CN102636779A - Extraction method for coverage rate of sub-pixel accumulated snow based on resampling regression analysis - Google Patents

Abstract

The invention relates to an extraction method for coverage rate of sub-pixel accumulated snow based on resampling regression analysis. The method does not depend on ground actual measured data or synchronous high resolution ratio, the resolution ratio of an image is reduced, and the image is resampled, the data after being subjected to resampling and the resolution ratio reduction are used as the sample data; and a multivariate linear model between the coverage rate of the sub-pixel accumulated snow and reflectivity is established. The technical scheme of the extraction method is small in calculated amount and is suitable for remote-sensing images with larger area range, larger data amount, different areas and different time.

Description

A kind of sub-pix accumulated snow coverage rate method for distilling based on the resampling regretional analysis

Technical field

The invention belongs to the remote sensing image application, particularly relate to a kind of new sub-pix accumulated snow coverage rate method for distilling.

Background technology

Two-value Xue Gaitu only is divided into pixel and avenges and two kinds of situation of non-snow, and therefore, the two-value snow that middle low resolution image produces covers product, is difficult to satisfy interior among a small circle accumulated snow research accuracy requirement.Therefore, the accumulated snow coverage information method for distilling based on sub-pix has just arisen.At present, inverting mainly contains two kinds of research methods based on the snow of sub-pix lid: the one, and mixed pixel decomposition method, the 2nd, statistical regression analysis method (Xu Lina, 2006).

Ground return that remote sensor obtained or emission spectrum signal are unit record with the pixel; It is the comprehensive of the pairing terrestrial materials spectral signal of pixel; If this pixel only comprises one type; Then be pure pixel (Pure Pixel), the spectral response characteristics or the spectral signal of the type just that it writes down; If this pixel comprises more than a kind of soil cover type, then form mixed pixel (Mixed Pixel), what it write down is comprehensive (Kanfman etc., 2002) of pairing different soils cover type spectral response characteristics.

Find the solution the mixed pixel problem, set up the funtcional relationship of pixel reflectivity and end member spectral signature and area occupied number percent exactly.The common methods that mixed pixel decomposes mainly can be divided into two big types, i.e. wave band mixed reflection rate decomposition method and fuzzy classifier method (Cao Meisheng etc., 2006).

People have sought the whole bag of tricks to solve the mixed pixel problem; Like the linear hybrid analysis: be expressed as pixel the combination of all atural object components of different proportion; Its mechanism is that in every spectrum band, the spectral reflectivity of arbitrary pixel can be expressed as; Long-pending linear combination (Adams, 1986 of the spectral reflectivity of all atural objects and its area occupied ratio in pixel in this pixel; Gong et al, 1994; Novo and Shimabukuro, 1994); C fuzzy classification: confirm that through fuzzy clustering method a certain pixel belongs to the degree of membership of certain atural object, thereby extrapolate, such atural object proportion size method (Foody, 1994) in this pixel; Feedforward reverse transmittance nerve network: the conversion between the different pieces of information; When neural network is used for the branch time-like; Just can be regarded as from a kind of conversion of feature space to classifying space; Compare with traditional supervised classification, it is to distribute for data source not require to have tangible advantage (Foody, 996) that neural network classification has a significant advantage.

Spectrum mixed decomposition technology is a kind of effective sub-pix accumulated snow coverage rate method for distilling.1999, Nolin, Nozier and Mertes etc. were used for it to avenge at first and cover charting (Nolin etc., 1999).Decompose in the charting algorithm at accumulated snow coverage rate mixed pixel, the result that we obtain is the shared area ratio of pixel moderate snow end member.

At present; Linear hybrid pixel decomposition technique has been used in the accumulated snow drawing of multiple remotely-sensed data, for example: AVIRIS data and TM data, the main difference of these algorithms are the selection technology of spectrum end member: as far back as 1993; Nolin is through manually selecting the training area end member; Utilize supervision mixed pixel decomposition algorithm, handle 18 spectral band data (Nolin etc., 1993) of AVIRIS; People such as Rosenthal have used non-supervision mixed pixel decomposition algorithm at 1,996 6 reflected wavebands to the TM data, utilize the convex surface geometric techniques to select end member, have obtained and the suitable precision (Rosenthal etc., 1996) of aerophotograph classification; People such as Painter have confirmed through multiterminal unit mixed decomposition technology that 1998 introducing comprises varigrained multiple snow spectrum end member can improve the precision (Painter etc., 1998) of mixing picture decomposition snow charting algorithm; People such as Vikhama and Solberg through geometric optical model simulated spectra combined ground measured spectra, has proposed the method (Vikhama etc., 2002) of forest land inverting accumulated snow coverage rate 2002.People such as Painter have studied sub-pix drawing and the snow crystal particle size inverting (Painter etc., 2003) based on the mixed pixel decomposition model in 2003.

Statistical regression analysis is through quantitative contact between the variable, obtains the method for regression equation and Changing Pattern thereof.Extract in the application in the accumulated snow coverage rate, suppose that there are certain linearity or nonlinear regression relation in the reflectivity of pixel and the long-pending number percent of the interior snow of pixel capping.This method is fit to the accumulated snow drawing research of intermediate-resolution yardstick, so, the research emphasis that based on the application of accumulated snow coverage rate method for distilling in the drawing of MODIS accumulated snow of statistical regression analysis always is.

People such as Kaufman on the basis that the inversion algorithm of its aerosol optical depth is studied, propose will avenge at 2.1 μ m places to regard dark target as in calendar year 2001, with the accumulated snow coverage rate in the clutter reflections rate inverting pixel at 0.66 μ m and 2.1 μ m places.Calendar year 2001, people such as Barton utilize Landsat TM data inversion NDSI value, obtain the snow lid ratio in the pixel through the repeatedly regression equation of setting up NDSI.The similar principles of human Barton such as Salomonson; To the MODIS data; Proposed in 2003 a kind of simplification, based on normalization snow index (normalize difference snow index; NDSI) MODIS data accumulated snow coverage rate linear inversion model, and with the two kinds of models in itself and front relatively, experiment show that this model obtained higher inversion accuracy.

To the accumulated snow coverage rate inverting based on the statistical regression analysis method, Chinese scholar has also been carried out a large amount of research.Chinese scholar Cao Yun is just on people's such as Salomonson research basis; Considering under the situation that the face of land covers; Having set up pixel snow covers rate and covers the linear relationship model between index, the vegetation index with avenging; And utilize the ETM+ data that the snow lid rate of model assessment is verified. the result shows that this method can be extracted the accumulated snow information (Cao Yungang etc., 2006) of sub-pix yardstick effectively.People such as Jin Cui revise model according to the Northeast's geographical environment and climatic characteristic on Salomoson model basis, and inverting the Northeast snow covers rate, and adopts different schemes the stability of model to be analyzed and error assessment (Jin Cui etc., 2008).And people such as Zhou Qiang attempt on this basis, and the accumulated snow coverage rate is classified according to NDSI; Carry out modeling respectively to different classes of then, and utilize the ETM+ data that data model assessment result is verified that the result shows; Segmented model has some improvement to the snow lid rate inverting in the high value of NDSI district; But segmented model still can provide estimated value (Zhou Qiang etc., 2008) accurately at the zone of transition that accumulated snow covers.People such as Zhang Xu are study area with cajaput state, Qinghai Province; Adopt MODIS data and HJ-1-B data; Model parameter is estimated, accomplished the drawing of study area sub-pix snow lid, and the correlationship between snow lid rate (FRA) and its two correlation factor surface temperatures (LST) and the vegetation index (NDVI) has been discussed respectively; Conception (Zhang Xu etc., 2009) based on the inverting of polyfactorial snow lid rate has been proposed.

Summary of the invention

To the problems referred to above, the present invention proposes a kind of sub-pix accumulated snow coverage rate method for distilling based on the resampling regretional analysis, overcomes the existing methods shortcoming, improves the extraction efficiency of remote sensing image accumulated snow coverage rate.

Technical scheme of the present invention is a kind of sub-pix accumulated snow coverage rate method for distilling based on the resampling regretional analysis, it is characterized in that, may further comprise the steps:

Step 1 is extracted the reflectivity of each pixel in the original MODIS remote sensing image, calculates the normalization snow index NDSI of each pixel;

ND?SI=(R4-R6)/(R4+R6)

Wherein, R4 is the reflectivity of pixel the 4th wave band, and R6 is the reflectivity of pixel the 6th wave band;

Step 2 is carried out atmospheric correction and topographic correction, the remote sensing image after obtaining proofreading and correct to the reflectivity of each pixel in the original MODIS remote sensing image of step 1 gained;

Step 3 detects the distribution of Snow Cover Over scope of the remote sensing image after step 2 gained is proofreaied and correct, and obtains accumulated snow scope two-value image; Detection mode is following,

If the normalization snow index NDSI of certain pixel in the remote sensing image after proofreading and correct>the reflectivity R6 < 0.2 of the 0.4, the 6th wave band; And the reflectivity R2 of the 2nd wave band>0.2; Judge that this pixel belongs to the distribution of Snow Cover Over scope; The image value of respective pixel is 1 in the accumulated snow scope two-value image, otherwise judges that this pixel does not belong to the distribution of Snow Cover Over scope, and the image value of respective pixel is 0 in the accumulated snow scope two-value image;

Step 4 resamples to the remote sensing image after the correction of step 2 gained, reduces resolution, the reflectivity image after obtaining resampling; The implementation that resamples is following,

If the reflectivity of certain pixel is ρ in the reflectivity image after resampling ^Cr, there is N pixel the corresponding region in the remote sensing image of this pixel after step 2 gained is proofreaied and correct, and wherein the reflectivity of i pixel does

The value of i is 1,2 ..., N is calculated as follows the reflectivity of each pixel in the reflectivity image after the resampling,

${\mathrm{\&rho;}}^{\mathrm{cr}}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i^{\mathrm{fr}}}{N}$

Step 5 resamples to step 3 gained accumulated snow scope two-value image, reduces resolution, the accumulated snow coverage rate image after obtaining resampling; The resolution of the reflectivity image after the accumulated snow coverage rate image after the resampling and step 4 gained resample is consistent, and the implementation of resampling is following,

If the accumulated snow coverage rate of certain pixel is FRA in the accumulated snow coverage rate image after resampling ^Cr, this pixel has N pixel in the corresponding region in step 3 gained accumulated snow scope two-value image, and wherein the image value of i pixel does

The value of i is 1,2 ..., N is calculated as follows the accumulated snow coverage rate of each pixel in the accumulated snow coverage rate image after the resampling,

${\mathrm{FRA}}^{\mathrm{cr}}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{FRA}}_i^{\mathrm{fr}}}{N}$

Step 6; Accumulated snow coverage rate image after reflectivity image after stack step 4 gained resamples and step 5 gained resample; Randomly draw the partial pixel of superimposed image; And the reflectivity that extracts pixel and accumulated snow coverage values carry out regretional analysis as sample point, sets up the multiple linear regression model between the accumulated snow coverage rate and reflectivity afterwards that resamples; The accumulated snow coverage rate FRA of each pixel was expressed as after said multiple linear regression model will resample:

$\mathrm{FRA}=\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{a}_n{\mathrm{\&rho;}}_n+b$

Wherein, ρ _nBe the reflectivity of n wave band, a _nBe the regression coefficient of n wave band, b is for returning constant coefficient, and M is the wave band sum;

Step 7, the multiple linear regression model that utilizes step 6 to set up, the reflectivity of each pixel extracts the sub-pix accumulated snow coverage rate of original MODIS remote sensing image in the remote sensing image after proofreading and correct according to step 2 gained.

The present invention is a kind of sub-pix accumulated snow coverage rate method for distilling based on statistical study, and calculated amount is little, is applicable to that regional extent is bigger, and data volume is big, zones of different, remote-sensing images in different times.Do not rely on ground measured data or synchronous high resolving power,, the data behind the resampling resolution decreasing as sample data, are returned and set up the multivariate linear model between sub-pix accumulated snow coverage rate and the reflectivity directly through the image resolution decreasing is resampled.The present invention selects the multiband reflectivity to carry out regretional analysis as variable; Propose a kind of new statistical analysis technique, solved the difficulty of utilizing ground measured data or the statistical sample of high-resolution data acquisition synchronously.The present invention is based on sub-pix accumulated snow coverage rate and the statistical relationship between the pixel reflectivity and the sub-pix accumulated snow coverage rate of high resolution image and similar this assumed condition of the statistical relationship between the pixel reflectivity of low resolution remote sensing image.

Description of drawings

Fig. 1 is the process flow diagram of the embodiment of the invention.

Embodiment

Technical scheme of the present invention can adopt computer software technology to realize operation automatically by those skilled in the art.Specify technical scheme of the present invention below in conjunction with accompanying drawing and embodiment, the flow process of embodiment is referring to Fig. 1:

Step 1, MODIS data radiation calibration promptly extracts the reflectivity of each pixel in the original MODIS remote sensing image, calculates the normalization snow index NDSI of each pixel;

NDSI=(R4-R6)/(R4+R6)

Wherein, R4 is the reflectivity of pixel the 4th wave band, and R6 is the reflectivity of pixel the 6th wave band.

Step 2 is carried out atmospheric correction and topographic correction, the remote sensing image after obtaining proofreading and correct to the reflectivity of each pixel in the original MODIS remote sensing image of step 1 gained.Subsequent step adopts the reflectivity of each pixel in the remote sensing image after this step gained is proofreaied and correct.

Topographic correction and atmospheric correction are prior art, general first atmospheric correction, topographic correction then.For the purpose of the enforcement reference, introduce as follows:

Atmospheric correction

The FLAASH atmospheric correction has used the code of MODTRAN4+ radiation delivery model, based on the correction of Pixel-level, is the highest atmosphere radiation calibration model of present precision.Proofread and correct because the process effects that diffuse reflection causes, comprise the classification chart of cirrus and opaque cloud layer, can adjust and to carry out wave spectrum level and smooth.MODTRN4+。Atmospheric correction mainly was divided into for three steps among the FLAASH.At first be from image, to obtain atmospheric parameter, comprise visibility (aerosol optical depth), aerosol type and atmosphere vapour post content.Second step was to obtain reflectivity data through finding the solution the atmosphere radiation transmission equation.Be to utilize the pixel that spectrum is level and smooth in the image that image is carried out the level and smooth computing of spectrum at last, to eliminate the noise that retains in the trimming process.

The topographic correction algorithm

The cosine calibration model is a simple optical function, and its ultimate principle is to proofread and correct built-up radiation that built-up radiation that the back pixel accepts and domatic pixel accept a direct proportionate relationship that is determined by incident angle (be defined as sun zenith with perpendicular to domatic orientation angle) cosine is arranged.Definition a is a solar incident angle, and cosa is the cosine value of corresponding solar incident angle, i.e. the illumination coefficient.Its computing method are:

cosa＝cosθcosβ+sinθsinβcos(λ-ω)

Wherein, θ is the angle of gradient on plane, pixel place, and λ is a solar azimuth, and β is a solar zenith angle, and ω is the aspect angle on plane, pixel place.Wherein, θ and ω can be calculated by dem data through the mountain.

The cosine calibration model is expressed as:

$L_H=L_T\frac{\cos \mathrm{\&beta;}}{\cos \mathrm{\&alpha;}}$

L wherein _HWith radiation value after the correction of ground point, L _TRadiation value for the sloping floor point.

Step 3 detects the distribution of Snow Cover Over scope of the remote sensing image after step 2 gained is proofreaied and correct, and obtains accumulated snow scope two-value image; Detection mode is following,

If the normalization snow index NDSI of certain pixel in the remote sensing image after proofreading and correct>the reflectivity R6 < 0.2 of the 0.4, the 6th wave band; And the reflectivity R2 of the 2nd wave band>0.2; Judge that this pixel belongs to the distribution of Snow Cover Over scope; The image value of respective pixel is 1 in the accumulated snow scope two-value image, otherwise judges that this pixel does not belong to the distribution of Snow Cover Over scope, and the image value of respective pixel is 0 in the accumulated snow scope two-value image.The reflectivity R2 of the reflectivity R6 of the 6th wave band, the 2nd wave band is the reflectivity after step 2 is proofreaied and correct here.

Step 4 resamples to the remote sensing image after the correction of step 2 gained, reduces resolution, the reflectivity image after obtaining resampling; The implementation that resamples is following,

If the reflectivity of certain pixel is ρ in the reflectivity image after resampling ^Cr, in the corresponding region N pixel arranged in the remote sensing image of this pixel after step 2 gained is proofreaied and correct, wherein the reflectivity of i pixel does

The value of i is 1,2 ..., N is calculated as follows the reflectivity of each pixel in the reflectivity image after the resampling,

${\mathrm{\&rho;}}^{\mathrm{cr}}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i^{\mathrm{fr}}}{N}$

The reflectivity of each pixel of back that resamples be the mean value of the reflectivity of all pixels on the original resolution image of these all corresponding regions of pixel, promptly in the remote sensing image after the correction of step 2 gained in the corresponding region reflectivity of N pixel make even all.

Step 5 resamples to step 3 gained accumulated snow scope two-value image, reduces resolution, the accumulated snow coverage rate image after obtaining resampling.The resolution of the reflectivity image after the accumulated snow coverage rate image after the resampling and step 4 gained resample must be consistent in case follow-up carry out overlapping.The implementation that resamples is following,

If the accumulated snow coverage rate of certain pixel is FRA in the accumulated snow coverage rate image after resampling ^Cr, this pixel has N pixel in the corresponding region in step 3 gained accumulated snow scope two-value image, and wherein the image value of i pixel does

The value of i is 1,2 ..., N is calculated as follows the accumulated snow coverage rate of each pixel in the accumulated snow coverage rate image after the resampling,

${\mathrm{FRA}}^{\mathrm{cr}}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{FRA}}_i^{\mathrm{fr}}}{N}$

The accumulated snow coverage rate of each pixel of back that resamples be on the original resolution image of these all corresponding regions of pixel the mean value of accumulated snow coverage rate of pixel, promptly in the step 3 gained accumulated snow scope two-value image in the corresponding region image value of N pixel make even all.

Step 6; Accumulated snow coverage rate image after reflectivity image after stack step 4 gained resamples and step 5 gained resample; Randomly draw the partial pixel of superimposed image; And the reflectivity that extracts pixel and accumulated snow coverage values carry out regretional analysis as sample point, sets up the multiple linear regression model between the accumulated snow coverage rate and reflectivity afterwards that resamples.When embodiment randomly drawed the partial pixel of superimposed image, setting was to randomly draw 20% pixel.During practical implementation, the user can preestablish voluntarily.

The accumulated snow coverage rate of pixel and the reflectivity of pixel are linear, and the accumulated snow coverage rate FRA of each pixel was expressed as after said multiple linear regression model will resample:

$\mathrm{FRA}=\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{a}_n{\mathrm{\&rho;}}_n+b$

Wherein, ρ _nBe the reflectivity of n wave band, a _nBe the regression coefficient of n wave band, b is for returning constant coefficient, and M is the wave band sum.

During practical implementation, the existing preparatory regression analysis of a young waiter in a wineshop or an inn be can adopt, accumulated snow coverage rate FRA and reflectivity ρ set up ₁, ρ ₂..., ρ _MBetween regression model, preserve model file.

Step 7, the multiple linear regression model that utilizes step 6 to set up, the reflectivity of each pixel extracts the sub-pix accumulated snow coverage rate of original MODIS remote sensing image in the remote sensing image after proofreading and correct according to step 2 gained.The reflectivity that is about to each pixel in the remote sensing image after step 2 gained is proofreaied and correct is brought step 6 gained formula into, can obtain the accumulated snow coverage rate of each pixel in the original resolution image.

Export step 7 gained result at last, promptly final accumulated snow coverage rate image, this image is consistent with the resolution of original MODIS remote sensing image.

During practical implementation, also can adopt the modular design mode that such scheme is provided, for example a kind of sub-pix accumulated snow coverage rate extraction system based on the resampling regretional analysis comprises with lower module:

Characteristic extracting module is extracted the reflectivity of each pixel in the original MODIS remote sensing image and is imported correction module, calculates the normalization snow index NDSI of each pixel and imports accumulated snow scope extraction module;

Correction module; Reflectivity to each pixel in the original MODIS remote sensing image of step 1 gained carries out atmospheric correction and topographic correction; Remote sensing image after obtaining proofreading and correct, and input accumulated snow scope extraction module, accumulated snow coverage rate regretional analysis module and accumulated snow coverage rate output module;

Accumulated snow scope extraction module detects the distribution of Snow Cover Over scope of the remote sensing image after the correction, obtains accumulated snow scope two-value image and also imports accumulated snow coverage rate regretional analysis module;

Accumulated snow coverage rate regretional analysis module resamples to the remote sensing image after proofreading and correct, and reduces resolution, the reflectivity image after obtaining resampling; Accumulated snow scope two-value image is resampled, reduce resolution, the accumulated snow coverage rate image after obtaining resampling; The resolution of the reflectivity image after the accumulated snow coverage rate image after the resampling and step 4 gained resample is consistent; Reflectivity image after stack resamples and the accumulated snow coverage rate image after the resampling; Randomly draw the partial pixel of superimposed image; And reflectivity and the accumulated snow coverage values of extracting pixel are as sample point; Carry out regretional analysis, set up the multiple linear regression model that resamples between back accumulated snow coverage rate and the reflectivity and output to accumulated snow coverage rate output module;

Accumulated snow coverage rate output module utilizes multiple linear regression model, extracts the sub-pix accumulated snow coverage rate of original MODIS remote sensing image according to the reflectivity of each pixel in the remote sensing image after proofreading and correct, and is output as accumulated snow coverage data file at last.

Specific embodiment described herein only is that the present invention's spirit is illustrated.Person of ordinary skill in the field of the present invention can make various modifications or replenishes or adopt similar mode to substitute described specific embodiment, but can't depart from spirit of the present invention or surmount the defined scope of appended claims.

Claims (1)

1. the sub-pix accumulated snow coverage rate method for distilling based on the resampling regretional analysis is characterized in that, may further comprise the steps:

Step 1 is extracted the reflectivity of each pixel in the original MODIS remote sensing image, calculates the normalization snow index NDSI of each pixel;

ND?SI=(R4-R6)/(R4+R6)

Wherein, R4 is the reflectivity of pixel the 4th wave band, and R6 is the reflectivity of pixel the 6th wave band;

Step 2 is carried out atmospheric correction and topographic correction, the remote sensing image after obtaining proofreading and correct to the reflectivity of each pixel in the original MODIS remote sensing image of step 1 gained;

Step 3 detects the distribution of Snow Cover Over scope of the remote sensing image after step 2 gained is proofreaied and correct, and obtains accumulated snow scope two-value image; Detection mode is following,

If the normalization snow index NDSI of certain pixel in the remote sensing image after proofreading and correct>the reflectivity R6 < 0.2 of the 0.4, the 6th wave band; And the reflectivity R2 of the 2nd wave band>0.2; Judge that this pixel belongs to the distribution of Snow Cover Over scope; The image value of respective pixel is 1 in the accumulated snow scope two-value image, otherwise judges that this pixel does not belong to the distribution of Snow Cover Over scope, and the image value of respective pixel is 0 in the accumulated snow scope two-value image;

Step 4 resamples to the remote sensing image after the correction of step 2 gained, reduces resolution, the reflectivity image after obtaining resampling; The implementation that resamples is following,

If the reflectivity of certain pixel is ρ in the reflectivity image after resampling ^Cr, there is N pixel the corresponding region in the remote sensing image of this pixel after step 2 gained is proofreaied and correct, and wherein the reflectivity of i pixel does The value of i is 1,2 ..., N is calculated as follows the reflectivity of each pixel in the reflectivity image after the resampling,

${\mathrm{\&rho;}}^{\mathrm{cr}}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&rho;}}_i^{\mathrm{fr}}}{N}$

Step 5 resamples to step 3 gained accumulated snow scope two-value image, reduces resolution, the accumulated snow coverage rate image after obtaining resampling; The resolution of the reflectivity image after the accumulated snow coverage rate image after the resampling and step 4 gained resample is consistent, and the implementation of resampling is following,

If the accumulated snow coverage rate of certain pixel is FRA in the accumulated snow coverage rate image after resampling ^Cr, this pixel has N pixel in the corresponding region in step 3 gained accumulated snow scope two-value image, and wherein the image value of i pixel does

The value of i is 1,2 ..., N is calculated as follows the accumulated snow coverage rate of each pixel in the accumulated snow coverage rate image after the resampling,

${\mathrm{FRA}}^{\mathrm{cr}}=\frac{\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{FRA}}_i^{\mathrm{fr}}}{N}$

Step 6; Accumulated snow coverage rate image after reflectivity image after stack step 4 gained resamples and step 5 gained resample; Randomly draw the partial pixel of superimposed image; And the reflectivity that extracts pixel and accumulated snow coverage values carry out regretional analysis as sample point, sets up the multiple linear regression model between the accumulated snow coverage rate and reflectivity afterwards that resamples; The accumulated snow coverage rate FRA of each pixel was expressed as after said multiple linear regression model will resample:

$\mathrm{FRA}=\underset{n=1}{\overset{M}{\mathrm{\&Sigma;}}}{a}_n{\mathrm{\&rho;}}_n+b$

Wherein, ρ _nBe the reflectivity of n wave band, a _nBe the regression coefficient of n wave band, b is for returning constant coefficient, and M is the wave band sum;

Step 7, the multiple linear regression model that utilizes step 6 to set up, the reflectivity of each pixel extracts the sub-pix accumulated snow coverage rate of original MODIS remote sensing image in the remote sensing image after proofreading and correct according to step 2 gained.