CN116385683B - Three-dimensional small drainage basin channel fractal dimension calculation method and system - Google Patents
Three-dimensional small drainage basin channel fractal dimension calculation method and system Download PDFInfo
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Abstract
The invention discloses a method and a system for calculating fractal dimension of a three-dimensional small-drainage-basin channel, which relate to the technical field of rock mass engineering and comprise the following steps: acquiring a digital elevation model DEM of a region to be researched, and extracting a channel grid; establishing three-dimensional geographic coordinates of a small-river basin channel grid, and establishing a cube space; dividing the cube space into a plurality of cube grid cells; sequentially judging whether each cube grid unit comprises a channel or not; taking the logarithm of the number of the cube grid cells occupied by the small watershed channels as an ordinate, taking the logarithm of the side lengths of the cube grid cells as an abscissa, drawing a scatter diagram, and determining a non-scale interval in the scatter diagram; fitting a straight line to points within the scale-free interval, the opposite number of slopes of the straight line being the fractal dimension of the small-drainage-basin channel in the area to be studied. The invention greatly reduces errors in the calculation process, and ensures extremely high precision while having high efficiency.
Description
Technical Field
The invention relates to the technical field of rock mass engineering, in particular to a method and a system for calculating a fractal dimension of a three-dimensional small-drainage-basin channel.
Background
Fractal dimension is a concept in geometric shape division theory, can reflect the degree of space occupied by irregular shapes, and has been proposed by Hausdorff in 1910, because the concept is simple, easy to program and high in applicability, and has wide application in description and evaluation of small-drainage-basin channels.
The development condition of the small watershed channels in mountain areas has promotion effects on occurrence of geological disasters such as landslide, debris flow and the like to different degrees, and fractal dimension is used as a good tool for describing the complexity degree of irregular shapes in space and is increasingly and widely applied to determining quantization indexes of the small watershed channel structures, so that basis for risk evaluation is provided for the channel structures which are likely to be disasters.
The prior art is mainly characterized in that the fractal dimension calculation of the small-drainage-basin channel is performed by manual calculation, the efficiency is low, the accuracy is low, the requirement on a programmer is high when the calculation is performed by a programming method, the calculation is basically performed by the relation between points on a line and grids, and thus errors can be generated under the condition of finer grid division.
Disclosure of Invention
The invention provides a three-dimensional small-drainage-basin channel fractal dimension calculation method and a three-dimensional small-drainage-basin channel fractal dimension calculation system, which are used for solving the problems that the traditional fractal dimension calculation method is time-consuming, large in error and sensitive to subjective factor change in calculation result.
The invention provides a three-dimensional small-drainage-basin channel fractal dimension calculation method, which comprises the following steps:
acquiring a digital elevation model DEM of a region to be researched, and extracting a channel grid;
establishing three-dimensional geographic coordinates of small-river-basin channel grids in the channel grids, and establishing a cube space according to the three-dimensional geographic coordinates;
determining the number of dividing intervals, and dividing a cube space into a plurality of cube grid cells;
sequentially judging whether each cube grid cell comprises channels or not, and counting the number of the cube grid cells occupied by the channels of the small drainage basin;
taking the logarithm of the number of the cube grid units occupied by the small drainage basin channels as an ordinate, taking the logarithm of the side length of the cube grid units as an abscissa, drawing a scatter diagram, differentiating the ordinate, eliminating scattered points in a coordinate interval with a differential result always smaller than a singular value separation point, and taking the coordinate interval formed by the residual scattered points as a non-scale interval;
fitting a straight line to points within the scale-free interval, the opposite number of slopes of the straight line being the fractal dimension of the small-drainage-basin channel in the area to be studied.
Further, the method further comprises the following steps:
when the determined dividing interval number n does not reach the maximum dividing interval number, the dividing interval number n is gradually increased by 1, and the number of the cube grid units occupied by the small watershed channels is counted when the cube space is divided by the increased dividing interval number n.
Further, the method further comprises the step of judging the special intersection condition of the channel and each cube grid cell, wherein the method comprises the following steps:
when the channel only contacts the top point, side, face of the outer surface of the cube grid cell, or the channel is only located on one face of the cube grid cell, then the cube grid cell is eliminated from the cube grid cells occupied by the small basin channel.
Further, the step of obtaining the digital elevation model DEM of the area to be studied and extracting the channel grid includes the following steps:
acquiring positive photographic image data of an area to be studied;
modeling the positive photographic image data in ContextCapture to obtain a digital surface model DSM of the region to be studied;
converting the digital surface model DSM into point cloud data in a GlobalMapper, and removing vegetation and ground point cloud data by using point cloud filtering to obtain a digital elevation model DEM of the area to be researched;
and (3) importing the digital elevation model DEM into ArcGis, splicing the digital elevation model DEM, and sequentially carrying out filling depression, flow direction analysis, ditch net grading, grid ditch net vectorization and ditch net grading optimization display on the digital elevation model DEM, so as to extract and obtain the channel grid.
Further, the establishing a three-dimensional geographic coordinate of the small-river-basin channel grid in the channel grid, and establishing a cube space according to the three-dimensional geographic coordinate, includes the following steps:
vectorizing a small-drainage-basin channel grid in the channel grid, and adding a plurality of control points into the vectorized small-drainage-basin channel grid;
respectively extracting longitude, latitude and elevation data of a plurality of control points from ArcGis, respectively importing the longitude, latitude and elevation data into an Excel table, and converting the longitude, latitude and elevation data of each control point to obtain three-dimensional geographic coordinates of a small-drainage-basin channel grid;
and taking the maximum value of the length, width and height of the three-dimensional geographic coordinates of the small watershed grid as the side length, and establishing a cube space.
Further, the calculation formula of the fractal dimension of the small-drainage-basin channel is as follows:
wherein D is f For fractal dimension, i.e. lnN (r) Relative toSlope values of (2);
N (r) the number of cubic grid cells occupied by the channels of the small watershed, namely the number of cubic grid cells intersected with the channels;
m is the side length of the cube space; n is the number of dividing intervals;
r is the side length of the divided cube grid cell.
The invention also provides a three-dimensional small-drainage-basin channel fractal dimension calculation system, which comprises:
the channel grid acquisition module is used for acquiring a digital elevation model DEM of the area to be researched and extracting a channel grid;
the cube space construction module is used for establishing three-dimensional geographic coordinates of the small-river basin channel grids in the channel grids and establishing a cube space according to the three-dimensional geographic coordinates;
the grid cell dividing module is used for determining the dividing interval number and dividing the cube space into a plurality of cube grid cells;
the intersecting grid determining module is used for sequentially judging whether each cube grid unit comprises channels or not and counting the number of the cube grid units occupied by the channels of the small drainage basin;
the scale-free interval determining module is used for drawing a scatter diagram by taking the logarithm of the number of the cube grid cells occupied by the small drainage basin channels as an ordinate and the logarithm of the side length of the cube grid cells as an abscissa; differentiating the ordinate of the coordinate interval, excluding scattered points in the coordinate interval of which the differential result is always smaller than the singular value separation point, and taking the coordinate interval formed by the rest scattered points as a scale-free interval;
the fractal dimension determining module is used for fitting a straight line to points in the scale-free interval, and the opposite number of the slope of the straight line is the fractal dimension of the small-drainage-basin channel in the area to be studied.
Compared with the prior art, the invention has the beneficial effects that:
when the fractal dimension of the channel in the small drainage basin is calculated, firstly, an unmanned aerial vehicle aerial image and ArcGis are utilized to obtain the coordinates of the channel, then, the cube space occupied by the channel is determined, the cube space is divided at equal intervals for a plurality of times according to the determined dividing interval number, a plurality of cube grid units are obtained, the number of the cube grid units occupied by the channel is counted after grid division is carried out for each time, after grid division and counting are carried out for a plurality of times, a coordinate system is drawn, the abscissa is the logarithm of the dividing interval number each time, the ordinate is the logarithm of the side length of the cube grid unit occupied by the channel obtained by counting each time, and the opposite number of the slope is the fractal dimension result of the channel. The three-dimensional small-drainage-basin channel fractal dimension calculation method provided by the invention can obtain a fractal dimension result with higher precision according to the set dividing interval number only by measuring the coordinates of the channel flow direction under the coordinate system.
According to the method, the special condition that the channels are intersected with each divided cube grid unit is further judged and excluded in the traditional fractal dimension calculation method, the calculation accuracy of the fractal dimension is improved, and a complete fractal dimension calculation working scheme is formed. The fractal dimension algorithm of the invention ensures that a higher-precision fractal dimension result of the channel can be obtained by only determining the number of the cube grid units after final halving by using personnel, has low using threshold and high calculating efficiency, calculates by using the relation of the line and the grid, and simultaneously considers the special relation of the line and the grid which are intersected in parallel, thereby greatly reducing errors in the calculating process and ensuring extremely high precision while having high efficiency.
Drawings
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention. In the drawings:
FIG. 1 is a flow diagram of a three-dimensional small drainage basin channel fractal dimension calculation method extracted by the invention;
FIG. 2 is a schematic illustration of a partial basin channel of an area to be studied in an embodiment of the invention;
FIG. 3 is a schematic diagram of a special intersection of channels with a cubic grid cell in an embodiment of the invention;
fig. 4 is a schematic diagram showing a calculation result of a fractal dimension of one channel applied in a black river domain in the embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, but it should be understood that the protection scope of the present invention is not limited by the specific embodiments.
Example 1
As shown in fig. 1, the invention provides a three-dimensional small drainage basin channel fractal dimension calculation method, which comprises the following steps:
step S1: acquiring a digital elevation model DEM of a region to be researched, and extracting a channel grid;
step S2: establishing three-dimensional geographic coordinates of small-river-basin channel grids in the channel grids, and establishing a cube space according to the three-dimensional geographic coordinates;
step S3: determining the number of dividing intervals, and dividing a cube space into a plurality of cube grid cells;
step S4: sequentially judging whether each cube grid cell comprises channels or not, and counting the number of the cube grid cells occupied by the channels of the small drainage basin;
step S5: when the determined dividing interval number n does not reach the maximum dividing interval number, the dividing interval number n is gradually increased by 1, and the number of the cube grid units occupied by the small watershed channels is counted by the increasing dividing interval number n through repeating the steps S3 and S4 respectively;
step S6: taking the logarithm of the number of the cube grid units occupied by the small drainage basin channels as an ordinate, taking the logarithm of the side length of the cube grid units as an abscissa, drawing a scatter diagram, differentiating the ordinate, eliminating scattered points in a coordinate interval with a differential result always smaller than a singular value separation point, and taking the coordinate interval formed by the residual scattered points as a non-scale interval;
step S7: fitting a straight line to points within the scale-free interval, the opposite number of slopes of the straight line being the fractal dimension of the small-drainage-basin channel in the area to be studied.
In step S1, a digital elevation model DEM of the area to be studied is obtained, and a channel grid is extracted, including the steps of:
acquiring positive photographic image data of an area to be researched, wherein the positive photographic image data can be acquired by unmanned aerial vehicle aerial photography;
modeling the positive photographic image data in ContextCapture to obtain a digital surface model DSM of the region to be studied;
converting the digital surface model DSM into point cloud data in a GlobalMapper, and removing vegetation and ground point cloud data by using point cloud filtering to obtain a digital elevation model DEM of the area to be researched;
and (3) importing the digital elevation model DEM into ArcGis, specifically splicing the digital elevation model DEM by using Data Management tools.tbx in a toolbox in the ArcGis, and sequentially filling the depression, analyzing the flow direction, analyzing the ditch network, grading the ditch network, vectorizing the ditch network of the ditch and grading and optimizing the ditch network of the ditch by using the Spatial analysis tools.tbx to extract the ditch network.
In step S2, three-dimensional geographic coordinates of a small-basin trench grid in the trench grid are established, and a cube space is established according to the three-dimensional geographic coordinates, including the steps of:
step S2.1: vectorizing a small-drainage-basin channel grid in the channel grid, adding a plurality of control points in the vectorized small-drainage-basin channel grid, specifically utilizing Data Management tools.tbx-sampling-generating points along the line in a toolbox in ArcGis, and adding the control points through the density of the set points;
step S2.1: respectively extracting longitude, latitude and elevation data of a plurality of control points from ArcGis, respectively importing the longitude, latitude and elevation data into an Excel table, and converting the longitude, latitude and elevation data of each control point to obtain three-dimensional geographic coordinates of a small-drainage-basin channel grid;
specifically, importing longitudes and latitudes of a plurality of control points into an Excel table, and inputting the formula (1) and the formula (2) into the Excel table to perform coordinate conversion to obtain x-axis coordinates and y-axis coordinates in a two-dimensional coordinate system;
MID(A2,1,3)+MID(A2,6,2)/60+MID(A2,10,5)/3600 (1)
MID(B2,1,2)+MID(B2,5,2)/60+MID(B2,9,5)/3600 (2)
wherein MID (A2, 1, 3) represents taking three numbers of data in A2 cells from the first; the rest MID (A2, 6, 2), MID (A2, 10, 5), MID (B2, 1, 2), MID (B2, 5, 2) and MID (B2, 9, 5) are the same, and the longitude and latitude coordinates can be converted into the needed digital form through the formula.
Adding a z-axis field in an attribute list of an Excel table, and importing elevation data of a plurality of control points into the Excel table to serve as a z-axis coordinate;
based on the obtained x-axis, y-axis and z-axis coordinates in the Excel table, three-dimensional geographic coordinates of the small-basin channel grid are obtained. During the operation of step S2.1, the coordinate system of the control points needs to be kept consistent, and in this embodiment the wgs_1984 coordinate system is used.
Step S2.3: and taking the maximum value of the length, width and height of the three-dimensional geographic coordinates of the small watershed grid as the side length, and establishing a cube space.
In step S3, the three-dimensional cube space is divided into 8 new cubes by default starting with 2-partition, then 3-partition, 4-partition, … …, and so on, until the artificially determined n-partition is cut, at which time the three-dimensional space is divided into n 3 New cube grid cells. For different channels, the number of suitable equally-divided intervals is determined according to the actual situation.
In step S4, the cube space under investigation is n-etc. fractal, generating n 3 Sequentially judging whether each cubic grid unit contains a part of channels or not, if so, adding one to the number s of the cubic grid units occupied by the channels of the small drainage basin, and if not, judging the next cubic grid unit until all grids are judged to be finished, and for each equally dividing study of the cubic space, judging the number s of the cubic grid units occupied by the channels of the small drainage basin min ＝1，s max ＝n 3 。
As shown in FIG. 3, the intersection of the channels in three-dimensional space with the cube grid elements is normally evident, but when the channels only contact the vertices, edges, faces of the outer surfaces of the cube grid elements, or the channels are only located on a certain face of the cube grid elements, the computer will normally determine that the channels belong to the cube grid elements, but in actual cases these should not logically belong to the cube space, so in order to optimize the result obtained in step 4 further, the cube grid elements are removed from the cube grid elements occupied by the small basin channels, and the cube grid elements in the above cases are not counted, resulting in a new result N (r) ,N (r) ≤s。
In step S6, the fractal characteristics of the channel can be effectively reflected only in the scale-free interval and the fractal dimension can be effectively reflected by the method, and in combination with the existing method for determining the scale-free interval, a new algorithm for determining the scale-free interval is developed by considering the characteristics of the drainage basin channel, and good effects are obtained in multiple calculations, and the method specifically comprises the following steps:
as shown in fig. 4, coordinates of the scatter diagram are calculated for the channel fractal dimension, data of the y axis of the scatter diagram is differentiated, 0.05 is taken as a singular value separation point, a section with a difference result always smaller than the singular value is a section which does not meet the fractal requirement, scattered points in the section which does not meet the requirement are removed, and a section formed by the rest scattered point coordinates is a scale-free section.
In step S7, the calculation formula of the fractal dimension of the small-drainage-basin channel is as follows:
wherein D is f For fractal dimension, i.e. ln N (r) Relative toSlope values of (2);
N (r) the number of cubic grid cells occupied by the channels of the small watershed, namely the number of cubic grid cells intersected with the channels;
m is the side length of the cube space; n is the number of dividing intervals;
r is the side length of the divided cube grid cell.
Example 2
The invention also provides a three-dimensional small-drainage-basin channel fractal dimension calculation system, which comprises:
the channel grid acquisition module is used for acquiring a digital elevation model DEM of the area to be researched and extracting a channel grid;
the cube space construction module is used for establishing three-dimensional geographic coordinates of the small-river basin channel grids in the channel grids and establishing a cube space according to the three-dimensional geographic coordinates;
the grid cell dividing module is used for determining the dividing interval number and dividing the cube space into a plurality of cube grid cells;
the intersecting grid determining module is used for sequentially judging whether each cube grid unit comprises channels or not and counting the number of the cube grid units occupied by the channels of the small drainage basin;
the scale-free interval determining module is used for drawing a scatter diagram by taking the logarithm of the number of the cube grid cells occupied by the small drainage basin channels as an ordinate and the logarithm of the side length of the cube grid cells as an abscissa; differentiating the ordinate of the coordinate interval, excluding scattered points in the coordinate interval of which the differential result is always smaller than the singular value separation point, and taking the coordinate interval formed by the rest scattered points as a scale-free interval;
the fractal dimension determining module is used for fitting a straight line to points in the scale-free interval, and the opposite number of the slope of the straight line is the fractal dimension of the small-drainage-basin channel in the area to be studied.
The following describes the technical scheme of the present invention in detail with reference to specific examples.
Taking a black river basin partial channel as an example, the method for calculating the fractal dimension of the channel is specifically described, and the specific implementation steps are as follows:
and step 1, obtaining the DEM of the black river basin area.
The method comprises the following specific steps: obtaining an orthographic image picture of a black river basin area by unmanned aerial vehicle aerial photography, modeling in ContextCapture to obtain a digital surface model DSM, turning the digital surface model DSM into point cloud data in a Global map, removing vegetation and ground objects by using point cloud filtering, and then generating a digital elevation model DEM.
And 2, extracting a channel network of the research area.
The method comprises the following specific steps: the digital elevation model DEM is imported into ArcGis, the DEM Data is spliced by using the Data Management tools.tbx in the tool box, and the simple extraction of the channel network is completed by sequentially filling the depressions, analyzing the flow direction, analyzing the channel network, grading the channel network, vectorizing the grid channel network and optimizing the channel network by using the Spatial analysis tools.tbx. Wherein, ditch net classification defaults to STRAHOLE method, river net in this example is classified into 6 grades, as shown in FIG. 2.
And 3, vectorizing the channel network for research.
After ditch network extraction, manual vectorization is carried out, only small-river-basin channels of a research area are vectorized, points are generated along the line in Data Management tools.
And 4, extracting geographical coordinates of the channel network.
The method comprises the following specific steps: firstly, extracting longitude and latitude of a control point obtained in the step 3 from ArcGis, importing the longitude and latitude into an Excel table, inputting the formula (1) and the formula (2) in the above content into the Excel table to perform coordinate conversion, importing x-axis and y-axis coordinates into ArcGis, converting geographic coordinates into projections (note coordinates must be unified), and generating a sheet file. And directly converting the three-dimensional channel network geographic coordinates into a plane coordinate system after adding an x-axis and a y-axis, adding a z-axis field in an attribute list, loading a digital elevation model DEM to generate an elevation, and finally exporting the x-axis, the y-axis and the z-axis in the attribute list.
During operation, it should be noted that the coordinate system needs to be consistent, and the wgs_1984 coordinate system is used for extraction in this embodiment.
And 5, determining the side length M of the research space generated by the channel.
According to the coordinates of the channel, the maximum value of the length, width and height determined by the three-dimensional coordinates of the channel is 63850 of the space occupied by the channel, so that the side length m= 63850 of the three-dimensional cube space is selected.
And 6, determining the number of intervals to be divided.
From the M obtained in step 1, it is determined that the three-dimensional cube space is equally divided into 100, and by default, the three-dimensional space is divided into 8 new cubes from 2 equal divisions, then 3 equal divisions, 4 equal divisions … … and so on until 100 equal divisions.
And 7, counting the number s of grids occupied by the equally divided grid channels.
Dividing the research space by n equally, generating n for three-dimensional condition 3 Each grid is judged according to the equal volume of the cube grid units, whether the cube grid units contain a part of the channels or not is judged, if so, the number s of the cube grid units occupied by the channels is increased by one, and if not, the next is judgedA plurality of cube grid cells until all cube grid cells are judged to end, s for each aliquoting study space min ＝1，s max ＝n 3 。
Step 8, judging the special intersection condition of the channel and the grid to improve the statistical result N (r) Is a function of the accuracy of (a).
As shown in FIG. 3, when the channel is in contact with only the vertices, edges, faces or on a certain face of the outer surface of the cube grid cell, the computer will typically determine that the channel belongs to the cube grid cell, but in practice these cases should not logically belong to the cube grid cell, so that the result obtained in step 7 is further optimized, and the counts of the cube grid cells in the above cases are removed to obtain a new result N (r) ,N (r) ≤s。
Step 9, repeating the steps 7 and 8 to obtain an equal division number increased by 1 and a grid number N corresponding to the channels obtained by each equal division cube (r) . The final result is an aliquot number of increasing from 2 to 1 to 100, and 99N (r) 。
And step 10, a calculation formula of the fractal dimension is shown in a formula (3) in the content.
And 11, determining a scale-free interval.
Only the fractal dimension in the scale-free interval can effectively reflect the fractal characteristics of the channel, and the scale-free interval algorithm of the invention is applied to obtain the scale-free abscissa interval [8.1,10.2] as shown in the right side of the figure 4.
And step 12, fitting a straight line to points in the scale-free interval.
As shown in fig. 4, the opposite number of the slope of the straight line is the fractal dimension of the study channel, and the linear correlation coefficient of the fitted straight line and the calculated value is 0.9931, so that the better the fitting effect is.
According to the invention, by utilizing unmanned aerial vehicle photogrammetry technology and three-dimensional modeling technology and combining ArcGis to rapidly and accurately extract the three-dimensional geographic coordinates of the channel so as to facilitate calculation of fractal dimension, the special condition that the channel is intersected with each divided cube grid unit is further judged and eliminated in the traditional fractal dimension calculation method, so that the calculation accuracy of the fractal dimension is improved, and a complete fractal dimension calculation working scheme is formed. The fractal dimension algorithm of the invention ensures that a fractal dimension result with higher accuracy of a channel can be obtained by using personnel to determine the number of cube grid cells after final halving, has low using threshold and high calculating efficiency, and solves the problems of time consumption, large error and sensitivity of the result to subjective factor change in the traditional fractal dimension calculating method.
The last explanation is: the above disclosure is only one specific embodiment of the present invention, but the embodiment of the present invention is not limited thereto, and any changes that can be thought by those skilled in the art should fall within the protection scope of the present invention.
Claims (5)
1. The method for calculating the fractal dimension of the three-dimensional small-drainage-basin channel is characterized by comprising the following steps of:
acquiring a digital elevation model DEM of a region to be researched, and extracting a channel grid;
establishing three-dimensional geographic coordinates of small-river-basin channel grids in the channel grids, and establishing a cube space according to the three-dimensional geographic coordinates;
determining the number of dividing intervals, and dividing a cube space into a plurality of cube grid cells;
sequentially judging whether each cube grid cell comprises channels or not, and counting the number of the cube grid cells occupied by the channels of the small drainage basin;
taking the logarithm of the number of the cube grid units occupied by the small drainage basin channels as an ordinate, taking the logarithm of the side length of the cube grid units as an abscissa, drawing a scatter diagram, differentiating the ordinate, eliminating scattered points in a coordinate interval with a differential result always smaller than a singular value separation point, and taking the coordinate interval formed by the residual scattered points as a non-scale interval;
fitting a straight line to points in the scale-free interval, wherein the opposite number of the slope of the straight line is the fractal dimension of a small-drainage-basin channel in the area to be researched;
the method for acquiring the digital elevation model DEM of the area to be researched and extracting the channel grid comprises the following steps:
acquiring positive photographic image data of an area to be studied;
modeling the positive photographic image data in ContextCapture to obtain a digital surface model DSM of the region to be studied;
converting the digital surface model DSM into point cloud data in a GlobalMapper, and removing vegetation and ground point cloud data by using point cloud filtering to obtain a digital elevation model DEM of the area to be researched;
importing the digital elevation model DEM into ArcGis, splicing the digital elevation model DEM, sequentially filling the depressions, analyzing the flow direction, analyzing the ditch net, grading the ditch net, vectorizing the grid ditch net and grading and optimizing the ditch net, and extracting to obtain the channel grid;
the method for establishing the three-dimensional geographic coordinates of the small-river-basin channel grids in the channel grids comprises the following steps of:
vectorizing a small-drainage-basin channel grid in the channel grid, and adding a plurality of control points into the vectorized small-drainage-basin channel grid;
respectively extracting longitude, latitude and elevation data of a plurality of control points from ArcGis, respectively importing the longitude, latitude and elevation data into an Excel table, and converting the longitude, latitude and elevation data of each control point to obtain three-dimensional geographic coordinates of a small-drainage-basin channel grid;
and taking the maximum value of the length, width and height of the three-dimensional geographic coordinates of the small watershed grid as the side length, and establishing a cube space.
2. The method for calculating the fractal dimension of a three-dimensional small-drainage-basin channel as recited in claim 1, further comprising:
when the determined dividing interval number n does not reach the maximum dividing interval number, the dividing interval number n is gradually increased by 1, and the number of the cube grid units occupied by the small watershed channels is counted when the cube space is divided by the increased dividing interval number n.
3. The method of calculating the fractal dimension of a three-dimensional small-basin channel according to claim 1, further comprising re-judging the special intersection of said channel with each of said cubic grid cells as follows:
when the channel only contacts the top point, side, face of the outer surface of the cube grid cell, or the channel is only located on one face of the cube grid cell, then the cube grid cell is eliminated from the cube grid cells occupied by the small basin channel.
4. The method for calculating the fractal dimension of a three-dimensional small-drainage-basin channel according to claim 1, wherein the calculation formula of the fractal dimension of the small-drainage-basin channel is as follows:
wherein D is f For fractal dimension, i.e. lnN (r) Relative toSlope values of (2);
N (r) the number of cubic grid cells occupied by the channels of the small watershed, namely the number of cubic grid cells intersected with the channels;
m is the side length of the cube space; n is the number of dividing intervals;
r is the side length of the divided cube grid cell.
5. A three-dimensional small-drainage-basin channel fractal dimension calculation system, comprising:
the channel grid acquisition module is used for acquiring a digital elevation model DEM of the area to be researched and extracting a channel grid; the method specifically comprises the following steps: acquiring positive photographic image data of an area to be studied; modeling the positive photographic image data in ContextCapture to obtain a digital surface model DSM of the region to be studied; converting the digital surface model DSM into point cloud data in a GlobalMapper, and removing vegetation and ground point cloud data by using point cloud filtering to obtain a digital elevation model DEM of the area to be researched; importing the digital elevation model DEM into ArcGis, splicing the digital elevation model DEM, sequentially filling the depressions, analyzing the flow direction, analyzing the ditch net, grading the ditch net, vectorizing the grid ditch net and grading and optimizing the ditch net, and extracting to obtain the channel grid;
the cube space construction module is used for establishing three-dimensional geographic coordinates of the small-river basin channel grids in the channel grids and establishing a cube space according to the three-dimensional geographic coordinates; the method specifically comprises the following steps: vectorizing a small-drainage-basin channel grid in the channel grid, and adding a plurality of control points into the vectorized small-drainage-basin channel grid; respectively extracting longitude, latitude and elevation data of a plurality of control points from ArcGis, respectively importing the longitude, latitude and elevation data into an Excel table, and converting the longitude, latitude and elevation data of each control point to obtain three-dimensional geographic coordinates of a small-drainage-basin channel grid; taking the maximum value of the length, width and height of the three-dimensional geographic coordinates of the small watershed grid as the side length, and establishing a cube space;
the grid cell dividing module is used for determining the dividing interval number and dividing the cube space into a plurality of cube grid cells;
the intersecting grid determining module is used for sequentially judging whether each cube grid unit comprises channels or not and counting the number of the cube grid units occupied by the channels of the small drainage basin;
the scale-free interval determining module is used for drawing a scatter diagram by taking the logarithm of the number of the cube grid cells occupied by the small drainage basin channels as an ordinate and the logarithm of the side length of the cube grid cells as an abscissa; differentiating the ordinate of the coordinate interval, excluding scattered points in the coordinate interval of which the differential result is always smaller than the singular value separation point, and taking the coordinate interval formed by the rest scattered points as a scale-free interval;
the fractal dimension determining module is used for fitting a straight line to points in the scale-free interval, and the opposite number of the slope of the straight line is the fractal dimension of the small-drainage-basin channel in the area to be studied.
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