hydrological models based on digital elevation models (DEMs) can reflect the spatial changes in rainfall and underlying surface conditions, and have become a research hotspot and an important development direction for watershed hydrological models. Distributed hydrological models usually divide the watershed into several orthogonal grid cells. First, the runoff depth generated is calculated in each grid cell, and then the flood process at the outlet of the watershed is obtained by combining the confluence calculation method. It is an important tool for flood forecasting in small and medium-sized watersheds. The reasonable estimation of the flow velocity of the slope water flow is a key factor affecting the results of the confluence calculation, and it is also a key and difficult problem in the construction and development of distributed hydrological models.

[0003] To further promote the development of distributed watershed hydrological models, it is necessary to conduct more in-depth research on the estimation methods of spatial distribution of overland flow velocity.

[0004] At present, the main method for estimating slope flow velocity is to establish a functional relationship between factors such as slope and runoff depth and slope flow velocity. However, the average slope, catchment area, vegetation type and other terrain and vegetation characteristics are different among watersheds, and their slope flow velocity characteristics are also quite different. It is difficult to reasonably quantify the spatial distribution characteristics of slope flow velocity in different watersheds by only using terrain factors such as slope, which increases the difficulty of constructing distributed models and is not conducive to the promotion and application of models and research and development.

[0005] In view of the above shortcomings, how to quantify the impact of terrain and vegetation characteristics on the spatial distribution of slope flow velocity and achieve a reasonable estimation of the spatial distribution of slope flow velocity is the problem that needs to be solved at present. Summary of the invention

[0006] In order to solve the deficiencies in the prior art, the present invention provides a method for estimating the spatial distribution of slope flow velocity based on terrain and vegetation characteristics. The method has the advantages of stable and reliable data source, high calculation efficiency, and objective and reasonable results. It is conducive to the rapid calculation of the spatial distribution of slope flow velocity and is worthy of promotion.

[0007] In order to solve the above problems, the present invention specifically adopts the following technical solutions:

[0008] A method for estimating the spatial distribution of overland flow velocity based on terrain and vegetation characteristics is proposed. The following steps are performed for the target period of the target watershed during rainfall to obtain the spatial distribution of overland flow velocity in the target watershed:

[0009] Step S1, based on the digital elevation data of the target watershed, calculating the slope value and the runoff accumulation value of each grid cell in the target watershed, and obtaining the slope grid matrix and the runoff accumulation grid matrix of the target watershed;

[0010] Step S2, based on the slope grid matrix and the confluence accumulation grid matrix of the target watershed, the average slope value of the target watershed and the confluence area at the outlet of the target watershed are obtained, and then the average flow velocity factor of the target watershed is calculated;

[0011] Step S3, collecting spatial distribution data of vegetation cover types in the target watershed, assigning values ​​to the roughness of each vegetation cover type in the target watershed according to the preset values ​​of the roughness of each vegetation cover type, and obtaining the spatial distribution data of the roughness of the target watershed;

[0012] Step S4, based on the slope value and roughness of each grid in the target watershed, and the average flow velocity factor of the target watershed, the spatial distribution of the slope flow velocity in the target watershed is obtained.

[0013] As a preferred technical solution of the present invention, in step 1, each grid in the target watershed is traversed to execute steps S1.1 to S1.4, and the slope value S and the runoff accumulation value A of each grid unit are calculated to obtain the slope grid matrix Raster_Slope and the runoff accumulation grid matrix Raster_Acc of the target watershed:

[0014] Step S1.1, based on the digital elevation data of the target watershed, with the grid cell Cell in the target watershed as the center, compare the elevation values ​​of the grid cell Cell with the 8 adjacent grid cells around it, and determine the grid cell Cell with the lowest elevation value compared with the grid cell Cell among the 8 adjacent grid cells around the grid cell Cell D ; If the elevation values ​​of the eight adjacent grid cells around the grid cell Cell are all higher than the grid cell Cell, within the range of the grid cell Cell and the eight adjacent grid cells around it, the grid cell Cell is filled with elevation values ​​using the fill-in method to obtain the grid cell Cell with the lowest elevation value compared with the grid cell Cell among the eight adjacent grid cells around the grid cell Cell. D ;

[0015] Step S1.2, calculate the grid cell Cell and the corresponding grid cell Cell D The height difference between max and horizontal projection distance Dis;

[0016] Step S1.3, based on the grid cell Cell and the corresponding grid cell Cell D The height difference between maxThe horizontal projection distance Dis is used in the following formula to obtain the slope value S of the grid cell Cell:

[0017] S = DH max / Dis

[0018] Step S1.4: Take the grid cell Cell as the outflow grid, and the corresponding grid cell Cell D as the inflow grid. Add 1 to the cumulative flow value of the grid cell serving as the inflow grid. The initial value of the cumulative flow value of each grid cell is 0.

[0019] As a preferred technical solution of the present invention, step 2 specifically includes the following steps:

[0020] Step S2.1: Based on the slope grid matrix of the target basin, use the following formula to obtain the average slope value of the target basin;

[0021]

[0022] In the formula, i is the grid cell number in the target basin, 1 < i < N, and N is the total number of grid cells in the target basin; S i is the slope value of the grid cell numbered i; S ave is the average slope value of the target basin;

[0023] Step S2.2: Based on the cumulative flow grid matrix of the target basin, obtain the catchment area at the outlet of the target basin;

[0024] R = A max ×z 2

[0025] In the formula, A max is the maximum cumulative flow value in the cumulative flow grid matrix of the target basin; z is the side length of the grid cell; R is the catchment area at the outlet of the target basin;

[0026] Step S2.3: Calculate the average flow velocity factor of the target basin based on the average slope of the target basin and the catchment area at the outlet of the target basin;

[0027]

[0028] In the formula, V mean is the average water flow velocity of the target basin, obtained from the runoff observation data of the outlet section of the target basin; b is the average slope index of the target basin; c is the catchment area index of the target basin; F is the average flow velocity factor of the target basin.

[0029] As a preferred technical solution of the present invention, step 3 specifically includes the following steps:

[0030] Step S3.1: Collect the spatial distribution data of vegetation cover types within the target basin.

[0031] Using the vegetation cover type data with a preset range larger than the target basin as the source data and the target basin range as the mask, collect the spatial distribution data of vegetation cover types within the target basin.

[0032] Based on the collected spatial distribution data of vegetation cover types within the target basin, conduct grid-by-grid inspection for each grid cell within the target basin to check whether there are null values in the spatial distribution data of the vegetation cover type of each grid cell. If there are null values, set the grid cell with the data null value as the center and make a circle with a radius of 3z. Assign the vegetation cover type with the highest area proportion within this circular range to the grid cell with the data null value to perform interpolation of the spatial distribution data of the vegetation cover type and update the spatial distribution data of the vegetation cover type within the target basin.

[0033] Step S3.2: Based on the spatial distribution data of vegetation cover types within the target basin, divide the vegetation cover types within the target basin into each preset vegetation cover type, and assign values to the roughness coefficients of each vegetation cover type within the target basin according to the preset values of the roughness coefficients of each vegetation cover type to obtain the spatial distribution data of the roughness coefficient of the target basin.

[0034] As a preferred technical solution of the present invention, the specific steps in step 4 include the following steps:

[0035] In each grid cell within the target basin, estimate the overland flow velocity of each grid cell within the target basin according to the following formula. Traverse each grid cell within the target basin according to this formula to obtain the spatial distribution of the overland flow velocity within the target basin.

[0036]

[0037] In the formula: q i,t is the runoff depth in the grid cell numbered i at time t, which is obtained by the Green-Ampt method based on the rainfall amount during rainfall. 1 < i < N, where N is the total number of grid cells within the target basin, and t is the target time period, and t ranges from the initial rainfall time period 1 to the end time period T of the rainfall process; n i is the roughness coefficient of the grid cell numbered i, S i is the slope of the grid cell numbered i; d is the slope index of the target basin, and k is the runoff depth index of the target basin; v i,t is the overland flow velocity of the grid cell numbered i at time t; F is the average flow velocity factor of the target basin.

[0038] The beneficial effects of the present invention are as follows: the present invention provides a method for estimating the spatial distribution of slope flow velocity based on terrain and vegetation characteristics. Based on the physical factors that affect water flow movement, the method quantifies the influence of local terrain factors such as the slope and roughness of each grid unit in the basin and the overall characteristics of the basin such as the average slope and total area on the slope flow velocity, and estimates the spatial distribution of slope flow velocity during rainfall. It not only ensures the accuracy and reliability of the calculation results, but also solves the problem of estimating the spatial distribution of slope flow velocity in a basin that lacks observation data. In addition, the method mainly uses remote sensing observation data such as the digital elevation model of the basin and the vegetation cover type. The data source is stable and reliable, and the functional relationship between the variables in the method is clear, which is conducive to the computer automation execution of the estimation of the spatial distribution of slope flow velocity. At the same time, the digital watershed technology is used to simplify the extraction steps to ensure the objectivity and rationality of the results, which is conducive to the promotion and application of distributed hydrological models and the in-depth development of digital hydrology research. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 Schematic diagram of the calculation process;

[0040] Figure 2 Slope spatial distribution map;

[0041] Figure 3 Confluence cumulative distribution diagram;

[0042] Figure 4 Vegetation cover distribution map;

[0043] Figure 5 Spatial distribution map of watershed roughness;

[0044] Figure 6 Spatial distribution of slope flow velocity. DETAILED DESCRIPTION

[0045] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0046] Taking the Chenhe River Basin in Shaanxi Province as an example, the original DEM data of the study area uses the 90m resolution SRTM (Shuttle Radar Topography Mission) data jointly provided by the National Aeronautics and Space Administration (NASA) and the National Mapping and Surveying Administration (NIMA) of the Ministry of Defense. The vegetation coverage data in the basin is provided by the global 1km (30") precision vegetation coverage dataset produced by the University of Maryland (UMD).

[0047] A method for estimating the spatial distribution of overland flow velocity based on terrain and vegetation characteristics performs the following steps for the target period of the target watershed during rainfall, such as Figure 1 As shown, the spatial distribution of slope flow velocity in the target basin is obtained:

[0048] Step S1, based on the digital elevation data of the target watershed, calculating the slope value and the runoff accumulation value of each grid cell in the target watershed, and obtaining the slope grid matrix and the runoff accumulation grid matrix of the target watershed;

[0049] In step 1, each grid in the target watershed is traversed to execute steps S1.1 to S1.4, and the slope value S and the runoff accumulation value A of each grid unit are calculated to obtain the slope grid matrix Raster_Slope and the runoff accumulation grid matrix Raster_Acc of the target watershed, such as Figure 2 and Figure 3 As shown:

[0050] Step S1.1, based on the digital elevation data of the target watershed, with the grid cell Cell in the target watershed as the center, compare the elevation values ​​of the grid cell Cell with the 8 adjacent grid cells around it, and determine the grid cell Cell with the lowest elevation value compared with the grid cell Cell among the 8 adjacent grid cells around the grid cell Cell D ; If the elevation values ​​of the eight adjacent grid cells around the grid cell Cell are all higher than the grid cell Cell, within the range of the grid cell Cell and the eight adjacent grid cells around it, the grid cell Cell is filled with elevation values ​​using the fill-in method to obtain the grid cell Cell with the lowest elevation value compared with the grid cell Cell among the eight adjacent grid cells around the grid cell Cell. D ;

[0051] Step S1.2, calculate the grid cell Cell and the corresponding grid cell Cell D The height difference between max and horizontal projection distance Dis;

[0052] Step S1.3, based on the grid cell Cell and the corresponding grid cell Cell D The height difference between max And the horizontal projection distance Dis, use the following formula to get the slope value S of the grid cell Cell:

[0053] S=DH max / Dis

[0054] Step S1.4, use the grid cell Cell as the outflow grid, and the corresponding grid cell Cell D As the inflow grid, the cumulative flow value of the grid unit as the inflow grid is increased by 1, and the initial value of the cumulative flow value of each grid unit is 0.

[0055] Step S2: Based on the slope grid matrix and the flow accumulation grid matrix of the target basin, obtain the average slope value of the target basin and the flow accumulation area at the outlet of the target basin, and then calculate the average flow velocity factor of the target basin.

[0056] The specific steps of Step 2 are as follows:

[0057] Step S2.1: Based on the slope grid matrix of the target basin, use the following formula to obtain the average slope value of the target basin;

[0058]

[0059] In the formula, i is the grid cell number in the target basin, 1 < i < N, where N is the total number of grid cells in the target basin; S i is the slope value of the grid cell numbered i; S ave is the average slope value of the target basin;

[0060] Step S2.2: Based on the flow accumulation grid matrix of the target basin, obtain the flow accumulation area at the outlet of the target basin;

[0061] R = A max × z 2

[0062] In the formula, A max is the maximum flow accumulation value in the flow accumulation grid matrix of the target basin; z is the side length of the grid cell; R is the flow accumulation area at the outlet of the target basin; the maximum flow accumulation value in the flow accumulation grid matrix of the target basin is defined as the flow accumulation value corresponding to the grid cell at the outlet of the target basin, and this grid cell covers the outlet of the target basin;

[0063] Step S2.3: Based on the average slope of the target basin and the flow accumulation area at the outlet of the target basin, calculate the average flow velocity factor of the target basin;

[0064]

[0065] In the formula, V mean is the average water flow velocity of the target basin, obtained from the runoff observation data of the outlet section of the target basin; b is the average slope index of the target basin, with a value of 0.15; c is the area index of the target basin, with a value of 0.02; F is the average flow velocity factor of the target basin.

[0066] Step S3: Collect the spatial distribution data of the vegetation cover types in the target basin, and assign values to the roughness coefficients of each vegetation cover type in the target basin according to the preset values of the roughness coefficients of each vegetation cover type, to obtain the spatial distribution data of the roughness coefficient of the target basin;

[0067] The specific steps of Step 3 are as follows:

[0068] Step S3.1: Collect the spatial distribution data of vegetation cover types within the target basin.

[0069] Using the vegetation cover type data with a preset range larger than the target basin as the source data and the target basin range as the mask, collect the spatial distribution data of vegetation cover types within the target basin.

[0070] Based on the collected spatial distribution data of vegetation cover types within the target basin, conduct a grid-by-grid inspection for each grid cell within the target basin to check whether there are null values in the spatial distribution data of the vegetation cover type of each grid cell. If there are null values, set the grid cell with the data null value as the center and make a circle with a radius of 3z. Assign the vegetation cover type with the highest area proportion within this circular range to the grid cell with the data null value, perform interpolation of the spatial distribution data of the vegetation cover type, and update the spatial distribution data of the vegetation cover type within the target basin, as Figure 4 shown.

[0071] Step S3.2: Based on the spatial distribution data of vegetation cover types within the target basin, divide the vegetation cover types within the target basin into forest land, grassland, crops, and bare land. According to the preset values of the roughness coefficients of each vegetation cover type, assign the roughness coefficients of 0.1, 0.17, 0.35, and 0.01 to each vegetation cover type within the target basin respectively to obtain the spatial distribution data of the roughness coefficient of the target basin, as Figure 5 shown.

[0072] Step S4: Estimate the spatial distribution of overland flow velocity within the target basin based on the slope values, roughness coefficients, and the average flow velocity factor of the target basin for each grid.

[0073] The specific steps in Step 4 include the following:

[0074] Establish a functional relationship between slope, roughness coefficient, basin average flow velocity factor, and runoff depth and overland flow velocity for each grid cell within the target basin. According to the following formula, estimate the overland flow velocity of each grid cell within the target basin for each grid cell within the target basin. Traverse each grid cell within the target basin according to this formula to obtain the spatial distribution of overland flow velocity within the target basin, as Figure 6 shown,

[0075]

[0076] In the formula: q i,t is the runoff depth in the grid cell numbered i at time t, obtained by the Green-Ampt method based on the rainfall amount during rainfall. 1 < i < N, where N is the total number of grid cells within the target basin, and t is the target time period, with t ranging from the initial rainfall time period 1 to the end time period T of the rainfall process; n iis the roughness of the grid cell numbered i, S i is the slope of the grid cell numbered i; d is the target basin slope index, which can be 0.5; k is the target basin runoff depth index, which can be 0.76, both of which are formula parameters; v i,t is the slope flow velocity of the grid unit numbered i in period t, and F is the average flow velocity factor of the target basin.

[0077] At any time during the rainfall process, the above method can be executed to traverse all grid cells to calculate the spatial distribution of slope flow velocity in the basin.

[0078] The above technical solution provides a method for estimating the spatial distribution of slope flow velocity based on terrain and vegetation characteristics. Based on the physical factors that affect water flow movement, it quantifies the influence of local terrain factors such as slope and roughness of each grid unit in the basin and the overall characteristics of the basin such as average slope and total area on the slope flow velocity, and estimates the spatial distribution of slope flow velocity during rainfall. It not only ensures the accuracy and reliability of the calculation results, but also solves the problem of estimating the spatial distribution of slope flow velocity in a basin with a lack of observation data. In addition, this method mainly uses remote sensing observation data such as the digital elevation model of the basin and vegetation cover type. The data source is stable and reliable, and the functional relationship between the variables in the method is clear, which is conducive to the computer automation of the estimation of the spatial distribution of slope flow velocity. At the same time, the digital watershed technology is used to simplify the extraction steps to ensure the objectivity and rationality of the results, which is conducive to the promotion and application of distributed hydrological models and the in-depth development of digital hydrology research.

[0079] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present invention will not further describe various possible combinations.

[0080] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention to be protected. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for estimating the spatial distribution of slope flow velocity based on terrain and vegetation characteristics, characterized by: For the target period of the target watershed during rainfall, perform the following steps to obtain the spatial distribution of overland flow velocity in the target watershed: Step S1, based on the digital elevation data of the target watershed, calculating the slope value and the runoff accumulation value of each grid cell in the target watershed, and obtaining the slope grid matrix and the runoff accumulation grid matrix of the target watershed; Step S2, based on the slope grid matrix and the confluence accumulation grid matrix of the target watershed, the average slope value of the target watershed and the confluence area at the outlet of the target watershed are obtained, and then the average flow velocity factor of the target watershed is calculated; Step S3, collecting spatial distribution data of vegetation cover types in the target watershed, assigning values ​​to the roughness of each vegetation cover type in the target watershed according to the preset values ​​of the roughness of each vegetation cover type, and obtaining the spatial distribution data of the roughness of the target watershed; Step S4, based on the slope value, roughness of each grid in the target watershed, and the average flow velocity factor of the target watershed, obtain the spatial distribution of the slope flow velocity in the target watershed; In step 1, traverse each grid in the target basin and execute steps S1.1 to S1.4 to calculate the slope value S and the runoff accumulation value A of each grid cell, and obtain the slope grid matrix Raster_Slope and the runoff accumulation grid matrix Raster_Acc of the target basin: Step S1.1, based on the digital elevation data of the target watershed, with the grid cell Cell in the target watershed as the center, compare the elevation values ​​of the grid cell Cell with the 8 adjacent grid cells around it, and determine the grid cell Cell with the lowest elevation value compared with the grid cell Cell among the 8 adjacent grid cells around the grid cell Cell D ; If the elevation values ​​of the eight adjacent grid cells around the grid cell Cell are all higher than the grid cell Cell, within the range of the grid cell Cell and the eight adjacent grid cells around it, the grid cell Cell is filled with elevation values ​​using the fill-in method to obtain the grid cell Cell with the lowest elevation value compared with the grid cell Cell among the eight adjacent grid cells around the grid cell Cell. D ; Step S1.2, calculate the grid cell Cell and the corresponding grid cell Cell D The height difference between max and horizontal projection distance Dis; Step S1.3, based on the grid cell Cell and the corresponding grid cell Cell D The height difference between max And the horizontal projection distance Dis, use the following formula to get the slope value S of the grid cell Cell: S=DH max / Dis Step S1.4, use the grid cell Cell as the outflow grid, and the corresponding grid cell Cell D As the inflow grid, the cumulative flow value of the grid unit as the inflow grid is increased by 1, and the initial value of the cumulative flow value of each grid unit is 0.

2. The method for estimating the spatial distribution of slope flow velocity based on terrain and vegetation characteristics according to claim 1, characterized in that: The step 2 specifically includes the following steps: Step S2.1, based on the slope grid matrix of the target watershed, the average slope value of the target watershed is obtained using the following formula; where i is the grid cell number in the target basin, 1 < i < N, and N is the total number of grid cells in the target basin; S i is the slope value of the grid cell numbered i; S ave is the average slope value of the target basin; Step S2.2, based on the confluence accumulation grid matrix of the target basin, obtain the confluence area at the outlet of the target basin; R=A max ×z 2 In the formula, A max is the maximum cumulative flow value in the cumulative flow grid matrix of the target basin; z is the side length of the grid unit; R is the flow area at the outlet of the target basin; Step S2.3, calculating the average flow velocity factor of the target watershed based on the average slope of the target watershed and the confluence area at the outlet of the target watershed; Where V mean is the average water flow velocity of the target basin, which is obtained from the runoff observation data of the outlet section of the target basin; b is the average slope index of the target basin; c is the area index of the target basin; and F is the average flow velocity factor of the target basin.

3. The method for estimating the spatial distribution of slope flow velocity based on terrain and vegetation characteristics according to claim 1 is characterized in that: The step 3 specifically includes the following steps: Step S3.1, collecting spatial distribution data of vegetation cover types in the target watershed; Using the vegetation coverage type data preset larger than the target watershed range as the source data and the target watershed range as the mask, the spatial distribution data of the vegetation coverage type within the target watershed range is collected; Based on the collected spatial distribution data of vegetation cover types within the target watershed, each grid cell in the target watershed is checked grid by grid cell to check whether there is a null value in the spatial distribution data of vegetation cover types of each grid cell. If there is a null value, the grid cell with the null value is set as the center of the circle and the 3z distance is used as the radius to draw a circle. The vegetation cover type with the highest area proportion within the circular range is assigned to the grid cell with the null value of the data, and the spatial distribution data of vegetation cover types is interpolated to update the spatial distribution data of vegetation cover types in the target watershed. Step S3.2, based on the spatial distribution data of vegetation cover types in the target watershed, divide the vegetation cover types in the target watershed into preset vegetation cover types, assign a value to the roughness of each vegetation cover type in the target watershed according to the preset value of the roughness of each vegetation cover type, and obtain the spatial distribution data of the roughness of the target watershed.

4. The method for estimating the spatial distribution of slope flow velocity based on terrain and vegetation characteristics according to claim 1 is characterized in that: The step 4 specifically includes the following steps: The slope flow velocity of each grid cell in the target watershed is estimated according to the following formula. The spatial distribution of the slope flow velocity in the target watershed is obtained by traversing each grid cell in the target watershed according to this formula. Where: q i,t is the runoff depth in the grid cell numbered i at time t, obtained by the Green-Ampt method based on the rainfall amount during the rainfall process, 1 < i < N, where N is the total number of grid cells in the target basin, and t is the target time period, with t ranging from the initial rainfall time period 1 to the end time period T of the rainfall process; n i is the roughness coefficient of the grid cell numbered i, S i is the slope of the grid cell numbered i; d is the slope index of the target basin, and k is the runoff depth index of the target basin; v i,t is the overland flow velocity of the grid cell numbered i at time t; F is the average flow velocity factor of the target basin.

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