An ensemble forecasting method based on physical processes and structured perturbations of parameters

Abstract

The present invention discloses an ensemble forecasting method based on structured perturbations of physical processes and parameters, which includes screening key uncertain parameters from boundary layer, microphysics, radiation and cumulus convection parameterization schemes of high-resolution numerical models; establishing multiple parameter-physical quantity correlation groups based on physical mechanisms and statistical correlations; calculating the within-group covariance matrix according to different parameter values and physical quantity output data to quantify the variance weights of correlated perturbations and independent perturbations; combining correlated perturbations and independent perturbations to construct structured perturbations of physical processes and parameters; and combining the constructed structured perturbations with existing perturbations to generate model parameter perturbations for ensemble forecasting. The present invention can effectively characterize the uncertainties of severe convective weather, solve problems such as small improvement degree and low dispersion in ensemble forecasting results in existing parameter perturbation methods; improve the ensemble forecasting effect of severe convective weather and enhance the model forecasting skill.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical weather forecasting, and particularly to an ensemble forecasting method based on physical process and parameter structured perturbation with a large improvement degree of forecasting results and a relatively high dispersion degree. Background Art

[0002] With the wide application of high-performance computers, high-resolution numerical models (such as the Weather Research and Forecasting, WRF model) have become a powerful tool for forecasting severe convections. However, due to factors such as limited observation conditions, chaotic characteristics of the atmosphere, and uncertainties in physical processes, there are non-negligible errors in single deterministic numerical forecasting. Ensemble forecasting is currently recognized as the main means of estimating forecasting uncertainty, which realizes error estimation by adding perturbations that conform to the error distribution characteristics to variables with errors. Therefore, reasonably characterizing the sources of model errors and designing perturbation methods that can effectively estimate forecasting uncertainty are the keys to ensemble forecasting.

[0003] Numerical forecasting errors mainly come from initial values, model physical processes, and lateral boundary conditions, etc. Among them, model errors mainly consider the errors generated by sub-grid parameterization processes in physical schemes. Currently, initial value perturbation methods have been developed relatively maturely, and model perturbation methods have gradually received more attention. Common model perturbation methods include multi-model and multi-physics combination schemes based on different models and physical processes, as well as stochastic physical perturbation methods (such as Stochastic Parameterization Perturbation Tendency SPPT, Stochastic Kinetic Energy Backscatter SKEB, and Stochastic Parameter Perturbation SPP, etc.) and multi-parameter methods that characterize the uncertainty of model physical process parameterization schemes. The combination of different perturbation methods can even greatly improve the dispersion degree and forecasting skill of ensemble forecasting. However, more challenges are faced when implementing multi-parameter methods that can directly characterize the parameter uncertainties in physical processes. Because the WRF model contains 7 different types of parameterization schemes, and each scheme covers a large number of parameters used to calculate different physical quantities. These parameters are not only valued by theory or experience, but may also interact with different quantities. A large number of studies have shown that parameter perturbation has great research value in ensemble forecasting, which can ensure the consistency of physical processes and satisfy the law of energy conservation, etc. The parameter perturbation method has developed from the early fixed perturbation values to the current introduction of perturbation quantities that vary with time and space. Most of them focus on the impact of parameter value changes on ensemble forecasting, pay less attention to the coordination between parameters, and also ignore the direct impact of parameter value changes on their computational amount, resulting in problems such as a small improvement degree and a low dispersion degree in ensemble forecasting results. Summary of the Invention

[0004] Object of the Invention: The object of the present invention is to provide an ensemble forecasting method based on physical process and parameter structured perturbation with a large improvement degree of forecasting results and a relatively high dispersion degree.

[0005] Technical solution: The ensemble forecasting method based on the structural perturbation of physical processes and parameters of the present invention includes the following steps:

[0006] Step 1: Screen key uncertain parameters from the boundary layer, microphysics, radiation, and cumulus convection parameterization schemes of a high-resolution numerical model;

[0007] Step 2: Establish multiple parameter-physical quantity correlation groups based on physical mechanisms and statistical correlations;

[0008] Step 3: Calculate the within-group covariance matrix according to different parameter values and physical quantity output data, and quantify the variance weights of correlated perturbations and independent perturbations;

[0009] Step 4: Combine correlated perturbations and independent perturbations to construct the structural perturbation of physical processes and parameters;

[0010] Step 5: Combine the structural perturbation constructed in Step 4 with the existing perturbation to generate the model parameter perturbation for ensemble forecasting.

[0011] Further, Step 1 includes designing sensitivity tests for the parameters in the parameterization scheme, analyzing the influence of different values of each parameter on the model output variables, identifying the parameters with strong sensitivity to the model output variables, and taking them as key uncertain parameters.

[0012] Further, Step 2 includes dividing the multiple key uncertain parameters screened in Step 1 and the physical quantities affected by them into several independent groups , , …, , indicating the number of independent groups; within each group the parameters and physical quantities are physically or statistically correlated, that is , where[[ID=३६]] represents the 1st and 2nd parameters or physical quantities within the i th group; the groups are relatively independent of each other , i ≠ j , where represents the i, j th group of parameters or physical quantities, and there is no mutual influence between the two groups.

[0013] Further, the within-group covariance matrix in Step 3 is expressed as:

[0014] [[ID=5३]] ,

[0015] where represents the within-group covariance matrix, nIndicates the number of internal physical quantities in each group; matrix element Indicates the i th parameter and the j th parameter within the group, and the covariance, i, j = 1 , 2 ,…,n .

[0016] Furthermore, step 3 includes:

[0017] Step 3.1: Derive the covariance based on the physical relationship and of the internal parameters within the group );

[0018] Step 3.2: Calculate the covariance from the statistical correlation coefficient of the internal parameters and within the group:

[0019] ,

[0020] where, represents the covariance, represents and 's correlation coefficient, represents the standard deviation;

[0021] Step 3.3: According to the calculated covariance within each group, further calculate the proportion of the variance explained by the correlation function or correlation coefficient in the total variance, and quantify the variance weights of the correlated perturbation and the independent perturbation.

[0022] Furthermore, step 4 includes:

[0023] Generate a structured perturbation field of the physical process and parameters through the weighted combination of the correlated perturbation and the independent perturbation r , and the expression is:

[0024] ,

[0025] where, is the covariance matrix of each group; represents the perturbation of the M th parameter's correlated part, represents the perturbation of the M th parameter's independent part, and the subscripts s and t represent the correlated part and the random part in the perturbation respectively; the subscript M represents the number of groups of the perturbed parameters; is the proportionality coefficient of the correlated part and the random part, determined by the proportion of the variance explained by the correlation coefficient in the total variance, denotes the Hadamard product, i.e., element-wise multiplication.

[0026] Further, the and use the same perturbation structure, and the phase is selected to be opposite or the same.

[0027] Further, step 5 includes:

[0028] Combine the structured perturbation constructed in step 4 with fixed-parameter perturbation, mainstream random-parameter perturbation, and multi-parameter perturbation, that is, calculate and using fixed-parameter perturbation, mainstream random-parameter perturbation, and multi-parameter perturbation, and then conduct a large number of ensemble prediction numerical experiments using historical case data, and optimize the optimal parameter configuration of the perturbation of the model physical process by adjusting the perturbation structure.

[0029] Further, the perturbation structure includes covariance matrix elements and the proportionality coefficients of the correlation part and the random part .

[0030] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: The structured collaborative perturbation method of the present invention based on physical constraints and statistical relationships directly perturbs the correlation and constraint relationships between different parameters and between parameters and physical quantities in the physical process, and can effectively characterize the uncertainty of severe convective weather, and solve the problems in the existing parameter perturbation methods such as small improvement degree of ensemble prediction results and low dispersion due to the failure to consider parameter interactions and spatio-temporal variations of errors; The structured collaborative perturbation method of the present invention can effectively affect the physical process of model prediction, thereby reducing the difference from the actual error evolution caused by unreasonable parameter perturbation, improving the ensemble prediction effect of severe convective weather, and improving the model prediction skill. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a flowchart of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0032] The technical solution of the present invention will be further described below with reference to the drawings.

[0033] As Figure 1 shown, the ensemble prediction method based on physical process and parameter structured perturbation of the present invention includes the following steps:

[0034] Step 1: Screen key uncertain parameters from the boundary layer, microphysics, radiation, and cumulus convection parameterization schemes of a high-resolution numerical model;

[0035] In the parameterization schemes of the WRF model, such as those for the boundary layer, microphysics, radiation, and cumulus convection, there are a large number of uncertain parameters whose values are determined based on theory or experience. Sensitivity tests are designed for these parameters to analyze the effects of different values of each parameter on model output variables such as temperature, humidity, wind speed, and precipitation. Parameters that are strongly sensitive to these variables are identified and used as the key parameters to be perturbed.

[0036] Step 2: Establish multiple parameter - physical quantity association groups based on physical mechanisms and statistical correlations;

[0037] According to the physical formulas or statistical relationships described in the model parameterization scheme, multiple key uncertain parameters selected in Step 1 and the physical quantities affected by them (such as the density parameter and the terminal velocity of particle fall in the microphysical process) are divided into several independent groups , , …, , denotes the number of independent groups; within each group the parameters and physical quantities are physically or statistically correlated, that is , where denotes the 1st and 2nd parameters or physical quantities within the i th group; the groups are relatively independent of each other , i ≠ j , where denotes the i, j th group of parameters or physical quantities, and there is no mutual influence between the two groups.

[0038] Step 3: Calculate the within - group covariance matrix based on the output data of different parameter values and physical quantities to quantify the variance weights of correlated perturbations and independent perturbations;

[0039] Design different values for each group of parameters and substitute them into the WRF model to obtain the model output data of different parameter values and corresponding physical quantities, in order to calculate the covariance of each group of parameters and physical quantities and establish the within - group covariance matrix :

[0040]

[0041] where n denotes that there are a total of n parameters and physical quantities within each group; the matrix element denotes the covariance between the i th parameter (parameter or physical quantity) and the j th parameter within the group, which is mainly determined in the following way:

[0042] Based on the physical relationship and of the parameters within the group ) deduce the covariance;

[0043] Calculate the covariance from the statistical correlation coefficients of the intra-group parameters and ; After obtaining the covariance matrix within each group, further calculate the proportion of the variance explained by the correlation function or correlation coefficient to quantify the variance weights of the correlated perturbations and the independent perturbations

[0044] Step 4: Combine the correlated perturbations and the independent perturbations to construct a structured perturbation of the physical process and parameters

[0045] Generate a structured perturbation field of the physical process and parameters through a weighted combination of the correlated perturbations and the independent perturbations

[0046] , and its expression is r :

[0047]

[0048] where is the covariance matrix of each group; the subscripts s and t represent the correlated part and the random part in the perturbation respectively; the subscript M indicates that the perturbation parameters are divided into M groups is the ratio of the correlated part to the random part, which is determined by the proportion of the variance explained by the correlation coefficient to the total variance

[0049] In the above formula, is determined based on the physical characteristics of each group. Although , are relatively independent of each other, in order to characterize the uncertainty of the state of an isolated convective system (initiation, development, maturity, dissipation) as a whole and ensure the continuity of the perturbation , etc. all use the same perturbation structure, but the phases may be opposite or the same, depending on whether they jointly represent the developing or maintaining state of the convection, etc

[0050] Step 5: Combine the structured perturbation constructed in Step 4 with the existing perturbation to generate a perturbation of the model parameters for ensemble forecasting

[0051] Combine the structured perturbation method with techniques such as fixed-parameter perturbation, mainstream SPP, and RP, that is, provide and by techniques such as fixed-parameter perturbation, SPP, and RP, and then carry out a large number of ensemble forecasting numerical experiments using historical case data. By adjusting the perturbation structure (such as the covariance matrix elements, proportionality coefficient etc.), optimize the optimal parameter configuration of the perturbation of the model physical process

[0052] The following takes the ensemble prediction of isolated convective systems as an example to illustrate:

[0053] (1) Select the empirical parameters with uncertainties in the WRF model microphysical parameterization scheme and the planetary boundary layer parameterization scheme, such as the rainfall intercept parameter ( nor ), the proportionality coefficient of the ice fall velocity ( ice_ stokes_fac ), the finite maximum value of the cloud ice diameter ( dimax ), and the automatic conversion rate from cloud to rain ( peaut ), as well as the profile shape index for calculating the momentum diffusion coefficient ( pfac ), the coefficient of the Prandtl number at the top of the surface layer ( bfac ), and the critical Richardson number of the land surface boundary layer ( Brcr_sb ) in the YSU boundary layer scheme. Based on severe convective weather, conduct sensitivity tests to analyze the effects of different values of each parameter on the model output variables such as precipitation, temperature, and wind field, and identify the key parameters ice_stokes_fac, dimax, pfac and bfac .

[0054] (2) According to the physical formulas or statistical relationships described in the WSM6 scheme and the YSU scheme, find the physical quantities directly affected by the 4 key parameters identified in step (1) (the ice crystal fall velocity and the boundary layer height PBLH ), and then establish parameter-physical quantity association groups based on physical mechanisms and statistical correlations, which are divided into the following two groups:

[0055] WSM6 microphysical scheme: : ice_stokes_fac , dimax , ;

[0056] PBL planetary boundary layer scheme: : pfac , bfac , PBLH ;

[0057] Among them, the internal parameters and physical quantities in the microphysical scheme group and the planetary boundary layer scheme group respectively satisfy physical relationships or statistical correlations, that is, ; while the microphysical process parameters and the boundary layer parameters are divided into independent groups due to different physical mechanisms, that is, , i ≠ j .

[0058] Taking as an example, the fall velocity of the ice crystal is obtained by calculating the diameter of the ice crystal and then using an empirical formula. The calculation process is as follows:

[0059] ,

[0060] ,

[0061] wherein dicon is a constant xmi is the ice crystal mass. It can be seen that the physical quantity and the empirical parameter dimax, ice_stokes_fac contain the physical relationship

[0062] (3)For the parameters and physical quantities in the microphysics scheme group ( ice_stokes_fac, dimax 、 ), construct the covariance matrix based on physical relationships or statistical correlations ]>

[0063] (3.1)Derive the covariance using physical relationships

[0064] Calculate according to the formula The partial derivative of ice_stokes_fac is: ,

[0065] For dimax the partial derivative is calculated by the chain rule as:

[0066] ,

[0067] Then the covariance matrix element can be approximated as: * * wherein is the standard deviation of the parameter or physical quantity (which can be calculated from historical simulation data)

[0068] (3.2)Calculate the covariance matrix using statistical correlation coefficients

[0069] Based on different values of the WRF model ice_stokes_fac, dimax output the values of at the grid points to calculate the statistical correlation coefficientr of the parameters within the group, that is ice_stokes_fac the correlation coefficient between dimax and 、 ice_ stokes_fac the correlation coefficient between and and dimax the correlation coefficient between and . Then the covariance matrix element can be expressed as: , where is the correlation coefficient between different parameters.

[0070] (4) Generate the optimal perturbation of the physical process.

[0071] According to the covariance matrix calculated in (3.2), calculate the correlation coefficient matrix of the intra-group parameters (or directly obtain the correlation coefficient between different parameters from 3.2.2). Calculate the explained variance of the correlation coefficient for different parameters such as ice_stokes_fac and dimax, ice_ stokes_fac and , dimax and respectively. Calculate the proportion of the explained variance of the correlation coefficient in the total variance to determine the respective proportions of the correlated perturbation and the independent perturbation in the combined perturbation. Standardize the covariance matrix calculated in (3.2) to eliminate the influence of the magnitude. Use the structured perturbation field expression to generate the optimal perturbation of the physical process through the weighted combination of the correlated perturbation and the independent perturbation.

[0072] (5) Combine the existing perturbation technology to generate the final perturbation.

[0073] (5.1) Combine with the multi-parameter scheme

[0074] Adopt a Gaussian random perturbation with a mean of and a standard deviation of 0.25 * ( ) to provide the perturbation field, where represents the parameter to be perturbed. Then substitute this perturbation field into the expression as , to generate the structured perturbation of the physical process and parameters.

[0075] (5.2) Combine with the mainstream RP / SPP scheme

[0076] Use the spatio-temporally varying perturbation field generated by the RP / SPP scheme to provide the initial perturbation field. Modify the decorrelation time scale, decorrelation space scale, and grid standard deviation in the SPP scheme, and adjust the duration, spatial distribution, and numerical size of the initial perturbation, etc., to generate a more reasonable initial perturbation field. Then combine the covariance matrix C and the proportion of the correlated part and the random part to generate the final perturbation. According to the value range of the parameters, calculate the reasonable range of the perturbation field, and then use the constraint function or transformation function to ensure that the perturbed parameter values are always within their normal value ranges.

Claims

1. An ensemble forecasting method based on structured perturbations of physical processes and parameters, characterized in that, It includes the following steps: Step 1: Screen key uncertain parameters from the boundary layer, microphysics, radiation, and cumulus convection parameterization schemes of the high-resolution numerical model; Step 2: Establish multiple parameter-physical quantity correlation groups based on physical mechanisms and statistical correlations; Step 3: Calculate the within-group covariance matrix according to different parameter values and physical quantity output data, and quantify the variance weights of the correlated perturbation and the independent perturbation; Step 4: Combine the correlated perturbation and the independent perturbation to construct a structured perturbation of the physical process and parameters; Step 5: Combine the structured perturbation constructed in Step 4 with the existing perturbation to generate the model parameter perturbation for ensemble forecasting, Step 1 includes designing sensitivity tests for the parameters in the parameterization scheme, analyzing the influence of different values of each parameter on the model output variables, identifying the parameters with strong sensitivity to the model output variables, and taking them as the key uncertain parameters, Step 2 includes dividing a plurality of key uncertain parameters and physical quantities affected by them selected in Step 1 into several independent groups , , …, , denotes the number of independent groups; within each group , the parameters and physical quantities have physical or statistical correlations, that is , where denotes the 1st and 2nd parameters or physical quantities within the i th group; the groups are relatively independent of each other , i ≠ j , where denotes the i, j th group of parameters or physical quantities, and there is no mutual influence between the two groups Step 3 includes: Step 3.1: Based on the intra-group parameters and physical relationship ) to derive the covariance; Step 3.2: Calculate the covariance from the statistical correlation coefficients of the in-group parameters and : ， Among them, represents covariance, represents and the correlation coefficient of represents the standard deviation; Step 3.3: According to the covariance within each calculated group, further calculate the proportion of the variance explained by the correlation function or correlation coefficient, and quantify the variance weights of the correlated perturbation and the independent perturbation; Step 4 includes: Generating a structured perturbation field of physical processes and parameters through a weighted combination of correlated perturbations and independent perturbations r , the expression is: ， Among them, are the covariance matrices for each group; represents the perturbation of the M th parameter correlation part, represents the perturbation of the M th parameter independent part. The subscripts s and t represent the correlated part and the random part in the perturbation respectively; the subscript M represents the number of groups of perturbed parameters; is the proportionality coefficient between the correlated part and the random part, determined by the proportion of the explained variance of the correlation coefficient in the total variance, represents the Hadamard product, that is, element-wise multiplication.

2. The ensemble prediction method based on the structured perturbation of physical processes and parameters according to claim 1, characterized in that The within-group covariance matrix in Step 3 is expressed as: ， Among them, represents the within-group covariance matrix, n represents the number of physical quantities within each group; the matrix element represents the covariance between the i th parameter and the j th parameter within the group, i, j = 1 , 2 ,…,n .

3. The ensemble prediction method based on the structured perturbation of physical processes and parameters according to claim 1, characterized in that The said and use the same perturbation structure, and the phases are selected to be opposite or the same.

4. The ensemble prediction method based on structured perturbations of physical processes and parameters according to claim 1, characterized in that Step 5 includes: Combine the structured perturbations constructed in step 4 with fixed-parameter perturbations, mainstream stochastic parameter perturbations, and multi-parameter perturbations, that is, calculate and , and then conduct a large number of ensemble prediction numerical experiments using historical case data to optimize the optimal parameter configuration of the model physical process perturbations by adjusting the perturbation structure.

5. The ensemble prediction method based on the structured perturbation of physical processes and parameters according to claim 4, wherein The perturbation structure includes covariance matrix elements and a proportionality coefficient that relates a correlated part and a random part .

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