CN115204303A - Foundation and satellite-borne measurement precipitation data fusion algorithm under Bayesian framework - Google Patents
Foundation and satellite-borne measurement precipitation data fusion algorithm under Bayesian framework Download PDFInfo
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Abstract
The invention discloses a fusion algorithm of ground-based and satellite-borne measurement precipitation data under a Bayesian framework, which comprises the following steps: the method comprises the steps of selecting data of satellite-borne measurement precipitation and ground-based radar measurement precipitation examples matched in time and space, setting a certain space window and a certain time window during matching, wherein the time window is the time difference between the time when the satellite-borne measurement sweeps through the matched space window and the time when the ground-based radar starts one-time body sweep, and the space window is the region where the ground-based radar is used as the center and a circular region with the radius r is intersected with a surveying and mapping band of the satellite-based radar.
Description
Technical Field
The invention relates to the technical field of meteorological detection data processing, in particular to a fusion algorithm of ground-based and satellite-borne measurement precipitation data under a Bayesian framework.
Background
Accurate precipitation estimation is very important for hydrology, weather forecast early warning, flood disaster monitoring, development and reasonable utilization of water resources and the like. At present, precipitation detection means mainly include a ground rain gauge, a ground-based weather radar, and active and passive sensors carried on a satellite, such as a Dual-frequency rain radar (DPR) carried on a global precipitation observation plan (GPM) main satellite. With the rapid development of weather radar and satellite remote sensing detection technologies and the constantly improved ground rainfall station observation network, various detected rainfall data are optimized and integrated into a set of more complete rainfall information to reduce the uncertainty of rainfall estimation, and the method is a powerful power for developing a multi-source rainfall data fusion algorithm. Precipitation data from different sources have own spatio-temporal scale and error characteristics, and on the basis of quantitative analysis of uncertainty of different precipitation data, advantages and error structures of different precipitation data are integrated, so that the purpose of finally obtaining an optimal rainfall estimation result on the spatio-temporal scale is mainly fusion of different precipitation data.
Conventional precipitation data fusion typically corrects remotely estimated precipitation results such as radar precipitation measurements using ground level rain gauges. The fusion method mainly comprises a probability matching method, a Kalman filtering method, a variation method, a neural network method, a Bayesian cooperative kriging method and the like. In the methods, a rain gauge is used as a true value, and a certain method is applied to correct remote sensing measurement precipitation. However, the rain gauge is mainly used for local point measurement, and has great limitation in the aspect of continuous monitoring of a large-range rainfall dynamic space.
Another concept is to fuse the ground-based radar measurement and the satellite remote sensing measurement precipitation data, such as Guptaetal (2006, amethodolography for measuring multisensonification information basedon radar bipectation maximum knowledge and scale-recursion estimation) combining TRMM satellite-based radar precipitation product and ground-based radar measurement based on Kalman filtering, and Cheneal (2020, amachinelering system for predicting precipitation using deep learning and ground-based radar network concept) fusing the satellite measurement precipitation data and ground-based radar network measurement precipitation by using a deep learning multi-layer sensing structure. In the fusion process, prior information is often needed, the ground-based radar precipitation estimation data and the satellite-based radar precipitation estimation data have self measurement error structural characteristics and represented space-time scales, and the key problem of obtaining the optimal fusion result is how to accurately depict the ground-based radar precipitation estimation system and random errors.
The Bayes framework can be used for calculating the posterior probability distribution of unknown real rainfall according to the known data information, and the uncertainty of the result can be quantified. In hydrologic modeling, we need not only accurate rainfall input, but also quantification of uncertainty in rainfall results. Conventional Bayesian fusion generally describes the overall uncertainty of multi-source information, but the error of precipitation estimation is not only related to the sensor and the represented space-time scale of precipitation measurement, but also related to the type of precipitation and the intensity of precipitation. The invention provides a layered Bayesian fusion algorithm, the uncertainty of prior information is divided into layered cloud and convective precipitation according to radar precipitation error structural characteristics, and then the layered cloud and convective precipitation are divided into precipitation with different intensities according to precipitation intensities under different types of precipitation. Firstly, carrying out system deviation correction on ground radar precipitation estimation by utilizing ground rain gauge data, estimating error model parameters of a layered precipitation structure, secondly, taking the ground radar precipitation estimation after the system deviation correction as prior information of a rainfall true value, and further, calculating posterior distribution of an unknown true rainfall value by using a likelihood function of satellite-borne measurement precipitation and the prior information of the rainfall. The model parameters are influenced by the uncertainty factors, are not fixed values, but are distributed in a certain way, so that a layered Bayesian structure is formed. The prior characteristics and the error structure of rainfall are well described by using the layered structure, so that a more accurate fusion result of real rainfall values and a corresponding uncertainty description can be obtained.
Disclosure of Invention
In order to solve the defects in the background technology, the invention aims to provide a fusion algorithm of ground-based and satellite-borne measurement rainfall data under a Bayesian framework, wherein an error model of rainfall observed by a ground-based radar and an error structure of a likelihood function are modeled into layered structures of rainfall with different types and different intensities according to the error structure characteristics of the rainfall, and then the fusion of the ground-based and satellite-borne measurement rainfall data is carried out by utilizing the Bayesian framework, so that the estimation of the ground-based radar rainfall is fused into the satellite-borne measurement rainfall, the estimation precision of the satellite-borne rainfall is improved, and the uncertainty of the fusion rainfall is described, so that the fusion algorithm can be better applied to weather forecast or a hydrological model.
The purpose of the invention can be realized by the following technical scheme:
a fusion algorithm of ground-based and satellite-borne measurement precipitation data under a Bayesian framework comprises the following steps:
(1) Selecting data of satellite-borne measurement precipitation and ground-based radar measurement precipitation examples matched in time and space, setting a certain space window and a certain time window during matching, wherein the time window is the time difference between the sweep time of the satellite-borne measurement sweeping the matched space window and the start time of one-time volume sweep of the ground-based radar, the space window is the area intersected by the ground-based radar as the center and a circular area with radius r and a satellite-borne radar surveying and mapping zone, wherein r is the scanning range of the ground-based radar, and a lattice point matching method is utilized during pixel space matching,
(2) The time-space matched ground radar and each pixel of the satellite-borne measured precipitation data are divided into two types of laminar cloud precipitation and convective precipitation according to the precipitation type,
(3) On the basis of precipitation classification, layered cloud precipitation pixels are divided into medium and small rains and heavy rains according to precipitation intensity, convective precipitation pixels are divided into medium and small rains and heavy rains according to precipitation intensity, more than 7.6mm/h is divided into heavy rains according to precipitation intensity classification standards, otherwise, the heavy rains are divided into medium and small rains,
(4) Based on matched ground-based radar of different rainfall types and different rainfall intensities and satellite-borne measured rainfall data, a layered Bayesian framework is established to calculate posterior distribution of unknown real rainfall, a result RR of rainfall estimation of the ground-based radar is approximated to prior information of a real rainfall value RT, the conditional probability of the satellite-borne measured rainfall RS under the given real rainfall condition is a likelihood function, the real rainfall is obtained by calculating posterior distribution of the real rainfall under the known satellite-borne rainfall condition, as the prior distribution parameters and the likelihood function parameters are not fixed values but related to the rainfall types and the factors such as the rainfall intensities, the model parameters are influenced by uncertainty factors to form certain probability distribution, and thus the following layered Bayesian structural form is formed:
f(R T |R S )∝f(R s |R T )f(R T )
f(R T )～N(R G ,σ 1 )
σ 1 ～Exp(σ 1 |λ 1 )
f(R s |R T )～N(a+α+(b+β)R R ,σ 2 )
α～N(0,σ α ),β～N(0,σ β ),σ 2 ～Exp(σ 2 |λ 2 )
where ∈ denotes that the expression is proportional to, the expression takes the form of a certain probability distribution, f () denotes the probability distribution, f (R) s |R T ) Representing the conditional probability of the satellite-borne measured precipitation RS given the true rainfall RT, i.e. the likelihood function, N () representing the normal distribution, exp () the exponential distribution, f (R) T )～N(R G ,σ 1 ) Prior probability f (R) representing true rainfall T ) Variance is σ with mean RG 1 The likelihood function a and b are systematic error parameters of the satellite-borne measured precipitation relative to the ground radar precipitation estimation data, and are influenced by the precipitation type and precipitation intensity, wherein the parameters alpha and beta are mean values of 0 and variance of sigma α ，σ β Normal distribution of (a) < lambda > 1 ，λ 2 Is a scale parameter of the exponential distribution,
(5) Estimating prior error model parameter lambda of foundation radar rainfall data under different rainfall types and different rainfall intensities by using space-time matched foundation radar rainfall data and rainfall meter data training samples 1
(6) Estimating likelihood function model parameters a, b, sigma under different precipitation types and different precipitation intensities by using space-borne measurement precipitation data and ground radar precipitation data training samples matched in time and space α ，σ β ,λ 2
(7) Substituting the prior model parameters in the step (3) and the likelihood function model parameters in the step (4) into the step (2) to construct a hierarchical Bayes fusion structure model, and solving the posterior probability distribution f (R) of the real rainfall T |R S )
(8) And (3) solving posterior probability distribution parameters of the step (7) of the real rainfall by utilizing a Monte Carlo method, wherein the mean value of the estimated posterior probability distribution of each pixel is a fusion result, and the variance is the corresponding uncertainty of the fusion result.
The method for obtaining the layered prior error model parameter module through training in the step (5) specifically comprises the following steps:
5.1 Quality control is carried out on the observation data of the ground-based radar, ground clutter removal is carried out on the observation data of the ground-based radar by adopting a fuzzy logic method, attenuation correction is carried out on a reflectivity factor Z and a differential reflectivity ZDR by adopting a self-adaptive constraint method, median filtering is carried out on a differential phase-shifting ratio KDP,
5.2 The ground radar observation parameters are used for estimating the near-ground rainfall, the dual-polarization radar can obtain an observation parameter reflectivity factor Z, a differential reflectivity ZDR and a differential phase shift rate KDP, the R (Z) relation, an R (KDP) method and an R (Z, ZDR) method can be used for jointly estimating the rainfall, wherein R is the hour rainfall, the rainfall relation is obtained by the raindrop spectrum data fitting,
5.3 Quality control of the rain gauge data in the observation range of the ground-based radar, such as removal of excessively high or excessively low rainfall data,
5.4 Time-space matching is carried out on the rain gauge data and the dual-polarization radar data to obtain a time-space matched dual-polarization radar data sample and a rain gauge data sample, the time resolution of the rain gauge data is 1 hour, and the time resolution of the ground radar data is 5-8 minutes, so that the time matching is that a plurality of ground radar data within 1 hour and the rain gauge data within 1 hour are taken as matching data, the space matching is that 6 ground radar library data closest to the rain gauge are taken as the matching data of the rain gauge,
5.5 Carrying out quantitative statistical comparison by using the matched rain gauge data and the ground radar data, obtaining the system deviation of the ground radar rainfall data by taking the rain gauge data as a standard, and carrying out system deviation correction on the ground radar data,
5.6 Classifying the types of the matched precipitation data, firstly fitting the relation between polarization parameters and drop spectrum parameters by using the rain drop spectrum data, further inverting the drop spectrum parameters by using ground radar measurement data based on the fitted relation, classifying the types of the precipitation into laminar cloud precipitation and convective precipitation according to a drop spectrum parameter relation method,
5.7 Based on different precipitation types, classifying the precipitation intensity according to the precipitation intensity, classifying the precipitation intensity of more than 7.6mm/h as heavy rain, and on the contrary, classifying the precipitation intensity as medium and small rain,
5.8 Based on the matched ground radar precipitation data and rain gauge data, the error of the ground radar precipitation data and the rain gauge data is modeled to be 0 in mean and sigma in variance 1 Gaussian distribution of (i.e. f (R) R -R G )～N(0,σ 1 ) Due to variance σ 1 Influenced by the type and intensity of precipitation, the model is further modeled as an exponential distribution sigma 1 ～Exp(σ 1 |λ 1 ) Wherein the index distribution parameter is λ 1 ，
5.9 Estimate error variance distribution parameter lambda of laminar cloud precipitation light rain, laminar cloud precipitation heavy rain, convective precipitation light rain, convective precipitation heavy rain based on matched data statistics 1 。
The step (6) of training to obtain parameters of the layered likelihood function model specifically comprises the following steps:
6.1 Quality control is carried out on the satellite-borne measured precipitation data, the satellite-borne measured precipitation data often have existing precipitation products, suitable precipitation products can be selected from the coverage range and the product precision, precipitation data above the sensitivity of satellite-borne measurement are selected,
6.2 Space-time matching is carried out on the spaceborne measured precipitation data and the ground-based radar precipitation data subjected to the deviation correction of the rain gauge system, wherein the space-time matching method is as the step (1), as a large number of samples are needed for training data, a plurality of space-time matching examples independent of an application module are selected as training samples,
6.3 ) the precipitation types are classified into laminar cloud precipitation and convective precipitation according to the matched ground-based radar and satellite-borne measured precipitation data,
6.4 Based on different precipitation types, classifying the precipitation intensity according to the precipitation intensity, classifying the precipitation intensity of more than 7.6mm/h as heavy rain, and on the contrary, classifying the precipitation intensity as medium and small rain,
6.5 Based on the matched ground-based radar and satellite-borne measurement precipitation data, constructing likelihood functions of the ground-based radar and the satellite-borne measurement precipitation data, and modeling the likelihood functions as a normal distribution form f (R) s |R T )～N(a+α+(b+β)R R ,σ 2 ) Based on different precipitation types and precipitation intensities, the distribution parameters alpha and beta are further modeled to be 0 in mean value and sigma in variance α ，σ β Normal distribution of (2) alpha to N (0, sigma) α ),β～N(0,σ β )，σ 2 Further modeled as an exponential distribution σ 2 ～Exp(σ 2 |λ 2 )，
6.6 Estimate distribution base parameters a, b based on matched data statistics, and distribution hyper-parameters (σ) of light rain in laminar cloud precipitation, heavy rain in laminar cloud precipitation, light rain in convective precipitation, and heavy rain in convective precipitation α ,σ β ,λ 2 )。
The invention has the beneficial effects that:
the method disclosed by the invention is used for fusing the ground radar and the satellite-borne rainfall measurement data based on the layered Bayesian method, improving the accuracy of the satellite-borne instantaneous rainfall measurement, obtaining the high-accuracy and high-resolution rainfall estimation result of comprehensive multi-source rainfall observation, and quantitatively giving the uncertainty contained in the fusion result, so that the method can be better applied to a hydrological model.
Drawings
The invention will be further described with reference to the accompanying drawings.
FIG. 1 is a Bayesian framework fusion general flow chart of ground-based radar and spaceborne measured precipitation data in the invention;
FIG. 2 is a flow chart of precipitation classification based on ground based radar data in accordance with the present invention;
FIG. 3 is a frame chart of precipitation data versus precipitation type versus precipitation intensity in accordance with the present invention;
fig. 4 is a flow chart of parameter estimation of the layered likelihood function model in the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a general flow chart for implementing hierarchical bayesian fusion of ground-based radar estimated precipitation data and spaceborne measured precipitation data in the present invention, which is mainly divided into two modules: training module and application module, the data of training module and application module are independent each other, and wherein the training module mainly divide into two parts: layered prior modeling and likelihood function modeling. The layered prior modeling provides prior model distribution parameters for a layered Bayesian framework in the application module, and the likelihood function modeling provides likelihood model parameters for the layered Bayesian framework in the application module. The basis of the layered modeling is that different precipitation types and precipitation intensities can influence the parameters of the prior model and the likelihood model, so that the final fusion result is influenced. A flow chart for classification of precipitation type based on ground-based radar data is shown in fig. 2. Fig. 3 shows a probability frame chart of precipitation data type and strength. To illustrate the estimation of the distribution parameters and the hyperparameters of the layered likelihood function model in the training module, fig. 4 shows the estimation process of the distribution parameters in the satellite-borne measured precipitation likelihood function.
The general process of fusion of ground-based radar precipitation estimation data and spaceborne measurement precipitation data based on hierarchical Bayes is shown in a general flow chart of figure 1, and comprises the following specific steps:
1. and selecting satellite-borne measurement precipitation and ground radar measurement precipitation which are matched in time and space, and rain gauge data in a corresponding range. The selection method comprises the steps of searching the transit orbit and estimating the transit time by knowing the swath width of the satellite scanning and the intersected earth coordinate position of the swath width and combining the longitude of the track of the satellite reaching the highest latitude, the satellite orbit intercept and the time of the start of the orbit according to the swath shape model. The satellite-borne measurement and ground-based radar data matching area set when the radar transit data is matched is an area where a circular area with the ground-based radar as the center and the ground-based radar detection range as the radius are intersected with the satellite-borne radar surveying and mapping belt. The pixel space matching uses a lattice matching method, namely, the ground radar detection data and the satellite detection data are resampled into a three-dimensional lattice Cartesian coordinate system with a certain resolution by a linear interpolation method. The time for completing one body scan of the foundation radar is 6min, so the matching time window of the set satellite-borne measurement and the data of the foundation radar is +/-6 min, namely the time difference between the time for sweeping the matching space window by the satellite-borne sensor and the time for starting one body scan of the foundation radar is within +/-6 min.
2. And (3) dividing each pixel of the ground radar and the satellite-borne measured precipitation data which are matched in time and space into two types of laminar cloud precipitation and convective precipitation according to the precipitation type. Because the ground radar data has higher resolution and higher precision relative to the satellite-borne measurement, the precipitation type classification is carried out by utilizing the drop spectrum data inverted by the ground radar. A flowchart of rainfall type classification based on ground-based radar data is shown in fig. 2, and the specific steps are as follows:
21. based on raindrop spectrum data N (D) obtained by raindrop spectrometer measurement, calculating by utilizing a T matrix algorithm to obtain scattering amplitudes f of particles with different diameters D, and further calculating to obtain dual-polarization parameters: reflectance factor Z' H And differential reflectance Z' DR ：
Z' H ＝10log 10 (Z' h ),[dBZ]
Z' V ＝10log 10 (Z' v ),[dBZ]
Where λ is the wavelength, K is the particle refractive index, f hh (π,D),f vv (π, D) represents the horizontal and vertical backscatter amplitudes, respectively.
22. Set the blob spectrum model N' (D) as a normalized gamma model, i.e.
Based on actually measured raindrop spectrum data N (D), calculating by utilizing a moment method to obtain a raindrop spectrum parameter N' w ，D' 0 ：
Where < x > represents the desired value, p w Indicating the density of the water.
22. Fitting Z 'with multivariate Linear regression method' H ，Z' DR And a droplet spectrum parameter N' w ，D' 0 Obtaining a relation N 'between the two' w (Z' H ,Z' DR )，D' 0 (Z' H ,Z' DR )。
23. And substituting the reflectivity factor data ZH and the differential reflectivity ZDR which are measured by the foundation radar and correspond to each pixel into the relational expression obtained in the step 22, and performing inversion calculation to obtain the drop spectrum parameters Nw and D0 corresponding to each pixel of the foundation radar.
24. Substituting the drop spectrum parameter D0 calculated in the step 23 into the empirical relation of the precipitation type boundary
Nw1 is calculated and the empirical relationship is found in the literature by Thuraitetal (2016, separation and conversion for conversion into and conversion of microorganisms and decomposition and analysis data).
25. Comparing Nw obtained in the step 23 with Nw1 obtained in the step 24, if Nw > Nw1, the precipitation is convective precipitation, and if Nw < Nw1, the precipitation is lamellar cloud precipitation.
3. On the basis of precipitation classification, the lamellar cloud precipitation pixels are divided into medium and small rains and heavy rains according to precipitation intensity, and the convective precipitation pixels are divided into medium and small rains and heavy rains according to precipitation intensity. According to the precipitation intensity classification standard, the rain with the length of more than 7.6mm/h is classified as heavy rain, and the rain is medium-small rain otherwise.
4. And establishing a layered Bayesian framework to calculate the posterior distribution of unknown real rainfall based on the matched ground-based radar with different rainfall types and different rainfall intensities and satellite-borne measured rainfall data. Because the resolution and precision of the ground-based radar for measuring the rainfall are higher, the result of the ground-based radar for estimating the rainfall is approximate to the prior information of the real rainfall value, and the conditional probability of the satellite-borne rainfall measurement under the condition of the given real rainfall is a likelihood function. The real rainfall is obtained by solving the posterior distribution of the real rainfall under the known satellite-borne rainfall condition. The conventional bayesian framework is given by:
f(R T |R S )∝f(R s |R T )f(R T )
f(R T )～N(R G ,σ 1 )
f(R s |R T )～N(a+bR R ,σ 2 )
where ∈ indicates that is proportional to, indicates that is in a certain probability distribution form, RT is the true rainfall to be solved, RS is the satellite-borne measurement rainfall, RG is the rainfall measured by the rainfall meter, RR is the radar estimated rainfall, and f (x) indicates the probability distribution of x. f (R) s |R T ) Representing the conditional probability of the satellite-borne measured precipitation RS given the true rainfall RT, i.e. the likelihood function, N (x) representing the normal distribution, exp (x) representing the exponential distribution, f (R) T )～N(R G ,σ 1 ) Prior probability f (R) representing true rainfall T ) Variance is σ with mean RG 1 Normal distribution form of (2). And a and b in the likelihood function are systematic error parameters of the satellite-borne measured precipitation relative to the ground-based radar precipitation estimation data. In the formula (a, b, sigma) 1 ,σ 2 ) A bayesian model parameter set theta is constructed. Because the prior distribution parameters and the likelihood function parameters are related to the precipitation type and the precipitation intensity, and the like, the model parameters are not fixed values, but are influenced by uncertainty factors to form certain probability distribution, thereby forming the following hierarchical Bayesian structure form:
f(R T )～N(R G ,σ 1 )
σ 1 ～Exp(σ 1 ｜λ 1 )
f(R s ｜R T )～N(a+α+(b+β)R R ,σ 2 )
α～N(0,σ α ),β～N(0,σ β ),σ 2 ～Exp(σ 2 |λ 2 )
thereby forming a new Bayesian model parameter set theta new (a,b,σ α ,σ β ,λ 1 ,λ 2 ). Wherein Exp (x) represents an exponential distribution. Model parameter sigma α ,σ β ,λ 1 ,λ 2 And (4) carrying out classification estimation under the influence of the type and the intensity of the precipitation. This influence is contained in the parameters α, β, σ 1 ,σ 2 In the formula, alpha and beta are 0 in mean value and sigma in variance α ，σ β Normal distribution of (a) ("lambda") 1 ，λ 2 Is a scale parameter of exponential distribution.
5. And (4) substituting the parameters of the layered prior model obtained in the training module into the layered Bayesian fusion framework in the step (4). The method comprises the following steps of estimating prior error model parameters of the ground radar rainfall data under different rainfall types and different rainfall intensities by using a ground radar rainfall data and rain gauge data training sample matched in time and space, and specifically comprises the following steps:
51. and performing quality control on the observation data of the ground radar, such as clutter removal, attenuation correction and the like. Ground clutter removal is carried out on the ground radar data by adopting a fuzzy logic method, attenuation correction is carried out on a reflectivity factor Z and a differential reflectivity ZDR by adopting a self-adaptive constraint method, and median filtering is carried out on a differential phase shift rate KDP.
52. Because the observation parameters of the ground radar are not rainfall data, rainfall estimation is carried out by a certain inversion algorithm. The ground-based dual-polarization radar can obtain an observation parameter reflectivity factor Z, a differential reflectivity ZDR and a differential phase shift rate KDP, and then the R (Z) relation, an R (KDP) method and an R (Z, ZDR) method can be used for jointly estimating precipitation, wherein R is the hourly precipitation. The precipitation relation can be obtained by fitting raindrop spectrum data.
53. And (3) performing quality control on the rain gauge data in the observation range of the ground radar by adopting a singular point removing method, wherein data with the rainfall less than 0.1mm/h and more than 150mm/h in an hour is removed.
54. And performing space-time matching on the rain gauge data and the dual-polarization radar data to obtain a space-time matched dual-polarization radar data sample and a rain gauge data sample. The time resolution of the rain gauge data is 1 hour, and the time resolution of the ground radar data is about 7 minutes, so that the time matching is performed by using a plurality of ground radar data within 1 hour and the rain gauge data within 1 hour as matching data. The space matching is to take the 6 foundation radar library data closest to the rain gauge as the matching data of the rain gauge.
55. And carrying out system deviation correction on the precipitation data of the ground radar based on the rainfall meter data, wherein the specific method is to use a regression analysis method to count and compare the system deviation between the precipitation data of the ground radar and the rainfall meter data. When the system deviation is statistically compared, in order to avoid the random difference as much as possible, the optimal data set with the correlation coefficient of the matched ground radar precipitation data and rain gauge data which is obtained in the step 54 and is greater than or equal to 0.8 is firstly obtained, the rain gauge data is taken as a reference, the quantitative comparison between the ground radar precipitation data and the rain gauge data is carried out, the system deviation of the ground radar precipitation data is obtained, and the system deviation correction of the radar precipitation data is carried out.
56. And classifying the types of precipitation according to the matched precipitation data. Firstly, fitting the relation between the polarization parameter and the drop spectrum parameter by utilizing the raindrop spectrum data, further utilizing the ground radar measurement data to invert the drop spectrum parameter based on the fitted relation, and dividing the types of precipitation into lamellar cloud precipitation and convective precipitation according to a drop spectrum parameter relation method. The specific precipitation type classification method and steps can refer to step 2.
57. On the basis of different precipitation types, precipitation intensity classification is carried out according to the precipitation intensity. The rain with the length of more than 7.6mm/h is classified as heavy rain, and the rain is classified as medium and light rain otherwise. The conceptual frame diagram for classifying precipitation data into types and intensities is shown in fig. 3, because the precipitation data greatly influence the prior model parameters and the likelihood function model parameters, firstly, the precipitation data are classified into lamellar cloud precipitation and convective precipitation according to the types, the intensity of the precipitation also has larger influence on parameter estimation, and then the lamellar cloud precipitation is further classified into medium-small rain and heavy rain according to the intensity of the precipitation, and the convective precipitation is further classified into medium-small rain and heavy rain.
58. The ground radar rainfall estimation data after the system deviation correction is assumed as prior information of the true rainfall data, and the prior information is distributed f (R) T ) Namely prior distribution f (R) of ground-based radar precipitation estimation data R ) It is assumed to be normally distributed:
f(R T )≈f(R R )～N(R G ,σ 1 )
wherein the distribution parameter σ 1 By estimating the matchAnd obtaining the relative error variance of the radar precipitation data and the rain gauge data of the foundation. Based on the matched ground radar precipitation data and rain gauge data, the error of the ground radar precipitation data and the rain gauge data is modeled to be 0 as a mean value and sigma as a variance 1 Normal distribution of (i.e.
f(R R -R G )～N(0,σ 1 )
Due to variance σ 1 Influenced by the type and intensity of precipitation, the model is further modeled as an exponential distribution
σ 1 ～Exp(σ 1 |λ 1 )
Wherein the exponential distribution parameter is λ 1 . Based on the matched data, the error variance of the foundation radar relative to the rain gauge of different precipitation types and different precipitation intensities is counted, and then the distribution parameters lambda of the small rain in laminar cloud precipitation, the heavy rain in laminar cloud precipitation, the small rain in convective precipitation and the heavy rain in convective precipitation are estimated 1 。
6. And substituting the likelihood function model parameters obtained in the training module into the layered Bayes fusion framework in the step 4. The method comprises the following steps of estimating likelihood function model parameters of different precipitation types and different precipitation intensities by using space-time matched ground radar precipitation data and spaceborne measurement precipitation data training samples, and specifically comprises the following steps:
61. and performing quality control on the satellite-borne measured precipitation data. The satellite-borne measurement precipitation data usually have existing precipitation products, and suitable precipitation products can be selected from the coverage range and the product precision, and the precipitation data above the sensitivity of satellite-borne measurement is selected.
62. And performing space-time matching on the satellite-borne measured precipitation data and the ground-based radar precipitation data subjected to the system deviation correction of the rain gauge. The method of spatio-temporal matching is identical to the method in step 1. Because a large number of samples are needed for training data, a plurality of space-time matching examples independent of the application module are selected as training samples.
63. And according to the matched ground radar and satellite-borne measured precipitation data, dividing each pixel into two types of laminar cloud precipitation and convective precipitation. The precipitation type classification method is consistent with the step 2.
64. On the basis of different precipitation types, precipitation intensity classification is carried out according to the precipitation intensity. When the rain is heavy rain, or medium rain, the rain is laminar cloud medium light rain, laminar cloud heavy rain, convective medium light rain, and convective heavy rain as shown in fig. 3.
65. Based on the matched ground-based radar and satellite-borne measurement precipitation data, likelihood functions of the ground-based radar and the satellite-borne measurement precipitation data are constructed and modeled into a Gaussian distribution form
f(R s |R T )～N(a+α+(b+β)R R ,σ 2 )
Wherein the distribution parameters alpha, beta, sigma 2 Are all affected by the type of precipitation and the intensity of precipitation. Based on different precipitation types and precipitation intensities, the distribution parameters alpha and beta are further modeled into normal distribution alpha-N (0, sigma) with the mean value of 0 α ),β～N(0,σ β )，σ 2 Further modeled as an exponential distribution σ 2 ～Exp(σ 2 |λ 2 )。
66. And (3) estimating distribution base parameters a and b based on matched data statistics, and distribution hyper-parameters (sigma) of light rain in laminar cloud precipitation, heavy rain in laminar cloud precipitation, light rain in convective precipitation and heavy rain in convective precipitation α ,σ β ,λ 2 ). The flowchart of likelihood function model parameter estimation is shown in fig. 4, and the specific steps are as follows:
661. and quantitatively comparing the space-borne measurement precipitation data matched with the space-time space-borne measurement precipitation data with the ground-based radar precipitation data corrected by the system deviation, and calculating the difference between the space-borne measurement precipitation data and the ground-based radar precipitation data.
662. And (4) constructing the difference between the two in the step 661 as an addition model, and performing unary linear regression on the satellite-borne measured precipitation data and the ground-based radar precipitation data:
R s ＝a+bR R +ξ
wherein a and b are fitting parameters of linear regression, and are used for explaining the system deviation of the satellite-borne measurement precipitation data and the ground radar precipitation data, xi is a random error and meets the normal distribution, namely xi-N (0, sigma) 2 )。
663. And performing least square fitting on the additive model parameters a and b in the step 662 by using the matched satellite-borne measurement precipitation data and the ground radar precipitation data samples, and calculating to obtain model base parameters a and b.
664. Because the difference between the satellite-borne measured precipitation data and the ground radar precipitation data is influenced by the precipitation type and the precipitation intensity, influence factors alpha and beta are added on the basis of model base parameters a and b, wherein the prior distribution of the alpha and the beta is alpha-N (0, sigma) α ),β～N(0,σ β ). Calculating posterior probability distribution of system deviation parameters of laminar cloud precipitation light rain, laminar cloud precipitation heavy rain, convective precipitation light rain and convective precipitation heavy rain by using Monte Carlo sampling method to obtain hyper-parameter sigma α ,σ β 。
665. The probability distribution of residual xi of the satellite-borne measurement rainfall data and the ground radar rainfall data is calculated in a statistical mode and modeled into a normal distribution form, namely xi-N (0, sigma) 2 )。
666.σ 2 Influenced by the type of precipitation and the intensity of the precipitation, and takes an exponential distribution form sigma 2 ～Exp(σ 2 |λ 2 ). Calculating the posterior probability distribution of residual error parameters of the laminar cloud precipitation light rain, the laminar cloud precipitation heavy rain, the convective precipitation light rain and the convective precipitation heavy rain by using a Monte Carlo sampling method to obtain the hyper-parameter lambda 2 。
7. Substituting the layered prior model parameters obtained by calculation in the step 5 and the layered likelihood function model parameters obtained by calculation in the step 6 into a Bayesian frame f (R) T |R S )∝f(R s |R T )f(R T ) And calculating the posterior probability distribution parameters of the real ground rainfall by using a Monte Carlo sampling method.
8. The mean value 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.
The foregoing shows and describes the general principles, principal features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are described in the specification and illustrated only to illustrate the principle of the present invention, but that various changes and modifications may be made therein without departing from the spirit and scope of the present invention, which fall within the scope of the invention as claimed.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and should not be taken as limiting the invention, and any modifications, equivalents and simple improvements made on the spirit of the present invention should be included in the scope of the present invention.
Claims (3)
1. A fusion algorithm of ground-based and satellite-borne measurement precipitation data under a Bayesian framework is characterized by comprising the following steps:
(1) Selecting data of satellite-borne measurement precipitation and ground-based radar measurement precipitation examples matched in time and space, setting a certain space window and a certain time window during matching, wherein the time window is the time difference between the sweep time of the satellite-borne measurement sweeping the matched space window and the start time of one-time volume sweep of the ground-based radar, the space window is the area intersected by the ground-based radar as the center and a circular area with radius r and a satellite-borne radar surveying and mapping zone, wherein r is the scanning range of the ground-based radar, and a lattice point matching method is utilized during pixel space matching,
(2) The time-space matched ground radar and each pixel of the satellite-borne measured precipitation data are divided into two types of laminar cloud precipitation and convective precipitation according to the precipitation type,
(3) On the basis of precipitation classification, layered cloud precipitation pixels are divided into medium and small rains and heavy rains according to precipitation intensity, convective precipitation pixels are divided into medium and small rains and heavy rains according to precipitation intensity, more than 7.6mm/h is divided into heavy rains according to precipitation intensity classification standards, otherwise, the heavy rains are divided into medium and small rains,
(4) Based on matched ground-based radar of different rainfall types and different rainfall intensities and satellite-borne measured rainfall data, a layered Bayesian framework is established to calculate posterior distribution of unknown real rainfall, a result RR of rainfall estimation of the ground-based radar is approximated to prior information of a real rainfall value RT, the conditional probability of the satellite-borne measured rainfall RS under the given real rainfall condition is a likelihood function, the real rainfall is obtained by calculating posterior distribution of the real rainfall under the known satellite-borne rainfall condition, as the prior distribution parameters and the likelihood function parameters are not fixed values but related to the rainfall types and the factors such as the rainfall intensities, the model parameters are influenced by uncertainty factors to form certain probability distribution, and thus the following layered Bayesian structural form is formed:
f(R T |R S )∝f(R s |R T )f(R T )
f(R T )～N(R G ,σ 1 )
σ 1 ～Exp(σ 1 |λ 1 )
f(R s |R T )～N(a+α+(b+β)R R ,σ 2 )
α～N(0,σ α ),β～N(0,σ β ),σ 2 ～Exp(σ 2 |λ 2 )
where ∈ indicates that the expression is proportional to, the expression is in the form of a certain probability distribution, f (x) indicates the probability distribution, and f (R) s |R T ) Representing the conditional probability of the satellite-borne measured precipitation RS given the true rainfall RT, i.e. the likelihood function, N (x) representing the normal distribution, exp (x) representing the exponential distribution, f (R) T )～N(R G ,σ 1 ) Prior probability f (R) representing true rainfall T ) Variance is σ with mean RG 1 The likelihood function a and b are systematic error parameters of the satellite-borne measured precipitation relative to the ground radar precipitation estimation data, and are influenced by the precipitation type and precipitation intensity, wherein the parameters alpha and beta are mean values of 0 and variance of sigma α ，σ β Normal distribution of (a) < lambda > 1 ，λ 2 Is a scale parameter of the exponential distribution,
(5) Estimating prior error model parameter lambda of foundation radar rainfall data under different rainfall types and different rainfall intensities by using space-time matched foundation radar rainfall data and rainfall meter data training samples 1
(6) Estimating likelihood function model parameters a, b, sigma under different precipitation types and different precipitation intensities by using space-borne measurement precipitation data and ground radar precipitation data training samples matched in time and space α ，σ β ,λ 2
(7) The prior model parameter in the step (3) and the likelihood in the step (4) are comparedSubstituting the function model parameters into the hierarchical Bayes fusion structure model constructed in the step (2) to solve the posterior probability distribution f (R) of the real rainfall T |R S )
(8) And (3) solving posterior probability distribution parameters of the step (7) of the real rainfall by utilizing a Monte Carlo method, wherein the mean value of the estimated posterior probability distribution of each pixel is a fusion result, and the variance is the corresponding uncertainty of the fusion result.
2. The module for obtaining parameters of a layered prior error model trained in step (5) according to claim 1, specifically comprising the steps of:
5.1 Quality control is carried out on the observation data of the ground-based radar, ground clutter removal is carried out on the observation data of the ground-based radar by adopting a fuzzy logic method, attenuation correction is carried out on a reflectivity factor Z and a differential reflectivity ZDR by adopting a self-adaptive constraint method, median filtering is carried out on a differential phase-shifting ratio KDP,
5.2 The ground radar observation parameters are used for estimating the near-ground rainfall, the dual-polarization radar can obtain an observation parameter reflectivity factor Z, a differential reflectivity ZDR and a differential phase shift rate KDP, the R (Z) relation, an R (KDP) method and an R (Z, ZDR) method can be used for jointly estimating the rainfall, wherein R is the hour rainfall, the rainfall relation is obtained by the raindrop spectrum data fitting,
5.3 Quality control of the rain gauge data in the observation range of the ground-based radar, such as removal of excessively high or excessively low rainfall data,
5.4 Time-space matching is carried out on the rain gauge data and the dual-polarization radar data to obtain a dual-polarization radar data sample and a rain gauge data sample which are matched in time-space mode, the time resolution of the rain gauge data is 1 hour, the time resolution of the ground radar data is 5-8 minutes, therefore, the time matching is that a plurality of ground radar data within 1 hour and the rain gauge data within 1 hour are used as matching data, the space matching is that 6 ground radar base data which are nearest to the rain gauge are used as the matching data of the rain gauge,
5.5 Carrying out quantitative statistical comparison by using the matched rain gauge data and the ground radar data, obtaining the system deviation of the ground radar rainfall data by taking the rain gauge data as a standard, and carrying out system deviation correction on the ground radar data,
5.6 Classifying the types of the matched precipitation data, firstly fitting the relation between polarization parameters and drop spectrum parameters by using the rain drop spectrum data, further inverting the drop spectrum parameters by using ground radar measurement data based on the fitted relation, classifying the types of the precipitation into laminar cloud precipitation and convective precipitation according to a drop spectrum parameter relation method,
5.7 Based on different precipitation types, classifying the precipitation intensity according to the precipitation intensity, classifying the precipitation intensity of more than 7.6mm/h as heavy rain, and on the contrary, classifying the precipitation intensity as medium and small rain,
5.8 Based on the matched ground radar precipitation data and rain gauge data, the error of the ground radar precipitation data and the rain gauge data is modeled to be 0 in mean and sigma in variance 1 Gaussian distribution of (i.e. f (R) R -R G )～N(0,σ 1 ) Due to variance σ 1 Influenced by the type and intensity of precipitation, the model is further modeled as an exponential distribution sigma 1 ～Exp(σ 1 |λ 1 ) Wherein the index distribution parameter is λ 1 ，
5.9 Estimate error variance distribution parameter lambda of laminar cloud precipitation light rain, laminar cloud precipitation heavy rain, convective precipitation light rain, convective precipitation heavy rain based on matched data statistics 1 。
3. The method of claim 1, wherein the step (6) of training obtains parameters of the model of the hierarchical likelihood function, and specifically comprises the steps of:
6.1 Quality control is carried out on the satellite-borne measured precipitation data, the satellite-borne measured precipitation data often have existing precipitation products, suitable precipitation products can be selected from the coverage range and the product precision, precipitation data above the sensitivity of satellite-borne measurement are selected,
6.2 Space-time matching is carried out on the spaceborne measured precipitation data and the ground-based radar precipitation data subjected to the deviation correction of the rain gauge system, wherein the space-time matching method is as the step (1), as a large number of samples are needed for training data, a plurality of space-time matching examples independent of an application module are selected as training samples,
6.3 ) the precipitation types are classified into lamellar cloud precipitation and convective precipitation according to the matched ground-based radar and satellite-borne measured precipitation data,
6.4 Based on different precipitation types, classifying the precipitation intensity according to the precipitation intensity, classifying the precipitation intensity of more than 7.6mm/h as heavy rain, and on the contrary, classifying the precipitation intensity as medium and small rain,
6.5 Constructing likelihood functions of the ground-based radar and the satellite-borne measurement precipitation data based on matching, and modeling the likelihood functions as a normal distribution form f (R) s |R T )～N(a+α+(b+β)R R ,σ 2 ) Based on different precipitation types and precipitation intensities, the distribution parameters alpha and beta are further modeled to be 0 in mean value and sigma in variance α ，σ β Normal distribution of (2) alpha to N (0, sigma) α ),β～N(0,σ β )，σ 2 Further modelled as exponential distribution σ 2 ～Exp(σ 2 |λ 2 )，
6.6 Estimate distribution base parameters a, b based on matched data statistics, and distribution hyper-parameters (σ) of light rain in laminar cloud precipitation, heavy rain in laminar cloud precipitation, light rain in convective precipitation, and heavy rain in convective precipitation α ,σ β ,λ 2 )。
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| CN117540173A (en) * | 2024-01-09 | 2024-02-09 | 长江水利委员会水文局 | Flood simulation uncertainty analysis method based on Bayesian joint probability model |
| CN117540173B (en) * | 2024-01-09 | 2024-04-19 | 长江水利委员会水文局 | Flood simulation uncertainty analysis method based on Bayesian joint probability model |
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