Ensemble forecasting method based on physical process and parameter structured disturbance

Abstract

The invention discloses an ensemble forecasting method based on a physical process and parameter structured disturbance. The method comprises the following steps: screening key uncertain parameters from a boundary layer, micro-physics, radiation and cumulus convection parameterization scheme of a high-resolution numerical mode; establishing a plurality of parameter-physical quantity association groups based on a physical mechanism and statistical correlation; calculating an intra-group covariance matrix according to different parameter values and physical quantity output data, and quantifying correlation disturbance and independent disturbance variance weights; constructing structured disturbance of the physical process and the parameters by combining the associated disturbance and the independent disturbance; and combining the constructed structured disturbance with the existing disturbance to generate ensemble forecast mode parameter disturbance. According to the method, the uncertainty of severe convection weather can be effectively represented, and the problems of small improvement degree, low dispersion and the like of an ensemble forecast result in an existing parameter disturbance method are solved; the ensemble forecasting effect of severe convection weather is improved, and the mode forecasting skill is improved.

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 forecast 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 powerful tools for forecasting severe convections. However, due to factors such as limited observation conditions, the chaotic characteristics of the atmosphere, and the uncertainty of physical processes, there are non-negligible errors in single deterministic numerical forecasts. Ensemble forecasting is currently recognized as the main means of estimating forecast 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 forecast uncertainty are the keys to ensemble forecasting.

[0003] Numerical forecast 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 forecast skill of ensemble forecasting. However, more challenges are faced when implementing multi-parameter methods that can directly characterize the parameter uncertainty 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. And parameter perturbation methods have developed from 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 forecast results and a relatively high dispersion degree.

[0005] Technical solution: The ensemble forecasting method based on the structured perturbation of physical processes and parameters of the present invention includes the following steps: Step 1: Screen key uncertain parameters from the boundary layer, microphysics, radiation, and cumulus convection parameterization schemes of high-resolution numerical models; 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 correlated perturbations and independent perturbations; Step 4: Combine correlated perturbations and independent perturbations to construct structured perturbations of physical processes and parameters; Step 5: Combine the structured perturbations constructed in Step 4 with existing perturbations to generate mode parameter perturbations for ensemble forecasting.

[0006] Further, Step 1 includes designing sensitivity tests for the parameters in the parameterization scheme, analyzing the effects of different values of each parameter on the model output variables, identifying the parameters with strong sensitivity to the model output variables, and using them as key uncertain parameters.

[0007] 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 , , …, , representing the number of independent groups; within each group the parameters and physical quantities are physically or statistically correlated, that is , where represents the first and second parameters or physical quantities within the i th group; the groups are relatively independent , i ≠ j , where represents the i, j th group of parameters or physical quantities, and there is no mutual influence between the two groups.

[0008] Further, the within-group covariance matrix in Step 3 is expressed as: , where 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 。

[0009] Further, step 3 includes: Step 3.1: Derive the covariance based on the physical relationship and of the intra-group parameters ); Step 3.2: Calculate the covariance from the statistical correlation coefficient of the intra-group parameters and : , where represents the covariance, represents and 's correlation coefficient, represents the standard deviation; 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.

[0010] Further, step 4 includes: Generate a structured perturbation field of physical processes and parameters through a weighted combination of correlated perturbations and independent perturbations r , and the expression is: , 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 perturbed parameters; is the proportionality coefficient between the correlated part and the random part, determined by the proportion of the variance explained by the correlation coefficient in the total variance, represents the Hadamard product, that is, element-wise multiplication.

[0011] Further, the and use the same perturbation structure, and the phase can be opposite or the same.

[0012] Further, step 5 includes: Combine the structured perturbation constructed in step 4 with the fixed-parameter perturbation, the mainstream random-parameter perturbation, and the multi-parameter perturbation, that is, calculate through the fixed-parameter perturbation, the mainstream random-parameter perturbation, and the multi-parameter perturbation and , a large number of ensemble prediction numerical experiments are carried out using historical case data, and the optimal parameter configuration of the perturbation of the model physical process is optimized by adjusting the perturbation structure.

[0013] Furthermore, the perturbation structure includes covariance matrix elements and proportionality coefficients for the correlation part and the random part .

[0014] Beneficial effects: Compared with the prior art, the present invention has the following remarkable advantages: The structured collaborative perturbation method based on physical constraints and statistical relationships in the present invention directly perturbs the correlation and constraint relationships between different parameters, between parameters and physical quantities in the physical process, and can effectively characterize the uncertainty of severe convective weather, solving the problems such as small improvement degree of ensemble prediction results and low dispersion in the existing parameter perturbation method due to the failure to consider parameter interactions and spatio-temporal changes 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

[0015] Figure 1 is a flowchart of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0016] The technical solution of the present invention will be further described below with reference to the drawings.

[0017] As Figure 1 shown, the ensemble prediction method based on physical process and parameter structured perturbation of the present invention 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; There are a large number of uncertain parameters with theoretical or empirical values in the parameterization schemes such as the boundary layer, microphysics, radiation and cumulus convection of the WRF model. 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. Identify the parameters that are strongly sensitive to these variables and use them as the key parameters to be perturbed.

[0018] Step 2: Establish multiple parameter-physical quantity correlation groups based on physical mechanisms and statistical correlations; According to the physical formulas or statistical relationships described in the model parameterization scheme, the multiple key uncertain parameters screened in Step 1 and the physical quantities affected by them (such as density parameters and terminal velocity of particle fall in the microphysical process) are divided into several independent groups , , …, , represents the number of independent groups; within each group the parameters and physical quantities are physically or statistically correlated, that is , where represents the first and second i parameters or physical quantities within the 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.

[0019] Step 3: Calculate the within-group covariance matrix based on the output data of different parameter values and physical quantities, and quantify the variance weights of the correlated perturbation and the independent perturbation; Design different values for each group of parameters, substitute them into the WRF model to obtain the model output data of different parameter values and corresponding physical quantities, calculate the covariance of each group of parameters and physical quantities, and establish the covariance matrix within each group :

[0020] where n represents that there are a total of n parameters and physical quantities within each group; the matrix element represents 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 ways: Derive the covariance based on the physical relationship and of the parameters within the group ); Calculate the covariance from the statistical correlation coefficient of the parameters and within the group;

[0021] After obtaining the covariance matrix within each group, further calculate the proportion of the explained variance of the correlation function or correlation coefficient in the total variance to quantify the variance weights of the correlated perturbation and the independent perturbation.

[0022] Step 4: Combine the correlated perturbation and the independent perturbation to construct a structured perturbation of the physical process and parameters; 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 its expression is:

[0023] where, is the covariance matrix of each group; the subscript s andt respectively represent the correlated part and the random part in the perturbation; the subscript M indicates that the perturbation parameters are divided into M groups; is the ratio of the correlated part to the random part, determined by the proportion of the explained variance of the correlation coefficient in the total variance.

[0024] 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.

[0025] Step 5: Combine the structured perturbation constructed in Step 4 with the existing perturbation to generate the perturbation of the model parameters for ensemble forecasting.

[0026] 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 conduct 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.

[0027] The following takes the ensemble forecasting of an isolated convective system as an example to illustrate: (1) Select the empirical parameters with uncertainty in the WRF model microphysical parameterization scheme and the planetary boundary layer parameterization scheme, such as the rainfall intercept parameter ( nor ) in the WSM6 microphysical scheme, 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 ) in the YSU boundary layer scheme, the coefficient of the surface layer top Prandtl number ( bfac ), and the critical Richardson number of the land surface boundary layer ( Brcr_sb ), etc. Conduct sensitivity tests based on severe convective weather, analyze the influence 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 .

[0028] (2) Find the physical quantities directly affected by the four key parameters identified in step (1) according to the physical formulas or statistical relationships described by the WSM6 scheme and the YSU scheme (the ice crystal fall speed and the boundary layer height PBLH ). Then, based on the physical mechanism and statistical correlation, establish a parameter-physical quantity association grouping, which is divided into the following two groups:

[0029] WSM6 microphysical scheme: : ice_stokes_fac , dimax , ; PBL planetary boundary layer scheme: : pfac , bfac , PBLH ; Among them, the internal parameters and physical quantities of the microphysical scheme group and the planetary boundary layer scheme group respectively satisfy the physical relationship formula or statistical correlation, that is ; while the microphysical process parameters and boundary layer parameters are divided into independent groups due to different physical mechanisms, that is , i ≠ j .

[0030] Take as an example. The ice crystal fall speed is calculated by calculating the diameter of the ice crystal and then using the empirical formula. The calculation process is: , , Among them 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.

[0031] (3) For the parameters and physical quantities in the microphysical scheme group ( ice_stokes_fac, dimax , ), construct a covariance matrix based on the physical relationship formula or statistical correlation.

[0032] (3.1) Derive the covariance using the physical relationship formula Calculate according to the formula The partial derivative of ice_stokes_fac is: , For dimax the partial derivative is calculated by the chain rule as: ,

[0033] Then the elements of the covariance matrix can be approximated as: * * , where is the standard deviation of the parameter or physical quantity (which can be calculated from historical simulation data).

[0034] (3.2) Calculate the covariance matrix using the statistical correlation coefficient Based on different values of the WRF model ice_stokes_fac, dimax , output the values at the grid points to calculate the statistical correlation coefficient of the intra-group parameters , 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 elements of the covariance matrix can be expressed as: , where is the correlation coefficient between different parameters.

[0035] (4) Generate the optimal perturbation of the physical process.

[0036] According to the covariance matrix calculated in (3.2), calculate the correlation coefficient matrix of the intra-group parameters (or directly obtain the correlation coefficients between different parameters from 3.2.2). Calculate the proportion of the explained variance of the correlation coefficients between different parameters such as ice_stokes_fac and dimax, ice_ stokes_fac and , dimax and . Calculate the proportion of the explained variance of the correlation coefficient in the total variance to determine the proportions of the correlated perturbation and the independent perturbation in the combined perturbation respectively. 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.

[0037] (5) Combine the existing perturbation techniques to generate the final perturbation.

[0038] (5.1) Combine with the multi-parameter scheme Adopt a Gaussian random perturbation with a mean of and a standard deviation of 0.25 * ( to provide the perturbation field, where Indicates the parameter to be perturbed. Then substitute this perturbation field into the expression as , Generate structured perturbations of physical processes and parameters.

[0039] (5.2) Combine with the mainstream RP / SPP scheme Use the perturbation field that varies with time and space 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 magnitude of the initial perturbation, etc., to generate a more reasonable initial perturbation field. Then combine the covariance matrix C and the ratio of the correlated part to the random part Generate the final perturbation. According to the value range of the parameter, calculate the reasonable range of the perturbation field, and then use the constraint function or transformation function to ensure that the perturbed parameter value is always within its normal value range.

Claims

1. An ensemble forecasting method based on physical processes and parameter structured disturbances, characterized in that: The steps include: Step 1: Screen key uncertain parameters from the boundary layer, microphysics, radiation and cumulus convection parameterization schemes of high-resolution numerical models; Step 2: Establish multiple parameter-physical quantity association groups based on physical mechanisms and statistical correlations; Step 3: Calculate the intra-group covariance matrix based on different parameter values ​​and physical quantity output data to quantify the variance weights of associated disturbances and independent disturbances; Step 4: Combine the correlated perturbations with the independent perturbations to construct structured perturbations of physical processes and parameters; Step 5: Combine the structured perturbation constructed in step 4 with the existing perturbation to generate the model parameter perturbation for the ensemble forecast.

2. The ensemble forecasting method based on physical process and parameter structured disturbance according to claim 1, characterized in that: The step 1 includes designing sensitivity tests on the parameters in the parameterization scheme, analyzing the impact of different values ​​of each parameter on the model output variables, identifying parameters that are highly sensitive to the model output variables, and treating them as key uncertain parameters.

3. The ensemble forecasting method based on physical process and parameter structured disturbance according to claim 1, characterized in that: The step 2 includes dividing the multiple key uncertain parameters and the physical quantities affected by them selected in step 1 into a number of independent groups. , , …, , Indicates the number of independent groups; in each group Internally, parameters and physical quantities have physical or statistical connections, i.e. ,in Indicates i The first and second parameters or physical quantities within a group; each group is relatively independent , i≠j ,in Indicates i, j There is no mutual influence between the two groups of parameters or physical quantities.

4. The ensemble forecasting method based on physical process and parameter structured disturbance according to claim 1, characterized in that: The intra-group covariance matrix of step 3 is expressed as: ， in, represents the within-group covariance matrix, n Indicates the number of physical quantities in each group; matrix elements Indicates the first i Parameters and j The covariance of the parameters, i, j = 1 , 2 ,…,n .

5. The ensemble forecasting method based on physical process and parameter structured disturbance according to claim 1, characterized in that: The step 3 comprises: Step 3.1: Based on the intra-group parameters and The physical relationship )Derivation of covariance; Step 3.2: By group parameters and Calculate the covariance of the statistical correlation coefficient: ， in, represents the covariance, express and The correlation coefficient of represents standard deviation; Step 3.3: Based on the calculated covariance within each group, further calculate the proportion of the variance explained by the correlation function or correlation coefficient to the total variance, and quantify the variance weights of associated disturbances and independent disturbances.

6. The ensemble forecasting method based on physical process and parameter structured disturbance according to claim 1, characterized in that: The step 4 comprises: Generate structured perturbation fields of physical processes and parameters through weighted combination of correlated and independent perturbations r , the expression is: ， in, is the covariance matrix of each group; Indicates M The disturbance of the associated part of the parameters, Indicates M The perturbation of the independent part of the parameter, subscript s and t denote the correlated and random parts of the disturbance respectively; M Indicates the number of groups of disturbance parameters; is the ratio coefficient of the correlation part and the random part, which is determined by the proportion of the variance explained by the correlation coefficient to the total variance. represents the Hadamard product, which is the multiplication of corresponding elements.

7. The ensemble forecasting method based on physical process and parameter structured disturbance according to claim 6, characterized in that: Said and Using the same perturbation structure, the phase selection is opposite or the same.

8. The ensemble forecasting method based on physical process and parameter structured disturbance according to claim 1, characterized in that: The step 5 comprises: Combine the structured perturbation constructed in step 4 with fixed parameter perturbation, mainstream random parameter perturbation and multi-parameter perturbation, that is, calculate and , and then use historical case data to carry out a large number of ensemble forecast numerical experiments, and optimize the optimal parameter configuration of the model physical process disturbance by adjusting the disturbance structure.

9. The ensemble forecasting method based on physical process and parameter structured disturbance according to claim 8, characterized in that: The disturbance structure includes the covariance matrix elements and the proportional coefficients of the correlated part and the random part .

Images