CN116312871B - CO (carbon monoxide) 2 Downscaling method and system for concentration inversion data - Google Patents

CO (carbon monoxide) 2 Downscaling method and system for concentration inversion data Download PDF

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CN116312871B
CN116312871B CN202310226270.3A CN202310226270A CN116312871B CN 116312871 B CN116312871 B CN 116312871B CN 202310226270 A CN202310226270 A CN 202310226270A CN 116312871 B CN116312871 B CN 116312871B
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赵娜
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Abstract

The application relates to the technical field of a method or a device for identifying by using electronic equipment, and provides a CO (carbon monoxide) 2 A downscaling method and system for concentration inversion data. The method comprises the following steps: establishing a mathematical mapping model between the first concentration data and the second concentration data; carrying out Taylor expansion on the mathematical mapping model at the target pixel point according to the neighborhood pixel point of the target point to any target pixel point on the second concentration data to obtain an error expression model corresponding to the mathematical mapping model; converting the error expression model into a weighted least square problem by utilizing a local windowing kernel function to construct a downscaling model, and solving to obtain second concentration data; correcting the second concentration data based on an improved high-precision curved surface modeling method to obtain corrected high-resolution CO 2 Concentration inversion data. Therefore, the high-resolution CO after the downscaling can be solved without introducing auxiliary variables 2 Concentration data, uncertainty of a downscaling result is reduced, and accuracy is improved.

Description

CO (carbon monoxide) 2 Downscaling method and system for concentration inversion data
Technical Field
The application relates to the technical field of a method or a device for identifying by using electronic equipment, in particular to a CO (carbon monoxide) 2 A downscaling method and system for concentration inversion data.
Background
Existing CO 2 The downscaling method of the concentration inversion data can be roughly divided into: a ground observation data inversion method and a satellite remote sensing inversion method. Wherein, CO obtained by inversion method of foundation observation data 2 The concentration data has high precision, but the observation quantity is very limited, the number of the global observation sites is only tens, and the observation cost is high. The satellite remote sensing inversion method can obtain data with long time sequence, continuity and wide coverage range, but the inversion resolution is often lower, and the high-precision requirement of local scale simulation cannot be met. CO at present 2 Most satellite observations belong to passive remote sensing, are influenced by cloud, aerosol and the like, and the effective data volume is difficult to fully cover, so that foundation observations and multi-satellite-loaded CO are caused 2 And the data are fused, and full coverage still cannot be realized. Therefore, CO2 concentration data obtained by single observation means such as foundation observation and satellite remote sensing have advantages and disadvantages, and meanwhile, the observation precision of the CO2 concentration data does not reach the unified standard.
In particular, existing inversion methods tend to observe coarse-resolution CO with limited sites and based on other auxiliary variables on the site 2 The concentration inversion data is corrected and the concentration inversion data is corrected,although the method can correct inversion data to a certain extent in a local area, when the method is applied to other areas, the inversion correction results of the other areas have large uncertainty due to the introduction of observation errors and errors of auxiliary variables, and the uncertainty cannot be effectively evaluated, so that the accuracy of downscaling is insufficient.
Accordingly, there is a need to provide an improved solution to the above-mentioned deficiencies of the prior art.
Disclosure of Invention
The application aims to provide a novel method and a system for downscaling CO2 concentration inversion data, which are used for solving or relieving the problems in the prior art.
In order to achieve the above object, the present application provides the following technical solutions:
the application provides a CO 2 A downscaling method of concentration inversion data, comprising:
establishing a mathematical mapping model between the first concentration data and the second concentration data; the first concentration data is the original coarse resolution CO 2 Concentration inversion data, wherein the second concentration data is high-resolution CO after downscaling 2 Concentration inversion data;
carrying out taylor expansion on the mathematical mapping model at the target pixel point according to the neighborhood pixel point of the target pixel point to any target pixel point on the second concentration data to obtain an error expression model corresponding to the mathematical mapping model;
converting the error expression model into a weighted least squares problem using a local windowed kernel function to construct CO 2 A downscaling model of the concentration inversion data is solved based on the downscaling model to obtain the second concentration data; the support set of the local windowing kernel function is constructed based on the relationship between geographic environment influence factors and the neighborhood pixels;
correcting the second concentration data obtained by solving based on an improved high-precision curved surface modeling method to obtain corrected high-resolution CO 2 Concentration inversion data.
Preferably, the expression of the mathematical mapping model is as follows:
g i ＝u(p i )+ε i ，i＝1,2,…,M，
in the formula g i Represents the ith pixel point p in the first density data i ＝(x i ,y i ) T CO on 2 Concentration value, x i 、y i Is the pixel point p i And u represents the second concentration data, u (p i ) Representation and pixel point p i Raw CO at pixel point in corresponding second concentration data 2 Concentration value, epsilon i Is the error, M is the pixel point p i Is used for the number of neighborhood pixel points.
Preferably, the pixel point p i ＝(x i ,y i ) T The expression of the support set of the corresponding local windowed kernel function is as follows:
C i ＝(X T (F i (x i ,y i ))X) -1 X T F i (x i ,y i )，
in which W is i Is the pixel point p i ＝(x i ,y i ) T Corresponding support set of local windowed kernel function, pixel point p i X is the neighborhood pixel of the target pixel point i 、y i Is the pixel point p i Coordinates of C i Is based on pixel point p i CO at site 2 Local geographical environment influence factor of concentration value and pixel point p i A parameter matrix constructed by relation between the pixel and the neighborhood pixels, wherein X is a matrix formed by local geographic environment influence factors, and F i (x i ，y i ) And estimating a parameter matrix based on the covariance matrix of the neighborhood gradient.
Preferably, the error expression model corresponding to the mathematical mapping model is:
wherein u (p) i ) Representation and pixel point p i Raw CO at pixel point in corresponding second concentration data 2 The concentration value, p is the target pixel point, u (p) is the CO corresponding to the second concentration data at the target pixel point 2 The concentration value of the liquid is calculated,the gradient operator, H is a sea plug matrix operator, and vech is a matrix half-vector operator.
Preferably, the expression of the downscaling model is:
where N is the Taylor expansion order, β 0 =u (p), i.e. the CO2 concentration value corresponding to the second concentration data at the target pixel point, m is the pixel point p i ＝(x i ,y i ) T The number of neighborhood pixel points, x i 、y i Is the pixel point p i Is the matrix half-vectorization operator, g i Represents the ith pixel point p in the first density data i CO on 2 Concentration value, p is the target pixel point, p= (x, y) T And x and y are coordinates of the target pixel point p, K is a local windowing kernel function and is used for calculating weights between the target pixel point and pixel points in a local window, and W represents a support set of the local windowing kernel function.
Preferably, the method further comprises the step of improving the high-precision curved surface modeling method, and specifically comprises the following steps:
taking variances of a target site and surrounding adjacent sites as weight coefficients of the target site, constructing an algebraic equation set corresponding to a high-precision curved surface modeling method by utilizing a French equation set method,
the second concentration data obtained by solving is taken as the initial value of the algebraic equation set, and is combined with the CO observed by the site 2 And constructing constraint conditions of the high-precision curved surface modeling method by the concentration data to obtain an improved high-precision curved surface modeling method.
The embodiment of the application provides a CO 2 A downscaling system for concentration inversion data, comprising:
a construction unit configured to establish a mathematical mapping model between the first concentration data and the second concentration data; the first concentration data is the original coarse resolution CO 2 Concentration inversion data, wherein the second concentration data is high-resolution CO after downscaling 2 Concentration inversion data;
the expansion unit is configured to perform taylor expansion on the mathematical mapping model at any target pixel point on the second concentration data according to the neighborhood pixel point of the target point, and construct an error expression model corresponding to the mathematical mapping model;
a solving unit configured to convert the error expression model into a weighted least squares problem by using a local windowed kernel function to construct CO 2 A downscaling model of the concentration inversion data is solved based on the downscaling model to obtain the second concentration data; the support set of the local windowing kernel function is constructed based on the relationship between geographic environment influence factors and neighborhood pixels;
the correction unit is configured to correct the second concentration data obtained by solving based on an improved high-precision curved surface modeling method to obtain corrected high-resolution CO 2 Concentration inversion data.
Preferably, the expression of the mathematical mapping model is as follows:
g i ＝u(p i )+ε i ，i＝1,2,…,M，
in the formula g i Represents the ith pixel point p in the first density data i ＝(x i ,y i ) T CO on 2 Concentration value, x i 、y i Is the pixel point p i And u represents the second concentration data, u (p i ) Representation and pixel point p i Raw CO at pixel point in corresponding second concentration data 2 Concentration value, epsilon i Is the error, M is the pixel point p i Is used for the number of neighborhood pixel points.
Preferably, the pixel point p i ＝(x i ,y i ) T The expression of the support set of the corresponding local windowed kernel function is as follows:
C i ＝(X T (F i (x i ,y i ))X) -1 X T F i (x i ,y i )，
in which W is i Is the pixel point p i ＝(x i ,y i ) T Corresponding support set of local windowed kernel function, pixel point p i X is the neighborhood pixel of the target pixel point i 、y i Is the pixel point p i Coordinates of C i Is based on pixel point p i CO at site 2 Local geographical environment influence factor of concentration value and pixel point p i A parameter matrix constructed by relation between the pixel and the neighborhood pixels, wherein X is a matrix formed by local geographic environment influence factors, and F i (x i ，y i ) And estimating a parameter matrix based on the covariance matrix of the neighborhood gradient.
Preferably, the error expression model corresponding to the mathematical mapping model is:
wherein u (p) i ) Representation and pixel point p i The original CO2 concentration value at the pixel point in the corresponding second concentration data, wherein p is the target pixel point, and u (p) is the target pixel pointThe concentration value of CO2 corresponding to the second concentration data,the gradient operator, H is a sea plug matrix operator, and vech is a matrix half-vector operator.
The beneficial effects are that:
in the embodiment of the application, a mathematical mapping model between first concentration data and second concentration data is firstly established; wherein the first concentration data is CO with original coarse resolution 2 Concentration inversion data, wherein the second concentration data is high-resolution CO after downscaling 2 Concentration inversion data; then, for any target pixel point on the second concentration data, according to the neighborhood pixel point of the target point, carrying out Taylor expansion on the mathematical mapping model at the target pixel point to obtain an error expression model corresponding to the mathematical mapping model; then, converting the error expression model into a weighted least square problem by utilizing a local windowing kernel function, and solving to obtain second concentration data; the support set of the local windowing kernel function is constructed based on the relationship between the geographic environment influence factors and the neighborhood pixels; after solving to obtain second concentration data, correcting the second concentration data based on an improved high-precision curved surface modeling method to obtain corrected high-resolution CO 2 Concentration inversion data. In the process, taylor decomposition is carried out on any target pixel point based on the neighborhood pixel point, and a local windowing kernel function is utilized to combine with CO 2 Spatial heterogeneity and correlation of concentration data, and construction of CO expressed by weighted least squares problem in combination with relation between geographic environmental influence factors and neighborhood pixels 2 The downscaling model of the concentration data does not need to introduce auxiliary variables, the downscaling high-resolution CO2 concentration data (second concentration data) can be obtained by solving only according to the geographical environment influence factors of the local area and the relation between the neighborhood pixels, the uncertainty of an inversion result is reduced, and the second concentration data which is more stable and has higher precision can be obtained when the downscaling model is applied to other areas due to the consideration of the spatial heterogeneity and the correlation of the CO2 concentration data. After solving to obtain the downscaledHigh resolution CO 2 After the concentration data, the concentration data is corrected by combining an improved high-precision curved surface modeling method (High Accuracy Surface Modeling, abbreviated as HASM method), so that the CO is further improved 2 Accuracy of the concentration data.
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The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application. Wherein:
FIG. 1 is a schematic illustration of a CO provided in accordance with some embodiments of the application 2 A flow diagram of a downscaling method of the concentration inversion data;
FIG. 2 is a block diagram of CO provided in accordance with some embodiments of the application 2 A schematic of the structure of a downscaling system for concentration inversion data.
Detailed Description
The application will be described in detail below with reference to the drawings in connection with embodiments. The examples are provided by way of explanation of the application and not limitation of the application. Indeed, it will be apparent to those skilled in the art that modifications and variations can be made in the present application without departing from the scope or spirit of the application. For example, features illustrated or described as part of one embodiment can be used on another embodiment to yield still a further embodiment. Accordingly, it is intended that the present application encompass such modifications and variations as fall within the scope of the appended claims and their equivalents.
In the following description, the terms "first/second/third" are used merely to distinguish between similar objects and do not represent a particular ordering of the objects, it being understood that the "first/second/third" may be interchanged with a particular order or precedence where allowed, to enable embodiments of the application described herein to be implemented in other than those illustrated or described herein.
Exemplary method
The embodiment of the application provides a CO 2 A method for downscaling concentration inversion data, as shown in fig. 1, the method comprising:
step S101, establishing a mathematical mapping model between the first concentration data and the second concentration data.
Downscaling (Downscaling) is the process of obtaining high resolution data information from low resolution information by a certain technical means while improving its accuracy, that is, CO 2 And the process of downscaling the concentration inversion data is to downscale the CO2 concentration data based on the coarse resolution, so as to obtain the high-resolution CO2 concentration inversion data. For ease of description, the original coarse resolution CO will be described herein 2 The concentration inversion data is called first concentration data, and can be coarse resolution CO2 concentration inversion data obtained from data products provided by a satellite platform and the like; high resolution CO after downscaling 2 The concentration inversion data is referred to as second concentration data.
Let g be the acquired coarse resolution CO 2 Concentration inversion data, i.e. first concentration data, u is the high resolution CO to be obtained 2 Concentration inversion data, i.e. second concentration data, i-th pixel point p in g i ＝(x i ,y i ) T CO at location 2 Concentration value g i ，ε i If the difference is the error, a mathematical mapping model is established for each pixel point based on the first concentration data and the second concentration data according to the neighborhood relation among the pixel points, and the relation between the first concentration data and the second concentration data is represented by the mathematical mapping model, so that CO 2 The downscaling result of the concentration inversion data is more objective and rigorous.
In some embodiments, the mathematical mapping model is expressed as follows:
g i ＝u(p i )+ε i ，i＝1,2,…,M (1)
in the formula g i Represents the ith pixel point p in the first density data i ＝(x i ,y i ) T CO on 2 Concentration value, x i 、y i Is the pixel point p i And u represents the second concentration data, u (p i ) Representation and pixel point p i Raw CO at pixel point in corresponding second concentration data 2 Concentration value, epsilon i Is the error, M is the pixel point p i Is used for the number of neighborhood pixel points.
Above expression, constructing CO on each pixel point under coarse resolution 2 CO on corresponding pixel point under high resolution after concentration value and downscaling 2 Mathematical mapping model between concentration values, i.e. CO of coarse resolution 2 The concentration value is expressed as the concentration value of CO2 on the corresponding pixel point after the scale is reduced and the error is added, so that the relationship between the concentration value and the concentration value is always established, and the rigor of the concentration value is further ensured.
Step S102, for any target pixel point on the second concentration data, according to the neighborhood pixel point of the target pixel point, the Taylor (Taylor) expansion is carried out on the mathematical mapping model at the target pixel point, and an error expression model corresponding to the mathematical mapping model is obtained.
In the embodiment of the application, the CO on the target pixel point is obtained by carrying out Taylor expansion based on the neighborhood pixel point 2 And an error expression model of the concentration value lays a mathematical foundation for subsequent solving.
In some embodiments, if the target pixel point p= (x, y) T Is pixel point p i ＝(x i ,y i ) T Based on the taylor expansion, the error expression model corresponding to the mathematical mapping model is:
wherein u (p) i ) Representation and pixel point p i Raw CO at pixel point in corresponding second concentration data 2 The concentration value, p is the target pixel point, u (p) is the CO corresponding to the second concentration data at the target pixel point 2 The concentration value of the liquid is calculated,for gradient operators, H is a sea plug matrix operator (also called a Hesession operator), and vech is a matrix half-vector operator.
Wherein the dimension of the gradient operator is 2×1 and the dimension of the Hesession operator is 2×2. The matrix half-vectorization operator vech is used to convert a matrix into a vector in dictionary order, defined as:
step S103, converting the error expression model into a weighted least squares problem by utilizing the local windowed kernel function to construct the CO 2 The downscaling model of the concentration inversion data is used for solving to obtain second concentration data based on the downscaling model; the support set of the local windowing kernel function is constructed based on the relationship between the geographic environment influence factors and the neighborhood pixel points.
After the error expression model is obtained, the following steps are carried out: beta 0 ＝u(p)， The error expression model of equation (2) can be written as:
wherein beta is 0 =u (p), i.e. pixel point p= (x, y) T CO2 concentration values at that point.
Thus, coarse resolution CO 2 The high-resolution reconstruction of the concentration remote sensing inversion data is realized by utilizing the current interest point (namely the target pixel point) p= (x, y) T CO at adjacent pixel points of (c) 2 Concentration valueTo estimate u (p), i.e. beta 0 And obtaining a downscaling result.
The above problem can be described in terms of data as a weighted least squares problem, considering the heterogeneity between adjacent pixels:
wherein, the liquid crystal display device comprises a liquid crystal display device,k is a local windowing kernel function used for representing the weight between a pixel point in a local window and a current pixel point, wherein the weight is small when the distance is far, and the weight is large when the distance is close. The W matrix determines the support set of kernel functions.
The conventional support set is typically set to: w=σi. Since W determines the high resolution CO obtained by the finally constructed downscaled model 2 In order to further improve the accuracy of the concentration data, therefore, in the embodiment of the present application, the obtained high-resolution CO 2 Accuracy of concentration data, according to coarse resolution CO 2 And (3) the characteristics of the concentration data, and the spatial heterogeneity and correlation of the geographic environment influence factors are combined, and a corresponding local content adaptive matrix W is designed for each pixel point.
Specifically, a pixel point p i ＝(x i ,y i ) T The expression of the support set of the corresponding local windowed kernel function is as follows:
C i ＝(X T (F i (x i ,y i ))X) -1 X T F i (x i ,y i ) (5)
in which W is i Is the pixel point p i ＝(x i ,y i ) T Corresponding support set of local windowed kernel function, pixel point p i Is the neighborhood pixel of the target pixel point, x i 、y i Is the pixel point p i Coordinates of C i Is based on pixel point p i CO at site 2 Local geographical environment influence factor of concentration value and pixel point p i A parameter matrix constructed by relation between the pixel and the neighborhood pixels, wherein X is a matrix formed by local geographic environment influence factors, T represents transposition of the matrix, F i (x i ，y i ) Is based on neighborhood gradientA parameter matrix obtained by estimation is carried out on the covariance matrix of the matrix.
Wherein the pixel point p i ＝(x i ,y i ) T Is N (p) i ) And if the number of the adjacent pixel points in the adjacent area is M, calculating derivatives in two directions in the adjacent area to form an M multiplied by 2 derivative matrix, namely:
another:
the CO can be obtained by taking the formula (3) into the formula (4) 2 A downscaling model of the concentration inversion data, whereby, in some embodiments, the downscaling model is expressed as:
where N is the Taylor expansion order, β 0 =u (p), i.e. CO corresponding to the second concentration data at the target pixel point 2 The concentration value of the liquid is calculated, m is the pixel point p i ＝(x i ,y i ) T The number of neighborhood pixel points, x i 、y i Is the pixel point p i Is the matrix half-vectorization operator, g i Represents the ith pixel point p in the first density data i CO on 2 Concentration value, p is the target pixel point, p= (x, y) T And x and y are coordinates of a target pixel point p, K is a local windowing kernel function and is used for calculating weights between the target pixel point and pixel points in a local window, and W represents a support set of the local windowing kernel function.
Solving the downscaling model, at this time, the following steps are provided:
g＝[g 1 g 2 … g M ] T ，
K＝diag[K W (p 1 -p) K W (p 2 -p) … K W (p M -p)]，
where N is the regression order (i.e., the order of taylor expansion), diag refers to the diagonal matrix.
The downscaling model expressed by the above equation (7) can be converted into:
the model expressed by equation (9) has a solution, which can be expressed as:
thus, CO at the high resolution pixel point of the current solution 2 Concentration value beta 0 Can be obtained from adjacent coarse resolution pixels by weighted linear combination, and the expression is as follows:
a kernel function.
When the regression order is N, X T KX is an (N+1) × (N+1) blocking matrix having the following structure:
wherein a is lm Is an lxm matrix.
When the regression order n=0, 1,2, the equivalent kernel w i (K W ,N,p i -p) are respectively:
wherein A is 12 ＝a 12 -a 13 a 33 -1 a 32 ，A 22 ＝a 22 -a 23 a 33 -1 a 32 ，A 13 ＝a 13 -a 12 a 22 -1 a 23 ，A 33 ＝a 33 -a 32 a 22 -1 a 23 。
And according to the previous step, solving based on the downscaling model to obtain second concentration data.
Step S104, correcting the second concentration data obtained by solving based on the improved high-precision curved surface modeling method to obtain corrected high-resolution CO 2 Concentration inversion data.
In the embodiment of the application, the high-precision advantage of the high-precision curved surface modeling method is combined with the CO observed by the site 2 And correcting the second concentration data obtained by solving the downscaling model, and improving the traditional high-precision curved surface modeling method before correcting the second concentration data in order to further improve the precision.
That is, the embodiment of the application further comprises the step of improving the high-precision curved surface modeling method, and the method specifically comprises the following steps: taking variances of the target site and surrounding adjacent sites as weight coefficients of the target site, and constructing a high-precision curved surface modeling method by using a normal equation set methodThe algebraic equation set uses the second concentration data obtained by solving as the initial value of the algebraic equation set, and combines the CO observed by the site 2 And constructing constraint conditions of the high-precision curved surface modeling method by the concentration data to obtain an improved high-precision curved surface modeling method.
In order to facilitate understanding of the technical solution of the embodiments of the present application, the HASM method is described in detail below.
The theoretical basis of HASM is the principle of surface theory, and assuming that the first type of base E, F, G and the second type of base L, M and N of the surface satisfy symmetry, E, F, G is positive, E, F, G, L, M and N satisfy gaussian (Gauss) equation set, then the full differential equation set is defined as f (x, y) =f (x 0 ，y 0 )(x＝x 0 ，y＝y 0 ) There is a unique solution z=f (x, y).
The expression of the Gaussian equation set is:
wherein, the liquid crystal display device comprises a liquid crystal display device,F＝f x ·f y ，/>
wherein f represents a simulated curved surface of the HASM; f (f) x 、f y First order partial derivatives of f in x and y directions, f xx 、f yy Respectively, f is the second partial derivative of f in the x and y directions xy Is the mixed partial derivative of f in the x and y directions; E. f, G is a first base amount; l, M, N is a second base amount; is a second class of kristolochial symbols; e (E) x 、F x 、G x 、E y 、F y 、G y First partial derivatives of E, F, G in x and y directions, respectively.
If { (x) i ，y i ) The orthogonal subdivision of the computation field (i.e., target region) Ω is calculated using [0, L ] x ]×[0，L y ]Dimensionless normalized computational domain, max { L x ，L y } =1, h is the calculation step size, andwherein I, J is the number of grids of the calculation domain in the x and y directions, respectively, { (x) i ，y i ) I0 is less than or equal to i+1, J0 is less than or equal to j+1 is a grid (namely a grid, also called pixel point) of a standardized calculation domain, and the finite difference approximation expression of the first type basic quantity is:
where (i, j) is the row and column coordinates of grid points on the HASM simulated surface, E i,j 、F i,j 、G i,j E, F, G values at grid points (i, j), f i+1，j Is the analog value at grid point (i+1, j).
The finite difference approximation expression of the second type of basis quantity is:
wherein L is i，j 、M i，j 、N i，j Each being a value of L, M, N at grid point (i, j).
The finite differential expression of the second class of kristolochial symbols is:
in the method, in the process of the application,respectively-> Values at grid points (i, j).
The finite difference form of the Gaussian equation set is shown as equation (14), equation (14) is as follows:
the matrix form of equation (14) can be written as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
/>
equation (15) is a constrained least squares problem, where I J For the J-order identity matrix, d, q, and p are the right-hand terms of the equations in equation (14), respectively.
In connection with efficient constraint control of the sampled information, the constrained least squares problem represented by equation (15) may be represented as an equality constrained least squares problem solved by HASM, represented by equation (16), equation (16) as follows:
wherein S is a sampling matrix, and g is a sampling vector; if it isIs z=f (x, y) at the mth sampling point (x i ，y i ) And S is the value of m，(i+1)×J+j ＝1，/>Wherein the sampling points may be from different sources, such as high-precision punctiform data extracted from other data sources, or sampling facilities specially arranged for collecting data, in the embodiment of the application, the sampling points are used for observing CO 2 Concentration sites.
As shown in formula (16), the HASM is finally converted into an equation constraint least square problem constrained by ground sampling, and the purpose of the HASM is to ensure that the overall simulation error is kept to be minimum under the condition that the simulation value of the curved surface at the sampling point is equal to the sampling value, so that the sampling information is fully utilized for optimization control, and the HASM is an effective means for ensuring that the iteration approaches to the optimal simulation effect.
Using the French equation set method, the least squares problem of the equation constraint represented by equation (16) above can be converted into the algebraic equation set represented by equation (17), equation (17) as follows:
wherein, the liquid crystal display device comprises a liquid crystal display device,b＝A T d+B T q+C T p+θ 2 S T g, θ is the weighting coefficient of the station.
In the conventional HASM model solving process, the weights of the sampling points are often set according to human experience, usually set to a fixed value of 2, or set to a mean value, and these settings are applied to the CO 2 The accuracy is still insufficient during the downscaling process. To further improve accuracy while eliminating the effects of outliers on sites and considering CO between sites 2 In the embodiment of the application, the variance of the target site and surrounding neighboring sites is used as the weight coefficient theta of the current target site, so as to further improve the scale-down precision.
In addition, the conventional HASM method is usually obtained by a simple interpolation method for the initial value of the algebraic equation set (17), such as using the inverse distance weight to observe the siteMeasured CO 2 Concentration data and raw coarse resolution CO obtained 2 Interpolation is carried out on the concentration data to obtain CO with higher resolution 2 Concentration data was used as initial value. In the embodiment of the application, the result obtained by solving the downscaled model is used as the initial value of the algebraic equation set (17) and is combined with high-precision CO obtained by site observation 2 Concentration data, constructing a constraint condition of HASM, and solving a downscaling model to obtain high-precision CO 2 Further correction of the concentration data to obtain higher accuracy high resolution CO 2 Concentration data.
In summary, the method provided by the application is based on coarse resolution CO 2 Taylor decomposition of the concentration data and CO combination 2 The spatial heterogeneity and the correlation of the concentration data are combined with the geographic environment influence factors to construct a downscaling model; and for high resolution CO after downscaling 2 Concentration data, combined with site observation information and improved HASM method, for the downscaled high resolution CO described above 2 The concentration data is corrected, and finally the CO is further improved 2 The concentration data is downscaled to the accuracy of the results. The method can be used for CO with coarse resolution 2 The concentration inversion data is downscaled to improve the resolution and the precision of the concentration inversion data, and can also be used for realizing the observation of the blank area CO 2 The effective interpolation of the concentration data is a new CO which is easy to realize and has wide application range 2 A concentration inversion data downscaling method.
Exemplary System
The embodiment of the application provides a CO 2 A downscaling system for concentration inversion data, as shown in fig. 2, the system comprising: a construction unit 201, an expansion unit 202, a solving unit 203 and a correction unit 204.
Wherein:
a construction unit 201 configured to establish a mathematical mapping model between the first concentration data and the second concentration data; the first concentration data is the original coarse resolution CO 2 Concentration inversion data, wherein the second concentration data is high-resolution CO after downscaling 2 Concentration inversion data.
And the expansion unit 202 is configured to perform taylor expansion on the mathematical mapping model at the target pixel point according to the neighborhood pixel point of the target point for any target pixel point on the second concentration data, and construct an error expression model corresponding to the mathematical mapping model.
A solving unit 203 configured to convert the error expression model into a weighted least squares problem using a local windowed kernel function to construct CO 2 A downscaling model of the concentration inversion data is solved based on the downscaling model to obtain second concentration data; the support set of the local windowing kernel function is constructed based on the relationship between the geographic environment influence factors and the neighborhood pixels.
A correction unit 204 configured to correct the second concentration data obtained by solving based on the improved high-precision curved surface modeling method, to obtain a corrected high-resolution CO 2 Concentration inversion data.
In some embodiments, the mathematical mapping model is expressed as follows:
g i ＝u(p i )+ε i ，i＝1,2,…,M，
in the formula g i Represents the ith pixel point p in the first density data i ＝(x i ,y i ) T CO on 2 Concentration value, x i 、y i Is the pixel point p i And u represents the second concentration data, u (p i ) Representation and pixel point p i Original CO2 concentration value epsilon at pixel point in corresponding second concentration data i Is the error, M is the pixel point p i Is used for the number of neighborhood pixel points.
In some embodiments, pixel point p i ＝(x i ,y i ) T The expression of the support set of the corresponding local windowed kernel function is as follows:
C i ＝(X T (F i (x i ,y i ))X) -1 X T F i (x i ,y i )，
in which W is i Is the pixel point p i ＝(x i ,y i ) T Corresponding support set of local windowed kernel function, pixel point p i Is the neighborhood pixel of the target pixel point, x i 、y i Is the pixel point p i Coordinates of C i Is based on pixel point p i CO at site 2 Local geographical environment influence factor of concentration value and pixel point p i A parameter matrix constructed by relation between the pixel and the neighborhood pixels, wherein X is a matrix formed by local geographic environment influence factors, and F i (x i ，y i ) And estimating a parameter matrix based on the covariance matrix of the neighborhood gradient.
In some embodiments, the error expression model corresponding to the mathematical mapping model is:
wherein u (p) i ) Representation and pixel point p i Raw CO at pixel point in corresponding second concentration data 2 The concentration value, p is the target pixel point, u (p) is the concentration value of CO2 corresponding to the second concentration data at the target pixel point,the gradient operator, H is a sea plug matrix operator, and vech is a matrix half-vector operator.
The CO provided by the embodiment of the application 2 The downscaling system of the concentration inversion data can realize the CO provided by any embodiment 2 The flow and steps of the downscaling method of the concentration inversion data reach the same technical effects, and are not described in detail herein.
The above description is only of the preferred embodiments of the present application and is not intended to limit the present application, but various modifications and variations can be made to the present application by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims (5)

1. CO (carbon monoxide) 2 A method for downscaling concentration inversion data, comprising:
establishing a mathematical mapping model between the first concentration data and the second concentration data; the first concentration data is the original coarse resolution CO 2 Concentration inversion data, wherein the second concentration data is high-resolution CO after downscaling 2 Concentration inversion data;
carrying out taylor expansion on the mathematical mapping model at the target pixel point according to the neighborhood pixel point of the target pixel point to any target pixel point on the second concentration data to obtain an error expression model corresponding to the mathematical mapping model;
the error expression model corresponding to the mathematical mapping model is as follows:
，
in the method, in the process of the application,u（p i ）representation and pixel pointp i Raw CO at pixel point in corresponding second concentration data 2 The concentration value of the liquid is calculated,pfor the target pixel point of the image to be displayed,u（p）for the CO corresponding to the second concentration data at the target pixel point 2 The concentration value of the liquid is calculated,for the purpose of the gradient operator,Hfor the sea plug matrix operator,vechis a matrix half-vector operator;
converting the error expression model into a weighted least squares problem using a local windowed kernel function to construct CO 2 A downscaling model of the concentration inversion data is obtained, and the second concentration data is obtained based on solving of the downscaling model; the support set of the local windowing kernel function is constructed based on the relationship between the geographic environment influence factors and the neighborhood pixel points;
the expression of the downscaling model is as follows:
，
in the method, in the process of the application,Nfor the order of the taylor expansion,pfor the target pixel point of the image to be displayed,，x、yfor the target pixel pointpIs defined by the transverse and longitudinal coordinates of (c),β 0 =u（p）namely the CO corresponding to the second concentration data at the target pixel point 2 Concentration value->、/>Coefficients of the first and second terms of the taylor expansion polynomial, respectively, +.>，，MIs pixel dot +.>Is used for determining the number of neighborhood pixel points,x i 、y i is a pixel pointp i Is used for the purpose of determining the coordinates of (a),vechfor the matrix half-vector operator,g i representing the first concentration dataiCO at individual pixel points 2 The concentration value of the liquid is calculated,K w for the variables->The specific functional expression is:，Kkernel for local windowingThe number of the product is the number,Wrepresenting a support set of local windowed kernel functions;
pixel dotThe expression of the support set of the corresponding local windowed kernel function is as follows:
，
，
in the method, in the process of the application,W i is a pixel pointA corresponding support set of local windowed kernel functions,C i is based on pixel pointsp i CO at site 2 Local geographical environment influence factor of concentration value and pixel pointp i The relation between the pixel and the neighborhood pixel is constructed to obtain a parameter matrix,Xa matrix of local geographical environment influencing factors,X T is a matrixXIs used to determine the transposed matrix of (a),F i （x i ，y i ）a parameter matrix which is obtained by estimation for a covariance matrix based on a neighborhood gradient;
correcting the second concentration data obtained by solving based on an improved high-precision curved surface modeling method to obtain corrected high-resolution CO 2 Concentration inversion data.
2. The CO according to claim 1 2 The downscaling method of the concentration inversion data is characterized in that the expression of the mathematical mapping model is as follows:
，
in the method, in the process of the application,g i representing the first concentration dataiIndividual pixel pointsCO on 2 The concentration value of the liquid is calculated,x i 、y i is a pixel pointp i Is used for the purpose of determining the coordinates of (a),uthe second concentration data is represented by a second concentration data,u（p i ）representation and pixel pointp i Raw CO at pixel point in corresponding second concentration data 2 The concentration value of the liquid is calculated,ε i as a result of the error in the error,Mis a pixel pointp i Is used for the number of neighborhood pixel points.
3. The CO according to claim 1 2 The downscaling method of the concentration inversion data is characterized by further comprising the step of improving a high-precision curved surface modeling method, and specifically comprises the following steps of:
taking variances of a target site and surrounding adjacent sites as weight coefficients of the target site, and constructing an algebraic equation set corresponding to a high-precision curved surface modeling method by using a French equation set method;
the second concentration data obtained by solving is taken as the initial value of the algebraic equation set, and is combined with the CO observed by the site 2 And constructing constraint conditions of the high-precision curved surface modeling method by the concentration data to obtain an improved high-precision curved surface modeling method.
4. CO (carbon monoxide) 2 A downscaling system for concentration inversion data, comprising:
a construction unit configured to establish a mathematical mapping model between the first concentration data and the second concentration data; the first concentration data is the original coarse resolution CO 2 Concentration inversion data, wherein the second concentration data is high-resolution CO after downscaling 2 Concentration inversion data;
the expansion unit is configured to perform taylor expansion on the mathematical mapping model at the target pixel point according to the neighborhood pixel point of the target pixel point for any target pixel point on the second concentration data, and construct an error expression model corresponding to the mathematical mapping model;
the error expression model corresponding to the mathematical mapping model is as follows:
，
in the method, in the process of the application,u（p i ）representation and pixel pointp i Raw CO at pixel point in corresponding second concentration data 2 The concentration value of the liquid is calculated,pfor the target pixel point of the image to be displayed,u（p）for the CO corresponding to the second concentration data at the target pixel point 2 The concentration value of the liquid is calculated,for the purpose of the gradient operator,Hfor the sea plug matrix operator,vechis a matrix half-vector operator;
a solving unit configured to convert the error expression model into a weighted least squares problem by using a local windowed kernel function to construct CO 2 A downscaling model of the concentration inversion data is obtained, and the second concentration data is obtained based on solving of the downscaling model; the support set of the local windowing kernel function is constructed based on the relationship between the geographic environment influence factors and the neighborhood pixel points;
the expression of the downscaling model is as follows:
，
in the method, in the process of the application,Nfor the order of the taylor expansion,pfor the target pixel point of the image to be displayed,，x、yfor the target pixel pointpIs defined by the transverse and longitudinal coordinates of (c),β 0 =u（p）i.e. the target imageCO corresponding to second concentration data at pixel point 2 Concentration value->、/>Coefficients of the first and second terms of the taylor expansion polynomial, respectively, +.>，，MIs pixel dot +.>Is used for determining the number of neighborhood pixel points,x i 、y i is a pixel pointp i Is used for the purpose of determining the coordinates of (a),vechfor the matrix half-vector operator,g i representing the first concentration dataiCO at individual pixel points 2 The concentration value of the liquid is calculated,K w for the variables->The specific functional expression is:，Kfor the local windowing of the kernel function,Wrepresenting a support set of local windowed kernel functions;
pixel dotThe expression of the support set of the corresponding local windowed kernel function is as follows:
，
，
in the method, in the process of the application,W i is a pixel pointA corresponding support set of local windowed kernel functions,C i is based on pixel pointsp i CO at site 2 Local geographical environment influence factor of concentration value and pixel pointp i The relation between the pixel and the neighborhood pixel is constructed to obtain a parameter matrix,Xa matrix of local geographical environment influencing factors,X T is a matrixXIs used to determine the transposed matrix of (a),F i （x i ，y i ）a parameter matrix which is obtained by estimation for a covariance matrix based on a neighborhood gradient;
the correction unit is configured to correct the second concentration data obtained by solving based on an improved high-precision curved surface modeling method to obtain corrected high-resolution CO 2 Concentration inversion data.
5. The CO of claim 4 2 The downscaling system of the concentration inversion data is characterized in that the expression of the mathematical mapping model is as follows:
，
in the method, in the process of the application,g i representing the first concentration dataiIndividual pixel pointsCO on 2 The concentration value of the liquid is calculated,x i 、y i is a pixel pointp i Is used for the purpose of determining the coordinates of (a),uthe second concentration data is represented by a second concentration data,u（p i ）representation and pixel pointp i Corresponding firstRaw CO at pixel point in two-concentration data 2 The concentration value of the liquid is calculated,ε i as a result of the error in the error,Mis a pixel pointp i Is used for the number of neighborhood pixel points.
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