A coordinated perturbation method for multi-source errors in ensemble forecasting based on error characteristic evolution and dispersion resonance

Abstract

The present invention provides a collaborative perturbation method for ensemble forecasting multi-source errors based on error characteristic evolution and discreteness resonance. The method selects three single error sources, namely initial value, lateral boundary and physical process, and uses a perturbation method to generate a perturbation set of single error sources and multi-error source combinations. The ensemble forecast error energy of the single error source and multi-error source is calculated and decomposed into different spatial scales. The error evolution characteristics of the single error source and multi-error source are analyzed. The ESA technology is combined to explore the sensitive areas and sensitive elements of the perturbation errors of each single error source and multi-error source, compare the error evolution characteristics of the multi-error source perturbation and the single error source perturbation, analyze the interaction mechanism between the perturbations of different error sources, construct a discreteness resonance model, evaluate the synergistic effect of the multi-error source combination perturbation in sensitive areas or sensitive elements, and construct a collaborative perturbation of multi-source errors. The present invention reveals the key mechanism of single-source error growth and the interaction mechanism of multi-source errors, thereby improving the prediction accuracy of ensemble forecasting.

Description

Technical Field

[0001] The present invention relates to the technical field of numerical weather forecasting, and in particular to a collaborative perturbation method for ensemble forecasting multi-source errors based on error feature evolution and discreteness resonance. Background Art

[0002] Ensemble forecasting is a method that reflects the uncertainty of weather forecasts by generating multiple different forecast results. Its core lies in quantifying probability distributions through multi-member simulations. Ensemble forecasting has the following characteristics: Multi-perturbation generation: introducing small perturbations to initial conditions, boundary conditions, and physical process parameterization schemes, or using different numerical models to generate multiple forecast members; Probabilistic output: the differences between members can reflect the probability distribution of the forecast quantity (such as precipitation probability and typhoon path probability), rather than a single deterministic conclusion; and Uncertainty Management: accounting for both initial field errors (such as observation errors and insufficient model initialization) and the randomness of model physical processes (such as physical process parameterization schemes).

[0003] However, the sources of error in convective-scale forecasts are complex (e.g., initial values, lateral boundaries, and physical process errors). Existing technologies struggle to effectively separate the contributions of different error sources, and lack quantitative analysis of the interaction mechanisms of multi-source perturbations. Randomly matching multi-source error perturbations can lead to irrational distributions of meteorological elements that do not conform to physical laws or irrational temporal trends, affecting ensemble forecast error estimates. Consequently, it is difficult to determine which perturbation combinations will resonate with the ensemble discreteness, resulting in limitations in ensemble discreteness design and poor synergy between multi-source perturbations. Summary of the Invention

[0004] Objective of the invention: The objective of the present invention is to provide a collaborative perturbation method for multi-source errors in ensemble forecasting based on error characteristic evolution and discreteness resonance.

[0005] Technical solution: A collaborative perturbation method for multi-source errors in ensemble forecasting based on error feature evolution and discreteness resonance, including the following steps:

[0006] S1. Set the initial value, lateral boundary and physical process as single error sources, and use the perturbation methods of the initial value, lateral boundary and physical process to generate the perturbation set of single error source and the perturbation set of multiple error sources respectively;

[0007] S2. Calculate the error energy (RMDTE) of the single error source ensemble forecast and the multi-error source ensemble forecast respectively, decompose the RMDTE at different spatial scales using the scale separation method, and analyze the error evolution characteristics of the single error source disturbance and the multi-error source disturbance respectively;

[0008] S3. Using RMDTE combined with the ensemble sensitivity analysis method, we obtain the sensitive areas and corresponding sensitive factors where the disturbance errors of single error sources and multiple error sources grow rapidly.

[0009] S4. Compare the error evolution characteristics, sensitive areas and sensitive elements of multi-error source disturbances and single-error source disturbances, and analyze the interaction mechanism of different single-error source disturbances in multi-error source disturbances;

[0010] S5. Construct a discrete resonance model to dynamically evaluate the synergistic effect of multi-source disturbance combinations in sensitive areas or sensitive elements, adjust the disturbance phase according to the evaluation results and the interaction mechanism of different single error source disturbances in the multi-error source disturbance, and construct a collaborative disturbance set of multiple error sources.

[0011] Specifically, in step S1, the initial value perturbation methods include local growth mode propagation method, singular vector method, rescaling ensemble transformation and ensemble Kalman filtering; the lateral boundary perturbation methods include dynamic downscaling; the physical process perturbation methods include random physical process parameterization tendency perturbation, random kinetic energy backscattering scheme and random parameter perturbation.

[0012] Preferably, in step S1, the initial value perturbation method is the local growth mode propagation method; the lateral boundary perturbation method is dynamic downscaling; and the physical process perturbation method is random parameter perturbation.

[0013] Specifically, in step S2, the calculation formula of the error energy RMDTE is:

[0014] ,

[0015] Where: is the error energy, is the total error energy, 、 and represent the differences in zonal wind U, meridional wind V, and temperature T between the perturbed forecast and the unperturbed control forecast, respectively; is the specific heat capacity in dry air at constant pressure; is the reference temperature; i 、 j represents the horizontal grid points of the pattern region, t represents the integration moment; p is the air pressure of the corresponding model layer, n is the number of set members, l Indicates the number of model layers used for vertical integration.

[0016] Specifically, in step S2, analyzing the error evolution characteristics of single error source disturbances and multiple error source disturbances includes: based on the disturbance set, analyzing the error evolution characteristics of single error source disturbances and multiple error source disturbances from two aspects: RMDTE and spatial scale, and summarizing the evolution laws of the longitude and latitude propagation, amplitude peaks, and amplitude troughs of each single error source disturbance error and multiple error source disturbance error.

[0017] Specifically, step S3 includes: using the RMDTE obtained in step S2, calculating the ensemble sensitivity analysis results of RMDTE and 500 hPa geopotential height, 850 hPa wind field, convective effective potential energy, and high- and low-altitude vertical wind shear in the peak area of RMDTE, and identifying the sensitive areas and corresponding sensitive elements where the disturbance errors of each single error source and multiple error sources grow rapidly based on the ensemble sensitivity analysis results.

[0018] Specifically, in step S4, analyzing the interaction mechanism of different single error source disturbances in the multi-error source disturbance includes: analyzing the error evolution characteristics, sensitive areas and sensitive variables of single-source errors and multi-source errors, and establishing the interaction mechanism of different single error source disturbances in the multi-error source disturbance based on the gain or suppression effect brought by the multi-error source disturbance relative to the single error source disturbance.

[0019] Specifically, step S5 includes:

[0020] The synergistic effect of the multi-error source combination in sensitive areas or sensitive elements is evaluated by using the disturbance sets of single error sources and multi-error source combinations, by calculating the disturbance set discreteness of the interaction of the disturbances of each single error source in the multi-error source combination disturbance. If the disturbance set discreteness is less than or equal to 0, the phase of the combined disturbance is adjusted according to the interaction mechanism of the disturbances of different single error sources in the multi-error source disturbance, and the disturbance set discreteness is recalculated until the disturbance set discreteness is greater than 0, thus obtaining the synergistic disturbance set of multiple error sources.

[0021] Specifically, in step S5, the calculation formula of the disturbance set discreteness is:

[0022] ,

[0023] Where: is the perturbation set discreteness, is the combined disturbance of multiple error sources, and are two different single error source disturbances, is the number of samples.

[0024] Specifically, in step S2, the spatial scale includes medium γ, medium β and medium α scales.

[0025] Beneficial effect: Compared with the prior art, the significant effect of the present invention is: the present invention adopts corresponding disturbance methods for the three single error sources of initial value, lateral boundary and physical process to generate disturbance sets of single error source and multi-error source combination, and then calculates the error energy predicted by the single error source and multi-error source set, combines scale separation to decompose the error energy into different spatial scales, and then analyzes the evolution characteristics of the disturbance errors of single error source and multi-error source from the two perspectives of the amplitude and structure of the disturbance; then combines the set sensitivity analysis ESA technology to explore the sensitive areas and matching sensitive elements of each single error source with rapid growth, compares the error evolution characteristics of the multi-error source combination disturbance and the single error source disturbance, analyzes the interaction mechanism between different single error source disturbances in the multi-error source combination disturbance, and finally constructs a discrete resonance model to achieve the purpose of dynamically evaluating the synergistic effect of the multi-error source combination disturbance in the sensitive area or sensitive element, adjusts the disturbance phase according to the evaluation results, and finally constructs the collaborative disturbance of multi-source errors. The present invention reveals the key mechanism that causes the growth of single-source errors and the interaction mechanism of multi-source errors through multi-scale separation of multi-source errors, ensemble sensitivity analysis and discrete resonance model, which is conducive to building a reasonable and coordinated multi-source error collaborative disturbance, thereby improving the error prediction accuracy and warning timeliness of the convective-scale ensemble forecast system for severe convective weather. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0027] A preferred embodiment of the present invention is further described below with reference to the accompanying drawings.

[0028] See also Figure 1 As shown, the present invention provides an ensemble forecast multi-source error coordinated disturbance method based on error feature evolution and discreteness resonance, comprising the following steps:

[0029] S1. Set the initial value, lateral boundary and physical process as single error sources, and use the perturbation methods of the initial value, lateral boundary and physical process to generate a single error source disturbance set and a multi-error source disturbance set composed of multiple single error sources. There are 7 groups in total, namely: single initial value disturbance, single lateral boundary disturbance, single physical process disturbance, initial value + lateral boundary disturbance, initial value + physical process disturbance, lateral boundary + physical process disturbance and initial value + lateral boundary + physical process disturbance.

[0030] The specific perturbation method used is as follows:

[0031] Initial value perturbation methods: local growing mode propagation method (LBGM), singular vector method, rescaling ensemble transformation and ensemble Kalman filter (EnKF).

[0032] Lateral boundary perturbation method: dynamic downscaling.

[0033] Physical process perturbation methods: stochastic physical process parameterized tendency perturbation (SPPT), stochastic kinetic energy backscattering scheme (SKEB) and stochastic parameter perturbation (SPP).

[0034] The present invention selects one method for each of the three single error sources.

[0035] The local growth mode reproduction method is used as the initial value perturbation method, which is explained in detail below.

[0036] The Growth Mode Reproduction Method (BGM) first superimposes an arbitrary perturbation on the model initial field. The control test initial field and the initial field after the superimposed perturbation are integrated simultaneously. After a period of integration, the control forecast and the perturbation forecast are obtained. The perturbation is scaled to the same magnitude as the initial perturbation. The analysis perturbation is then superimposed on the new atmospheric initial field. The propagation is repeated continuously to finally obtain the desired fastest growth mode. The BGM method scales the perturbation at the end of the propagation cycle:

[0037] ,

[0038] Where: c is the adjustment coefficient, and the model layer k related, represents the forecast disturbance, represents the disturbance after scale adjustment; c(k) is the preset disturbance RMS e 0 (k) and the predicted disturbance root mean square e n ( k ) ratio.

[0039] The local growth model reproduction method (LBGM) e 0 (k) and e n ( k ) is adjusted from the complete forecast area of the traditional BGM method to the neighborhood area of each grid point, with a neighborhood radius of r , scaling factor c(k) Adjusted to:

[0040] ,

[0041] Where: subscript t express t The disturbance coefficient at time .

[0042] The lateral boundary perturbation method adopts dynamic downscaling, which is explained in detail below.

[0043] Dynamical downscaling directly uses the analytical perturbations from the global ensemble forecast system and interpolates them onto the model's initial fields, providing initial values and lateral boundary perturbations for regional ensemble forecasts. This method is simple, computationally inexpensive, and offers good performance.

[0044] The physical process perturbation method uses random parameter perturbation, which is explained in detail below.

[0045] The random parameter perturbation method characterizes the uncertainty of the model by perturbing the empirical and adjustable parameters in the subgrid parameterization scheme, which can better reflect the forecast uncertainty of small-scale systems. The random parameter perturbation method assumes that the size of the model error is proportional to the size of the parameter. The perturbation is constructed by multiplying the uncertain parameters of the parameterization scheme by a random number (usually between -0.5 and 0.5) through the multiplication method. The general expression is:

[0046] ,

[0047] Where: is the parameter value after perturbation, is the unperturbed parameter value, A two-dimensional random disturbance field with time and space correlation generated by a random mode generator.

[0048] The expansion in spectral space is:

[0049] ,

[0050] Where: k，l Represents the weft direction x Direction and longitude y The wave number component in the x direction (the wave number component in the x direction K+1 indivual, y Directional wave number L+1 ), Fourier modulus In the rectangular area ( 0 <x<X, 0<y<Y ) form a set of orthogonal basis functions.

[0051] Each spectral coefficient They all evolve according to the following first-order autoregressive equation:

[0052] ,

[0053] Where: is the linear autoregressive coefficient, is the decorrelation time scale, is the model time step; is the noise amplitude that depends on the wave number; is a Gaussian white noise process with a mean of 0 and a standard deviation of 1. The disturbance mode generated by this process is spatially uniform, and its horizontal length scale is L , the grid perturbation variance is ; is the effective radial wave number, is the spectral variance, which produces a zero-mean variance at each grid point. The Gaussian perturbation of , that is, the perturbation mode depends entirely on three parameters: the grid standard deviation , length scale and decorrelation time At the same time, because Gaussian distribution can lead to abnormally large values, the range of random numbers needs to be limited.

[0054] S2. Calculate the error energy RMDTE of the single error source ensemble forecast and the multi-error source ensemble forecast respectively. RMDTE is the weighted average of the total error energy (DTE) in the vertical direction. The calculation formula is:

[0055] ,

[0056] Where: is the error energy, is the total error energy, 、 and represent the differences in zonal wind U, meridional wind V, and temperature T between the perturbed forecast and the unperturbed control forecast, respectively; is the specific heat capacity in dry air at constant pressure, ; is the reference temperature, ; i 、 j represents the horizontal grid points of the pattern region, t represents the integration moment; p is the air pressure of the corresponding model layer, n is the number of set members, l Indicates the number of model layers used for vertical integration.

[0057] Since the occurrence and development of severe convective weather is often affected by environmental factors at different altitudes and scales, RMDTE introduces a weighting function in the vertical direction of DTE calculation, so as to describe the error distribution characteristics of the entire atmospheric layer.

[0058] Scale separation methods, such as discrete cosine transforms, are then used to decompose the RMDTE at different spatial scales (medium γ, medium β, and medium α) to quantify disturbances of different scales. Finally, based on the resulting collective sample set, the error evolution characteristics of single and multiple error source disturbances are analyzed from two perspectives: disturbance amplitude (RMDTE) and structure (spatial scale). Specifically, by analyzing the propagation of RMDTE at different scales in the longitude and latitude directions and their temporal variations, the patterns of longitude and latitude propagation and the evolution of amplitude peaks (valleys) for single and multiple error source disturbances are summarized.

[0059] S3. Use RMDTE combined with the ensemble sensitivity analysis method (ESA) to obtain the sensitive areas and corresponding sensitive elements where the disturbance errors of each single error source and the disturbance errors of multiple error sources grow rapidly; specifically, in the peak area of RMDTE, calculate the ensemble sensitivity analysis results of RMDTE and forecast variables such as 500 hPa potential height, 850 hPa wind field, convective effective potential energy, and high and low altitude vertical wind shear. Based on the ensemble sensitivity analysis results, identify the sensitive areas and corresponding sensitive elements where the disturbance errors of each single error source and the disturbance errors of multiple error sources grow rapidly.

[0060] S4. By comparing the error evolution characteristics of multi-source and single-source disturbances, explore the relative contributions of different single-source disturbances to the temporal and spatial variations of the error. Based on the gain or suppression effects of multi-source disturbances compared to single-source disturbances, establish the interaction mechanism between different single-source disturbances in a multi-source combination. In other words, establish a physical conceptual model of the interaction of multi-source disturbances to deepen understanding of the growth of different disturbances in convective-scale weather.

[0061] S5. Construct a discrete resonance model and use the disturbance set of single error source and multi-error source combination to dynamically evaluate the synergistic effect of multi-source disturbance combination in sensitive areas or sensitive elements, that is, by adjusting the discreteness of the disturbance set of the interaction of each single error source disturbance in the multi-error source combination disturbance. S , so that the disturbance effects of multiple error sources develop in a coordinated direction. The following is the calculation of the discreteness of the disturbance set:

[0062] ,

[0063] Where: is the perturbation set discreteness, is the combined disturbance of multiple error sources, and are two different single error source disturbances, is the number of samples.

[0064] like , indicating that the combined disturbance of multiple error sources can make the collective discreteness grow resonantly. , it is necessary to analyze the difference in disturbance phases of different single error sources in sensitive areas according to the error evolution characteristics of single error sources and the interaction mechanism of disturbances of different single error sources in multi-error source disturbances, and adjust the phase of the combined disturbance by modifying the random number sign in the disturbance method so that The disturbance is smoothly changed in the direction of the resonant disturbance until the discreteness of the disturbance set is greater than 0, and the coordinated disturbance set of multiple error sources is obtained.

[0065] The above method is described in detail below in a specific implementation scenario:

[0066] Application scenario: Ensemble forecast of isolated convective systems.

[0067] Step 1: Download the ECMWF global ensemble forecast product (resolution ), which is used to provide the ensemble analysis perturbations required by the dynamical downscaling method.

[0068] Based on the WRF model, seven perturbation sets were designed, including single and multiple error source combinations. The initial perturbation was performed using the LBGM method, the lateral boundary perturbation was performed using the dynamical downscaling method, and the physical process perturbation was performed using the SPP method. Each set contains 16 members.

[0069] Step 2: Calculate the RMDTE for each single-error source ensemble forecast and the multi-error source ensemble forecast by integrating over 30 model layers. Use the discrete cosine transform to decompose the RMDTE at the medium-γ (2-20 km range), medium-β (20-200 km range), and medium-α (200-2000 km range) scales. Based on the resulting ensemble sample set, the latitudinal and longitudinal propagation characteristics and temporal evolution characteristics of various single-error source and multi-error source perturbations are discussed from the perspectives of the calculated RMDTE and at different spatial scales.

[0070] Step 3. Using the RMDTE obtained in Step 2, calculate the ESA results of RMDTE and forecast variables such as 500 hPa geopotential height, 850 hPa wind field (U / V), convective effective potential energy (CAPE), and high- and low-level vertical shear in the peak area of RMDTE. Based on the positive and negative areas and magnitudes of the sensitivity values of each variable, identify the sensitive areas where the disturbance errors of each single error source and multiple error sources grow rapidly (i.e., areas with large positive and negative values) and their matching sensitive factors or diagnostic quantities.

[0071] Step 4: Compare the spatiotemporal evolution patterns of RMDTE at different scales of multiple error sources and single error sources, as well as the sensitive areas of different forecast variables, analyze the differences in amplitude, longitude and latitude propagation, sensitive areas and sensitive variables between the two, explore the gain or suppression effects caused by the interaction of multiple single error sources, and explore the interaction mechanism of disturbances from different sources.

[0072] Step 5: To reduce the antagonistic (inhibitory) effect between the disturbances of multiple error sources, adjust the disturbance set discreteness of the above-mentioned multi-error source combined disturbance according to the evolution law of the errors of each source. If , it is necessary to explore the phase difference of the corresponding single error source disturbance according to the error evolution characteristics to adjust the phase of the multi-error source combined disturbance (such as changing the inverse phase to the same phase), and then recalculate until the multi-error source combined disturbance induces discrete resonance ( ).based on S The maximization principle is used to optimize the weights and phases of the multi-error source disturbance combination and generate a more reasonable multi-error source collaborative disturbance set.

Claims

1. A collaborative perturbation method for ensemble forecasting multi-source errors based on error feature evolution and discreteness resonance, characterized by: The following steps are involved: S1. Set the initial value, lateral boundary and physical process as single error sources, and use the perturbation methods of the initial value, lateral boundary and physical process to generate the perturbation set of single error source and the perturbation set of multiple error sources respectively; S2. Calculate the error energy (RMDTE) of the single error source ensemble forecast and the multi-error source ensemble forecast respectively, decompose the RMDTE at different spatial scales using the scale separation method, and analyze the error evolution characteristics of the single error source disturbance and the multi-error source disturbance respectively; S3. Using RMDTE combined with the ensemble sensitivity analysis method, we obtain the sensitive areas and corresponding sensitive factors where the disturbance errors of single error sources and multiple error sources grow rapidly. S4. Compare the error evolution characteristics, sensitive areas and sensitive elements of multi-error source disturbances and single-error source disturbances, and analyze the interaction mechanism of different single-error source disturbances in multi-error source disturbances; S5. Construct a discrete resonance model to dynamically evaluate the synergistic effect of multi-source disturbance combinations in sensitive areas or sensitive elements. Adjust the disturbance phase based on the evaluation results and the interaction mechanism of different single error source disturbances in the multi-error source disturbances to construct a multi-error source coordinated disturbance set. Specifically, the following steps are included: The synergistic effect of the multi-error source combination in sensitive areas or sensitive elements is evaluated by using the disturbance sets of single error sources and multi-error source combinations and calculating the dispersion of the disturbance sets of the interaction of the disturbances of each single error source in the multi-error source combination disturbance. If the dispersion of the disturbance set is less than or equal to 0, the phase of the combined disturbance is adjusted according to the interaction mechanism of the disturbances of different single error sources in the multi-error source disturbance, and the dispersion of the disturbance set is recalculated until the dispersion of the disturbance set is greater than 0, thus obtaining the synergistic disturbance set of the multi-error sources. The calculation formula of the disturbance set discreteness is: ， Where: is the perturbation set discreteness, is the combined disturbance of multiple error sources, and are two different single error source disturbances, is the number of samples.

2. The ensemble forecast multi-source error coordinated perturbation method according to claim 1, characterized in that: In step S1, the initial value perturbation method includes the local growth mode propagation method, the singular vector method, the rescaling ensemble transformation and the ensemble Kalman filter; the lateral boundary perturbation method includes the dynamic downscaling; the physical process perturbation method includes the random physical process parameterization tendency perturbation, the random kinetic energy backscattering scheme and the random parameter perturbation.

3. The ensemble forecast multi-source error coordinated perturbation method according to claim 2, characterized in that: In step S1, the initial value perturbation method is the local growth mode propagation method; the lateral boundary perturbation method is the dynamic downscaling method; and the physical process perturbation method is the random parameter perturbation method.

4. The ensemble forecast multi-source error coordinated perturbation method according to claim 1, characterized in that: In step S2, the calculation formula of the error energy RMDTE is: ， Where: is the error energy, is the total error energy, 、 and denote the differences in zonal wind U, meridional wind V, and temperature T between the perturbed forecast and the unperturbed control forecast, respectively; is the specific heat capacity in dry air at constant pressure; is the reference temperature; i 、 j represents the horizontal grid points of the pattern region, t represents the integration moment; p is the air pressure of the corresponding model layer, n is the number of set members, l Indicates the number of model layers used for vertical integration.

5. The ensemble forecast multi-source error coordinated perturbation method according to claim 1, characterized in that: In step S2, analyzing the error evolution characteristics of the single error source disturbance and the multi-error source disturbance includes: based on the disturbance set, analyzing the error evolution characteristics of the single error source disturbance and the multi-error source disturbance from two aspects of RMDTE and spatial scale, and summarizing the evolution laws of the longitude and latitude propagation, amplitude peaks, and amplitude troughs of each single error source disturbance error and multi-error source disturbance error.

6. The ensemble forecast multi-source error coordinated perturbation method according to claim 1, characterized in that: Step S3 includes: using the RMDTE obtained in step S2, calculating the ensemble sensitivity analysis results of RMDTE and 500 hPa geopotential height, 850 hPa wind field, convective effective potential energy, and high- and low-altitude vertical wind shear in the peak area of RMDTE, and identifying the sensitive areas where each single error source and multiple error sources grow rapidly and the corresponding sensitive elements based on the ensemble sensitivity analysis results.

7. The ensemble forecast multi-source error coordinated perturbation method according to claim 1, characterized in that: In step S4, analyzing the interaction mechanism of different single error source disturbances in the multi-error source disturbance includes: analyzing the evolution characteristics of single-source errors and multi-source errors, the differences in sensitive areas and sensitive variables, and establishing the interaction mechanism of different single error source disturbances in the multi-error source disturbance based on the gain or suppression effect brought by the multi-error source disturbance relative to the single error source disturbance.

8. The ensemble forecast multi-source error coordinated perturbation method according to claim 1, characterized in that: In step S2, the spatial scale includes medium γ, medium β and medium α scales.

Images