CN110020607A - A method of analogy basin is found based on Spatial Fractal Dimension theory - Google Patents

A method of analogy basin is found based on Spatial Fractal Dimension theory Download PDF

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CN110020607A
CN110020607A CN201910191140.4A CN201910191140A CN110020607A CN 110020607 A CN110020607 A CN 110020607A CN 201910191140 A CN201910191140 A CN 201910191140A CN 110020607 A CN110020607 A CN 110020607A
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slope
grid
gradient
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elevation
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CN110020607B (en
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童冰星
李致家
刘墨阳
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Hohai University HHU
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    • G06F18/22—Matching criteria, e.g. proximity measures
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
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    • G06F18/23—Clustering techniques
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
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    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
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Abstract

The invention discloses a kind of methods for finding analogy basin based on Spatial Fractal Dimension theory, first, basin is divided into several orthogonal grid cells based on dem data, obtain the elevation in each grid cell, to obtain the elevation grid Raster_Ele in basin, and elevation fractal dimension value Fra_Ele is calculated；Secondly, calculating the gradient in each grid cell, the gradient grid Raster_Slope in basin is obtained, and gradient fractal dimension value Fra_Slope is calculated；Then, the slope aspect in each grid cell is calculated, obtains the slope aspect grid Raster_SlopeDir in basin, and slope aspect fractal dimension value Fra_SlopeDir is calculated；Finally, building fractal feature space is labeled in fractal feature space by watershed generalization at data point, and data point is classified, it is thus regarded that being divided into a kind of basin is analogy basin.

Description

A method of analogy basin is found based on Spatial Fractal Dimension theory
Technical field
The present invention relates to hydrology technology fields, and in particular to a kind of side that analogy basin is found based on Spatial Fractal Dimension theory Method.
Background technique
China river is numerous, drainage area 200 to 3000km2Middle small watershed nearly 9000.In recent years, climate changes It influences, the sudden flood of the middle and small river as caused by Local Heavy Precipitation frequently occurs, it has also become the main disasters to cause casualties Kind.Middle small watershed easily forms harm due to being generally in remote mountain areas with a varied topography, that the gradient is steep, the flood hurriedly to go up The flood of local resident's personal safety and social economy, thus the sudden flood of centering small watershed carry out quick early warning at For major issue urgently to be resolved.
Important tool of the hydrological model formula to carry out flood forecasting, when constructing hydrological model, it is necessary first to be exactly Based on the rainfall in basin, the observational datas such as evaporation and flow carry out Offered model parameters.However small watershed is often in the property of mountain area Remoteness, observation website are sparse, it is difficult to obtain hydrometeorological data abundant to carry out the building of model.For this feelings Condition, common method are exactly that the basin for lacking data is replaced to carry out mould using the data in the similar basin of nature geography characteristic The calibration of shape parameter.Therefore searching out suitable analogy basin just becomes the committed step of Cross Some Region Without Data hydrological model building. However the method for finding analogy basin existing at present is mostly using basin mean inclination, slope aspect and elevation are as feature Value.This method is merely capable of reflecting the rough nature geography characteristic in basin, and the geographical feature space inside watershed Difference is but difficult to consider, so that the searching belt to analogy basin carrys out biggish uncertainty.Based on remote sensing, geography information and number The development of the technologies such as word basin describes grid digital elevation model (DEM, the Digital of surface elevation change using numerical matrix Elevation Model) it is gradually mature, and be widely used.The small watershed especially in mountain area property with a varied topography In, dem data has important application value due to it can relatively accurately consider topography variation in basin.How to utilize The judgment method that advantage of the dem data in mountain area property basin carrys out analogy basin carry out it is perfect, to improve to a certain extent For the key points and difficulties during the attention and basin Study on Similarity of basin inside nature geography characteristic Spatial Variations One of.
In order to further promote basin Study on Similarity, needs deeper to enter research and consider basin inside nature geography characteristic The analogy basin method of discrimination of Spatial Variations.
Point dimension is called and does fractal dimension, is a most important concept in fractal theory, it be to Non-smooth surface, it is irregular, The important parameter that the extremely complex point shape object such as broken is quantitatively portrayed, it characterizes the complexity, thick of fractal Rough degree.Divide dimension bigger, object is more complicated, more coarse, and vice versa.Usually widely known integer dimension can only indicate several What object occupies several specific dimensions in objective world, such as one-dimensional, two dimension, three-dimensional etc..However as graphics and mathematics Continuous development, it has been found that the figures that can not simply be described using integer dimensions of many either function, such as wriggle song The dimension in the coastline of folding is exactly between peacekeeping two dimension.
Fractals and its a point dimension concept are negated property is entirely different between point, line, surface, body etc. in conventional geometric Absolutely clearly demarcated boundary, profoundly prompted between point-line-surface body, between shaping (i.e. regular figure) and point shape, dimension it is discrete With it is continuous between dialectical relationship.Propose a kind of dynamic dimension measurement side for describing geometric object during development and change Method.Landform for basin under natural conditions, due to the collective effect by internal and external agencies, in basin in each region The feature such as gradient, during slope aspect and elevation etc. are constantly in continuous development variation, therefore it is simply average using one Numerical value the features of terrain in basin cannot have been described accurately, to be easy to cause mistake when the Study on Similarity of basin Sentence, and then it is unreasonable to cause hydrological model to construct, so that final flood forecasting result is in the property of mountain area there are large error The mountain torrents prevention and treatment of small watershed leaves hidden danger.
The hair of basin Study on Similarity thus is unfavorable for for ignoring for the Spatial Variations feature of physical feature in basin Exhibition.
Against the above deficiency, how to consider the Spatial Variations feature of physical feature in basin, calculate the gradient, slope aspect and The Spatial Fractal Dimension number of the factors such as elevation, and then the similarity degree between watershed is quantified, positive inventor needs what is solved to ask Topic.
Summary of the invention
The technical problem to be solved by the present invention is to provide a kind of based on sky for defect involved in background technique Between the theoretical method for finding analogy basin of point dimension, have that data source is reliable and stable, computational efficiency is high, result is objective rationally etc. excellent Point is conducive to the further further investigation of basin similitude.
The present invention uses following technical scheme to solve above-mentioned technical problem:
A method of analogy basin is found based on Spatial Fractal Dimension theory, comprising the following steps:
Basin is divided into several orthogonal grid cells based on Law of DEM Data, i.e. dem data by step 1), The elevation in each grid cell is obtained, to obtain the elevation grid Raster_Ele in basin, and elevation point is calculated Dimension value Fra_Ele；
Step 2) calculates the gradient in each grid cell, obtains the gradient grid Raster_Slope in basin, and count Calculation obtains gradient fractal dimension value Fra_Slope；
Step 3) calculates the slope aspect in each grid cell, obtains the slope aspect grid Raster_SlopeDir in basin, And slope aspect fractal dimension value Fra_SlopeDir is calculated；
Step 4), building fractal feature space are labeled in fractal feature space by watershed generalization at data point, and will Data point is classified, and being divided into a kind of basin is analogy basin, specific as follows:
Step 4.1), with three mutually orthogonal unit vectorsFor base, fractal feature space is constructed, whereinDivide the unit vector in dimension for elevation,Divide the unit vector in dimension for the gradient,For the unit vector in slope aspect point dimension；
Step 4.2), elevation fractal dimension value, gradient fractal dimension value and slope aspect fractal dimension value according to basin are by watershed generalization at number Strong point is labeled in fractal feature space；
Step 4.3) is based on spectral clustering (spectral clustering) data analysing method, will be in fractal feature space Data point between be split classification, being divided into a kind of basin is analogy basin.
It is described as a kind of further prioritization scheme of method for finding analogy basin based on Spatial Fractal Dimension theory of the present invention Specific step is as follows for step 1):
Basin is divided into several orthogonal grid cells based on dem data, obtains each grid cell by step 1.1) In elevation, to obtain the elevation grid Raster_Ele in basin；
Step 1.2), using resolution ratio as sampling step length, obtains height line by line on the basis of elevation grid Raster_Ele Journey section, and calculate the Spatial Fractal Dimension value FCele of elevation section line by line, i.e., to every a line elevation section, with each of which grid The height value of lattice unit is ordinate, is constructed elevation section curve CurC_ using the side length accumulated value of grid cell as abscissa Elei, and row elevation section curve CurC_Ele is calculated using package topologyiSpatial Fractal Dimension value FCelei, finally obtain elevation Divide the column vector Col_Ele of dimension:
Col-Ele={ FCele0,FCele1,…FCelei,…FCeleI}
In formula: i is the number of row elevation section, and for value from 0 to I, I is total line number of elevation grid；
Step 1.3), using resolution ratio as sampling step length, obtains height by column on the basis of elevation grid Raster_Ele Journey section, and calculate the Spatial Fractal Dimension value FRele of elevation section by column, i.e., to each column elevation section, with each of which grid The height value of lattice unit is ordinate, and elevation section curve CurR_ is constructed using the side length accumulated value of grid cell as abscissa Elej, and row elevation section curve CurR_Ele is calculated using package topologyjSpatial Fractal Dimension value FCelei, finally obtain elevation Divide the row vector Row_Ele of dimension:
Row-Ele={ FRele0,FRele1,…FRelej,…FReleJ}
In formula: j is the number of column elevation section, and for value from 0 to J, J is total columns of elevation grid；
Elevation fractal dimension value Fra_ is calculated in step 1.4) on the basis of row vector Row_Ele and column vector Col_Ele Ele:
It is described as a kind of further prioritization scheme of method for finding analogy basin based on Spatial Fractal Dimension theory of the present invention Specific step is as follows for step 2):
Step 2.1) calculates the gradient in each grid cell, obtains the gradient grid Raster_Slope in basin；
Centered on grid cell Cell, pass through pair of the height value of the height value and grid cell of grid cell around Than finding out grid cell Cell minimum in contrastD, and calculate Cell and CellDBetween depth displacement DHmaxAnd floor projection Distance Dis, in conjunction with DHmaxWith the gradient S of Dis computation grid unit Cell:
S=DHmax/Dis
Step 2.2), using resolution ratio as sampling step length, obtains line by line on the basis of gradient grid Raster_Slope Gradient section, and calculate the Spatial Fractal Dimension value FCslope of gradient section line by line, i.e., it is each with its to every a line gradient section The value of slope of a grid cell is ordinate, and gradient section curve is constructed using the side length accumulated value of grid cell as abscissa CurC_Slopem, and row gradient section curve CurC_Slope is calculated using package topologymSpatial Fractal Dimension value FCslopem, most The column vector Col_Slope of the gradient point dimension is obtained eventually:
Col_Slope={ FCslope0, FCslope1... FCslopem... FCslopeM}
In formula: m is the number of row gradient section, and for value from 0 to M, M is total line number of gradient grid；
Step 2.3), using resolution ratio as sampling step length, obtains by column on the basis of gradient grid Raster_Slope Gradient section, and calculate the Spatial Fractal Dimension value FRslope of gradient section by column, i.e., it is each with its to each column gradient section The value of slope of a grid cell is ordinate, and gradient section curve is constructed using the side length accumulated value of grid cell as abscissa CurR_Slopen, and row gradient section curve CurR_Slope is calculated using package topologynSpatial Fractal Dimension value FCslopen, most The row vector Row_Slope of the gradient point dimension is obtained eventually:
Row_Slope={ FRslope0, FRslope1... FCslopen... FRslopeN}
In formula: n is the number of column gradient section, and for value from 0 to N, N is total columns of gradient grid；
Gradient fractal dimension value is calculated on the basis of row vector Row_Slope and column vector Col_Slope in step 2.4) Fra_ Slope:
It is described as a kind of further prioritization scheme of method for finding analogy basin based on Spatial Fractal Dimension theory of the present invention Specific step is as follows for step 3):
Step 3.1) calculates the slope aspect in each grid cell, obtains the slope aspect grid Raster_ in basin SlopeDir；
Step 3.2), on the basis of slope aspect grid Raster_SlopeDir, using resolution ratio as sampling step length, obtain by Capable slope aspect section, and calculate the Spatial Fractal Dimension value FCslopeDir of slope aspect section line by line, i.e., to every a line slope aspect section, with The value of slope of each of which grid cell is ordinate, and slope aspect section is constructed using the side length accumulated value of grid cell as abscissa Curve CurC_SlopeDirp, and row slope aspect section curve CurC_SlopeDir is calculated using package topologypSpatial Fractal Dimension value FCslopeDirp, finally obtain the column vector Col_SlopeDir of slope aspect point dimension:
Col_SlopeDir={ FCslopeDir0, FCslopeDir1... FCslopeDirp... FCslopeDirP}
In formula: p is the number of row slope aspect section, and for value from 0 to P, P is total line number of slope aspect grid；
Step 3.3), on the basis of slope aspect grid Raster_SlopeDir, using resolution ratio as sampling step length, obtain by The slope aspect section of column, and calculate the Spatial Fractal Dimension value FRslopeDir of slope aspect section by column, i.e., to each column slope aspect section, with The slope aspect value of each of which grid cell is ordinate, and slope aspect section is constructed using the side length accumulated value of grid cell as abscissa Curve CurR_SlopeDirq, and row slope aspect section curve CurR_SlopeDir is calculated using package topologyqSpatial Fractal Dimension value FCslopeDirq, finally obtain the row vector Row-SlopeDir of slope aspect point dimension:
Row_SlopeDir={ FRslopeDir0, FRslopeDir1... FCslopeDirq... FRslopeDirQ}
In formula: q is the number of column slope aspect section, and for value from 0 to Q, Q is total columns of slope aspect grid；
Slope aspect is calculated on the basis of row vector Row_SlopeDir and column vector Col_SlopeDir in step 3.4) Fractal dimension value Fra_SlopeDir:
The invention adopts the above technical scheme compared with prior art, has following technical effect that
A kind of method that analogy basin is found based on Spatial Fractal Dimension theory provided by the invention, with the gradient, slope aspect and height Based on journey, the gradient in fractal dimension space, the fractal dimension of slope aspect and elevation are quantified, and then use the method for data mining to phase As between carry out clustering and discriminant.It both ensure that the precision and reliability of calculated result in this way, while having solved using similar stream The data in domain carries out the hydrological model Construct question of Cross Some Region Without Data.And this method mainly applies basin digital elevation model, Data source is reliable and stable, and the functional relation in method between variable is clear, and the fast automatic classification for being conducive to analogy basin is sentenced Not, by digital basin technology to simplify extraction step, meanwhile, it ensure that the objective rationality of result, be conducive to analogy basin Quickly calling directly for method of discrimination, can further promote small watershed mountain torrents study on prevention in digital hydrology and mountain area property Deep development.
Detailed description of the invention
Fig. 1 is flow diagram of the invention；
Fig. 2 is big sill may drainage basin height difference grid schematic diagram；
Fig. 3 is big sill may basin grandient grid schematic diagram；
Fig. 4 is big sill may basin slope aspect grid schematic diagram；
Fig. 5 is big sill may drainage basin height difference horizontal section schematic diagram；
Fig. 6 is big sill may drainage basin height difference longitudinal profile schematic diagram；
Fig. 7 is big sill may basin grandient horizontal section schematic diagram；
Fig. 8 is big sill may basin grandient longitudinal profile schematic diagram；
Fig. 9 is big sill may basin slope aspect horizontal section schematic diagram；
Figure 10 is big sill may basin slope aspect longitudinal profile schematic diagram.
Specific embodiment
Technical solution of the present invention is described in further detail by taking big sill may basin as an example with reference to the accompanying drawing:
As shown in Figure 1, the invention discloses a kind of method for finding analogy basin based on Spatial Fractal Dimension theory, including it is following Step:
Basin is divided into several orthogonal grid cells based on Law of DEM Data, i.e. dem data by step 1), The elevation in each grid cell is obtained, to obtain the elevation grid Raster_Fle in basin, and elevation point is calculated Dimension value Fra_Ele, specific as follows:
Basin is divided into several orthogonal grid cells based on dem data, obtains each grid cell by step 1.1) In elevation, to obtain the elevation grid Raster_Fle in basin, as shown in Figure 2；
DEM (digital elevation model, Digital Elevation Model) is to indicate ground elevation with numerical matrix form A kind of actual ground model.Ground is generally melted into orthogonal grid unit adjacent to each other, grid cell (generally rectangular) by it Side length be dem data resolution ratio, and grid cell attribute value be earth's surface in the grid cell elevation.
The structure for using for reference dem data, is divided into several orthogonal grids for basin using resolution ratio identical with dem data Unit, the attribute value in each grid cell is elevation, to obtain the elevation grid Raster_Ele in basin；
Step 1.2), using resolution ratio as sampling step length, obtains height line by line on the basis of elevation grid Raster_Fle Journey section, as shown in figure 5, and calculate the Spatial Fractal Dimension value FCele of elevation section line by line, finally obtain the column of elevation point dimension to Measure Col_Fle；
Col_Ele={ FCele0, FCele1... FCelei... FCeleI}
In formula: i is the number of row elevation section, and for value from 0 to I, I is total line number of elevation grid.It is to adopt with resolution ratio Sample step-length, using the height value of each grid cell in this line as ordinate, using the side length accumulated value of grid cell as cross Coordinate constructs elevation section curve CurC_Elei, and row elevation section curve CurC_Ele is calculated using package topologyiSpace Fractal dimension value FCelei.All row elevation grid cells are traversed using same method, obtain the column vector Col_ of elevation point dimension Fle。
Step 1.3), using resolution ratio as sampling step length, obtains height by column on the basis of elevation grid Raster_Ele Journey section, as shown in fig. 6, and calculate the Spatial Fractal Dimension value FRele of elevation section by column, finally obtain the row of elevation point dimension to Measure Row_Ele；
Row_Ele={ FRele0, FRele1... FRelej... FReleJ}
In formula: j is the number of column elevation section, and for value from 0 to J, J is total columns of elevation grid.It is to adopt with resolution ratio Sample step-length, using the height value of each grid cell in this line as ordinate, using the side length accumulated value of grid cell as cross Coordinate constructs elevation section curve CurR_Elej, and row elevation section curve CurR_Ele is calculated using package topologyjSpace Fractal dimension value FCelei.All row elevation grid cells are traversed using same method, obtain the column vector Col_ of elevation point dimension Fle。
Elevation fractal dimension value Fra_ is calculated in step 1.4) on the basis of row vector Row_Fle and column vector Col_Ele Ele；
Step 2) calculates the gradient in each grid cell, obtains the gradient grid Raster_Slope in basin, and count Calculation obtains gradient fractal dimension value Fra_Slope, specific as follows:
Step 2.1) calculates the gradient in each grid cell, obtains the gradient grid Raster_Slope in basin, such as Shown in Fig. 3；
Centered on grid cell Cell, pass through pair of the height value of the height value and grid cell of grid cell around Than finding out grid cell Cell minimum in contrastD, and calculate Cell and CellDBetween depth displacement DHmaxAnd floor projection Distance Dis, in conjunction with DHmaxWith the gradient S of Dis computation grid unit Cell:
S=DHmax/Dis
According to each grid cell in above method traversal basin, to obtain gradient grid Raster_Slope.
Step 2.2), using resolution ratio as sampling step length, obtains line by line on the basis of gradient grid Raster_Slope Gradient section, and calculate the Spatial Fractal Dimension value FCslope of gradient section line by line, i.e., it is each with its to every a line gradient section The value of slope of a grid cell is ordinate, and gradient section curve is constructed using the side length accumulated value of grid cell as abscissa CurC_Slopem, and row gradient section curve CurC_Slope is calculated using package topologymSpatial Fractal Dimension value FCslopem, most The column vector Col_Slope of the gradient point dimension is obtained eventually:
Col_Slope={ FCslope0, FCslope1... FCslopem... FCslopeM}
In formula: m is the number of row gradient section, and for value from 0 to M, M is total line number of gradient grid；
Step 2.3), using resolution ratio as sampling step length, obtains by column on the basis of gradient grid Raster_Slope Gradient section, and calculate the Spatial Fractal Dimension value FRslope of gradient section by column, i.e., it is each with its to each column gradient section The value of slope of a grid cell is ordinate, and gradient section curve is constructed using the side length accumulated value of grid cell as abscissa CurR_Slopen, and row gradient section curve CurR_Slope is calculated using package topologynSpatial Fractal Dimension value FCslopen, most The row vector Row_Slope of the gradient point dimension is obtained eventually:
Row_Slope={ FRslope0, FRslope1... FCslopen... FRslopeN}
In formula: n is the number of column gradient section, and for value from 0 to N, N is total columns of gradient grid；
Gradient fractal dimension value is calculated on the basis of row vector Row_Slope and column vector Col_Slope in step 2.4) Fra_ Slope:
Step 3) calculates the slope aspect in each grid cell, obtains the slope aspect grid Raster_SlopeDir in basin, And slope aspect fractal dimension value Fra_SlopeDir is calculated, it is specific as follows:
Step 3.1) calculates the slope aspect in each grid cell, obtains the slope aspect grid Raster_ in basin SlopeDir, as shown in Figure 4；
Step 3.2), on the basis of slope aspect grid Raster_SlopeDir, using resolution ratio as sampling step length, obtain by Capable slope aspect section, and calculate the Spatial Fractal Dimension value FCslopeDir of slope aspect section line by line, i.e., to every a line slope aspect section, with The value of slope of each of which grid cell is ordinate, and slope aspect section is constructed using the side length accumulated value of grid cell as abscissa Curve CurC_SlopeDirp, and row slope aspect section curve CurC_SlopeDir is calculated using package topologypSpatial Fractal Dimension value FCslopeDirp, finally obtain the column vector Col_SlopeDir of slope aspect point dimension:
Col_SlopeDir={ FCslopeDir0, FCslopeDir1... FCslopeDirp... FCslopeDirP}
In formula: p is the number of row slope aspect section, and for value from 0 to P, P is total line number of slope aspect grid；
Step 3.3), on the basis of slope aspect grid Raster_SlopeDir, using resolution ratio as sampling step length, obtain by The slope aspect section of column, and calculate the Spatial Fractal Dimension value FRslopeDir of slope aspect section by column, i.e., to each column slope aspect section, with The slope aspect value of each of which grid cell is ordinate, and slope aspect section is constructed using the side length accumulated value of grid cell as abscissa Curve CurR_SlopeDirq, and row slope aspect section curve CurR_SlopeDir is calculated using package topologyqSpatial Fractal Dimension value FCslopeDirq, finally obtain the row vector Row_SlopeDir of slope aspect point dimension:
Row_SlopeDir={ FRslopeDir0, FRslopeDir1... FCslopeDirq... FRslopeDirQ}
In formula: q is the number of column slope aspect section, and for value from 0 to Q, Q is total columns of slope aspect grid；
Slope aspect is calculated on the basis of row vector Row_SlopeDir and column vector Col_SlopeDir in step 3.4) Fractal dimension value Fra_SlopeDir:
Step 4), building fractal feature space are labeled in fractal feature space by watershed generalization at data point, and will Data point is classified, and being divided into a kind of basin is analogy basin, specific as follows:
Step 4.1), with three mutually orthogonal unit vectorsFor base, fractal feature space is constructed, whereinDivide the unit vector in dimension for elevation,Divide the unit vector in dimension for the gradient,For the unit vector in slope aspect point dimension；
Step 4.2), elevation fractal dimension value, gradient fractal dimension value and slope aspect fractal dimension value according to basin are by watershed generalization at number Strong point is labeled in fractal feature space；
Step 4.3) is based on spectral clustering (spectral clustering) data analysing method as shown in Figure 10, will divide Classification is split between data point in dimensional feature space, being divided into a kind of basin is analogy basin.
Those skilled in the art can understand that unless otherwise defined, all terms used herein (including skill Art term and scientific term) there is meaning identical with the general understanding of those of ordinary skill in fields of the present invention.Also It should be understood that those terms such as defined in the general dictionary should be understood that have in the context of the prior art The consistent meaning of meaning will not be explained in an idealized or overly formal meaning and unless defined as here.
Above-described specific embodiment has carried out further the purpose of the present invention, technical scheme and beneficial effects It is described in detail, it should be understood that being not limited to this hair the foregoing is merely a specific embodiment of the invention Bright, all within the spirits and principles of the present invention, any modification, equivalent substitution, improvement and etc. done should be included in the present invention Protection scope within.

Claims (4)

1. a kind of method for finding analogy basin based on Spatial Fractal Dimension theory, which comprises the following steps:
Basin is divided into several orthogonal grid cells based on Law of DEM Data, i.e. dem data, obtained by step 1) To obtain the elevation grid Raster_Ele in basin, and elevation fractal dimension value is calculated in elevation in each grid cell Fra_Ele；
Step 2) calculates the gradient in each grid cell, obtains the gradient grid Raster_Slope in basin, and calculate To gradient fractal dimension value Fra_Slope；
Step 3) calculates the slope aspect in each grid cell, obtains the slope aspect grid Raster_SlopeDir in basin, and count Calculation obtains slope aspect fractal dimension value Fra_SlopeDir；
Step 4), building fractal feature space are labeled in fractal feature space by watershed generalization at data point, and by data Point is classified, and being divided into a kind of basin is analogy basin, specific as follows:
Step 4.1), with three mutually orthogonal unit vectorsFor base, fractal feature space is constructed, whereinFor Unit vector in elevation point dimension,Divide the unit vector in dimension for the gradient,For the unit vector in slope aspect point dimension；
Step 4.2), elevation fractal dimension value, gradient fractal dimension value and slope aspect fractal dimension value according to basin by watershed generalization at data point, It is labeled in fractal feature space；
Step 4.3) is based on spectral clustering data analysing method, classification will be split between the data point in fractal feature space, Being divided into a kind of basin is analogy basin.
2. a kind of method for finding analogy basin based on Spatial Fractal Dimension theory according to claim 1, which is characterized in that institute Stating step 1), specific step is as follows:
Basin is divided into several orthogonal grid cells based on dem data, obtained in each grid cell by step 1.1) Elevation, to obtain the elevation grid Raster_Ele in basin；
Step 1.2), on the basis of elevation grid Raster_Ele, using resolution ratio as sampling step length, the elevation obtained line by line is cutd open Face, and calculate the Spatial Fractal Dimension value FCele of elevation section line by line, i.e., to every a line elevation section, with each of which grid list The height value of member is ordinate, is constructed elevation section curve CurC_Ele using the side length accumulated value of grid cell as abscissai, And row elevation section curve CurC_Ele is calculated using package topologyiSpatial Fractal Dimension value FCelei, finally obtain elevation point dimension Column vector Col_Ele:
Col_Ele={ FCele0,FCele1,…FCelei,…FCeleI}
In formula: i is the number of row elevation section, and for value from 0 to I, I is total line number of elevation grid；
Step 1.3), on the basis of elevation grid Raster_Ele, using resolution ratio as sampling step length, the elevation obtained by column is cutd open Face, and calculate the Spatial Fractal Dimension value FRele of elevation section by column, i.e., to each column elevation section, with each of which grid list The height value of member is ordinate, and elevation section curve CurR_Ele is constructed using the side length accumulated value of grid cell as abscissaj, And row elevation section curve CurR_Ele is calculated using package topologyjSpatial Fractal Dimension value FCelei, finally obtain elevation point dimension Row vector Row_Ele:
Row_Ele={ FRele0,FRele1,…FRelej,…FReleJ}
In formula: j is the number of column elevation section, and for value from 0 to J, J is total columns of elevation grid；
Elevation fractal dimension value Fra_Ele is calculated in step 1.4) on the basis of row vector Row_Ele and column vector Col_Ele:
3. a kind of method for finding analogy basin based on Spatial Fractal Dimension theory according to claim 1, which is characterized in that institute Stating step 2), specific step is as follows:
Step 2.1) calculates the gradient in each grid cell, obtains the gradient grid Raster_Slope in basin；
Centered on grid cell Cell, by the comparison of the height value of the height value and grid cell of grid cell around, Find out grid cell Cell minimum in contrastD, and calculate Cell and CellDBetween depth displacement DHmaxWith floor projection away from From Dis, in conjunction with DHmaxWith the gradient S of Dis computation grid unit Cell:
S=DHmax/Dis
Step 2.2), using resolution ratio as sampling step length, obtains the gradient line by line on the basis of gradient grid Raster_Slope Section, and calculate the Spatial Fractal Dimension value FCslope of gradient section line by line, i.e., to every a line gradient section, with each of which grid The value of slope of lattice unit is ordinate, and gradient section curve CurC_ is constructed using the side length accumulated value of grid cell as abscissa Slopem, and row gradient section curve CurC_Slope is calculated using package topologymSpatial Fractal Dimension value FCslopem, final The column vector Col_Slope tieed up to the gradient point:
Col_Slope={ FCslope0,FCslope1,…FCslopem,…FCslopeM}
In formula: m is the number of row gradient section, and for value from 0 to M, M is total line number of gradient grid；
Step 2.3), using resolution ratio as sampling step length, obtains the gradient by column on the basis of gradient grid Raster_Slope Section, and calculate the Spatial Fractal Dimension value FRslope of gradient section by column, i.e., to each column gradient section, with each of which grid The value of slope of lattice unit is ordinate, and gradient section curve CurR_ is constructed using the side length accumulated value of grid cell as abscissa Slopen, and row gradient section curve CurR_Slope is calculated using package topologynSpatial Fractal Dimension value FCslopen, final The row vector Row_Slope tieed up to the gradient point:
Row_Slope={ FRslope0,FRslope1,…FCslopen,…FRslopeN}
In formula: n is the number of column gradient section, and for value from 0 to N, N is total columns of gradient grid；
Gradient fractal dimension value Fra_ is calculated in step 2.4) on the basis of row vector Row_Slope and column vector Col_Slope Slope:
4. a kind of method for finding analogy basin based on Spatial Fractal Dimension theory according to claim 1, which is characterized in that institute Stating step 3), specific step is as follows:
Step 3.1) calculates the slope aspect in each grid cell, obtains the slope aspect grid Raster_SlopeDir in basin；
Step 3.2), using resolution ratio as sampling step length, obtains line by line on the basis of slope aspect grid Raster_SlopeDir Slope aspect section, and calculate the Spatial Fractal Dimension value FCslopeDir of slope aspect section line by line, i.e., it is every with it to every a line slope aspect section The value of slope of one grid cell is ordinate, and slope aspect section curve is constructed using the side length accumulated value of grid cell as abscissa CurC_SlopeDirp, and row slope aspect section curve CurC_SlopeDir is calculated using package topologypSpatial Fractal Dimension value FCslopeDirp, finally obtain the column vector Col_SlopeDir of slope aspect point dimension:
Col_SlopeDir={ FCslopeDir0,FCslopeDir1,…FCslopeDirp,…FCslopeDirP}
In formula: p is the number of row slope aspect section, and for value from 0 to P, P is total line number of slope aspect grid；
Step 3.3), using resolution ratio as sampling step length, obtains by column on the basis of slope aspect grid Raster_SlopeDir Slope aspect section, and calculate the Spatial Fractal Dimension value FRslopeDir of slope aspect section by column, i.e., it is every with it to each column slope aspect section The slope aspect value of one grid cell is ordinate, and slope aspect section curve is constructed using the side length accumulated value of grid cell as abscissa CurR_SlopeDirq, and row slope aspect section curve CurR_SlopeDir is calculated using package topologyqSpatial Fractal Dimension value FCslopeDirq, finally obtain the row vector Row_SlopeDir of slope aspect point dimension:
Row_SlopeDir={ FRslopeDir0,FRslopeDir1,…FCslopeDirq,…FRslopeDirQ}
In formula: q is the number of column slope aspect section, and for value from 0 to Q, Q is total columns of slope aspect grid；
Slope aspect point dimension is calculated in step 3.4) on the basis of row vector Row_SlopeDir and column vector Col_SlopeDir Value Fra_SlopeDir:
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