Radar data assimilation method based on lag set-variation mixing

Abstract

The invention provides a radar data assimilation method based on lag set-variation mixing. The radar data assimilation method comprises the steps of constructing a set sample based on a time lag method, constructing a flow-dependent background error covariance based on set members in the set sample, and assimilating radar data based on the set sample and the flow-dependent background error covariance. According to the radar data assimilation method based on lag set-variation mixing provided by the invention, radar data assimilation can be realized based on lag set-variation mixing, and the method is convenient to use.

Description

Technical Field

[0001] This invention relates to the field of weather forecasting technology, and in particular to a radar data assimilation method based on hysteresis-variational hybridization. Background Technology

[0002] Convective-scale heavy precipitation is mainly triggered by small- to medium-scale strong convective systems, characterized by strong locality, suddenness, and short duration, often accompanied by short-duration heavy rainfall, and even extreme short-duration heavy rainfall. In recent years, due to the expansion of urban areas, urban flooding caused by short-duration heavy rainfall events has resulted in huge property losses and even casualties. Numerical weather forecasting is a core technology for weather forecasting operations and disaster prevention and mitigation. Improving data assimilation efficiency and the forecasting effectiveness of convective-scale heavy precipitation is of great significance for disaster prevention and mitigation in large cities. Currently, ensemble forecasting, as an effective method to reduce the uncertainty of numerical forecasts, has been widely used in convective-scale numerical weather forecasting; however, constructing high-resolution ensemble samples requires a large amount of computational resources. Therefore, it is essential to design a radar data assimilation method based on lag ensemble-variational hybrid approach. Summary of the Invention

[0003] The purpose of this invention is to provide a radar data assimilation method based on hysteresis set-variational hybridization, which can realize radar data assimilation based on hysteresis set-variational hybridization and is easy to use.

[0004] To achieve the above objectives, the present invention provides the following solution:

[0005] A radar data assimilation method based on hysteresis-variational hybridization includes the following steps:

[0006] Constructing a set of samples based on the time lag method;

[0007] Step 2: Construct the background error covariance of the flow dependency based on the set members in the set sample;

[0008] Step 3: Assimilate radar data based on ensemble samples and flow-dependent background error covariance.

[0009] Optionally, in step 1, the set of samples is constructed based on the time lag method, specifically as follows:

[0010] The ensemble samples are constructed based on a fast-updating assimilation system. Each iteration generates high-frequency forecast fields, contributing new ensemble members. The total number of ensemble members N for the forecast field at time t0 is calculated using the following formula:

[0011] (1)

[0012] Optionally, in step 2, the background error covariance of the flow dependency is constructed based on the set members in the set sample, specifically as follows:

[0013] Based on the ensemble sample, an ensemble error covariance that varies with weather conditions is constructed by means of ensemble perturbation, and coupled with the background error covariance fixed in variational assimilation to obtain the flow-dependent background error covariance.

[0014] Optionally, in step 3, radar data assimilation is achieved based on the ensemble samples and the flow-dependent background error covariance, specifically as follows:

[0015] The flow-dependent background error covariance is introduced into the objective function of variational assimilation using the extended variable method. The analytical increment representing the mixing and assimilation is defined as:

[0016] (2)

[0017] In the formula, It is the analytical increment of three-dimensional variational static covariance correlation. It is an analytical increment related to set covariance. It is a quantity that determines the localized scale of the set covariance and varies with spatial distribution. Let represent the standardized set perturbation field of the i-th set member, i.e.:

[0018] (3)

[0019] In the formula, For the i-th set member, For set averages, where N is the number of set members, the objective function for set-variable mixture assimilation is expressed as:

[0020] (4)

[0021] In the formula, and These are the objective functions for three-dimensional variational and set-related functions, respectively. Let B be the objective function of the observation term, B be the static background error covariance matrix, and A be the result of... The matrix consists of the spatial covariances, where H is the nonlinear observation factor mapping the model field to the observation field, and R is the observation field error covariance matrix. and Let be the weight coefficient, and satisfy...

[0022] (5)

[0023] According to specific embodiments provided by the present invention, the present invention discloses the following technical effects: The radar data assimilation method based on lag ensemble-variational hybrid provided by the present invention includes constructing ensemble samples based on time lag methods, constructing flow-dependent background error covariance based on ensemble members in the ensemble samples, and realizing radar data assimilation based on the ensemble samples and the flow-dependent background error covariance. This method can improve the data assimilation effect, reduce the computational load, and improve the forecasting effect of convective-scale heavy precipitation. Attached Figure Description

[0024] Figure 1 This is a schematic diagram showing the 24-hour precipitation from 06:00 on August 12th to 06:00 on August 13th, 2020.

[0025] Figure 2 A schematic diagram showing the temporal evolution of hourly precipitation at representative rainfall stations in the Beijing-Tianjin-Hebei region.

[0026] Figure 3a This diagram shows the upper-level 200 hPa jet stream (≥30 m / s, black arrow), 500 hPa geopotential height (solid black line), temperature (dashed red line), and divergence at 09:00 on August 12.

[0027] Figure 3b This is a schematic diagram of the wind field at 850 hPa (vector arrow) and water vapor flux divergence at 9:00 AM on August 12th.

[0028] Figure 4 A schematic diagram for constructing matrix B;

[0029] Figure 5 Map showing the distribution of the model area and radar sites;

[0030] Figure 6a A schematic diagram of TS scores for 6-hour precipitation testing in nine groups of experiments;

[0031] Figure 6b A schematic diagram of BIAS scores for 6-hour precipitation testing in nine groups of experiments.

[0032] Figure 7 The forecast performance of 6-h cumulative precipitation at different thresholds for four sets of experiments and a 3dvar experiment with fg as the background field is shown in the figure (the horizontal axis is the success rate, the vertical axis is the hit rate, the dashed line is the bias, the purple line is the TS score, a: ≥1 mm; b: ≥4 mm; c: ≥13 mm; d: ≥25 mm; e: ≥60 mm).

[0033] Figure 8This image shows the actual distribution of cumulative precipitation over 6 hours from 09:00 to 15:00 on August 12, 2020, and the forecasts for precipitation during this period from five sets of experiments (unit: mm) (a: Actual; b: 3D VAR forecast; c: H-f20 forecast; d: H-f50 forecast; e: H-f80 forecast; f: Jf forecast).

[0034] Figure 9 This is a schematic diagram of radar combined reflectivity at 09:00, 12:00, and 15:00 on August 12 (ac: real-time data, sourced from the China Meteorological Administration; df: 3dvar experimental forecast; gi: H-f80 experimental forecast; jl: Jf experimental forecast, unit: dBZ).

[0035] Figure 10 For the 3dvar and H-f80 test routes at 09:00, 12:00 and 15:00 on August 12th. Figure 8 (g,h,i) Radar emissivity factor profiles of line segments AB, CD, and EF (filled in, unit: dBZ), (U, 10*W) Composite wind (vector arrow, unit: m / s), Pseudo-equivalent potential temperature (blue dashed line, unit: K) (ac: 3dvar test; df: H-f80 test);

[0036] Figure 11 To analyze the Talagrand distribution at time points (a: U10; b: V10; c: T2; d: RH2);

[0037] Figure 12 The analysis increments (shaded, unit: m / s) of the wind field at the 16th layer of the single-point test of different zonal winds U at 09:00 on August 12th are shown. Schematic diagrams of the wind field (wind mast, unit: m / s) and geopotential height (blue dashed line, unit: gpm) at ERA5 500 hPa height are also shown (a: 3dvar test; b: H-f20 test; c: H-f50 test; d: Jf test).

[0038] Figure 13 This is a schematic diagram of the 850 hPa wind field (vector arrow, unit: m / s) and relative humidity (shaded, unit: %) at 09:00 on August 12; (a: ERA5 reanalysis data; b: 3dvar test analysis field; c: H-f80 test analysis field; d: Jf test analysis field)

[0039] Figure 14 The three test groups were scheduled to begin at 09:00 on August 12th. Figure 7(e) Schematic diagram of pseudo-equivalent potential temperature (filled in, unit: K), specific humidity (isoline, unit: g / kg), and (U, 10*W) composite wind (vector arrow, unit: m / s) of line segment AB (a: 3dvar test analysis field; b: H-f80 test analysis field; c: Jf test analysis field).

[0040] Figure 15 This is a schematic diagram of the 850 hPa wind field (vector arrow, unit: m / s) and relative humidity (shaded, unit: %) at 11:00, 12:00, 13:00 and 14:00 on August 12 (ad: ERA5 reanalysis data; eh: 3dvar experimental forecast; il: H-f80 experimental forecast; mp: Jf experimental forecast).

[0041] Figure 16 The three test routes were scheduled for 11:00, 12:00, 13:00 and 14:00 on August 12th. Figure 7 (e) Schematic diagram of pseudo-equivalent potential temperature (filled in, unit: K), specific humidity (isoline, unit: g / kg), and (U, 10*W) composite wind (vector arrow, unit: m / s) for line segment AB (ad: 3dvar test prediction; eh: H-f80 test prediction; il: Jf test prediction).

[0042] Figure 17 This is a schematic diagram of the radar data assimilation method based on hysteresis set-variational hybridization according to an embodiment of the present invention. Detailed Implementation

[0043] The purpose of this invention is to provide a radar data assimilation method based on hysteresis set-variational hybridization, which can realize radar data assimilation based on hysteresis set-variational hybridization and is easy to use.

[0044] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] like Figure 17 As shown, the radar data assimilation method based on hysteresis set-variational hybrid provided by the embodiments of the present invention includes the following steps:

[0046] Step 1: Construct a set of samples based on the time lag method;

[0047] Step 2: Construct the background error covariance of the flow dependency based on the set members in the set sample;

[0048] Step 3: Assimilate radar data based on ensemble samples and flow-dependent background error covariance.

[0049] In step 1, the set of samples is constructed based on the time lag method, specifically as follows:

[0050] The ensemble samples are constructed based on a fast-updating assimilation system. Each iteration generates high-frequency forecast fields, contributing new ensemble members. The total number of ensemble members N for the forecast field at time t0 is calculated using the following formula:

[0051] (1)

[0052] In step 2, the background error covariance of the flow dependency is constructed based on the set members in the set sample, specifically as follows:

[0053] Based on the ensemble sample, an ensemble error covariance that varies with weather conditions is constructed by means of ensemble perturbation, and coupled with the background error covariance fixed in variational assimilation to obtain the flow-dependent background error covariance.

[0054] In step 3, radar data assimilation is achieved based on ensemble samples and the background error covariance dependent on flow, specifically as follows:

[0055] The flow-dependent background error covariance is introduced into the objective function of variational assimilation using the extended variable method. The analytical increment representing the mixing and assimilation is defined as:

[0056] (2)

[0057] In the formula, It is the analytical increment of three-dimensional variational static covariance correlation. It is an analytical increment related to set covariance. It is a quantity that determines the localized scale of the set covariance and varies with spatial distribution. Let represent the standardized set perturbation field of the i-th set member, i.e.:

[0058] (3)

[0059] In the formula, For the i-th set member, For set averages, where N is the number of set members, the objective function for set-variable mixture assimilation is expressed as:

[0060] (4)

[0061] In the formula, and These are the objective functions for three-dimensional variational and set-related functions, respectively. Let B be the objective function of the observation term, B be the static background error covariance matrix, and A be the result of... The matrix consists of the spatial covariances, where H is the nonlinear observation factor mapping the model field to the observation field, and R is the observation field error covariance matrix. and Let be the weight coefficient, and satisfy...

[0062] (5)

[0063] This invention provides an embodiment to verify the method described in this application, selecting a warm-sector rainstorm that occurred in North China on August 12-13, 2020 as a numerical weather prediction case. This precipitation event was mainly concentrated between 06:00 on the 12th and 06:00 on the 13th (UTC, the same below), with heavy rainfall primarily in western Beijing, western Tianjin, and central Hebei (e.g.,...). Figure 1 (As shown). Heavy rainfall was mainly concentrated between 09:00 and 15:00, with many stations experiencing short-duration heavy rainfall. For example, the rainfall intensity at Wen'an station in Hebei Province reached 116.6 mm / h at 12:00 (as shown). Figure 2 (as shown)

[0064] The weather pattern of this rainstorm was analyzed using 0.25°*0.25° ERA5 reanalysis data (ECMWF Reanalysis V5), as shown in Figure 3. Figure 3a At 09:00, the Beijing-Tianjin-Hebei region was located in the 200 hPa upper-level jet stream divergence zone, where strong upper-level suction provided favorable dynamic lifting for the occurrence and development of rainstorms; at 500 hPa, it was located in the southeast quadrant of the Mongolian cold vortex, where the cold vortex remained stable in the Mongolian area, and the divergence in western Beijing intensified, with the maximum value exceeding 25 10⁻⁵ s⁻¹. Figure 3b The data shows an increase in the low-level southwest jet stream at the 850 hPa level along the border of southern Beijing and Hebei, while simultaneously, moisture convergence intensifies at the 925 hPa level. The moisture convergence zone runs northeast-southwest, reaching its maximum in southern Beijing, which coincides with the location of the area with the highest precipitation. As can be seen from the above circulation pattern, influenced by the 200 hPa jet stream, the 500 hPa strong divergence zone, and the 850 hPa low-level jet stream, there is strong upward motion in the Beijing-Tianjin-Hebei region. This is accompanied by an intensification of the low-level jet stream on the warm side and strong moisture convergence, coupled with significant high humidity conditions at the surface (dew point above 22℃, temperature-dew point difference within 2℃) (figure omitted). Therefore, the precipitation during this stage is a warm-sector rainstorm process with convective characteristics.

[0065] To analyze the impact of time-lag ensemble samples on convective rainfall, the study period focused on the period of high precipitation efficiency from 09:00 to 15:00 on August 12th;

[0066] Using NCEP (National Centers for Environmental Prediction) GFS (Global Forecast System) data as the background field, the cold start integration began at 18:00 the previous day and continued until 00:00, followed by a hot start every 3 hours and a 24-hour forecast. Therefore, according to formula (1), the ensemble sample size at each analysis time is 8. Figure 4 To construct a schematic diagram;

[0067] Forecasting was performed using the WRF 3.9.1 model, employing a two-layer nested scheme (e.g., Figure 5 As shown), the number of grid points in the horizontal direction are 341×337 and 591×498, respectively, with horizontal grid spacing of 9 km and 3 km. The vertical direction has 51 layers. The physical parameterization schemes adopted by the system are: the new Thompson microphysics scheme, the MM5 similarity theory near-surface layer scheme, the Noah land surface scheme, the ACM2 PBL planetary boundary layer scheme, the Kain-Fritsch cumulus parameterization scheme (d02 region cumulus-free parameterization scheme), the RRTM long-wave scheme, and the Dudhia short-wave radiation scheme.

[0068] During the cyclic assimilation process, conventional data assimilation was performed in both regions, but radar data was added only in region d02. Furthermore, a hybrid assimilation scheme was used only for region d02; no hybrid assimilation was applied to region d01. The focus of the analysis is on the experimental results for region d02 at 3km resolution. The assimilated observational data included ship, buoy, sounding, and surface reports (SYNOP). The radar data came from seven Doppler radars in the Beijing-Tianjin-Hebei region (e.g., [missing data]). Figure 5 As shown in the figure, 5 of them (Beijing, Tianjin, Shijiazhuang, Qinhuangdao and Cangzhou) are S-band and 2 (Zhangbei and Chengde) are C-band.

[0069] To study the impact of the method described in this application on convective precipitation, a 3dvar experiment, a mixed experiment with different weighting coefficients, and an ensemble forecast experiment were set up. For the background field, a sensitivity experiment was conducted using the forecast field (fg) generated by near-time thermal initiation or the ensemble mean, for a total of nine experimental schemes.

[0070] All nine experimental groups were localized at a scale of 100 km, as shown in Table 1. The sample members were as follows: Figure 4 As shown, the analysis time is 09:00 on August 12, 2020. The 09:00 forecast field predicted at 06:00 on the 12th is used as the background field (fg), and the ensemble mean of the eight ensemble members is used as another background field (ensemble mean). Both are predicted 24 hours apart.

[0071] Table 1 Numerical Experiment Scheme

[0072] Test name Background field Collection weight factor 3dvar fg 0 H-m20 ensemblemean 0.2 H-f20 fg 0.2 H-m50 ensemblemean 0.5 H-f50 fg 0.5 H-m80 ensemblemean 0.8 H-f80 fg 0.8 J-m ensemblemean 1 J-f fg 1

[0073] The experimental results are as follows:

[0074] Precipitation verification: 6-hour precipitation verification and evaluation were conducted on nine groups of experiments using TS (Threat Score) and Bias scores. The TS score showed (e.g.) Figure 6a As shown), in the mixed assimilation experiments, with the same ensemble weighting coefficient, the four experiments selecting fg for the background field were superior to the four mixed experiments selecting the ensemble mean and 3dvar, especially in the precipitation ranges greater than 13 mm, 25 mm, and 60 mm. The mixed experiment H-f80 performed better, but all experiments had poor forecasts for precipitation greater than 120 mm. The Bias score test results showed (as shown) Figure 6b As shown), the mixed assimilation experiment with the addition of time-lag set samples has a bias closer to 1 than the 3dvar experiment. The H-f50, H-f80 and Jf experiments performed well. Based on the test results, the subsequent analysis of this invention mainly focuses on the mixed experiment with fg as the background field.

[0075] To further evaluate the impact of different ensemble weighting coefficients on precipitation effects, the 3dvar, H-f20, H-f50, H-f80, and Jf experiments were re-evaluated using FAR (False Alarm Rate) and POD (Probability of Detection) scores. Figure 7 This indicates that the 3dvar experiment had low TS scores across all precipitation thresholds, while the time-lag-based mixed experiment achieved higher precipitation scores (hit rate, success rate, TS) when the precipitation threshold was ≥1 mm. Figure 7 a) The differences in scores among the five groups were small, with the RMSE value of the TS score being approximately 0.0096. The scores gradually decreased in the order of H-f20, H-f50, and H-f80. When the precipitation threshold was ≥4 mm ( Figure 7 b) The differences in scoring became more pronounced, with the RMSE value of the TS score being approximately 0.02. The scores for the H-f20, H-f50, and H-f80 tests were relatively close, but the H-f50 test had the highest scores in all categories; ≥13 mm ( Figure 7 c) Although the H-f80 test has a higher TS score and success rate, the H-f20 test has a better hit rate; when the precipitation threshold is ≥25 mm and 60 mm ( Figure 7 When de), the H-f80 test scores were the highest in all categories;

[0076] Figure 7Overall, the results show that the effect of the ensemble weighting coefficient on precipitation gradually becomes apparent as the precipitation threshold increases. At lower precipitation thresholds (≥1 mm, ≥4 mm), the advantage of the mixed experiment is slightly weaker. However, as the precipitation threshold increases, the advantage of the mixed experiment gradually becomes apparent, especially for precipitation ≥60 mm. The H-f80 experiment with an ensemble weighting coefficient of 0.8 has better forecast performance (high hit rate, success rate, TS score, and bias score closer to 1). Even though the Jf experiment with an ensemble weighting coefficient of 1 does not have high scores (hit rate, success rate, TS), the bias score is closer to 1 and the forecast bias is the smallest when the precipitation threshold is 1 mm, 4 mm, 13 mm, and 25 mm.

[0077] The above is the result of the objective precipitation score verification, and the actual precipitation distribution map is shown. Figure 8 a) shows that the rainband is concentrated in western Beijing and central Hebei, and runs in a northeast-southwest direction, with maximum precipitation exceeding 120 mm. The distribution maps of the five forecast experiments (3dvar, H-f20, H-f50, H-f80, and Jf) show that the direction of the rainband is similar to the actual situation, but the overall precipitation in central and western Beijing is lower than expected. The 3dvar experiment ( Figure 8 (b) The areas with the highest precipitation are mainly in western Tianjin and the border area between Hebei and Shandong. However, as the weighting coefficient increases to 0.8 ( Figure 8 e), the area of ​​high precipitation in western Tianjin gradually moved northwest (as a reference, the white stations on the map are Baodi Station in Tianjin, with actual precipitation of 13.9 mm and Xiongxian Station in Hebei, with actual precipitation of 145.7 mm); however, when the ensemble weighting coefficient is 1, it is obvious that the Jf experiment's forecast range for the area of ​​high precipitation (above 60 mm) is too small, which is consistent with the precipitation deviation score (<1); for the area of ​​high precipitation at the border of Hebei and Shandong in the 3dvar experiment, the mixed assimilation experiment ( Figure 8 cf) shows a trend of decreasing the area and size of precipitation;

[0078] Analysis of the development process and structure of the simulated mesoscale convective system:

[0079] The reflectivity of the combined radar mosaic image of North China at 09:00 on the 12th ( Figure 9 a) There is a northeast-southwest echo band west of Shanxi, and a strong convection center with a frequency of over 50 dBZ exists near Baoding, Hebei. There is an arc-shaped echo with a frequency of about 40 dBZ in eastern Tianjin and near Tangshan. According to the actual radar combined reflectivity, the strong convection system affecting this rainstorm is mainly the strong convection located in Baoding, Hebei.

[0080] A comparison of five sets of experiments with fg as the background field revealed that at 09:00, the five sets of experiments were relatively consistent in their grasp of the location of the northeast-southwest echo band. The main differences lay in the strong convection center in Baoding, Hebei, and the echoes near Tangshan. (3dvar experiment)Figure 9 d) The strong convection in Baoding, Hebei Province, was scattered and generally weaker than the actual cluster convection; meanwhile, the area of ​​high value bow echoes in eastern Tianjin did not extend to Tangshan, and there were relatively strong echoes in eastern Tianjin. With the addition of ensemble information, the experimental H-f20, H-f50, and H-f80 values ​​were... Figure 9 g) Echoes in the Baoding area of ​​Hebei Province converged into clusters of convection, with relatively weak intensity (H-f20 and H-f50 figures omitted), but the H-80f test showed that the area of ​​high echo values ​​located in eastern Tianjin had extended to the vicinity of Tangshan. Meanwhile, the Jf test... Figure 9 j) The radar echoes located in the Baoding area show splitting and weakening intensity, while the radar echoes located in Tangshan also show weakening intensity.

[0081] To study the effect of ensemble weighting coefficients on the short-term prediction of radar combined reflectivity, the combined reflectivity of different experiments at 12:00 and 15:00 was compared and analyzed.

[0082] 12 o'clock live broadcast ( Figure 9 (b) shows that a strong convective system located in Baoding, Hebei Province, moved to the border area between Tianjin and Hebei and developed into a squall line. At the same time, a linear strong convection developed at the border area between Shandong and Hebei Province. 3DVAR experiment ( Figure 9 e) The forecast for System A is presented in segments, with intensity close to the actual situation, but the radar intensity in central Beijing is weaker; the system intensity and range in Shandong are a strong over-prediction phenomenon. Tests were conducted at H-f20, H-f50, and H-f80. Figure 9 h) and Jf ( Figure 9 k) Experiments show that adding time-lag aggregate samples can effectively suppress the intensity and range of the system's C-radar combined reflectivity (H-f20, H-f50 figures omitted), exhibiting a gradual weakening trend, and even disappearing (experiment Jf, Figure 9 k). The H-f80 experiment showed enhanced echoes in central Beijing and central Hebei, but weaker echoes compared to the actual echoes in eastern Hebei, corresponding to the precipitation distribution map ( Figure 8 e); The Jf test completely weakened the echo in eastern Hebei;

[0083] At 3 PM, the echo pattern worsened towards Langfang, but the intensity remained at 50 dBZ. The strong center was partly located in southwestern Tianjin and partly in central Beijing. Figure 9 c), 3dvar experiment ( Figure 9 f) The predicted radar reflectivity location was further west than the actual location and did not enter the Tianjin area; and the predicted echoes overestimated the area within Shandong Province. The mixed tests H-f20, H-f50, and H-f80 ( Figure 9 i) The forecast range of strong echoes in Langfang is gradually shrinking and even slightly dispersed, but the location is shifting eastward; while the ensemble forecast Jf experiment ( Figure 9l) There are no scattered echoes in southern Tianjin; for the convective system in Shandong, the mixed test predicted that the echo intensity would gradually decrease, and the Jf test showed that the system had disappeared;

[0084] Through comparative analysis of the combined radar reflectivity analysis fields, the ensemble test showed minor adjustments compared to the 3dvar test, while the mixed test H-f80 enhanced the echo intensity at Tangshan. The differences among the three sets of tests were primarily in the forecast fields. The 3dvar test consistently overestimated the strong convective systems in Shandong, resulting in an excessively large area of ​​high precipitation. Simultaneously, the strong echo forecast for central Hebei was off-center, with the corresponding high precipitation area mainly concentrated in eastern Hebei. The mixed test H-f80 underestimated the echo forecast for central Hebei at 12:00 and the echoes were also dispersed at 15:00, but the echo forecast deviation for Shandong was smaller. Compared to the other two sets of tests, the ensemble forecast Jf test showed a weaker echo intensity and a smaller predicted area.

[0085] Figure 10 For the 3dvar and H-f80 tests, at 09, 12 and 15 respectively, along Figure 8 Radar reflectivity factors of AB, CD and EF, and pseudo-equivalent potential temperature (θ) se and the vertical profile of the wind vector field, θ se It is a physical quantity that integrates atmospheric temperature and humidity characteristics and can characterize the stability of atmospheric stratification;

[0086] At 09:00, the vertical structure of reflectivity factors in both sets of tests east of 115.887°E was similar, with three strong echo centers, the maximum being 45 dBZ; the difference in reflectivity factors between the two sets of tests was mainly around 115.883°E, H-f80 test ( Figure 10 d) A high reflectivity center exists at 500 hPa–850 hPa, reaching 40 dBZ, but the 3dvar test ( Figure 10 a) The reflectivity factor is relatively small, only 20 dBZ, and the altitude only reaches 800 hPa; in terms of thermal conditions, the thermal distribution of the two sets of experiments is similar, with the θ value near 500 hPa in the middle layer east of 115.887°E. se The values ​​are the lowest, especially in the 3dvar experiment ( Figure 10 a) Its θ se At approximately 344 K, the H-f80 test ( Figure 10 d) Approximately 348 K, meaning the middle layer in the 3dvar experiment is relatively dry and cold. Below 500 hPa, θ se The values ​​are relatively evenly distributed, around 352 K; in terms of vertical velocity, the two sets of experiments are similar in size and distribution.

[0087] At 12 o'clock, the 3dvar experiment ( Figure 10b) The radar reflectivity factor has three large value regions, with the maximum value at 116.83°E, extending from the ground to 600 hPa, and a reflectivity of 45 dBZ; the maximum radar reflectivity factor is 40 dBZ at 116.17°E and 116.33°E, extending to approximately 750 hPa and 600 hPa respectively. The H-f80 test ( Figure 10 e) A continuous radar reflectivity factor structure between 115.87°E and 117°E, extending from the ground to 350 hPa, with the maximum reflectivity factor of 45 dBZ located between 115.83°E and 116.5°E, extending to 650 hPa; from a thermodynamic perspective, near 500 hPa in the middle layer, 3dvar tests ( Figure 10 b) θ se The value is as low as 344 K, and extends eastward from 115.5°E to 115.83°E, H-f80 test ( Figure 10 e) It only stagnates at 115.67°E, and the range of dry, cold air is also smaller than that of the 3dvar experiment. The lower atmosphere also shows that the θse value is 2 K smaller than that of the 3dvar experiment. At this location, θ... se The value decreases with increasing altitude, indicating an unstable atmospheric stratification; from a dynamic field perspective, the H-f80 experiment ( Figure 10 b) Vertical motion is significantly enhanced at 116.17°E, with upward motion reaching 400 hPa and a maximum vertical velocity of 2 m / s; however, the upward motion is more pronounced at 116.83°E in the 3dvar test.

[0088] At 15:00, the 3dvar experiment ( Figure 10 c) The radar reflectivity range is relatively small at this location, therefore the vertical profile distribution range of its radar reflectivity factor is also small, mainly around 116.53°E. There is upward motion at 925 hPa–700 hPa with a vertical velocity of 1 m / s. Dry, cold air exists around 116.2°E and 117.2°E at a distance of 600 hPa. se The value is approximately 346 K, lower layer θ se The maximum value is 364 K, and θ increases with height. se The value decreases significantly, indicating an unstable atmospheric stratification; while H-f80 ( Figure 10 f) At 116.53°E, the radar reflectivity factor is 50 dBZ, exhibiting significant upward motion, with a maximum vertical velocity of 4 m / s at 500 hPa, θ se The value distribution does not change significantly with altitude; at approximately 117.2°E and 600 hPa, the air is warmer and more humid compared to the 3dvar test. se The value is approximately 352K, and θ increases with altitude. se The gradient is relatively small, indicating weak atmospheric instability at that location.

[0089] Analysis shows that the hybrid assimilation technique based on the time lag method enables the background field to better absorb radar observation data, increases the radar reflectivity factor, and improves the meso-level thermal stratification. As the model's thermodynamic field gradually adjusts to equilibrium, the meso-level air is warmer and more humid in the hybrid experiment H-f80 compared to the 3dvar experiment, and the range of the upward motion area is wider.

[0090] Dispersion test:

[0091] For an ideal ensemble forecast system, observed data should fall near ensemble members with approximately the same probability. The Talagrand distribution (Hamill, et al., 2000) can describe the consistency between ensemble members and observed true values ​​and is an indicator of the reliability of the ensemble forecast system. When Talagrand exhibits a relatively flat distribution, it indicates an ensemble forecast with perfect dispersion (Zhang et al., 2014). Figure 11 The Talagrand distributions for 8 sample pairs of four variables, U10, V10, RH2, and T2, show that all four variables exhibit a certain degree of set dispersion at the time of analysis. V10 and T2 ( Figure 11 b,c) are distributed in an L-shape, meaning that the analyzed field values ​​of V10 and T2 are too large, exhibiting positive bias and small dispersion; RH2 ( Figure 11 The distribution of d) is slightly inverted L-shaped, reflecting that the analyzed field value is too small, with obvious negative bias and small dispersion; compared with the other three variables, U10 ( Figure 11 a) has a relatively flat distribution, with the observed values ​​falling into each member with a probability of about 10%, indicating good dispersion.

[0092] One criterion for evaluating the quality of an ensemble forecasting system is whether the ensemble dispersion is roughly equivalent to the ensemble root mean square error (RMSE). Table 2 shows the ensemble dispersion and RMSE for eight time-lag samples at 09:00, with the same parameters: U10, V10, T2, and RH2. The comparison reveals that the ensemble dispersion of U10 is quite close to its RMSE value, indicating good dispersion, consistent with the conclusions of the Talagrand distribution plot. The ensemble dispersion of V10 and T2 differs slightly from their RMSE values, while the difference is significant for RH2, with its RMSE almost twice that of its dispersion.

[0093] Table 2. Set dispersion and root mean square error between samples at analysis time.

[0094] Variable Dispersion Root mean square error U10 1.45 1.89 V10 1.59 2.57 T2 1.39 2.53 RH2 7.55 15.22

[0095] By examining the dispersion of the four sets of variables U10, V10, T2, and RH2 at the analysis time, it was found that the samples constructed by the time lag method can also produce dispersion between sets. By comparison, the Talagrand distribution of U10 is relatively flat, and the set dispersion and root mean square error are also closer, reflecting reliable set dispersion characteristics.

[0096] Incremental analysis of weight coefficients for different sets:

[0097] To investigate the impact of different weighting coefficients on the assimilation system, a single-point observation ideal experiment was first conducted. An ideal zonal wind observation with an information vector of 1.0 m / s was placed at 115°E and 39°N in the 16th layer of the model (approximately 500 hPa). Figure 12 The analysis increments for the wind field (shaded) are overlaid with the wind field reanalysis data at the corresponding time points. Among them, the 3dvar single-point experiment ( Figure 12 The wind field increment in experiment H-f20 is isotropic, while experiments containing ensemble members all exhibit anisotropic characteristics. Figure 12 b) is no longer isotropic; as the set weight coefficient increases, the H-f50 experiment ( Figure 12 c) shows dispersion along the southwest direction of the wind field, while H-f80 and Jf ( Figure 12 d) The incremental analysis shows a more dispersed pattern, and its dispersion trend is more consistent with the flow field. That is, when the set members are provided by time-lag samples, the background error covariance also has flow-dependent characteristics.

[0098] Thermodynamic analysis:

[0099] Excluding experiments using the ensemble mean as the background field, the background fields of 3dvar and other mixed experiments are consistent; the differences in the analytical fields are mainly due to the different ensemble weights. Based on precipitation distribution and verification evaluation, the H-f80 experiment showed better forecasting. To further discuss the specific impact of time-lag ensemble samples on forecasting, the effects of the 3dvar, H-f80, and Jf experiments on the low-level wind field, humidity field, and thermodynamic vertical profile are compared and analyzed.

[0100] Analysis field:

[0101] Analysis of low-level wind field and water vapor:

[0102] According to ERA5 real-time data, at 09:00, humidity conditions were relatively good in western Hebei, southern Beijing, and western Tianjin, with relative humidity generally above 90%. Humidity in central Shandong was around 70%. The low-pressure center was located in central Hebei, with convergence of southerly and southeasterly winds in southern Beijing. Figure 13 a), while 3dvar experiment ( Figure 13b) The simulated low-pressure vortex was located further southwest than the actual location, resulting in prevailing southeasterly winds in southern Beijing, with wind speeds of 16 m / s, significantly higher than the actual wind speeds. Simultaneously, humidity conditions in central Beijing were poor, below 60%, while relative humidity in western Shandong was higher than the actual humidity, and a narrow dry zone existed in central Shandong. After incorporating hysteresis samples, the H-f80 experiment ( Figure 13 c) shows improved humidity conditions in central Beijing, with the low-vortex location similar to the 3dvar experiment, lower relative humidity at the Shandong-Hebei border, little change in the dry area of ​​central Shandong, and southeasterly winds still stronger than observed; while the Jf experiment ( Figure 13 d) The relative humidity in central Beijing has also improved slightly, but the humidity conditions have not yet reached 80% of the actual situation. The relative humidity in central Shandong has decreased, the position of the low vortex has not changed significantly, and the southeasterly wind in western Tianjin has strengthened compared with the 3dvar test.

[0103] Analysis of the field and comparison of low-level humidity and wind field revealed that the addition of hysteresis samples can improve the humidity conditions of the 3dvar experiment, but has little effect on the low-level wind field.

[0104] Vertical structure analysis:

[0105] along Figure 8 Draw a perpendicular section AB from line segment e. Figure 14 The 3dvar test showed that the entire middle layer east of 116.07°E was relatively dry and cold, with a specific humidity of approximately 14 g / kg near 850 hPa; while the H-f80 mixed test ( Figure 14 b) The air at 1000 hPa is warmer and more humid than that at 3dvar, with a θse value of 354 K. The specific humidity at 850 hPa is approximately 15 g / kg. In the Jf experiment, the air at 1000 hPa is even warmer and more humid, with a θse value of 358 K. The distribution of the specific humidity line in the lower layer is similar to that in the 3dvar experiment. Since the mesoscale system has not yet reached the location of the profile, there is no obvious vertical movement in any of the three sets of experiments.

[0106] Figure 14 The data shows that at analysis time 09, the lower θ level of the three sets of experiments... se All values ​​are at 350 K, and east of 116.07°E, θse generally decreases with altitude, indicating an unstable atmospheric stratification. Under this unstable stratification, combined with dynamic triggering conditions in the lower atmosphere, this is conducive to the generation of heavy rainfall. Furthermore, it is evident that incorporating hysteresis sample information improves the thermodynamic conditions of the 3dvar experiment, resulting in a deeper and warmer atmosphere in the lower atmosphere.

[0107] Forecast location:

[0108] Analysis of low-level wind field and water vapor:

[0109] From the ERA5 reanalysis data, it can be seen that ( Figure 15(ad) The relative humidity in the Beijing-Tianjin-Hebei region (excluding northeastern Hebei) at 850 hPa was almost always above 90%, and the humidity range gradually expanded. The low-pressure system moved slightly northeast, causing the low-level wind direction in southern Beijing to gradually shift from southeast to south. The convergence point of the southeast and south winds also gradually moved northward from southern Beijing to northern Beijing. The southeast wind speed did not change much, remaining around 16 m / s, while the south wind gradually increased, reaching a maximum wind speed of 20 m / s in Langfang at 13:00.

[0110] From the analysis field at the lower level ( Figure 13 The comparison revealed that the three sets of experiments had poor predictions of the location of the low-pressure vortex, showing a more southwestern bias compared to the actual situation. The 3dvar experiment prediction field at 11:00 (…) Figure 15 e) The low-level vortex is still located further southwest than actually observed, and is slowly moving northeast, resulting in southeasterly winds predominant in the lower atmosphere over Beijing and Tianjin. At 13:00 ( Figure 15 g) Southwest and southeast winds converge in central Hebei. However, as the forecast time increases, the southeast wind gradually increases until 14:00 ( Figure 15 h) The maximum wind speed was 30 m / s, which is significantly different from the actual situation. The humidity conditions were not much different from the actual situation, but the humidity conditions in eastern Shandong were higher than the actual situation.

[0111] H-f80 test prediction field ( Figure 15 Compared to the 3dvar experiment, the position of the low vortex did not change much, the southeasterly wind speed decreased, and the southerly wind in central Hebei strengthened. At 13:00 ( Figure 15 k) Southerly and southeasterly winds converged at the border of Beijing and Hebei, and at the same time, the convergence was observed in central Beijing. The convergence point then continued to move northward, reaching its peak at 14:00. Figure 15 l) is located south of Beijing. The Jf experiment only showed a low-pressure system at the time of analysis; the low-pressure system is no longer predicted. Figure 15 mp), from 12 o'clock ( Figure 15 (n) Initially, central Hebei was under the convergence of southeast and southwest winds. As the southwest winds strengthened, the convergence area gradually moved northeastward from southwestern Tianjin. Humidity conditions were not significantly different from those in the 3dvar experiment.

[0112] By analyzing three sets of experimental prediction fields ( Figure 8 Analysis shows that even though the 3dvar experiment had poor accuracy in humidity prediction, the humidity forecast field became similar to that of the H-f80 and Jf experiments as the model was gradually adjusted. However, the wind field forecast had a large deviation, resulting in a significant shift in the convergence position. By incorporating lag ensemble information, the H-f80 experiment improved the low-level wind field, gradually bringing the wind convergence position closer to the actual situation. Although the low-level vortex disappeared in the Jf experiment's forecast field, it still weakened the southeasterly winds compared to the 3dvar experiment, but the forecast for southerly winds was weaker, resulting in a significant shift in the wind convergence position relative to the actual situation.

[0113] Analysis of the low-level wind field showed that the 3dvar experiment predicted a strong southwest wind and significant cyclonic shear at the border of Shandong and Hebei at 12:00 and 13:00. Therefore, the echo intensity in Shandong gradually increased, which differed greatly from the actual situation. Figure 14 e).

[0114] Vertical structure analysis:

[0115] Vertical profile of the analysis field ( Figure 16 The data shows that there are unstable stratifications east of 116.07°E, and precipitation can be easily triggered as long as there is low-level wind convergence.

[0116] Depend on Figure 16 It can be seen that the 3dvar experimental prediction field ( Figure 16 The data shows that the upward motion is mainly east of 116.07°E and above 750 hPa, with a relatively fast movement speed. At 13:00 ( Figure 16 c) The upward motion has moved to around 117.13°E, with a maximum vertical velocity of 4 m / s. The corresponding precipitation map shows weaker precipitation west of 117°E. At 14:00 ( Figure 16 d) Upward motion exists in the lower layers near 750 hPa and 117.3°E, with a maximum vertical velocity of 3 m / s. (Surface θ) se Most of them are at 350 K; at the same time, dry and cold air invades at the 600 hPa level, and the nature of precipitation changes, no longer being warm-sector precipitation.

[0117] H-f80 test 11-14 hours ( Figure 16 The upward motion (eh) persisted between 115.71°E and 117.13°E, and was located at a low level of 850 hPa (950 hPa at 13:00). At 14:00 ( Figure 16 h) The upward motion moves to around 117°, where cold and warm air masses meet. This upward motion extends from 1000 hPa at the surface to 500 hPa in the troposphere, resulting in significant transport of warm, moist air, which condenses to produce precipitation. The 6-hour precipitation map also shows that 117°E is in a region of high precipitation. At 13:00 ( Figure 16 g) At 117.3°E, upward motion only exists at a pressure above 650 hPa, with a vertical velocity of around 1 m / s, significantly weaker than in the 3dvar experiment, corresponding to reduced precipitation at this location (with Baodi station at 117.27°E as a reference). Although the H-f80 mixed experiment also showed dry and cold air intrusion in the mid-levels, comparison revealed that the addition of the lag ensemble sample suppressed the degree of dry and cold air intrusion, with a lag of approximately 0.36°E.

[0118] Jf test ( Figure 16The surface θse value (il) was larger than the other two groups of experiments, and the distribution of the rising motion area was more consistent with the 3dvar experiment, but smaller than the range of the rising motion area in the mixed experiment H-f80. The degree of intrusion of mid-level dry and cold air was also consistent with the 3dvar experiment. At 13:00 ( Figure 16 At k), there is already upward motion in the lower layer (850 hPa) near 117.13°E, with an upward airflow velocity of 4 m / s. At 14:00 ( Figure 16 l) There is still weak upward motion at the lower level of 850 hPa, but compared with the H-f80 test ( ​ The upward motion is weak, and at heights of 925 hPa and 1000 hPa, the motion is mainly horizontal with no obvious vertical motion.

[0119] Analysis of the vertical profile shows that the H-f80 experiment had a long duration and high speed of upward motion near 117°E, resulting in an increase in precipitation between 116°E and 117.13°E. At 117.3°E, the lower layers were dominated by horizontal motion, and even a weak downdraft appeared at 14:00, which reduced precipitation at Baodi station, making it closer to the actual situation.

[0120] This application uses samples constructed using time lag technology as set members. When the weight coefficient increases, the B-flow dependence characteristic becomes more obvious. At the same time, the set dispersion test is performed on U10, V10, T2, and RH2. By comparing the Talagrand distribution, dispersion, and root mean square error, it is found that the samples constructed by the time lag method still have set dispersion characteristics, with U10 performing better.

[0121] When using time-lag samples, the background field fg generated by the heat start-up at a nearby time is better than the ensemble mean as the background field, and its 6-hour precipitation TS score is higher. As the ensemble weight coefficient increases to 0.8, the area of ​​high precipitation value moves to the northwest, and the H-f80 experiment forecast is better.

[0122] Compared to three-dimensional variational assimilation, the hysteresis-variational hybrid assimilation technique achieves better assimilation of radar data. Field analysis shows that the combined radar reflectivity of the H-f80 hybrid experiment is closer to reality.

[0123] When time lag is used as a ensemble sample, it has a certain improvement effect on the lower humidity conditions of the analysis field relative to 3dvar, but its effect on the location of the low vortex and the wind field of the analysis field is not obvious.

[0124] Even though the wind field differences between the 3dvar, H-f80 mixed experiment, and ensemble experiment Jf analysis fields were not significant, after model adjustments, the differences in wind field forecasts between the 3dvar, H-f80, and Jf experiments gradually became apparent. The 3dvar experiment significantly overestimated the southeasterly winds, while the H-f80 and Jf experiments predicted less southeasterly winds than the 3dvar experiment. Due to the enhanced southerly wind forecast in the H-f80 experiment, the wind field convergence location gradually approached the actual situation, and the precipitation distribution shifted northwestward, becoming closer to the actual situation. The 3dvar experiment exhibited a significant cyclonic shear at the Shandong provincial border, resulting in an overestimated radar strong echo forecast range. The H-f80 and Jf experiments showed weaker shear at this location, mitigating the excessively large radar strong echo range.

[0125] Analysis of the vertical profile forecast field shows that when time-lag samples are added as ensemble members, the mixed assimilation experiment can improve the warm and humid conditions in the lower layer. The H-f80 experiment shows that there is a significant warm and humid air transport in the entire layer near 117°E, with obvious upward motion and long duration. The precipitation level is larger than that of 3dvar and J-f80, which is closer to the actual situation.

[0126] The present invention provides a radar data assimilation method based on time lag ensemble-variational hybrid. The method includes constructing an ensemble sample based on the time lag method, constructing a flow-dependent background error covariance based on the ensemble members in the ensemble sample, and realizing radar data assimilation based on the ensemble sample and the flow-dependent background error covariance. The method can improve the data assimilation effect, reduce the amount of computation, and improve the forecasting effect of convective-scale heavy precipitation.

[0127] Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. Furthermore, those skilled in the art will recognize that, based on the ideas of this invention, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A radar data assimilation method based on hysteresis-variational hybrid approach, characterized in that, Includes the following steps: Step 1: Construct a set of samples based on the time lag method; Step 2: Construct the background error covariance of the flow dependency based on the set members in the set sample; Step 3: Assimilate radar data based on ensemble samples and flow-dependent background error covariance.

2. The radar data assimilation method based on hysteresis-variational hybrid as described in claim 1, characterized in that, In step 1, the set of samples is constructed based on the time lag method, specifically as follows: The ensemble samples are constructed based on a fast-updating assimilation system. Each iteration generates high-frequency forecast fields, contributing new ensemble members. The total number of ensemble members N for the forecast field at time t0 is calculated using the following formula: （1）。 3. The radar data assimilation method based on hysteresis-variational hybrid as described in claim 2, characterized in that, In step 2, the background error covariance of the flow dependency is constructed based on the set members in the set sample, specifically as follows: Based on the ensemble sample, an ensemble error covariance that varies with weather conditions is constructed by means of ensemble perturbation, and coupled with the background error covariance fixed in variational assimilation to obtain the flow-dependent background error covariance.

4. The radar data assimilation method based on hysteresis-variational hybrid as described in claim 3, characterized in that, In step 3, radar data assimilation is achieved based on ensemble samples and the background error covariance dependent on flow, specifically as follows: The flow-dependent background error covariance is introduced into the objective function of variational assimilation using the extended variable method. The analytical increment representing the mixing and assimilation is defined as: （2） In the formula, It is the analytical increment of three-dimensional variational static covariance correlation. It is an analytical increment related to set covariance. It is a quantity that determines the localized scale of the set covariance and varies with spatial distribution. Let represent the standardized set perturbation field of the i-th set member, i.e.: （3） In the formula, For the i-th set member, For set averages, where N is the number of set members, the objective function for set-variable mixture assimilation is expressed as: （4） In the formula, and These are the objective functions for three-dimensional variational and set-related functions, respectively. Let B be the objective function of the observation term, B be the static background error covariance matrix, and A be the result of... The matrix consists of the spatial covariances, where H is the nonlinear observation factor mapping the model field to the observation field, and R is the observation field error covariance matrix. and Let be the weight coefficient, and satisfy... （5）。

Images