A method for inverting the coverage of biological soil crust based on a linear kernel-driven model

Abstract

The present invention provides a method for retrieving the coverage of biological soil crust based on a linear kernel-driven model. First, a biological soil crust index FCCI based on the radiative transfer principle is constructed. FCCI is used to extract the biological soil crust area. The Beer's law is introduced to construct a multi-angle joint equation and the corresponding solution method to estimate FCCI in the GI model. max and FCCI min . Finally, the calculation of the biological soil crust coverage FCC is completed based on the GI model. The beneficial effects are as follows: The present invention constructs a biological soil crust index based on the radiative transfer principle to make up for the deficiency of the index method based on spectral linear combination in lacking consideration of physical mechanisms; the linear kernel-driven model is introduced, and a solution method for a multi-angle index is proposed, expanding the pixel dichotomy method based on multiple angles to high-spatial-resolution remote sensing images to realize the inversion of the biological soil crust coverage with high spatial resolution; a method combining chessboard segmentation and Monte Carlo algorithm is adopted to improve the calculation efficiency of the algorithm for retrieving the biological soil crust coverage of large areas.

Description

Technical Field

[0001] The present invention relates to the field of biological soil crust coverage, and particularly to a method for retrieving biological soil crust coverage based on a linear kernel-driven model. Background Art

[0002] Biological soil crust is an organic complex formed by bacteria, cyanobacteria, diatoms, green algae, microfungi, lichens, bryophytes, and other related organisms "cemented" with the surface particles of soil (sand and gravel) through mycelia, rhizoids, and secretions. It is a powerful indicator for evaluating the health of desert ecosystems. Therefore, understanding the spatio-temporal changes of biological soil crust is particularly important for ecosystem management and desertification research. The development of remote sensing technology provides an effective means for understanding the spatio-temporal changes of biological soil crust.

[0003] When using remote sensing technology to retrieve biological soil crust coverage, it is mainly divided into two steps. The first step is to extract the areas where biological soil crust exists. This step first analyzes the spectral information of biological soil crust, screens out its characteristic bands, or further constructs relevant spectral indices based on these characteristic bands, and extracts the areas where biological soil crust exists on remote sensing images through machine learning algorithms or band operations. The second step is to determine the percentage of biological soil crust in the extracted area, that is, the biological soil crust coverage. This step is achieved by establishing a relevant model based on the relationship between the spectral information of biological soil crust and its coverage.

[0004] Currently, when extracting biological soil crusts, there are mainly three methods, namely the spectral direct analysis method, the index method based on spectral linear combination, and the index method based on radiative transfer principle. The earliest developed is the spectral direct analysis method, which analyzes the spectral information of biological soil crusts obtained by measurement and uses its spectral sensitive regions to distinguish the differences between biological soil crusts and "background" information, so as to achieve the goal of extracting biological soil crust information. Subsequently, with the popularization of hyperspectral technology, many scholars have screened out more sensitive bands for biological soil crusts through methods such as continuum removal method and principal component analysis method. However, as an organic complex of lower vegetation, the spectral information of biological soil crusts is a comprehensive display of the spectra of various organisms, which brings great uncertainty to the acquisition of its spectral information and greatly limits the inversion of the coverage of biological soil crusts by the spectral direct analysis method. To solve this problem, the index method based on spectral linear combination was proposed. This method performs mathematical operations on the bands corresponding to the "peaks" and "valleys" of the spectral curve of biological soil crusts to establish a biological soil crust index, so as to highlight the spectral signal of biological soil crusts and suppress the spectral information of the "background" (gravel, soil) of biological soil crusts, in order to achieve the goal of extracting biological soil crusts. For example, BSCI, CI, SRCI, DRCI, etc. These are all biological soil crust indices constructed by linearly combining spectra. Since these indices do not consider physical mechanisms, they cannot accurately describe the quantitative relationship between spectral information and coverage, resulting in an underestimated phenomenon in the inversion of the coverage of biological soil crusts. The proposal of the index method based on radiative transfer principle further makes up for the deficiencies of the index method based on spectral linear combination. It starts from the radiative transfer mechanism and constructs an index based on the physical equation between spectral information and coverage, which can well explain the quantitative relationship between spectral information and coverage. However, at present, the physical models involved in this method are mostly related to the research of vegetation canopy and soil background modeling, and less involved in the research of the inversion of biological soil crust coverage. Therefore, how to construct a biological soil crust index based on the radiative transfer principle is a key problem to be solved for accurately extracting the distribution area of biological soil crusts.

[0005] After the distribution area of biological soil crusts is obtained, the next step is to further obtain the percentage of biological soil crusts in this area, that is: the coverage of biological soil crusts. At present, there is less research on the inversion of the coverage of biological soil crusts and there is no mature method. The inversion methods of the coverage of biological soil crusts mostly originate from the inversion methods of vegetation coverage. Currently, the main inversion methods of vegetation coverage include empirical algorithms, spectral mixture analysis methods, and physical model methods. Considering the comprehensive inversion efficiency of operation time and calculation accuracy, the pixel dichotomy method extended from the spectral mixture method is currently the best choice, and its equation form is:

[0006]

[0007] Where: FVC is the vegetation coverage, VI is the vegetation index to be resampled in the image, VI max and VI min are the maximum and minimum values of the vegetation index respectively. The above equation is usually called the GI model. From the GI model, it can be seen that determining the extreme values of the index is the key to calculating its coverage. At present, there are mainly methods based on observational data, methods based on direct image analysis, and methods based on multi-angle to determine the extreme values of the index. In the method based on observational data, field measurements and high-spatial-resolution image data are usually used to obtain the extreme values of the index. This method is easy to implement, but a large number of samples are required to ensure the accuracy of the extreme values of the index, so it is difficult to be widely used. To solve this problem, the method based on direct image analysis was proposed. In the method based on direct image analysis, the maximum value of the index is usually the maximum vegetation index in high-density vegetation, and its data is relatively easy to obtain. While the minimum value of the index is usually the "background" information, which is affected by the composition, grain size, and moisture of the "background", resulting in a large uncertainty in the minimum value of the index. The proposal of the multi-angle method well solves the problem of the uncertainty of the minimum value of the index. This method uses the zenith angle of 57.5° to calculate the multi-angle vegetation index (VI), and then solves the Beer's law related to FVC to determine VI max and VI min . Therefore, we can use the multi-angle pixel dichotomy method to invert the biological soil crust coverage.

[0008] When using the pixel dichotomy method to invert the biological soil crust coverage, in addition to determining the extreme values of the index, the high or low spatial resolution of the remote sensing data will also directly affect the inversion accuracy. Biological soil crusts are widely distributed in vast desert and sandy areas, and their spectral information is affected by other surface components. The indices proposed in previous studies are mostly applicable to remote sensing images with low spatial resolution, which limits their ability to extract biological soil crusts, resulting in an underestimation of the inverted biological soil crust coverage. Therefore, using high-spatial-resolution images for biological soil crust information extraction and coverage estimation has become the main development trend of large-scale biological soil crust monitoring.

[0009] However, at present, most high-spatial-resolution remote sensing images are vertically observed. Due to the lack of high-spatial-resolution multi-angle data, it is impossible to extend the multi-angle pixel dichotomy method to high-spatial-resolution remote sensing images to achieve the inversion of biological soil crust coverage. Therefore, how to calculate the multi-angle reflectance data based on vertically observed high-spatial-resolution remote sensing images is the key to solving the extended application of the multi-angle pixel dichotomy method to high-spatial-resolution images, and it is also another key problem to be solved for realizing the inversion of high-spatial-resolution biological soil crust coverage. Summary of the Invention

[0010] Based on at least one of the above technical problems, the present invention proposes a method for retrieving the coverage of biological soil crusts based on a linear kernel-driven model.

[0011] A method for retrieving the coverage of biological soil crusts based on a linear kernel-driven model, the steps of which include:

[0012] S1. Construct a biological soil crust index FCCI based on the radiation transfer principle. FCCI is used to extract the biological soil crust area. The biological soil crust index is constructed by the single-layer summation method. The biological soil crust canopy is assumed to be a homogeneous scatterer. After derivation, the biological soil crust coverage index FCCI based on the radiation transfer principle is obtained, that is:

[0013]

[0014] In the formula, FCCI is the biological soil crust coverage index, t and f are the adjustment parameters of the biological soil crust coverage index and are also the comprehensive manifestations of the radiation of the biological soil crust canopy and the soil radiation. R(red+green), R(nir), and R(blue) are the reflectivities of the red-green combined band, the near-infrared band, and the blue band, respectively;

[0015] S2. Construct a pixel dichotomy model of the biological soil crust, and then estimate the proportion of the biological soil crust in this area, that is, the biological soil crust coverage. To estimate the biological soil crust coverage, the GI model in the pixel dichotomy method is introduced to describe the relationship between FCCI and the biological soil crust coverage. The expression of the GI model is:

[0016]

[0017] In the formula: FCC is the biological soil crust coverage, FCCI(0°) is the biological soil crust coverage index to be resampled in the vertical observation image; FCCI max and FCCI min are the maximum and minimum values of the biological soil crust coverage index respectively, FCCI max and FCCI min refer to the FCCI of the high-coverage biological soil crust and the FCCI of the biological soil crust "background" (gravel, soil);

[0018] S3. Construct a multi-angle joint equation, introduce the value of the G function in Beer's law related to the coverage, that is, the value of the leaf area projection function: G(57.5°)=0.5. Combine the GI model to determine FCCI max and FCCI min , in this method, 55° and 60° are used to approximate 57.5°, that is, G(57.5°)≈G(55°)≈G(60°). Then, after derivation, the formula for solving FCCI max and FCCImin Multi - angle combined equation:

[0019]

[0020] Where: FCCI(55°) and FCCI(60°) are the FCCIs on the pixel when the solar zenith angle is 55° and 60° respectively;

[0021] S4. Obtain high - spatial - resolution FCCI(55°) and FCCI(60°) images, and introduce the linear kernel - driven model:

[0022] r(θ i ) = f iso g iso + f vol g vol + f geo g geo (5)

[0023] Where: g 0iso = g 0iso + g 1iso θ 2 + g 2iso θ 3 ,g vol = g 0vol + g 1vol θ 2 + g 2vol θ 3 ,g geo = g 0geo + g 1geo θ 2 + g 2geo θ 3 ,where g 0vol ,g 1vol ,g 2vol ,g 0geo ,g 1geo and g 2geo are the polynomial factors of the linear kernel - driven model, and θ i is the solar zenith angle;

[0024] The calculation of the black - sky albedo value is summarized as follows:

[0025] Table (5) Polynomial parameters of the linear kernel - driven model

[0026]

[0027] Extract the reflectance from the vertically - observed high - spatial - resolution remote - sensing image using a 2×2 moving window. According to Equation (5), four equations are established for fiso, fvol, and fgeo:

[0028]

[0029] Transform equation (6) to obtain the equation for inverting the parameter image of the linear kernel-driven model:

[0030] F = (G T G) -1 G T R (7)

[0031] Where: F is the parameter image of the linear kernel-driven model, G is the polynomial factor of the linear kernel-driven model, and R is the reflectance of the high-spatial-resolution remote sensing image for vertical observation; the obtained reflectance of the high-spatial-resolution remote sensing image is obtained from vertical observation (i.e., θ i = 0°). However, when θ i = 0°, it causes fiso, fvol, and fgeo to be unsolvable. Therefore, approximate θ i = 5° as θ i = 0° and substitute it into equation (7) to solve the equation;

[0032] Substitute the parameter images F of the high-spatial-resolution linear kernel-driven model for each band obtained by inversion back into the linear kernel-driven model (5), and the directional reflectance images for each band can be obtained. The high-spatial-resolution FCCI(55°) and FCCI(60°) images can be obtained from the directional reflectance images for each band;

[0033] S5. Obtain FCCI max and FCCI min . First, use the checkerboard partitioning method to segment the high-spatial-resolution FCCI(55°) and FCCI(60°) images into several representative sub-block images. Secondly, in each segmented sub-block image, use the Monte Carlo method to randomly select a certain number of pixels of the FCCI(55°) and FCCI(60°) images, set the value range of the parameters to be solved FCCI max and FCCI min , and use the selected pixel values to construct a multi-angle joint equation system in combination with equation (4). The number of equations in the system is greater than the number of unknowns. Finally, based on the least squares principle, solve the multi-angle joint equation system to obtain the optimal FCCI max and FCCI min ;

[0034] S6. Substitute the FCCI max and FCCI min obtained in step S5 into equation (3) to calculate the FCC in the GI model of the biological soil crust.

[0035] Furthermore, in step S1, the derivation process of the biological soil crust coverage index FCCI is as follows:

[0036] S11. Introduce the approximate radiative transfer equation of the single-layer summation method, and its equation is as follows:

[0037]

[0038] In the formula: R bc (λ) is the reflectivity of the primary scattering of the biological soil crust, T ↓bc (λ) is the total downward transmittance of the biological soil crust, T ↑bc (λ) is the total upward transmittance of the biological soil crust, R s (λ) is the reflectivity of the Lambertian soil "background", R ↓bc (λ) is the reflectivity of the radiation of the soil "background" entering the bottom of the biological soil crust and transmitting downward, R h (λ) is the reflectivity of the homogeneous biological soil crust "canopy", where λ is the spectral band;

[0039] S12. Use the concept of geometric mean to define the average values of T ↓bc (λ) and T ↑bc (λ), perform Taylor series expansion on the second term on the right side of equation (8), and approximately retain the first two orders of the Taylor series to obtain the following equation:

[0040]

[0041] Let T 2 bc (λ)=a, The simplified radiative transfer equation can be obtained:

[0042] R h (λ)=R bc (λ)+aR s (λ)+b (10)

[0043] S13. Take the blue band, the red-green combined band, and the near-infrared band as the sensitive bands of the biological soil crust index; Expression of the red-green combined band:

[0044] R(red + green)=R(red)+R(green) (11)

[0045] Substitute the blue band, the red-green combined band, and the near-infrared band into the simplified radiative transfer equation (10) to obtain the equations related to the near-infrared, blue band, and red-green combined band:

[0046] R h (nir)=R bc (nir)+a 1 R s (nir)+b 1 (12)

[0047] R h (blue)=R bc (blue)+a 2 R s (blue)+b 2 (13)

[0048] R h (red + green)=R bc (red + green)+a 3 R s (red + green)+b 3 (14)

[0049] where: a 1 , a 2 , a 3 , b 1 , b 2 , b 3 are parameters after symbolic simplification, R bc (red + green) and R s (red + green) are the reflectance of biological soil crusts in the red - green combined band and the reflectance of the radiation of the soil "background" entering the bottom of the biological soil crusts; R bc (nir) and R s (nir) are the reflectance of biological soil crusts in the near - infrared band and the reflectance of the radiation of the soil "background" entering the bottom of the biological soil crusts; R bc (blue) and R s (blue) are the reflectance of biological soil crusts in the blue band and the reflectance of the radiation of the soil "background" entering the bottom of the biological soil crusts; R h (red + green), R h (nir) and R h (blue) are the reflectances of homogeneous biological soil crusts in the red - green combined band, near - infrared band and blue band;

[0050] s14. The concept of "soil line" is introduced. That is, by analyzing the spectral information of biological soil crusts under different humidities, it is found that when the red band and the green band are combined, the spectral feature space forms of the blue band and the near - infrared band are similar to the "soil line" in the near - red - red spectral feature space. In the past, when establishing vegetation indices, the "soil line" was often used to reduce the influence of the soil "background" on the research results. Therefore, a mathematical equation between the sensitive spectral bands of each biological soil crust is constructed:

[0051] R s (nir)=A 1 R s (red + green)+B1 (15)

[0052] R s (blue) = A 2 R s (red + green) + B 2 (16)

[0053] In the formula: A 1 , A 2 , B 1 , B 2 are the slope and intercept of the "soil line";

[0054] s15. In order to construct the quantitative relationship between the sensitive spectral band and the biological crust coverage, the proportional equation between the biological crust and the soil "background" is introduced:

[0055] R α (λ) = vR h (λ) + (1 - v)R s (λ) (17)

[0056] In the formula: v is the biological crust proportion factor, R α (λ) is the reflectance of the heterogeneous biological crust, R h (λ) is the reflectance of the homogeneous biological crust canopy, R s (λ) is the reflectance of the radiation of the soil "background" entering the bottom of the biological crust;

[0057] Substitute the near-infrared, blue band, and red - green combined band into formula (17), and we can get:

[0058] R α (nir) = vR h (nir) + (1 - v)R s (nir) (18)

[0059] R α (blue) = vR h (blue) + (1 - v)R s (blue) (19)

[0060] R α (red + green) = vR h (red + green) + (1 - v)R s (red + green) (20)

[0061] Substitute equation (12) into equation (18), equation (13) into equation (19), and equation (14) into equation (20), and we can get:

[0062]

[0063] Substituting equations (21) and (23) into equation (15), and equations (22) and (23) into equation (16), two quadratic equations in one variable about v can be obtained. Let:

[0064] R bc (nir)+b 1 =C 1 、R bc (red + green)+b 3 =C 2 、R bc (blue)+b 2 =C 3 、

[0065] C 1 -C 1 a 3 -A 1 C 2 -B 1 +a 3 B 1 +a 1 A 1 C 2 +a 1 B 1 -a 1 a 3 B 1 =D 1 、

[0066] C 3 -C 3 a 3 -A 2 C 2 -B 2 +a 3 B 2 +a 2 A 2 C 2 +a 2 B 2 -a 2 a 3 B 2 =D 2 、

[0067] a 3 R α (nir)-A 1 a 1 R α (red + green)-C 1 +A 1 C 2 +2B 1-a 3 B 1 -a 1 B 1 =E 1 、

[0068] a 3 R α (blue)-A 2 a 2 R α (red+green)-C 3 +A 2 C 2 +2B 2 -a 3 B 2 -a 2 B 2 =E 2 、

[0069] 2D 1 -R α (nir)-R α (red+green)=h 1 、2D 2 -R α (blue)-R α (red+green)=h 2 、

[0070]

[0071] Let F 1 -E 1 =g 1 , F 2 -E 2 =g 2 It can be obtained that:

[0072]

[0073] By combining Equation (24) and Equation (25) and letting:

[0074] It can be obtained that:

[0075] R α (nir)=kR α (red+green)-IR α (blue)+m (26)

[0076] Substitute Equation (26) into Equation (24), and it can be obtained that:

[0077]

[0078] Let (k - A 1 - 1)R α (red + green)-(l - 1)R α (blue)+g 1 +m = t, h 1 = f, the biocrust coverage index FCCI based on the radiation transfer principle that can reflect the biocrust coverage information can be obtained:

[0079]

[0080] Furthermore, in step s14, for the spectral feature space formed by the reflectance data R(red + green) of the red - green combination band and the reflectance data R(blue) of the blue band of the biocrust under different humidity conditions, the straight line fitted by the data points is the "soil line" in this feature space; for the spectral feature space formed by the biocrust red - green combination band data R(red + green) and the near - infrared spectral band data R(nir) under different humidity conditions, the straight line fitted by the data points is the "soil line" in this feature space, where the reflectance data of each band is obtained through the spectral response function of the corresponding band of Sentinel - 2 data from the experimentally measured hyperspectral data.

[0081] Furthermore, in step S3, the specific construction method of the multi - angle joint equation is as follows:

[0082] s31. Introduce the Beer's law equation:

[0083]

[0084] In the formula: P(θ i ) is the gap fraction related to the coverage, θ i is the solar zenith angle; Ω E is the aggregation index; G(θ i ) is the G function, representing the leaf area projection function in the θ i direction; L is the leaf area index;

[0085] s32. Substitute formula (28) into formula 3, and the FCC expression becomes:

[0086]

[0087] Let θ i = 55°, θ i = 60°, substitute into formula (29), and we can get:

[0088]

[0089] Since G(55°)≈G(55°)≈G(57.5°), by combining Equation (30) and Equation (31), a multi-angle joint equation can be obtained:

[0090]

[0091] The beneficial effects are as follows:

[0092] 1. The present invention constructs a biological soil crust index based on the radiation transfer principle to make up for the deficiency of the index method based on spectral linear combination that lacks consideration of physical mechanisms;

[0093] 2. By improving a pixel dichotomy model applicable to the inversion of biological soil crust coverage, introducing a linear kernel-driven model, and proposing a solution method for multi-angle indices, the present invention extends the pixel dichotomy method based on multiple angles to high-spatial-resolution remote sensing images, realizing the inversion of biological soil crust coverage with high spatial resolution;

[0094] 3. The present invention adopts a method combining checkerboard segmentation and Monte Carlo algorithm to improve the calculation efficiency of the inversion method for biological soil crust coverage in large areas. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 shows the technical flow chart of the present invention;

[0096] Figure 2 shows the schematic diagrams of the sliding window algorithm, the checkerboard segmentation method + Monte Carlo method;

[0097] Figure 3 shows the schematic diagram of the single-layer cumulative method;

[0098] Figure 4 shows the schematic diagrams of "soil lines" in different spectral feature spaces. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0099] In order to more clearly understand the above objects, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the drawings and specific embodiments. It should be noted that, without conflict, the embodiments of the present application and the features in the embodiments can be combined with each other.

[0100] As Figures 1 to 4 shown, a method for inverting biological soil crust coverage based on a linear kernel-driven model includes the following steps:

[0101] S1. Construct a biological soil crust index FCCI based on the radiation transfer principle. FCCI is used to extract the biological soil crust area. The biological soil crust index is constructed by the single-layer cumulative method. The biological soil crust canopy is assumed to be a homogeneous scatterer. After derivation, the biological soil crust coverage index FCCI based on the radiation transfer principle is obtained, that is:

[0102]

[0103] In the formula, FCCI is the biological soil crust coverage index, and t, f are the adjustment parameters of the biological soil crust coverage index, which are also the comprehensive manifestations of the radiation of the biological soil crust canopy and soil radiation. R(red+green), R(nir), and R(blue) are the reflectances of the red-green combined band, near-infrared band, and blue band, respectively;

[0104] S2. Construct a pixel dichotomy model for biological soil crust, and then estimate the proportion of biological soil crust in this area, that is, the biological soil crust coverage. To estimate the biological soil crust coverage, the GI model in the pixel dichotomy method is introduced to describe the relationship between FCCI and the biological soil crust coverage. The expression of this GI model is:

[0105]

[0106] In the formula: FCC is the biological soil crust coverage, and FCCI(0°) is the biological soil crust coverage index to be resampled in the vertically observed image; FCCI max and FCCI min are the maximum and minimum values of the biological soil crust coverage index respectively. FCCI max and FCCI min refer to the FCCI of high-coverage biological soil crust and the FCCI of the biological soil crust "background" (gravel, soil);

[0107] S3. Construct a multi-angle joint equation, introduce the value of the G function in Beer's law related to the coverage, that is, the value of the leaf area projection function: G(57.5°)=0.5, and combine the GI model to determine FCCI max and FCCI min , in this method, 55° and 60° are used to approximate 57.5°, that is, G(57.5°)≈G(55°)≈G(60°), and then through derivation, the multi-angle joint equation for solving FCCI max and FCCI min is obtained:

[0108]

[0109] In the formula: FCCI(55°) and FCCI(60°) are the FCCIs on this pixel when the solar zenith angles are 55° and 60° respectively;

[0110] S4. Obtain high-spatial-resolution FCCI(55°) and FCCI(60°) images, and introduce the linear kernel-driven model:

[0111] r(θ i) = f iso g iso +f vol g vol +f geo g geo (5),

[0112] In the formula: g 0iso = g 0iso +g 1iso θ 2 +g 2iso θ 3 , g vol = g 0vol +g 1vol θ 2 +g 2vol θ 3 , g geo = g 0geo +g 1geo θ 2 +g 2geo θ 3 , where g 0vol , g 1vol , g 2vol , g 0geo , g 1geo and g 2geo are the polynomial factors of the linear kernel-driven model, and θ i is the solar zenith angle;

[0113] The calculation of the black-sky albedo value is summarized as follows:

[0114] Table (5) Polynomial parameters of the linear kernel-driven model

[0115]

[0116] Here, a 2×2 sliding window iteration algorithm is used to solve the problem, as shown in Figure 2 . (a) is a schematic diagram of the 2×2 sliding window algorithm. The three boxes are the 2×2 sliding windows, and the gray squares are the pixels in the repeated calculation area; (b) is a schematic diagram of the checkerboard segmentation method + Monte Carlo method. Here, the outer large box is the sub-region after the image checkerboard segmentation, and the multiple small boxes inside are the pixels randomly selected using the Monte Carlo method;

[0117] First, assume that the linear kernel-driven model parameters in the 2×2 moving window have the same value under the initial conditions (as shown in Figure 2 . (a)); then use the 2×2 moving window to extract the reflectance from the high-spatial-resolution remotely sensed image of the vertical observation. According to equation (5), four equations are established for f iso , f vol and f geo :

[0118]

[0119] Transform Equation (6) to obtain the equation for inverting the parameter image of the linear kernel-driven model:

[0120] F = (G T G) -1 G T R (7)

[0121] where: F is the parameter image of the linear kernel-driven model, G is the polynomial factor of the linear kernel-driven model, and R is the reflectance of the high-spatial-resolution remote sensing image for vertical observation; the obtained reflectance of the high-spatial-resolution remote sensing image is obtained from vertical observation (i.e., θ i = 0°). However, when θ i = 0°, it causes f iso , f vol and f geo to be unsolvable. Therefore, approximate θ i = 5° as θ i = 0° and substitute it into Equation (7) to solve the equation;

[0122] Substitute the parameter image F of the high-spatial-resolution linear kernel-driven model for each band obtained by inversion back into the linear kernel-driven model (5), and the directional reflectance image for each band can be obtained. Through the directional reflectance images for each band, the high-spatial-resolution FCCI(55°) and FCCI(60°) images can be obtained. As shown in Figure 1 , B2, B3, B4, and B8 respectively represent the blue, green, red, and near-infrared band image data of the Sentinel-2A / B product;

[0123] S5. To obtain FCCI max and FCCI min , first use the checkerboard partitioning method to segment the high-spatial-resolution FCCI(55°) and FCCI(60°) images to make them into several representative sub-block images. Secondly, in each segmented sub-block image, use the Monte Carlo method to randomly select a certain number of pixels of the FCCI(55°) and FCCI(60°) images, set the value range of the parameters to be solved FCCI max and FCCI min , and use the selected pixel values to construct a multi-angle joint equation set in combination with Equation (4), where the number of equations is greater than the number of unknowns. Finally, based on the least squares principle, solve the multi-angle joint equation set to obtain the optimal FCCI max and FCCI min ;

[0124] S6. The FCCI obtained in step S5max and FCCI min Substitute into Equation (3) to calculate FCC in the GI model of biological soil crusts.

[0125] In step S1, the derivation process of the biological soil crust coverage index FCCI is as follows:

[0126] s11. Introduce the approximate radiative transfer equation of the single-layer summation method, and its equation is as follows:

[0127]

[0128] In the formula: R bc (λ) is the reflectivity of the first-order scattering of the biological soil crust, T ↓bc (λ) is the total downward transmittance of the biological soil crust, T ↑bc (λ) is the total upward transmittance of the biological soil crust, R s (λ) is the reflectivity of the Lambertian soil "background", R ↓bc (λ) is the reflectivity of the radiation of the soil "background" entering the bottom of the biological soil crust and transmitting downward, R h (λ) is the reflectivity of the homogeneous biological soil crust "canopy", where λ is the spectral band;

[0129] As Figure 3 shown, the line reaching R bc (λ) represents the process of the solar radiation reaching the canopy of the biological soil crust and undergoing first-order scattering; the line reaching T ↓bc (λ) represents the process that the solar radiation transmits into the canopy of the biological soil crust, is reflected after reaching the soil surface, and then transmits to the surface layer of the canopy of the biological soil crust again; R ↓bc (λ) represents the process that the solar radiation transmits into the canopy of the biological soil crust and undergoes multiple scattering after reaching the soil surface; here λ is the spectral wave, the lowermost area represents the biological soil crust soil "background", and the middle area represents the organisms in the biological soil crust community;

[0130] s12. Use the concept of geometric mean to define the average values of T ↓bc (λ) and T ↑bc (λ), perform Taylor series expansion on the second term on the right side of Equation (8), approximately retain the first two orders of the Taylor series, and obtain the following equation:

[0131]

[0132] Let T 2 bc (λ) = a, The simplified radiative transfer equation can be obtained:

[0133] R h (λ) = R bc(λ) + aR s (λ) + b(10)

[0134] s13. Use the blue band, the red - green combined band, and the near - infrared band as the sensitive bands of the biological soil crust index; The expression of the red - green combined band:

[0135] R(red + green)=R(red)+R(green)(11)

[0136] Substitute the blue band, the red - green combined band, and the near - infrared band into the simplified radiative transfer equation (10) to obtain the radiative transfer equations for the near - infrared, blue, and red - green combined bands:

[0137] R h (nir)=R bc (nir)+a 1 R s (nir)+b 1 (12)

[0138] R h (blue)=R bc (blue)+a 2 R s (blue)+b 2 (13)

[0139] R h (red + green)=R bc (red + green)+a 3 R s (red + green)+b 3 (14)

[0140] Where: a 1 , a 2 , a 3 , b 1 , b 2 , b 3 are the parameters after symbolic simplification, R bc (red + green) and R s (red + green) are the biological soil crust reflectance of the red - green combined band and the reflectance of the radiation of the soil "background" entering the bottom of the biological soil crust; R bc (nir) and R s (nir) are the biological soil crust reflectance of the near - infrared band and the reflectance of the radiation of the soil "background" entering the bottom of the biological soil crust; R bc (blue) and R s (blue) are the biological soil crust reflectance of the blue band and the reflectance of the radiation of the soil "background" entering the bottom of the biological soil crust; Rh (red + green), R h (nir) and R h (blue) represents the reflectance of the homogeneous biological soil crust in the red - green combined band, near - infrared band, and blue band;

[0141] s14. Introduce the concept of "soil line", as Figure 4 shown. The spectral feature spaces formed by the reflectance data R(red + green) of the biological soil crust in the red - green combined band and the reflectance data R(blue) in the blue band under different humidity conditions, and the straight line fitted by the data points is the "soil line" in this feature space. The spectral feature spaces formed by the reflectance data R(red + green) of the biological soil crust in the red - green combined band and the reflectance data R(nir) in the near - infrared spectral band under different humidity conditions, and the straight line fitted by the data points is the "soil line" in this feature space. Among them, the reflectance data of each band are obtained from the hyperspectral data measured in the experiment through the spectral response function of the corresponding band of Sentinel - 2 data. That is, by analyzing the spectral information of the biological soil crust under different humidities, it is found that when the red band and the green band are combined, the spectral feature space forms with the blue band and the near - infrared band is similar to the "soil line" in the near - red - red spectral feature space. In the past, when establishing vegetation indices, the "soil line" was often used to reduce the influence of the soil "background" on the research results. Therefore, a mathematical equation between the sensitive spectral bands of each biological soil crust is constructed:

[0142] R s (nir) = A 1 R s (red + green) + B 1 (15)

[0143] R s (blue) = A 2 R s (red + green) + B 2 (16)

[0144] In the formula: A 1 , A 2 , B 1 , B 2 are the slope and intercept of the "soil line";

[0145] s15. In order to construct a quantitative relationship between the sensitive spectral bands and the coverage of the biological soil crust, introduce the proportion equation between the biological soil crust and the soil "background":

[0146] R α (λ) = vR h (λ) + (1 - v)R s (λ) (17)

[0147] where: v is the biological crust proportion factor, R α (λ) is the reflectance of the heterogeneous biological crust, R h (λ) is the reflectance of the homogeneous biological crust canopy, R s (λ) is the reflectance of the radiation of the soil "background" entering the bottom of the biological crust;

[0148] Substituting the near-infrared, blue band, and red-green combined band into Equation (17), we can obtain:

[0149] R α (nir) = vR h (nir) + (1 - v)R s (nir) (18)

[0150] R α (blue) = vR h (blue) + (1 - v)R s (blue) (19)

[0151] R α (red + green) = vR h (red + green) + (1 - v)R s (red + green) (20)

[0152] Substituting Equation (12) into Equation (18), Equation (13) into Equation (19), and Equation (14) into Equation (20), we can obtain:

[0153]

[0154] Substituting Equations (21) and (23) into Equation (15), and Equations (22) and (23) into Equation (16), two quadratic equations in one variable about v can be obtained. Let:

[0155] R bc (nir) + b 1 = C 1 、R bc (red + green) + b 3 = C 2 、R bc (blue) + b 2 = C 3 、

[0156] C 1 -C 1 a 3 -A 1 C 2 -B 1 +a 3B 1 +a 1 A 1 C 2 +a 1 B 1 -a 1 a 3 B 1 = D 1 、

[0157] C 3 -C 3 a 3 -A 2 C 2 -B 2 +a 3 B 2 +a 2 A 2 C 2 +a 2 B 2 -a 2 a 3 B 2 = D 2 、

[0158] a 3 R α (nir)-A 1 a 1 R α (red+green)-C 1 +A 1 C 2 +2B 1 -a 3 B 1 -a 1 B 1 = E 1 、

[0159] a 3 R α (blue)-A 2 a 2 R α (red+green)-C 3 +A 2 C 2 +2B 2 -a 3 B 2 -a 2 B 2 = E 2 、

[0160] 2D 1 -R α (nir)-R α(red + green)= h 1 、2D 2 -R α (blue)-R α (red + green)= h 2 、

[0161]

[0162] Let F 1 -E 1 = g 1 , F 2 -E 2 = g 2 , we can get:

[0163]

[0164] Combine equation (24) and equation (25), let:

[0165] (h 2 A 1 -h 1 A 2 +g 2 -g 1 ) / (h 2 -g 2 ) = k, (g 1 -h 1 ) / (h 2 -g 2 ) = l,

[0166] ((A 1 -1)R α (blue)R α (red + green)-(1 + A 2 )R α (nir)R α (red + green)+(A 1 -A 2 )R α 2 (red + green)+g 2 h 1 -g 1 h 2 ) / (h 2 -g 2 ) = m

[0167] We can get:

[0168] R α (nir)= kR α (red + green)-IR α(blue)+m (26)

[0169] Substituting equation (26) into equation (24), we can obtain:

[0170]

[0171] Let (kA 1 -1)R α (red+green)-(l-1)R α (blue)+g 1 +m=t,h 1 =f can get the biocrust coverage index FCCI based on the radiation transmission principle, which can reflect the coverage information of biocrust:

[0172]

[0173] In step S3, the specific method of constructing the multi-angle joint equation is as follows:

[0174] s31. Introduce Beer's law equation:

[0175]

[0176] Where: P(θ i ) is the gap fraction related to coverage, θ i is the solar zenith angle; Ω E is the aggregation index; G(θ i ) is the G function, representing θ i Directional leaf area projection function; L is the leaf area index;

[0177] s32. Substituting formula (28) into formula 3, the FCC expression becomes:

[0178]

[0179] Let θ i =55°,θ i =60°, substituting into formula (29), we get:

[0180]

[0181] Since G(55°)≈G(55°)≈G(57.5°), formula (30) and formula (31) can be combined to obtain a multi-angle joint equation:

[0182]

[0183] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for retrieving the coverage of biological soil crust based on a linear kernel-driven model, characterized in that, its steps include: S1. Construct a biological soil crust index FCCI based on the radiation transfer principle. FCCI is used to extract the biological soil crust area. The biological soil crust index is constructed by the single-layer cumulative method. The biological soil crust canopy is assumed to be a homogeneous scatterer. After derivation, the biological soil crust coverage index FCCI based on the radiation transfer principle is obtained, that is: In the formula, FCCI is the biological soil crust coverage index, t and f are the adjustment parameters of the biological soil crust coverage index, and they are also the comprehensive manifestations of the radiation of the biological soil crust canopy and the soil radiation. R(red+green), R(nir), and R(blue) are the reflectances of the red-green combined band, the near-infrared band, and the blue band respectively; S2. Construct a pixel dichotomy model of the biological soil crust to estimate the proportion of the biological soil crust in this area, that is, the biological soil crust coverage. In order to estimate the biological soil crust coverage, the GI model in the pixel dichotomy method is introduced to describe the relationship between FCCI and the biological soil crust coverage. The expression of this GI model is: Where: FCC is the biological soil crust coverage, and FCCI(0°) is the biological soil crust coverage index to be resampled in the vertical observation image; FCCI max and FCCI min are the maximum and minimum values of the biological soil crust coverage index respectively, FCCI max and FCCI min refer to the FCCI of high-coverage biological soil crust and the FCCI of the biological soil crust "background"; S3. Construct a multi-angle joint equation, introduce the value of the G function in Beer's law related to the coverage, that is, the value of the leaf area projection function: G(57.5°) = 0.5, and determine FCCI in combination with the GI model max and FCCI min , in this method, 55° and 60° are used to approximate 57.5°, that is, G(57.5°) ≈ G(55°) ≈ G(60°), and then through derivation, a multi-angle joint equation for solving FCCI max and FCCI min is obtained: In the formula: FCCI(55°) and FCCI(60°) are the FCCI on this pixel when the solar zenith angle is 55° and 60° respectively; S4. Obtain high-spatial-resolution FCCI(55°) and FCCI(60°) images, and introduce a linear kernel-driven model: r(θ i ) = f iso g iso + f vol g vol + f geo g geo (5) where: g iso = g 0iso + g 1iso θ 2 + g 2iso θ 3 , g vol = g 0vol + g 1vol θ 2 + g 2vol θ 3 , g geo = g 0geo + g 1geo θ 2 + g 2geo θ 3 , where g 0vol , g 1vol , g 2vol , g 0geo , g 1geo and g 2geo are polynomial factors of the linear kernel driving model, and θ i is the solar zenith angle; The calculation of the black-sky albedo value is summarized as follows: Table (5) Polynomial parameters of the linear kernel-driven model Extract the reflectance from the vertically observed high-spatial-resolution remote sensing image using a 2×2 moving window. According to Equation (5), four equations are established for f iso , f vol and f geo : Transform equation (6) to obtain an equation for inverting the linear kernel-driven model parameter images: F = (G T G) -1 G T R(7) Where: F is the parameter image of the linear kernel drive model, G is the polynomial factor of the linear kernel drive model, and R is the reflectance of the high-spatial-resolution remote sensing image obtained by vertical observation; the reflectance of the obtained high-spatial-resolution remote sensing image is obtained by vertical observation (i.e., θ i = 0°). However, when θ i = 0°, it causes f iso , f vol and f geo to be unsolvable. Therefore, θ i = 5° is approximated as θ i = 0°, and substituted into Equation (7) to solve the equation; Substitute the inverted high-spatial-resolution linear kernel-driven model parameter images F of each band into the linear kernel-driven model (5) again, and the directional reflectance images of each band can be obtained. Through the directional reflectance images of each band, high-spatial-resolution FCCI(55°) and FCCI(60°) images can be obtained; S5. Obtain FCCI max and FCCI min , first, use the chessboard segmentation method to segment the high-spatial-resolution FCCI(55°) and FCCI(60°) images, making them into several representative sub-block images. Secondly, in each segmented sub-block image, use the Monte Carlo method to randomly select a certain number of pixels of the FCCI(55°) and FCCI(60°) images, set the value range of the parameter FCCI max and FCCI min , and use the selected pixel values to construct a multi-angle joint equation set in combination with Equation (4), where the number of equations is greater than the number of unknowns. Finally, based on the least squares principle, solve the multi-angle joint equation set to obtain the optimal FCCI max and FCCI min ; S6. Substitute the FCCI obtained in step S5 max and FCCI min into equation (3) to calculate the FCC in the GI model of the biological soil crust.

2. The method for retrieving the coverage of biological soil crust based on the linear kernel-driven model according to claim 1, characterized in that, In step S1, the derivation process of the biological soil crust coverage index FCCI is as follows: s11. Introduce an approximate radiation transfer equation of the single-layer cumulative method, and its equation is as follows: Where: R bc (λ) is the reflectance of the first - order scattering of the biological soil crust, T ↓bc (λ) is the total downward transmittance of the biological soil crust, T ↑bc (λ) is the total upward transmittance of the biological soil crust, R s (λ) is the reflectance of the Lambertian soil "background", R ↓bc (λ) is the reflectance of the radiation of the soil "background" entering the bottom of the biological soil crust and transmitting downward, R h (λ) is the reflectance of the homogeneous biological soil crust "canopy", where λ is the spectral band; s12. Define T using the concept of geometric mean ↓bc and the average of T ↑bc (λ). Perform a Taylor series expansion on the second term on the right side of Equation (8), approximately retaining the first two orders of the Taylor series, to obtain the following equation: Let T 2 bc (λ) = a, The simplified radiative transfer equation can be obtained: R h R(λ) = bc R(λ) + aR s R(λ) + b(10) s13. Use the blue band, the red-green combined band, and the near-infrared band as the biological soil crust index sensitive bands; The expression form of the red-green combined band: R(red+green) = R(red) + R(green) (11) Substitute the blue band, the red-green combined band, and the near-infrared band into the simplified radiation transfer equation (10) to obtain an equation related to the near-infrared, blue, and red-green combined bands: R h R(nir) bc R(nir) + a 1 R s R(nir) + b 1 (12) R h R(blue) bc R(blue)+a 2 R s R(blue)+b 2 (13) R h (red + green) = R bc (red + green) + a 3 R s (red + green) + b 3 (14) Where: a 1 , a 2 , a 3 , b 1 , b 2 , b 3 are the parameters after symbolic simplification, R bc (red + green) and R s (red + green) are the reflectance of the biological soil crust in the red - green combined band and the reflectance of the radiation of the soil "background" entering the bottom of the biological soil crust; R bc (nir) and R s (nir) are the reflectance of the biological soil crust in the near - infrared band and the reflectance of the radiation of the soil "background" entering the bottom of the biological soil crust; R bc (blue) and R s (blue) are the reflectance of the biological soil crust in the blue band and the reflectance of the radiation of the soil "background" entering the bottom of the biological soil crust; R h (red + green), R h (nir) and R h (blue) are the reflectances of the homogeneous biological soil crust in the red - green combined band, near - infrared band and blue band; s14. Introduce the concept of "soil line", that is, by analyzing the spectral information of biological soil crust under different humidities, it is found that when the red band and the green band are combined, the spectral feature space representation with the blue band and the near-infrared band is similar to the "soil line" in the near-infrared-red spectral feature space. In the past, when establishing vegetation indices, the "soil line" was often used to reduce the influence of soil "background" on the research results. Therefore, a mathematical equation between the sensitive spectral bands of each biological soil crust is constructed: R s (nir) = A 1 R s (red + green) + B 1 (15) R s (blue) = A 2 R s (red + green) + B 2 (16) Where: A 1 , A 2 , B 1 , B 2 are the slope and intercept of the "soil line"; s15. In order to construct a quantitative relationship between the sensitive spectral band and the coverage of biological crust, the proportional equation between biological crust and soil "background" is introduced: R α R(λ) = vR h R(λ) + (1 - v)R s R(λ) (17) Where: v is the biological soil crust proportion factor, R α (λ) is the reflectance of the heterogeneous biological soil crust, R h (λ) is the reflectance of the homogeneous biological soil crust canopy, R s (λ) is the reflectance of the radiation of the soil "background" entering the bottom of the biological soil crust; Substituting the near infrared, blue band, and red-green combined band into formula (17), we can obtain: R α (nir) = vR h (nir) + (1 - v)R s (nir) (18) R α R(blue) = vR h R(blue) + (1 - v)R s R(blue) (19) R α (red + green) = vR h (red + green) + (1 - v)R s (red + green) (20) Substituting equation (12) into equation (18), equation (13) into equation (19), and equation (14) into equation (20), we can obtain: Substituting equations (21) and (23) into equation (15), and equations (22) and (23) into equation (16), we can obtain two quadratic equations about v. Let: R bc (nir)+b 1 =C 1 、R bc (red+green)+b 3 =C 2 、R bc (blue)+b 2 =C 3 、 C 1 -C 1 a 3 -A 1 C 2 -B 1 +a 3 B 1 +a 1 A 1 C 2 +a 1 B 1 -a 1 a 3 B 1 =D 1 、 C 3 -C 3 a 3 -A 2 C 2 -B 2 +a 3 B 2 +a 2 A 2 C 2 +a 2 B 2 -a 2 a 3 B 2 =D 2 、 a 3 R α (nir)-A 1 a 1 R α (red+green)-C 1 +A 1 C 2 +2B 1 -a 3 B 1 -a 1 B 1 =E 1 、 a 3 R α (blue)-A 2 a 2 R α (red+green)-C 3 +A 2 C 2 +2B 2 -a 3 B 2 -a 2 B 2 =E 2 、 2D 1 -R α (nir)-R α (red + green)= h 1 、2D 2 -R α (blue)-R α (red + green)= h 2 、 Let F 1 - E 1 = g 1 ,F 2 - E 2 = g 2 It can be obtained that: Combining equation (24) and equation (25), let: (h 2 A 1 -h 1 A 2 +g 2 -g 1 ) / (h 2 -g 2 )=k,(g 1 -h 1 ) / (h 2 -g 2 )=l, ((A 1 -1)R α (blue)R α (red + green)-(1 + A 2 )R α (nir)R α (red + green)+(A 1 -A 2 )R α 2 (red + green)+g 2 h 1 -g 1 h 2 ) / (h 2 -g 2 ) = m gives: R α (nir) = kR α (red + green) - R α (blue) + m(26) Substituting equation (26) into equation (24), we can obtain: Let (k - A 1 - 1)R α (red + green)-(l - 1)R α (blue)+g 1 +m = t, h 1 = f to obtain the biological soil crust coverage index FCCI based on the radiation transfer principle that can reflect the information of biological soil crust coverage:

3. The biocrust coverage inversion method based on the linear kernel driven model according to claim 2, It is characterized in that In step s14, the spectral feature space composed of the red-green combined band reflectance data R(red+green) and the blue band reflectance data R(blue) of the biological crust under different humidity conditions, the straight line fitted by the data points is the "soil line" in the feature space, the spectral feature space composed of the red-green combined band data R(red+green) and the near-infrared spectral band data R(nir) under different humidity conditions, the straight line fitted by the data points is the "soil line" in the feature space, wherein the reflectance data of each band are obtained from the experimentally measured hyperspectral data through the spectral response function of the corresponding band of Sentinel-2 data.

4. The biocrust coverage inversion method based on the linear kernel driven model according to claim 1, It is characterized in that In step S3, the specific method of constructing the multi-angle joint equation is as follows: s31. Introduce Beer's law equation: where: P(θ i ) is the gap fraction related to the coverage, θ i is the solar zenith angle; Ω E is the aggregation index; G(θ i ) is the G function, representing the leaf area projection function in the θ i direction; L is the leaf area index; s32. Substituting formula (28) into formula 3, the FCC expression becomes: Let θ i = 55°, θ i = 60°, substituting into formula (29), we get: Since G(55°)≈G(55°)≈G(57.5°), formula (30) and formula (31) can be combined to obtain a multi-angle joint equation:

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