CN108509702A - Soil erosion optimal spatial scale selection model and its computational methods - Google Patents
Soil erosion optimal spatial scale selection model and its computational methods Download PDFInfo
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Abstract
The invention discloses a kind of soil erosion optimal spatial scale selection model and its computational methods, the model is OSSMt=W (E) Et+W(S)StWherein t is scale；OSSMtFor the model calculation value under scale t；W (E) is the weight of comentropy；W (S) is the weight of fractal dimension similarity；EtTo normalize information entropy；St is normalization fractal dimension similarity value；OSSMtThe scale t for reaching corresponding when maximum value is optimal spatial scale.Described method includes following steps, and 1) it obtains data and data is pre-processed；2) data redudancy of soil erosion intensity grade figure is calculated；3) the fractal dimension similarity of soil erosion intensity grade figure is calculated；4) optimal spatial scale selection model is established.The present invention proposes the soil erosion optimal spatial scale selection method based on comentropy and fractal theory, this method is from two aspects of data redudancy and space characteristics ability to express, more single selection criteria is more reasonable, and selected optimal spatial scale makes the two reach optimum balance.
Description
Technical field
The present invention relates to earth science and technology field is belonged to, in particular to a kind of soil erosion optimal spatial scale selection mould
Type and its computational methods.
Background technology
Soil is the important component of terrestrial ecosystem, is the basis of human survival and development.With people contradiction
Aggravation, phenomenon of soil erosion getting worse, the strong influence development of natural environment and human society.Physcial geographical process
Generally existing spatial scale effects, the soil erosion also have certain dependence to space scale.Space scale is often referred to space
Amplitude and spatial granularity, the former refers to duration ranges of the research object in space, and the latter refers to that minimum discernable is known representated by unit
Characteristic length, area or volume, the scale of this paper refers to spatial granularity.With the development of Spatial Information Technology, remote sensing becomes soil
A kind of technical way of earth erosion research, and varigrained remote sensing image can lead to the difference of result of study, therefore, soil
The optimal spatial scale selection that earth corrodes has important theory value and reality for the process and mechanism study of the soil erosion
Meaning.
Scale effect has important meaning to the soil erosion and the research of other related fields (such as physical geography, the hydrology)
Justice, because it significantly affects the quality of data, model foundation, result output and decision support.For optimal sky
Between scale selection, have scholar propose judged according to the relationship of the space characteristics of grating image and scale, such as landscape index scale
Effect curve method, i.e., using the catastrophe point of spatial scale effects curve or the scale domain of held stationary as optimal spatial scale,
The theoretical foundation of this method is grating image has similitude on different scale, space characteristics index (landscape index)
There are certain rules for scale effect.Widely applied method is Geostatistics Method, method such as based on local variance, based on becoming
The method of different function, this method are to judge optimal spatial scale directly against the situation of change of grating image gray value, are managed
It is that spatially apart the similitude of closer atural object is better than atural object apart from each other by foundation.Geostatistics Method Main Analysis is distant
The linear character for feeling data, however, linear character is same as nonlinear characteristic notable in remotely-sensed data.Fractal theory is as non-
The important research tool of linear character can weigh the complexity of image, and multiple dimensioned lower fractal dimension situation of change can be with table
Up to the change procedure of image space feature, many scholars judge optimal spatial scale using this characteristic of point shape.
In the above research, landscape index scale effect curve method is mutated in view of information preservation amount, and Geostatistical side
Method Criterion of Selecting is that special heterogeneity is larger, and point shape is then to choose optimal spatial ruler with the power of space characteristics ability to express
Degree.Criterion of Selecting is different, as a result also can be variant, therefore, chooses optimal spatial scale with single criterion, has certain limitation
Property.
Invention content
The purpose of the present invention is to solve deficiencies existing for above-mentioned background technology, and a kind of soil erosion proposed is optimal
Space scale preference pattern and its computational methods, with the data redudancy of soil erosion intensity grade figure under different spaces scale and
Space characteristics ability to express is utilized respectively comentropy and fractal dimension similarity carrys out quantitatively evaluating index as measurement index, comprehensive
Close the optimal spatial scale of the two selection soil erosion study.
To achieve the above object, the soil erosion optimal spatial scale selection model designed by the present invention, special character
It is, the model is
OSSMt=W (E) Et+W(S)St
Wherein, t is scale, and value is the integral multiple of image original spatial resolution；OSSMtFor the model meter under scale t
Calculation value；W (E) is the weight of comentropy；W (S) is the weight of fractal dimension similarity；EtFor the normalization comentropy under scale t
Value；StFor the normalization fractal dimension similarity value under scale t；OSSMtThe scale t for reaching corresponding when maximum value is optimal sky
Between scale.
Preferably, the normalization information entropy E under the scale ttLetter between two pixels on symmetrical four direction
Cease the average value of entropy.
Preferably, the normalization fractal dimension similarity value S under the scale ttFor soil erosion intensity etc. at scale t
The similarity of the fractal dimension and the fractal dimension of soil erosion intensity grade figure under smallest dimension of grade figure.
The present invention also proposes that a kind of computational methods of soil erosion optimal spatial scale selection model, special character exist
In described method includes following steps：
1) data prediction, the soil erosion intensity grade figure under acquisition is multiple dimensioned are carried out to acquisition image data；
2) data redudancy for calculating the soil erosion intensity grade figure under each scale t, that is, solve under scale t at four
The comentropy in direction, is averaged, and is normalized to the comentropy mean value under all scales, obtains the normalization under scale t
Information entropy Et；
3) fractal dimension for calculating the soil erosion intensity grade figure under each scale t, solves the soil erosion at scale t
The similarity of the fractal dimension of strength grade figure and the fractal dimension of soil erosion intensity grade figure under smallest dimension, to all
Fractal dimension similarity under scale is normalized, and obtains the normalization fractal dimension similarity value S under scale tt；
4) according to optimal spatial scale selection model OSSMt=W (E) Et+W(S)St, t is scale, and value is that image is original
The integral multiple of spatial resolution；OSSMtFor the model calculation value under scale t；W (E) is the weight of comentropy；W (S) is FRACTAL DIMENSION
The weight of number similarity；It solves in OSSMtReach the scale t that maximum value is corresponding, obtains optimal spatial scale.
Preferably, the normalization information entropy E under step 2) the mesoscale ttComputational methods be：
Wherein, HtFor the information entropy of scale t hypographs；Max (H) and min (H) is respectively information entropy under all scales
In maximum value and minimum value.
Preferably, the computational methods of described information entropy H are：
Wherein, a, b, m, n=0,1,2 ..., h are the gray values of pixel pair, and h is highest gray value, and p (m, n, d, θ) is picture
The probability that (m, n) occurs in member, θ are direction of the pixel between (m, n).
Preferably, normalization fractal dimension similarity value S in the step 3)tComputational methods be：
Wherein, simtThe fractal dimension similarity of scale t hypographs；Max (sim) and min (sim) is respectively all scales
Maximum value and minimum value in lower fractal dimension similarity.
Preferably, the computational methods of the fractal dimension similarity sim are
Wherein, sim (A, the B) fractal dimension of soil erosion intensity grade figure and soil under smallest dimension at scale t
The similarity of the fractal dimension of erosion intensity grade figure；AWMFD (A), AWMFD (B) are illustrated respectively under scale t and in minimum ruler
The fractal dimension of the lower soil erosion intensity grade figure of degree, max (AWMFD (A), AWMFD (B)) is AWMFD (A), AWMFD (B) two
Higher value in person.
Preferably, the computational methods for the Probability p (m, n, d, θ) that (m, n) occurs in the pixel are
The frequency that (m, n) occur in P (m, n, d, θ) pixels；The frequency that (a, b) occur in P (a, b, d, θ) pixels.
Preferably, the computational methods of the fractal dimension AWMFD are：
Wherein, periijRefer to the perimeter of patch；areaijRefer to plaque area；I and j respectively refers to the jth of the i-th class plaque type
A patch；L and g respectively refers to patch quantity in plaque type quantity and certain type.
The advantage of the invention is that：
(1) selection of the present invention by data redudancy with space characteristics ability to express simultaneously as optimal spatial scale refers to
Mark, more fully than single selective goal.
(2) present invention constructs Two indices integrated model, can preferable equilibrium criterion redundancy and space characteristics expression
Ability, data redudancy and space characteristics ability to express reach optimum balance under selected optimal spatial scale.
Description of the drawings
Fig. 1 is optimal spatial scale selection model construction flow
Fig. 2 is the variation tendency that comentropy rises with scale
Fig. 3 is the variation tendency that fractal dimension similarity rises with scale
Fig. 4 is optimal spatial scale selection curve
Specific implementation mode
Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.Soil proposed by the present invention is invaded
Losing optimal spatial scale selection model is
OSSMt=W (E) Et+W(S)St
Wherein, t is scale, and value is the integral multiple of image original spatial resolution；OSSMtFor the model meter under scale t
Calculation value；W (E) is the weight of comentropy；W (S) is the weight of fractal dimension similarity；EtFor the normalization comentropy under scale t
Value；StFor the normalization fractal dimension similarity value under scale t；OSSMtThe scale t for reaching corresponding when maximum value is optimal sky
Between scale.
The computational methods of the model include the following steps：
1) data prediction, the soil erosion intensity grade figure under acquisition is multiple dimensioned are carried out to acquisition image data；
2) data redudancy for calculating the soil erosion intensity grade figure under each scale t, that is, solve under scale t at four
The comentropy in direction, is averaged, and is normalized to the comentropy mean value under all scales, obtains the normalization under scale t
Information entropy Et；
3) fractal dimension for calculating the soil erosion intensity grade figure under each scale t, solves the soil erosion at scale t
The similarity of the fractal dimension of strength grade figure and the fractal dimension of soil erosion intensity grade figure under smallest dimension, to all
Fractal dimension similarity under scale is normalized, and obtains the normalization fractal dimension similarity value S under scale tt；
4) according to optimal spatial scale selection model OSSMt=W (E) Et+W(S)St, t is scale, and value is that image is original
The integral multiple of spatial resolution；OSSMtFor the model calculation value under scale t；W (E) is the weight of comentropy；W (S) is FRACTAL DIMENSION
The weight of number similarity；It solves in OSSMtReach the scale t that maximum value is corresponding, obtains optimal spatial scale.
1. data prediction
Atmospheric correction, radiation calibration are carried out to remote sensing image data using remote sensing software ENVI, except making an uproar and cut, then is based on
Remote sensing image is carried out land use class by the Maximum likelihood classification of supervised classification.Digital elevation model (DEM) data are spelled
It connects, cut, filling out depression reason, the tool that spatial analysis software ArcMap is provided then is utilized to calculate the data such as the gradient, length of grade.According to
Area's precipitation and soil survey information are studied, the grid map of precipitation and soil class is obtained by interpolation.Using modified general
The soil erosion modulus in research area is calculated in soil loss equation (RUSLE), further according to country《Classification of soil erosion classification mark
It is accurate》The soil erosion is divided into mired and corrodes, slight erosion, moderate erosion, strong erosion, extremely strong strong invades by (SL190-2007)
Erosion and acutely six classes of erosion.Based on the figure, using the resampling tool of ArcMap, more rulers are obtained based on closest interpolation method
Soil erosion intensity grade figure under degree.
2. calculating the data redudancy of soil erosion intensity grade figure
The present invention utilizes the computational methods of entropy in gray level co-occurrence matrixes, to describe soil erosion intensity grade figure in difference
Data redudancy on scale.Gray level co-occurrence matrixes are that spatially a pair of of pixel gray scale (a, b) with certain position relationship goes out
The matrix of existing frequency P (a, b, d, θ) compositions, mathematic(al) representation are
P (a, b, d, θ) [(x, y), (x+Dx, y+Dy) | f (x, y)=a, f (x+Dx, y+Dy)=b] }
(1)
Wherein, x=0,1,2 ..., M-1 and y=0,1,2 ..., N-1 are the coordinate of pixel, and M and N respectively refers to the row of image
And line number；A, b=0,1,2 ..., h are the gray values of pixel pair, and h is highest gray value；M, n=0,1,2 ..., h is pixel pair
Gray value, can similarly calculate P (m, n, d, θ)；Step-lengths of the d between two pixels；θ between two pixels direction (usually take 0 °,
45°、90°、135°)；Dx, Dy are the offsets between pixel pair under the rule of d and θ, and f (x, y) refers to the coordinate in grid map
For the gray value of the pixel of (x, y).Then pixel is to (m, n) probability occurred
Due to consider data redudancy, step-length d should be minimized 1, θ take common 4 directions (0 °, 45 °, 90 °,
135 °), then the comentropy H (θ) in the directions θ is
The information entropy on 4 directions can be calculated according to formula (3), mean value H is last result.
Information entropy H is bigger, then shows that data redudancy is smaller.
3. calculating the fractal dimension similarity of soil erosion intensity grade figure
Fractal theory is an important tool for expressing figure complexity, the soil erosion intensity grade figure of different scale
With self-similarity, if the complete self similarity of image under each scale, the complexity of image is constant, and fractal dimension is constant.
But during dimensional variation, image self-similarity can constantly successively decrease, and fractal dimension changes therewith, this process is known as a point shape
Decaying.The present invention describes the process that soil erosion intensity grade figure changes with scale increase using fractal attenuation, due to soil
Earth erosion intensity grade figure spot block area discrepancy is excessive, therefore selects Area-weighted average plaque fractal dimension (AWMFD) (formula
(5)) (abbreviation fractal dimension) measures the complexity of image, meanwhile, it is weighed under different scale using fractal dimension similarity
The similarity degree of image complexity and truth.
Wherein, periijRefer to the perimeter of patch；areaijRefer to plaque area；I and j respectively refers to the jth of the i-th class plaque type
A patch；L and g respectively refers to patch quantity in plaque type quantity and certain type；Sim (A, B) soil erosions at scale t are strong
Spend the similarity of the fractal dimension and the fractal dimension of soil erosion intensity grade figure under smallest dimension of grade figure；AWMFD(B)
Be illustrated respectively under scale t and under smallest dimension soil erosion intensity grade figure fractal dimension, max (AWMFD (A),
AWMFD (B)) it is AWMFD (A), the higher value in AWMFD (B) the two.Fractal dimension similarity is bigger, image and truth
Closer, space characteristics ability to express is stronger.
4. establishing optimal spatial scale selection model
The present invention considers to choose optimal spatial in terms of the data redudancy of image and space characteristics ability to express two
Scale, using comentropy and fractal dimension similarity respectively as the evaluation index of these two aspects.The lower data redudancy the better,
I.e. the higher the better for comentropy, while the stronger space characteristics ability to express the better, i.e. fractal dimension similarity is the bigger the better.To eliminate
Two indices are normalized dimension impact, such as formula (7) and formula (8), then calculate separately two indices and scale
Related coefficient and related coefficient account for the ratio of its summation, respectively using the ratio as weight (formula (9) and the public affairs of two indexes
Formula (10)) it is weighted summation, to establish the optimal spatial scale selection model of the soil erosion, mathematic(al) representation such as formula
(11) and formula (7).
OSSMt=W (E) Et+W(S)St (11)
OSS=[t | max (OSSMt)] (12)
Wherein, t is scale, and value is the integral multiple of image original spatial resolution；EtFor the normalization information under scale t
Entropy；StFor the normalization fractal dimension similarity value under scale t；HtFor the information entropy of scale t hypographs；max(Ht) and
min(Ht) it is respectively maximum value and minimum value under all scales in information entropy, simtThe fractal dimension phase of scale t hypographs
Like degree；max(simt) and min (simt) it is respectively maximum value and minimum value under all scales in fractal dimension similarity；W(E)
For the weight of comentropy；W (S) is the weight of fractal dimension similarity；Related coefficients of the R (E) between comentropy and scale；R
(S) related coefficient between fractal dimension similarity and scale；OSSMtFor the model calculation value under scale t, OSSMtReach most
Corresponding scale t is optimal spatial scale when big value.
By taking Reservoir Area of Danjiangkou as an example, the Landsat TM remote sensing images and dem data of Reservoir Area of Danjiangkou in 2002 are obtained, it is auxiliary
It includes studying the precipitation and soil survey information in area to help data.
1. data prediction
Atmospheric correction, radiation calibration are carried out to the Landsat TM image datas of acquisition using remote sensing software ENVI, except making an uproar
And cut, then remote sensing image is divided by waters, forest land, arable land, building site, not based on the Maximum likelihood classification of supervised classification
Utilize five class of ground.Digital elevation model (DEM) data are spliced, are cut, fill out depression reason, then utilize spatial analysis software
The tool that ArcMap is provided calculates the data such as the gradient, length of grade.According to research area's precipitation and soil survey information, obtained by interpolation
The grid map of precipitation and soil class.The soil in research area is calculated using modified universal soil loss equation (RUSLE)
Earth erosion modulus, further according to country《Classification of soil erosion grade scale》The soil erosion is divided into mired by (SL190-2007)
Erosion, slight erosion, moderate erosion, six classes of strong erosion, pole strong erosion and violent erosion.Based on the figure, utilize
The resampling tool of ArcMap, based on closest interpolation method obtain resolution ratio be 60m-450m (step-length 30m) it is multiple dimensioned under
Soil erosion intensity grade figure.
2. calculating the data redudancy of soil erosion intensity grade figure
Multiple dimensioned soil erosion intensity grade figure is calculated in the comentropy of four direction, then seeks mean value, then is analyzed
Relationship between value and scale, is as a result shown in attached drawing 1.It is found that when scale is less than 90m, curvilinear motion amplitude is big, illustrates at this
The fluctuation of soil erosion intensity grade diagram data redundancy is larger in range, and in 90m to 150m ranges, curve slowly rises, and arrives
After 150m, curve fluctuates about 0.280, it is seen that within the scope of this, the influence that scale becomes larger to data redudancy is smaller.
3. the fractal dimension similarity of calculating soil erosion intensity grade figure is in this example, soil when resolution ratio is 30m
Erosion intensity grade figure represents truth closest to truth, therefore with the image under the scale.Calculate multiple dimensioned soil
Then the fractal dimension of erosion intensity grade figure calculates the FRACTAL DIMENSION of the fractal dimension and 30m image in different resolution of multi-scale image
Number similarity, is as a result shown in attached drawing 2.It is found that fractal dimension similarity remains downward trend with dimensional variation curve, and decline
Trend slows down as scale increases, it is seen that soil erosion intensity grade figure and the image of (30m*30m) under highest resolution
Similarity can reduce with the increase of scale, and the real information that image includes is fewer and fewer, and soil erosion patch shape is more next
It is simpler.
4. establishing optimal spatial scale selection model
According to the inventive step 4, the optimal spatial scale of the Reservoir Area of Danjiangkou soil erosion is chosen.It utilizes with comentropy and divides
The optimal spatial scale selection model of shape dimension similarity structure calculates the model value of different scale.The ruler known to correlation analysis
Degree and the related coefficient of comentropy are 0.780, and the related coefficient with fractal dimension similarity is 0.945, then the two weight difference
For 0.45 and 0.55, result of calculation is shown in Table 1 and attached drawing 3, and as scale increases, result of calculation first increases, and then concussion reduces, ruler
Highest when degree is 90m.Illustrate, when scale is 90m, both to have considered data redudancy and in turn ensured space characteristics ability to express, and be
Optimal spatial scale.
1. optimal spatial scale selection of table
It will be understood by those of skill in the art that specific embodiments described herein, which is only used, explains patent of the present invention, and
It is not used in limitation patent of the present invention.Any modification for being made within the spirit and principle of patent of the present invention and changes equivalent replacement
Into etc., it should be included among the protection domain of patent of the present invention.
Claims (10)
1. a kind of soil erosion optimal spatial scale selection model, it is characterised in that：The model is
OSSMt=W (E) Et+W(S)St
Wherein, t is scale, and value is the integral multiple of image original spatial resolution；OSSMtFor the model calculation value under scale t；W
(E) it is the weight of comentropy；W (S) is the weight of fractal dimension similarity；EtFor the normalization information entropy under scale t；StFor
Normalization fractal dimension similarity value under scale t；OSSMtThe scale t for reaching corresponding when maximum value is optimal spatial scale.
2. soil erosion optimal spatial scale selection model according to claim 1, it is characterised in that：Under the scale t
Normalization information entropy EtThe average value of comentropy between two pixels on symmetrical four direction.
3. soil erosion optimal spatial scale selection model according to claim 1, it is characterised in that：Under the scale t
Normalization fractal dimension similarity value StFor the fractal dimension of soil erosion intensity grade figure at scale t and in smallest dimension
The similarity of the fractal dimension of lower soil erosion intensity grade figure.
4. a kind of computational methods of soil erosion optimal spatial scale selection model, it is characterised in that：The method includes as follows
Step：
1) data prediction, the soil erosion intensity grade figure under acquisition is multiple dimensioned are carried out to acquisition image data；
2) data redudancy for calculating the soil erosion intensity grade figure under each scale t, that is, solve under scale t in four direction
Comentropy, be averaged, the information entropy under all scales be normalized, obtain the normalization comentropy under scale t
Value Et；
3) fractal dimension for calculating the soil erosion intensity grade figure under each scale t, solves the soil erosion intensity at scale t
The similarity of the fractal dimension of grade figure and the fractal dimension of soil erosion intensity grade figure under smallest dimension, to all scales
Under fractal dimension similarity be normalized, obtain the normalization fractal dimension similarity value S under scale tt；
4) according to optimal spatial scale selection model OSSMt=W (E) Et+W(S)St, t is scale, and value is image luv space
The integral multiple of resolution ratio；OSSMtFor the model calculation value under scale t；W (E) is the weight of comentropy；W (S) is fractal dimension phase
Like the weight of degree；It solves in OSSMtReach the scale t that maximum value is corresponding, obtains optimal spatial scale.
5. the computational methods of soil erosion optimal spatial scale selection model according to claim 4, it is characterised in that：Institute
State the normalization information entropy E under step 2) mesoscale ttComputational methods be：
Wherein, HtFor the information entropy of scale t hypographs；Max (H) and min (H) is respectively under all scales in information entropy
Maximum value and minimum value.
6. the computational methods of soil erosion optimal spatial scale selection model according to claim 5, it is characterised in that：Institute
The computational methods for stating comentropy H are：
Wherein, a, b, m, n=0,1,2 ..., h are the gray values of pixel pair, and h is highest gray value, and p (m, n, d, θ) is pixel pair
The probability that (m, n) occurs, θ are direction of the pixel between (m, n).
7. the computational methods of soil erosion optimal spatial scale selection model according to claim 4, it is characterised in that：Institute
State normalization fractal dimension similarity value S in step 3)tComputational methods be：
Wherein, simtThe fractal dimension similarity of scale t hypographs；Max (sim) and min (sim) is respectively lower point of all scales
Maximum value and minimum value in shape dimension similarity.
8. the computational methods of soil erosion optimal spatial scale selection model according to claim 7, it is characterised in that：Institute
The computational methods for stating fractal dimension similarity sim are
Wherein, sim (A, the B) fractal dimension of soil erosion intensity grade figure and soil erosion under smallest dimension at scale t
The similarity of the fractal dimension of strength grade figure；AWMFD (A), AWMFD (B) are illustrated respectively under scale t and under smallest dimension
The fractal dimension of soil erosion intensity grade figure, max (AWMFD (A), SWMFD (B)) is AWMFD (A), in AWMFD (B) the two
Higher value.
9. soil erosion optimal spatial scale selection model according to claim 6, it is characterised in that：The pixel pair
The computational methods of Probability p (m, n, d, θ) that (m, n) occurs are
The frequency that (m, n) occur in P (m, n, d, θ) pixels；The frequency that (a, b) occur in P (a, b, d, θ) pixels.
10. soil erosion optimal spatial scale selection model according to claim 8, it is characterised in that：The FRACTAL DIMENSION
Number AWMFD computational methods be：
Wherein, periijRefer to the perimeter of patch；areaijRefer to plaque area；I and j respectively refers to j-th of spot of the i-th class plaque type
Block；L and g respectively refers to patch quantity in plaque type quantity and certain type.
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