CN114417646B - A high-dimensional heterogeneous precipitation data fusion method and system - Google Patents

Abstract

The present application relates to the technical field of identification methods or apparatuses using electronic equipment, and provides a high-dimensional heterogeneous precipitation data fusion method and system. The method includes: obtaining a scale according to a scale effect matrix, a scale transfer operator matrix, and precipitation data. Then, according to the station observation data and precipitation influencing factors, the precipitation observation model is obtained based on the geographically weighted regression model; finally, based on the scale unification operator, the multi-source and multi-scale precipitation fusion model is obtained with the precipitation observation model as the constraint term , and based on the multi-source and multi-scale precipitation fusion model to fuse high-dimensional heterogeneous precipitation data. In this way, the advantages of precipitation data from different sources can be fully and effectively utilized, which can not only fuse precipitation data from two or three sources, but also realize multi-source and multi-scale precipitation data from more than three different sources and different data structures. Data fusion to obtain high-precision high-spatial-resolution precipitation data products.

Description

A high-dimensional heterogeneous precipitation data fusion method and system

technical field

The present application relates to the technical field of methods or apparatuses for identification using electronic equipment, and in particular, to a method and system for fusion of high-dimensional heterogeneous precipitation data.

Background technique

Precipitation data contains information about the temporal and spatial characteristics of precipitation, and obtaining more accurate precipitation data is the basis for hydrological water resources management, flood and drought detection, geological disaster warning and risk assessment. The methods commonly used to obtain precipitation data mainly include interpolation methods based on ground meteorological observation stations, inversion methods based on satellite remote sensing, and simulation methods based on physical process models. Due to the strong temporal and spatial heterogeneity of precipitation, the spatial distribution information of precipitation obtained by a single method has great uncertainty.

With the rapid development of meteorological observation systems, more and more data are obtained from ground-based meteorological observation stations, radars and satellites, and massive multi-source and multi-scale precipitation data have been accumulated. It is one of the research difficulties in this field to integrate precipitation data from different sources, different precisions, and different temporal and spatial resolutions to obtain high-precision, fine temporal-spatial-scale precipitation data through certain optimization criteria. In the related art, the precipitation fusion data is usually obtained by constructing a background field of precipitation data and correcting the background field in combination with ground measured data. Scale precipitation data fusion method. This method fuses the precipitation products retrieved by the CMORPH satellite with the station data by constructing an energy functional model, and obtains the precipitation data fusion results. However, these methods are only based on the fusion of two or three data products in station data or remote sensing data, and do not fully and effectively utilize the current massive multi-source (more than three) multi-scale precipitation estimation products.

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

SUMMARY OF THE INVENTION

The purpose of the present application is to provide a high-dimensional heterogeneous precipitation data fusion method and system, so as to solve or alleviate the above-mentioned problems in the prior art.

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

The present application provides a high-dimensional heterogeneous precipitation data fusion method, which includes:

Step S101: Obtain a scale unification operator according to the scale effect matrix, the scale transfer operator matrix, and the precipitation data; wherein the precipitation data includes a plurality of first precipitation data and second precipitation data with different sources and different spatial resolutions , and the spatial resolution of the second precipitation data is higher than the spatial resolution of the first precipitation data; the scale effect matrix is used to represent that the precipitation data is constrained by precipitation influencing factors in the process of precipitation data fusion ; The scale transfer operator matrix is used to characterize the spatial resolution conversion relationship between the first precipitation data and the second precipitation data;

Step S102, obtaining a precipitation observation model based on the site observation data, the precipitation influencing factors, and a geographically weighted regression model;

Step S103: Based on the scale unification operator and taking the precipitation observation model as a constraint term, a multi-source and multi-scale precipitation fusion model is obtained, and high-dimensional heterogeneous precipitation data is fused based on the multi-source and multi-scale precipitation fusion model. .

Preferably, in step S101, the scale effect matrix is obtained by the following steps:

Based on the stepwise regression method, the precipitation influencing factors are screened to obtain an optimized set of precipitation influencing factors;

obtaining the scale effect matrix based on the spatial relationship heterogeneity between the optimized set of precipitation influencing factors and the precipitation data;

The precipitation influencing factor indicates that the spatial distribution of the precipitation data is influenced by meteorological, geographical and topographical factors.

Preferably, according to the formula:

calculating the scale effects matrix;

表示所述权重矩阵；

表示所述降水数据中第j个点的坐标，j为正整数。In the formula, M represents the scale effect matrix; X represents the optimized set of precipitation influencing factors;

represents the weight matrix;

Indicates the coordinate of the jth point in the precipitation data, where j is a positive integer.

Preferably, according to the formula:

calculating the scale transfer operator matrix;

表示从L到l的尺度转移算子矩阵；L表示所述第一降水数据的空间分辨率；l表示所述第二降水数据的空间分辨率；Y _L 表示将所述第一降水数据的空间分辨率转换为所述第二降水数据的空间分辨率后，所述第一降水数据中每一个网格的降水平均值；y _l 表示所述第二降水数据中每一个网格的降水平均值。In the formula,

represents the scale transfer operator matrix from L to l ; L represents the spatial resolution of the first precipitation data; l represents the spatial resolution of the second precipitation data; Y _L represents the spatial resolution of the first precipitation data After the resolution is converted to the spatial resolution of the second precipitation data, the precipitation average value of each grid in the first precipitation data; y _l represents the precipitation average value of each grid in the second precipitation data .

Preferably, according to the precipitation average value and the spatial resolution improvement factor of each grid in the second precipitation data, after calculating the spatial resolution of the first precipitation data converted to the spatial resolution of the second precipitation data , the average precipitation of each grid in the first precipitation data;

Wherein, the spatial resolution improvement factor represents the number of grids in each grid of the first precipitation data including each grid size of the second precipitation data.

Preferably, in step S101, the scale unification operator is:

In the formula, g represents the vector obtained by the column expansion of the first precipitation data; H represents the overall degradation matrix; u represents the vector obtained by the column expansion of the second precipitation data; n represents the random error.

Preferably, in step S102, according to the formula:

obtaining the precipitation observation model;

In the formula, y represents the second precipitation data; X represents the optimized set of precipitation influencing factors; β represents a regression coefficient.

Preferably, in step S103, the multi-source multi-scale precipitation fusion model is:

In the formula, g represents the vector obtained by the column expansion of the first precipitation data; H represents the overall degradation matrix; u represents the vector obtained by the column expansion of the second precipitation data; X represents the optimized set of precipitation influencing factors, β represents Regression coefficients.

Preferably, in step S103, the fusion of high-dimensional heterogeneous precipitation data based on the multi-source multi-scale precipitation fusion model is specifically:

Taking the high-dimensional heterogeneous precipitation data as the input parameters of the multi-source and multi-scale precipitation fusion model, the multi-source and multi-scale precipitation fusion model is solved based on the split Bregman iteration method, and the fusion of high-dimensional heterogeneous precipitation data is obtained. data.

The embodiment of the present application also provides a high-dimensional heterogeneous precipitation data fusion system, the system includes:

The scale unification unit is configured to: obtain a scale unification operator according to the scale effect matrix, the scale transfer operator matrix, and the precipitation data; wherein, the precipitation data includes the first precipitation data with different data sources and different spatial resolutions, and the first precipitation data with different spatial resolutions. 2. Precipitation data, and the spatial resolution of the second precipitation data is higher than the spatial resolution of the first precipitation data; the scale effect matrix is used to represent the precipitation data in the process of precipitation data fusion. The precipitation influence factors constraints; the scale transfer operator matrix is used to represent the spatial resolution conversion relationship between the first precipitation data and the second precipitation data;

A constraint building unit, configured to: obtain a precipitation observation model based on the site observation data, the precipitation influencing factors, and a geographically weighted regression model;

The model building unit is configured to: based on the scale unification operator, taking the precipitation observation model as a constraint term, to obtain a multi-source multi-scale precipitation fusion model, and based on the multi-source multi-scale precipitation fusion model for high-dimensional heterogeneous Fusion of precipitation data.

Beneficial effects:

In this application, the scale unification operator is obtained according to the scale effect matrix, the scale transfer operator matrix, and the precipitation data; then, the precipitation observation model is obtained based on the site observation data, the precipitation influencing factors, and the geographically weighted regression model; finally, based on the The scale unification operator takes the precipitation observation model as the constraint term to obtain a multi-source and multi-scale precipitation fusion model, and fuses high-dimensional heterogeneous precipitation data based on the multi-source and multi-scale precipitation fusion model. Through the scale transfer operator matrix, the scale conversion between the multi-source and multi-scale first precipitation data and the second precipitation data is realized; thus, the advantages of precipitation data from different sources are fully and effectively utilized, and the problem of scale unification is solved while merging. This method can not only fuse precipitation data from two or three sources, but also realize multi-source and multi-scale data fusion of precipitation data from more than three different sources and different data structures to obtain high-precision and high-spatial-resolution precipitation. data product.

By adding meteorology, geography, terrain and other precipitation influencing factors into the scale effect matrix, in the process of precipitation data fusion, the constraints of precipitation influencing factors in the process of precipitation data fusion are fully considered, and according to the spatial heterogeneity of precipitation data spatial distribution Fusion of multi-source and multi-scale precipitation data to improve the accuracy of precipitation data fusion results.

Description of drawings

The accompanying drawings that form a part of the present application are used to provide further understanding of the present application, and the schematic embodiments and descriptions of the present application are used to explain the present application and do not constitute improper limitations on the present application. in:

1 is a schematic flowchart of a high-dimensional heterogeneous precipitation data fusion method provided according to some embodiments of the present application;

2 is a technical roadmap of a high-dimensional heterogeneous precipitation data fusion method provided according to some embodiments of the present application;

3 is a schematic diagram of a technical principle of spatial resolution conversion provided according to some embodiments of the present application;

FIG. 4 is a schematic structural diagram of a high-dimensional heterogeneous precipitation data fusion system provided according to some embodiments of the present application.

Detailed ways

The present application will be described in detail below with reference to the accompanying drawings and in conjunction with the embodiments. The various examples are provided by way of explanation of the application and do not limit the application. In fact, 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 yet another embodiment. Therefore, it is intended that this application cover such modifications and variations as come within the scope of the appended claims and their equivalents.

In the prior art, the station observation data, satellite remote sensing data and model data are usually obtained based on the interpolation method of the ground meteorological observation station, the inversion method of satellite remote sensing and the simulation method of the physical process model, respectively. The essence of the precipitation spatial distribution data product of continuous spatial information relies on a single method to obtain the precipitation spatial distribution information. However, the accuracy and comprehensiveness of the precipitation spatial distribution information obtained by a single method cannot meet the needs.

For example, for the interpolation method of surface meteorological observation stations, the existing technology converts point-like and discretely distributed observation station data into planar and continuous precipitation data by means of interpolation method, which is affected by the number of observation stations and the distribution positions of observation stations. As a result, the precipitation data at the location of the observation station is more accurate, and the accuracy of the precipitation data decreases greatly with the increase of the distance from the observation station. In addition, for daily-scale precipitation with strong spatial variability or precipitation in areas with complex terrain, the use of interpolation methods based on surface meteorological observation stations to obtain precipitation data has great uncertainty. Satellite remote sensing data has the characteristics of strong spatial continuity and can cover areas with complex geographical environment. However, satellite remote sensing data is easily affected by the performance of sensors, the nature of cloud layers during mapping, and the inversion algorithm, which makes the inversion of satellite remote sensing data. Precipitation data is subject to uncertainty. In addition, satellite remote sensing data usually have low spatial resolution, which cannot meet the needs of fine-scale climate change and hydrological simulation. The precipitation data obtained by the simulation method based on the physical process model is also called model data. The physical process model can better simulate factors such as the upper atmospheric field, near-surface climate characteristics and atmospheric circulation characteristics. However, this method involves many physical processes of the model. , such as surface evaporation, water vapor in the atmosphere, convective cloud microphysical processes, etc., which bring many challenges for the physical process model to accurately simulate precipitation. For reasons such as determination, the accuracy of the current physical process model for simulating precipitation needs to be improved. It is precisely because of the above-mentioned problems in the precipitation spatial distribution information obtained by the existing single method, it is necessary to introduce multi-source precipitation data fusion to quantitatively estimate the precipitation spatial data.

At present, common fusion methods of multi-source precipitation data include objective analysis method, probability density method, optimal weight method, conditional fusion method, geostatistical method, Bayesian estimation method and machine learning-based method. The basic idea of these fusion methods is: under certain premise assumptions, by constructing the background field of precipitation data, using the optimization scheme combined with the ground measured data to correct the background field, and then obtain the optimal estimate of the real distribution of precipitation. At present, most of the research on multi-source precipitation fusion is based on two or three precipitation data products in the station and remote sensing data or model results using different methods for fusion, and does not fully and effectively utilize the current massive multi-source and multi-scale precipitation data. product. In addition, in the prior art, a precipitation data set with high precision and high spatial resolution is obtained by a downscaling-fusion two-step method, which is a complicated process and numerous steps.

This application proposes a high-dimensional heterogeneous precipitation data fusion method, which integrates the original precipitation data of different natures and sources, such as observation sites, satellite remote sensing, and model data, into a quantitative model. The fused precipitation data reflecting the true distribution of precipitation.

Exemplary method

1 is a schematic flowchart of a high-dimensional heterogeneous precipitation data fusion method provided according to some embodiments of the present application; FIG. 2 is a technical roadmap of a high-dimensional heterogeneous precipitation data fusion method provided according to some embodiments of the present application; As shown in Figure 1 and Figure 2, the high-dimensional heterogeneous precipitation data fusion method includes:

Step S101 , obtaining a scale unification operator according to the scale effect matrix, the scale transfer operator matrix, and the precipitation data.

It should be noted that high-dimensional heterogeneous precipitation data can also be called multi-source and multi-scale precipitation data. In the process of precipitation data fusion, precipitation data from different sources is expressed by multiple data dimensions. High-dimensionality can be understood as precipitation data from multiple sources. Further, high-dimensionality can be understood as more than three data sources, and different sources. The data structure of the precipitation data is also different.

The precipitation data includes a plurality of first precipitation data and second precipitation data with different sources and different spatial resolutions, and the spatial resolution of the second precipitation data is higher than the spatial resolution of the first precipitation data The scale effect matrix is used to characterize the condition that the precipitation data is constrained by precipitation influencing factors in the process of precipitation data fusion; the scale transfer operator matrix is used to characterize the relationship between the first precipitation data and the second precipitation data The spatial resolution conversion relationship.

In the embodiment of the present application, the precipitation data is a plurality of first and second precipitation data from different sources and different spatial resolutions. The first and second precipitation data may include site observation data, satellite remote sensing data, and model data. , it can be understood that the first precipitation data and the second precipitation data may also be derived from other data acquisition methods. The spatial resolution of the second precipitation data is higher than the spatial resolution of the first precipitation data. For example, the first precipitation data may be satellite remote sensing data or model data, and the second precipitation data may be site observation data.

In the embodiment of the present application, the scale effect matrix is used to represent the condition that the precipitation data is constrained by the precipitation influencing factors in the process of precipitation data fusion. The study found that the spatial distribution of precipitation is affected by a variety of meteorological, geographical, and topographical factors, and has strong spatial heterogeneity. Therefore, in the process of fusing multi-source and multi-scale precipitation data, the The influence of geographical and topographical factors is used to construct a scale effect matrix.

In some optional embodiments, the scale effect matrix is obtained by the following steps: screening precipitation influencing factors based on a stepwise regression method to obtain an optimized set of precipitation influencing factors; based on the space between the optimized set of precipitation influencing factors and precipitation data The relationship heterogeneity is obtained, and the scale effect matrix is obtained; among them, the precipitation influencing factors represent that the spatial distribution of precipitation data is affected by meteorological, geographical and topographical factors.

In the embodiment of the present application, the factors affecting precipitation may include cloud amount, cloud optical thickness, cloud particle effective radius, cloud top temperature, cloud top pressure, cloud water path, 500hPa and 800hPa geopotential heights, air temperature, latent heat flux, sensible heat flux amount, shortwave radiation, longwave radiation, relative humidity, maximum relative humidity, minimum relative humidity, specific humidity (ground, 500hPa and 800hPa), sea level pressure, wind speed, elevation, slope, longitude, latitude, distance to coastline, vegetation return The unification index NDVI, the precipitation value of each grid and its surrounding grids in the first precipitation data, and the above-mentioned precipitation influencing factors are used to characterize that the spatial distribution of the precipitation data is affected by meteorological, geographical, and topographical factors.

In specific applications, the above-mentioned precipitation influencing factors are first expressed in a matrix form, and each precipitation influencing factor can be regarded as an explanatory variable of a multi-source and multi-scale precipitation fusion model. Then, based on the stepwise regression method, the precipitation influencing factors are screened to obtain an optimized set of precipitation influencing factors. The optimized set of precipitation influencing factors is obtained by screening explanatory variables (precipitation influencing factors), which reduces the complexity of the model and reduces the amount of calculation in the process of data fusion while ensuring that the explanatory variables can correctly express their influence on precipitation.

In the embodiment of the present application, based on the spatial relationship heterogeneity between the optimized set of precipitation influencing factors and precipitation data, a scale effect matrix is obtained, which is expressed by formula (1), and formula (1) is as follows:

表示权重矩阵；

表示降水数据中第j个点的坐标，j为正整数。In the formula, M represents the scale effect matrix; X represents the optimized set of precipitation influencing factors;

represents the weight matrix;

Indicates the coordinate of the jth point in the precipitation data, where j is a positive integer.

In the embodiment of the present application, the scale transfer operator matrix is used to represent the spatial resolution conversion relationship between the first precipitation data and the second precipitation data, and is used to compare the precipitation data of different scales in the process of multi-source and multi-scale precipitation data fusion. Unify the scale. Here, when fusion is performed based on spatial resolution, scale can be understood as spatial resolution; when fusion is performed based on temporal resolution, scale can also be understood as temporal resolution. The following takes the fusion based on spatial resolution as an example to introduce the construction process of the scale transfer operator matrix.

In the specific implementation, the precipitation data from different sources and different scales are seen in multiple images, and the signal processing method is used to obtain images with higher resolution than the original input image while improving the image quality. Resolution of precipitation data. Here, precipitation data from different sources and different scales are seen in multiple images, which are divided into first precipitation data and second precipitation data according to different spatial resolutions.

In some optional embodiments, let L be the spatial resolution of the first precipitation data, and l be the spatial resolution of the second precipitation data, then the formula can be:

（2）

(2)

Calculate the scale transfer operator matrix;

表示从L到l的尺度转移算子矩阵；L表示第一降水数据的空间分辨率；l表示第二降水数据的空间分辨率；Y _L 表示将第一降水数据的空间分辨率转换为第二降水数据的空间分辨率后，第一降水数据中每一个网格的降水平均值；y _l 表示第二降水数据中每一个网格的降水平均值。In the formula,

represents the scale transfer operator matrix from L to l ; L represents the spatial resolution of the first precipitation data; l represents the spatial resolution of the second precipitation data; Y _L represents the conversion of the spatial resolution of the first precipitation data to the second After the spatial resolution of the precipitation data, the precipitation average of each grid in the first precipitation data; y _l represents the precipitation average of each grid in the second precipitation data.

In some other optional embodiments, according to the precipitation average value and the spatial resolution improvement factor of each grid in the second precipitation data, after calculating the spatial resolution of the first precipitation data converted to the spatial resolution of the second precipitation data , the average precipitation for each grid in the first precipitation data.

The spatial resolution improvement factor represents the number of grids of each grid size containing the second precipitation data in each grid of the first precipitation data. According to the formula:

Calculate the spatial resolution improvement factor;

In the formula, m is the spatial resolution improvement factor.

According to the precipitation average value and the spatial resolution improvement factor of each grid in the second precipitation data, after calculating the spatial resolution of the first precipitation data and converting it to the spatial resolution of the second precipitation data, each grid in the first precipitation data The average precipitation of the grid can be expressed by formula (4), and formula (4) is as follows:

（4）

(4)

表示第二降水数据中第p个网格的降水值；In the formula,

represents the precipitation value of the pth grid in the second precipitation data;

的区域，则该图像的空间分辨率是1m。示例性地，如图3所示，粗线表示第一降水数据的像元边界，细线表示第二降水数据的像元边界，假设需要将空间分辨率为2.5m的第一降水数据（即每个像元边长2.5m），转换为空间分辨率为1m（每个像元边长1m），L为第一降水数据的空间分辨率，l为第二降水数据的空间分辨率，以计算第一降水数据中像元(I，J)的降水值为例，L=2.5m，l=1m，则计算第一降水数据中像元(I，J)的降水值是步骤如下：按照公式（3）将每一个2.5m×2.5m的像元重新划分为多个1m×1m像元，这里，将每一个2.5m×2.5m的像元划分为

个1m×1m像元，得到(i-1，j-2)、(i，j-2)、(i+1，j-2)……(i-1，j+1)、(i，j+1)、(i+1，j+1)序列像元，并按照公式（4）计算从第一降水数据的空间分辨率转换为第二降水数据的空间分辨率后，第一降水数据中每一个像元的降水平均值。Taking precipitation data from different sources and different scales as multiple images, each image consists of multiple pixels (grids), and each pixel is a square with equal side lengths. The row and column numbers indicate its position in the image. The geographic space area corresponding to each pixel in different images is different, and the spatial resolution can be generally understood as the proportional relationship between the size of the pixel and the size of the geographic space. For example, a pixel on the image indicates that the area on the ground is

area, the spatial resolution of the image is 1m. Exemplarily, as shown in Figure 3, the thick line represents the pixel boundary of the first precipitation data, and the thin line represents the pixel boundary of the second precipitation data. It is assumed that the first precipitation data with a spatial resolution of 2.5m needs to be The side length of each pixel is 2.5m), which is converted into a spatial resolution of 1m (the side length of each pixel is 1m), where L is the spatial resolution of the first precipitation data, l is the spatial resolution of the second precipitation data, and Taking the calculation of the precipitation value of the pixel (I, J) in the first precipitation data as an example, L=2.5m, l=1m, then the steps to calculate the precipitation value of the pixel (I, J) in the first precipitation data are as follows: Formula (3) divides each 2.5m×2.5m pixel into multiple 1m×1m pixels. Here, each 2.5m×2.5m pixel is divided into

1m×1m pixels, get (i-1, j-2), (i, j-2), (i+1, j-2)...(i-1, j+1), (i, j+1), (i+1, j+1) sequence pixels, and after converting from the spatial resolution of the first precipitation data to the spatial resolution of the second precipitation data according to formula (4), the first precipitation data The average precipitation for each pixel in .

In some optional embodiments, in step S101, the scale unification operator is:

（5）

(5)

In the formula, g is the vector obtained by column expansion of the first precipitation data; H is the overall degradation matrix; u is the vector obtained by column expansion of the second precipitation data; n is the random error.

The first precipitation data has a lower spatial resolution, and the second precipitation data has a higher spatial resolution than the first precipitation data.

The image corresponding to the first precipitation data is represented by the data sequence g _k :

（6）

(6)

In the formula, g _k represents the image corresponding to the k -th first precipitation data; k=1, 2, ..., K ; K is the total number of images, and K is a positive integer.

Expanding g _k by columns, we get:

（7）

(7)

表示图像g _k 按列展开得到的向量，N为图像g _k 对应的栅格矩阵的维度，设g _k 为由N ₁ 行N ₂ 列像元组成的图像，则

。In the formula,

Represents the vector obtained by expanding the image g _k by columns, N is the dimension of the grid matrix corresponding to the image g _k , and let g _k be an image composed of N ₁ row and N ₂ columns of pixels, then

.

The image corresponding to the second precipitation data is denoted by u , and the second precipitation data is expanded in columns to obtain:

（8）

(8)

In the formula, u represents the vector obtained by the column expansion of the image corresponding to the second precipitation data, and M is the dimension of the grid matrix of u .

The scale unification operator between the image g _k and the image u is constructed, which is expressed by formula (9), and formula (9) is as follows:

（9）

(9)

where D _k represents the scale transfer operator matrix between the image g _k and the image u ; M _k represents the scale effect matrix between the image g _k and the image u ; n _k represents the random error after the scale transfer of the image g _k .

，则公式（9）可以写为：make

, then formula (9) can be written as:

（10）

(10)

For the scale transformation of multi-source precipitation data, it can be expressed in vector form:

（11）

(11)

In formula (11), let:

（12）

(12)

Substituting formula (12) into formula (11) can obtain the scale unification operator of multi-source precipitation data represented by formula (5).

According to the scale effect matrix, scale transfer operator matrix, and precipitation data, a scale unification operator for multi-source precipitation data is constructed to unify multi-scale spatial data into the same spatial resolution, which lays the foundation for subsequent data fusion.

Step S102: Obtain a precipitation observation model based on the site observation data, the precipitation influencing factors, and a geographically weighted regression model.

In the embodiment of the present application, the site observation data may be data collected by a ground meteorological observation station. The ground meteorological observation station is provided with a variety of sensors for meteorological observation, which can detect the meteorological element values of the atmosphere near the ground and the free atmosphere. Some phenomena in the system can be observed, such as air temperature, air pressure, air humidity, wind direction and speed, clouds, visibility, weather phenomena, precipitation, evaporation, sunshine, snow depth, ground temperature and other meteorological data.

Due to the strong spatial heterogeneity of precipitation, in order to express the influence of factors such as geography, topography, and atmospheric circulation on precipitation, in the embodiment of the present application, based on the geographically weighted regression model, on the basis of fully characterizing the spatial variability of precipitation, according to the site The observation data and precipitation influencing factors are used to construct a precipitation observation model, which is expressed by formula (13), and formula (13) is as follows:

（13）

(13)

In the formula, y represents the second precipitation data; X represents the optimized set of precipitation influencing factors; β represents a regression coefficient.

Here, the observation value of the station observation data and the precipitation influencing factors are used as the input of the geographically weighted regression model, and the precipitation observation model is obtained by fitting. Fitting results to the second precipitation data for the geographic location.

Step S103: Based on the scale unification operator and taking the precipitation observation model as a constraint term, a multi-source and multi-scale precipitation fusion model is obtained, and high-dimensional heterogeneous precipitation data is fused based on the multi-source and multi-scale precipitation fusion model. .

In some optional embodiments, combining formula (1) and formula (5), and using the precipitation observation model as a constraint term, a multi-source multi-scale precipitation fusion model is obtained, which is expressed by formula (14), and formula (14) is as follows:

（14）

(14)

In the formula, g represents the vector obtained by the column expansion of the first precipitation data; H represents the overall degradation matrix; u represents the vector obtained by the column expansion of the second precipitation data; X represents the optimized set of precipitation influencing factors, β represents Regression coefficients.

In some optional embodiments, the high-dimensional heterogeneous precipitation data is fused based on a multi-source multi-scale precipitation fusion model, specifically: using the high-dimensional heterogeneous precipitation data as the input parameters of the multi-source multi-scale precipitation fusion model, based on splitting The Bregman iteration method solves the multi-source and multi-scale precipitation fusion model, and obtains the fusion data of high-dimensional heterogeneous precipitation data.

In formula (14), the multi-source and multi-scale precipitation fusion model is an optimization model, and the optimization model is transformed into a model without constraints, and formula (15) is obtained, and formula (15) is as follows:

（15）

(15)

By transforming the optimized model into a model without constraints, the model solution is made more convenient.

称为正则化参数，从该正则化参数形式可以看出，其属于L ² 范数。本申请实施例中，采用L ¹ 范数替换约束项中的L ² 范数，则公式（15）的不含约束条件的模型可以进一步写成公式（16），公式（16）如下：In the model without constraints expressed by Equation (15),

is called the regularization parameter, and it can be seen from the regularization parameter form that it belongs to the L ² norm. In the embodiment of the present application, the L ¹ norm is used to replace the L ² norm in the constraint term, and the model without constraints in formula (15) can be further written as formula (16), and formula (16) is as follows:

（16）

(16)

By replacing the L ¹ norm in the constraint term with the L ² norm, the image details of the precipitation data obtained after the unification of the scale can be better maintained, the fusion result can be prevented from being over-smoothed, and the accuracy of the precipitation data fusion result can be improved.

In the embodiment of the present application, the high-dimensional heterogeneous precipitation data is used as the input parameter of the multi-source multi-scale precipitation fusion model, and the multi-source multi-scale precipitation fusion with L ¹ norm expressed by formula (16) is based on the split Bregman iteration method. The model is solved to obtain the fusion data of high-dimensional heterogeneous precipitation data. The detailed process of solving is as follows:

，则公式（16）可以写为：Since the parameter α does not need to tend to infinity, it can be set as a constant, noting

, then formula (16) can be written as:

（17）

(17)

，则公式（17）可以转化为含有约束条件下的优化模型，用公式（18）表示，公式（18）如下：make

, then the formula (17) can be transformed into an optimization model with constraints, which is expressed by the formula (18), and the formula (18) is as follows:

（18）

(18)

Converting formula (18) into an unconstrained model, formula (19) is obtained, and formula (19) is as follows:

（19）

(19)

When the values of u and d are fixed, using split Bregman to iteratively solve formula (19), we can get:

（20）

(20)

Among them, u can be obtained by Gauss-Seidel iterative solution, d can be obtained by formula (21), formula (21) is as follows:

（21）

(twenty one)

。in,

.

In the equation system represented by formula (20), the parameter β can be obtained by the sensitivity experiment of the following steps:

In the sensitivity experiment, the values of parameter β were set as: 1×10 ^-3 , 1×10 ^-2 , 1×10 ^-1 , 1, 2, 5, 10, 20, 50, 100, 500, 1000.

和观测模型约束项

的变化，从而选择最优的参数β值。Observation scale unification operator under different parameter values

and observation model constraints

, so as to select the optimal parameter β value.

为纵坐标，

为横坐标，绘制L-曲线，其中，L-曲线的曲率定义为：Calculate the value of parameter α according to the L- curve method, and the specific calculation process is as follows:

is the vertical coordinate,

As the abscissa, draw an L- curve, where the curvature of the L- curve is defined as:

（22）

(twenty two)

表示X的一阶导数；

表示X的二阶导数；

表示Y的一阶导数；

表示Y的二阶导数。In the formula,

represents the first derivative of X ;

represents the second derivative of X ;

represents the first derivative of Y ;

represents the second derivative of Y.

The multi-source and multi-scale precipitation fusion model is iteratively solved by the split Bregman iteration method, which can solve the extreme value problem containing the L ¹ norm and improve the solution efficiency.

In the embodiment of the present application, the high-dimensional heterogeneous precipitation data may include: IMERG precipitation products, GsMAP data, ERA5 data, CFSv2 data, CMORPH data, APHRODITE data, PERSIANN data, and observation data from more than 2,400 surface meteorological stations across the country. After the high-dimensional heterogeneous precipitation data is fused based on the multi-source and multi-scale precipitation fusion model, it also includes:

Based on the multi-source and multi-scale precipitation fusion model, the high-dimensional heterogeneous precipitation data was fused to obtain the national daily precipitation spatial distribution data in the past ten years from 2010 to 2020.

Then, the fusion data of high-dimensional heterogeneous precipitation data and the existing data sources are used as the input parameters of the hydrological model SWAT, combined with other parameters and the Taylor plot obtained from the analysis of the SWAT hydrological model to compare and verify the accuracy of the spatiotemporal scale. Each data source can be a precipitation fusion data product (referred to as CMPA_Daily) retrieved by the CMORPH satellite, or a multi-source ensemble weighted precipitation product (referred to as MSWEP).

To sum up, in this application, the scale unification operator is obtained according to the scale effect matrix, the scale transfer operator matrix, and the precipitation data; then, the precipitation observation is obtained based on the site observation data, the precipitation influencing factors, and the geographically weighted regression model. Finally, based on the scale unification operator and the precipitation observation model as the constraint term, the multi-source and multi-scale precipitation fusion model is obtained, and the high-dimensional heterogeneous precipitation data is fused based on the multi-source and multi-scale precipitation fusion model. Through the scale transfer operator matrix, the scale conversion between the multi-source and multi-scale first precipitation data and the second precipitation data is realized; thus, the advantages of precipitation data from different sources are fully and effectively utilized, and the problem of scale unification is solved while merging. This method can not only fuse precipitation data from two or three sources, but also realize multi-source and multi-scale data fusion of precipitation data from more than three different sources and different data structures to obtain high-precision and high-spatial-resolution precipitation. data product.

By adding meteorology, geography, terrain and other precipitation influencing factors into the scale effect matrix, in the process of precipitation data fusion, the constraints of precipitation influencing factors in the process of precipitation data fusion are fully considered, and according to the spatial heterogeneity of precipitation data spatial distribution Fusion of multi-source and multi-scale precipitation data to improve the accuracy of precipitation data fusion results.

This application combines multidisciplinary research ideas, gives full play to the advantages of more different data sources, and studies the effective fusion method of multi-source and multi-scale precipitation data, so as to obtain precipitation spatial distribution information with high temporal and spatial resolution and small uncertainty, which will help In order to enrich and develop the current theoretical and methodological framework of precipitation simulation, it can provide effective data support for the smooth implementation of regional disaster prevention and mitigation, rational development and utilization of water resources, and climate change assessment, and can also provide method reference for the integration of other geographical environment variables. .

Exemplary System

FIG. 4 is a schematic structural diagram of a high-dimensional heterogeneous precipitation data fusion system provided according to some embodiments of the present application. As shown in FIG. 4 , the high-dimensional heterogeneous precipitation data fusion system includes: a scale unification unit 401 and a constraint construction unit 402 and model building unit 403, where:

The scale unification unit 401 is configured to: obtain a scale unification operator according to the scale effect matrix, the scale transfer operator matrix, and the precipitation data; wherein, the precipitation data includes the first precipitation data with different data sources and different spatial resolutions, and the first precipitation data with different spatial resolutions. 2. Precipitation data, and the spatial resolution of the second precipitation data is higher than the spatial resolution of the first precipitation data; the scale effect matrix is used to represent the precipitation data in the process of precipitation data fusion by precipitation influence factors The constraint condition of ; the scale transfer operator matrix is used to represent the spatial resolution conversion relationship between the first precipitation data and the second precipitation data.

The constraint construction unit 402 is configured to: obtain a precipitation observation model based on a geographically weighted regression model according to the site observation data and the precipitation influencing factors.

The model building unit 403 is configured to: based on the scale unification operator, take the precipitation observation model as a constraint, obtain a multi-source multi-scale precipitation fusion model, and based on the multi-source multi-scale precipitation fusion model for high-dimensional heterogeneous Fusion of precipitation data.

The high-dimensional heterogeneous precipitation data fusion system provided by the embodiment of the present application can implement the steps and processes of the high-dimensional heterogeneous precipitation data fusion method in any of the above embodiments, and achieve the same technical effect, which is not repeated here.

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

Claims (7)

1. A high-dimensional heterogeneous precipitation data fusion method is characterized by comprising the following steps:

s101, obtaining a scale unification operator according to the scale effect matrix, the scale transfer operator matrix and precipitation data; the rainfall data comprises a plurality of first rainfall data and second rainfall data which are different in source and spatial resolution, and the spatial resolution of the second rainfall data is higher than that of the first rainfall data; the scale effect matrix is used for representing the constraint condition of precipitation data influenced by precipitation influence factors in the precipitation data fusion process; the scale transfer operator matrix is used for representing a spatial resolution conversion relation between the first precipitation data and the second precipitation data;

wherein the scale unification operator is:

in the formula,ga vector representing the first precipitation data spread by columns;Hrepresenting an overall degradation matrix;ua vector representing the second precipitation data spread by columns;nrepresenting a random error;

s102, obtaining a precipitation observation model based on a geographical weighted regression model according to station observation data and the precipitation influence factors;

wherein the precipitation observation model is:

in the formula,yrepresenting the second precipitation data;Xrepresenting an optimized precipitation influence factor set;βrepresenting a regression coefficient;

step S103, based on the scale unification operator, obtaining a multi-source multi-scale precipitation fusion model by taking the precipitation observation model as a constraint item, and fusing high-dimensional heterogeneous precipitation data based on the multi-source multi-scale precipitation fusion model;

wherein, the multi-source multi-scale precipitation fusion model is as follows:

in the formula,ga vector representing the first precipitation data spread by columns;Hrepresenting an overall degradation matrix;ua vector obtained by expanding the second precipitation data according to columns is represented;Xrepresents an optimized set of precipitation influencing factors,βthe regression coefficients are represented.

2. The method for fusing high-dimensional heterogeneous precipitation data according to claim 1, wherein in step S101, the scale effect matrix is obtained by:

screening the precipitation influence factors based on a stepwise regression method to obtain an optimized precipitation influence factor set;

obtaining the scale effect matrix based on the spatial relationship heterogeneity between the optimized precipitation influence factor set and the precipitation data;

wherein the precipitation influencing factor represents that the spatial distribution of the precipitation data is influenced by meteorological, geographical and topographic factors.

3. The method of fusing high-dimensional heterogeneous precipitation data according to claim 2, wherein the method comprises, according to the formula:

calculating the scale effect matrix;

in the formula,Mrepresenting the scale effect matrix;Xrepresenting the optimized set of precipitation influencing factors;

representing a weight matrix;

representing the first in said precipitation datajThe coordinates of the points are such that,jis a positive integer.

4. The method of fusing high-dimensional heterogeneous precipitation data according to claim 1, wherein, according to the formula:

calculating the scale transfer operator matrix;

in the formula,

represents fromLTolThe scale transfer operator matrix of (2);La spatial resolution representing the first precipitation data;la spatial resolution representing the second precipitation data;Y _L representing an average value of precipitation for each grid in the first precipitation data after converting the spatial resolution of the first precipitation data to the spatial resolution of the second precipitation data;y _l an average value of precipitation for each of the grids in the second precipitation data is represented.

5. The method of claim 4, wherein the average value of the precipitation of each grid in the first precipitation data is calculated after the spatial resolution of the first precipitation data is converted into the spatial resolution of the second precipitation data according to the average value of the precipitation of each grid in the second precipitation data and a spatial resolution improvement factor;

and the spatial resolution improvement factor represents the number of grids of each grid size containing the second precipitation data in each grid in the first precipitation data.

6. The method according to claim 1, wherein in step S103, the fusing the high-dimensional heterogeneous precipitation data based on the multi-source multi-scale precipitation fusion model is specifically:

and solving the multi-source multi-scale precipitation fusion model based on a split Bregman iteration method by taking the high-dimensional heterogeneous precipitation data as input parameters of the multi-source multi-scale precipitation fusion model to obtain fusion data of the high-dimensional heterogeneous precipitation data.

7. A high-dimensional heterogeneous precipitation data fusion system, comprising:

a scale unifying unit configured to: obtaining a scale unifying operator according to the scale effect matrix, the scale transfer operator matrix and the precipitation data; the rainfall data comprises first rainfall data and second rainfall data which are different in data source and spatial resolution, and the spatial resolution of the second rainfall data is higher than that of the first rainfall data; the scale effect matrix is used for representing the constraint condition of precipitation data influenced by precipitation influence factors in the precipitation data fusion process; the scale transfer operator matrix is used for representing a spatial resolution conversion relation between the first precipitation data and the second precipitation data;

wherein the scale unification operator is:

in the formula,ga vector representing the first precipitation data spread by columns;Hrepresenting an overall degradation matrix;ua vector representing the second precipitation data spread by columns;nrepresenting a random error;

a constraint building unit configured to: obtaining a precipitation observation model based on a geographical weighted regression model according to the station observation data and the precipitation influence factors;

wherein the precipitation observation model is:

in the formula,yrepresenting the second precipitation data;Xrepresenting an optimized precipitation influence factor set;βrepresenting a regression coefficient;

a model building unit configured to: based on the scale unified operator, the precipitation observation model is used as a constraint item to obtain a multi-source multi-scale precipitation fusion model, and high-dimensional heterogeneous precipitation data is fused based on the multi-source multi-scale precipitation fusion model;

wherein, the multi-source multi-scale precipitation fusion model is as follows:

in the formula,ga vector representing the first precipitation data spread by columns;Hrepresenting an overall degradation matrix;urepresenting a vector obtained by expanding the second precipitation data by columns;Xrepresents an optimized set of precipitation influencing factors,βthe regression coefficients are represented.

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