A dual-parameter method for polarimetric radar data integration based on raindrop mass-weighted mean diameter

Abstract

The present invention discloses a polarimetric radar data assimilation method based on the mass-weighted average diameter of raindrops under a dual-parameter scheme, comprising the following steps: reading the total raindrop concentration and mixing ratio of the background field, and diagnosing the mass-weighted average diameter of the background field raindrops based on the relationship between the gamma distribution parameters in the dual-parameter microphysics scheme; performing explicit or implicit updates on the grid points within the influence range of the polarimetric radar observation; further correcting the total raindrop concentration and mixing ratio using the assimilated analysis field; and further improving the accuracy of the microphysical state estimation of the pattern analysis field.

Description

Technical Field

[0001] The present invention relates to the field of atmospheric science and technology, and in particular to a polarization radar data integration and 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 polarization quantities, such as α, β, and β, provide information about the type, shape, size, and orientation of cloud and precipitation particles, deepening our understanding of the microphysical processes in precipitation systems. Therefore, dual-polarization radar data assimilation holds great promise for application in numerical weather forecasting.

[0003] At present, the theories of data assimilation methods such as variational, ensemble, and hybrid are relatively mature. In comparison, the ensemble assimilation method uses the ensemble 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 more accurate error estimates. 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, the average diameter of raindrops is not good enough. Non-model forecast quantity, radar data Z DR In the collection assimilation of the implicit 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 dual-parameter scheme based on the average diameter of raindrop mass weights for polarization radar data integration and assimilation, 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 assimilation method based on the raindrop mass-weighted average diameter under a dual-parameter scheme described in the present invention includes the following steps:

[0006] (1) Read the total raindrop concentration of the background field and mixing ratio , based on the relationship between the gamma distribution parameters in the dual-parameter microphysics scheme, through the formula

[0007] ;

[0008] ;

[0009] 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;

[0010] (2) For the grid points within the influence range of polarization 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 ;

[0011] (3) Use the assimilated analysis field to further correct the total concentration and mixing ratio of raindrops.

[0012] Furthermore, in step (1), the gamma distribution of the dual-parameter microphysics scheme is:

[0013] ;

[0014] in, is the intercept parameter, is the shape parameter, is the slope parameter, and Set to a fixed value.

[0015] Furthermore, in step (2), explicitly update The method includes: using it as an analysis variable, updating it through the collective assimilation formula based on the collective covariance relationship; the formula is as follows:

[0016] ;

[0017] 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.

[0018] 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:

[0019] ;

[0020] 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.

[0021] Furthermore, step (3) is as follows: If step (2) is an explicit update, use the formula of 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 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 analytical field.

[0022] Furthermore, in step (3), and The formula is:

[0023] ;

[0024] ;

[0025] 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.

[0026] 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.

[0027] The computer-readable storage medium of the present invention stores a computer program, which implements the steps of any one of the methods when executed by a processor.

[0028] Beneficial effects: Compared with the existing technology, 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 the method Z DR and Direct relationship through assimilation Z DR Observations are updated explicitly, based on the explicit update and then correct and , improve the accuracy of the microphysical state estimation of the model initial field, thereby improving the polarization Z DR Assimilated forecasting techniques. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a flow chart of the present invention;

[0030] Figure 2 Under the exponential distribution of the present invention Z DR and D m The relationship between them. DETAILED DESCRIPTION

[0031] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0032] like Figure 1 As shown, an embodiment of the present invention provides a polarization radar data collection and assimilation method based on raindrop mass weighted average diameter under a dual-parameter scheme, comprising the following steps:

[0033] Step 1: Diagnose the mass-weighted mean diameter of background raindrops

[0034] Most microphysical parameterization schemes in numerical models use the gamma distribution to describe the number concentration of raindrops. :

[0035] (1);

[0036] in, is the intercept parameter, is the shape parameter, is the slope parameter. For the dual-parameter microphysics scheme, and It is 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 raindrops can be diagnosed with the help of these two forecast quantities using the following formula:

[0037] (2);

[0038] (3);

[0039] 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.

[0040] Step 2: Check the consistency of set members and update variables

[0041] According to the radar observation operator, the level of raindrops ( ) and vertical ( ) The reflectivity factor is calculated by the following formula:

[0042] (4);

[0043] (5);

[0044] in, ;

[0045] ;

[0046] ;

[0047] 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 tilt 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:

[0048] (6);

[0049] (7);

[0050] Fitting results , , Substituting the fitting results into equations (4) and (5) and integrating the diameter, we can get the raindrop level ( ) and vertical ( ) The reflectivity factor is:

[0051] (8);

[0052] (9);

[0053] Differential reflectivity of raindrops ( Z DR ) is defined as:

[0054] (10);

[0055] Substituting (3) into (10) we can obtain Z DR and The following relationship exists between them:

[0056] (11);

[0057] Therefore, the raindrops Z DR and There is a one-to-one relationship between . 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.

[0058] 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 of the 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 this 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, the ensemble covariance relationship is used as the analysis variable to update the total raindrop concentration, and the updated total raindrop concentration can be obtained ( )、Mixture ratio( ) and 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:

[0059] (12);

[0060] (13);

[0061] 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 collective assimilation, use (2) and (3) to get the total concentration and mixing ratio of raindrops from the analyzed 、 、 Diagnosed and , replacing the original and :

[0062] (14);

[0063] (15);

[0064] 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 assimilation method based on raindrop mass-weighted average diameter under a dual-parameter scheme, characterized by: The following steps are involved: (1) Read the total raindrop concentration of the background field and mixing ratio , based on the relationship between the gamma distribution parameters 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 the grid points within the influence range of polarization 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; specifically: If step (2) is an explicit update, use the formula in step (1) to get the total raindrop concentration from the analysis. , mixing ratio and the mass-weighted mean diameter of raindrops The total raindrop concentration analyzed in the diagnosis and the mixing ratio of the analysis , and replace the original analysis field as the final input of the model; if it is an implicit update, directly use and as a field of analysis; in, 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.

2. The polarization radar data collection and normalization method based on raindrop mass weighted average diameter under a dual-parameter scheme according to claim 1 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. The polarization radar data collection and normalization method based on raindrop mass weighted average diameter under a dual-parameter scheme according to claim 2 is characterized in that: In step (2), explicitly update The method includes: using 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. The polarization radar data collection and normalization method based on raindrop mass weighted average diameter under a dual-parameter scheme according to claim 3 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. 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 4 are implemented.

6. 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 4 are implemented.

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