CN116090315A - Precipitation space distribution simulation method considering space heterogeneity and data real-time update - Google Patents
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Abstract
The application relates to the technical field of electric digital data processing, and provides a precipitation space distribution simulation method considering space heterogeneity and data real-time updating. The method comprises the steps of constructing an influence factor matrix of a rainfall data simulation process based on environmental factor data, and constructing a first simulation model of the rainfall data by combining a high-precision curved surface modeling HASM method; constructing a space structure matrix of the precipitation data by using the original remote sensing precipitation data as a precipitation background field, and optimizing the first simulation model through the space structure matrix to obtain a second simulation model of the precipitation data; and carrying out real-time dynamic updating on the second simulation model of the precipitation data by utilizing the sampling point data obtained in real time, and solving the second simulation model of the precipitation data to obtain a simulation result of the precipitation data. The method fully utilizes the characteristics of high-precision curved surface simulation provided by the HASM method, simultaneously introduces an influence factor matrix and a space structure matrix to optimize the rainfall data simulation process, and improves the precision of the rainfall data simulation result.
Description
Technical Field
The application relates to the technical field of electric digital data processing, in particular to a precipitation space distribution simulation method considering space heterogeneity and data real-time updating.
Background
The high-resolution high-precision precipitation spatial distribution data has important significance for hydrologic water resources, regional disaster prevention and reduction and agricultural precision intelligence.
The common method for obtaining the high-precision precipitation space distribution data of the real ground surface comprises the following steps: site-based methods, simulation methods based on remote sensing data, or climate pattern-based methods. The site-based method obtains precipitation space distribution data by interpolating the observed data of the ground meteorological sites, and the precipitation space distribution data obtained by the method is discontinuous in space and is limited by the number and the distribution characteristics of the ground meteorological sites, so that the application requirements of some scenes are difficult to meet. The climate mode can better simulate the high-rise atmospheric field, the near-ground climate characteristics, the atmospheric circulation characteristics and the like, but the simulation of the precipitation involves a plurality of physical processes of the mode, and the problem of parameterization uncertainty of the physical processes exists, so that a plurality of challenges are added to accurately simulating the precipitation. The simulation method based on the remote sensing data provides an effective way for obtaining the precipitation information with continuous space in a large range, but the current process for simulating the precipitation space distribution data based on the remote sensing data has great uncertainty due to the influence of inversion algorithm, cloud layer property, sensor performance and the like. In recent years, a high-precision surface modeling (HASM) method has been widely used for simulating environmental elements such as precipitation. However, the method only considers the spatial correlation of precipitation in a simulation area, ignores the influence of spatial heterogeneity and surrounding environment factors on the precipitation spatial distribution simulation, and can not meet the requirement of high-precision simulation research of fine-scale heterogeneous elements because precipitation has stronger spatial heterogeneity.
Accordingly, there is a need to provide an improved solution to the above-mentioned deficiencies of the prior art.
Disclosure of Invention
The purpose of the application is to provide a precipitation space distribution simulation method considering space heterogeneity and data real-time updating, so as to improve the precision of precipitation space distribution data and realize dynamic real-time simulation requirements.
In order to achieve the above object, the present application provides the following technical solutions:
the application provides a precipitation space distribution simulation method considering space heterogeneity and data real-time update, which comprises the following steps:
acquiring original remote sensing precipitation data and environmental factor data of a research area;
according to the environmental factor data, constructing an influence factor matrix of a precipitation space distribution simulation process; the influence factor matrix is used for representing the influence of environmental factors of the research area on a precipitation process;
based on the influence factor matrix, a first simulation model of precipitation data is constructed by combining a high-precision curved surface modeling HASM method;
constructing a space structure matrix of the precipitation data by using the original remote sensing precipitation data as a precipitation background field; the spatial structure matrix is used for representing the spatial heterogeneity of precipitation in the research area;
optimizing the first simulation model through the space structure matrix to obtain a second simulation model of precipitation data;
and dynamically updating the second simulation model of the precipitation data in real time by utilizing the sampling point data acquired in real time, and solving the second simulation model of the precipitation data to obtain a simulation result of the precipitation data.
Preferably, the constructing a first simulation model of precipitation data based on the influence factor matrix and combined with a high-precision curved surface modeling HASM method specifically includes:
constructing a regression constraint equation by utilizing a multiple regression method based on the influence factor matrix;
and converting the algebraic solving equation set of the HASM into a constraint least square problem by using the regression constraint equation so as to obtain a first simulation model of the precipitation data.
Preferably, the first simulation model of precipitation data is:
Preferably, the method uses the original remote sensing precipitation data as a precipitation background field to construct a spatial structure matrix of the precipitation data, specifically:
taking the original remote sensing precipitation data as a precipitation background field, and calculating a feature matrix corresponding to the original remote sensing precipitation data by using a feature vector decomposition method;
calculating the average value of each column vector of the feature matrix, and subtracting the corresponding average value from each column vector to obtain a difference matrix;
and calculating a covariance matrix of the difference matrix to be used as a space structure matrix of the precipitation data.
Preferably, the second simulation model of precipitation data is:
Preferably, the real-time dynamic updating of the second simulation model of the precipitation data by using the sampling point data acquired in real time specifically includes:
according to the original sampling points obtained in advance, meshing the research area, and constructing a sampling matrix and a sampling equation of the HASM based on Taylor expansion;
and dynamically updating the sampling matrix according to the sampling point data acquired in real time, and dynamically decomposing the updated sampling matrix to dynamically update the second simulation model of the precipitation data in real time.
Preferably, the dynamically updating the sampling matrix according to the sampling point data acquired in real time specifically includes:
if the sampling points are dynamically increased and the sampling points acquired in real time fall on the first research areakDividing grids, and performing forward multiplication on the original sampling matrix to obtain a replacement matrix
Converting the original sampling matrix into a form of adding sampling point data acquired in real time as new lines to serve as an updated sampling matrix; wherein,Iis a matrix of units which is a matrix of units,mthe number of sampling points in the original sampling matrix is the number;
if the sampling points are dynamically reduced, the submatrices of the sampling matrix after the sampling points are reduced are used as updated sampling matrices.
Preferably, the updated sampling matrix is dynamically decomposed, specifically:
performing double diagonalization decomposition on the original sampling matrix to obtain a decomposition matrix corresponding to the original sampling matrix;
based on the decomposition matrix corresponding to the original sampling matrix, the Givens transformation is adopted to carry out rapid double-diagonalization decomposition on the updated sampling matrix, so as to obtain the decomposition matrix corresponding to the updated sampling matrix.
Preferably, the second simulation model of precipitation data is solved by:
adopting a truncation method, and introducing Lagrange multipliers to convert a second simulation model of precipitation data into a corresponding augmentation matrix;
decomposing the augmentation matrix by using a dual-diagonal orthogonalization decomposition strategy, and constructing the second simulation model of precipitation datanApproximation solution and first iterationn+1A recursive relation between the approximate solutions of the sub-iterations;
based on a generalized cross-validation minimization method, an estimated expression of the Lagrangian multiplier is given;
the second simulation model solving process combining the estimation expression of Lagrange multiplier and precipitation datanApproximation solution and first iterationn+1The recursive relation between the approximate solutions of the sub-iterations,and solving a second simulation model of the precipitation data.
Preferably, the environmental factor data includes at least: elevation, longitude, latitude, grade, and leaf area index NDVI.
The beneficial effects are that:
in the application, original remote sensing precipitation data and environmental factor data of a research area are firstly obtained; according to the environmental factor data, constructing an influence factor matrix of the precipitation space distribution simulation process; the influence factor matrix is used for representing influence of environmental factors of the research area on a precipitation process; based on an influence factor matrix, constructing a first simulation model of precipitation data by combining a high-precision curved surface modeling HASM method; constructing a space structure matrix of precipitation data by using the original remote sensing precipitation data as a precipitation background field; the space structure matrix is used for representing the space heterogeneity of precipitation in the research area; optimizing the first simulation model through the space structure matrix to obtain a second simulation model of precipitation data; and carrying out real-time dynamic updating on the second simulation model of the precipitation data by utilizing the sampling point data obtained in real time, and solving the second simulation model of the precipitation data to obtain a simulation result of the precipitation data. By the technical scheme, the characteristics of high-precision curved surface simulation provided by the HASM method are fully utilized, the influence factor matrix and the space structure matrix are introduced to optimize the precipitation space distribution simulation process, and the real-time acquired sampling point data are combined to dynamically adjust the solving process of the second simulation model of the precipitation data in real time.
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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 application, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute an undue limitation to the application. Wherein:
FIG. 1 is a flow chart of a method for simulating precipitation spatial distribution, which takes into account spatial heterogeneity and real-time data update, according to some embodiments of the present application;
FIG. 2 is a schematic diagram comparing simulation results of a second simulation model with simulation results of a conventional HASM method provided in accordance with some embodiments of the present application;
FIG. 3 is a diagram illustrating a comparison of the mean absolute error of a second simulation model with the mean absolute error of a conventional HASM method, provided in accordance with some embodiments of the present application.
Detailed Description
The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments. Various examples are provided by way of explanation of the present application and not limitation of the present 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 include such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.
The embodiment of the application provides a precipitation space distribution simulation method considering space heterogeneity and data real-time update, as shown in fig. 1-3, the method comprises the following steps:
and step S101, acquiring original remote sensing precipitation data and environmental factor data of a research area.
The original remote sensing precipitation data may be: any one of IMERG precipitation product, gsMAP data, ERA5 data, CFSv2 data, and CMORPH data. Among the above remote sensing precipitation data, IMERG (Integrated multi-satellite retrievals for GPM) is a main precipitation data product provided by a global rainfall observation plan (Globalprecipitation measurement, GPM) satellite, and compared with other precipitation products, IMERG precipitation product has the following characteristics: the coverage is wide (global coverage), the time resolution reaches 1 hour, and the spatial resolution is 0.1 degree multiplied by 0.1 degree. Therefore, the technical scheme is described by taking IMERG precipitation products as an example.
In this embodiment of the present application, the environmental factor data at least includes: elevation, longitude, latitude, grade, and leaf area index NDVI.
And S102, constructing an influence factor matrix of the precipitation space distribution simulation process according to the environmental factor data.
The influence factor matrix is used for representing influence of environmental factors of the research area on a precipitation process.
According to the embodiment of the application, the geographical environment factors are introduced into the rainfall spatial distribution simulation process, the influence factor matrix is constructed, the influence of the environment factors on the rainfall spatial distribution is fully considered, and therefore the accuracy of the rainfall spatial distribution simulation result is improved.
Specifically, for influencing factor matrixFRepresentation, matrixFIs a vector of different environmental factors.
Step S103, based on the influence factor matrix, a first simulation model of precipitation data is constructed by combining a high-precision curved surface modeling HASM method.
In this embodiment, the first simulation model of precipitation data is constructed based on the conventional HASM method, and for convenience of understanding, the conventional HASM method is described below.
The theoretical basis of (1) is the theory of the basis of the theory of the curved surface, and the first basic quantity of the curved surface is setE、F、GAnd a second type of basic quantityL、MAndNthe symmetry is satisfied and the degree of freedom is,E、F、Gis positively fixed, and the position of the device is positively fixed,E、F、G、L、MandNmeeting Gaussian (Gauss) equation set, then the full differential equation set isf （x，y）=f（x 0 ，y 0 ）（x=x 0 ，y=y 0 ）Under the initial conditions of (a), there is a unique solutionz=f（x，y）。
The expression of the Gaussian equation set is:
wherein ,
，
，
，
in the formula ,fa simulated surface representing a HASM;f x 、f y respectively isfAt the position ofx、yThe first partial derivative of the direction is used,f xx 、f yy respectively isfAt the position ofx、yThe second partial derivative of the direction,f xy is thatfAt the position ofx、yMixed partial derivatives of direction;E、F、Gis a first base amount;L、M、Nis the second basicAn amount of;
、
、
、
、
、
is a second class of kristolochial symbols;E x 、F x 、 G x 、E y 、F y 、G y respectively isE、F、GAt the position ofx、yFirst partial derivative of direction.
If { a（x i ，y i ）The orthogonal subdivision of the computation field, i.e., the target region, Ω, is performed using 0,L x ]×[0，L y ]dimensionless normalized computational domain, max {L x ，L y ｝=1，hTo calculate the step length, and
, wherein ,I、Jrespectively in the computing domainx、 yThe number of grids in the direction {（x i ，y i ）|0≤i≤I+1，0≤j≤J+1} is a grid (i.e., a mesh, also known as a pixel) of a normalized computational domain, then the finite difference approximation expression for the first class of basis quantities is: />
in the formula ,（i，j）is the row and column coordinates of the grid points on the HASM simulated surface,
、
、
respectively isE、F、GAt grid points（i，j）The value at which the value is to be calculated,f i+1，j for grid points（i+1，j）Analog value at.
The finite difference approximation expression of the second type of basis quantity is:
in the formula ,L i，j 、M i，j 、N i，j respectively isL、M、NAt grid points（i，j）A value at.
The finite differential expression of the second class of kristolochial symbols is:
in the formula ,
、
、
、
、
、
respectively is
、
、
、
、
、
At grid points（i，j）A value at.
The finite difference form of the Gaussian equation set is shown as formula (2), and formula (2) is as follows:
the matrix form of equation (2) can be written as:
wherein ,
，/>
equation (3) is a constrained least squares problem, in which,I J is thatJThe order-unit matrix is used for the data processing,d、q、pthe right-hand terms of the equations in equation (2), respectively.
In connection with the effective constraint control of the sampling information, the constrained least squares problem represented by equation (3) may be represented as an equality constrained least squares problem solved by HASM, represented by equation (4), equation (4) as follows:
in the formula ,Sin order to sample the matrix of samples,gis a sampling vector; if it is
Is thatz=f（x，y）In the first placemSample points [ ]x i ，y i ) The value of (1)S m，（i+1）×J+j =1，g m =
. 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, and in the embodiment of the application, the sampling points are sites for observing the concentration of CO 2. />
As shown in formula (4), 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 (4) above can be converted into the algebraic equation set represented by equation (17), equation (5) as follows:
wherein ,
，
，θis the weighting coefficient of the station.
In the precipitation space distribution simulation process, the same model generally has different forms in different application backgrounds and different research areas. According to the HASM construction process, the traditional HASM method is based on the Gauss equation set, and is converted into the linear equation set for solving by means of Taylor expansion, wherein in the process, only the spatial correlation of adjacent points is considered, the spatial heterogeneity is ignored, the influence of surrounding environment factors on the simulated elements is not considered, the accuracy of a precipitation data simulation result is insufficient, and the requirement of high-accuracy simulation research of the heterogeneous elements with fine scales cannot be met.
The embodiment of the application improves the traditional HASM precipitation space distribution simulation method: on the one hand, in the constraint space condition of the original HASM, introducing environmental influence factors of the spatial distribution of the precipitation, and establishing an equation constraint equation (i.e. a regression constraint equation) combining the environmental elements, wherein the environmental influence factors of the precipitation comprise: constructing a first simulation model of precipitation data on the basis of a regression constraint equation so as to further improve the simulation precision of precipitation space distribution; on the other hand, the space structure matrix is introduced by considering the space heterogeneous characteristic of the simulated precipitation space distribution curved surfaceMAnd optimizing the first simulation model, and constructing a second simulation model of precipitation data, so that the original high-precision curved surface modeling method is developed into a high-precision heterogeneous curved surface modeling method considering space variation characteristics and environmental factors.
In some embodiments, based on the influence factor matrix, a first simulation model of precipitation data is constructed by combining a high-precision curved surface modeling HASM method, specifically: constructing a regression constraint equation by utilizing a multiple regression method based on the influence factor matrix; and converting the algebraic solving equation set of the HASM into a constraint least square problem by using a regression constraint equation so as to obtain a first simulation model of precipitation data.
In the present embodiment, the influence factor matrix is obtainedFThen, firstly, constructing a regression constraint equation by utilizing a multiple regression method as follows:
in the formula ,Xto investigate the matrix of split grid points of a region,Gfor the coefficient matrix of the regression constraint equation,Fis a matrix of influencing factors.
Further, coefficients of regression constraint equationsMatrix arrayGThe calculation mode of (2) is as follows:
order theX=X 0 Converting the regression constraint equation of equation (6) into
； wherein ,X 0 the original remote sensing precipitation data IMERG is obtained by resampling calculation, and then the geographical weighting method is adopted to calculate +.>
Obtaining coefficient matrix of regression constraint equationG。
Solving to obtain coefficient matrix of regression constraint equationGAnd then, converting the algebraic solving equation set of the HASM (namely the equation (5)) into a constraint least square problem so as to obtain a first simulation model of precipitation data.
Specifically, the first simulation model of precipitation data is:
Step S104, constructing a space structure matrix of the precipitation data by using the original remote sensing precipitation data as a precipitation background field.
The spatial structure matrix is used for representing the spatial heterogeneity of precipitation in the research area.
The traditional HASM method only considers the spatial correlation of precipitation in a research area, ignores the spatial heterogeneity, and in the embodiment, uses original remote sensing precipitation data as a precipitation background field to construct a spatial structure matrixMSpace heterogeneity of precipitation in research area is characterized by utilizing space structure matrix, and precipitation space distribution mode is further improvedAnd (5) simulating precision.
To construct a spatial structure matrixMIn some embodiments, the original remote sensing precipitation data is used as a precipitation background field to construct a space structure matrix of the precipitation data, specifically: the original remote sensing precipitation data is used as a precipitation background field, and a feature matrix corresponding to the original remote sensing precipitation data is calculated by utilizing a feature vector decomposition method; calculating the average value of each column vector of the feature matrix, and subtracting the corresponding average value from each column vector to obtain a difference matrix; and calculating a covariance matrix of the difference matrix to be used as a space structure matrix of the precipitation data.
Specifically, original remote sensing precipitation data IMERG is used as a precipitation background field, and a feature vector decomposition method is adopted to calculate a feature matrixH n×n Wherein the matrixHEach column of the plurality is a feature, and includesnFeatures, i.e
The mean value of each column is calculated, and then the mean value corresponding to the column is subtracted from all columns to obtain a difference matrix as follows:
next, a difference matrix is calculated
Is a covariance matrix of (a):
using covariance matrix expressed by formula (9) as space structure matrix of precipitation dataM。
According to the embodiment, the characteristic matrix of the original remote sensing precipitation data is utilized, on the basis of solving the characteristic mean value of the characteristic matrix, the mean value (namely the characteristic mean value) is subtracted by each column (namely the characteristic mean value), and then the covariance matrix is calculated and is used as the space structure matrix, so that the solving process of the space structure matrix is more rigorous and standard, and a solid theoretical basis is laid for constructing a second simulation model of the precipitation data.
Step S105, optimizing the first simulation model through the space structure matrix to obtain a second simulation model of precipitation data.
Specifically, the second simulation model of precipitation data is:
And S106, carrying out real-time dynamic update on the second simulation model of the precipitation data by utilizing the sampling point data obtained in real time, and solving the second simulation model of the precipitation data to obtain a simulation result of the precipitation data.
The second simulation model of the precipitation data is constructed based on a traditional HASM method, the traditional HASM method is mainly based on a differential equation set, taylor expansion is carried out on the differential equation set, and the differential equation set is obtained through discrete solution, and in the running process of model solution, the solution algorithm of the model is required to be adjusted in real time due to the addition and rejection of sampling points. In this embodiment, the sampling matrix is adjusted by adding or deleting rows and the equation is adopted, and the matrix is dynamically decomposed, so that the real-time dynamic adjustment operation of the model is realized, and the matrix dynamic decomposition optimization strategy is provided. At the same time, the influence of the change of the sample point information on the simulation result is detected by this method.
In some embodiments, the real-time dynamic updating of the second simulation model of precipitation data is performed by using sampling point data acquired in real time, specifically: according to the original sampling points obtained in advance, meshing a research area, and constructing a sampling matrix and a sampling equation of the HASM based on Taylor expansion; and dynamically updating the sampling matrix according to the sampling point data acquired in real time, and dynamically decomposing the updated sampling matrix to dynamically update the second simulation model of the precipitation data in real time.
The real-time updating of data is an important content for the dynamic monitoring of precipitation space distribution. The prior HASM has low efficiency on newly added data (i.e. newly added sampling points) only through a strategy of re-analyzing operation, and can not meet the requirement of real-time dynamic simulation. Because the HASM method is constructed based on the basic equation of the curved surface and the sampling equation controlled by the sampling point constraint, the embodiment utilizes the sampling point data acquired in real time, and improves the solving process of the HASM method from the sampling equation, thereby realizing the dynamic real-time modeling of the curved surface.
Specifically, firstly, a calculation area is determined according to original sampling point distribution, and mesh subdivision is carried out by taking the calculation area as a research area, so that a subdivision mesh of the simulated curved surface is obtained. Then, a sampling matrix of the HASM is constructed based on Taylor expansionSAnd sampling equationSX=g. Wherein the sampling matrixSIs the first of (2)kThe row represents the firstkSample point data. Then, according to the sampling point data acquired in real time, the sampling matrix is sampledSAnd dynamically updating, dynamically decomposing the updated sampling matrix, and realizing the dynamic real-time of the second simulation model solving process of the precipitation data.
Further, the updating of the sampling points includes two cases of dynamic increasing of the sampling points and dynamic decreasing of the sampling points, and for this purpose, in some embodiments, the updating of the sampling matrix is performed dynamically according to sampling point data acquired in real time, specifically: if the sampling points are dynamically increased and the sampling points acquired in real time fall on the first research areakDividing grids, and performing forward multiplication on the original sampling matrix to obtain a replacement matrix
The original sampling matrix is converted into sampling point data acquired in real time as new additionA form of row addition; wherein,Iis a matrix of units which is a matrix of units,mthe number of the original sampling points; if the sampling points are dynamically reduced, the submatrices of the sampling matrix after the sampling points are reduced are used as updated sampling matrices.
That is, if the sampling points are newly added based on the original sampling matrix, the sampling matrix is equivalent to that of the sampling matrixSRows are newly added. Assuming that one sample point is added at a time, the newly added sample point is added to the original sample matrix, which can be expressed as
, wherein ,wa vector of data is sampled. Thus, the problem of dynamically increasing sampling points in HASM curved surface modeling can be expressed as a problem of dynamically updating a sampling matrix and dynamically decomposing the sampling matrix in real time.
In some embodiments, the updated sampling matrix is dynamically decomposed, specifically: performing double diagonalization decomposition on the original sampling matrix to obtain a decomposition matrix corresponding to the original sampling matrix; based on the decomposition matrix corresponding to the original sampling matrix, the Givens transformation is adopted to carry out rapid double-diagonalization decomposition on the updated sampling matrix, so as to obtain the decomposition matrix corresponding to the updated sampling matrix.
Based on a large-scale rapid algorithm, the original sampling matrix is subjected to double diagonalization decomposition in the model solving process. Assume that the original sampling matrix has been decomposed into:
in the formula ,Sis the original sampling matrix of the sample,S n to decompose the resulting upper Hessenberg matrix,Ufor one of the orthogonal matrices obtained after decomposition,V T for the other orthogonal matrix after the decomposition,Tis a transpose of the matrix.
In the model solving and running process, in order to realize the problem of dynamically increasing sampling points, givens transformation pair is adopted on the basis of original sampling matrix decompositionNovel sampling matrix
Realizing rapid dual diagonalization decomposition to obtain a decomposition matrix corresponding to the updated sampling matrix:
in the formula , 
for the updated sampling matrix +.>
The resulting upper Hessenberg-type matrix is decomposed for the updated sampling matrix.
Here, the updated sampling matrix is dynamically decomposed using a Givens transform, and the result is that
The Hessenberg type is kept, and the subsequent solving process is simplified.
When the region with sparse sampling points is additionally sampled based on the existing sampling points, if the newly added sampling points acquired in real time fall on the first research areakThe mesh is split, in which case the newly added row in the sampling matrix is at the firstkLine and the firstk+1Between rows. For such cases, the sample point data cannot be directly appended to the original sample matrix as a new added line, and the original sample matrix can be first addedSPre-multiplying a permutation matrix, i.e. a pre-multiplying permutation matrix
The original sampling matrix is converted into a new sampling point form, and the new sampling point data is added into the replaced sampling matrix as a new adding row to be used as an updated sampling matrix.
For the problem of dynamically reducing sampling points, the sub-matrix corresponding to the sampling matrix after the sampling points are reduced is used as the updated sampling matrix.
And then, dynamically decomposing the updated sampling matrix by using Givens transformation to realize the dynamic updating of the original sampling matrix.
The step of dynamically updating the sampling matrix can ensure the quick dynamic realization of a large-scale problem, and the updated sampling matrix is dynamically decomposed by using Givens transformation, so that the sparse characteristic of the matrix in the decomposition process is ensured, the quick solution of the model is facilitated, and meanwhile, the memory and the computing resources are saved.
In some embodiments, the second simulation model of precipitation data is solved by: adopting a truncation method, and introducing Lagrange multipliers to convert a second simulation model of precipitation data into a corresponding augmentation matrix; decomposing the augmentation matrix by using a dual-diagonal orthogonalization decomposition strategy, and constructing the second simulation model of precipitation datanApproximation solution and first iterationn+1A recursive relation between the approximate solutions of the sub-iterations; based on a generalized cross-validation minimization method, an estimated expression of the Lagrangian multiplier is given; the second simulation model solving process combining the estimation expression of Lagrange multiplier and precipitation datanApproximation solution and first iterationn+1And solving a second simulation model of the precipitation data according to a recursion relation between the approximate solutions of the iterations.
Specifically, the second simulation model of precipitation data constructed by introducing an influence factor matrix and a space structure matrix is essentially a least square problem constrained by an equation, and in the solving process, a truncated method is adopted to introduce a Lagrange multiplierλThe least squares problem of the equality constraint of the second simulation model is translated into an increase matrix as follows:
in the formula , 
。
the dual diagonal orthogonalization decomposition strategy is adopted for the augmentation matrix (13), QR decomposition is adopted, and the matrix sparsity is keptGivens transformation of characteristics, constructing the second simulation model solving process of precipitation datanApproximation solution and first iterationn+1The recursive relation between the approximate solutions of the secondary iteration is used for obtaining a solving and calculating formula of the least square problem constrained by the equation, and the matrix always maintains sparse characteristics through matrix decomposition and Givens transformation, so that the method is beneficial to saving memory and calculation resources and is beneficial to quickly solving a large-scale problem.
Meanwhile, an estimation expression of the Lagrangian multiplier is given based on a generalized cross-validation minimization methodλCombining the estimated expression of Lagrange multiplier and the second simulation model of precipitation datanApproximation solution and first iterationn+1And solving a second simulation model of the precipitation data according to a recursion relation between the approximate solutions of the iterations.
In order to verify the method provided by the application, in this embodiment, taking the simulation of the annual precipitation spatial distribution in the china area as an example, the second simulation model (i.e. formula (10)) of the precipitation data provided by the invention is compared with the simulation performance of the conventional HASM method (i.e. formula (5)), and the ten-fold cross-validation method is adopted for verification, and the comparison of the obtained simulation value and the difference of the observed value is shown in fig. 2. As can be seen from fig. 2, compared with the conventional HASM method, the precipitation simulation value obtained by the method provided by the embodiment is closer to the actual observed value obtained from the meteorological site, which indicates that the method provided by the embodiment can further improve the simulation precision of the precipitation spatial distribution.
In addition, 10% of all weather sites are randomly selected for verification experiments, and the experiments are repeated for 20 times to obtain average absolute error values MAE of the conventional HASM method and the method provided by the embodiment at the verification points, as shown in FIG. 3. As can be seen from fig. 3, the mean absolute error MAE value of the simulation result obtained by the method provided in this embodiment is significantly smaller than that of the conventional HASM method. Specifically, in 20 repeated experiments, the method provided by the embodiment has 6 times of average absolute errors between 30 and 40mm, and most of average absolute errors are between 30 and 60 mm; and the average absolute error of the simulation result obtained by the traditional HASM method is mostly 80-100 mm.
In summary, in the technical scheme provided by the application, on the basis of analyzing the simulation process of the precipitation space distribution by the traditional HASM method, only the first law of geography, namely the space correlation, is considered, but the second law of geography and the third law of geography, namely the problem of influence characteristics of space heterogeneity and space environment variables, are ignored, so that in order to more accurately apply the HASM method to the simulation research of the precipitation space distribution, the improvement is performed on the basis of the traditional HASM method, and on the one hand, the real-time simulation problem caused by the real-time update of sampling data is considered according to the geography characteristics, and the traditional HASM method is developed into a dynamic curved surface modeling method facing the real-time update of data; on the other hand, the traditional HASM method is developed into a high-precision precipitation space distribution simulation method taking the spatial heterogeneity and the environmental elements into consideration by taking the geographical features of the simulation elements, namely the spatial heterogeneity and the spatial constraint relation features of the simulation elements and the surrounding environment variables into consideration. Specifically, the method comprises the steps of firstly acquiring original remote sensing precipitation data and environmental factor data of a research area; according to the environmental factor data, constructing an influence factor matrix of the precipitation space distribution simulation process; the influence factor matrix is used for representing influence of environmental factors of the research area on a precipitation process; based on an influence factor matrix, constructing a first simulation model of precipitation data by combining a high-precision curved surface modeling HASM method; constructing a space structure matrix of precipitation data by using the original remote sensing precipitation data as a precipitation background field; the space structure matrix is used for representing the space heterogeneity of precipitation in the research area; optimizing the first simulation model through the space structure matrix to obtain a second simulation model of precipitation data; and carrying out real-time dynamic updating on the second simulation model of the precipitation data by utilizing the sampling point data obtained in real time, and solving the second simulation model of the precipitation data to obtain a simulation result of the precipitation data. By the technical scheme, the characteristics of high-precision curved surface simulation provided by the HASM method are fully utilized, an influence factor matrix and a space structure matrix are introduced to optimize the precipitation space distribution simulation process, and the real-time acquired sampling point data are combined to dynamically adjust the solving process of the second simulation model of the precipitation data in real time.
The foregoing description is only of the preferred embodiments of the present application and is not intended to limit the same, but rather, various modifications and variations may be made by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.
Claims (10)
1. A precipitation space distribution simulation method considering space heterogeneity and data real-time update is characterized by comprising the following steps:
acquiring original remote sensing precipitation data and environmental factor data of a research area;
according to the environmental factor data, constructing an influence factor matrix of a precipitation space distribution simulation process; the influence factor matrix is used for representing the influence of environmental factors of the research area on a precipitation process;
based on the influence factor matrix, a first simulation model of precipitation data is constructed by combining a high-precision curved surface modeling HASM method;
constructing a space structure matrix of the precipitation data by using the original remote sensing precipitation data as a precipitation background field; the spatial structure matrix is used for representing the spatial heterogeneity of precipitation in the research area;
optimizing the first simulation model through the space structure matrix to obtain a second simulation model of precipitation data;
and dynamically updating the second simulation model of the precipitation data in real time by utilizing the sampling point data acquired in real time, and solving the second simulation model of the precipitation data to obtain a simulation result of the precipitation data.
2. The precipitation space distribution simulation method considering space heterogeneity and data real-time update according to claim 1, wherein the constructing a first simulation model of precipitation data based on the influence factor matrix and combined with a high-precision curved surface modeling HASM method specifically comprises:
constructing a regression constraint equation by utilizing a multiple regression method based on the influence factor matrix;
and converting the algebraic solving equation set of the HASM into a constraint least square problem by using the regression constraint equation so as to obtain a first simulation model of the precipitation data.
3. The precipitation spatial distribution simulation method considering spatial heterogeneity and real-time data update according to claim 2, wherein the first simulation model of precipitation data is:
4. The precipitation space distribution simulation method considering space heterogeneity and data real-time update according to claim 3, wherein the method is characterized in that the original remote sensing precipitation data is used as a precipitation background field to construct a space structure matrix of precipitation data, specifically:
taking the original remote sensing precipitation data as a precipitation background field, and calculating a feature matrix corresponding to the original remote sensing precipitation data by using a feature vector decomposition method;
calculating the average value of each column vector of the feature matrix, and subtracting the corresponding average value from each column vector to obtain a difference matrix;
and calculating a covariance matrix of the difference matrix to be used as a space structure matrix of the precipitation data.
5. The precipitation spatial distribution simulation method considering spatial heterogeneity and real-time data update according to claim 4, wherein the second simulation model of precipitation data is:
6. The precipitation space distribution simulation method considering space heterogeneity and data real-time update according to claim 1, wherein the real-time dynamic update of the second simulation model of the precipitation data by using sampling point data acquired in real time is specifically:
according to the original sampling points obtained in advance, meshing the research area, and constructing a sampling matrix and a sampling equation of the HASM based on Taylor expansion;
and dynamically updating the sampling matrix according to the sampling point data acquired in real time, and dynamically decomposing the updated sampling matrix to dynamically update the second simulation model of the precipitation data in real time.
7. The precipitation space distribution simulation method considering space heterogeneity and data real-time update according to claim 6, wherein the dynamic update of the sampling matrix according to the sampling point data acquired in real time is specifically:
if the sampling points are dynamically increased and the sampling points acquired in real time fall on the first research areakDividing grids, and performing forward multiplication on the original sampling matrix to obtain a replacement matrix
Converting the original sampling matrix into a form of adding sampling point data acquired in real time as new lines to serve as an updated sampling matrix; wherein,Iis a matrix of units which is a matrix of units,mthe number of sampling points in the original sampling matrix is the number;
if the sampling points are dynamically reduced, the submatrices of the sampling matrix after the sampling points are reduced are used as updated sampling matrices.
8. The precipitation space distribution simulation method considering space heterogeneity and data real-time update according to claim 6, wherein the updated sampling matrix is dynamically decomposed, specifically:
performing double diagonalization decomposition on the original sampling matrix to obtain a decomposition matrix corresponding to the original sampling matrix;
based on the decomposition matrix corresponding to the original sampling matrix, the Givens transformation is adopted to carry out rapid double-diagonalization decomposition on the updated sampling matrix, so as to obtain the decomposition matrix corresponding to the updated sampling matrix.
9. The precipitation spatial distribution simulation method considering spatial heterogeneity and real-time data update according to claim 1, wherein the second simulation model of precipitation data is solved by:
adopting a truncation method, and introducing Lagrange multipliers to convert a second simulation model of precipitation data into a corresponding augmentation matrix;
decomposing the augmentation matrix by using a dual-diagonal orthogonalization decomposition strategy, and constructing the second simulation model of precipitation datanApproximation solution and first iterationn+1A recursive relation between the approximate solutions of the sub-iterations;
based on a generalized cross-validation minimization method, an estimated expression of the Lagrangian multiplier is given;
the second simulation model solving process combining the estimation expression of Lagrange multiplier and precipitation datanApproximation solution and first iterationn+1And solving a second simulation model of the precipitation data according to a recursion relation between the approximate solutions of the iterations.
10. The precipitation spatial distribution simulation method considering spatial heterogeneity and real-time data update according to claim 1, wherein the environmental factor data at least comprises: elevation, longitude, latitude, grade, and leaf area index NDVI.
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