Multi-scale four-dimensional initial value perturbation method for ensemble forecasting based on incremental analytical updating

Abstract

The present invention provides a multi-scale four-dimensional initial value perturbation method for ensemble forecasting based on incremental analysis and updating. The method first uses a scale separation method to separate the initial value perturbation into three scales: large, medium, and small. The perturbation discreteness of different scales and the discreteness of mutual influence between different scales are calculated respectively. Then, the potential analysis method is combined to use the adjustment coefficient to dynamically adjust the discreteness of mutual influence between different scales in real time. Then, corresponding rescaling coefficients are assigned to different scales, and the perturbation discreteness of the corresponding scales is adjusted to obtain a multi-scale perturbation field. Finally, the incremental analysis and updating method is used to add the perturbation increment consisting of the multi-scale perturbation field and the time coefficient to the perturbation pattern integration process until the ensemble forecast is completed. The present invention effectively solves the problems of rapid discreteness decay and mismatch between perturbation and weather conditions in traditional initial value perturbations, thereby improving the forecast accuracy of severe convective weather.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical weather forecasting, and in particular to a multi-scale four-dimensional initial value perturbation method for ensemble forecasting based on incremental analysis and updating. Background Art

[0002] Numerical Weather Prediction (NWP) is a core method for predicting future weather conditions in modern meteorological operations. However, due to limitations in model accuracy, initial value errors, and computational conditions, NWP results inevitably contain uncertainties. Therefore, identifying key error sources and properly characterizing their impact on forecasts is a core challenge in achieving high-confidence forecasts.

[0003] Ensemble forecasting, a mainstream approach to addressing these issues, generates multi-member forecasts by introducing perturbations at error-sensitive locations, thereby quantifying the probability distribution of future weather. Initial value perturbations and model perturbations are two major approaches. Initial value perturbations account for the uncertainty of the initial atmospheric state by generating different initial values using perturbation methods such as Monte Carlo, growing mode propagation (BGM), singular vector method (SV), constraint analysis, conditional nonlinear optimal perturbation (CNOP), and ensemble Kalman filtering. However, traditional methods have limitations: the BGM method lacks independence, the SV method relies on linear approximations and is computationally complex, and the CNOP method, while capable of characterizing nonlinear errors, is expensive. Furthermore, to integrate multiscale error characteristics, blending perturbation methods combine large-scale perturbations from global models with small- and medium-scale perturbations from regional models. Ensemble data assimilation (EDA) mitigates the multiscale information imbalance to some extent by optimizing the perturbation structure. However, since mixed disturbances rely on complex filtering techniques, and the interaction between moist convective instabilities and multi-scale circulations can significantly amplify small errors, this type of method still has many problems.

[0004] Excellent initial perturbations must simultaneously reflect multiscale error modes, nonlinear interactions, and dynamic alignment with weather patterns. However, existing technologies struggle to achieve these goals: SV and BGM methods are insufficiently responsive to nonlinear physical processes, while analytical constraint schemes, while improving the representation of small and medium-scale errors, lack a four-dimensional spatiotemporal coordination mechanism. Furthermore, the rapid decay of perturbation discreteness with integration in high-resolution modes remains unresolved. Summary of the Invention

[0005] Purpose of the invention: The purpose of the present invention is to provide an ensemble forecast multi-scale four-dimensional initial value perturbation method based on incremental analysis and update, which can dynamically integrate multi-scale error information, adapt to nonlinear evolution and maintain reasonable discreteness, so as to improve the ensemble forecast capability of disastrous weather.

[0006] Technical solution: A multi-scale four-dimensional initial value perturbation method for ensemble forecasting based on incremental analysis and updating, including the following steps:

[0007] S1. Generate the initial perturbation field of ensemble forecast using the initial value perturbation method;

[0008] S2. Use the scale separation method to decompose the initial disturbance field into several disturbances of different scales, and calculate the disturbance discreteness of different scales and the discreteness of mutual influence between different scales respectively;

[0009] S3. Use potential analysis to determine the state of the predicted isolated convective system. Based on the state of the isolated convective system, use the adjustment coefficient to dynamically adjust the discreteness of the mutual influence between different scales in real time.

[0010] S4. Based on historical observation statistics, the error magnitude of the isolated convective system is obtained, and corresponding rescaling coefficients are assigned to different scales. The disturbance discreteness of the corresponding scale is adjusted, and the disturbance field is reconstructed based on the adjusted disturbance discreteness to obtain a multi-scale disturbance field.

[0011] S5. Use the incremental analysis update method to add the disturbance increment consisting of multi-scale disturbance field and time coefficient in the disturbance model integration process until the ensemble forecast is completed.

[0012] Specifically, the initial value perturbation methods include growth mode propagation method, ensemble Kalman filtering and rescaling ensemble transformation.

[0013] Preferably, step S1 includes:

[0014] The growth mode propagation method is selected as the initial value perturbation method to generate the initial perturbation field of the ensemble forecast: a set of WRF model ensemble forecasts including one control experiment member and several ensemble members is set, and then the perturbation variable is set. An arbitrary initial perturbation is superimposed on the model initial field of the ensemble member. The model initial field of the control experiment member and the model initial field of the ensemble member after the superimposed perturbation are integrated simultaneously. After the integration of the set time is completed, the control forecast and the perturbation forecast are obtained respectively. The perturbation forecast is subtracted from the control forecast to obtain the perturbation at the current moment. Then, the perturbation scale at the current moment is adjusted to the same magnitude as the initial perturbation using scaling processing.

[0015] Specifically, in step S2, the calculation formula for the discrete degree of mutual influence between different scales is:

[0016] ,

[0017] Where: is the dispersion of mutual influence between scales, represents the combined perturbations of different scales, represents a perturbation of scale i, represents a disturbance of scale j, is the number of samples.

[0018] Specifically, in step S2, the initial disturbance field is decomposed into large-scale, medium-scale and small-scale disturbances based on the model resolution, where the small scale is the scale with a wavelength less than 48 km, the medium scale is the scale with a wavelength of 48-120 km, and the large scale is the scale with a wavelength greater than 120 km.

[0019] Specifically, step S3 includes:

[0020] Based on the predicted state of the isolated convective system and the large-scale and mesoscale environmental states, the state of the isolated convective system is judged in combination with the potential analysis method. If the isolated convective system is in a developing, mature or maintaining state, the mutual influence dispersion related to the small-scale disturbance near the isolated convective system is calculated. If the mutual influence dispersion is less than 0, the adjustment coefficient multiplied by the mutual influence dispersion is set to a positive value less than 1. If the mutual influence dispersion is greater than or equal to 0, the adjustment coefficient multiplied by the mutual influence dispersion is set to 1.

[0021] Specifically, the potential analysis method includes: calculating the convective effective potential energy, K index, lifting index, 700hPa pseudo equivalent potential temperature and vertical wind shear of the predicted isolated convective system to determine the status of the isolated convective system.

[0022] Preferably, step S4 further comprises: performing Gaussian filtering on the rescaling coefficients, and performing local constraints on the rescaling coefficients.

[0023] Specifically, in step S4, the adjusted disturbance discreteness calculation formula is:

[0024] ,

[0025] Where: is the adjusted disturbance discreteness, is the adjustment coefficient, is the dispersion of mutual influence between scales, is the rescaling coefficient of the lth band, represents that the initial disturbance is decomposed into M bands, is the disturbance of the lth band.

[0026] Specifically, in step S5, the model integral equation after adding the disturbance increment composed of the multi-scale disturbance field and the time coefficient is:

[0027] ,

[0028] Where: For time, Represents the pattern variable, subscript Indicates the overall tendency, subscript Indicates the tendency of pattern dynamics and physical processes, is the time coefficient, Indicates the duration of the disturbance period. Represents the multi-scale disturbance field.

[0029] Beneficial effect: Compared with the existing technology, the significant effect of the present invention is: the present invention uses the scale separation method to separate the initial value disturbance into disturbances of three scales: large, medium and small, and then combines the potential analysis method, multi-scale disturbance interaction, etc. to reconstruct the disturbance field, and continuously adds dynamic disturbances within the full cycle of the model integration through the incremental analysis method. First, the present invention sets a time coefficient for the disturbance increment, and improves the disturbance method into a "four-dimensional" disturbance method including the time dimension, which solves the problem that the traditional disturbance method only introduces disturbance in the initial stage of the forecast and cannot be dynamically updated as the weather system evolves, resulting in a mismatch between the disturbance structure and the subsequent weather situation; secondly, the existing technology does not effectively separate the influence of large, medium and small scale disturbances, and lacks a dynamic control mechanism for the interaction between scales, which easily causes disturbance suppression or excessive growth. The present invention fully considers the influence of disturbances of different scales, and uses the quantized discreteness of the mutual influence between different scales to construct the disturbance increment, which solves this problem well; finally, the traditional disturbance method is difficult to take into account the model integration stability and disturbance intensity requirements, especially in the forecast of severe convective systems, which is easy to cause numerical oscillation. The present invention ensures that under the premise of stable model integration, dynamic disturbances are continuously added within the full cycle of the model integration through the incremental analysis method, which solves the problems of fast discreteness decay and mismatch between disturbance and weather situation in the traditional initial value disturbance, and improves the forecast accuracy of disastrous severe convective weather. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0031] A preferred embodiment of the present invention is further described below with reference to the accompanying drawings.

[0032] Example 1

[0033] See also Figure 1 As shown, this embodiment provides a multi-scale four-dimensional initial value perturbation method for ensemble forecast based on incremental analysis and updating, comprising the following steps:

[0034] S1. Generate the initial perturbation field for ensemble forecast using the initial value perturbation method.

[0035] Existing initial value perturbation methods include growth mode reproduction method, singular vector method, rescaling set transformation and ensemble Kalman filtering.

[0036] The principle of the growth mode reproduction method (BGM) is as follows: first, an arbitrary perturbation is superimposed on the initial field of the model, the initial field of the control test and the initial field after the superimposed perturbation are integrated simultaneously, and after a period of integration, the control forecast and the perturbation forecast are obtained. The scale of the perturbation is adjusted to the same order of magnitude as the initial perturbation, and then the analysis perturbation is superimposed on the new atmospheric initial field. The reproduction is repeated continuously, and finally the required fastest growth mode is obtained. The growth mode reproduction method scales the perturbation at the end of the reproduction cycle:

[0037] ,

[0038] Where: c is the adjustment coefficient, and the model layer k related, and denote the forecast disturbance and the scale-adjusted disturbance, respectively; It is the ratio of the preset disturbance root mean square to the predicted disturbance root mean square.

[0039] In this embodiment, the growth mode propagation method is used to generate the initial disturbance field of the ensemble forecast. :

[0040] Reproduction cycle: From a few hours before model integration to the initial moment (e.g., 12 hours before model integration to 0 hours), the mode with the fastest error growth is reproduced through multiple cycles of integration to generate the initial disturbance field and characterize the uncertainty of the initial value conditions.

[0041] Scaling: The disturbance field after reproduction is scaled to ensure that its disturbance amplitude matches the disturbance magnitude before reproduction.

[0042] S2. Use the scale separation method to decompose the initial disturbance field into several disturbances of different scales, and calculate the disturbance discreteness of different scales and the discreteness of mutual influence between different scales respectively.

[0043] In this embodiment, the initial disturbance field generated by S1 is decomposed into large-scale, medium-scale, and small-scale disturbances, and then different combinations of disturbances of different scales are obtained. The discreteness of the mutual influence between disturbances of different scales is calculated:

[0044] ,

[0045] Where: is the dispersion of mutual influence between scales, represents the combined perturbations of different scales, represents a perturbation of scale i, represents a disturbance of scale j, is the sample size; if If it is less than 0, it means that the interaction between multi-scale disturbances will suppress the growth of disturbances (for example, large-scale downdrafts suppress small-scale updrafts). If it is greater than or equal to 0, it means that there is no significant inhibition or synergistic enhancement between multi-scale disturbances.

[0046] S3. Use the potential analysis method to determine the state of the predicted isolated convective system. According to the state of the isolated convective system, use the adjustment coefficient to dynamically adjust the discreteness of the mutual influence between different scales in real time.

[0047] Based on the predicted state of the isolated convective system and the large-scale and mesoscale environmental conditions, the potential analysis method is used to determine the state of the isolated convective system. If the isolated convective system is in the developing, mature or maintaining state, the dispersion of the mutual influence related to the small-scale disturbance near the isolated convective system is calculated. ,like If it is less than 0, the adjustment factor multiplied by is set to a positive value less than 1. Greater than or equal to 0, will be Multiplicative adjustment factor Set to 1.

[0048] S4. Based on the error magnitudes of isolated convective systems and their large-scale and medium-scale environmental fields obtained from historical observation statistics, rescaling coefficients are assigned to different scales, the disturbance discreteness of the corresponding scales is adjusted, and the disturbance field is reconstructed based on the adjusted disturbance discreteness to obtain a multi-scale disturbance field. .

[0049] The calculation formula of the adjusted disturbance discreteness is:

[0050] ,

[0051] Where: is the adjusted disturbance discreteness, is the adjustment coefficient, is the dispersion of mutual influence between scales, is the rescaling coefficient of the lth band, represents that the initial disturbance is decomposed into M bands, is the disturbance of the lth band.

[0052] Although both the adjustment coefficient and the rescaling coefficient are determined based on objective methods, it is still necessary to ensure the stability of the integral. Therefore, the rescaling coefficient is Gaussian filtered to make it smoothly distributed in the pattern space and to impose local constraints on the rescaling coefficient.

[0053] S5. Use the incremental analysis update method to add the disturbance increment consisting of multi-scale disturbance field and time coefficient in the disturbance model integration process until the ensemble forecast is completed.

[0054] In this embodiment, the incremental analysis update (IAU) is used to add the perturbation increment in the whole process of model integration. , that is, the multi-scale disturbance field For the selected pattern variable , IAU can be expressed as:

[0055] ,

[0056] Where: For time, Represents the pattern variable, subscript Indicates the overall tendency, subscript Indicates the tendency of pattern dynamics and physical processes, is the time coefficient, Indicates the duration of the disturbance period. represents the multi-scale disturbance field; A reference calculation method is In actual use, it needs to be adjusted according to the evolution stage of the weather system (such as convection outbreak period) , increasing the disturbance intensity during critical periods.

[0057] Repeat the above steps until the ensemble forecast is complete. This four-dimensional "initial value" perturbation method adds continuous and smooth perturbation increments to the corresponding model variables throughout the integration process to maintain the discreteness of small and medium-scale perturbations. Compared to traditional methods that only introduce perturbations at the initial stage of the forecast and cannot be dynamically updated based on the evolution of the weather system, the "initial values" of this invention refer to initial values that are continuously embedded during the model integration forecast process.

[0058] This embodiment further illustrates the above method in a specific application scenario.

[0059] Application scenario: Ensemble forecast of isolated convective systems.

[0060] S1. Design a 16-member WRF model ensemble forecast, including one control member without perturbation and 15 ensemble members with perturbation. Set the perturbation variables as zonal wind U, meridional wind V, temperature T, and specific humidity Q. That is, the perturbations will be superimposed on these four basic atmospheric variables.

[0061] An arbitrary disturbance is superimposed on the initial field of the model of the ensemble member. The initial field of the control test and the initial field after the superimposed disturbance are integrated simultaneously. After 3 hours of integration, the disturbance forecast and the control forecast are obtained. The subtraction of the two is the disturbance at the current moment. Then, the scale of the disturbance at the current moment is adjusted to the same magnitude as the initial disturbance using the scaling process. The above is the disturbance generated by the growth mode reproduction method in one cycle (3 hours). The cycle is set to 3 hours to continuously provide the initial disturbance field for subsequent steps. .

[0062] S2. Use the discrete cosine transform method to decompose the initial disturbance field into three scales: large, medium, and small. Unlike traditional scale definitions, this embodiment uses a setting based on model resolution, defining scales with wavelengths less than 48 km as small, scales with wavelengths between 48 and 120 km as medium, and scales with wavelengths greater than 120 km as large.

[0063] Calculate the perturbation discreteness of each scale at the current integration moment The subscript i can represent three different scales: large, medium, and small. The discreteness of the disturbance at each scale is used to calculate the discreteness of the mutual influence between disturbances of different scales. .

[0064] S3. Based on the predicted isolated convective system and large- and medium-scale environmental field data, use the potential analysis method to calculate the predicted convective effective potential energy, K index, lifting index, 700hPa pseudo-equivalent potential temperature, vertical wind shear and other factors of the isolated convective system to determine the status of the isolated convective system.

[0065] Further calculations are made of the discreteness of the mutual influences between the convective system and the small-scale disturbances when the convection is in different states, such as development, maturity, and maintenance. .like , it means that the interaction between small-scale disturbances and mesoscale environmental fields suppresses the growth of disturbances, and the adjustment coefficient needs to be set to less than 1; if , then the adjustment coefficient is set to 1 to maintain the natural evolution of the disturbance.

[0066] S4. Assign a rescaling coefficient to each scale based on the error magnitude of historical observation statistics .

[0067] Counterweight scale factor Gaussian filtering is performed to avoid spatial mutations. Local constraints are also imposed on the rescaling coefficients, such as increasing the weight of small-scale perturbations in strong convection areas (e.g., CAPE>2000 J / kg).

[0068] Using the adjustment factor and rescaling coefficient Calculate the adjusted disturbance discreteness , based on Reconstructing a new disturbance field , the reconstructed disturbance field is the multi-scale disturbance field after dynamic optimization .

[0069] S5, the reconstructed disturbance field It is added as a disturbance increment into the whole process of model integration.

[0070] set up , and dynamically adjust the value during critical weather stages. For example, during a convective outbreak (radar echo intensity > 40 dBZ), Increase to , to enhance the disturbance intensity.

[0071] Repeat the above steps every 3 hours, and add the generated four-dimensional “initial value” disturbance to the model variables U, V, T, and Q until the entire forecast process is completed.

Claims

1. A multi-scale four-dimensional initial value perturbation method for ensemble forecasting based on incremental analysis and updating, characterized by: The following steps are involved: S1. Generate the initial perturbation field of ensemble forecast using the initial value perturbation method; S2. Use the scale separation method to decompose the initial disturbance field into several disturbances of different scales, and calculate the disturbance discreteness of different scales and the discreteness of mutual influence between different scales respectively; S3. Use potential analysis to determine the state of the predicted isolated convective system. Based on the state of the isolated convective system, use the adjustment coefficient to dynamically adjust the discreteness of the mutual influence between different scales in real time. S4. Based on historical observation statistics, the error magnitude of the isolated convective system is obtained, and corresponding rescaling coefficients are assigned to different scales. The disturbance discreteness of the corresponding scale is adjusted, and the disturbance field is reconstructed based on the adjusted disturbance discreteness to obtain a multi-scale disturbance field. S5. Use the incremental analysis update method to add the disturbance increment consisting of multi-scale disturbance field and time coefficient in the disturbance model integration process until the ensemble forecast is completed.

2. The ensemble forecast multi-scale four-dimensional initial value perturbation method according to claim 1, characterized in that: The initial value perturbation method includes growing mode propagation method, ensemble Kalman filtering and rescaling ensemble transformation.

3. The ensemble forecast multi-scale four-dimensional initial value perturbation method according to claim 2, characterized in that: The step S1 comprises: The growth mode propagation method is selected as the initial value perturbation method to generate the initial perturbation field of the ensemble forecast: a set of WRF model ensemble forecasts including one control experiment member and several ensemble members is set, and then the perturbation variable is set. An arbitrary initial perturbation is superimposed on the model initial field of the ensemble member. The model initial field of the control experiment member and the model initial field of the ensemble member after the superimposed perturbation are integrated simultaneously. After the integration of the set time is completed, the control forecast and the perturbation forecast are obtained respectively. The perturbation forecast is subtracted from the control forecast to obtain the perturbation at the current moment. Then, the perturbation scale at the current moment is adjusted to the same magnitude as the initial perturbation using scaling processing.

4. The ensemble forecast multi-scale four-dimensional initial value perturbation method according to claim 1, characterized in that: In step S2, the calculation formula for the discrete degree of mutual influence between different scales is: ， Where: is the dispersion of mutual influence between scales, represents the combined perturbations of different scales, represents a perturbation of scale i, represents a disturbance of scale j, is the number of samples.

5. The ensemble forecast multi-scale four-dimensional initial value perturbation method according to claim 1, characterized in that: In step S2, the initial disturbance field is decomposed into large-scale, medium-scale and small-scale disturbances based on the model resolution, where the small scale is the scale with a wavelength less than 48 km, the medium scale is the scale with a wavelength of 48-120 km, and the large scale is the scale with a wavelength greater than 120 km.

6. The ensemble forecast multi-scale four-dimensional initial value perturbation method according to claim 5, characterized in that: The step S3 comprises: Based on the predicted state of the isolated convective system and the large-scale and mesoscale environmental states, the state of the isolated convective system is judged in combination with the potential analysis method. If the isolated convective system is in a developing, mature or maintaining state, the mutual influence dispersion related to the small-scale disturbance near the isolated convective system is calculated. If the mutual influence dispersion is less than 0, the adjustment coefficient multiplied by the mutual influence dispersion is set to a positive value less than 1. If the mutual influence dispersion is greater than or equal to 0, the adjustment coefficient multiplied by the mutual influence dispersion is set to 1.

7. The ensemble forecast multi-scale four-dimensional initial value perturbation method according to claim 6, characterized in that: The potential analysis method includes: calculating the convective effective potential energy, K index, lifting index, 700hPa pseudo equivalent potential temperature and vertical wind shear of the predicted isolated convective system, and judging the state of the isolated convective system.

8. The ensemble forecast multi-scale four-dimensional initial value perturbation method according to claim 1, characterized in that: The step S4 further includes: performing Gaussian filtering on the rescaling coefficients and performing local constraints on the rescaling coefficients.

9. The ensemble forecast multi-scale four-dimensional initial value perturbation method according to claim 1, characterized in that: In step S4, the adjusted disturbance discreteness calculation formula is: ， Where: is the adjusted disturbance discreteness, is the adjustment coefficient, is the dispersion of mutual influence between scales, is the rescaling coefficient of the lth band, represents that the initial disturbance is decomposed into M bands, is the disturbance of the lth band.

10. The ensemble forecast multi-scale four-dimensional initial value perturbation method according to claim 1, characterized in that: In step S5, the model integral equation after adding the disturbance increment composed of the multi-scale disturbance field and the time coefficient is: ， Where: For time, Represents the pattern variable, subscript Indicates the overall tendency, subscript Indicates the tendency of pattern dynamics and physical processes, is the time coefficient, Indicates the duration of the disturbance period. Represents the multi-scale disturbance field.

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