CN114781501A - Multi-source precipitation fusion method based on principal component regression - Google Patents

Multi-source precipitation fusion method based on principal component regression Download PDF

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CN114781501A
CN114781501A CN202210377401.3A CN202210377401A CN114781501A CN 114781501 A CN114781501 A CN 114781501A CN 202210377401 A CN202210377401 A CN 202210377401A CN 114781501 A CN114781501 A CN 114781501A
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陈韬
林锦
王会容
柳鹏
李士军
曾振宇
李伟
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Nanjing Hydraulic Research Institute of National Energy Administration Ministry of Transport Ministry of Water Resources
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Abstract

The invention discloses a multisource rainfall fusion method based on principal component regression, which comprises the steps of obtaining and arranging ground station observation data, remote sensing inversion rainfall data and terrain factor data; comparing the observed precipitation at each ground station with remote sensing inversion precipitation, and estimating precipitation background errors at the grids of the stations; fusing multi-source rainfall information and terrain factors by adopting a principal component regression method to obtain a grid background field residual error; selecting an addition model to obtain a multi-source precipitation estimation result; according to the scheme, the multi-source rainfall information is fused through a principal component regression method, the problem of collinearity among independent variables is eliminated, meanwhile, important information is kept, and the precision of rainfall spatial distribution estimation is further improved.

Description

Multi-source precipitation fusion method based on principal component regression
Technical Field
The invention relates to the technical field of rainfall space estimation, in particular to a multi-source rainfall fusion method based on principal component regression.
Background
Precipitation is an important driving factor of moisture and energy circulation, has spatial-temporal discontinuity and difference, and is a meteorological variable which is difficult to accurately obtain. Accurate and reliable precipitation data is not only a key for researching precipitation space-time change rules, but also an important input condition parameter for improving hydrological simulation precision, and plays a vital role in regional disaster monitoring, flood control and reduction and water resource management.
For a long time, the rainfall spatial distribution is estimated based on the observation data of ground rainfall stations, and the method has the characteristics that the precision of measuring points is high, the spatial interpolation method is various, however, the rainfall observed by the ground stations can only reflect the rainfall information of discrete points, the spatial distribution is not uniform, and the rainfall is influenced by factors such as terrain, environment and technology.
With the development of science and technology, the observation of precipitation based on satellite remote sensing becomes a second approach, the characteristics of wide coverage area, high space-time resolution and capability of realizing global scale precipitation observation make up for short boards observed by ground stations, but the precision difference of satellite precipitation products is large, and the applicability needs to be verified.
The space continuous satellite precipitation data and the accurate ground station observation data can be combined, and a new idea is provided for obtaining high-quality high-space-time resolution precipitation data. At present, the mainstream fusion methods comprise probability matching, objective analysis, Bayes technology, geography weighted regression and the like, most of the methods are based on the traditional multiple regression model, and the problem of multiple linear autocorrelation among independent variables can be caused in the process of rainfall space estimation, so that the symbols and the numerical values of the calculated regression coefficients are inconsistent with the theory, and the accuracy of the result is influenced.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a multi-source precipitation fusion method based on principal component regression, which can solve the problem of multiple collinearity existing among independent variables in the fusion process and improve the accuracy of precipitation space estimation.
The technical scheme is as follows: the invention relates to a multi-source precipitation fusion method based on principal component regression, which comprises the following steps:
(1) collecting and sorting multi-source rainfall information, matching spatial scale of rainfall data, and acquiring DEM data, spatial information and topographic factor data required by fusion, wherein the DEM data refers to a data elevation model, and the spatial information and the topographic factor data are longitude, latitude, elevation, gradient and slope of grids;
(2) constructing a precipitation observation field P through the information and the data acquired in the step (1)0And precipitation background field Pb
(3) Acquiring the rainfall background value error e-P according to the rainfall observation field and background field information acquired in the step (2)0(i)-Pb(i) And i is a ground station observation station, i is 1,2,3
Figure BDA0003591240270000021
The fitting formula is:
Figure BDA0003591240270000022
in the above formula, X1i,X2i,X3i,X4i,X5iLongitude, latitude, elevation, slope and slope at the ith grid,
Figure BDA0003591240270000023
is the regression coefficient of each variable;
(4) and acquiring multi-source fusion precipitation spatial distribution of the research region based on the addition model.
In the technical scheme, the influence of the macroscopic terrain factors (longitude and latitude and elevation) and the microscopic terrain factors (gradient and slope direction) is considered, the problem of multiple collinearity existing between independent variables in the process of fusing a satellite precipitation product and ground observation precipitation is solved, and the accuracy of precipitation space estimation is effectively improved.
Preferably, in the step (1), the obtained multi-source precipitation information includes ground station observation precipitation data and remote sensing inversion precipitation data.
Preferably, after the ground station observation precipitation data and the remote sensing inversion precipitation data are obtained, the grid spatial resolution of the precipitation estimation of the research area is determined, and the spatial resolutions of different remote sensing inversion precipitations are unified.
Preferably, in step (1), the background residual field is fitted by principal component regression
Figure BDA0003591240270000024
Comprises the following steps: (3.1) normalizing the independent variable data; (3.2) judging the correlation between indexes; (3.3) correlation matrix eigenvalues and corresponding eigenvectors among the indexes; (3.4) determining an expression of the principal component; (3.5) regression analysis of the Components and the inspected dependent variables
Preferably, in the step (4), the estimated value of the precipitation at the unknown point is obtained by superposing the estimated value of the background residual field and the background field, and the calculation formula of the estimated value of the grid precipitation is as follows:
Figure BDA0003591240270000025
in the above equation, j is the grid anywhere within the study area.
Has the beneficial effects that: compared with the prior art, the invention has the advantages that: according to the scheme, a principal component regression method capable of eliminating the variable collinearity problem is adopted, satellite precipitation product data capable of integrating spatially continuous and rainfall site data discrete on the ground are constructed, local watershed regional characteristics and a multi-source precipitation information fusion model of terrain and meteorological factors are considered, and the accuracy of precipitation space estimation is effectively improved.
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FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram of geographical locations of a research area and a distribution diagram of a ground hydrometeorology station in an embodiment;
FIG. 3 is a line diagram of the accuracy evaluation of satellite precipitation products in the yellow river source area;
FIG. 4 is a line graph of accuracy evaluation of the result of fusion precipitation in the yellow river source area;
FIG. 5 is a confusion matrix of aquatic products and site observations from a yellow river source area satellite;
FIG. 6 is a confusion matrix of the yellow river source zone fused precipitation results with site observations.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
The embodiment is as follows: in this embodiment, as shown in fig. 1, taking the yellow river source area of China as an example research area specifically includes the following steps:
(1) collect arrangement multisource precipitation information, match precipitation data space scale, acquire and fuse required DEM data, spatial information, terrain factor data, wherein, multisource precipitation information specifically is:
as shown in fig. 2, daily precipitation observation data of weather stations on a day-by-day basis in the yellow river source area 2008.01.01-2013.12.31 are collected as ground station precipitation data, wherein the yellow river source area has 13 stations; collecting four satellite precipitation products (TMPA 3B42V7, TMPA 3B42RT, CMORPH _ CRT and IMERG _ Final) covering the yellow river source area as remote sensing inversion precipitation data; then, resampling the acquired 0.1 degree multiplied by 0.1 degree IMERG _ Final data to 0.25 degree multiplied by 0.25 degree spatial resolution by a bilinear interpolation method, unifying the spatial resolution of the four remote sensing inversion data, finally cutting the boundary of a research area by using 90mDEM data of SRTM V4.1 and adopting geographic information system software, and extracting longitude, latitude, elevation, gradient and slope information of a research weather station and a grid of 0.25 degree multiplied by 0.25 degree;
(2) precipitation observation field P for constructing yellow river source area by observing precipitation data through ground station and remotely sensing and inverting precipitation data0And precipitation background field PbThe method specifically comprises the following steps:
constructing a precipitation observation field P of 13 weather stations in the yellow river source area of 2008.01.01-2013.12.31 day by day0Ambient field of daily precipitation P at 250 grids for TMPA 3B42V7, TMPA 3B42RT, CMORPH _ CRT, IMERG _ Finalb
(3) Constructing air space based on principal component regression model according to the information of the rainfall observation field and the background field acquired in the step (2)Background residual field at any place without ground rainfall observation in interval range
Figure BDA0003591240270000041
The method comprises the following specific steps:
firstly based on a rainfall observation field P0And precipitation background field PbAnd calculating the error e of the background value of the precipitation: e ═ P0(i)-Pb(i);
In the above formula, i is a ground station observation station, i is 1,2,3,., n, and n is 13 corresponding to the yellow river source zone;
then, for any position j in the space range where the ground rainfall is not observed, the rainfall background value residual error
Figure BDA00035912402700000412
The fitting estimation can be carried out by utilizing the difference e between actual measuring point rainfall data and a background value, namely:
Figure BDA0003591240270000042
in the above formula, j is a grid at any position in the research area, j is 1,2,.. k, and j is 250 corresponding to the yellow river source area;
finally, a principal component regression method is adopted to fit a background residual error field
Figure BDA0003591240270000043
The background error e used in the regression calculation is used as a dependent variable, and the longitude, the latitude, the height, the gradient and the slope direction of the weather station are used as input variables, so that a background residual error field is obtained:
Figure BDA0003591240270000044
in the above formula, X1i,X2i,X3i,X4i,X5iLongitude, latitude, elevation, slope and slope at the ith grid,
Figure BDA0003591240270000045
are regression coefficients for each variable.
The principal component regression method comprises the following specific steps: for n precipitation observations, there are p variables x for each data1,x2,...,xpThe kth observed data can be expressed as (x)k-1,xk-2,...,xk-p),ZiThe load on (i ═ 1, 2., p) is aij(i 1,2, p, j 1,2, p), and the background residual field is fitted by a principal component regression method in step (3)
Figure BDA0003591240270000046
Comprises the following steps:
(3.1) normalization processing of the independent variable data: first, the standard deviation s of the sample is obtainedjAnd sample mean xjRemember sjIs xjSample standard deviation of (2), i.e.
Figure BDA0003591240270000047
Figure BDA0003591240270000048
Is xjSample mean of (i)
Figure BDA0003591240270000049
Normalized transformation of raw data
Figure BDA00035912402700000410
X is the normalized data matrix and,
Figure BDA00035912402700000411
(3.2) determination of correlation between indices: the correlation coefficient of X is the covariance matrix of X,
Figure BDA0003591240270000051
in the above-mentioned formula, the compound of formula,
Figure BDA0003591240270000052
r is a semi-positive definite matrix;
(3.3) correlation matrix eigenvalues and corresponding eigenvectors between the indexes: a first principal component Z1Information reflecting the most p original variables, i.e. Var (Z)1) The variance is maximum, and the first principal component Z is obtained1=a1' X, i.e. to find a1=(a11,a21,...,ap1) ', such that under the condition a1'a1Var (Z) under 11) Reaches a maximum value, known as Var (Z)1)=Var(a1'X)=a1'Ra1R is a correlation coefficient matrix of X, and
Figure BDA0003591240270000053
Figure BDA0003591240270000054
the method can be obtained by the formula,
Figure BDA0003591240270000055
namely Ra1=λ1a1,λ1Is a characteristic value of R, a1Is λ1Corresponding unit orthogonal feature vector, and according to Var (Z)1)=Var(a1’X)=a1’Ra1=a1’λ1a1=λ1The variance Var (Z) of the first principal component can be obtained1) Reaches a maximum value of the characteristic value of R1And Z is1=a1' A in X1=(a11,a21,...,ap1) Is λ1Corresponding orthogonal feature vector, second principal component variance Var (Z)2) To less than Var (Z)1) Is the characteristic value lambda of R2And λ2<λ1
Let the eigenvalue λ of R1≥λ2≥…≥λp≥0,a1,a2,...,apIs corresponding unit orthogonal characteristic vector, and the notation A is (a)1,a2,...ap) The main component Z ═ I (Z) satisfies AA ═ I1,Z2,...,Zp) ', wherein Zi=ai'X, according to var (z) ═ a' XX 'a ═ a' RA ═ Λ, Λ ═ diag (λ)12,...,λp) RA ═ a Λ, expressed in matrix form as
Figure BDA0003591240270000056
After transformation to obtain
Figure BDA0003591240270000061
(3.4) determining an expression of the principal component: p principal components are obtained by principal component regression, and the contribution ratio of the ith principal component is used
Figure BDA0003591240270000062
The number of the principal components is determined by adopting the following two criteria:
firstly, the accumulated contribution rate is determined, and the accumulated contribution rate of the first m principal components is
Figure BDA0003591240270000063
When the contribution rate reaches 70% -85%, selecting the first m main components; secondly, according to the size of p characteristic values, assuming that p-m characteristic values have lambdam+1,λm+2,…,λpWhen the value is approximately equal to 0, the main component Z corresponding to p-m characteristic valuesm+1,Zm+2,…,ZpThe contribution rate of the method is small, p-m principal components are omitted, and m principal components Z with larger corresponding characteristic values are selected1,Z2,…,Zm
(3.5) regression analysis of principal components and consideration dependent variables: for p principal components Z1,Z2,…,ZpAccording to model requirements and the selection of the first m principal components Z1,Z2,…,ZmThe model assumes yt=b0+b1Zt1+b2Zt2+...+bmZtmt,t=1,2,...,n,E(εt)=0,Var(εt)=σ2,Cov(εiI ≠ j, 0 ∈ j
Figure BDA0003591240270000064
Then the matrix of the regression model is Y ═ CB + Epsilon, Epsilon to Nn(0,σ2In) In the model, the parameters are obtained by the least square method
Figure BDA0003591240270000065
Is estimated value of
Figure BDA0003591240270000066
So that the sum of squares of errors
Figure BDA0003591240270000067
To the minimum
Figure BDA0003591240270000068
Wherein
Figure BDA0003591240270000069
Can obtain
Figure BDA00035912402700000610
Is a least squares estimate of B, thereby yielding Y and Z1,Z2,…,ZmAccording to a linear regression equation of
Figure BDA0003591240270000071
Figure BDA0003591240270000072
The first m principal components Z1,Z2,…,ZmAnd X1,X2,…,XpThe relation between Y and CB + epsilon is substituted to obtain Y and independent variable X1,X2,…,XpLinear regression equation of (c).
(4) Based on the addition model, the multisource fusion precipitation spatial distribution in the research area is obtained, and the method specifically comprises the following steps:
the background residual field and the background field are superposed by adopting an addition model to obtain a 0.25 degree multiplied by 0.25 degree grid precipitation estimated value P every day in the yellow river source area in 2008-2013a(j):
Figure BDA0003591240270000073
The method is characterized in that four ground observation-satellite product fusion precipitations are obtained by a multi-source precipitation fusion method based on principal component regression, and are TMPA 3B42V7_ M, TMPA 3B42RT _ M, CMORPH _ CRT _ M and IMERF _ Final _ M respectively. The method is characterized in that the ground station day-to-day rainfall observation in the yellow river source area 2008-2013 is used as datum data, and the precision of four kinds of fusion rainfall is evaluated. The adopted precision evaluation indexes comprise: three quantitative indexes of Correlation Coefficient (CC), deviation (BIAS) and Root Mean Square Error (RMSE), three classification indexes of hit rate (POD), False Alarm Rate (FAR) and Critical Success Index (CSI), and the Detection capability of fusion results on precipitation with different magnitudes is evaluated by using a Confusion Matrix (fusion Matrix).
The following table is an evaluation index table of this example:
Figure BDA0003591240270000074
Figure BDA0003591240270000081
as shown in fig. 3 and 4, the accuracy statistical line graphs of remote sensing inversion precipitation and fusion precipitation in the yellow river source area are respectively given. In the aspect of quantitative indexes, the ranges of CC, BIAS and RMSE of TMPA 3B42RT _ M are increased to 0.25-0.39/27.8-168% and 18-30.1 mm, and the ranges of the other three fusion results are increased to 0.39-0.58, -33.1-31.2% and 8.7-15.6 mm; for the detection capability, POD of the four fused products is increased to 0.6-0.8, FAR is reduced to 0.3-0.56, and the highest value of CSI is 0.57. In general, each statistical index of IMERG _ Final _ M shows better results, and the average values of CC, BIAS and RMSE are 0.52, -1.6% and 10.8 mm; the detection capability is also significantly higher than other fusion results, with the mean values of POD, FAR and CSI being 0.77, 0.39, 0.47.
Fig. 5 and 6 respectively show confusion matrixes of remote sensing inversion rainfall and fusion rainfall reconstruction station network observation capacity in the yellow river source area. The precipitation data of four satellite precipitation products and ground stations are fused, so that the precipitation under different levels can be detected more accurately, and the value of the grid at the diagonal is increased. The fused precipitation sequences reduce the phenomenon that the precipitation amount of the original satellite data in the yellow river source area is concentrated between 0.1mm and 1mm, and improve the correlation with actually measured precipitation. Specifically, after the TMPA 3B42V7 is subjected to fusion treatment, the accuracy of the lower-grade precipitation is improved from 0.43 to 0.77, and the accuracy of the middle-high-grade precipitation (10-20 mm, 20-30 mm and 30-40 mm) is obviously improved. The confusion matrix of TMPA 3B42RT _ M improves the accuracy of TMPA 3B42RT on days without precipitation and heavy rain (> 40mm), but still has a big gap with the statistical index on the diagonal of the rest of the fusion results. The confusion matrix of CMORPH _ CRT _ M and IMERG _ Final _ M showed good results, especially for the identification of moderate to high category precipitation (10mm to 20mm, 20mm to 30 mm).
According to the scheme, the main component regression method is adopted to integrate the satellite precipitation product and the ground observation data aiming at the characteristics of continuous satellite precipitation space and high ground station accuracy, and the problem of multiple collinearity among independent variables is effectively avoided. The overall precision of the four fusion precipitation results in the yellow river source area is improved to some extent, and the precipitation detection rate is improved. The fusion method constructed by the scheme can also be popularized to other drainage basins, and provides a new idea for hydrological and meteorological research by utilizing satellite-ground precipitation data fusion.
The foregoing description has described the general principles, general features, and operational steps of the present invention. It should be understood by those skilled in the art that the present invention should not be limited by the above preferred embodiments, and the above examples and descriptions are only illustrative of the principles of the invention, and any modifications, equivalents, improvements and the like which fall within the spirit and principle of the invention should be construed as being included in the scope of the present invention. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (6)

1. A multi-source precipitation fusion method based on principal component regression is characterized by comprising the following steps:
(1) collecting and sorting multi-source rainfall information, matching spatial scale of rainfall data, and acquiring DEM data, spatial information and topographic factor data required by fusion, wherein the DEM data refers to a data elevation model, and the spatial information and the topographic factor data are longitude, latitude, elevation, gradient and slope of grids;
(2) constructing a precipitation observation field P through the information and data acquired in the step (1)0And precipitation background field Pb
(3) Acquiring a precipitation background value error e which is P according to the information of the precipitation observation field and the background field obtained in the step (2)0(i)-Pb(i) And i is a ground station observation station, i is 1,2,3, and n, and a background residual error field is estimated by fitting a principal component regression model to a background value error e
Figure FDA0003591240260000011
The fitting formula is:
Figure FDA0003591240260000012
in the above formula, X1i,X2i,X3i,X4i,X5iLongitude, latitude, elevation, slope and slope at the ith grid,
Figure FDA0003591240260000013
is the regression coefficient of each variable;
(4) and acquiring multi-source fusion precipitation spatial distribution of the research area based on the addition model.
2. The principal component regression-based multi-source precipitation fusion method of claim 1, wherein in step (1), the obtained multi-source precipitation information comprises ground station observed precipitation data and remote sensing inverted precipitation data.
3. The principal component regression-based multi-source precipitation fusion method of claim 2, wherein after the ground station observed precipitation data and the remote sensing inversion precipitation data are obtained, grid spatial resolution of precipitation estimation in a research region is determined, and spatial resolutions of different remote sensing inversion precipitations are unified.
4. The multi-source precipitation fusion method based on principal component regression of claim 1, wherein in step (1), the principal component regression method is adopted to fit the background residual error field
Figure FDA0003591240260000015
Comprises the following steps: (3.1) normalizing the independent variable data; (3.2) judging the correlation between indexes; (3.3) correlation matrix eigenvalues and corresponding eigenvectors among the indexes; (3.4) determining an expression of the principal component; (3.5) regression analysis of the composition and the examined dependent variable.
5. The principal component regression-based multi-source precipitation fusion method according to claim 1, wherein in step (4), the precipitation estimation value at an unknown point is obtained by superposing the estimation value of the background residual field and the background field, and the grid precipitation estimation value is calculated by the formula:
Figure FDA0003591240260000014
in the above equation, j is the grid anywhere within the study area.
6. The multi-source precipitation fusion method based on principal component regression of claim 1, wherein the estimation results of the spatial distribution of precipitation of the researched watershed grids at each time step are obtained by repeating the steps (2) to (4).
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