CN116090315A - Simulation method of precipitation spatial distribution considering spatial heterogeneity and real-time data update - Google Patents

Abstract

This application relates to the technical field of electrical digital data processing, and provides a method for simulating spatial distribution of precipitation in consideration of spatial heterogeneity and real-time data update. Based on the environmental factor data, the method constructs the influencing factor matrix of the precipitation data simulation process, and combines the high-precision surface modeling HASM method to construct the first simulation model of the precipitation data; uses the original remote sensing precipitation data as the precipitation background field to construct the spatial structure of the precipitation data Matrix, optimize the first simulation model through the spatial structure matrix to obtain the second simulation model of precipitation data; use the real-time acquisition of sampling point data to dynamically update the second simulation model of precipitation data in real time, and solve the second simulation model of precipitation data The second simulation model obtains the simulation results of precipitation data. This method makes full use of the characteristics of high-precision surface simulation provided by the HASM method, and at the same time introduces the influencing factor matrix and the spatial structure matrix to optimize the precipitation data simulation process and improve the accuracy of the precipitation data simulation results.

Description

A method for simulating spatial distribution of precipitation taking into account spatial heterogeneity and real-time data updating

Technical Field

The present application relates to the technical field of electronic digital data processing, and in particular to a method for simulating spatial distribution of precipitation taking into account spatial heterogeneity and real-time data updating.

Background Art

High-resolution and high-precision precipitation spatial distribution data are of great significance to hydrology and water resources, regional disaster prevention and mitigation, and agricultural precision intelligence.

Common methods for obtaining high-precision spatial distribution data of precipitation on the real surface include: site-based methods, simulation methods based on remote sensing data, or methods based on climate models. Among them, the site-based method obtains precipitation spatial distribution data by interpolating the observation data of ground meteorological stations. Limited by the number and distribution characteristics of ground meteorological stations, the precipitation spatial distribution data obtained by this method is spatially discontinuous and difficult to meet the application requirements of some scenarios. Climate models can simulate high-level atmospheric fields, near-surface climate characteristics, and atmospheric circulation characteristics well, but the simulation of precipitation involves many physical processes in the model, and there is a problem of parameterization uncertainty of physical processes, which adds many challenges to the accurate simulation of precipitation. Simulation methods based on remote sensing data provide an effective way to obtain continuous precipitation information over a large range of space, but the current process of simulating spatial distribution data of precipitation based on remote sensing data is usually affected by inversion algorithms, cloud properties, and sensor performance, and has great uncertainty. In recent years, the high-accuracy surface modeling (HASM) method has been widely used in the simulation of environmental factors such as precipitation. However, this method only considers the spatial correlation of simulated regional precipitation, while ignoring the impact of spatial heterogeneity and surrounding environmental factors on the simulation of precipitation spatial distribution. Due to the strong spatial heterogeneity of precipitation, the precipitation data directly simulated using this method has low accuracy and cannot meet the needs of high-precision simulation research of fine-scale heterogeneous elements.

Therefore, it is necessary to provide an improved technical solution to address the above-mentioned deficiencies in the prior art.

Summary of the invention

The purpose of this application is to provide a method for simulating the spatial distribution of precipitation that takes into account spatial heterogeneity and real-time data updating, so as to improve the accuracy of spatial distribution data of precipitation and meet the needs of dynamic real-time simulation.

In order to achieve the above objectives, this application provides the following technical solutions:

The present application provides a method for simulating spatial distribution of precipitation taking into account spatial heterogeneity and real-time data updating, including:

Obtain original remote sensing precipitation data and environmental factor data in the study area;

According to the environmental factor data, an influencing factor matrix of the precipitation spatial distribution simulation process is constructed; the influencing factor matrix is used to characterize the influence of the environmental factors of the study area on the precipitation process;

Based on the influencing factor matrix and in combination with the high-precision surface modeling HASM method, a first simulation model of precipitation data is constructed;

Using the original remote sensing precipitation data as the precipitation background field, constructing a spatial structure matrix of precipitation data; the spatial structure matrix is used to characterize the spatial heterogeneity of precipitation in the study area;

Optimizing the first simulation model through the spatial structure matrix to obtain a second simulation model of precipitation data;

The second simulation model of the precipitation data is dynamically updated in real time by using the sampling point data acquired in real time, and the second simulation model of the precipitation data is solved to obtain a simulation result of the precipitation data.

Preferably, the first simulation model of precipitation data is constructed based on the influencing factor matrix in combination with the high-precision surface modeling HASM method, specifically as follows:

Based on the influencing factor matrix, a regression constraint equation is constructed using a multiple regression method;

The regression constraint equation is used to convert the algebraic solution equation group of HASM into a constrained least squares problem to obtain the first simulation model of the precipitation data.

Preferably, the first simulation model of precipitation data is:

，

,

，b为HASM的代数求解方程组的系数矩阵，X为所述研究区域的剖分网格点组成的矩阵，G ^-1 为所述回归约束方程的系数矩阵的逆矩阵，F为所述影响因素矩阵。

, b is the coefficient matrix of the algebraic solution equation group of HASM, X is the matrix composed of the subdivided grid points of the study area, G ^-1 is the inverse matrix of the coefficient matrix of the regression constraint equation, and F is the influencing factor matrix.

Preferably, the original remote sensing precipitation data is used as the precipitation background field to construct the spatial structure matrix of precipitation data, specifically:

The original remote sensing precipitation data is used as a precipitation background field, and a characteristic matrix corresponding to the original remote sensing precipitation data is calculated using an eigenvector decomposition method;

Calculate the mean of each column vector of the feature matrix, and subtract the corresponding mean from each column vector to obtain a difference matrix;

The covariance matrix of the difference matrix is calculated as the spatial structure matrix of the precipitation data.

Preferably, the second simulation model of precipitation data is:

，

,

，b为HASM的代数求解方程组的系数矩阵，X为所求解的研究区域的剖分网格点组成的矩阵，G ^-1 为所述回归约束方程的系数矩阵的逆矩阵，F为所述影响因素矩阵，M为所述降水数据的空间结构矩阵。

, b is the coefficient matrix of the algebraic solution equation group of HASM, X is the matrix composed of the subdivided grid points of the research area to be solved, G ^-1 is the inverse matrix of the coefficient matrix of the regression constraint equation, F is the influencing factor matrix, and M is the spatial structure matrix of the precipitation data.

Preferably, the second simulation model of the precipitation data is dynamically updated in real time using the sampling point data acquired in real time, specifically:

According to the original sampling points obtained in advance, the study area is meshed, and based on Taylor expansion, a sampling matrix and a sampling equation of HASM are constructed;

The sampling matrix is dynamically updated according to the sampling point data acquired in real time, and the updated sampling matrix is dynamically decomposed to dynamically update the second simulation model of the precipitation data in real time.

Preferably, the sampling matrix is dynamically updated according to the sampling point data acquired in real time, specifically:

，以将原有的采样矩阵转换为以实时获取的采样点数据作为新增行追加的形式，作为更新后的采样矩阵；其中，I为单位矩阵，m为原有的采样矩阵中采样点的个数；If the sampling points are increased dynamically, and the real-time sampling points fall on the kth subdivision grid of the study area, the original sampling matrix is pre-multiplied by the permutation matrix

, so as to convert the original sampling matrix into a form in which the sampling point data obtained in real time are added as new rows, as an updated sampling matrix; wherein, I is the unit matrix, and m is the number of sampling points in the original sampling matrix;

If the sampling points are dynamically reduced, the sub-matrix of the sampling matrix after the sampling points are reduced is used as the updated sampling matrix.

Preferably, the updated sampling matrix is dynamically decomposed, specifically as follows:

The original sampling matrix is decomposed into a double diagonal to obtain a decomposition matrix corresponding to the original sampling matrix;

Based on the decomposition matrix corresponding to the original sampling matrix, the Givens transform is used to perform fast bidiagonal decomposition on the updated sampling matrix to obtain the decomposition matrix corresponding to the updated sampling matrix.

Preferably, the second simulation model of precipitation data is solved by the following steps:

The truncation method is adopted and Lagrange multipliers are introduced to transform the second simulation model of precipitation data into the corresponding augmented matrix;

The augmented matrix is decomposed by using the double diagonal orthogonal decomposition strategy, and the recursive relationship between the approximate solution of the nth iteration and the approximate solution of the n+1th iteration in the second simulation model of precipitation data is constructed.

Based on the minimization method of generalized cross validation, the estimation expression of Lagrange multiplier is given;

The second simulation model of precipitation data is solved by combining the estimation expression of Lagrange multipliers with the recursive relationship between the approximate solution of the nth iteration and the approximate solution of the n+1th iteration in the process of solving the second simulation model of precipitation data.

Preferably, the environmental factor data at least include: altitude, longitude, latitude, slope and leaf area index NDVI.

Beneficial effects:

In the present application, the original remote sensing precipitation data and environmental factor data of the study area are first obtained; based on the environmental factor data, an influencing factor matrix of the precipitation spatial distribution simulation process is constructed; the influencing factor matrix is used to characterize the influence of the environmental factors of the study area on the precipitation process; based on the influencing factor matrix, combined with the high-precision surface modeling HASM method, a first simulation model of the precipitation data is constructed; using the original remote sensing precipitation data as the precipitation background field, a spatial structure matrix of the precipitation data is constructed; the spatial structure matrix is used to characterize the spatial heterogeneity of precipitation in the study area; the first simulation model is optimized by the spatial structure matrix to obtain a second simulation model of the precipitation data; using the sampling point data obtained in real time, the second simulation model of the precipitation data is dynamically updated in real time, and the second simulation model of the precipitation data is solved to obtain the simulation result of the precipitation data. Through the above technical scheme, the high-precision surface simulation characteristics provided by the HASM method are fully utilized, the influencing factor matrix and the spatial structure matrix are introduced to optimize the precipitation spatial distribution simulation process, and the solution process of the second simulation model of the precipitation data is dynamically adjusted in real time in combination with the sampling point data obtained in real time. This technical scheme not only takes into account the spatial correlation of precipitation in the study area, but also takes into account the spatial heterogeneity of precipitation in the area and the influence of environmental factors on the precipitation spatial distribution simulation process, thereby improving the accuracy of the precipitation spatial distribution simulation results.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings constituting part of the present application are used to provide a further understanding of the present application. The exemplary embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. Among them:

FIG1 is a schematic flow chart of a precipitation spatial distribution simulation method taking into account spatial heterogeneity and real-time data updating according to some embodiments of the present application;

FIG2 is a schematic diagram showing a comparison between simulation results of a second simulation model provided according to some embodiments of the present application and simulation results of a traditional HASM method;

FIG3 is a schematic diagram showing a comparison between the mean absolute error of a second simulation model provided according to some embodiments of the present application and the mean absolute error of a traditional HASM method.

DETAILED DESCRIPTION

The present application will be described in detail below with reference to the accompanying drawings and in conjunction with embodiments. Each example is provided by way of explanation of the present application but does not limit the present application. In fact, it will be clear to those skilled in the art that modifications and variations may be made in the present application without departing from the scope or spirit of the present application. For example, a feature shown or described as a part of an embodiment may be used in another embodiment to produce yet another embodiment. Therefore, it is desired that the present application includes such modifications and variations within the scope of the appended claims and their equivalents.

The present application embodiment provides a method for simulating spatial distribution of precipitation taking into account spatial heterogeneity and real-time data updating, as shown in FIG. 1 to FIG. 3 , the method includes:

Step S101, obtaining original remote sensing precipitation data and environmental factor data of the study area.

The original remote sensing precipitation data may be any one of: IMERG precipitation products, GsMAP data, ERA5 data, CFSv2 data, and CMORPH data. Among the above remote sensing precipitation data, IMERG (Integrated multi-satelliteretrievals for GPM) is the main precipitation data product provided by the Global Precipitation Measurement (GPM) satellite. Compared with other precipitation products, IMERG precipitation products have the following characteristics: wide coverage (global coverage), time resolution of 1 hour, and spatial resolution of 0.1°×0.1°. Therefore, this embodiment takes the IMERG precipitation product as an example to illustrate the technical solution.

In the embodiment of the present application, the environmental factor data at least includes: altitude, longitude, latitude, slope and leaf area index NDVI.

Step S102: construct an influencing factor matrix of the precipitation spatial distribution simulation process according to the environmental factor data.

Among them, the influencing factor matrix is used to characterize the impact of environmental factors in the study area on the precipitation process.

The embodiment of the present application introduces geographical environmental factors into the precipitation spatial distribution simulation process, and fully considers the influence of environmental factors on the precipitation spatial distribution by constructing an influencing factor matrix, thereby improving the accuracy of the precipitation spatial distribution simulation results.

Specifically, the influencing factor matrix is represented by F , and each column of the matrix F is a vector composed of different environmental factors.

Step S103: Based on the influencing factor matrix and in combination with the high-precision surface modeling HASM method, a first simulation model of precipitation data is constructed.

In the embodiment of the present application, the first simulation model of precipitation data is constructed on the basis of the traditional HASM method. For ease of understanding, the traditional HASM method is described below.

The theoretical basis is the basic theorem of surface theory. Assume that the first-class basic quantities E , F , G and the second-class basic quantities L , M and N of the surface satisfy symmetry, E , F , G are positive definite, and E , F , G, L , M and N satisfy the Gaussian equations. Then, under the initial condition of f (x, y) = f (x ₀ , y ₀ ) (x = x ₀ , y = y ₀ ) , the total differential equations have a unique solution z = f (x, y) .

The expression of Gaussian equations is:

（1）

(1)

，

，

，in,

,

,

,

，

，

，

,

,

,

,

,

，

,

，

,

，

,

，

,

。

.

、

、

、

、

、

为第二类克里斯托弗尔符号；E _x 、F _x 、 G _x 、E _y 、F _y 、G _y 分别为E、F、G在x、y方向的一阶偏导数。Wherein, f represents the simulated surface of HASM; f _x and f _y are the first-order partial derivatives of f in the x and y directions, respectively; f _xx and f _yy are the second-order partial derivatives of f in the x and y directions, respectively; f _xy is the mixed partial derivative of f in the x and y directions; E, F, G are the first basic quantities; L, M, N are the second basic quantities;

,

,

,

,

,

is the Christoph symbol of the second kind; Ex _, Fx _, Gx _, Ey _, Fy _, Gy are the first-order partial derivatives of E, F, and G _in the x and y directions respectively.

，其中，I、J分别为计算域在x、 y方向的网格数量，｛（x _i ，y _i ）|0≤i≤I+1，0≤j≤J+1｝为标准化计算域的栅格（也就是网格，又称像素点），则第一类基本量的有限差分逼近表达式为：If { (xi _, yi ₎ } _is the orthogonal partition of the computational domain (i.e., the target region) Ω, the computational domain is dimensionlessly normalized using [0, Lx _] ×[0, Ly ], max{ Lx , Ly _} =1, h is the computational step size, _and

, where I and J are the number of grids in the computational domain in the x and y directions, respectively, and { (xi _, yi ₎ | 0≤i≤I + 1,0≤j≤J + 1 } is the grid (i.e., grid, also known as pixel point) of the standardized computational domain . The finite difference approximation expression of the first type of basic quantity is:

，

,

、

、

分别为E、F、G在网格点（i，j）处的值，f _i+1，j 为网格点（i+1，j）处的模拟值。Where (i, j) is the row and column coordinates of the grid point on the HASM simulation surface.

,

,

are the values of E , F , and G at the grid point (i, j) respectively, and fi _+1,j is the simulated value at the grid point (i+1, j) .

The finite difference approximation expression of the second type of basic quantity is:

，

,

Where Li _,j , Mi _,j and Ni _,j are the values of L , M and N at the grid point (i, j) respectively.

The finite difference expression for the second kind of Christophel symbol is:

，

,

，

,

，

,

，

,

，

,

，

,

、

、

、

、

、

分别为

、

、

、

、

、

在网格点（i，j）处的值。In the formula,

,

,

,

,

,

They are

,

,

,

,

,

The value at the grid point (i, j) .

The finite difference form of the Gaussian equations is shown in formula (2), which is as follows:

（2）

(2)

The matrix form of formula (2) can be written as:

（3）

(3)

，in,

,

，

，

,

,

，

，

,

,

，

，

,

,

。

.

Formula (3) is a constrained least squares problem, where I _J is the J -order identity matrix, and d, q, and p are the right-hand terms of the equation in formula (2).

Combined with the effective constraint control of sampling information, the constrained least squares problem expressed by formula (3) can be expressed as the equality constrained least squares problem solved by HASM, expressed by formula (4), which is as follows:

（4）

(4)

是z=f（x，y）在第m个采样点（x _i ，y _i ）的值，则S _{m，（i+1）×J+j} =1，g _m =

。其中，采样点可以来自不同来源，比如从其他数据源提取的高精度点状数据，或者专为采集数据而布设的采样设施，本申请实施例中，采样点为用于观测CO2浓度的站点。Where S is the sampling matrix and g is the sampling vector; if

is the value of z=f(x, y) at the mth sampling point ( xi _, yi ), then Sm _{, (i+1)×J+j =} 1, gm ₌

The sampling points may come from different sources, such as high-precision point data extracted from other data sources, or sampling facilities specially arranged for collecting data. In the embodiment of the present application, the sampling points are sites for observing CO2 concentration.

As shown in formula (4), HASM is finally transformed into an equality-constrained least squares problem constrained by ground sampling. Its purpose is to ensure that the overall simulation error is minimized under the condition that the simulation value of the surface at the sampling point is equal to the sampling value. In this way, the sampling information is fully utilized for optimization control, and it is also an effective means to ensure that the iteration approaches the optimal simulation effect.

Using the method of normal equations, the least squares problem with equality constraints expressed by the above formula (4) can be transformed into a system of algebraic equations expressed by formula (17), and formula (5) is as follows:

（5）

(5)

，

，θ为站点的权重系数。in,

,

, θ is the weight coefficient of the site.

In the process of simulating the spatial distribution of precipitation, the same model generally has different forms in different application backgrounds and different research areas. From the above HASM construction process, it can be seen that the traditional HASM method is based on the Gauss equations and uses Taylor expansion to transform them into linear equations for solution. In this process, only the spatial correlation of adjacent points is considered, while spatial heterogeneity is ignored, and the influence of surrounding environmental factors on the simulated elements is not considered, resulting in insufficient precision of precipitation data simulation results, which cannot meet the needs of high-precision simulation research of heterogeneous elements at fine scales.

The embodiment of the present application improves the traditional HASM precipitation spatial distribution simulation method: on the one hand, the environmental influencing factors of the spatial distribution of precipitation are introduced into the constraint space conditions of the original HASM, and an equation constraint equation (i.e., a regression constraint equation) combining environmental factors is established, wherein the environmental influencing factors of precipitation include: altitude, longitude, latitude, slope and leaf area index NDVI; a first simulation model of precipitation data is constructed on the basis of the regression constraint equation to further improve the simulation accuracy of the spatial distribution of precipitation; on the other hand, considering the spatial heterogeneity characteristics of the simulated precipitation spatial distribution surface, the spatial structure matrix M is introduced to optimize the first simulation model, and a second simulation model of precipitation data is constructed, thereby developing the original high-precision surface modeling method into a high-precision heterogeneous surface modeling method that considers spatial variation characteristics and environmental factors.

In some embodiments, based on the influencing factor matrix and combined with the high-precision surface modeling HASM method, a first simulation model of precipitation data is constructed, specifically: based on the influencing factor matrix, a multivariate regression method is used to construct a regression constraint equation; using the regression constraint equation, the algebraic solution of the HASM equation group is converted into a constrained least squares problem to obtain the first simulation model of precipitation data.

In this embodiment, after obtaining the influencing factor matrix F , the multivariate regression method is first used to construct the regression constraint equation as follows:

（6）

(6)

Where X is the matrix composed of the grid points of the study area, G is the coefficient matrix of the regression constraint equation, and F is the influencing factor matrix.

Furthermore, the coefficient matrix G of the regression constraint equation is calculated as follows:

；其中，X ⁰ 由原始遥感降水数据IMERG经过重采样计算得到，然后采用地理加权方法解算

，得到回归约束方程的系数矩阵G。Let X = X ⁰ , and transform the regression constraint equation of formula (6) into

^; where X0 is obtained by resampling the original remote sensing precipitation data IMERG and then solving it using the geographical weighting method

, and obtain the coefficient matrix G of the regression constraint equation.

After solving the coefficient matrix G of the regression constraint equation, the algebraic solution equation group of HASM (i.e., formula (5)) is converted into a constrained least squares problem to obtain the first simulation model of precipitation data.

Specifically, the first simulation model of precipitation data is:

（7）

(7)

，b为HASM的代数求解方程组的系数矩阵，X为研究区域的剖分网格点组成的矩阵，G ^-1 为回归约束方程的系数矩阵的逆矩阵，F为影响因素矩阵。

, b is the coefficient matrix of the algebraic solution equation group of HASM, X is the matrix composed of the grid points of the study area, G ^-1 is the inverse matrix of the coefficient matrix of the regression constraint equation, and F is the influencing factor matrix.

Step S104: Use the original remote sensing precipitation data as the precipitation background field to construct a spatial structure matrix of the precipitation data.

Among them, the spatial structure matrix is used to characterize the spatial heterogeneity of precipitation in the study area.

The traditional HASM method only considers the spatial correlation of precipitation in the study area and ignores the spatial heterogeneity. In this embodiment, the original remote sensing precipitation data is used as the precipitation background field to construct the spatial structure matrix M. The spatial structure matrix is used to characterize the spatial heterogeneity of precipitation in the study area, thereby further improving the accuracy of precipitation spatial distribution simulation.

In order to construct the spatial structure matrix M , in some embodiments, the original remote sensing precipitation data is used as the precipitation background field to construct the spatial structure matrix of the precipitation data, specifically: the original remote sensing precipitation data is used as the precipitation background field, and the characteristic matrix corresponding to the original remote sensing precipitation data is calculated using the eigenvector decomposition method; the mean of each column vector of the characteristic matrix is calculated, and the corresponding mean is subtracted from each column vector to obtain a difference matrix; the covariance matrix of the difference matrix is calculated as the spatial structure matrix of the precipitation data.

，计算各个列的均值，然后将所有列减去该列对应的均值，得到差值矩阵如下：Specifically, the original remote sensing precipitation data IMERG is used as the precipitation background field, and the eigenvector decomposition method is used to calculate its feature matrix H _n×n , where each column in the matrix H is a feature, including n features in total, namely

, calculate the mean of each column, and then subtract the mean corresponding to the column from all columns to get the difference matrix as follows:

（8）

(8)

的协方差矩阵：Next, calculate the difference matrix

The covariance matrix of is:

（9）

(9)

The covariance matrix expressed in formula (9) is used as the spatial structure matrix M of precipitation data.

This embodiment uses the characteristic matrix of the original remote sensing precipitation data. On the basis of solving the mean of each feature of the characteristic matrix, the mean (i.e., the feature mean) is subtracted from each column (i.e., the feature) and then the covariance matrix is calculated as the spatial structure matrix. This makes the solution process of the spatial structure matrix more rigorous and standardized, thereby laying a solid theoretical foundation for constructing the second simulation model of precipitation data.

Step S105: Optimize the first simulation model through the spatial structure matrix to obtain a second simulation model of precipitation data.

Specifically, the second simulation model of precipitation data is:

（10）

(10)

，b为HASM的代数求解方程组的系数矩阵，X为所求解的研究区域的剖分网格点组成的矩阵，G ^-1 为回归约束方程的系数矩阵的逆矩阵，F为影响因素矩阵，M为降水数据的空间结构矩阵。

, b is the coefficient matrix of the algebraic solution equation group of HASM, X is the matrix composed of the grid points of the research area to be solved, G ^-1 is the inverse matrix of the coefficient matrix of the regression constraint equation, F is the influencing factor matrix, and M is the spatial structure matrix of precipitation data.

Step S106: using the sampling point data acquired in real time, dynamically updating the second simulation model of precipitation data in real time, and solving the second simulation model of precipitation data to obtain a simulation result of precipitation data.

The second simulation model of precipitation data is constructed based on the traditional HASM method. The traditional HASM method is mainly based on a group of differential equations, which are obtained by Taylor expansion and discrete solution. During the operation of the model solution, due to the addition and removal of sampling points, the model solution algorithm must be adjusted in real time. In this embodiment, the sampling point data obtained in real time is used, and the newly obtained sampling point data is used as a new row. The sampling matrix and the adopted equation are adjusted by adding or deleting rows, and the strategy of dynamically decomposing the matrix is used to achieve real-time dynamic adjustment and operation of the model, and a matrix dynamic decomposition optimization strategy is given. At the same time, this method is used to detect the impact of changes in sample point information on the model simulation results.

In some embodiments, the second simulation model of precipitation data is dynamically updated in real time using the sampling point data acquired in real time, specifically: the study area is gridded according to the original sampling points acquired in advance, and the sampling matrix and sampling equation of HASM are constructed based on Taylor expansion; the sampling matrix is dynamically updated according to the sampling point data acquired in real time, and the updated sampling matrix is dynamically decomposed to dynamically update the second simulation model of precipitation data in real time.

Real-time data updating is an important part of dynamic monitoring of spatial distribution of precipitation. In the past, HASM could only re-analyze and run the newly added data (i.e., newly added sampling points), which was inefficient and could not meet the needs of real-time dynamic simulation. Since the HASM method is constructed based on the basic equation of the surface and the sampling equation controlled by the sampling point constraints, this embodiment uses the sampling point data obtained in real time, starts from the sampling equation, improves the solution process of the HASM method, and realizes the dynamic real-time surface modeling.

Specifically, the calculation area is first determined for the original sampling point distribution, and it is used as the research area for meshing to obtain the mesh of the simulation surface. Then, the sampling matrix S and sampling equation SX=g of HASM are constructed based on Taylor expansion. Among them, the k-th row of the sampling matrix S represents the k -th sampling point data. Then, according to the sampling point data obtained in real time, the sampling matrix S is dynamically updated, and the updated sampling matrix is dynamically decomposed to realize the dynamic real-time solution process of the second simulation model of precipitation data.

，以将原有的采样矩阵转换为以实时获取的采样点数据作为新增行追加的形式；其中，I为单位矩阵，m为原始采样点的个数；若采样点动态减少，则将采样点减少后的采样矩阵的子矩阵作为更新后的采样矩阵。Furthermore, the updating of sampling points includes two situations: dynamic increase of sampling points and dynamic decrease of sampling points. Therefore, in some embodiments, the sampling matrix is dynamically updated according to the 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 kth subdivision grid of the study area, the original sampling matrix is pre-multiplied by the permutation matrix

, so as to convert the original sampling matrix into a form in which the sampling point data obtained in real time is added as the new row appended; wherein, I is the unit matrix, and m is the number of original sampling points; if the sampling points are dynamically reduced, the sub-matrix of the sampling matrix after the sampling points are reduced is used as the updated sampling matrix.

，其中，w为采样点数据构成的向量。这样，对于HASM曲面建模中的动态增加采样点问题，数学上可表述为对采样矩阵进行动态更新并实时动态分解问题。That is to say, if a new sampling point is added to the original sampling matrix, it is equivalent to adding a new row to the sampling matrix S. Assuming that one sampling point is added at a time, the newly added sampling point is appended to the original sampling matrix, and the new sampling matrix can be expressed as

, where w is a vector of sampling point data. In this way, the problem of dynamically adding sampling points in HASM surface modeling can be mathematically expressed as a problem of dynamically updating the sampling matrix and dynamically decomposing it in real time.

In some embodiments, the updated sampling matrix is dynamically decomposed, specifically: the original sampling matrix is double-diagonalized to obtain a decomposition matrix corresponding to the original sampling matrix; based on the decomposition matrix corresponding to the original sampling matrix, the updated sampling matrix is quickly double-diagonalized using the Givens transform to obtain a decomposition matrix corresponding to the updated sampling matrix.

Based on a large-scale fast algorithm, the original sampling matrix is decomposed into a double diagonal form during the model solving process. Assume that the original sampling matrix has been decomposed into:

（11）

(11)

Wherein, S is the original sampling matrix, Sn is the upper Hessenberg type matrix obtained by decomposition, _U is one of the orthogonal matrices obtained after decomposition , VT ^is another orthogonal matrix after decomposition, and T is the transpose of the matrix.

实现快速双对角化分解，得到更新后的采样矩阵对应的分解矩阵：In the process of model solving, in order to dynamically increase the sampling points, it is necessary to use Givens transformation to decompose the new sampling matrix based on the original sampling matrix.

Implement fast double diagonal decomposition and obtain the decomposition matrix corresponding to the updated sampling matrix:

（12）

(12)

为更新后的采样矩阵，

为更新后的采样矩阵分解得到的上Hessenberg型矩阵。In the formula,

is the updated sampling matrix,

is the upper Hessenberg matrix obtained by decomposing the updated sampling matrix.

保持上Hessenberg型，有利于简化后续的求解过程。Here, Givens transform is used to dynamically decompose the updated sampling matrix, and make

Maintaining the upper Hessenberg type helps to simplify the subsequent solution process.

，将原有的采样矩阵转换为新增采样点的形式，并将新增的采样点数据作为新增行追加到置换后的采样矩阵中，作为更新后的采样矩阵。When additional sampling is performed on the basis of existing sampling points in areas with sparse sampling points, if the newly added sampling points acquired in real time fall on the kth subdivision grid of the study area, then the newly added row in the sampling matrix is between the kth row and the k+1th row. In such cases, the sampling point data cannot be directly added to the original sampling matrix as a newly added row. Instead, the original sampling matrix S can be pre-multiplied by a permutation matrix, that is, pre-multiplied by a permutation matrix.

, convert the original sampling matrix into the form of newly added sampling points, and append the newly added sampling point data as new rows to the replaced sampling matrix as the 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.

Then, the updated sampling matrix is dynamically decomposed using Givens transform to achieve dynamic update of the original sampling matrix.

The above-mentioned step of dynamically updating the sampling matrix can ensure the rapid dynamic realization of large-scale problems. In addition, the Givens transformation is used to dynamically decompose the updated sampling matrix, which ensures the sparse characteristics of the matrix during the decomposition process, is conducive to the rapid solution of the model, and saves memory and computing resources.

In some embodiments, the second simulation model of precipitation data is solved by the following steps: using a truncation method and introducing Lagrange multipliers to convert the second simulation model of precipitation data into a corresponding augmented matrix; using a double diagonal orthogonal decomposition strategy to decompose the augmented matrix, and constructing a recursive relationship between the approximate solution of the nth iteration and the approximate solution of the n+1th iteration in the process of solving the second simulation model of precipitation data; based on a minimization method of generalized cross-validation, an estimated expression for the Lagrange multiplier is given; combining the estimated expression for the Lagrange multiplier with the recursive relationship between the approximate solution of the nth iteration and the approximate solution of the n+1th iteration in the process of solving the second simulation model of precipitation data, the second simulation model of precipitation data is solved.

Specifically, the second simulation model of precipitation data constructed by introducing the influencing factor matrix and the spatial structure matrix is essentially an equality-constrained least squares problem. In the solution process, the truncation method is adopted and the Lagrange multiplier λ is introduced to transform the equality-constrained least squares problem of the second simulation model into the following added matrix:

（13）

(13)

。In the formula,

.

The augmented matrix (13) is subjected to a double diagonal orthogonal decomposition strategy, QR decomposition and Givens transformation that maintains the sparse characteristics of the matrix. The recursive relationship between the approximate solution of the nth iteration and the approximate solution of the n+1th iteration in the second simulation model of precipitation data is constructed, thereby obtaining the solution calculation formula of the least squares problem constrained by the equation. In addition, through matrix decomposition and Givens transformation, the matrix always maintains its sparse characteristics, which is beneficial to saving memory and computing resources and is conducive to the rapid solution of large-scale problems.

At the same time, based on the minimization method of generalized cross-validation, the estimated expression λ of the Lagrange multiplier is given, and the second simulation model of precipitation data is solved by combining the estimated expression of the Lagrange multiplier with the recursive relationship between the approximate solution of the nth iteration and the approximate solution of the n+1th iteration in the solution process of the second simulation model of precipitation data.

In order to verify the method provided by the present application, this embodiment takes the simulation of the spatial distribution of annual precipitation in the Chinese region as an example, and compares the simulation performance of the second simulation model of precipitation data provided by the present invention (i.e., formula (10)) with that of the traditional HASM method (i.e., formula (5)), and verifies it by using the ten-fold cross validation method. The comparison of the difference between the obtained simulation value and the observed value is shown in Figure 2. As can be seen from Figure 2, compared with the traditional HASM method, the precipitation simulation value obtained by the method provided by the present embodiment is closer to the actual observed value obtained from the meteorological station, indicating that the method provided by the present embodiment can further improve the simulation accuracy of the spatial distribution of precipitation.

In addition, 10% of the meteorological stations were randomly selected from all the meteorological stations for verification experiments, and the experiments were repeated 20 times to obtain the mean absolute error MAE of the traditional HASM method and the method provided in this embodiment at the verification point, as shown in Figure 3. As can be seen from Figure 3, the mean absolute error MAE value of the simulation results obtained by the method provided in this embodiment is significantly smaller than the mean absolute error MAE value of the traditional HASM method. Specifically, in the 20 repeated experiments, the method provided in this embodiment had 6 mean absolute errors between 30 and 40 mm, and most of the mean absolute errors were between 30 and 60 mm; while the mean absolute errors of the simulation results obtained by the traditional HASM method were mostly between 80 and 100 mm.

To summarize, in the technical solution provided by the present application, based on the analysis of the simulation process of the spatial distribution of precipitation by the traditional HASM method, it is aimed at the problem that the HASM method only considers the first law of geography, namely spatial correlation, while ignoring the second law and the third law of geography, namely spatial heterogeneity and the influence characteristics of spatial environmental variables. In order to more accurately apply the HASM method to the simulation study of the spatial distribution of precipitation, improvements are made on the basis of the traditional HASM method. According to the geographical characteristics, on the one hand, the real-time simulation problem caused by the real-time update of the sampling data is considered, and the traditional HASM method is developed into a dynamic surface modeling method for real-time data updating; on the other hand, the geographical characteristics of the simulation elements, namely spatial heterogeneity and the spatial constraint relationship characteristics of the simulation elements and the surrounding environmental variables are considered, and the traditional HASM method is developed into a high-precision precipitation spatial distribution simulation method that considers spatial heterogeneity and environmental elements. Specifically, the method first obtains the original remote sensing precipitation data and environmental factor data of the study area; constructs the influencing factor matrix of the precipitation spatial distribution simulation process according to the environmental factor data; the influencing factor matrix is used to characterize the influence of the environmental factors of the study area on the precipitation process; based on the influencing factor matrix, combined with the high-precision surface modeling HASM method, the first simulation model of precipitation data is constructed; the original remote sensing precipitation data is used as the precipitation background field to construct the spatial structure matrix of precipitation data; the spatial structure matrix is used to characterize the spatial heterogeneity of precipitation in the study area; the first simulation model is optimized through the spatial structure matrix to obtain the second simulation model of precipitation data; the second simulation model of precipitation data is dynamically updated in real time using the sampling point data obtained in real time, and the second simulation model of precipitation data is solved to obtain the simulation result of precipitation data. Through the above technical scheme, the high-precision surface simulation characteristics provided by the HASM method are fully utilized, the influencing factor matrix and the spatial structure matrix are introduced to optimize the precipitation spatial distribution simulation process, and the solution process of the second simulation model of the precipitation data is dynamically adjusted in real time in combination with the sampling point data obtained in real time. This method not only takes into account the spatial correlation of precipitation in the study area, but also takes into account the spatial heterogeneity of precipitation in the region and the influence of environmental factors on the precipitation spatial distribution simulation process, thereby improving the accuracy of the precipitation spatial distribution simulation results.

The above description is only a preferred embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims (10)

1. A method for simulating spatial distribution of precipitation taking into account spatial heterogeneity and real-time data updating, characterized by comprising: Obtain original remote sensing precipitation data and environmental factor data in the study area; According to the environmental factor data, an influencing factor matrix of the precipitation spatial distribution simulation process is constructed; the influencing factor matrix is used to characterize the influence of the environmental factors of the study area on the precipitation process; Based on the influencing factor matrix and in combination with the high-precision surface modeling HASM method, a first simulation model of precipitation data is constructed; Using the original remote sensing precipitation data as the precipitation background field, constructing a spatial structure matrix of precipitation data; the spatial structure matrix is used to characterize the spatial heterogeneity of precipitation in the study area; Optimizing the first simulation model through the spatial structure matrix to obtain a second simulation model of precipitation data; The second simulation model of the precipitation data is dynamically updated in real time by using the sampling point data acquired in real time, and the second simulation model of the precipitation data is solved to obtain a simulation result of the precipitation data. 2. The precipitation spatial distribution simulation method taking into account spatial heterogeneity and real-time data updating according to claim 1 is characterized in that the first simulation model of precipitation data is constructed based on the influencing factor matrix in combination with the high-precision surface modeling HASM method, specifically: Based on the influencing factor matrix, a regression constraint equation is constructed using a multiple regression method; The regression constraint equation is used to convert the algebraic solution equation group of HASM into a constrained least squares problem to obtain the first simulation model of the precipitation data. 3. The precipitation spatial distribution simulation method taking into account spatial heterogeneity and real-time data updating according to claim 2 is characterized in that the first simulation model of the precipitation data is:

,

, b is the coefficient matrix of the algebraic solution equation group of HASM, X is the matrix composed of the subdivided grid points of the study area, G ^-1 is the inverse matrix of the coefficient matrix of the regression constraint equation, and F is the influencing factor matrix. 4. The precipitation spatial distribution simulation method taking into account spatial heterogeneity and real-time data updating according to claim 3 is characterized in that the spatial structure matrix of precipitation data is constructed by using the original remote sensing precipitation data as the precipitation background field, specifically: The original remote sensing precipitation data is used as a precipitation background field, and a characteristic matrix corresponding to the original remote sensing precipitation data is calculated using an eigenvector decomposition method; Calculate the mean of each column vector of the feature matrix, and subtract the corresponding mean from each column vector to obtain a difference matrix; The covariance matrix of the difference matrix is calculated as the spatial structure matrix of the precipitation data. 5. The precipitation spatial distribution simulation method taking into account spatial heterogeneity and real-time data updating according to claim 4, characterized in that the second simulation model of precipitation data is:

,

, b is the coefficient matrix of the algebraic solution equation group of HASM, X is the matrix composed of the subdivided grid points of the study area, G ^-1 is the inverse matrix of the coefficient matrix of the regression constraint equation, F is the influencing factor matrix, and M is the spatial structure matrix of the precipitation data. 6. The precipitation spatial distribution simulation method taking into account spatial heterogeneity and real-time data updating according to claim 1 is characterized in that the second simulation model of the precipitation data is dynamically updated in real time using the sampling point data obtained in real time, specifically: According to the original sampling points obtained in advance, the study area is meshed, and based on Taylor expansion, a sampling matrix and a sampling equation of HASM are constructed; The sampling matrix is dynamically updated according to the sampling point data acquired in real time, and the updated sampling matrix is dynamically decomposed to dynamically update the second simulation model of the precipitation data in real time. 7. The precipitation spatial distribution simulation method taking into account spatial heterogeneity and real-time data updating according to claim 6 is characterized in that the sampling matrix is dynamically updated according to the sampling point data obtained in real time, specifically: If the sampling points are increased dynamically, and the real-time sampling points fall on the kth subdivision grid of the study area, the original sampling matrix is pre-multiplied by the permutation matrix

, so as to convert the original sampling matrix into a form in which the sampling point data obtained in real time are added as new rows, as an updated sampling matrix; wherein, I is the unit matrix, and m is the number of sampling points in the original sampling matrix; If the sampling points are dynamically reduced, the sub-matrix of the sampling matrix after the sampling points are reduced is used as the updated sampling matrix. 8. The precipitation spatial distribution simulation method taking into account spatial heterogeneity and real-time data updating according to claim 6 is characterized in that the updated sampling matrix is dynamically decomposed, specifically: The original sampling matrix is decomposed into a double diagonal to obtain a decomposition matrix corresponding to the original sampling matrix; Based on the decomposition matrix corresponding to the original sampling matrix, the Givens transform is used to perform fast bidiagonal decomposition on the updated sampling matrix to obtain the decomposition matrix corresponding to the updated sampling matrix. 9. The precipitation spatial distribution simulation method taking into account spatial heterogeneity and real-time data updating according to claim 1 is characterized in that the second simulation model of precipitation data is solved by the following steps: The truncation method is adopted and Lagrange multipliers are introduced to transform the second simulation model of precipitation data into the corresponding augmented matrix; The augmented matrix is decomposed by using the double diagonal orthogonal decomposition strategy, and the recursive relationship between the approximate solution of the nth iteration and the approximate solution of the n+1th iteration in the second simulation model of precipitation data is constructed. Based on the minimization method of generalized cross validation, the estimation expression of Lagrange multiplier is given; The second simulation model of precipitation data is solved by combining the estimation expression of Lagrange multipliers with the recursive relationship between the approximate solution of the nth iteration and the approximate solution of the n+1th iteration in the process of solving the second simulation model of precipitation data. 10. The precipitation spatial distribution simulation method taking into account spatial heterogeneity and real-time data updating according to claim 1, characterized in that the environmental factor data at least includes: altitude, longitude, latitude, slope and leaf area index NDVI.

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