CN111611541A - Copula function-based method and system for calculating rainfall data of data-free area - Google Patents
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Abstract
The invention discloses a method and a system for calculating rainfall data of a data-free area based on a Copula function, belongs to the field of rainfall prediction, fully considers the influence of each meteorological element on rainfall based on the latest re-analyzed meteorological data, combines measured rainfall data of the data-free area, obtains a rainfall influence index by adopting a principal component analysis method, constructs a multidimensional joint distribution model of the rainfall influence index, simulated rainfall and measured rainfall through the Copula function, interpolates parameters of the multidimensional Copula joint distribution model to the data-free area based on a kriging spatial interpolation method, reconstructs the multidimensional joint distribution model in the data-free area, uses the rainfall influence index and the simulated rainfall as input, and calculates a measured rainfall length sequence of the data-free area through condition most possible combination design. The method can fully consider the advantages of reanalysis data and the comprehensive influence of meteorological elements on precipitation, and can provide an important reference basis with strong operability for the calculation of precipitation information in data-free areas.
Description
Technical Field
The invention belongs to the technical field of precipitation prediction, and particularly relates to a Copula function-based method and a Copula function-based system for calculating precipitation data in a data-free area.
Background
Precipitation is a direct source of land water resources and a first link of hydrologic cycle, precipitation data is one of the first basic data of regional water resources and water environments, and the method has important significance for comprehensive planning and utilization of the water resources in the drainage basin, flood control and drought resistance and protection of the water environments and water ecological systems. Due to the limitation of precipitation observation means, remote areas often severely restrict the development and utilization of local water resources and the maintenance of ecological environment due to the lack of precipitation basic information, and how to deduce precipitation data of data-free areas is a hotspot and a difficulty of current research.
In summary, the acquisition of current precipitation data mainly includes three approaches: weather radar, satellite remote sensing and ground rainfall survey stations. The meteorological radar has high measurement cost and is difficult to popularize; the satellite remote sensing technology has the problem of low space-time resolution, and generally cannot meet the actual requirement; the ground rainfall station is used as the only method for directly observing rainfall, has the highest precision and is the mainstream rainfall information acquisition source. But the distribution density of the rainfall stations is limited and the distribution is uneven. For the precipitation research of the data area without the measuring station, a scholars proposes to supplement precipitation information of the data area by using atmosphere reanalysis data (reconstructing meteorological data by a numerical weather mode and a data assimilation method). Compared with meteorological radar or satellite remote sensing data, the reanalysis data has the advantages of comprehensive space coverage, long time scale, dynamic and physical significance and high space-time resolution. The horizontal resolution of the new generation of reanalyzed data is as high as 31km, and the hourly basic weather element data is provided. But is limited by the time-space uncertainty of observed data, numerical prediction mode errors and system deviation caused by an assimilation method, and reanalyzed data still cannot be directly applied to engineering practice and needs to be preprocessed. For example, what fantastic et al, "ERA-intercerim reanalysis data set applicability to the upstream of the Yangtze river [ J ]. people Yangtze river, 2018,49(12): 30-33" evaluated the applicability of ERA-intercerim reanalysis data to the upstream of the Yangtze river, and found that although the ERA precipitation data and the rain measuring station data in the drainage basin have the same change trend, the values of the two data have certain difference; the corrected ERA data can well represent the rainfall information of the measured stations in the drainage basin.
But the study only considered the applicability of a single reanalyzed data across the watershed. The different reanalysis data products adopt different basic data, and the basic mode power framework is different from the physical process description and assimilation, and has the characteristics on the description of the precipitation process. In order to obtain more accurate and real rainfall information, reanalysis data for well capturing rainfall space-time distribution needs to be fused, and errors and advantages of different products are comprehensively considered. Common data fusion methods include simple arithmetic mean, maximum deviation removal, and bayesian model weighted averaging, among others. However, the arithmetic mean method considers that the precipitation describing capacity of each product is the same and is not in accordance with the actual situation; after the maximum deviation removing method removes the product with the maximum deviation, the residual data are averaged, the performance of each reanalysis data is considered to a certain extent, but the subsequent averaging process still causes the problem of the arithmetic averaging method. The Bayes model weighted average assumes that each sequence obeys normal distribution, and if the sequence has non-normal characteristics, normal conversion processing is required, which limits the accuracy and precision of the model to a certain extent. The existing research cannot fully utilize the information of each re-analysis meteorological phenomena and cannot solve the problem of rainfall information description in a data-free area.
Disclosure of Invention
Aiming at the defects or improvement requirements in the prior art, the invention provides a method and a system for deducing rainfall data of a data-free area based on a Copula function, so that the technical problems that the existing research cannot fully utilize the information of each re-analysis meteorological phenomena and cannot solve the description of the rainfall information of the data-free area are solved.
To achieve the above object, according to an aspect of the present invention, there is provided a method for calculating data of rainfall in a material-free area based on Copula function, including:
(1) dividing an area to be detected into a known grid and an unknown grid, and collecting a meteorological element length sequence and a rainfall length sequence of a rainfall measuring station in reanalysis data of the area to be detected, wherein the known grid comprises a ground rainfall measuring station;
(2) screening meteorological elements, of which the correlation with the actually-measured precipitation sequence obtained by the ground rainfall measuring station in the known grid meets the requirement of a preset correlation coefficient, in the re-analysis data through a correlation analysis method, and performing dimension reduction treatment on the screened meteorological elements through a principal component analysis method to obtain a precipitation influence index;
(3) respectively fitting the actually measured precipitation sequence of the known grid, the simulated precipitation in the reanalysis data of the known grid and the edge distribution function of the precipitation influence index, and estimating the parameters of each edge distribution function;
(4) constructing a joint distribution model of simulated precipitation, actually measured precipitation and the precipitation influence index in the known grid reanalysis data based on a high-dimensional Copula function according to each edge distribution, and estimating parameters of the joint distribution model;
(5) interpolating parameters of each edge distribution function in the known grid and parameters of the joint distribution model to the unknown grid by a Krigin space interpolation method, and building the joint distribution model for the unknown grid again;
(6) and constructing the most probable combination of conditions of simulated precipitation in the reanalysis data of the unknown grid and the actually-measured precipitation information of the unknown grid based on the maximum conditional probability density principle, inputting meteorological elements in the reanalysis data of the unknown grid into the reconstructed joint distribution model, and deducing the actually-measured precipitation information of the unknown grid.
Preferably, step (1) comprises:
(1.1) determining a region to be detected, acquiring a precipitation data long sequence of a rainfall measuring station in the region to be detected, and determining the size of a grid according to the position and distribution density of the rainfall measuring station so as to divide the region to be detected into a known grid and an unknown grid;
(1.2) collecting a plurality of sets of reanalysis data in the area to be detected, wherein meteorological elements in the reanalysis data comprise air temperature, relative humidity, sunshine duration and wind speed variables closely related to precipitation besides precipitation.
Preferably, step (2) comprises:
(2.1) performing correlation analysis on other meteorological elements except precipitation in the reanalysis data of each known grid and actually-measured precipitation obtained by a ground rainfall measuring station, and screening meteorological elements of which correlation coefficients meet the requirement of preset correlation coefficients by synthesizing the conditions of each known grid;
and (2.2) carrying out dimension reduction treatment on the screened meteorological elements on the basis of a principal component analysis method aiming at all grids in the area to be detected to obtain a meteorological element index with the largest factor load absolute value as a precipitation influence index.
Preferably, step (3) comprises:
let PM denote the measured precipitation sequence of the known grid, PF denote the precipitation impact index, Si(i ═ 1,2, … n) represents the simulated precipitation in the different reanalysis data corresponding to the known grid, n represents the number of reanalysis data corresponding to the known grid, and the gamma distribution function is adopted to respectively construct the edge distribution F of the measured precipitation of the known gridPM(pm), edge distribution of precipitation impact index FPF(pf) edge distribution of simulated precipitation in different reanalyzed data FSi(si) And estimating parameters of each edge distribution function by adopting a linear moment method, wherein FPM(pm) density function of fPM(pm)，FPF(pf) has a density function of fPF(pf)，FSi(si) Has a density function of fSi(si)。
Preferably, step (4) comprises:
and aiming at the known grid, based on the edge distribution function of each variable, constructing a combined distribution model of simulated precipitation, actually measured precipitation and the precipitation influence index in the reanalysis data of the known grid by adopting Gumbel-Hougaard Copula in an Archimedean Copula function family as a combined distribution function, and estimating parameters of the combined distribution model.
Preferably, the joint distribution model is:
Preferably, step (5) comprises:
(5.1) utilization ofMethod for solving interpolation weight coefficient lambda in Kriging space interpolation method by Lagrange multiplier methodiWherein the Kriging space interpolation value is represented as
The location of the unknown point is x0The position of the known parameter point is xiM is the number of known grids, γ (h) is the variation function of the interpolation fit, γ (x)i-xj) Is xiAnd xjThe value of the variation function between the two is solved by a Lagrange multiplier method, and mu represents a fitting residual error;
(5.2) obtaining parameters of each edge distribution function in the known grid, parameters of the joint distribution model and the obtained weight coefficient lambdaiFrom
Calculating model parameters of the unknown mesh, wherein Z*(x0) Is an unknown point x0Based on the results of parameter estimation by interpolation of the kriging method, Z (x)i) Is a known position xiIncluding parameters of known grid edge distribution functions and joint distribution functions;
and (5.3) constructing a Copula combined probability distribution model of actually measured rainfall of the unknown grid and the simulated rainfall and rainfall influence index in the reanalysis data of the unknown grid one by one on the unknown grid according to the parameters interpolated at the unknown points.
Preferably, step (6) comprises:
(6.1) for the unknown mesh, a reconstructed joint distribution function F (pm, pf, s) by means of the Copula function1,...,sn) Expressed as: f (pm, pf, s)1,...,sn)＝C(u,v1,v2,...vn+1) Wherein u is the edge distribution function u ═ F of the actual measured precipitation of the unknown gridPM(pm)，v1Edge distribution function v for precipitation impact index PF1＝FPF(pf)，v2,...vn+1Edge distribution function for each reanalysis simulation precipitation of unknown grids
C(u,v1,v2,...,vn+1) Represents a Copula model;
(6.2) constructing the most probable combination of conditions of the simulated rainfall of the unknown grid, the rainfall influence index and the actually measured rainfall information of the unknown grid based on the maximum conditional probability density principle of the Copula combined distribution function, wherein the conditional probability distribution function of the combined distribution function
Comprises the following steps:
conditional probability distribution function
Density function of
Comprises the following steps:
wherein,
as a density function of the Copula function, c (pf, s)2,...sn) Representing the density functions of other known variables except measured precipitation to be measured;
when in use
S.s. take the corresponding combination at the maximum (pm, pf, s 1.. s.)n) I.e. the most likely combination of conditions;
(6.3) preparation of
A non-linear equation of the most likely combination of conditions is obtained, wherein,
cn＝c(u,v1,v2,...,vn)，cn+1＝c(u,v1,v2,...,vn+1)，c、c(u,v1,v2,...,vn)、c(u,v1,v2,...,vn+1) Density function, f, which are Copula functionsPM(pm) is a density function, fP'M(pm) as a function of density fPM(pm) derivative of (pm);
(6.4) solving the approximate solution of the nonlinear equation by adopting a Newton iteration method to obtain the most possible combination (pm, pf, s) of the conditions of the actual precipitation and each forecast variable value2,…,sn)；
And (6.5) repeating the steps (6.1) to (6.4), and respectively calculating the unknown grid precipitation length sequence point by point and time interval by time interval.
According to another aspect of the present invention, there is provided a system for estimating data of rainfall in a material-free area based on Copula function, including:
the system comprises a grid dividing and data sampling module, a data acquisition module and a data analysis module, wherein the grid dividing and data sampling module is used for dividing a region to be detected into a known grid and an unknown grid, and collecting a weather element length sequence and a rainfall length sequence of a rainfall measuring station in reanalysis data of the region to be detected, wherein the known grid comprises a ground rainfall measuring station;
the rainfall influence index obtaining module is used for screening meteorological elements, the correlation between the reanalysis data and the actually-measured rainfall sequence obtained by the ground rainfall measuring station in the known grid meets the requirement of a preset correlation coefficient, and performing dimensionality reduction treatment on the screened meteorological elements through a principal component analysis method to obtain a rainfall influence index;
the first parameter estimation module is used for respectively fitting the actually measured precipitation sequence of the known grid, the simulated precipitation in the reanalysis data of the known grid and the edge distribution function of the precipitation influence index and estimating the parameters of each edge distribution function;
the second parameter estimation module is used for constructing a combined distribution model of simulated rainfall, actually-measured rainfall and the rainfall influence index in the known grid reanalysis data based on a high-dimensional Copula function according to each edge distribution and estimating parameters of the combined distribution model;
the joint model building module is used for interpolating parameters of each edge distribution function in the known grid and parameters of the joint distribution model to the unknown grid by a Krigin space interpolation method, and building the joint distribution model for the unknown grid again;
and the calculation module is used for constructing the most probable combination of the conditions of the simulated precipitation in the reanalysis data of the unknown grid and the actually-measured precipitation information of the unknown grid based on the principle of maximum conditional probability density, inputting the meteorological elements in the reanalysis data of the unknown grid into the reconstructed joint distribution model, and deducing the actually-measured precipitation information of the unknown grid.
According to another aspect of the present invention, there is provided a computer readable storage medium, having stored thereon program instructions, which when executed by a processor, implement any of the above-mentioned Copula function-based method for estimating data of rainfall in a material-free area.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
1. scientific and reasonable, close to engineering reality:
the Copula function is used for establishing a combined distribution model of rainfall influence factors, simulated rainfall and actually measured rainfall in reanalysis data, and a rainfall influence index, the simulated rainfall and the actually measured rainfall under the condition most possible combination scene are deduced, so that the method has a strong statistical basis and can objectively reflect the characteristics of the actually measured rainfall.
2. Can provide important and highly operable reference basis for rainfall information in data-free areas:
the advantages of reanalysis data and the comprehensive influence of meteorological elements on precipitation are fully considered, Copula combined distribution model parameters are extended to a non-material area (unknown grid) by utilizing precipitation data of a known grid and a Krigin interpolation method, and then reanalysis data of the non-material area is utilized to calculate an actually measured precipitation length sequence, so that a reference basis is provided for precipitation information acquisition of the non-material area.
Drawings
Fig. 1 is a schematic diagram of region division according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a method provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram of a most probable combination of two-dimensional Copula conditions according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of a system according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention comprehensively considers the advantages of each re-analysis meteorological product and the influence of each meteorological element on precipitation, and provides a method and a system for calculating precipitation information of a data-free area based on the most probable combination of conditions of a multi-dimensional Copula function and a kriging interpolation technology.
The method comprises the steps of calculating a precipitation influence index through correlation analysis and principal component analysis based on a latest reanalysis data set, constructing the precipitation influence index through a Copula function in a known grid precipitation area, reanalyzing a multi-dimensional joint distribution probability model simulating precipitation and actually measured precipitation, interpolating parameters of the multi-dimensional joint distribution probability model to a data-free area through a Kriging space interpolation method, rebuilding joint distribution in the data-free area, deducing a calculation expression of the most possible combination of conditions, and inputting the simulated precipitation and the precipitation influence index of the data-free area into the most possible combination model respectively to obtain a precipitation length sequence of the data-free area.
The technical solution of the present invention is further described in detail below by way of an embodiment with reference to the accompanying drawings, and fig. 2 is a schematic flow chart of a method for calculating a precipitation length sequence in a data-free area according to an embodiment of the present invention, and the method includes the following steps:
step S1: and grid division and data sampling. As shown in fig. 1, the area to be measured may be divided into a known grid and an unknown grid, where the known grid includes a ground rainfall measurement station, and a weather element length sequence and a rainfall measurement station rainfall length sequence in reanalysis data of the area to be measured are collected;
in the embodiment of the present invention, step S1 may be implemented as follows:
s1.1: and (4) dividing the area and collecting actually measured rainfall information. Determining a region to be detected, acquiring a precipitation data long sequence of a rainfall measuring station in the region to be detected, determining the size of a grid according to the position and distribution density of the rainfall measuring station, and dividing the region to be detected into a known grid and an unknown grid;
s1.2: and analyzing the data collection. Three sets of newly released reanalysis data with the highest resolution in the area to be tested are collected, wherein the three sets of reanalysis data comprise a Chinese atmosphere reanalysis data (CRA-Interim), a European center reanalysis data (ERA5) and a Japanese reanalysis data (JRA-55) data set. Meteorological elements in the collected reanalysis data include temperature, relative humidity, sunshine duration and wind speed variables closely related to precipitation besides precipitation.
Step S2: screening meteorological elements in the data, which satisfy the requirement of a preset correlation coefficient in correlation with an actually measured precipitation sequence obtained by a ground rainfall measuring station in a known grid, through a correlation analysis method, and performing dimension reduction treatment on the screened meteorological elements through a principal component analysis method to obtain a precipitation influence index;
in the embodiment of the invention, meteorological elements with higher correlation with an actually measured precipitation sequence obtained by a ground rainfall measurement station in the reanalysis data are screened, for example, the correlation coefficient is greater than 0.5.
In order to comprehensively capture precipitation information in reanalysis data, the embodiment utilizes simulated precipitation in reanalysis data, and simultaneously obtains meteorological elements closely related to precipitation, performs dimension reduction processing on the meteorological elements, and comprehensively considers the influence of the meteorological elements on precipitation so as to predict precipitation information of unknown grids (also referred to as grids without precipitation station data).
In the embodiment of the present invention, step S2 may be implemented as follows:
s2.1: screening precipitation influence factors. Aiming at the known grids, performing correlation analysis on other meteorological elements except precipitation in each piece of reanalysis data and actually-measured precipitation obtained by a ground rainfall measuring station respectively, and screening the meteorological elements with higher correlation coefficients (such as more than 0.5) by synthesizing the conditions of each known grid;
s2.2: and acquiring a precipitation influence index. And (3) aiming at all grids of the area to be detected, performing dimensionality reduction treatment on the screened meteorological elements based on a principal component analysis method to obtain a meteorological element index with the largest factor load absolute value, and recording the meteorological element index as a precipitation influence index (PF), wherein the variable reflects the comprehensive influence of other meteorological elements on a precipitation process.
Step S3: respectively fitting edge distribution functions based on an actually measured precipitation sequence of a known grid, the known grid and simulated precipitation and precipitation influence indexes in the reanalysis data, and estimating parameters of each edge distribution function;
in the embodiment of the present invention, step S3 may be implemented as follows:
let PM represent the measured precipitation sequence of the known grid; PF represents the precipitation influence index; si(i ═ 1,2, … n) represents simulated precipitation in the different reanalysis data for the known grid, n represents the number of reanalysis data for the known grid; adopting a gamma distribution function to construct precipitation and edge distribution of precipitation influence indexes, and respectively recording the edge distribution as FPM(pm)、FPF(pf)、FSi(si) Wherein F isPM(pm) denotes the edge distribution of the measured precipitation for a known grid, FPF(pf) edge distribution of the precipitation impact index, FSi(si) Representing the edge distribution of simulated precipitation in different reanalyzed data; fPM(pm) density function of fPM(pm)，FPF(pf) has a density function of fPF(pf)，FSi(si) Has a density function of fSi(si). The probability distribution function of the gamma distribution is:
α and β are shape and scale parameters respectively, parameters of a gamma distribution function are estimated by adopting a linear moment method, pm represents actually measured precipitation, pf represents precipitation influence index, and siRepresenting the simulated precipitation in the ith reanalyzed data.
Step S4: constructing a known grid based on a high-dimensional Copula function, then analyzing a combined distribution model of simulated precipitation, precipitation influence indexes and actually measured precipitation in data, and estimating Copula function parameters aiming at the grid (namely the known grid) of known precipitation information in an area to be detected;
in the embodiment of the present invention, step S4 may be implemented as follows:
aiming at the known grids, based on the edge distribution function of each variable, Gumbel-Hougaard Copula in an Archimedean Copula function family is adopted as a joint distribution function, a joint distribution model of actually measured precipitation and precipitation influence indexes in the known grids and simulated precipitation in reanalysis data of the known grids is constructed, and parameters of the joint distribution model are estimated.
The Copula function can link edge distributions of a plurality of random variables to construct a joint distribution. Let Q (pm, pf, s)1,...,sn) Is an n + 2-dimensional distribution function whose edge distribution is F estimated in step S3PM(pm)、FPF(pf)、FSi(si) (i ═ 1,2, … n), then there is an n +2 dimensional Copula function C (θ) such that:
wherein θ is a parameter of the Copula function, and the estimation is performed by using a maximum likelihood method in the embodiment of the invention.
Step S5: interpolating the known grid edge distribution function and the parameters of the joint distribution model to the unknown grid by a Krigin space interpolation method, and building the joint distribution model again aiming at the unknown grid;
in the embodiment of the present invention, step S5 may be implemented as follows:
s5.1: method for solving interpolation weight coefficient (lambda) in Kriging space interpolation method by utilizing Lagrange multiplier methodi)：
Wherein the position of the unknown point is x0The position of the known parameter point is xiM is the number of known grids, γ (h) is a variation function of interpolation fitting (in the embodiment of the present invention, a gaussian model may be selected as the variation function), and γ (x)i-xj) (i ≠ j) is xiAnd xjThe value of the variation function between the two is solved by a Lagrange multiplier method, and mu represents the fitting residual error.
S5.2: the parameters of the joint distribution probability model (including the parameters of the edge distribution function and the Copula model) according to the known grids and the solved weight coefficient (lambda)i) Calculating model parameters of the unknown mesh using:
wherein Z is*(x0) Is an unknown point x0A parameter estimation result based on a kriging interpolation; z (x)i) Is a known position xiThe parameter values of (including parameters of known grid edge distribution functions and joint distribution functions in particular);
s5.3: and according to the parameters of the interpolation, constructing a Copula combined probability distribution model for simulating precipitation and precipitation influence indexes in the actually measured precipitation of the unknown grid and the re-analysis data of the unknown grid one by one.
Step S6: based on the principle of maximum conditional probability density, the most probable combination of conditions of simulated precipitation in the reanalysis data of the unknown grids and the actually measured precipitation information of the unknown grids is constructed, meteorological elements (including precipitation influence indexes and simulated precipitation sequences) in the reanalysis data of the unknown grids are input into a newly-built joint distribution model, and the actually measured precipitation information of the unknown grids is deduced, as shown in fig. 3.
In the embodiment of the present invention, step S6 may be implemented as follows:
s6.1: for unknown grids, the reconstructed joint distribution function F (pm, pf, s) is subjected to Copula function1,...,sn) Expressed as:
F(pm,pf,s1,...,sn)＝C(u,v1,v2,...vn+1)(5)
wherein u is an edge distribution function u ═ F of actual measurement precipitation of unknown gridsPM(pm)，v1Marginal probability distribution function v for precipitation impact index PF1＝FPF(pf)，v2,...vn+1Edge distribution function for each reanalysis simulation precipitation of unknown grids
C(u,v1,v2,...,vn+1) Represents a Copula model;
s6.2: constructing a condition most probable combination of simulated rainfall of the unknown grid, a rainfall influence index and actual measurement rainfall information of the unknown grid based on a Copula combined distribution function condition probability density maximum principle;
wherein the conditional probability distribution function of the joint distribution function
The following were used:
further, a conditional probability distribution function
Density function of
The following were used:
in the formula,
as a density function of the Copula function, c (pf, s)2,...sn) Representing the density function of the remaining known variables, except for the measured precipitation to be measured.
When in use
S.s. take the corresponding combination at the maximum (pm, pf, s 1.. s.)n) I.e. the most likely combination of conditions.
For a univariate function of pm, taking the density function derivative of pm, one can obtain:
in the formula:
cn＝c(u,v1,v2,...,vn)，cn+1＝c(u,v1,v2,...,vn+1) Are density functions of Copula functions.
S6.3: to make the patient feel
Taking the maximum value, and letting the derivative be 0, the nonlinear equation with the most possible combination of conditions is obtained:
wherein,
density functions that are Copula functions; f. ofPM(pm) is a density function, fP'M(pm) as a function of density fPM(pm) derivative of (pm);
s6.4: and solving the nonlinear equation approximate solution by adopting a Newton iteration method to obtain the most possible combination of the actual precipitation and the conditions of each forecast variable value. That is, by solving the nonlinear equation in equation (9), it can be obtained that when the reanalysis precipitation and precipitation influence index are known: PF ═ PF, S1＝s1,…,Sn＝snAnd the actual measurement water reducing value PM of the unknown grid is PM. The nonlinear equation in equation (9) is a general calculation formula that is most likely to be satisfied by the composition method based on Copula function calculation conditions, and the equation has only one unknown pm (measured precipitation). According to the practical significance of the problem,
the maximum of (c) is objectively present and unique, so there must be a unique solution to the equation. Obviously, the maximum value does not exist in the boundary, so the stagnation point obtained by solving the equation with the partial derivative of zero is the maximum value point of the density function. In view of the complexity of the problem, it is proposed here to use a numerical method to obtain an approximate solution of the equation, such as the Newton's iteration, from which the most probable combination of conditions (pm, pf, s) is obtained2,…,sn)；
S6.5: and repeating the steps, and respectively calculating the unknown grid precipitation length sequence point by point and time period by time period according to the most possible combination general formula of the conditions.
Fig. 4 is a schematic diagram of a system structure provided in an embodiment of the present invention, including:
the grid division and data sampling module 401 is configured to divide the area to be measured into a known grid and an unknown grid, and collect a weather element length sequence and a rainfall length sequence of a rainfall measuring station in reanalysis data of the area to be measured, where the known grid includes a ground rainfall measuring station;
the rainfall influence index obtaining module 402 is used for screening meteorological elements in the reanalysis data, the correlation between the meteorological elements and an actually measured rainfall sequence obtained by a ground rainfall measuring station in a known grid meets the requirement of a preset correlation coefficient through a correlation analysis method, and performing dimensionality reduction treatment on the screened meteorological elements through a principal component analysis method to obtain a rainfall influence index;
a first parameter estimation module 403, configured to fit an actually measured precipitation sequence of a known grid, a simulated precipitation in reanalysis data of the known grid, and an edge distribution function of precipitation influence indexes, respectively, and estimate parameters of each edge distribution function;
a second parameter estimation module 404, configured to construct a joint distribution model of simulated precipitation, actually measured precipitation and precipitation influence indexes in known grids reanalyzing data based on the high-dimensional Copula function according to each edge distribution, and estimate parameters of the joint distribution model;
a joint model construction module 405, configured to interpolate, to an unknown grid, parameters of each edge distribution function in the known grid and parameters of a joint distribution model by a kriging spatial interpolation method, and construct a joint distribution model again for the unknown grid;
and the calculation module 406 is configured to construct a most probable combination of conditions of simulated precipitation in the reanalysis data of the unknown mesh and actual measurement precipitation information of the unknown mesh based on a conditional probability density maximum principle, input meteorological elements in the reanalysis data of the unknown mesh into the reconstructed joint distribution model, and derive the actual measurement precipitation information of the unknown mesh.
In the embodiment of the present invention, the specific implementation of each module may refer to the description of the above method embodiment, and the embodiment of the present invention will not be repeated.
In another embodiment of the present invention, a computer-readable storage medium is further provided, on which program instructions are stored, and the program instructions, when executed by a processor, implement the method for calculating the data-free area precipitation data based on Copula function as described above.
It should be noted that, according to the implementation requirement, each step/component described in the present application can be divided into more steps/components, and two or more steps/components or partial operations of the steps/components can be combined into new steps/components to achieve the purpose of the present invention.
The above-described method according to the present invention can be implemented in hardware, firmware, or as software or computer code storable in a recording medium such as a CD ROM, a RAM, a floppy disk, a hard disk, or a magneto-optical disk, or as computer code originally stored in a remote recording medium or a non-transitory machine-readable medium and to be stored in a local recording medium downloaded through a network, so that the method described herein can be stored in such software processing on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware such as an ASIC or FPGA. It will be appreciated that the computer, processor, microprocessor controller or programmable hardware includes memory components (e.g., RAM, ROM, flash memory, etc.) that can store or receive software or computer code that, when accessed and executed by the computer, processor or hardware, implements the processing methods described herein. Further, when a general-purpose computer accesses code for implementing the processes shown herein, execution of the code transforms the general-purpose computer into a special-purpose computer for performing the processes shown herein.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A method for calculating rainfall data of a data-free area based on a Copula function is characterized by comprising the following steps:
(1) dividing an area to be detected into a known grid and an unknown grid, and collecting a meteorological element length sequence and a rainfall length sequence of a rainfall measuring station in reanalysis data of the area to be detected, wherein the known grid comprises a ground rainfall measuring station;
(2) screening meteorological elements, of which the correlation with the actually-measured precipitation sequence obtained by the ground rainfall measuring station in the known grid meets the requirement of a preset correlation coefficient, in the re-analysis data through a correlation analysis method, and performing dimension reduction treatment on the screened meteorological elements through a principal component analysis method to obtain a precipitation influence index;
(3) respectively fitting the actually measured precipitation sequence of the known grid, the simulated precipitation in the reanalysis data of the known grid and the edge distribution function of the precipitation influence index, and estimating the parameters of each edge distribution function;
(4) constructing a joint distribution model of simulated precipitation, actually measured precipitation and the precipitation influence index in the known grid reanalysis data based on a high-dimensional Copula function according to each edge distribution, and estimating parameters of the joint distribution model;
(5) interpolating parameters of each edge distribution function in the known grid and parameters of the joint distribution model to the unknown grid by a Krigin space interpolation method, and building the joint distribution model for the unknown grid again;
(6) and constructing the most probable combination of conditions of simulated precipitation in the reanalysis data of the unknown grid and the actually-measured precipitation information of the unknown grid based on the maximum conditional probability density principle, inputting meteorological elements in the reanalysis data of the unknown grid into the reconstructed joint distribution model, and deducing the actually-measured precipitation information of the unknown grid.
2. The method of claim 1, wherein step (1) comprises:
(1.1) determining a region to be detected, acquiring a precipitation data long sequence of a rainfall measuring station in the region to be detected, and determining the size of a grid according to the position and distribution density of the rainfall measuring station so as to divide the region to be detected into a known grid and an unknown grid;
(1.2) collecting a plurality of sets of reanalysis data in the area to be detected, wherein meteorological elements in the reanalysis data comprise air temperature, relative humidity, sunshine duration and wind speed variables closely related to precipitation besides precipitation.
3. The method of claim 1 or 2, wherein step (2) comprises:
(2.1) performing correlation analysis on other meteorological elements except precipitation in the reanalysis data of each known grid and actually-measured precipitation obtained by a ground rainfall measuring station, and screening meteorological elements of which correlation coefficients meet the requirement of preset correlation coefficients by synthesizing the conditions of each known grid;
and (2.2) carrying out dimension reduction treatment on the screened meteorological elements on the basis of a principal component analysis method aiming at all grids in the area to be detected to obtain a meteorological element index with the largest factor load absolute value as a precipitation influence index.
4. The method of claim 3, wherein step (3) comprises:
let PM denote the measured precipitation sequence of the known grid, PF denote the precipitation impact index, Si(i ═ 1,2, … n) represents the simulated precipitation in the different reanalysis data corresponding to the known grid, n represents the number of reanalysis data corresponding to the known grid, and the gamma distribution function is adopted to respectively construct the edge distribution F of the measured precipitation of the known gridPM(pm), edge distribution of precipitation impact index FPF(pf) edge distribution of simulated precipitation in different reanalyzed data FSi(si) And estimating parameters of each edge distribution function by adopting a linear moment method, wherein FPM(pm) density function of fPM(pm)，FPF(pf) has a density function of fPF(pf)，FSi(si) Has a density function of fSi(si)。
5. The method of claim 4, wherein step (4) comprises:
and aiming at the known grid, based on the edge distribution function of each variable, constructing a combined distribution model of simulated precipitation, actually measured precipitation and the precipitation influence index in the reanalysis data of the known grid by adopting Gumbel-Hougaard Copula in an Archimedean Copula function family as a combined distribution function, and estimating parameters of the combined distribution model.
6. The method of claim 5, wherein the joint distribution model is:
7. The method of claim 6, wherein step (5) comprises:
(5.1) solving the interpolation weight coefficient lambda in the Krigin space interpolation method by using the Lagrange multiplier methodiWherein the Kriging space interpolation value is represented as
The location of the unknown point is x0The position of the known parameter point is xiM is the number of known grids, γ (h) is the variation function of the interpolation fit, γ (x)i-xj) Is xiAnd xjThe value of the variation function between the two is solved by a Lagrange multiplier method, and mu represents a fitting residual error;
(5.2) obtaining parameters of each edge distribution function in the known grid, parameters of the joint distribution model and the obtained weight coefficient lambdaiFrom
Calculating model parameters of the unknown mesh, wherein Z*(x0) Is an unknown point x0Based on the results of parameter estimation by interpolation of the kriging method, Z (x)i) Is a known position xiIncluding parameters of known grid edge distribution functions and joint distribution functions;
and (5.3) constructing a Copula combined probability distribution model of actually measured rainfall of the unknown grid and the simulated rainfall and rainfall influence index in the reanalysis data of the unknown grid one by one on the unknown grid according to the parameters interpolated at the unknown points.
8. The method of claim 7, wherein step (6) comprises:
(6.1) for the unknown mesh, a reconstructed joint distribution function F (pm, pf, s) by means of the Copula function1,...,sn) Expressed as: f (pm, pf, s)1,...,sn)＝C(u,v1,v2,...vn+1) Wherein u is the edge distribution function u ═ F of the actual measured precipitation of the unknown gridPM(pm)，v1Edge distribution function v for precipitation impact index PF1＝FPF(pf)，v2,...vn+1Edge distribution function for each reanalysis simulation precipitation of unknown grids
C(u,v1,v2,...,vn+1) Represents a Copula model;
(6.2) constructing the most probable combination of conditions of the simulated rainfall of the unknown grid, the rainfall influence index and the actually measured rainfall information of the unknown grid based on the maximum conditional probability density principle of the Copula combined distribution function, wherein the conditional probability distribution function of the combined distribution function
Comprises the following steps:
conditional probability distribution function
Density function of
Comprises the following steps:
wherein,
when in use
Taking the corresponding combination (pm, pf, s) at the maximum1,...sn) I.e. the most likely combination of conditions;
(6.3) preparation of
A non-linear equation of the most likely combination of conditions is obtained, wherein,
cn＝c(u,v1,v2,...,vn)，cn+1＝c(u,v1,v2,...,vn+1)，c、c(u,v1,v2,...,vn)、c(u,v1,v2,...,vn+1) Density function, f, which are Copula functionsPM(pm) is a density function, f'PM(pm) as a function of density fPM(pm) derivative of (pm);
(6.4) solving the approximate solution of the nonlinear equation by adopting a Newton iteration method to obtain the most possible combination (pm, pf, s) of the conditions of the actual precipitation and each forecast variable value2,…,sn)；
And (6.5) repeating the steps (6.1) to (6.4), and respectively calculating the unknown grid precipitation length sequence point by point and time interval by time interval.
9. A system for deducing rainfall data in a data-free area based on a Copula function is characterized by comprising the following steps:
the system comprises a grid dividing and data sampling module, a data acquisition module and a data analysis module, wherein the grid dividing and data sampling module is used for dividing a region to be detected into a known grid and an unknown grid, and collecting a weather element length sequence and a rainfall length sequence of a rainfall measuring station in reanalysis data of the region to be detected, wherein the known grid comprises a ground rainfall measuring station;
the rainfall influence index obtaining module is used for screening meteorological elements, the correlation between the reanalysis data and the actually-measured rainfall sequence obtained by the ground rainfall measuring station in the known grid meets the requirement of a preset correlation coefficient, and performing dimensionality reduction treatment on the screened meteorological elements through a principal component analysis method to obtain a rainfall influence index;
the first parameter estimation module is used for respectively fitting the actually measured precipitation sequence of the known grid, the simulated precipitation in the reanalysis data of the known grid and the edge distribution function of the precipitation influence index and estimating the parameters of each edge distribution function;
the second parameter estimation module is used for constructing a combined distribution model of simulated rainfall, actually-measured rainfall and the rainfall influence index in the known grid reanalysis data based on a high-dimensional Copula function according to each edge distribution and estimating parameters of the combined distribution model;
the joint model building module is used for interpolating parameters of each edge distribution function in the known grid and parameters of the joint distribution model to the unknown grid by a Krigin space interpolation method, and building the joint distribution model for the unknown grid again;
and the calculation module is used for constructing the most probable combination of the conditions of the simulated precipitation in the reanalysis data of the unknown grid and the actually-measured precipitation information of the unknown grid based on the principle of maximum conditional probability density, inputting the meteorological elements in the reanalysis data of the unknown grid into the reconstructed joint distribution model, and deducing the actually-measured precipitation information of the unknown grid.
10. A computer readable storage medium having stored thereon program instructions which, when executed by a processor, implement the Copula function-based method for estimating precipitation data in a data-free area according to any one of claims 1 to 8.
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