Polarization radar data set assimilation method based on raindrop mass weight average diameter under double-parameter scheme

Abstract

The invention discloses a polarization radar data set assimilation method based on a raindrop mass weight average diameter under a double-parameter scheme, and the method comprises the following steps: reading the total concentration and mixing ratio of background field raindrops, and diagnosing the mass weight average diameter of the background field raindrops based on a gamma distribution parameter relation in a double-parameter microphysical scheme; performing explicit updating or implicit updating on the grid points in the observation influence range of the polarization radar; further correcting the total concentration and the mixing ratio of the raindrops by using the assimilation analysis field; the method further improves the precision of mode analysis field micro-physical state estimation.

Description

Technical Field

[0001] The invention relates to the field of atmospheric science and technology, and in particular to a polarization radar data set assimilation method based on raindrop mass weighted average diameter under a dual-parameter scheme. Background Art

[0002] Dual polarization radar uses dual polarization technology to transmit and receive horizontal and vertical polarized electromagnetic waves. Compared with conventional Doppler weather radar, dual polarization radar can not only measure the horizontal reflectivity factor (Z H ), radial wind (V R ) In addition to these two basic information, the differential reflectivity ( Z DR These new detection quantities reflect the type, shape, size, direction and other information of clouds and precipitation particles, which can deepen our understanding of microphysical processes in precipitation systems. Therefore, dual-polarization radar data assimilation has a good application prospect in numerical weather forecasting.

[0003] At present, the theories of variational, ensemble, and hybrid data assimilation methods are relatively mature. In comparison, the ensemble assimilation method uses a set to represent the probability distribution of the system state, so it is suitable for nonlinear observation operators. In addition, the model error is directly introduced into the ensemble assimilation process, and when the number of ensemble samples is large enough, the representativeness and independence are good enough, it can provide a more accurate error estimate. Based on the above factors, the ensemble assimilation method is widely used in the assimilation of unconventional observation data such as radar and satellite; however, at present, due to the mass-weighted average diameter of raindrops Non-model forecast quantity, based on radar data Z DR In the collection assimilation of , implicit methods are often used to update , there is a lack of accurate estimation of the microphysical state of the model initial field. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a method for ensemble assimilation of polarized radar data based on the weighted average diameter of raindrop mass under a dual-parameter scheme, which explicitly introduces Z DR and Direct relationship, compared to implicit update , this explicit update This method is expected to obtain more accurate analysis results and further improve the accuracy of the estimation of the microphysical state of the model analysis field.

[0005] Technical solution: The polarization radar data set assimilation method based on the raindrop mass weighted average diameter under a dual-parameter scheme described in the present invention comprises the following steps: (1) Read the total raindrop concentration of the background field and mixing ratio , based on the gamma distribution parameter relationship in the dual-parameter microphysics scheme, through the formula ; ; Mass-weighted mean diameter of raindrops in the diagnostic background field ;in, and are the densities of water and air respectively, π is the circumference of a circle, is the shape parameter, is the slope parameter, represents the gamma function; (2) For grid points within the influence range of polarimetric radar observation, if the mass-weighted average diameter of the diagnostic background raindrops of all ensemble members is satisfy , then the average diameter update MDU method is used to explicitly update , get the updated total raindrop concentration Mixing ratio and mass weighted mean diameter If there are set members that do not meet the conditions, they are implicitly updated and only the updated total raindrop concentration is obtained. and mixing ratio ; (3) Use the assimilated analysis field to further correct the total raindrop concentration and mixing ratio.

[0006] Furthermore, in step (1), the gamma distribution of the dual-parameter microphysics scheme is: ; in, is the intercept parameter, is the shape parameter, is the slope parameter, and Set to a fixed value.

[0007] Furthermore, in step (2), explicitly update The method includes: taking it as an analysis variable, updating it through the collective assimilation formula based on the collective covariance relationship; the formula is as follows: ; Among them, X is the state variable vector, H is the observation operator, is the observation, K is the Kalman gain matrix, B is the background error covariance matrix, and R is the observation error covariance matrix, where the superscript anal stands for analysis, bk stands for background, and T stands for the transpose of the matrix.

[0008] Furthermore, based on the differential reflectivity Z DR The observation operator is constructed based on the direct relationship with the mass-weighted average diameter of raindrops, and the formula is as follows: ; in, is the shape parameter, and are the horizontal and vertical reflectivity factors of raindrops, and are the powers obtained by fitting the long-axis and short-axis backscattering amplitudes of raindrops using power fitting, respectively.

[0009] Furthermore, step (3) is as follows: If step (2) is an explicit update, use the formula in step (1) to calculate the total raindrop concentration from the analyzed , Mixing ratio and the mass-weighted mean diameter of raindrops The total raindrop concentration was diagnosed in Harmony ratio , and replace the original analysis field as the final input of the model; if it is an implicit update, it is directly used and As an analytical field.

[0010] Furthermore, in step (3), and The formula is: ; ; in, and are the densities of water and air respectively, π is the circumference of a circle, is the shape parameter, is the mass-weighted mean diameter of the raindrops analyzed, is the total raindrop concentration analyzed, is the raindrop mixing ratio under analysis and Γ represents the gamma function.

[0011] An electronic device described in the present invention includes a memory, a processor, and a computer program stored in the memory, and the processor implements the steps of any one of the methods when executing the program.

[0012] A computer-readable storage medium according to the present invention stores a computer program, and when the program is executed by a processor, the steps of any one of the methods are implemented.

[0013] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: Under the condition of the dual-parameter scheme, the present invention is better than the traditional implicit update The present invention is based on Z DR and Direct relationship through assimilation Z DR Observations are explicitly updated based on the explicit update and then correct and , improve the accuracy of the microphysical state estimation of the model initial value field, thereby improving the polarization Z DR Assimilation forecasting skills. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a flow chart of the present invention; Figure 2 For the exponential distribution of the present invention Z DR and D m The relationship between. DETAILED DESCRIPTION

[0015] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0016] like Figure 1 As shown, an embodiment of the present invention provides a polarization radar data set assimilation method based on raindrop mass weighted average diameter under a dual-parameter scheme, comprising the following steps: Step 1: Diagnose the mass-weighted mean diameter of background raindrops Most microphysical parameterization schemes in numerical models use the gamma distribution to describe the number concentration of raindrops. : (1); in, is the intercept parameter, is the shape parameter, is the slope parameter. For the dual-parameter microphysics scheme, and Usually set to a fixed value, so only the total raindrop concentration ( ) and mixing ratio ( ) are the two parameters for forecast. Read the QNRAIN ( ) and QRAIN ( ) variables, the mass-weighted average diameter of background field raindrops can be diagnosed with the help of these two prediction quantities through the following formula: (2); (3); in, and are the densities of water and air respectively, π is the circumference of a circle, is the shape parameter, is the slope parameter, Represents the gamma function.

[0017] Step 2: Check the consistency of set members and update variables According to the radar observation operator, the level of raindrops ( ) and vertical ( ) The reflectivity factor is calculated by the following formula: (4); (5); in, ; ; ; in, λ is the radar wavelength, is the dielectric constant of water. and are the backscattering amplitudes of the major and minor axes calculated by the T-matrix method, respectively. and are the mean and standard deviation of the raindrop inclination angle, both of which are 0, so we have A =1, B = C = 0. The power fitting method is used to fit the scattering amplitude of raindrops into a function of diameter: (6); (7); Fitting results , , Substituting the fitting results into equations (4) and (5) and integrating the diameter, we can obtain the raindrop level ( ) and vertical ( ) The reflectivity factor is: (8); (9); Differential reflectivity of raindrops ( Z DR ) is defined as: (10); Substituting (3) into (10), we can obtain Z DR and There is the following relationship between them: (11); Therefore, the raindrops Z DR and There is a one-to-one relationship between them. In particular, when , that is, when the gamma distribution in formula (1) is simplified to the exponential distribution, the relationship between the two is as follows: Figure 2 shown.

[0018] Raindrop-based Z DR and There is a one-to-one relationship between them. According to the consistency check results of the set members, the variables for set assimilation update are determined and assimilation analysis is performed: Z DR Observe a grid point within the influence range, if all the set members at the grid point If the values ​​are between 0 mm and 5 mm, the MDU method is used to directly update , that is, in the ensemble assimilation, it is also used as an analysis variable and updated using the ensemble covariance relationship to obtain the updated total raindrop concentration ( )、Mixture ratio( ) and the mass-weighted mean diameter ( ); If there is a set member that does not meet the conditions at the grid point, then As the analysis variable, only the updated total raindrop concentration ( ) and mixing ratio ( ). The update formula for the set assimilation is: (12); (13); Step 3: Use the assimilated analysis field to further correct the total concentration and mixing ratio of raindrops; the details are as follows: After the MDU method completes the ensemble assimilation, use equations (2) and (3) to obtain the total concentration and mixing ratio of raindrops from the analyzed , , Diagnosed in and , replacing the original and : (14); (15); in, and are the densities of water and air respectively, π is the circumference of a circle, is the shape parameter, is the mass-weighted mean diameter of the raindrops analyzed, is the total raindrop concentration analyzed, is the raindrop mixing ratio under analysis and Γ represents the gamma function.

Claims

1. A polarization radar data set assimilation method based on raindrop mass weighted average diameter under a dual-parameter scheme, characterized in that: The following steps are involved: (1) Read the total raindrop concentration of the background field and mixing ratio , based on the gamma distribution parameter relationship in the dual-parameter microphysics scheme, through the formula ； ； Mass-weighted mean diameter of raindrops in the diagnostic background field ;in, and are the densities of water and air respectively, π is the circumference of a circle, is the shape parameter, is the slope parameter, represents the gamma function; (2) For grid points within the influence range of polarimetric radar observation, if the mass-weighted average diameter of the diagnostic background raindrops of all ensemble members is satisfy , then the average diameter update MDU method is used to explicitly update , get the updated total raindrop concentration Mixing ratio and mass weighted mean diameter If there are set members that do not meet the conditions, they are implicitly updated and only the updated total raindrop concentration is obtained. and mixing ratio ; (3) Use the assimilated analysis field to further correct the total raindrop concentration and mixing ratio.

2. According to the method for normalizing polarization radar data collection based on raindrop mass weighted average diameter under a dual-parameter scheme of claim 1, it is characterized in that: In step (1), the gamma distribution of the dual-parameter microphysics scheme is: ； in, is the intercept parameter, is the shape parameter, is the slope parameter, and Set to a fixed value.

3. According to the method for normalizing polarization radar data collection based on raindrop mass weighted average diameter under a dual-parameter scheme as described in claim 2, it is characterized in that: In step (2), explicitly update The method includes: taking it as an analysis variable, updating it through the collective assimilation formula based on the collective covariance relationship; the formula is as follows: ； Among them, X is the state variable vector, H is the observation operator, is the observation, K is the Kalman gain matrix, B is the background error covariance matrix, and R is the observation error covariance matrix, where the superscript anal stands for analysis, bk stands for background, and T stands for the transpose of the matrix.

4. According to the method for normalizing polarization radar data collection based on raindrop mass weighted average diameter under a dual-parameter scheme of claim 3, it is characterized in that: Based on differential reflectivity Z DR The observation operator is constructed based on the direct relationship with the mass-weighted average diameter of raindrops, and the formula is as follows: ； in, is the shape parameter, and are the horizontal and vertical reflectivity factors of raindrops, and are the powers obtained by fitting the long-axis and short-axis backscattering amplitudes of raindrops using power fitting, respectively.

5. According to the method for normalizing polarization radar data collection based on raindrop mass weighted average diameter under a dual-parameter scheme as described in claim 4, it is characterized in that: Step (3) is as follows: If step (2) is an explicit update, use the formula in step (1) to calculate the total raindrop concentration from the analyzed , Mixing ratio and the mass-weighted mean diameter of raindrops The total raindrop concentration was diagnosed in Harmony ratio , and replace the original analysis field as the final input of the model; If it is an implicit update, directly use and As an analysis field.

6. The polarization radar data collection and normalization method based on the raindrop mass weighted average diameter under the dual-parameter scheme of claim 5 is characterized in that: In step (3), and The formula is: ； ； in, and are the densities of water and air respectively, π is the circumference of a circle, is the shape parameter, is the mass-weighted mean diameter of the raindrops analyzed, is the total raindrop concentration analyzed, is the raindrop mixing ratio under analysis and Γ represents the gamma function.

7. An electronic device comprising a memory, a processor and a computer program stored in the memory, characterized in that: When the processor executes the program, the steps of the method according to any one of claims 1 to 6 are implemented.

8. A computer-readable storage medium storing a computer program, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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