CN114417646B - High-dimensional heterogeneous precipitation data fusion method and system - Google Patents
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Abstract
The application relates to the technical field of methods or devices for identification by using electronic equipment, and provides a high-dimensional heterogeneous precipitation data fusion method and system, wherein the method comprises the following steps: obtaining a scale unifying operator according to the scale effect matrix, the scale transfer operator matrix and the precipitation data; then, obtaining a precipitation observation model based on a geographical weighted regression model according to the station observation data and precipitation influence factors; and finally, based on the scale unification 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. By this, the precipitation data advantage of abundant effectual utilization different sources not only can fuse the precipitation data of two kinds or three kinds of sources, can realize the data fusion of multisource multiscale to the precipitation data of different sources more than three, different data structure moreover to obtain high accuracy high spatial resolution precipitation data product.
Description
Technical Field
The application relates to the technical field of methods or devices for identification by using electronic equipment, in particular to a high-dimensional heterogeneous precipitation data fusion method and system.
Background
The precipitation data contain the space-time characteristic information of precipitation, acquire comparatively accurate precipitation data, and are the basis of works such as hydrology and water resource management, flood drought detection, geological disaster early warning and risk assessment. The common modes for acquiring precipitation data mainly comprise an interpolation method based on a ground meteorological observation station, an inversion method based on satellite remote sensing and a simulation method based on a physical process model. Due to the fact that precipitation has strong space-time heterogeneity, the precipitation space distribution information obtained by a single method has great uncertainty.
With the rapid development of meteorological observation systems, more and more data are acquired by using ground meteorological observation stations, radars, satellites and the like, and massive multi-source and multi-scale precipitation data are accumulated. Through a certain optimization criterion, precipitation data with different sources, different precisions, different time resolutions and space resolutions are integrated to obtain high-precision fine space-time scale precipitation data, which is one of the research difficulties in the field. In the prior art, a background field of precipitation data is usually constructed, and the background field is corrected by combining ground measured data to obtain precipitation fusion data, for example, in chinese patent application publication CN112699959A, a multi-source multi-scale precipitation data fusion method based on an energy functional model is disclosed. However, these methods only perform fusion based on two or three data products in site data or remote sensing data, and do not fully and effectively utilize the existing massive multi-source (more than three) multi-scale precipitation estimation products.
Therefore, there is a need to provide an improved solution to the above-mentioned deficiencies of the prior art.
Disclosure of Invention
The present application aims to provide a method and a system for fusing high-dimensional heterogeneous precipitation data, so as to solve or alleviate the problems in the prior art.
In order to achieve the above object, the present application provides the following technical solutions:
the application provides a high-dimensional heterogeneous precipitation data fusion method, which comprises 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;
s102, obtaining a precipitation observation model based on a geographical weighted regression model according to station observation data and the precipitation influence factors;
and 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.
Preferably, 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.
Preferably, 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 the weight matrix;
representing the first in said precipitation datajThe coordinates of the points are such that,jis a positive integer.
Preferably, according to the formula:
calculating the scale transfer operator matrix;
in the formula,
represents fromLTolMoment of scale transfer operatorArraying;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.
Preferably, after the spatial resolution of the first precipitation data is converted into the spatial resolution of the second precipitation data according to the precipitation average value and the spatial resolution improvement factor of each grid in the second precipitation data, the precipitation average value of each grid in the first precipitation data is calculated;
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.
Preferably, in step S101, 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;nindicating a random error.
Preferably, in step S102, according to the formula:
obtaining the precipitation observation model;
in the formula,yrepresenting the second precipitation data;Xrepresenting the optimized set of precipitation influencing factors;βthe regression coefficients are represented.
Preferably, in step S103, the multi-source multi-scale precipitation fusion model is:
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;Xa set of precipitation influencing factors representing the optimization,βthe regression coefficients are represented.
Preferably, in step S103, the fusing the high-dimensional heterogeneous precipitation data based on the multi-source multi-scale precipitation fusion model specifically includes:
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.
The embodiment of the present application still provides a high-dimensional heterogeneous precipitation data fusion system, and this system includes:
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;
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;
a model building unit configured to: and based on the scale unified 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.
Has the advantages that:
according to the method, a scale unified operator is obtained according to a scale effect matrix, a scale transfer operator matrix and precipitation data; then, obtaining a precipitation observation model based on a geographical weighted regression model according to the station observation data and precipitation influence factors; and finally, based on the scale unification 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. Scale conversion between the multisource and multiscale first precipitation data and the second precipitation data is achieved through the scale transfer operator matrix; therefore, the advantages of precipitation data from different sources are fully and effectively utilized, and the problem of unified scale is solved while fusion is carried out. The method can be used for fusing precipitation data from two or three sources, and can be used for realizing multi-source and multi-scale data fusion on precipitation data from more than three different sources and with different data structures so as to obtain a high-precision high-spatial-resolution precipitation data product.
Precipitation influence factors such as meteorology, geography and topography are added into the scale effect matrix, so that the constraint condition of the precipitation influence factors received in the precipitation data fusion process is fully considered in the precipitation data fusion process, and the multi-source multi-scale precipitation data are fused according to the spatial heterogeneity of the precipitation data spatial distribution, so that the precision of the precipitation data fusion result is improved.
Drawings
The accompanying drawings, which are incorporated in and constitute a part of this application, illustrate embodiments of the application and, together with the description, serve to explain the application and are not intended to limit the application. Wherein:
fig. 1 is a schematic flow diagram of a method for fusing high-dimensional heterogeneous precipitation data according to some embodiments of the present application;
FIG. 2 is a technical roadmap for a high-dimensional heterogeneous precipitation data fusion method provided in accordance with some embodiments of the present application;
fig. 3 is a schematic illustration 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 according to some embodiments of the present application.
Detailed Description
The present application will be described in detail below with reference to the embodiments with reference to the attached drawings. The various examples are provided by way of explanation of the application and are not limiting of 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 thereof. For instance, features illustrated or described as part of one embodiment, can be used with another embodiment to yield a still further embodiment. It is therefore intended that the present application cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.
In the prior art, a precipitation spatial distribution data product which can be used for decision analysis and has continuous spatial information is obtained based on station observation data, satellite remote sensing data and mode data which are respectively obtained by an interpolation method of a ground meteorological observation station, an inversion method of satellite remote sensing and a simulation method of a physical process model, and the essence of the precipitation spatial distribution data product is that precipitation spatial distribution information is obtained by a single method, however, the accuracy and the comprehensiveness of the precipitation spatial distribution information obtained by the single method cannot meet the requirements easily.
For example, for an interpolation method of a ground meteorological observation station, in the prior art, observation station data distributed in a dot-like and discrete manner is converted into planar and continuous precipitation data by means of an interpolation method, and the precipitation data at the positions of the observation stations are more accurate due to the influence of the number of the observation stations and the distribution positions of the observation stations, so that the accuracy of the precipitation data is greatly reduced along with the increase of the distance from the observation stations. In addition, the precipitation data obtained by the interpolation method based on the ground meteorological observation station has great uncertainty aiming at daily scale precipitation with strong spatial variability or precipitation in regions with complex terrain. The satellite remote sensing data has the characteristics of strong spatial continuity and capability of covering areas with complex geographic environments, but the satellite remote sensing data is easily influenced by the performance of a sensor, cloud layer properties during mapping and an inversion algorithm, so that uncertainty exists in precipitation data obtained by inverting the satellite remote sensing data. In addition, the satellite remote sensing data generally has lower spatial resolution, and cannot meet the requirements of fine-scale climate change, hydrological simulation and the like. Precipitation data obtained by a physical process model-based simulation method is also called mode data, the physical process model can well simulate factors such as a high-rise atmospheric field, near-ground climate characteristics, atmospheric circulation characteristics and the like, however, the method relates to various physical processes of modes such as surface evaporation, water vapor coordination in the atmosphere, convection cloud micro-physical processes and the like, a lot of challenges are brought to accurate precipitation simulation of the physical process model, and meanwhile, due to the reasons that the difference of initial fields, internal oscillation of a simulated climate system, difficult parameter determination and the like, the accuracy of the current physical process model in precipitation simulation is still to be improved. Due to the fact that precipitation space distribution information obtained by the existing single method has the problems, quantitative estimation on precipitation space data needs to be carried out by introducing multi-source precipitation data fusion.
At present, common fusion methods of multi-source precipitation data include an objective analysis method, a probability density method, an optimal weight method, a condition fusion method, a geostatistical method, a bayesian estimation method, a method based on machine learning, and the like. The basic ideas of the fusion methods are as follows: under certain premise assumption, a background field of precipitation data is constructed, and an optimization scheme is adopted to combine with ground measured data to correct the background field, so that the optimal estimation of the true distribution of precipitation is obtained. At present, most of research on multi-source precipitation fusion is based on that two or three precipitation data products in site and remote sensing data or mode results are fused by different methods, and the existing massive multi-source multi-scale precipitation data products are not fully and effectively utilized. In addition, in the prior art, a high-precision and high-spatial-resolution precipitation data set is obtained through a downscaling-fusion two-step method, and the process is complex and the steps are multiple.
The application provides a high-dimensional heterogeneous rainfall data fusion method, which integrates original rainfall data of different properties and different sources, such as observation sites, satellite remote sensing and mode data, into a quantitative model, and finally obtains fused rainfall data capable of accurately reflecting real distribution states of rainfall through complementary advantages and reasonable matching.
Exemplary method
FIG. 1 is a schematic flow diagram of a method of high-dimensional heterogeneous precipitation data fusion provided in accordance with some embodiments of the present application; FIG. 2 is a technical roadmap for a high-dimensional heterogeneous precipitation data fusion method provided in accordance with some embodiments of the present application; as shown in fig. 1 and 2, the high-dimensional heterogeneous precipitation data fusion method includes:
and 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 the high-dimensional heterogeneous precipitation data may also be referred to as multi-source, multi-scale precipitation data. In the precipitation data fusion process, precipitation data of different sources are expressed by a plurality of data dimensions, and the high dimension can be understood as precipitation data from a plurality of sources, further, the high dimension can be understood as more than three data sources, and the precipitation data of different sources have different data structures.
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.
In the embodiment of this application, precipitation data are first precipitation data, the second precipitation data that a plurality of sources are different, spatial resolution is different, and first precipitation data, second precipitation data can include website observation data, satellite remote sensing data and mode data, can understand ground, and first precipitation data, second precipitation data also can derive from other data acquisition modes. The spatial resolution of the second precipitation data is higher than that of the first precipitation data, for example, the first precipitation data may be satellite remote sensing data and mode data, and the second precipitation data may be site observation data.
In the embodiment of the application, the scale effect matrix is used for representing the constraint condition that the rainfall data is influenced by rainfall influence factors in the rainfall data fusion process. Researches show that the precipitation spatial distribution is influenced by various meteorological, geographical and topographic factors, and has strong spatial heterogeneity, so that the influence of the meteorological, geographical and topographic factors is fully considered in the process of fusing multi-source and multi-scale precipitation data, and a scale effect matrix is constructed.
In some alternative embodiments, the scale effect matrix is obtained by: screening precipitation influence factors based on a stepwise regression method to obtain an optimized precipitation influence factor set; obtaining a scale effect matrix based on the optimized spatial relationship heterogeneity between the precipitation influence factor set and the precipitation data; wherein, the precipitation influence factor represents that the spatial distribution of the precipitation data is influenced by meteorological, geographical and topographic factors.
In the embodiment of the present application, the precipitation influencing factors may include cloud amount, cloud optical thickness, cloud particle effective radius, cloud top temperature, cloud top pressure, cloud water path, potential altitude of 500hPa and 800hPa, air temperature, latent heat flux, sensible heat flux, short wave radiation, long wave radiation, relative humidity, maximum relative humidity, minimum relative humidity, specific humidity (ground, 500hPa and 800 hPa), sea level air pressure, wind speed, elevation, gradient, longitude, latitude, distance to a coastline, vegetation normalization index NDVI, and precipitation value of each grid and its peripheral grids in the first precipitation data, and the precipitation influencing factors are used for representing that the spatial distribution of the precipitation data is influenced by meteorological, geographical, and topographic factors.
When the model is applied specifically, the precipitation influence factors are expressed in a matrix mode, and each precipitation influence factor can be regarded as an explanatory variable of the multi-source multi-scale precipitation fusion model. And then screening precipitation influence factors based on a stepwise regression method to obtain an optimized precipitation influence factor set. The optimized precipitation influence factor set is obtained by screening the explanation variables (precipitation influence factors), so that the influence of the explanation variables on precipitation can be correctly expressed, the complexity of the model is reduced, and the calculated amount in the data fusion process is reduced.
In the embodiment of the application, a scale effect matrix is obtained based on the optimized heterogeneity of the spatial relationship between the precipitation influence factor set and the precipitation data, and is expressed by a formula (1), wherein the formula (1) is as follows:
in the formula,Mrepresenting a scale effect matrix;Xrepresenting an optimized precipitation influence factor set;
representing a weight matrix;
indicating the first in precipitation datajThe coordinates of the points are such that,jis a positive integer.
In the embodiment of the application, the scale transfer operator matrix is used for representing the spatial resolution conversion relation between the first precipitation data and the second precipitation data, and is used for carrying out scale unification on precipitation data of different scales in the multi-source multi-scale precipitation data fusion process. Here, when fusion is performed based on spatial resolution, the scale may be understood as spatial resolution; when blending is based on temporal resolution, scale may also be understood as temporal resolution. The following describes a construction process of a scale transfer operator matrix by taking fusion based on spatial resolution as an example.
In specific implementation, a plurality of images are obtained from precipitation data of different sources and different scales, and a signal processing method is adopted to improve the image quality and obtain an image with a resolution higher than that of an original input image so as to correspondingly obtain precipitation data with high precision and high spatial resolution. Here, the plurality of images are obtained from precipitation data of different sources and different scales, and are divided into first precipitation data and second precipitation data according to different spatial resolutions.
In some alternative embodiments, letLFor the spatial resolution of the first precipitation data,lfor the spatial resolution of the second precipitation data, then the following formula may be followed:
calculating a 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 the average value of the precipitation of each grid in the first precipitation data after the spatial resolution of the first precipitation data is converted into 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.
In other optional embodiments, the average precipitation value 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 precipitation value of each grid in the second precipitation data and the spatial resolution increasing factor.
The spatial resolution enhancement factor characterizes a number of meshes of each mesh size that include the second precipitation data in each mesh in the first precipitation data. According to the formula:
calculating to obtain a spatial resolution improvement factor;
in the formula,mfor spatial resolutionAn increase factor.
After the spatial resolution of the first precipitation data is converted into the spatial resolution of the second precipitation data according to the precipitation average value and the spatial resolution improvement factor of each grid in the second precipitation data, the precipitation average value of each grid in the first precipitation data can be represented by a formula (4), and the formula (4) is as follows:
in the formula,
indicating second precipitation datapThe water reduction value of each grid;
the rainfall data of different sources and different scales are regarded as a plurality of images, each image consists of a plurality of pixels (grids), each pixel is a square with equal side length, and the position of the pixel in the image can be represented by the row and column number of the point at the upper left corner of the square. The geographic space area corresponding to each pixel in different images is different in size, and the spatial resolution can be understood in a popular way as the proportional relation between the size of the pixel and the size of the geographic space area, for example, one pixel on an image represents that the ground area is
Then the spatial resolution of the image is 1 m. Illustratively, as shown in fig. 3, the bold lines represent the pixel boundaries of the first precipitation data, the thin lines represent the pixel boundaries of the second precipitation data, assuming that it is desired to convert the first precipitation data with a spatial resolution of 2.5m (i.e. 2.5m per pixel side length) to a spatial resolution of 1m (1 m per pixel side length),Lis the spatial resolution of the first precipitation data,ltaking the spatial resolution of the second precipitation data, 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，calculating the precipitation value of the pixel (I, J) in the first precipitation data according to the following steps: each one is expressed according to the formula (3)2.5m×2.5mIs subdivided into a plurality of picture elements1m×1mPicture elements, here each2.5m×2.5mIs divided into
An1m×1mAnd the image elements obtain sequence image elements of (i-1, j-2), (i +1, j-2) … … (i-1, j +1), (i, j +1) and (i +1, j +1), and the average value of the rainfall of each image element in the first rainfall data is calculated after the spatial resolution of the first rainfall data is converted into the spatial resolution of the second rainfall data according to a formula (4).
In some optional embodiments, in step S101, the scale unification operator is:
in the formula,grepresenting a vector obtained by expanding the first precipitation data by columns;Hrepresenting an overall degradation matrix;urepresenting a vector obtained by expanding the second precipitation data by columns;nindicating a random error.
Wherein the first precipitation data has a lower spatial resolution and the second precipitation data has a higher spatial resolution than the first precipitation data.
Data sequence for image corresponding to first precipitation datag k Represents:
in the formula,g k is shown askAn image corresponding to the first precipitation data;k=1，2，…，K；Kis the total number of the images,Ktaking a positive integer.
Will be provided withg k Expanding according to the column to obtain:
in the formula,
representing imagesg k The resulting vector is spread out by the columns,Nas an imageg k Dimension of the corresponding grid matrixg k Is composed ofN 1 Line ofN 2 An image composed of column pixels, then
。
Image corresponding to second precipitation datauAnd expressing that the second precipitation data is expanded according to columns to obtain:
in the formula,ua vector representing a column-wise expansion of the image corresponding to the second precipitation data,Mis composed ofuThe dimension of the grid matrix of (a).
Constructing imagesg k And imagesuThe unified operator of the scale between, expressed by formula (9), formula (9) is as follows:
in the formula,D k representing imagesg k And imagesuA scale transfer operator matrix in between;M k representing imagesg k And imagesuA scale effect matrix between;n k representing imagesg k Random error after scale transfer.
Order to
Then equation (9) can be written as:
for the scale conversion of multi-source precipitation data, the scale conversion can be expressed in a vector form:
in formula (11), let:
substituting the formula (12) into the formula (11) can obtain the scale unification operator of the multi-source precipitation data represented by the formula (5).
And constructing a scale unifying operator of the multi-source precipitation data according to the scale effect matrix, the scale transfer operator matrix and the precipitation data, unifying the multi-scale spatial data to the same spatial resolution, and laying a foundation for subsequent data fusion.
And S102, obtaining a precipitation observation model based on a geographical weighted regression model according to the station observation data and the precipitation influence factors.
In this application embodiment, website observation data can be the data that ground meteorological observation station gathered, is provided with multiple sensor that are used for meteorological observation in the ground meteorological observation station, can survey some phenomena in the meteorological element value and the free atmosphere that are close to the atmosphere on ground, can collect for example weather data such as temperature, atmospheric pressure, air humidity, wind direction wind speed, cloud, visibility, weather phenomenon, precipitation, evaporation, sunshine, snow depth, geothermal energy.
Due to the strong spatial heterogeneity of precipitation, in order to express the influence of factors such as geography, terrain, atmospheric circulation and the like on precipitation, in the embodiment of the application, based on a geography-weighted regression model, on the basis of fully depicting the spatial variability of precipitation, a precipitation observation model is constructed according to site observation data and precipitation influence factors, the model is expressed by a formula (13), and the formula (13) is as follows:
in the formula,yrepresenting the second precipitation data;Xrepresenting the optimized set of precipitation influencing factors;βthe regression coefficients are represented.
The observed value of the station observation data and the precipitation influence factor are used as the input of the geographical weighted regression model, the precipitation observation model is obtained through fitting, the model represents the correlation between the precipitation data and the precipitation influence factor,yand representing the fitting result of the precipitation observation model to the second precipitation data of any geographic position.
And 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.
In some alternative embodiments, combining formula (1) and formula (5), and taking 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:
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;Xa set of precipitation influencing factors representing the optimization,βthe regression coefficients are represented.
In some optional embodiments, the high-dimensional heterogeneous precipitation data is fused based on a multi-source multi-scale precipitation fusion model, 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.
In the formula (14), the multi-source multi-scale precipitation fusion model is an optimization model, and the optimization model is converted into a model without constraint conditions, so as to obtain a formula (15), wherein the formula (15) is as follows:
the optimization model is converted into a model without constraint conditions, so that the model solution is more convenient.
In the constraint-free model represented by equation (15),
referred to as regularization parameters, from which form it can be seen that they belong toL 2 And (4) norm. In the examples of this application, use is made ofL 1 Norm replacement in constraint termL 2 Norm, then the constraint-free model of equation (15) can be further written as equation (16), equation (16) is as follows:
by mixingL 1 Norm replacement in constraint termL 2 The norm can better keep the image details of the precipitation data obtained after the scales are unified, the fusion result is prevented from being excessively smooth, and the precision of the precipitation data fusion result is improved.
In the embodiment of the application, high-dimensional heterogeneous precipitation data are used as input parameters of a multi-source multi-scale precipitation fusion model, and the formula (16) expressed by the method based on a split Bregman iteration method hasL 1 And solving the multi-source multi-scale rainfall fusion model of the norm to obtain fusion data of the high-dimensional heterogeneous rainfall data. The detailed process of solving is as follows:
due to the parametersαThere is no need to go to infinity,it can be set as a constant
Then equation (16) can be written as:
order to
Then equation (17) can be converted into an optimization model with constraint conditions, which is expressed by equation (18), and equation (18) is as follows:
converting equation (18) to a model without constraints, resulting in equation (19), equation (19) is as follows:
in thatu，dUnder the condition of fixed value, the formula (19) is iteratively solved by adopting the splitting Bregman, and the following results can be obtained:
wherein,ucan be obtained by Gaussian-Seidel iterative solution,dcan be derived from equation (21), equation (21) is as follows:
wherein,
。
in the equation set represented by the formula (20), the parametersβCan be obtained by a sensitivity test through the following steps:
in the sensitivity test, parameters were set individuallyβThe values of (A) are as follows: 1X 10-3，1×10-2，1×10-1，1，2，5，10，20，50，100，500，1000。
Operator for observing unified scale under different parameter values
And observation model constraints
To select the optimum parametersβThe value is obtained.
According toL-Calculating parameters by curve methodαThe specific calculation process is as follows: norm of solution respectively
Is a vertical coordinate, and is a vertical coordinate,
for abscissa, drawingL-The curves are, among others,L-the curvature of the curve is defined as:
in the formula,
representXThe first derivative of (a);
to representXThe second derivative of (a);
to representYThe first derivative of (a);
to representYThe second derivative of (a).
Iterative solution is carried out on the multi-source multi-scale precipitation fusion model by a split Bregman iterative method, and solution containingL 1 And the extreme value problem of the norm improves the resolving efficiency.
In this embodiment of the application, high-dimensional heterogeneous precipitation data can include: IMERG precipitation products, GsMAP data, ERA5 data, CFSv2 data, CMORPH data, APHRODITE data, PERSIANN data and national 2400 ground meteorological station observation data. After fusing high-dimensional heterogeneous precipitation data based on the multi-source multi-scale precipitation fusion model, the method further comprises the following steps:
high-dimensional heterogeneous precipitation data are fused based on a multi-source multi-scale precipitation fusion model, and national 2010-2020 year-round day-by-day precipitation spatial distribution data are obtained.
And then, taking the fusion data of the high-dimensional heterogeneous rainfall data and the existing data sources as input parameters of a SWAT (water-wave analysis) hydrological model, and performing space-time scale precision comparison verification by combining other parameters and a Taylor diagram obtained by analyzing the SWAT hydrological model, wherein the existing data sources can be rainfall fusion data products (CMPA _ Daily for short) inverted by CMORPH satellites or multisource set weight rainfall products (MSWEP for short).
In summary, in the present application, the scale unification operator is obtained according to the scale effect matrix, the scale transfer operator matrix, and the precipitation data; then, obtaining a precipitation observation model based on a geographical weighted regression model according to the station observation data and precipitation influence factors; and finally, based on the scale unification 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. Scale conversion between the multi-source multi-scale first precipitation data and the second precipitation data is achieved through the scale transfer operator matrix; therefore, the advantages of precipitation data from different sources are fully and effectively utilized, and the problem of unified scale is solved while fusion is carried out. The method can be used for fusing precipitation data of two or three sources, and can be used for realizing multi-source and multi-scale data fusion of precipitation data of more than three different sources and different data structures so as to obtain a high-precision high-spatial-resolution precipitation data product.
Precipitation influence factors such as meteorology, geography and topography are added into the scale effect matrix, so that the constraint condition of the precipitation influence factors received in the precipitation data fusion process is fully considered in the precipitation data fusion process, and the multi-source multi-scale precipitation data are fused according to the spatial heterogeneity of the precipitation data spatial distribution, so that the precision of the precipitation data fusion result is improved.
The method combines the multidisciplinary research thinking, fully exerts the advantages of more different data sources, researches the effective fusion method of multisource and multiscale precipitation data to obtain precipitation space distribution information with high space-time resolution and small uncertainty, is beneficial to enriching and developing the current theoretical method framework of precipitation simulation, can provide effective data support for smooth implementation of regional disaster prevention and reduction, reasonable development and utilization of water resources, climate change evaluation and the like, and can also provide method reference for fusion research of other geographic environment variables.
Exemplary System
Fig. 4 is a schematic structural diagram of a high-dimensional heterogeneous precipitation data fusion system 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, a constraint construction unit 402, and a model construction unit 403, wherein:
the scale unification unit 401 is 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.
The constraint building unit 402 is configured to: and obtaining a precipitation observation model based on a geographical weighted regression model according to the station observation data and the precipitation influence factors.
The model construction unit 403 is configured to: and based on the scale unified 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.
The high-dimensional heterogeneous precipitation data fusion system provided by the embodiment of the application can realize the steps and the flows of the high-dimensional heterogeneous precipitation data fusion method of any one of the embodiments, achieves the same technical effect, and is not repeated one by one.
The above description is only a preferred embodiment of the present application and is not intended to limit the present application, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like made within the spirit and principle of the present application shall be included in the protection scope of the present 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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