Incremental analysis updating-based ensemble forecast multi-scale four-dimensional initial value perturbation method

Abstract

The invention provides an ensemble forecast multi-scale four-dimensional initial value disturbance method based on incremental analysis updating, which comprises the following steps of: firstly, separating initial value disturbance into disturbance of large, medium and small scales by using a scale separation method, and respectively calculating disturbance dispersion of different scales and mutual influence dispersion among different scales; the mutual influence dispersion between different scales is dynamically adjusted in real time by using an adjustment coefficient in combination with a potential analysis method; then, corresponding re-scale coefficients are distributed for different scales, disturbance dispersion of the corresponding scales is adjusted, and then a multi-scale disturbance field is obtained; and finally, adding a disturbance increment formed by a multi-scale disturbance field and a time coefficient in a disturbance mode integration process by utilizing an increment analysis updating method until ensemble forecasting is finished. According to the method, the problems of fast dispersion attenuation, disturbance and weather situation mismatch and the like in traditional initial value disturbance are effectively solved, and the forecasting precision of severe disastrous convective weather is improved.

Description

Technical Field

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

[0002] Numerical weather prediction (NWP) is the core means for predicting future weather conditions in modern meteorological operations. However, limited by model accuracy, initial value errors, and computing conditions, there are inevitably uncertainties in numerical prediction results. Therefore, identifying key error sources and reasonably characterizing their impacts on forecasting are the core challenges for achieving high-confidence forecasts.

[0003] As the mainstream means to address the above problems, ensemble forecasting technology generates multi-member forecasts by introducing perturbations at error-sensitive locations, thereby quantifying the probability distribution of future weather. Among them, initial value perturbation and model perturbation are two main directions. Initial value perturbation aims at the uncertainty of the initial atmospheric state and generates different initial values through perturbation methods such as the Monte Carlo method, breeding growing modes (BGM), singular vectors (SV), analysis constraint methods, conditional nonlinear optimal perturbation (CNOP), and ensemble Kalman filter. However, traditional methods have some limitations: for example, the BGM method has insufficient independence, the SV method relies on linear approximation and is computationally complex, and although the CNOP method can characterize nonlinear errors, it is costly. In addition, to fuse multi-scale error characteristics, the blending perturbation method combines large-scale perturbations of global models with medium and small-scale perturbations of regional models, while ensemble data assimilation technology (EDA) alleviates the problem of multi-scale information imbalance to a certain extent by optimizing the perturbation structure. However, since blending perturbations rely on complex filtering techniques and the interaction between moist convective instability and multi-scale circulation will significantly amplify small errors, there are still many problems with such methods.

[0004] An excellent initial value perturbation needs to simultaneously reflect multi-scale error modes, nonlinear interactions, and dynamic matching with weather flow patterns. However, existing technologies are difficult to achieve this: the SV and BGM methods have insufficient response to nonlinear physical processes, and although the analysis constraint scheme can improve the characterization of medium and small-scale errors, it lacks a four-dimensional spatio-temporal coordination mechanism. In addition, under high-resolution models, the problem of rapid decay of perturbation dispersion with integration has not been effectively solved. Summary of the Invention

[0005] Object of the Invention: The object of the present invention is to provide a multi-scale four-dimensional initial value perturbation method for ensemble forecasting based on incremental analysis update that can dynamically fuse multi-scale error information, adapt to nonlinear evolution, and maintain reasonable dispersion, so as to improve the ensemble forecasting ability for disastrous weather.

[0006] Technical Solution: A multi-scale four-dimensional initial value perturbation method for ensemble forecasting based on incremental analysis update, comprising the following steps: S1. Generate the initial perturbation field of the ensemble forecast using the initial value perturbation method; S2. Decompose the initial perturbation field into several perturbations of different scales using the scale separation method, and calculate the perturbation dispersions of different scales and the mutual influence dispersions between different scales respectively; S3. Use the potential analysis method to judge the state of the predicted isolated convective system, and according to the state of the isolated convective system, use the adjustment coefficient to dynamically adjust the magnitude of the mutual influence dispersion between different scales in real time; S4. Based on the historical observation statistics, obtain the error magnitude of the isolated convective system, allocate corresponding rescaling coefficients to different scales respectively, adjust the perturbation dispersions of the corresponding scales, and reconstruct the perturbation field based on the adjusted perturbation dispersions to obtain the multi-scale perturbation field; S5. Use the incremental analysis update method to add the perturbation increment composed of the multi-scale perturbation field and the time coefficient during the model integration of the perturbation until the ensemble forecast ends.

[0007] Specifically, the initial value perturbation methods include the breeding method of growing modes, ensemble Kalman filter, and rescaled ensemble transformation.

[0008] Preferably, step S1 includes: Select the breeding method of growing modes as the initial value perturbation method to generate the initial perturbation field of the ensemble forecast: Set a WRF model ensemble forecast including 1 control experiment member and several ensemble members, then set the perturbation variables, superimpose any initial perturbation on the model initial fields of the ensemble members, integrate the model initial field of the control experiment member and the model initial fields of the ensemble members after superimposing the perturbation simultaneously. After the integration of the set duration is completed, obtain the control forecast and the perturbation forecast respectively. Subtract the perturbation forecast from the control forecast to obtain the perturbation at the current moment, and then use the scaling process to adjust the perturbation scale at the current moment to the same order of magnitude as the initial perturbation.

[0009] Specifically, in step S2, the calculation formula for the mutual influence dispersion between different scales is: , where: is the mutual influence dispersion between scales, represents the combined perturbation of different scales, represents the perturbation of scale i, represents the perturbation of scale j, is the number of samples.

[0010] Specifically, in step S2, the initial perturbation field is decomposed into large-scale, medium-scale, and small-scale perturbations based on the pattern resolution. 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.

[0011] Specifically, step S3 includes: Based on the predicted state of the isolated convective system and the large-scale and medium-scale environmental states, combined with the potential analysis method to judge the state of the isolated convective system. If the isolated convective system is in a developing, mature, or maintaining state, calculate the mutual influence divergence related to the small-scale perturbation near the isolated convective system. If the mutual influence divergence is less than 0, set the adjustment coefficient multiplied by the mutual influence divergence to a positive value less than 1. If the mutual influence divergence is greater than or equal to 0, set the adjustment coefficient multiplied by the mutual influence divergence to 1.

[0012] Specifically, the potential analysis method includes: calculating the convective available potential energy, K-index, lifting index, 700 hPa pseudo-equivalent potential temperature, and vertical wind shear of the predicted isolated convective system to judge the state of the isolated convective system.

[0013] Preferably, step S4 further includes: performing Gaussian filtering on the rescaling coefficient and imposing local constraints on the rescaling coefficient.

[0014] Specifically, in step S4, the adjusted perturbation divergence calculation formula is: , where: is the adjusted perturbation divergence, is the adjustment coefficient, is the mutual influence divergence between scales, is the rescaling coefficient of the l-th band, represents that the initial perturbation is decomposed into M bands, is the perturbation of the l-th band.

[0015] Specifically, in step S5, the model integration equation after adding the perturbation increment composed of the multi-scale perturbation field and the time coefficient is: , where: is time, represents the model variable, and the subscript denotes the total tendency, and the subscript denotes the tendency of the model dynamic and physical processes, is the time coefficient, represents the period duration of the perturbation addition, represents the multi-scale perturbation field.

[0016] Beneficial effects: Compared with the prior art, the remarkable effects of the present invention are as follows: The present invention uses a scale separation method to separate the initial value perturbation into perturbations of large, medium, and small scales, and then combines the potential analysis method, multi-scale perturbation interaction, etc. to reconstruct the perturbation field, and continuously adds dynamic perturbations throughout the entire cycle of model integration through the incremental analysis method. First, the present invention sets a time coefficient for the perturbation increment, improving the perturbation method to a "four-dimensional" perturbation method including the time dimension, solving the problem that the traditional perturbation method only introduces perturbations at the initial stage of the forecast and cannot be dynamically updated as the weather system evolves, resulting in a mismatch between the perturbation structure and the subsequent weather situation; Secondly, the prior art has not effectively separated the influences of large, medium, and small scale perturbations and lacks a dynamic regulation mechanism for the interaction between scales, which is prone to cause perturbation suppression or excessive growth. The present invention fully considers the influences of different scale perturbations and constructs perturbation increments using the quantified discrete degree of mutual influence between different scales, thus well solving this problem; Finally, the traditional perturbation method is difficult to balance the requirements of model integration stability and perturbation intensity, especially prone to numerical oscillations in the forecast of severe convective systems. The present invention ensures that on the premise of stable model integration, dynamic perturbations are continuously added throughout the entire cycle of model integration through the incremental analysis method, solving the problems such as fast decay of the discrete degree and mismatch between perturbations and weather situations in traditional initial value perturbations, and improving the forecast accuracy of severe convective weather disasters. Description of the Drawings

[0017] Figure 1 It is the flowchart of the method of the present invention. Detailed Embodiment

[0018] The following further illustrates a preferred embodiment of the present invention with reference to the drawings.

[0019] Embodiment 1

[0020] Please refer to Figure 1 As shown, this embodiment provides a multi-scale four-dimensional initial value perturbation method for ensemble forecasting based on incremental analysis update, including the following steps: S1. Use the initial value perturbation method to generate the initial perturbation field of the ensemble forecasting.

[0021] Existing initial value perturbation methods include the breeding growth mode method, the singular vector method, rescaled ensemble transformation, and ensemble Kalman filtering, etc.

[0022] The principle of the breeding growth mode method (BGM) is as follows: First, an arbitrary perturbation is superimposed on the initial field of the model, and the initial field of the control experiment and the initial field after the superimposed perturbation are integrated simultaneously. After integrating for a period of time, 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 analyzed perturbation is superimposed on the new atmospheric initial field, and the breeding is repeated continuously until the fastest growing mode required is obtained. The breeding growth mode method scales the perturbation at the end of the breeding cycle: , wherein: c is an adjustment coefficient, related to the pattern layer k ; and respectively represent the forecast perturbation and the perturbation after scale adjustment; is the ratio of the preset root mean square of the perturbation to the root mean square of the forecast perturbation.

[0023] In this embodiment, the breeding mode initialization method is adopted to generate the initial perturbation field of the ensemble forecast : Breeding cycle: In the first few hours before the model integration to the initial time (such as from 12 hours before the model integration to 0 hour), the mode with the fastest growing error is bred through multiple cyclic integrations to generate the initial perturbation field, which characterizes the uncertainty of the initial value conditions.

[0024] Scaling process: Perform a scaling process on the bred perturbation field to ensure that its perturbation amplitude matches the perturbation magnitude before breeding.

[0025] S2. Use the scale separation method to decompose the initial perturbation field into several perturbations of different scales, and calculate the dispersion of perturbations of different scales and the mutual influence dispersion between different scales respectively.

[0026] In this embodiment, the initial perturbation field generated in S1 is decomposed into large-scale, medium-scale, and small-scale perturbations, and then different combinations of perturbations of different scales are obtained, and the mutual influence dispersion between perturbations of different scales is calculated: , wherein: is the mutual influence dispersion between scales, represents the combined perturbation of different scales, represents the perturbation of scale i, represents the perturbation of scale j, is the number of samples; if is less than 0, it means that the interaction between multi-scale perturbations will suppress the growth of perturbations (for example, large-scale subsidence airflow suppresses small-scale upward movement), and if is greater than or equal to 0, it means that there is no significant suppression or there is cooperative enhancement between multi-scale perturbations.

[0027] S3. Use the potential analysis method to judge the state of the forecast isolated convective system, and according to the state of the isolated convective system, use the adjustment coefficient to dynamically adjust the mutual influence dispersion between different scales in real time.

[0028] Based on the state of the isolated convective system predicted and the large-scale and mesoscale environmental states, combined with the potential analysis method to judge the state of the isolated convective system. If the isolated convective system is in a developing, mature or maintaining state, calculate the mutual influence dispersion related to small-scale perturbations near the isolated convective system. , if is less than 0, set the adjustment coefficient multiplied by it to a positive value less than 1. If is greater than or equal to 0, set the adjustment coefficient multiplied by to 1.

[0029] S4. Based on the error magnitudes of the isolated convective system and its large-scale and mesoscale environmental fields obtained from historical observations, assign rescaling coefficients to different scales, adjust the perturbation dispersion of the corresponding scales, and reconstruct the perturbation field based on the adjusted perturbation dispersion to obtain a multi-scale perturbation field. .

[0030] The formula for the adjusted perturbation dispersion is: , where: is the adjusted perturbation dispersion, is the adjustment coefficient, is the mutual influence dispersion between scales, is the rescaling coefficient for the l-th band, represents that the initial perturbation is decomposed into M bands, is the perturbation of the l-th band.

[0031] Although both the adjustment coefficient and the rescaling coefficient are determined based on objective methods, it is still necessary to ensure integral stability. Therefore, perform Gaussian filtering on the rescaling coefficient to make the rescaling coefficient smoothly distributed in the model space and impose local constraints on the rescaling coefficient.

[0032] S5. Use the incremental analysis update method to add the perturbation increment composed of the multi-scale perturbation field and the time coefficient during the model integration process of the perturbation until the ensemble forecast ends.

[0033] In this embodiment, use the incremental analysis update (IAU) to add the perturbation increment during the whole process of model integration, that is, the multi-scale perturbation field . For the selected model variable , IAU can be expressed as: , where: is time, represents the model variable, the subscript represents the total tendency, and the subscript Indicates the tendency of model dynamics and physical processes, is the time coefficient, represents the periodic duration when the perturbation is added, represents the multi-scale perturbation field; A reference calculation method for needs to be adjusted according to the evolution stage of the weather system (such as the convective outbreak period) in actual use to enhance the perturbation intensity during the critical period.

[0034] Repeat the above steps until the ensemble forecast ends. This four-dimensional "initial value" perturbation method will add continuous and smooth perturbation increment terms to the corresponding model variables throughout the integration process to maintain the dispersion of meso- and small-scale perturbations. Compared with the traditional method that only introduces perturbations at the initial stage of the forecast and cannot be dynamically updated according to the evolution of the weather system, the "initial value" in the present invention refers to the initial value continuously implanted during the model integration forecast process.

[0035] This embodiment further illustrates the above method in a specific application scenario.

[0036] Application scenario: Ensemble forecast of isolated convective systems.

[0037] S1. Design a WRF model ensemble forecast with 16 members, including 1 control experiment member without applying perturbations and 15 ensemble members with perturbations applied; 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 4 basic atmospheric variables subsequently.

[0038] Superimpose an arbitrary perturbation on the initial field of the ensemble members, integrate the initial field of the control experiment and the initial field after superimposing the perturbation simultaneously. After integrating for 3 h, obtain the perturbation forecast and the control forecast, and subtract the two to get the perturbation at the current moment. Then use the scaling process to adjust the scale of the perturbation at the current moment to the same order of magnitude as the initial perturbation. The above is the perturbation generated by the breeding method of growing modes in one cycle (3 h). Set the period to 3 h to continuously provide the initial perturbation field for the subsequent steps .

[0039] S2. Use the discrete cosine transform method to decompose the initial perturbation field into large, medium, and small scale perturbations. Different from the traditional scale definition, this embodiment adopts the setting based on the model resolution. The scale with a wavelength less than 48 km is defined as the small scale, the scale with a wavelength in the range of 48 - 120 km is set as the medium scale, and the scale with a wavelength greater than 120 km is regarded as the large scale.

[0040] Calculate the perturbation dispersion of each scale at the current integration moment , the subscript i can represent three different scales: large, medium, and small; the mutual influence dispersion between perturbations of different scales is calculated using the dispersion of perturbations at each scale. .

[0041] S3. Based on the data of the forecasted isolated convective system and the large and medium-scale environmental fields, using the potential analysis method, calculate elements such as the convective available potential energy, K-index, lifting index, 700 hPa pseudo-equivalent potential temperature, and vertical wind shear of the forecasted isolated convective system to judge the state of the isolated convective system.

[0042] Further calculate the mutual influence dispersion related to small-scale perturbations near the convective system when the convection is in different states such as development, maturity, and maintenance. . If , it means that the interaction between small-scale perturbations and the medium-scale environmental field inhibits the growth of perturbations, and the adjustment coefficient needs to be set to less than 1; if , the adjustment coefficient is set to 1 to maintain the natural evolution of perturbations.

[0043] S4. Based on the error magnitude of historical observations and statistics, assign rescaling coefficients to each scale. .

[0044] Perform Gaussian filtering on the rescaling coefficients to avoid spatial mutations. And impose local constraints on the rescaling coefficients, such as enhancing the weight of small-scale perturbations in strong convective regions (e.g., CAPE > 2000 J / kg).

[0045] Use the adjustment coefficient and the rescaling coefficient to calculate the adjusted perturbation dispersion , and then based on reconstruct a new perturbation field , and the reconstructed perturbation field is the dynamically optimized multi-scale perturbation field .

[0046] S5. Add the reconstructed perturbation field as a perturbation increment to the entire process of model integration.

[0047] Set , and dynamically adjust the value of during key weather stages. For example, during the convective outbreak period (radar echo intensity > 40 dBZ), increase to to enhance the perturbation intensity.

[0048] Repeat the above steps every 3 h, and add the generated four-dimensional "initial value" perturbation to the model variables U, V, T, and Q until the end of the entire forecast process.

Claims

1. A multi-scale four-dimensional initial value perturbation method for ensemble forecasting based on incremental analysis update, characterized in that It includes the following steps: S1. Generate the initial perturbation field of the ensemble forecast using the initial value perturbation method; S2. Decompose the initial perturbation field into perturbations of several different scales using the scale separation method, and calculate the dispersion of perturbations of different scales and the cross-scale influence dispersion between different scales respectively; S3. Use the potential analysis method to judge the state of the forecasted isolated convective system. According to the state of the isolated convective system, dynamically adjust the magnitude of the cross-scale influence dispersion in real time using the adjustment coefficient; S4. Based on the historical observation statistics, obtain the error magnitude of the isolated convective system, allocate corresponding rescaling coefficients to different scales respectively, adjust the perturbation dispersion of the corresponding scale, and reconstruct the perturbation field based on the adjusted perturbation dispersion to obtain the multi-scale perturbation field; S5. Use the incremental analysis update method to add the perturbation increment composed of the multi-scale perturbation field and the time coefficient during the model integration of the perturbation until the ensemble forecast ends.

2. The multi-scale four-dimensional initial value perturbation method for ensemble forecasting according to claim 1, characterized in that: The initial value perturbation method includes the breeding method of growing modes, the ensemble Kalman filter, and the rescaled ensemble transformation.

3. The multi-scale four-dimensional initial value perturbation method for ensemble prediction according to claim 2, characterized in that: The step S1 includes: Select the breeding method of growing modes as the initial value perturbation method to generate the initial perturbation field of the ensemble forecast: Set a WRF model ensemble forecast including 1 control experiment member and several ensemble members, then set the perturbation variables, superimpose any initial perturbation on the model initial fields of the ensemble members, integrate the model initial field of the control experiment member and the model initial fields of the ensemble members after superimposing the perturbation simultaneously. After the integration of the set duration is completed, obtain the control forecast and the perturbation forecast respectively. Subtract the control forecast from the perturbation forecast to obtain the perturbation at the current moment, and then use the scaling process to adjust the perturbation scale at the current moment to the same order of magnitude as the initial perturbation.

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

5. The multi-scale four-dimensional initial value perturbation method for ensemble forecasting according to claim 1, characterized in that: In the step S2, decompose the initial perturbation field into large-scale, medium-scale, and small-scale perturbations based on the model resolution. 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 multi-scale four-dimensional initial value perturbation method for ensemble prediction according to claim 5, characterized in that: The step S3 includes: Based on the state of the forecasted isolated convective system and the large-scale and medium-scale environmental states, combine the potential analysis method to judge the state of the isolated convective system. If the isolated convective system is in the developing, mature, or maintaining state, calculate the cross-scale influence dispersion related to the small-scale perturbation near the isolated convective system. If the cross-scale influence dispersion is less than 0, set the adjustment coefficient multiplied by the cross-scale influence dispersion to a positive value less than 1. If the cross-scale influence dispersion is greater than or equal to 0, set the adjustment coefficient multiplied by the cross-scale influence dispersion to 1.

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

8. The multi-scale four-dimensional initial value perturbation method for ensemble prediction according to claim 1, wherein: The step S4 further includes: performing Gaussian filtering on the rescaling coefficient and imposing local constraints on the rescaling coefficient.

9. The multi-scale four-dimensional initial value perturbation method for ensemble prediction according to claim 1, wherein: In the step S4, the adjusted formula for the disturbance dispersion is as follows: ， Wherein: is the adjusted disturbance dispersion,[[]] is the adjustment coefficient,[[]] is the mutual influence dispersion between scales,[[]] is the rescaling coefficient of the l-th band,[[]] represents that the initial disturbance is decomposed into M bands,[[]] is the disturbance of the l-th band.[[]] 10. The multi-scale four-dimensional initial value perturbation method for ensemble forecasting according to claim 1, characterized in that: In the step S5, the mode integral equation after adding the disturbance increment composed of the multi-scale disturbance field and the time coefficient is as follows: ， In the formula: is time, represents the mode variable, with the subscript indicating the total tendency, and the subscript indicating the tendency of the mode dynamics and physical processes, is the time coefficient, represents the period duration of the perturbation addition, represents the multi-scale perturbation field.

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