CN102902883A - Method for establishing bidirectional reflectance distribution function (BRDF) prototype library based on multi-angular measurement - Google Patents

Abstract

The invention relates to a method for establishing a bidirectional reflectance distribution function (BRDF) prototype library based on multi-angular measurement. Through self-defining bidirectional anisotropic flat index (AFX) and iterative self-organizing ISODATA clustering algorithm, a theory and a method for establishing the BRDF prototype library based on BRDF feature mode are provided and are realized by using 69 groups of ground surface multi-angular measurement data and the history data (MCD43A) of global EOS ground surface verification core point. According to the theory and the method, the conventional method for establishing a BRDF database based on the ecological form of ground surface is abandoned, the BRDF prototype library is different from the global pixel-to-pixel BRDF database of MODIS (Moderate-resolution Imaging Spectroradiometer) in the service operation at present; and is small in volume, simple and convenient to construct and easy to operate, and is applicable for other airborne and spaceborne multi-angular measurement data of ground surface. In the technical field of spatial information, the method particularly has theoretical and application values for extracting BRDF prior knowledge to invert ground surface parameters in the aspect of quantitative remote sensing.

Description

A kind of based on multiangular measurement structure two methods to sexual reflex distribution function (BRDF) prototype library

One, technical field

The present invention relates to a kind ofly make up two methods to sexual reflex distribution function (BRDF) prototype library based on multiangular measurement, belong to the Spatial Information Technology field.

Two, background technology

The anisotropic emission of earth surface be the occurring in nature object to the basic macroscopic appearance of reflection of electromagnetic wave, earth's surface two is optics Quantitative Remote Sensing Studies field important component part to the research of sexual reflex distribution function (BRDF).Since the seventies, the Vertical Observation mode is mainly taked in satellite remote sensing, obtains the biophysical parameters of surface vegetation canopy.Along with the development of remote sensing technology, the further investigation of vegetation and optical radiation interaction mechanism, and the various new demands that face, people more and more clearly realize that, aspect the deduction Land Surface Parameters, multi-angle remote sensing provides extra effectively information source, has played irreplaceable effect.Over nearly 20 years, along with succeeding in sending up of multi-angle satellite borne sensor, such as POLDER/ADEOS, CHRIS/PROBA, MISR/Terra and MODIS/Terra+Aqua, research has accumulated a large amount of multi-angle observation data over the ground, how to extract Useful Information as priori from these data of multiple angles, being that one of key issue that need to solve is demanded in the Spatial Information Technology field urgently, also is one of problem in science of just exploring in active research of quantitative remote sensing field various countries scientist.

At present based on aspect, multi-angle observation data configuration two tropism's reflectance data storehouse; usually adopt merging earth's surface ecotype to obtain earth's surface two tropism's change of reflection rules; but; there are some researches show that the variance in earth's surface ecotype two tropism's change of reflection classes usually can be greater than the variance between the class, this brings very large difficulty for the application at Global Scale of the method.At present, MODIS adopts pixel to the global BRDF database of pixel, this database is accumulated based on the high-quality historical data, but construct such data stock problem be: (1) is supposed not exclusively to set up, namely, need hypothesis different year BRDF vary stable mutually of the same period consistent, by data accumulation for many years with fill up, obtain phase same time high-quality BRDF data; (2) obtaining the complete data of multiple angles in the whole world has certain difficulty, that is, even in the situation that this hypothesis is set up, zone and high-latitude area owing to the impact of cloud and solar zenith angle, are difficult to obtain high-quality BRDF data under the line; (3) data volume is huge, that is, the BRDF database that the method produces usually has a hundreds of GB and can not obtain the BRDF basic change rule.At present, the MODIS sensor relies on such database to obtain the amount inverting of global albedo (magnitude inversion) quality.

The present invention adopts the anisotropy flattening index, make up one succinct two to sexual reflex distribution function prototype library, main characteristics is embodied in: do not consider the earth's surface ecotype with the time mutually variation, different-waveband is carried out cluster according to the Changing Pattern of BRDF, generation is based on the BRDF classification of BRDF Changing Pattern, and then obtaining the BRDF prototype, the variation of successively decreasing by least square fitting error in the class increases with number of categories determines the BRDF modal number.

Three, summary of the invention

1, purpose: the objective of the invention is the prototype from multiangular measurement extracting data BRDF, because earth's surface two is to the complicacy of sexual reflex, tradition can not fine statement BRDF Change of types based on the ecological class method for distinguishing in earth's surface, the present invention utilizes the variation characteristic of BRDF, by the anisotropy flattening index (AFX) of definition is carried out cluster, obtain the BRDF type, and then produce the prototype of BRDF.The present invention is aspect quantitative remote sensing, especially to the inverting vegetation structure or utilize the aspects such as crucial Land Surface Parameters such as BRDF priori inverting surface albedo that good theory and using value are arranged.

2, technical scheme: the present invention relates to a kind ofly make up two methods to sexual reflex distribution function (BRDF) prototype library, concrete steps following (such as Fig. 1) based on multiangular measurement:

Step 1: definition anisotropy flattening index

For the multiangular measurement data, need at first make up an angle index, obtain the Changing Pattern of two tropism's reflective-modes.Anisotropy flattening index (Anisotropic Flat Index, AFX) is defined as empty albedo (White Sky Albedo, WSA) and the isotropy parameter (f of semiempirical linear kernel driving model on daytime _Iso) ratio, namely

$\mathrm{AFX}\left(\mathrm{\λ}\right)=\frac{\mathrm{WSA}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}---\left(1\right)$

According to above-mentioned definition, can derive AFX and three parameters relationships examining driving model:

$\mathrm{AFX}\left(\mathrm{\λ}\right)=1+\frac{f_{\mathrm{vol}}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}*0.189184-\frac{f_{\mathrm{geo}}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}*1.377622---\left(2\right)$

The characteristic of anisotropy flattening index (AFX) shows as: AFX＞1 expression volume scattering is greater than the geometrical optics scattering, and at this moment, two tropism's reflective-modes are bowl-shape; AFX＜1 expression volume scattering is less than the geometrical optics scattering, and at this moment, two tropism's reflective-modes are dome-shaped; Otherwise AFX=1 represents that volume scattering and geometrical optics scattering equate, reflecting surface is Lambertian reflection.This characteristic of anisotropy flattening index can be used for the means of taxonomic research of two tropism's reflective-modes.

Calculate the anisotropy flattening index, need first with semiempirical nuclear driving model match multiangular measurement data, obtain three parameters of model, then calculate the anisotropy flattening index according to formula (2), if the existing two isotropy parameters to the daytime of sexual reflex product empty albedo and model also can directly be calculated according to definition (1).Linear semiempirical nuclear driving model is expressed as:

R(θ _v，θ _s，Δφ，λ)＝f _iso(λ)+f _vol(λ)K _vol(θ _v，θ _s，Δφ)+f _geo(λ)K _geo(θ _v，θ _s，Δφ)(3)

At this, R (θ _v, θ _s, Δ φ, λ) and be two to sexual reflex distribution function, f _Iso(λ), f _Vol(λ) and f _GeoBe three parameters of model (λ), be referred to as respectively the isotropy parameter, volume scattering parameter and geometrical optics parameter; K _Vol(θ _v, θ _s, Δ φ) and K _Geo(θ _v, θ _s, Δ φ) and be volume scattering and the geometrical optics kernel function of nuclear driving model.Given vegetation structure parameter, two kernel functions are trigonometric functions of observation and position of sun.

Step 2: cluster produces two to the sexual reflex class of distribution function

From the anisotropy flattening index of multiangular measurement data, obtain two to the sexual reflex class of distribution function with the ISODATA clustering algorithm, the present invention proposes to control two to sexual reflex class of distribution function quantity with the production decline law of average fit error, and method flow is as follows:

(1) for the anisotropy flattening index of each wave band of multiangular measurement, at first cluster produces multi-class continuously distribution of bi directional reflectance function class set { C _i(i=2,3 ..., m).I represents to be clustered into 2 situations during to the m class.

(2) set up anisotropy flattening index and the look-up table of examining three parameters of driving model according to formula (2), according to look-up table, to every kind of classification situation, three model parameters of each classification are average respectively, obtains all f directly of three model parameters in every kind of classification situation class _{M_iso}, f _{M_vol}And f _{M_geo}, this mean parameter represents in the class average two to the sexual reflex distribution pattern.

(3) with the multi-angle observation in two tropism's reflection parameters average match classes, obtain the least square fitting error RMSE of every group of measurement (j) in every kind of classification situation (i), the class _Ij(i=2,3 ..., m; J=1,2 ..., n), on average obtain the average of every kind of classification situation

Obtain

The figure that successively decreases that increases with classification quantity can judge when average minimum error of fitting based on this figure and to pass two tropism's reflective function class numbers when being reduced to level of approximation, is final two definite tropism's reflective function modal numbers.

(4) for MODIS two tropism's reflection parameters products (MCD43A1), in the situation that can not obtain the original observation of multi-angle, carry out spatial sampling by the whole model surface that model parameter is determined, determine that two tropism's reflection model values of corresponding sampled point are as observed reading, repeating step (3), the method of sampling: for different sun angles, observation angle is respectively 5 ° and 10 ° in zenith angle and azimuthal interval.

Step 3: calculate principal plane two to sexual reflex distribution function prototype

According to acquired two to sexual reflex prototype parameter f _{M_iso}, f _{M_vol}And f _{M_geo}, by the nuclear driving model, calculate principal plane two to sexual reflex distribution function prototype pattern, principal plane two to sexual reflex distribution function pattern, by the isotropy standard parameter of model, is obtained standardized two to sexual reflex distribution function pattern:

$\frac{R({\mathrm{\θ}}_v,{\mathrm{\θ}}_s,\mathrm{\Δ\φ},\mathrm{\λ})}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}=1+\frac{f_{\mathrm{vol}}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}{K}_{\mathrm{vol}}({\mathrm{\θ}}_v,{\mathrm{\θ}}_s,\mathrm{\Δ\φ})+\frac{f_{\mathrm{geo}}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}{K}_{\mathrm{geo}}({\mathrm{\θ}}_v,{\mathrm{\θ}}_s,\mathrm{\Δ\φ})---\left(4\right)$

The characteristics of this pattern can be to the two spectral reflectance amount standardization to sexual reflex distribution function pattern, and therefore, preferably visual judgement two is to the gradual change rule of sexual reflex distribution function pattern.

3, advantage and effect: the present invention has defined anisotropy flattening index (AFX), by adopting ISODATA algorithm cluster AFX, make up two to sexual reflex distribution function prototype library, can characterize well the Changing Pattern of BRDF, with the variation of number of categories, determine the BRDF modal number by RMSE average in the class.The inventive method is adapted to the multi-angle observation data set of various yardsticks, clear logic, strong adaptability, on zone and Global Scale, the Changing Pattern of the clear statement of energy BRDF has theory and using value to earth's surface key parameters such as quantitative inversion vegetation structure and knowledge-based inverting surface albedos.

Four, description of drawings

The schematic flow sheet of Fig. 1 the inventive method

The red wave band BRDF of Fig. 2 (a) type (69 groups of data)

Fig. 2 (b) near-infrared band BRDF type (69 groups of data)

The standardized BRDF type of the red wave band of Fig. 2 (c) (69 groups of data)

The standardized BRDF type of Fig. 2 (d) near-infrared band (69 groups of data)

The red wave band RMSE of Fig. 3 (a) is with the variation of BRDF modal number

Fig. 3 (b) near-infrared band RMSE is with the variation of BRDF modal number

Fig. 4 whole world earth observing system (EOS) earth's surface checking core point distribution (open data, 26 check posts, the whole world)

7 wave bands of Fig. 5 intermediate-resolution spectrometer (MODIS) (OK) BRDF prototype of (row) mutually during with 5

Phase RMSE is with the variation of BRDF modal number during 5 of 7 wave bands of Fig. 6 intermediate-resolution spectrometer (MODIS)

Five, embodiment

The present invention relates to a kind ofly make up two methods to sexual reflex distribution function (BRDF) prototype library, the method concrete steps following (such as Fig. 1) based on multiangular measurement:

Step 1: definition anisotropy flattening index

For the multiangular measurement data, need at first make up an angle index, obtain the Changing Pattern of two tropism's reflective-modes.Anisotropy flattening index (Anisotropic Flat Index, AFX) is defined as empty albedo (White Sky Albedo, WSA) and the isotropy parameter (f of semiempirical linear kernel driving model on daytime _Iso) ratio, namely

$\mathrm{AFX}\left(\mathrm{\λ}\right)=\frac{\mathrm{WSA}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}---\left(1\right)$

According to above-mentioned definition, can derive AFX and three parameters relationships examining driving model:

$\mathrm{AFX}\left(\mathrm{\λ}\right)=1+\frac{f_{\mathrm{vol}}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}*0.189184-\frac{f_{\mathrm{geo}}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}*1.377622---\left(2\right)$

The characteristic of anisotropy flattening index (AFX) shows as: AFX＞1 expression volume scattering is greater than the geometrical optics scattering, and at this moment, two tropism's reflective-modes are bowl-shape; AFX＜1 expression volume scattering is less than the geometrical optics scattering, and at this moment, two tropism's reflective-modes are dome-shaped; Otherwise AFX=1 represents that volume scattering and geometrical optics scattering equate, reflecting surface is Lambertian reflection.This characteristic of anisotropy flattening index can be used for the means of taxonomic research of two tropism's reflective-modes.

Calculate the anisotropy flattening index, need first with semiempirical nuclear driving model match multiangular measurement data, obtain three parameters of model, then calculate the anisotropy flattening index according to formula (2), if the existing two isotropy parameters to the daytime of sexual reflex product empty albedo and model also can directly be calculated according to definition (1).Linear semiempirical nuclear driving model is expressed as:

R(θ _v，θ _s，Δφ，λ)＝f _iso(λ)+f _vol(λ)K _vol(θ _v，θ _s，Δφ)+f _geo(λ)K _geo(θ _v，θ _s，Δφ)(3)

At this, R (θ _v, θ _s, Δ φ, λ) and be two to sexual reflex distribution function, f _Iso(λ), f _Vol(λ) and f _GeoBe three parameters of model (λ), be referred to as respectively the isotropy parameter, volume scattering parameter and geometrical optics parameter; K _Vol(θ _v, θ _s, Δ φ) and K _Geo(θ _v, θ _s, Δ φ) and be volume scattering and the geometrical optics kernel function of nuclear driving model.Given vegetation structure parameter, two kernel functions are trigonometric functions of observation and position of sun.

Step 2: cluster produces two to the sexual reflex class of distribution function

From the anisotropy flattening index of multiangular measurement data, obtain two to the sexual reflex class of distribution function with the ISODATA clustering algorithm, the present invention proposes to control two to sexual reflex class of distribution function quantity with the production decline law of average fit error, and method flow is as follows:

(1) for the anisotropy flattening index of each wave band of multiangular measurement, at first cluster produces multi-class continuously distribution of bi directional reflectance function class set { C _i(i=2,3 ..., m).I represents to be clustered into 2 situations during to the m class.

(2) set up anisotropy flattening index and the look-up table of examining three parameters of driving model according to formula (2), according to look-up table, to every kind of classification situation, three model parameters of each classification are distinguished on average, obtain the average f of three model parameters in every kind of classification situation class _{M_iso}, f _{M_vol}And f _{M_geo}, this mean parameter represents in the class average two to the sexual reflex distribution pattern.

(3) with the multi-angle observation in two tropism's reflection parameters average match classes, obtain the least square fitting error RMSE of every group of measurement (j) in every kind of classification situation (i), the class _Ij(i=2,3 ..., m; J=1,2 ..., n), on average obtain the average of every kind of classification situation

Obtain The figure that successively decreases that increases with classification quantity can judge when average minimum error of fitting based on this figure and to pass two tropism's reflective function class numbers when being reduced to level of approximation, is final two definite tropism's reflective function modal numbers.

(4) for MODIS two tropism's reflection parameters products (MCD43A1), in the situation that can not obtain the original observation of multi-angle, carry out spatial sampling by the whole model surface that model parameter is determined, determine that two tropism's reflection model values of corresponding sampled point are as observed reading, repeating step (3), the method of sampling: for different sun angles, observation angle is respectively 5 ° and 10 ° in zenith angle and azimuthal interval.

Step 3: calculate principal plane two to sexual reflex distribution function prototype

According to acquired two to sexual reflex prototype parameter f _{M_iso}, f _{M_vol}And f _{M_geo}, by the nuclear driving model, calculate principal plane two to sexual reflex distribution function prototype pattern, principal plane two to sexual reflex distribution function pattern, by the isotropy standard parameter of model, is obtained standardized two to sexual reflex distribution function pattern:

$\frac{R({\mathrm{\θ}}_v,{\mathrm{\θ}}_s,\mathrm{\Δ\φ},\mathrm{\λ})}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}=1+\frac{f_{\mathrm{vol}}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}{K}_{\mathrm{vol}}({\mathrm{\θ}}_v,{\mathrm{\θ}}_s,\mathrm{\Δ\φ})+\frac{f_{\mathrm{geo}}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}{K}_{\mathrm{geo}}({\mathrm{\θ}}_v,{\mathrm{\θ}}_s,\mathrm{\Δ\φ})---\left(4\right)$

The characteristics of this pattern can be to the two spectral reflectance amount standardization to sexual reflex distribution function pattern, and therefore, preferably visual judgement two is to the gradual change rule of sexual reflex distribution function pattern.

Embodiment 1:

Dispose Intel (R) Core at one ^TM2.5GHz4 processor, the 4G internal memory is implemented on the computing machine of ATI Radeon HD5670 figure video card.Adopt the historical data of 69 groups of earth's surface observations, and the MODIS two of global EOS earth's surface checking core point is to sexual reflex and albedo data (MCD43A, Fig. 4).

Two kinds of spatial resolution multiangular measurement data are carried out modeling (Fig. 2 and Fig. 5), can find out on the principal plane of extraction two to the sexual reflex distribution pattern exist gem-pure bowl-shape-variation of dome-shaped, this variation can be well by anisotropy flattening index statement (table 1).This invention does not rely on the position of pixel point, even cause the pixel disappearance of certain limit owing to reasons such as clouds, the present invention still can finely extract two to sexual reflex distribution pattern information from typical data of multiple angles, thereby make up two to sexual reflex distribution function prototype library, this prototype library is that a kind of knowledge of BRDF database is extracted and condensed.Fig. 3 be red and near-infrared band RMSE with the variation of BRDF modal number, can determine that according to this figure 69 groups of multiangular measurement data have 4 modal numbers at red and near-infrared band.Mutually (hibernation season, D when Fig. 6 is 5 of MODIS7 wave bands (red, NIR, blue, green, SWIR1, SWIR2 and SWIR3); Growth season, G; Ripe season, M; Wither season, S) RMSE changes with the BRDF modal number, determines that according to this figure 26 the EOS earth's surfaces checkings in the whole world core point phase and BRDF modal number in 1 whole year 4 time respectively are 6 prototypes at 7 wave bands.Fig. 2 be the present invention to the modeling result of the 69 groups of multiangular measurement data in earth's surface, wherein Fig. 2 (a) and Fig. 2 (b) are the primitive forms of observation principal plane BRDF classification, Fig. 2 (c) and Fig. 2 (d) they are the normalized forms that principal plane BRDF classifies.Fig. 5 is that the present invention is to the modeling result of check post, global EOS earth's surface.Table 1 is 4 BRDF prototypes from 2 wave bands of 69 groups of earth's surface multiangular measurement extracting data; Table 2 is 6 BRDF prototypes of 7 MODIS wave bands of 26 earth's surface checking core points extraction from the whole world.

The BRDF modal number that table 1. extracts from the 69 groups of historical datas in earth's surface (2 wave bands)

The prototype library (7 wave bands) of two tropism's reflective functions that 26 from whole world EOS earth's surface checking epipoles of table 2. are extracted

Claims (1)

1. one kind makes up two methods to sexual reflex distribution function (BRDF) prototype library based on multiangular measurement, and step comprises: step 1: definition anisotropy flattening index

For the multiangular measurement data, need at first make up an angle index, obtain the Changing Pattern of two tropism's reflective-modes.Anisotropy flattening index (Anisotropic Flat Index, AFX) is defined as empty albedo (White Sky Albedo, WSA) and the isotropy parameter (f of semiempirical linear kernel driving model on daytime _Iso) ratio, namely

$\mathrm{AFX}\left(\mathrm{\λ}\right)=\frac{\mathrm{WSA}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}---\left(1\right)$

According to above-mentioned definition, can derive AFX and three parameters relationships examining driving model:

$\mathrm{AFX}\left(\mathrm{\λ}\right)=1+\frac{f_{\mathrm{vol}}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}*0.189184-\frac{f_{\mathrm{geo}}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}*1.377622---\left(2\right)$

The characteristic of anisotropy flattening index (AFX) shows as: AFX＞1 expression volume scattering is greater than the geometrical optics scattering, and at this moment, two tropism's reflective-modes are bowl-shape; AFX＜1 expression volume scattering is less than the geometrical optics scattering, and at this moment, two tropism's reflective-modes are dome-shaped; Otherwise AFX=1 represents that volume scattering and geometrical optics scattering equate, reflecting surface is Lambertian reflection.This characteristic of anisotropy flattening index can be used for the means of taxonomic research of two tropism's reflective-modes.

Calculate the anisotropy flattening index, need first with semiempirical nuclear driving model match multiangular measurement data, obtain three parameters of model, then calculate the anisotropy flattening index according to formula (2), if the existing two isotropy parameters to the daytime of sexual reflex product empty albedo and model also can directly be calculated according to definition (1).Linear semiempirical nuclear driving model is expressed as:

R(θ _v，θ _s，Δφ，λ)＝f _iso(λ)+f _vol(λ)K _vol(θ _v，θ _s，Δφ)+f _geo(λ)K _geo(θ _v，θ _s，Δφ)(3)

At this, R (θ _v, θ _s, Δ φ, λ) and be two to sexual reflex distribution function, f _Iso(λ), f _Vol(λ) and f _GeoBe three parameters of model (λ), be referred to as respectively the isotropy parameter, volume scattering parameter and geometrical optics parameter; K _Vol(θ _v, θ _s, Δ φ) and K _Geo(θ _v, θ _s, Δ φ) and be volume scattering and the geometrical optics kernel function of nuclear driving model.Given vegetation structure parameter, two kernel functions are trigonometric functions of observation and position of sun.

Step 2: cluster produces two to the sexual reflex class of distribution function

From the anisotropy flattening index of multiangular measurement data, obtain two to the sexual reflex class of distribution function with the ISODATA clustering algorithm, the present invention proposes to control two to sexual reflex class of distribution function quantity with the production decline law of average fit error, and method flow is as follows:

(1) for the anisotropy flattening index of each wave band of multiangular measurement, at first cluster produces multi-class continuously distribution of bi directional reflectance function class set { C _i(i=2,3 ..., m).I represents to be clustered into 2 situations during to the m class.

(2) set up anisotropy flattening index and the look-up table of examining three parameters of driving model according to formula (2), according to look-up table, to every kind of classification situation, three model parameters of each classification are distinguished on average, obtain the average f of three model parameters in every kind of classification situation class _{M_iso}, f _{M_vol}And f _{M_geo}, this mean parameter represents in the class average two to the sexual reflex distribution pattern.

(3) with the multi-angle observation in two tropism's reflection parameters average match classes, obtain the least square fitting error RMSE of every group of measurement (j) in every kind of classification situation (i), the class _Ij(i=2,3 ..., m; J=1,2 ..., n), on average obtain the average of every kind of classification situation

Obtain The figure that successively decreases that increases with classification quantity can judge when average minimum error of fitting based on this figure and to pass two tropism's reflective function class numbers when being reduced to level of approximation, is final two definite tropism's reflective function modal numbers.

(4) for MODIS two tropism's reflection parameters products (MCD43A1), in the situation that can not obtain the original observation of multi-angle, carry out spatial sampling by the whole model surface that model parameter is determined, determine that two tropism's reflection model values of corresponding sampled point are as observed reading, repeating step (3), the method of sampling: for different sun angles, observation angle is respectively 5 ° and 10 ° in zenith angle and azimuthal interval.

Step 3; Calculate principal plane two to sexual reflex distribution function prototype

According to acquired two to sexual reflex prototype parameter f _{M_iso}, f _{M_vol}And f _{M_geo}, by the nuclear driving model, calculate principal plane two to sexual reflex distribution function prototype pattern, principal plane two to sexual reflex distribution function pattern, by the isotropy standard parameter of model, is obtained standardized two to sexual reflex distribution function pattern:

$\frac{R({\mathrm{\θ}}_v,{\mathrm{\θ}}_s,\mathrm{\Δ\φ},\mathrm{\λ})}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}=1+\frac{f_{\mathrm{vol}}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}{K}_{\mathrm{vol}}({\mathrm{\θ}}_v,{\mathrm{\θ}}_s,\mathrm{\Δ\φ})+\frac{f_{\mathrm{geo}}\left(\mathrm{\λ}\right)}{f_{\mathrm{iso}}\left(\mathrm{\λ}\right)}{K}_{\mathrm{geo}}({\mathrm{\θ}}_v,{\mathrm{\θ}}_s,\mathrm{\Δ\φ})---\left(4\right)$

The characteristics of this pattern can be to the two spectral reflectance amount standardization to sexual reflex distribution function pattern, and therefore, preferably visual judgement two is to the gradual change rule of sexual reflex distribution function pattern.

Images