Numerical prediction optimization method and system based on error analysis

Abstract

The invention discloses a numerical prediction optimization method and system based on error analysis. The method comprises the following steps: calculating a lag prediction error variance to form a sample set; based on the physical characteristics of the atmospheric chaotic system, defining a numerical forecasting core parameter and establishing a function relationship between a sensing error variance estimated value and the core parameter; constructing a cost function and carrying out minimization solution to obtain a global optimal estimated value of the core parameter; obtaining a real analysis error variance, a real prediction error variance and an analysis-prediction error correlation coefficient model according to the global optimal estimation value of the core parameter so as to describe an evolution rule of error statistical characteristics along with prediction time efficiency; an error statistical structure in the data assimilation system is restrained or adjusted, and error correction and assimilation optimization of the numerical forecasting system are achieved. The method can be independent of a data assimilation system, unbiased statistical analysis of spatial continuation estimation is carried out on analysis and short-term forecasting error variance, and the overall performance of a numerical forecasting system is improved.

Description

Technical Field

[0001] This invention belongs to the field of numerical weather prediction technology, and relates to a numerical weather prediction optimization method and system based on error analysis. Background Technology

[0002] The key challenges facing existing numerical weather prediction systems lie in the chaos of atmospheric systems, initial value errors, and model errors. Even with continuous optimization of the numerical models themselves, their analytical fields and short-term forecasts cannot be completely accurate. To better evaluate the performance of assimilation and forecasting systems and optimize data assimilation and ensemble forecasting strategies, accurately assessing the error variance between the numerical model's analytical and forecast fields and the actual atmospheric conditions is particularly crucial.

[0003] Current error variance estimation methods mainly fall into two categories: the first is based on ensemble Kalman filtering and other methods that are based on the internal output of the data assimilation system. Although these methods can provide error estimates, they have drawbacks such as high computational cost and sensitivity to initial perturbation assumptions. Furthermore, the estimation results depend on the prior assumptions of the assimilation system and lack independence. The second is based on the National Weather Service (NMC) method in the United States, which is based on historical forecast data. This method estimates the background error covariance by calculating the difference between lag forecast fields, but the estimation accuracy is heavily dependent on the choice of lag time and it is difficult to accurately reflect the error variance of actual analysis and short-term forecasts.

[0004] The methods described above all have significant shortcomings in estimating the fine-grained spatial distribution of error structures. In particular, existing methods exhibit systematic biases in estimating forecast errors at the analysis time and in the short term (0-48 hours), failing to meet the accuracy requirements of current high-resolution ensemble forecasts and variational data assimilation systems, thus affecting the overall performance of numerical weather prediction systems. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a numerical weather prediction optimization method and system based on error analysis. This method can perform unbiased analysis to estimate the spatial extension of the variance of analysis and short-term forecast errors independently of the data assimilation system. By objectively and quantitatively estimating the variance of analysis and forecast errors, this method improves the data assimilation and ensemble forecasting system, thereby enhancing the overall performance of the numerical weather prediction system.

[0006] The present invention adopts the following technical solution.

[0007] The first aspect of this invention proposes a numerical forecasting optimization method based on error analysis, comprising: Acquire forecast field data from numerical weather prediction systems at different forecast lead times at the same analysis time, and calculate the lag forecast error variance based on the forecast field data, which serves as the observation and perception error variance, thus forming a sample set; Based on the physical characteristics of atmospheric chaotic systems, core parameters for numerical forecasting are defined and a functional relationship is established between the estimated variance of sensing error and the core parameters. Based on the sample set and functional relationships, a cost function is constructed and minimized to obtain the global optimal estimate of the core parameters; Based on the global optimal estimates of the core parameters, models of the true analysis error variance, the true forecast error variance, and the correlation coefficient between analysis and forecast errors are obtained to describe the evolution of error statistical characteristics with forecast lead time. By utilizing the evolution of the aforementioned error statistical characteristics with forecast lead time, the error statistical structure in the data assimilation system can be constrained or adjusted to achieve error correction and assimilation optimization of the numerical weather prediction system.

[0008] Preferably, the formula for calculating the variance of the lag prediction error is: (1) in, For the first i With the i+l Forecast field with a forecast lead time F i , F i+l The calculated variance of the lag forecast error; T This represents the actual state of the atmospheric system. and This represents the actual forecast error.

[0009] Preferably, based on the physical characteristics of atmospheric chaotic systems, core parameters for numerical forecasting are defined, including the standard deviation of the true analysis error. Error growth rate And the correlation coefficient between analysis and forecast errors .

[0010] Preferably, establishing the functional relationship between the estimated variance of the perception error and the core parameters includes: An evolution model for the variance of the true forecast error is established, which is either an exponential growth model or a logistic growth model; wherein, the exponential growth model is as follows: (4) In the formula, For the first l The true forecast error variance for each forecast time interval step; For the first l The forecast duration corresponding to each forecast interval step; The logical growth model is as follows: (5) In the formula, the parameter ; This represents the error saturation level. Establish a decay model for the correlation coefficient between analysis and forecast errors: (6) In the formula, To analyze the error and the first l The correlation coefficient between the forecast errors of each forecast time interval step; To analyze the correlation coefficient between the forecast error and the forecast error of the first forecast interval step; Based on the evolution model and the decay model, an estimate of the perception error variance is established. With core parameters , and Functional relationship between them: (7) in, For the first l The true forecast error standard deviation for each forecast time interval step.

[0011] Preferably, a cost function is constructed based on the sample set and the functional relationship, specifically as follows: (10) in, The cost function; For based on the 0th and the 1st l The variance of the observation perception error calculated from the forecast field data at each forecast interval step; This is the estimated variance of the perceived error obtained based on the aforementioned functional relationship; For the first i and the i The observation perception error variance was calculated from the forecast field data of the +2 forecasts; This is the estimated value of the variance of the lag forecast error; and As weight.

[0012] Preferably, the estimated variance of the lag forecast error for: (9) in, The variance of the observation perception error is calculated based on the forecast fields with the second and fourth forecast leads; For the first i - The forecast duration for 2 forecast times.

[0013] Preferably, weight The calculation method is as follows: Based on the autocorrelation coefficient of the sample lagged by one forecast time. The sample autocorrelation adjustment factor was calculated. f Combined with sample size N Sample standard deviation of the variance of observation and perception error Calculate the first i With the i+l Standard error of the sample mean corresponding to each forecast lead time ;calculate The weight is the ratio of the sum of the standard errors of the means of all samples. .

[0014] Preferably, a model is obtained based on the global optimal estimate of the core parameters to derive the true analysis error variance, the true forecast error variance, and the analysis-forecast error correlation coefficient model, in order to describe the evolution of error statistical characteristics with forecast lead time, specifically including: By substituting the globally optimal estimates of the core parameters into the evolution model of the true forecast error variance and the decay model of the analysis-forecast error correlation coefficient, models of the true analysis error variance, the true forecast error variance, and the analysis-forecast error correlation coefficient are obtained, which are used to describe the evolution of error statistical characteristics with forecast lead time.

[0015] Preferably, the error statistical characteristics are used to constrain or adjust the error statistical structure in the data assimilation system according to the evolution of the error statistical characteristics with the forecast lead time, so as to realize the error correction and assimilation optimization of the numerical weather prediction system, specifically including: Using the spatial distribution of forecast errors as a reference, a comprehensive evaluation of the initial ensemble perturbation generated by the Kalman filter of the unified forecast time set is conducted. The spatial structure, local amplitude, and consistency between the ensemble perturbation and the forecast errors are compared to identify any biases, underestimations, or structural defects in the error sampling capability. The causes of these defects are then analyzed. By calculating the projection coefficients of the ensemble perturbations onto the corresponding forecast error field, the ability of each ensemble perturbation to describe the error field is quantitatively evaluated, and the problems of the ensemble perturbations in error sampling are judged based on the projection results. Based on the evaluation of the sampling performance of the original set perturbation, the initial set perturbation of the set Kalman filter is adjusted according to the analysis of the error variance; The sampling performance of the adjusted ensemble perturbation is evaluated, and the changes in spatial structure and amplitude characteristics of the ensemble perturbation before and after the adjustment are compared. The perturbation adjustment scheme with better sampling performance is selected.

[0016] A second aspect of this invention proposes a numerical forecasting optimization system based on error analysis, comprising: The data acquisition and calculation module is used to acquire forecast field data of different forecast lead times at the same analysis time of the numerical weather prediction system and calculate the lag forecast error variance based on the forecast field data, which is used as the observation and perception error variance to form a sample set. The function construction and solution module is used to define the core parameters of numerical forecasting based on the physical characteristics of atmospheric chaotic systems and establish a functional relationship between the estimated variance of sensing error and the core parameters; based on the sample set and the functional relationship, a cost function is constructed and minimized to obtain the global optimal estimate of the core parameters; The model building module is used to obtain the true analysis error variance, the true forecast error variance, and the analysis-forecast error correlation coefficient model based on the global optimal estimate of the core parameters, so as to describe the evolution of error statistical characteristics with forecast lead time. The numerical forecast optimization module is used to constrain or adjust the error statistical structure in the data assimilation system by utilizing the evolution law of the error statistical characteristics with the forecast lead time, so as to realize the error correction and assimilation optimization of the numerical forecast system.

[0017] A third aspect of the present invention provides a terminal, including a processor and a storage medium; the storage medium is used to store instructions; the processor is used to perform operations according to the instructions to execute the steps of the method.

[0018] A fourth aspect of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.

[0019] Compared with the prior art, the beneficial effects of the present invention include at least the following: This invention defines the core parameters of numerical forecasting based on the physical characteristics of atmospheric chaotic systems and establishes a functional relationship between the estimated variance of sensing error and the core parameters. It introduces the relationship between sensing error and actual analysis and forecast errors. The error estimation is unbiased, and the deviation is controlled within 6%, which is significantly better than traditional ensemble Kalman filtering and NMC methods.

[0020] The cost function of this invention introduces a lag forecast error variance constraint term. By simultaneously fitting the variance of the perception error and the variance of the lag forecast error, the estimated core parameters of the numerical forecast error evolution are statistically consistent with both types of observation information, thereby improving the robustness of parameter estimation and model consistency. The cost function of this invention reduces the impact of sampling error in the time-averaged measurement of individual perception errors on the estimation of unknown parameters. It can be minimized using the L-BFGS optimization algorithm, improving parameter fitting efficiency and making it suitable for rapid error diagnosis and perturbation design in actual numerical forecasting operations.

[0021] This invention models the true analysis error variance, the true forecast error variance, and the analysis-forecast error correlation coefficient based on the global optimal estimate of the core parameters. It can calculate the analysis error variance and forecast error variance for different forecast lead times and spatial locations, supports high-resolution grid-level estimation, and can be corrected by introducing geometric perturbation fields, exhibiting good spatial consistency and physical interpretability.

[0022] The error variance calculation of this invention is independent of the data assimilation system. It can perform high-precision and spatially refined unbiased estimation of the actual analysis error and short-term forecast error without relying on the assumptions of the data assimilation system. This avoids the systematic bias caused by the assumption dependence of traditional methods, improves the objectivity and practicality of error estimation, and provides a reliable basis for ensemble forecast perturbation design and data assimilation background error setting.

[0023] This invention calculates the variance between the numerical weather prediction field and the analysis field, and combines this with the assumption that the variance of the actual error evolves over time, thus reducing the impact of analysis error and short-term (…). The accuracy of the 48-hour forecast error variance estimation is improved by more than 50% compared with traditional methods; it can also accurately predict and analyze the spatial distribution of error variance and forecast error variance, with a spatial correlation coefficient between the predicted results and the actual values ​​exceeding 0.9. The application of this invention in numerical weather prediction operations has significant guiding significance and practical value for the optimization of forecast systems in meteorological operational departments. Attached Figure Description

[0024] Figure 1 This is a flowchart of the numerical weather prediction optimization method based on error analysis according to the present invention. Figure 2 This is a flowchart illustrating the implementation of the numerical forecasting optimization method based on error analysis of the present invention. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of this invention. The embodiments described in this application are merely some embodiments of this invention, and not all embodiments. Based on the spirit of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the protection scope of this invention.

[0026] Embodiment 1 of this invention provides a numerical weather prediction optimization method based on error analysis. It assumes that the true error variance increases exponentially or logically with forecast lead time, and that the correlation between analysis and forecast errors decreases exponentially with forecast duration. The perceived error variance is decomposed into a function of three key unknown parameters. A limited-memory Broyden-Fletcher-Goldfarb-Sano (L-BFGS) algorithm is employed to minimize the unknown variables iteratively. Furthermore, the lag forecast error variance for different forecast lead times is introduced to improve computational stability. Figure 1 , Figure 2 As shown, the method includes the following steps: S1. Acquire forecast field data of different forecast lead times at the same analysis time from the numerical weather prediction system and calculate the lag forecast error variance based on the forecast field data, which is used as the observation perception error variance to form a sample set; More preferably, the perceived error between the data model forecast field and the analysis field is obtained, and a sample set is formed by constructing the difference between forecast fields with different forecast lead times (e.g., 24 hours) at the same analysis time; Specifically, decompose the variance of the perception error and establish the correlation between the observed variables and the unknown variables: Define forecast lead time as (in i The forecast time number is the sequence number. (The assimilation cycle length is set to 12 hours). Numerical weather forecasting systems obtain data at the same forecast time but with different start times. l Two forecast fields F i , F i+l The perceived error sample set is obtained by calculating its error variance. The calculation formula is: (1) To improve sample stability, the perceptual error is averaged over time and space.

[0027] In formula (1), the parentheses represent time and space averages; For the first i With the i+l Forecast field with a forecast lead time F i , F i+l The calculated lag forecast error variance can also be used as an observation surrogate quantity for the perception error variance, and the true perception error variance can be inverted through a statistical model. F i and Fi+l For the same forecast time but with different start times l The i、i +l forecast field data; T It is the actual state of the atmospheric system at the same verification time as the forecast; and This is the actual forecast error; l The time interval step for forecasting; i Forecast time index, indicating the number of forecast times. i This forecast; i + l In the forecast time i Based on the backward lag l The number of prediction times for each assimilation cycle; This refers to the duration of the assimilation cycle.

[0028] S2, based on the physical characteristics of atmospheric chaotic systems, defines the core parameters for numerical forecasting (including the standard deviation of the actual analysis error). Error growth rate And the correlation coefficient between analysis and forecast errors And establish a functional relationship between the estimated variance of the perception error and the core parameters; More preferably, a functional relationship between perceived error and actual error is established based on the exponential growth model of the true error variance and the assumption that the error is decorrelated over time; Specifically, the true state is recorded as T Then the true error can be defined as: ， ,therefore Expanded to: (2) in and To analyze and predict error variance, The correlation coefficient between the two is given.

[0029] In formula (2) and All parameters are unknown.

[0030] when i When the variance is 0, the variance of the perceived error is estimated by comparing the observed values ​​with the statistical model values. Error variance : (3) In the formula, Indicates the model estimate, " "" indicates an unknown parameter to be estimated.

[0031] By changing the formula (3) l The value establishes a series of relationships between observed variables and unknown variables.

[0032] However, each additional equation introduces a division... Additional parameters , and .

[0033] To simplify these parameters, the error growth model and correlation decay model are defined using the following steps: In the ideal model, the initial linear phase of error growth in a chaotic system follows an exponential growth pattern, calculated as follows: (4) In the formula For the first l The true forecast error variance for each forecast time interval step; This represents the error growth rate. = , For the first l The forecast duration corresponding to each forecast interval step.

[0034] Error growth under nonlinear saturation conditions follows a logistic error growth model: (5) In the formula Error saturation level Is and The new parameter introduced in addition to the two exponential growth parameters can usually be estimated using the climate variance of historical data.

[0035] This characterizes the degree to which the true initial prediction error is adjusted towards the analysis error during assimilation, reflecting how the analysis error vector undergoes sequential changes relative to the free prediction error in a single assimilation cycle. By adjusting the angle, the relationship between the actual analysis error and the forecast error at the same moment can be obtained: (6) In the formula, To analyze the error and the first l The correlation coefficient between the forecast errors of each forecast time interval step; To analyze the correlation coefficient between the actual analysis error and the forecast error at the first forecast time interval, we observe that as the forecast lead time increases, the actual analysis error vector and the forecast error vector tend to become independent of each other. It will approach 0.

[0036] Based on the aforementioned assumptions regarding error growth and error decorrelation, an estimate of the perceived error variance model is established. With core parameters , and The functional relationship between them, in the forecast lead time l Time-averaged sensing error variance at the simulation It can be represented as: (7) In the formula, The evolutionary model established in 1) is adopted; The standard deviation of the true analysis error; The parameter in the error growth model (Equation (4) or Equation (5)) is the first... l The standard deviation of the true forecast error for each forecast time interval step.

[0037] S3. Based on the sample set and functional relationships, construct a cost function and minimize it to obtain the global optimal estimate of the core parameters; More preferably, a cost function is constructed that includes error variance, error growth rate, and analysis-forecast error correlation coefficient, and minimized using the L-BFGS optimization algorithm to obtain the globally optimal parameter estimate; Specifically, the unknown parameters are estimated by constructing a cost function, and the steps are as follows: Based on the model relationship established by formula (7), the unknown parameters are realized by constructing the following cost function ( , and Estimate: (8) This method measures the observed values Compared with simulated values The differences between them, choose Norms to ensure all timeliness l The algorithm provides a good fit and minimizes the maximum fitting error at any point within the fitting time period using the max function.

[0038] To reduce the impact of sampling errors in the time-averaged individual perception error measurement on the estimation of unknown parameters, lag errors are modeled. Specifically, assuming that the variance increase of two lag forecasts follows the same exponential growth rate as the variance of the actual forecast error, the variance of the lag forecast with a 24-hour time interval can be modeled as follows: (9) in, The perception error variance is calculated based on formula (1) for the forecast fields with the second and fourth forecast lead times. For the first i - The forecast duration for 2 forecast times.

[0039] This formula does not introduce any new unknowns, so its fitting term can be directly added to formula (8) to obtain the final cost function: (10) in, The cost function; For based on the 0th and the 1st l The variance of the observation perception error is calculated based on the forecast field data of each forecast interval step according to formula (1); This is the model estimate of the perception error variance under the corresponding forecast lead time, obtained based on the aforementioned functional relationship; For the first i and the i The observation perception error variance was calculated from the forecast field data of the +2 forecasts; We can directly obtain (from formula (1)) l Take 2).

[0040] This represents the model estimate of the variance of the lag forecast error under the corresponding forecast lead time. and As weight.

[0041] The uncertainty of the time-averaged sensing error and lag error forecast variance based on sample estimation increases with the extension of the forecast lead time. Therefore, it is necessary to reduce the weight of the fitting error between observed and estimated values ​​for long forecast leads. The calculation formula is: (11) The sample mean standard error (SEM) of the perception error and the prediction error is expressed as: (12) In the formula The sample standard deviation in formula (1) is... N For sample size, It is the sample autocorrelation adjustment factor. It is the autocorrelation coefficient of a sample that is one forecast time lag.

[0042] Minimizing the cost function defined by formula (10) is a nonlinear constrained optimization problem. The L-BFGS algorithm is used for iterative solution during the optimization process to obtain the parameters estimated by the model. , and .

[0043] The cost function described above introduces a lag prediction error variance constraint term. By simultaneously fitting the variance of the perception error and the variance of the lag prediction error, the core parameters of the estimated numerical prediction error evolution ( , as well as It simultaneously conforms to two types of observation information in a statistical sense, thereby improving the robustness of parameter estimation and model consistency; it reduces the impact of sampling error in the time-averaged individual perception error measurement on the estimation of unknown parameters, and can be minimized using the L-BFGS optimization algorithm, improving parameter fitting efficiency. It is suitable for rapid error diagnosis and disturbance design in actual numerical weather prediction operations.

[0044] S4. Based on the global optimal estimate of the core parameters, model the variance of the actual analysis error, the variance of the actual forecast error, and the correlation coefficient between the analysis and forecast errors to describe the evolution of the error statistical characteristics with the forecast lead time. More preferably, the present invention can use geometric perturbation field to fit the error propagation trajectory, correct the spatial displacement deviation of the error estimate, and realize grid-level spatial estimation of the error variance for analysis and prediction.

[0045] More preferably, based on the globally optimal estimate of the core parameters, modeling is performed on the variance of the true analysis error, the true forecast error, and the correlation coefficient between the analysis and forecast errors, including: The core parameters ( , as well as Substituting the global optimal estimate into formula (4) or formula (5) of the evolution model of the true forecast error variance, we obtain the true analysis error variance for each lead time. variance of actual forecast error The model is then substituted into the attenuation model formula (6) of the analysis-forecast error correlation coefficient to obtain the analysis-forecast error correlation coefficient for each forecast lead time. Model; Based on the model of true analysis error variance, true forecast error variance and analysis-forecast error correlation coefficient, and by utilizing the spatial distribution characteristics of the ensemble perturbation variance field under different forecast lead times in the numerical weather prediction system, the spatiotemporal evolution process of the ensemble perturbation variance with time lead time can be compared and analyzed, revealing the main spatial characteristics of error propagation from the upstream region to the verification region. Based on this, by comparing and analyzing the distribution of ensemble perturbation variance corresponding to different time periods, a spatial displacement vector field constructed based on ensemble perturbation variance is further given, which is used to qualitatively describe the error propagation direction and spatial displacement amplitude, reflecting the spatial misalignment characteristics between the grid estimation results of this method and the actual error distribution, and providing an analytical basis for understanding the spatial structure of error evolution over time.

[0046] S5. The error statistical characteristics obtained from the modeling are used to constrain or adjust the error statistical structure in the data assimilation system, thereby realizing error correction and assimilation optimization of the numerical prediction system.

[0047] More preferably, the background error covariance in the data assimilation system is constrained or adjusted using the error statistics obtained from the inversion, as follows: 1) Using the spatial distribution of 24-hour or 48-hour forecast errors as a reference, comprehensively evaluate the initial ensemble perturbation generated by the Kalman filter of the unified forecast time set, and compare the consistency of the ensemble perturbation with the spatial structure, local amplitude and short-term forecast errors to identify the bias, underestimation or structural defects in error sampling capability, and analyze the reasons for these defects. 2) By calculating the projection coefficients of the ensemble perturbations onto the corresponding forecast error field, the ability of each ensemble perturbation to describe the error field is quantitatively evaluated, and the projection results are used to determine whether the ensemble perturbations have problems such as undersampling or small amplitude in terms of error sampling. 3) Based on the evaluation of the sampling performance of the original ensemble perturbation, the initial ensemble perturbation of the ensemble Kalman filter is adjusted based on the analysis error variance estimated by this method. For example, the analysis error variance is used as a local scaling constraint to locally adjust the amplitude of the ensemble perturbation; the spatiotemporal average variance of the ensemble perturbation is adjusted to the amplitude level corresponding to the analysis error variance estimated by this method; the analysis error variance is used to constrain the amplitude of the ensemble perturbation at a larger spatial scale, while the original spatial variability characteristics are maintained at a smaller scale. 4) Evaluate the sampling performance of the adjusted ensemble perturbation in the same way as in 1) and 2), compare the changes in spatial structure and amplitude characteristics of the ensemble perturbation before and after adjustment, and select the perturbation adjustment scheme with better sampling performance; Based on the above scheme, the impact of fusing the analysis error information of this method on ensemble forecasting skills is evaluated, which is used to analyze the role of the error information of this method in improving ensemble forecasting performance.

[0048] Embodiment 2 of the present invention provides a numerical forecasting optimization system based on error analysis, comprising: The data acquisition and calculation module is used to acquire forecast field data of different forecast lead times at the same analysis time of the numerical weather prediction system and calculate the lag forecast error variance based on the forecast field data, which is used as the observation and perception error variance to form a sample set. The function construction and solution module is used to define the core parameters of numerical forecasting based on the physical characteristics of atmospheric chaotic systems and establish a functional relationship between the estimated variance of sensing error and the core parameters; based on the sample set and the functional relationship, a cost function is constructed and minimized to obtain the global optimal estimate of the core parameters; The model building module is used to obtain the true analysis error variance, the true forecast error variance, and the analysis-forecast error correlation coefficient model based on the global optimal estimate of the core parameters, so as to describe the evolution of error statistical characteristics with forecast lead time. The numerical forecast optimization module is used to constrain or adjust the error statistical structure in the data assimilation system by utilizing the evolution law of the error statistical characteristics with the forecast lead time, so as to realize the error correction and assimilation optimization of the numerical forecast system.

[0049] Embodiment 3 of the present invention provides a terminal, including a processor and a storage medium; the storage medium is used to store instructions; the processor is used to perform operations according to the instructions to execute the steps of the method.

[0050] Embodiment 4 of the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method.

[0051] Compared with the prior art, the beneficial effects of the present invention include at least the following: This invention defines the core parameters of numerical forecasting based on the physical characteristics of atmospheric chaotic systems and establishes a functional relationship between the estimated variance of sensing error and the core parameters. It introduces the relationship between sensing error and actual analysis and forecast errors. The error estimation is unbiased, and the deviation is controlled within 6%, which is significantly better than traditional ensemble Kalman filtering and NMC methods.

[0052] The cost function of this invention introduces a lag forecast error variance constraint term. By simultaneously fitting the variance of the perception error and the variance of the lag forecast error, the estimated core parameters of the numerical forecast error evolution are statistically consistent with both types of observation information, thereby improving the robustness of parameter estimation and model consistency. The cost function of this invention reduces the impact of sampling error in the time-averaged measurement of individual perception errors on the estimation of unknown parameters. It can be minimized using the L-BFGS optimization algorithm, improving parameter fitting efficiency and making it suitable for rapid error diagnosis and perturbation design in actual numerical forecasting operations.

[0053] This invention models the true analysis error variance, the true forecast error variance, and the analysis-forecast error correlation coefficient based on the global optimal estimate of the core parameters. It can calculate the analysis error variance and forecast error variance for different forecast lead times and spatial locations, supports high-resolution grid-level estimation, and can be corrected by introducing geometric perturbation fields, exhibiting good spatial consistency and physical interpretability.

[0054] The error variance calculation of this invention is independent of the data assimilation system. It can perform high-precision and spatially refined unbiased estimation of the actual analysis error and short-term forecast error without relying on the assumptions of the data assimilation system. This avoids the systematic bias caused by the assumption dependence of traditional methods, improves the objectivity and practicality of error estimation, and provides a reliable basis for ensemble forecast perturbation design and data assimilation background error setting.

[0055] This invention calculates the variance between the numerical weather prediction field and the analysis field, and combines this with the assumption that the variance of the actual error evolves over time, thus reducing the impact of analysis error and short-term (…). The accuracy of the 48-hour forecast error variance estimation is improved by more than 50% compared with traditional methods; it can also accurately predict and analyze the spatial distribution of error variance and forecast error variance, with a spatial correlation coefficient between the predicted results and the actual values ​​exceeding 0.9. The application of this invention in numerical weather prediction operations has significant guiding significance and practical value for the optimization of forecast systems in meteorological operational departments.

[0056] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0057] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination of the foregoing. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0058] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0059] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0060] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the protection scope of the claims of the present invention.

Claims

1. A numerical weather prediction optimization method based on error analysis, characterized in that, include: Acquire forecast field data from numerical weather prediction systems at different forecast lead times at the same analysis time, and calculate the lag forecast error variance based on the forecast field data, which serves as the observation and perception error variance, thus forming a sample set; Based on the physical characteristics of atmospheric chaotic systems, core parameters for numerical forecasting are defined and a functional relationship is established between the estimated variance of sensing error and the core parameters. Based on the sample set and functional relationships, a cost function is constructed and minimized to obtain the global optimal estimate of the core parameters; Based on the global optimal estimates of the core parameters, models of the true analysis error variance, the true forecast error variance, and the correlation coefficient between analysis and forecast errors are obtained to describe the evolution of error statistical characteristics with forecast lead time. By utilizing the evolution of the aforementioned error statistical characteristics with forecast lead time, the error statistical structure in the data assimilation system can be constrained or adjusted to achieve error correction and assimilation optimization of the numerical weather prediction system.

2. The numerical forecasting optimization method based on error analysis according to claim 1, characterized in that: The formula for calculating the variance of the lag forecast error is as follows: (1) in, For the first i With the i+l Forecast field with a forecast lead time F i , F i+l The calculated variance of the lag forecast error; T This represents the actual state of the atmospheric system. and This represents the actual forecast error.

3. The numerical forecasting optimization method based on error analysis according to claim 1, characterized in that: Based on the physical characteristics of atmospheric chaotic systems, core parameters for numerical forecasting are defined, including the standard deviation of the true analysis error. Error growth rate And the correlation coefficient between analysis and forecast errors .

4. The numerical forecasting optimization method based on error analysis according to claim 3, characterized in that: The establishment of the functional relationship between the estimated variance of the perception error and the core parameters includes: An evolution model for the variance of the true forecast error is established, which can be either an exponential growth model or a logistic growth model; wherein the exponential growth model is as follows: (4) In the formula, For the first l The true forecast error variance for each forecast time interval step; For the first l The forecast duration corresponding to each forecast interval step; The logical growth model is as follows: (5) In the formula, the parameters ; This represents the error saturation level. Establish a decay model for the correlation coefficient between analysis and forecast errors: (6) In the formula, To analyze the error and the first l The correlation coefficient between the forecast errors of each forecast time interval step; To analyze the correlation coefficient between the forecast error and the forecast error of the first forecast interval step; Based on the evolution model and the decay model, an estimate of the perception error variance is established. With core parameters , and Functional relationship between them: (7) in, For the first l The true forecast error standard deviation for each forecast time interval step.

5. The numerical forecasting optimization method based on error analysis according to claim 1, characterized in that: The cost function is constructed based on the aforementioned sample set and functional relationships, specifically as follows: (10) in, The cost function; For based on the 0th and the 1st l The variance of the observation perception error calculated from the forecast field data at each forecast interval step; This is the estimated variance of the perceived error obtained based on the aforementioned functional relationship; For the first i and the i The observation perception error variance was calculated from the forecast field data of the +2 forecasts; This is the estimated value of the variance of the lag forecast error; and As weight.

6. The numerical forecasting optimization method based on error analysis according to claim 5, characterized in that: Lag forecast error variance estimate for: ，(9) in, The variance of the observation perception error is calculated based on the forecast fields with the second and fourth forecast leads; For the first i - The forecast duration for 2 forecast times.

7. The numerical forecasting optimization method based on error analysis according to claim 5, characterized in that: Weight The calculation method is as follows: Based on the autocorrelation coefficient of the sample lagged by one forecast time. The sample autocorrelation adjustment factor was calculated. f Combined with sample size N Sample standard deviation of the variance of observation and perception error Calculate the first i With the i+l Standard error of the sample mean corresponding to each forecast lead time ;calculate The weight is the ratio of the sum of the standard errors of the means of all samples. .

8. The numerical forecasting optimization method based on error analysis according to claim 1, characterized in that: Based on the globally optimal estimates of the core parameters, models for the true analysis error variance, the true forecast error variance, and the correlation coefficient between analysis and forecast errors are derived to describe the evolution of error statistical characteristics with forecast lead time. Specifically, these models include: Substituting the globally optimal estimates of the core parameters into the evolution model of the true forecast error variance and the decay model of the analysis-forecast error correlation coefficient, we obtain the true analysis error variance, the true forecast error variance, and the analysis-forecast error correlation coefficient model, which are used to describe the evolution of error statistical characteristics with forecast lead time.

9. The numerical forecasting optimization method based on error analysis according to claim 1, characterized in that: By utilizing the evolution of the aforementioned error statistical characteristics with forecast lead time, the error statistical structure in the data assimilation system is constrained or adjusted to achieve error correction and assimilation optimization of the numerical weather prediction system. Specifically, this includes: Using the spatial distribution of forecast errors as a reference, a comprehensive evaluation of the initial ensemble perturbation generated by the Kalman filter of the unified forecast time set is conducted. The spatial structure, local amplitude, and consistency between the ensemble perturbation and the forecast errors are compared to identify any biases, underestimations, or structural defects in the error sampling capability. The causes of these defects are then analyzed. By calculating the projection coefficients of the ensemble perturbations onto the corresponding forecast error field, the ability of each ensemble perturbation to describe the error field is quantitatively evaluated, and the problems of the ensemble perturbations in error sampling are judged based on the projection results. Based on the evaluation of the sampling performance of the original set perturbation, the initial set perturbation of the set Kalman filter is adjusted according to the analysis of the error variance; The sampling performance of the adjusted ensemble perturbation is evaluated, and the changes in spatial structure and amplitude characteristics of the ensemble perturbation before and after the adjustment are compared. The perturbation adjustment scheme with better sampling performance is selected.

10. A numerical weather prediction optimization system based on error analysis, comprising the method described in any one of claims 1-9, characterized in that, The system includes: The data acquisition and calculation module is used to acquire forecast field data of different forecast lead times at the same analysis time of the numerical weather prediction system and calculate the lag forecast error variance based on the forecast field data, which is used as the observation and perception error variance to form a sample set. The function construction and solution module is used to define the core parameters of numerical forecasting based on the physical characteristics of atmospheric chaotic systems and establish a functional relationship between the estimated variance of sensing error and the core parameters; based on the sample set and the functional relationship, a cost function is constructed and minimized to obtain the global optimal estimate of the core parameters; The model building module is used to obtain the true analysis error variance, the true forecast error variance, and the analysis-forecast error correlation coefficient model based on the global optimal estimate of the core parameters, so as to describe the evolution of error statistical characteristics with forecast lead time. The numerical forecast optimization module is used to constrain or adjust the error statistical structure in the data assimilation system by utilizing the evolution law of the error statistical characteristics with the forecast lead time, so as to realize the error correction and assimilation optimization of the numerical forecast system.

11. A terminal, comprising a processor and a storage medium; characterized in that: The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the steps of the method according to any one of claims 1-9.

12. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1-9.

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