A fusion algorithm of ground and satellite measurement precipitation data under a Bayesian framework

Abstract

The application discloses a kind of ground and satellite-borne measurement precipitation data fusion algorithm under bayesian framework, comprising the following steps: selecting time and space matching satellite-borne measurement precipitation and ground radar measurement precipitation data, when matching, set certain space window and time window, time window is within ±6min with the time difference that ground radar starts once body scanning time that satellite-borne measurement sweeps matching space window, space window is the region that with ground radar as center, the circular region of r radius and the region that satellite-borne radar survey strip is intersected, the ground and satellite-borne measurement precipitation data fusion algorithm under bayesian framework of the application, based on hierarchical bayesian method, the fusion of ground radar and satellite-borne measurement precipitation data, improve satellite-borne measurement instantaneous precipitation precision, obtain the high-precision, high-resolution precipitation estimation result of comprehensive multi-source precipitation observation, and can quantitatively give the uncertainty size that fusion result contains, to better be applied to hydrological model.

Description

Technical Field

[0001] This invention relates to the field of meteorological observation data processing technology, specifically a ground-based and spaceborne precipitation measurement data fusion algorithm under a Bayesian framework. Background Technology

[0002] Accurate precipitation estimation is crucial for hydrology, weather forecasting and early warning, flood monitoring, and the development and rational utilization of water resources. Currently, precipitation detection methods mainly include ground-based rain gauges, ground-based weather radars, and active and passive sensors carried on satellites, such as the dual-frequency precipitation radar (DPR) carried on the main satellite of the Global Precipitation Mission (GPM). With the rapid development of weather radar and satellite remote sensing technologies, and the continuously improving ground-based rain gauge network, optimizing and integrating multiple precipitation data sources into a more complete set of precipitation information to reduce the uncertainty of precipitation estimation is a powerful driving force for developing multi-source precipitation data fusion algorithms. Precipitation data from different sources each have their own spatiotemporal scales and error characteristics. Based on a quantitative analysis of the uncertainties of different precipitation data, and by integrating the advantages and error structures of different precipitation data, the main purpose of fusion is to obtain the optimal precipitation estimate at this spatiotemporal scale.

[0003] Conventional precipitation data fusion typically involves using ground-based rain gauges to correct remote sensing estimates, such as radar precipitation measurements. Fusion methods mainly include probabilistic matching, Kalman filtering, variational methods, neural networks, and Bayesian co-kriging. These methods treat rain gauge readings as the true values ​​and apply specific techniques to correct for remote sensing precipitation measurements. However, rain gauges primarily provide local point measurements, which have significant limitations in large-scale, dynamic, and continuous monitoring of rainfall.

[0004] Another approach is to fuse precipitation data from ground-based radar measurements and satellite remote sensing measurements. For example, Gupta et al. (2006, A methodology forming multisensor precipitation estimates based on expectation maximization and scale-recursive estimation) combined TRMM satellite radar precipitation products with ground-based radar measurements using a Kalman filter-based scale recursive estimation method. Chenetal (2020, A machine learning system for precipitation estimation using satellite and ground radar network observations) fused satellite precipitation data with ground-based radar network precipitation measurements using a deep learning multilayer sensing structure. The fusion process often requires prior information. Both ground-based and satellite-based radar precipitation estimation data have their own measurement error structures and represent their own spatiotemporal scales. Accurately characterizing the systematic and random errors of ground-based and satellite-based radar precipitation estimation is a key issue in obtaining the optimal fusion result.

[0005] Bayesian frameworks can deduce the posterior probability distribution of unknown true rainfall based on known data and quantify the uncertainty of the results. In hydrological modeling, we need not only accurate rainfall input but also to quantify the uncertainty of rainfall outcomes. Conventional Bayesian fusion typically characterizes the uncertainty of multi-source information holistically, but precipitation estimation errors are related not only to the sensors used for precipitation measurement and the spatiotemporal scales they represent but also to the type and intensity of precipitation. This invention proposes a hierarchical Bayesian fusion algorithm. The uncertainty of prior information is divided into stratiform clouds and convective precipitation based on the structural characteristics of radar precipitation errors, and further categorized into different intensities based on precipitation intensity under different types of precipitation. First, ground-based radar precipitation estimation is systematically biased using ground-based rain gauge data, and the error model parameters of the hierarchical precipitation structure are estimated. Second, the systematically biased ground-based radar precipitation estimation is used as prior information for the true rainfall value. Finally, the posterior distribution of the unknown true rainfall value is deduced from the likelihood function of spaceborne precipitation measurement and the prior information of rainfall. The model parameters are influenced by uncertainty factors and are not fixed values, but rather exhibit a certain distribution, thus forming a hierarchical Bayesian structure. Utilizing this hierarchical structure allows for a better characterization of the prior features and error structure of precipitation, leading to more accurate fusion results of real rainfall values ​​and corresponding uncertainty characterization. Summary of the Invention

[0006] To address the shortcomings mentioned in the background art, the present invention aims to provide a Bayesian framework-based algorithm for fusing ground-based and spaceborne precipitation data. Based on the error structure characteristics of precipitation, the error structure of the ground-based radar observation precipitation model and the likelihood function is modeled as a layered structure of different types and intensities of precipitation. Then, the Bayesian framework is used to fuse ground-based and spaceborne precipitation data. The goal is to integrate ground-based radar precipitation estimation into spaceborne precipitation measurement, improve the accuracy of spaceborne precipitation estimation, and characterize the uncertainty of the fused precipitation, thereby enabling better application in weather forecasting or hydrological models.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A Bayesian framework algorithm for fusing ground-based and spaceborne precipitation data includes the following steps:

[0009] (1) Data from spaceborne and ground-based radar precipitation measurements were selected for temporal and spatial matching. During matching, specific spatial and temporal windows were set. The temporal window was defined as the time difference between the spaceborne measurement sweeping through the matching spatial window and the start of a single volume scan by the ground-based radar being within ±6 minutes. The spatial window was defined as the area where a circular region with radius r centered on the ground-based radar intersects with the mapping zone of the spaceborne radar, where r is the scanning range of the ground-based radar. Grid matching was used for pixel spatial matching.

[0010] (2) The pixels of the spatiotemporally matched ground-based radar and spaceborne precipitation data are divided into two categories according to precipitation type: stratiform cloud precipitation and convective precipitation.

[0011] (3) Based on the precipitation classification, stratiform cloud precipitation pixels are divided into light to moderate rain and heavy rain according to precipitation intensity, and convective precipitation pixels are divided into light to moderate rain and heavy rain according to precipitation intensity. According to the precipitation intensity grading standard, precipitation above 7.6 mm / h is classified as heavy rain, and vice versa as light to moderate rain.

[0012] (4) Based on the matching ground-based radar and spaceborne measurement precipitation data of different precipitation types and intensities, a hierarchical Bayesian framework is established to deduce the posterior distribution of unknown true rainfall. The precipitation result RR estimated by ground-based radar is approximated as the prior information of the true rainfall value RT. The conditional probability of the spaceborne measurement precipitation RS under the given true rainfall is the likelihood function. The true rainfall is obtained by calculating the posterior distribution of the true rainfall under the known spaceborne rainfall. Since the prior distribution parameters and likelihood function parameters are related to both precipitation type and precipitation intensity, the model parameters are not fixed values, but are affected by uncertainty factors and exhibit a certain probability distribution, thus forming the following hierarchical Bayesian structure:

[0013] f(R T |R S)∝f(R s |R T )f(R T )

[0014] f(R T )~N(R G ,σ1)

[0015] σ1~Exp(σ1|λ1)

[0016] f(R s |R T )~N(a+α+(b+β)R R ,σ2)

[0017] α~N(0,σ α ),β~N(0,σ β ),σ2~Exp(σ2|λ2)

[0018] In the formula, ∝ represents proportionality, ~ represents a certain probability distribution, f() represents the probability distribution, and f(R) represents the probability distribution. s |R T f(R) represents the conditional probability of satellite-measured precipitation RS given the actual rainfall RT, i.e., the likelihood function. N() represents the normal distribution, Exp() represents the exponential distribution, and f(R) represents the probability of the satellite-measured precipitation RS. T )~N(R G ,σ1) represents the prior probability f(R) of the actual rainfall. T The precipitation data exhibits a normal distribution with mean RG and variance σ1. In the likelihood function, a and b are systematic error parameters of spaceborne precipitation measurements relative to ground-based radar precipitation estimates. These errors are influenced by precipitation type and intensity, and are contained in parameters α and β, which have a mean of 0 and a variance of σ1. α , σ β The distribution follows a normal distribution, where λ1 and λ2 are the scaling parameters of the exponential distribution.

[0019] (5) Using spatiotemporally matched ground-based radar precipitation data and rain gauge data as training samples, the prior error model parameter λ1 of ground-based radar precipitation data under different precipitation types and intensities is estimated.

[0020] (6) Using spaceborne precipitation measurement data and ground-based radar precipitation data with spatiotemporal matching as training samples, the likelihood function model parameters a, b, and σ under different precipitation types and intensities are estimated. α , σ β ,λ2

[0021] (7) Substitute the prior model parameters from step (3) and the likelihood function model parameters from step (4) into the hierarchical Bayesian fusion structure model constructed in step (2) to solve for the posterior probability distribution f(R) of the actual rainfall. T|R S )

[0022] (8) The step of solving the real rainfall using the Monte Carlo method (7) is the posterior probability distribution parameter, where the mean of the estimated posterior probability distribution of each pixel is the fusion result, and the variance is the uncertainty of the corresponding fusion result.

[0023] Step (5) trains the hierarchical prior error model parameter module, which specifically includes the following steps:

[0024] 5.1) Quality control is performed on ground-based radar observation data. Fuzzy logic is used to remove ground clutter from the ground-based radar data, an adaptive constraint method is used for attenuation correction of the reflectivity factor Z and differential reflectivity ZDR, and median filtering is applied to the differential phase shift rate KDP.

[0025] 5.2) Near-surface precipitation can be estimated using ground-based radar observation parameters. Since dual-polarization radar can obtain observation parameters such as reflectivity factor Z, differential reflectivity ZDR, and differential phase shift rate KDP, precipitation can be estimated using the R(Z) relationship, the R(KDP) method, and the R(Z, ZDR) method, where R is the hourly precipitation. The precipitation relationship is obtained by fitting raindrop spectrum data.

[0026] 5.3) Perform quality control on rain gauge data within the observation range of ground-based radar, such as removing excessively high or low rainfall data.

[0027] 5.4) Spatiotemporal matching of rain gauge data and dual-polarization radar data is performed to obtain spatiotemporally matched dual-polarization radar data samples and rain gauge data samples. The time resolution of rain gauge data is 1 hour, and the time resolution of ground-based radar data is 5-8 minutes. Therefore, time matching involves using multiple ground-based radar data within 1 hour and the rain gauge data within that 1 hour as matching data. Spatial matching involves using data from the 6 ground-based radar databases closest to the rain gauge as matching data for that rain gauge.

[0028] 5.5) Quantitative statistical comparison is performed using matched rain gauge data and ground-based radar data. Using the rain gauge data as the standard, the systematic bias of the ground-based radar precipitation data is determined, and systematic bias correction is applied to the ground-based radar data.

[0029] 5.6) Precipitation type classification is performed on the matched precipitation data. First, the relationship between polarization parameters and droplet spectrum parameters is fitted using raindrop spectrum data. Then, based on the fitted relationship, droplet spectrum parameters are retrieved using ground-based radar measurement data. According to the droplet spectrum parameter relationship method, precipitation types are classified into stratiform cloud precipitation and convective precipitation.

[0030] 5.7) Based on different precipitation types, precipitation intensity is classified according to the magnitude of precipitation. Rainfall with a rate of 7.6 mm / h or higher is classified as heavy rain, while rainfall with a rate of less than 7.6 mm / h is classified as light to moderate rain.

[0031] 5.8) Based on the matched ground-based radar precipitation data and rain gauge data, the error between the two is modeled as a Gaussian distribution with a mean of 0 and a variance of σ1, i.e., f(R R -R G Since the variance σ1 is affected by precipitation type and precipitation intensity, it is further modeled as an exponential distribution σ1 ~ Exp(σ1|λ1), where the exponential distribution parameter is λ1.

[0032] 5.9) Based on the matched data, the error variance distribution parameter λ1 of stratiform cloud precipitation (light rain), stratiform cloud precipitation (heavy rain), convective precipitation (light rain), and convective precipitation (heavy rain) is estimated.

[0033] Step (6) involves training the hierarchical likelihood function model parameters, specifically including the following steps:

[0034] 6.1) Perform quality control on satellite-borne precipitation data. Satellite-borne precipitation data often have readily available precipitation products. Suitable precipitation products can be selected based on coverage and product accuracy, and data with a sensitivity exceeding that of satellite-borne measurements should be chosen.

[0035] 6.2) Spatiotemporal matching is performed between the satellite-borne precipitation data and the ground-based radar precipitation data corrected for rain gauge system bias. The spatiotemporal matching method is as described in step (1). Since a large number of samples are required for training data, multiple spatiotemporal matching cases independent of the application module are selected as training samples.

[0036] 6.3) Based on the matched ground-based radar and spaceborne precipitation data, precipitation types are divided into stratiform cloud precipitation and convective precipitation.

[0037] 6.4) Based on different precipitation types, precipitation intensity is classified according to the magnitude of precipitation. Rainfall with a rate of 7.6 mm / h or higher is classified as heavy rain, while rainfall with a rate of less than 7.6 mm / h is classified as light to moderate rain.

[0038] 6.5) Based on matched ground-based radar and spaceborne precipitation data, construct the likelihood function for both and model it as a normal distribution f(R). s |R T )~N(a+α+(b+β)R R Based on different precipitation types and intensities, the distribution parameters α and β are further modeled as having a mean of 0 and a variance of σ². α , σ β The normal distribution α~N(0,σ) α ),β~N(0,σ β ), σ² is further modeled as an exponential distribution σ²~Exp(σ²|λ²),

[0039] 6.6) Based on the matched data, statistically estimate the distribution basis parameters a and b, as well as the distribution hyperparameters (σ) of light rain in stratiform cloud precipitation, heavy rain in stratiform cloud precipitation, light rain in convective precipitation, and heavy rain in convective precipitation. α ,σ β ,λ2).

[0040] The beneficial effects of this invention are as follows:

[0041] This invention uses a hierarchical Bayesian method to fuse ground-based radar and spaceborne precipitation data, improving the accuracy of instantaneous precipitation measurements from spaceborne sources. It yields high-precision, high-resolution precipitation estimation results from integrated multi-source precipitation observations and can quantitatively provide the magnitude of uncertainty in the fused results, thus enabling better application in hydrological models. Attached Figure Description

[0042] The invention will now be further described with reference to the accompanying drawings.

[0043] Figure 1 This is the overall flowchart of the fusion of ground-based radar and spaceborne precipitation measurement data under the Bayesian framework in this invention;

[0044] Figure 2 This is a flowchart of precipitation classification based on ground-based radar data in this invention;

[0045] Figure 3 This is a framework diagram of precipitation data categorized by precipitation type and precipitation intensity in this invention;

[0046] Figure 4 This is a flowchart of parameter estimation for the hierarchical likelihood function model in this invention. Detailed Implementation

[0047] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] Figure 1This is the overall flowchart of the hierarchical Bayesian fusion of ground-based radar estimated precipitation data and spaceborne measured precipitation data in this invention. It is mainly divided into two modules: a training module and an application module. The data in the training and application modules are independent of each other. The training module is mainly divided into two parts: hierarchical prior modeling and likelihood function modeling. Hierarchical prior modeling provides the prior model distribution parameters for the hierarchical Bayesian framework in the application module, and likelihood function modeling provides the likelihood model parameters for the hierarchical Bayesian framework in the application module. The basis for hierarchical modeling is that different precipitation types and intensities will affect the parameters of the prior model and the likelihood model, thus affecting the final fusion result. The flowchart for precipitation type classification based on ground-based radar data is shown below. Figure 2 As shown. Figure 3 A probabilistic framework diagram illustrating the classification and intensity of precipitation data is presented. This is to explain the estimation of the distribution parameters and hyperparameters of the hierarchical likelihood function model in the training module. Figure 4 The process of estimating the distribution parameters in the likelihood function of precipitation measured by spaceborne instruments is demonstrated.

[0049] The overall process of fusing ground-based radar precipitation estimation data and spaceborne measurement precipitation data based on hierarchical Bayesian methods in this invention is as follows: Figure 1 The overall flowchart is shown below, and the specific steps are as follows:

[0050] 1. Select space-based and ground-based radar precipitation data, along with rain gauge data within the corresponding range, that are matched temporally and spatially. The selection method involves using the known satellite scan swath width and the Earth coordinates of their intersections, based on the swath shape model, and combining parameters such as the longitude of the satellite's trajectory at its highest latitude, the satellite orbital intercept, and the start time of the orbit, to search for transit orbits and estimate transit times. When matching radar transit data, the matching area between space-based measurements and ground-based radar data is set as the area where a circular region centered on the ground-based radar and with its detection range intersects with the space-based radar mapping zone. Pixel spatial matching utilizes a grid matching method, where both ground-based radar and satellite detection data are resampled to a three-dimensional gridded Cartesian coordinate system of a certain resolution using linear interpolation. Since the ground-based radar completes one volume scan in 6 minutes, the matching time window for space-based measurements and ground-based radar data is set to ±6 minutes, meaning the time difference between the space-based sensor scanning through the matching spatial window and the ground-based radar starting one volume scan is within ±6 minutes.

[0051] 2. The spatiotemporally matched ground-based radar and spaceborne precipitation data are categorized into two types based on precipitation type: stratiform cloud precipitation and convective precipitation. Since ground-based radar data has higher resolution and accuracy than spaceborne measurements, the droplet spectrum data retrieved from ground-based radar is used for precipitation type classification. The flowchart for precipitation type classification based on ground-based radar data is shown below. Figure 2 As shown, the specific steps are as follows:

[0052] 21. Based on raindrop spectral data N(D) obtained from a raindrop spectrometer, the scattering amplitude f of particles with different diameters D is calculated using the T-matrix algorithm, and then the dual polarization parameter, reflectivity factor Z', is calculated. H Differential reflectivity Z' DR :

[0053]

[0054]

[0055] Z' H =10log 10 (Z' h ),[dBZ]

[0056] Z' V =10log 10 (Z' v ),[dBZ]

[0057]

[0058] Where λ is the wavelength, K is the particle refractive index, and f is... hh (π,D),f vv (π, D) represent the horizontal and vertical backscattering amplitudes, respectively.

[0059] 22. Set the droplet spectral model N'(D) to a normalized gamma model, i.e.

[0060]

[0061] Based on measured raindrop spectrum data N(D), the droplet spectrum parameter N' is calculated using the step moment method. w D'0:

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] Where <x> represents the expected value, ρ w This indicates the density of water.

[0068] 22. Fit Z' using multiple linear regression. H Z' DR and droplet spectral parameter N' w, D'0, to obtain the relational expression N' between the two w (Z' H , Z' DR ), D'0(Z' H , Z' DR ).

[0069] 23. Substitute the reflectivity factor data ZH and differential reflectivity ZDR corresponding to each pixel measured by the ground-based radar into the relational expression obtained in step 22, and perform inversion calculation to obtain the drop size spectrum parameters Nw and D0 corresponding to each pixel of the ground-based radar.

[0070] 24. Substitute the drop size spectrum parameter D0 calculated in step 23 into the empirical relational expression of the precipitation type boundary to calculate Nw1. The empirical relational expression can be obtained from the reference Thurai et al (2016, Separating stratiform and convective rain types based on the drop size distribution characteristics using 2D video disdrometer data).

[0071] 25. Compare Nw obtained in step 23 and Nw1 obtained in step 24. If Nw > Nw1, it is convective precipitation; if Nw < Nw1, it is stratiform cloud precipitation.

[0072] [[ID=2,4]]3. Based on the precipitation classification, the pixels of stratiform cloud precipitation are divided into light and moderate rain and heavy rain according to the precipitation intensity, and the pixels of convective precipitation are divided into light and moderate rain and heavy rain according to the precipitation intensity. According to the precipitation intensity grading standard, those above 7.6 mm / h are classified as heavy rain, and vice versa as light and moderate rain.

[0073] 4. Based on the ground-based radar and spaceborne measured precipitation data of different precipitation types and different precipitation intensities obtained by matching, establish a hierarchical Bayesian framework to infer the posterior distribution of the unknown true rainfall amount. Since the resolution and accuracy of the ground-based radar measured precipitation are higher, approximate the precipitation estimation result of the ground-based radar as the prior information of the rainfall true value, and the conditional probability of the spaceborne measured precipitation under the given true rainfall amount is the likelihood function. The true rainfall amount is obtained by finding the posterior distribution of the true rainfall amount under the known spaceborne precipitation amount. The conventional Bayesian framework is as follows:

[0074] f(R T |R S ) ∝ f(R s |R T )f(R T )

[0075] f(R T ) ∼ N(R G , σ1)

[0076] f(R s |R T )~N(a+bR R ,σ2)

[0077] Where ∝ represents proportionality, ~ represents a certain probability distribution, RT is the actual rainfall to be determined, RS is the rainfall measured by spaceborne instruments, RG is the rainfall measured by a rain gauge, RR is the rainfall estimated by radar, and f(x) represents the probability distribution of x. s |R T f(R) represents the conditional probability of satellite-measured precipitation RS given the actual rainfall RT, i.e., the likelihood function. N(x) represents the normal distribution, Exp(x) represents the exponential distribution, and f(R) represents the probability of the satellite-measured precipitation RS. T )~N(R G ,σ1) represents the prior probability f(R) of the actual rainfall. T The precipitation data exhibits a normal distribution with mean RG and variance σ1. In the likelihood function, a and b are the systematic error parameters of spaceborne precipitation measurements relative to ground-based radar precipitation estimates. (a, b, σ1, σ2) constitute the Bayesian model parameter set θ. Since the prior distribution parameters and likelihood function parameters are related to both precipitation type and precipitation intensity, the model parameters are not fixed values ​​but rather exhibit a certain probability distribution influenced by uncertainty factors, thus forming the following hierarchical Bayesian structure:

[0078] f(R T )~N(R G ,σ1)

[0079] σ1~Exp(σ1|λ1)

[0080] f(R s |R T )~N(a+α+(b+β)R R ,σ2)

[0081] α~N(0,σ α ),β~N(0,σ β ),σ2~Exp(σ2|λ2)

[0082] This constitutes a new Bayesian model parameter set θ new (a,b,σ α ,σ β ,λ1,λ2). Where Exp(x) represents the exponential distribution. Model parameters σ α ,σ β λ1 and λ2 are affected by precipitation type and intensity, and will be estimated by classification. This influence is contained in the parameters α, β, σ1, and σ2, where α and β have a mean of 0 and a variance of σ. α , σβ The distribution is normally distributed, and λ1 and λ2 are the scaling parameters of the exponential distribution.

[0083] 5. Substitute the hierarchical prior model parameters obtained from the training module into the hierarchical Bayesian fusion framework of step 4. Using spatiotemporally matched ground-based radar precipitation data and rain gauge data as training samples, estimate the prior error model parameters for different precipitation types and intensities from the ground-based radar precipitation data. The specific steps are as follows:

[0084] 51. Perform quality control on ground-based radar observation data, such as clutter removal and attenuation correction. Fuzzy logic is used for ground-based radar data clutter removal, adaptive constraint method is used for attenuation correction of reflectivity factor Z and differential reflectivity ZDR, and median filtering is applied to differential phase shift rate KDP.

[0085] 52. Since ground-based radar observation parameters are not rainfall data, precipitation estimation requires a specific inversion algorithm. Ground-based dual-polarization radar can obtain the observed parameters reflectivity factor Z, differential reflectivity ZDR, and differential phase shift rate KDP. Precipitation can then be estimated using a combination of the R(Z) relationship, the R(KDP) method, and the R(Z, ZDR) method, where R represents hourly precipitation. The precipitation relationship can be obtained by fitting raindrop spectrum data.

[0086] 53. Use a singularity removal method to control the quality of rain gauge data within the observation range of ground-based radar, such as removing data with hourly rainfall below 0.1 mm / h and above 150 mm / h.

[0087] 54. Spatiotemporal matching of rain gauge data and dual-polarization radar data is performed to obtain spatiotemporally matched dual-polarization radar data samples and rain gauge data samples. The time resolution of rain gauge data is 1 hour, and the time resolution of ground-based radar data is approximately 7 minutes. Therefore, time matching involves using multiple ground-based radar data points within 1 hour and the rain gauge data within that 1 hour as the matching data. Spatial matching involves using data from the 6 ground-based radar databases closest to the rain gauge as the matching data for that rain gauge.

[0088] 55. Based on rain gauge data, systematic bias correction is performed on ground-based radar precipitation data. Specifically, regression analysis is used to statistically compare the systematic bias between ground-based radar precipitation data and rain gauge data. To minimize random differences during the statistical comparison of systematic bias, the optimal dataset with a correlation coefficient greater than or equal to 0.8, obtained in step 54, is first used as a benchmark. A quantitative comparison of the two datasets is then performed to determine the systematic bias of the ground-based radar precipitation data, and systematic bias correction is then applied to the radar precipitation data.

[0089] 56. Classify precipitation types based on the matched precipitation data. First, fit the relationship between polarization parameters and droplet spectrum parameters using raindrop spectrum data. Then, based on the fitted relationship, retrieve the droplet spectrum parameters using ground-based radar measurement data. According to the droplet spectrum parameter relationship method, classify precipitation types into stratiform cloud precipitation and convective precipitation. For specific precipitation type classification methods and steps, please refer to step 2.

[0090] 57. Based on different precipitation types, precipitation intensity is classified. Rainfall above 7.6 mm / h is classified as heavy rain, while rainfall below that is classified as light to moderate rain. A conceptual framework diagram for classifying and classifying precipitation data is shown below. Figure 3 As shown, since precipitation type greatly affects the prior model parameters and likelihood function model parameters, the precipitation data is first divided into stratiform cloud precipitation and convective precipitation according to type. The magnitude of precipitation intensity also has a significant impact on parameter estimation. Therefore, stratiform cloud precipitation is further divided into light to moderate rain and heavy rain according to precipitation intensity, and convective precipitation is further divided into light to moderate rain and heavy rain.

[0091] 58. The ground-based radar precipitation estimation data after systematic bias correction is assumed to be prior information of the true rainfall data. The prior information distribution f(R) T The prior distribution f(R) of the ground-based radar precipitation estimation data is... R We assume it to be normally distributed:

[0092] f(R T )≈f(R R )~N(R G ,σ1)

[0093] The distribution parameter σ1 is obtained by estimating the relative error variance of the matched ground-based radar precipitation data and rain gauge data. Based on the matched ground-based radar precipitation data and rain gauge data, the error between the two is modeled as a normal distribution with a mean of 0 and a variance of σ1, i.e.

[0094] f(R R -R G )~N(0,σ1)

[0095] Since the variance σ1 is affected by precipitation type and intensity, it is further modeled as an exponential distribution.

[0096] σ1~Exp(σ1|λ1)

[0097] The exponential distribution parameter is λ1. Based on the matched data, the error variance of ground-based radar relative to rain gauges for different precipitation types and intensities is statistically analyzed, and then the distribution parameters λ1 of light rain in stratiform cloud precipitation, heavy rain in stratiform cloud precipitation, light rain in convective precipitation, and heavy rain in convective precipitation are estimated.

[0098] 6. Substitute the likelihood function model parameters obtained from the training module into the hierarchical Bayesian fusion framework of step 4. Using spatiotemporally matched ground-based radar precipitation data and spaceborne measurement precipitation data as training samples, estimate the likelihood function model parameters for different precipitation types and intensities. The specific steps are as follows:

[0099] 61. Conduct quality control on spaceborne precipitation data. Spaceborne precipitation data often has readily available precipitation products. Suitable precipitation products can be selected based on coverage and product accuracy, and precipitation data with sensitivity above that of spaceborne measurements should be chosen.

[0100] 62. Perform spatiotemporal matching between the spaceborne precipitation data and the ground-based radar precipitation data corrected for rain gauge system bias. The spatiotemporal matching method is the same as in step 1. Since a large number of samples are needed for training data, select several spatiotemporal matching cases independent of the application module as training samples.

[0101] 63. Based on the matched ground-based radar and spaceborne precipitation data, each pixel is classified into two types: stratiform cloud precipitation and convective precipitation. The precipitation type classification method is the same as in step 2.

[0102] 64. Based on different precipitation types, precipitation intensity is classified according to its magnitude. Rainfall above 7.6 mm / h is classified as heavy rain, while rainfall below that is classified as light to moderate rain, resulting in precipitation patterns such as... Figure 3 The images show light rain in stratiform clouds, heavy rain in stratiform clouds, light to moderate convective rain, and heavy convective rain.

[0103] 65. Based on matched ground-based radar and spaceborne precipitation data, construct the likelihood functions of both and model them as Gaussian distributions.

[0104] f(R s |R T )~N(a+α+(b+β)R R ,σ2)

[0105] The distribution parameters α, β, and σ² are all influenced by precipitation type and intensity. Based on different precipitation types and intensities, the distribution parameters α and β are further modeled as normal distributions α~N(0,σ²) with a mean of 0. α ),β~N(0,σ β ), σ2 is further modeled as an exponential distribution σ2~Exp(σ2|λ2).

[0106] 66. Based on matched data, statistically estimate the distribution basis parameters a and b, and the distribution hyperparameters (σ) of light rain in stratiform cloud precipitation, heavy rain in stratiform cloud precipitation, light rain in convective precipitation, and heavy rain in convective precipitation. α ,σ β ,λ2). The flowchart for estimating the parameters of the likelihood function model is as follows: Figure 4 As shown, the specific steps are as follows:

[0107] 661. Quantitatively compare the spaceborne precipitation data with spatiotemporal matching and the ground-based radar precipitation data after systematic bias correction, and calculate the difference between the two.

[0108] 662. Construct an additive model from the differences between the two data points in step 661, and perform univariate linear regression on the spaceborne precipitation data and the ground-based radar precipitation data:

[0109] R s =a+bR R +ξ

[0110] Where a and b are the fitting parameters of the linear regression, used to explain the systematic bias between spaceborne precipitation data and ground-based radar precipitation data, and ξ is the random error, which follows a normal distribution, i.e., ξ ~ N(0,σ2).

[0111] 663. Using the matched satellite-borne precipitation data and ground-based radar precipitation data samples, perform least-squares fitting on the additive model parameters a and b from step 662 to calculate the model basis parameters a and b.

[0112] 664. Due to the differences between spaceborne precipitation data and ground-based radar precipitation data being affected by precipitation type and intensity, influencing factors α and β are added to the model's basis parameters a and b. The prior distributions of α and β are α~N(0,σ). α ),β~N(0,σ β The posterior probability distribution of the system bias parameters for light rain, heavy rain, light rain, and heavy rain in stratiform cloud precipitation, as well as convective precipitation, was calculated using the Monte Carlo sampling method to obtain the hyperparameter σ. α ,σ β .

[0113] 665. Statistically calculate the probability distribution of the residual ξ of the satellite-borne precipitation data and the ground-based radar precipitation data, and model it as a normal distribution, i.e., ξ ~ N(0,σ2).

[0114] 666. σ² is influenced by precipitation type and intensity, exhibiting an exponential distribution form σ²~Exp(σ²|λ²). The hyperparameter λ² is obtained by calculating the posterior probability distribution of the residual error parameters for light rain in stratiform clouds, heavy rain in stratiform clouds, light rain in convective precipitation, and heavy rain in convective precipitation using the Monte Carlo sampling method.

[0115] 7. Substitute the hierarchical prior model parameters obtained in step 5 and the hierarchical likelihood function model parameters obtained in step 6 into the Bayesian framework f(R) T |R S )∝f(Rs |R T )f(R T In this study, the parameters of the posterior probability distribution of actual ground rainfall are calculated using the Monte Carlo sampling method.

[0116] 8. The mean of the posterior probability distribution of each pixel obtained in step 7 is the fusion result, and the variance of the posterior probability distribution is the uncertainty of the corresponding fusion result.

[0117] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

[0118] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and simple improvements made on the substantive content of the present invention should be included within the protection scope of the present invention.

Claims

1. A fusion algorithm of ground and spaceborne measured precipitation data under a Bayesian framework, characterized in that, The method comprises the following steps: (1) selecting time and space matched satellite-borne and ground-based radar measured precipitation data, setting a certain spatial window and time window when matching, the time window is within ±6 minutes of the time difference between the satellite-borne scanning time of the matching spatial window and the ground-based radar starting time of one body scanning, the spatial window is a circular region with the ground-based radar as the center and r radius, and the region is intersected with the satellite-borne radar mapping strip, wherein r is the scanning range of the ground-based radar, and the pixel space matching uses the grid matching method; (2) dividing the time and space matched ground-based radar and satellite-borne measured precipitation data into two categories of stratiform cloud precipitation and convective precipitation according to the precipitation type; (3) on the basis of the precipitation classification, dividing the stratiform cloud precipitation pixels into light rain and heavy rain according to the precipitation intensity, and dividing the convective precipitation pixels into light rain and heavy rain according to the precipitation intensity, and dividing the precipitation intensity of more than 7.6 mm / h into heavy rain according to the precipitation intensity grading standard, and otherwise into light rain; (4) based on the matched ground-based radar and satellite-borne measured precipitation data of different precipitation types and different precipitation intensities, establishing a hierarchical Bayesian framework to deduce the posterior distribution of the unknown true rainfall, approximating the ground-based radar estimated precipitation result RR as the prior information of the true rainfall RT, giving the conditional probability of the satellite-borne measured precipitation RS under the condition of the true rainfall as the likelihood function, and obtaining the true rainfall through the posterior distribution of the true rainfall under the condition of the known satellite-borne precipitation, since the prior distribution parameters and the likelihood function parameters are related to the precipitation type and other factors such as the precipitation intensity, the model parameters are not fixed values, but are affected by the uncertainty factor to form a certain probability distribution, thereby forming the following hierarchical Bayesian structure form: where denotes proportional to, denotes in the form of a certain probability distribution, f(x) denotes the probability distribution, denotes the conditional probability of the spaceborne measured precipitation RS given the true precipitation RT, i.e. the likelihood function, N(x) denotes a normal distribution, Exp(x) denotes an exponential distribution, denotes the prior probability of the true precipitation in the form of a normal distribution with mean RG and variance a, b are system error parameters of the spaceborne measured precipitation with respect to the ground-based radar precipitation estimation data, which are affected by the precipitation type and the precipitation intensity, and this effect is included in the parameter , , , is in the form of a normal distribution with mean 0 and variance , , , is the scale parameter of the exponential distribution; (5) Using the training samples of ground-based radar precipitation data and rain gauge data with spatiotemporal matching, the prior error model parameters of ground-based radar precipitation data under different precipitation types and different precipitation intensities are estimated ; (6) Using the spatiotemporal matched satellite-borne measurement precipitation data and ground-based radar precipitation data training samples, estimating the likelihood function model parameters a, b under different precipitation types and different precipitation intensities, , , ; (7) Substitute the prior model parameters in step (3) and the likelihood function model parameters in step (4) into the hierarchical Bayesian fusion structure model constructed in step (2) to solve the posterior probability distribution of the real rainfall (8) using the Monte Carlo method to solve the posterior probability distribution parameters of the true rainfall in step (7), wherein the mean value of the estimated posterior probability distribution of each pixel is the fusion result, and the variance is the uncertainty of the corresponding fusion result.

2. The fusion algorithm of ground and spaceborne precipitation measurements under the Bayesian framework according to claim 1, characterized in that, The hierarchical prior error model parameters obtained by training in step (5) comprise the following steps: 5.1) performing quality control on the ground-based radar observation data, removing ground clutter of the ground-based radar data by using the fuzzy logic method, performing attenuation correction of the reflectivity factor Z and the differential reflectivity ZDR by using the adaptive constraint method, and performing median filtering on the differential phase shift rate KDP; 5.2) estimating the near-surface precipitation by using the ground-based radar observation parameters, since the dual-polarization radar can obtain the observation parameters of the reflectivity factor Z, the differential reflectivity ZDR and the differential phase shift rate KDP, the R(Z) relationship, the R(KDP) method and the R(Z, ZDR) method can be used to jointly estimate the precipitation, wherein R is the hourly precipitation, and the precipitation relationship is obtained by fitting the raindrop spectrum data; 5.3) performing quality control on the rain gauge data in the observation range of the ground-based radar, such as removing the too high or too small rainfall data; 5.4) Time and space matching of rain gauge data and dual-polarization radar data to obtain time and space matched dual-polarization radar data samples and rain gauge data samples, the time resolution of rain gauge data is 1 hour, the time resolution of ground-based radar data is 5-8 minutes, so the time matching is to take multiple ground-based radar data within 1 hour and the rain gauge data of 1 hour as matching data, and the space matching is to take the 6 ground-based radar data closest to the rain gauge as the matching data of the rain gauge; 5.5) Quantitative statistical comparison using matched rain gauge data and ground-based radar data, taking rain gauge data as the standard to obtain the systematic bias of ground-based radar precipitation data, and correcting the systematic bias of ground-based radar data; 5.6) Precipitation type classification of matched precipitation data, first using raindrop spectrum data to fit the relationship between polarization parameters and drop spectrum parameters, and then using ground-based radar measurement data to retrieve drop spectrum parameters based on the fitted relationship, and according to the drop spectrum parameter relationship method, the precipitation type is divided into stratiform cloud precipitation and convective precipitation; 5.7) On the basis of different precipitation types, according to the size of precipitation intensity, precipitation intensity classification is carried out, and precipitation intensity above 7.6 mm / h is classified as heavy rain, otherwise it is classified as light rain; 5.8) Based on matched ground-based radar precipitation data and rain gauge data, model the error of both as Gaussian distribution with mean 0 and variance , i.e. , since variance is affected by precipitation type, precipitation intensity, further model it as exponential distribution , where the exponential distribution parameter is ; 5.9) Error variance distribution parameters for stratiform light rain, stratiform heavy rain, convective light rain, convective heavy rain based on matched data statistics .

3. The fusion algorithm of ground and spaceborne precipitation measurements under the Bayesian framework according to claim 1, characterized in that, The model parameters of the hierarchical likelihood function trained in step (6) specifically include the following steps: 6.1) Quality control of spaceborne measurement precipitation data, there are ready-made precipitation products for spaceborne measurement precipitation data, suitable precipitation products can be selected from coverage and product accuracy, and precipitation data with sensitivity above spaceborne measurement is selected; 6.2) Time and space matching of spaceborne measurement precipitation data and ground-based radar precipitation data corrected by rain gauge systematic bias, wherein the time and space matching method is as in step (1), since the training data requires a large number of samples, multiple time and space matching cases independent of the application module are selected as training samples; 6.3) According to the matched ground-based radar and spaceborne measurement precipitation data, the precipitation type is divided into stratiform cloud precipitation and convective precipitation; 6.4) On the basis of different precipitation types, according to the size of precipitation intensity, precipitation intensity classification is carried out, and precipitation intensity above 7.6 mm / h is classified as heavy rain, otherwise it is classified as light rain; 6.5) Based on the matched ground-based radar and spaceborne measurement precipitation data, construct the likelihood function of both and model as normal distribution form , based on different precipitation types, precipitation intensity, further model the distribution parameters , as normal distribution with mean 0 and variance , , further model as exponential distribution ;​ 6.6) Estimate distribution base parameters a, b, and distribution hyperparameters for light rain in stratiform precipitation, heavy rain in stratiform precipitation, light rain in convective precipitation, heavy rain in convective precipitation based on matched data statistics .

Images