CN112558188B - A method for improving severe convection forecasting by assimilating lightning data - Google Patents

Abstract

The invention relates to a method for improving strong convection forecast by assimilating lightning data, which comprises the following steps: establishing an observation operator between lightning frequency and maximum vertical speed; extracting lightning data 20 minutes before the assimilation moment, converting the lightning data into the maximum vertical speed on a grid of 1 km, and distributing the maximum vertical speed of 1 km to a numerical mode grid; thirdly, according to the GGF method, calculating by using a background field to obtain a vertical localization function of each variable; fourthly, assimilating the maximum vertical speed of the agent by using an ensemble root mean square filtering method and combining a vertical localization function, and circularly assimilating for four times to obtain an analysis field; fifthly, continuously forecasting by utilizing the analysis field to obtain a forecasting field; sixthly, performing forecast inspection. The method effectively improves the dynamic field in the background field by assimilating total flash data, also improves the humidity field and the temperature field to a certain extent, is reasonable and effective, and obviously improves the forecast effect of rainfall and echo waves in a numerical mode.

Description

A method for improving severe convection forecasting by assimilating lightning data

technical field

The invention relates to a meteorological data processing method, in particular to a method for improving strong convection forecast by assimilating lightning data.

Background technique

Despite continuous improvements in weather forecasting, achieving the accuracy of early warnings of convective activity remains a great challenge due to the diversity of scales and physical processes involved in these events. Strong convective weather is usually accompanied by frequent lightning activities. Lightning can be used to monitor the occurrence and development of mesoscale convective activities. Lightning data assimilation is also a very useful method to improve the accuracy of initial conditions and thus improve weather forecasting.

Browning (1989) proposed that a possible method to adjust the initial field of the mesoscale numerical weather prediction model is to improve the water vapor analysis. At present, many lightning data assimilation studies are to improve the forecast by improving the water vapor field under the initial conditions. (1999) realized the assimilation of lightning data based on the relationship between rainfall rate and lightning. (2012) proposed that lightning data at the convective-resolved scale can be assimilated by changing the water-vapor mixing ratio in the mixing region (0°C and -20°C). Since then, a lot of lightning data assimilation work has been carried out based on Fierro's method. The results show that the forecast can be improved whether using different assimilation methods to assimilate the proxy water vapor mixing ratio, or assimilating the proxy water vapor mixing ratio based on different models.

In addition, Qie et al. (2014) established an empirical formula between the total lightning rate and the mixing ratio of ice-phase particles (graupel, ice, and snow) to adjust the mixing ratio of ice-phase particles in the mixing zone. Chen et al. (2018) used the method of Fierro and Qie to simultaneously adjust the low-level water vapor and graupel mass in the mixing zone using lightning data, and considered the thermodynamic and kinetic conditions in the model grid to maintain the model balance. In addition, Allen et al. (2016) and Kong et al. (2020) also assimilated lightning data using the observation operator between lightning and graupel mass and graupel volume.

Adjusting the vertical velocity distribution in the initial field of a numerical model is another feasible method to improve severe convection forecasts. At present, most of the researches focus on the assimilation of water vapor and water substances, and few studies consider the assimilation wind field, especially the vertical velocity. Previous studies have shown that there is a qualitative correlation between updraft strength and observed lightning frequency (Deierling and Petersen, 2008). Based on lightning observations, Williams and Earl (1985) showed that the total flash frequency during terrestrial convection has an approximately fifth power relationship with the height of convective clouds. Price and Rind (1992) pointed out that from many convective events, the maximum ascent velocity in convective clouds is related to cloud height, and they established empirical formulas for the maximum vertical velocity and total flash frequency in continental and oceanic clouds, respectively. (2020b) adopted the Nudging method to assimilate the lightning data and adjusted the dynamic field according to the formula of Price and Rind. Furthermore, few studies have aimed to optimize dynamic fields based on the relationship between lightning and updrafts.

Ensemble root mean square filtering (EnSRF) uses the predicted ensemble to estimate flow-dependent background error covariance, and it has been used to assimilate conventional observation, radar, satellite, and lightning data (Gao and Min, 2018; Wang et al., 2015). Localization (Anderson, 2007b; Hamill et al., 2001) and covariance inflation (Anderson, 2007a, 2008) are essential for EnSRF because they suffer from sampling errors due to small set numbers (Lei and Anderson, 2014). The commonly used localization function is an approximate Gaussian fifth-order polynomial function (Gaspari and Cohn, 1999, referred to as GC function), and the width parameter of GC needs to be adjusted for a given situation, which is for various observations and state variables. is not practical. In addition, there are some theoretical studies on adaptive covariance (Anderson and Lei, 2013; Lei et al., 2014; Lei and Anderson, 2014), but the concepts of maximum vertical velocity, vertical localization of two-dimensional variables are not very good definition. Lei et al. (2016) proposed a GGF (global group filter) method, which can provide an adaptive estimation of the vertical localization function. Subsequently, the GGF localization function was applied to the ANSU-A radiation data assimilation and obtained better results. forecast effect (Lei et al., 2016; Wang et al., 2020a).

Based on the strong convective event that occurred on July 6, 2019, the present invention uses the EnSRF method as well as the GGF localization method to assimilate the maximum vertical velocity ( EnSRF_Wmax), in order to improve the forecast of strong convective processes.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a reasonable and effective method for improving strong convection forecast by assimilating lightning data.

In order to solve the above problems, a method for improving strong convection forecasting by assimilating lightning data according to the present invention includes the following steps:

，而最大垂直速度与云顶高度之间的关系为

，建立闪电频数和最大垂直速度之间的观测算子：

；(1) According to the relationship between lightning frequency and cloud top height in convective activity:

, while the relationship between maximum vertical velocity and cloud top height is

, establish the observation operator between the lightning frequency and the maximum vertical velocity:

;

In the formula: w _max represents the maximum vertical speed, unit: m/s; F is the lightning frequency per kilometer per minute; Z is the height of cloud top, unit: km;

(2) Extract the lightning data 20 minutes before the assimilation time, convert the lightning data into the maximum vertical speed on a 1 km grid according to the observation operator between the lightning frequency and the maximum vertical speed, and then convert the 1 km The maximum vertical speed is assigned to the numerical mode grid;

(3) According to the GGF method, the vertical localization function of each variable is obtained by using the background field calculation;

(4) Using the ensemble root mean square filtering method, combined with the vertical localization function to assimilate the maximum vertical velocity of the agent, and obtain the analysis field after cyclic assimilation four times;

(5) Use the analysis field to continue forecasting to obtain the forecast field;

⑹ Carry out forecast inspection.

In the described step (3), the vertical localization function is calculated as follows:

表示来自第n个样本的第m层的第l个观测处的模式状态变量；其中

，

，

；

是

的集合平均；① Let N denote the sample size, L denote the number of observations, and M denote the vertical layer of the pattern,

represents the mode state variable at the lth observation from the mth layer of the nth sample; where

,

,

;

Yes

the ensemble average of ;

，

；式中：

代表来自第n个样本的第l个观测；

是由闪电转换的第l个最大垂直速度；

是计算得到的第n个样本的观测扰动；

是

的平均，其中

是

的平均，

，

是观测算子；②Construct a set of observation disturbances according to the background field according to the following methods:

,

; where:

represents the lth observation from the nth sample;

is the l -th maximum vertical velocity converted by lightning;

is the calculated observed disturbance of the nth sample;

Yes

the average of which

Yes

Average,

,

is the observation operator;

③ The correlation coefficient between observations and model variables can be calculated by the following formula:

；

;

为相关系数；

代表

的集合平均；where:

is the correlation coefficient;

represent

the ensemble average of ;

随机地分为G个组，每个组有Q个样本，则相关系数

表示为

，

以及

，所有的G个组中Q个样本的估计相关的均方根（RMS）差

表示为：④Correlation coefficient

Randomly divided into G groups, each group has Q samples, then the correlation coefficient

Expressed as

,

as well as

, the estimated correlated root mean square (RMS) difference of Q samples in all G groups

Expressed as:

；

;

，

是计算得到的自适应的垂直局地化函数，即GGF函数； G取16。Root mean square minimization yields:

,

is the calculated adaptive vertical localization function, namely the GGF function; G takes 16.

The observed variable in the ensemble root mean square filtering (EnSRF) method in the step (4) is the maximum vertical velocity w _max ; the analysis variables include wind field ( u, v, w ), perturbation potential temperature ( prt ), perturbation potential ( ph ) , water vapor mixing ratio ( qv ), rainwater mixing ratio ( qr ), ice mixing ratio ( qi ), graupel mixing ratio ( qg ), cloud mixing ratio ( qc ), snow mixing ratio ( qs ).

Compared with the prior art, the present invention has the following advantages:

1. Based on the mesoscale numerical model WRF, the present invention improves the background field dynamic information by assimilating lightning data (referred to as EnSRF_Wmax), establishes an observation operator between the total flash and the maximum vertical velocity, and uses the EnSRF method to assimilate the data from the lightning data. The proxy maximum vertical velocity of the conversion, and the GGF vertical localization scheme is used to effectively improve the dynamic information in the background field. Not only is the method reasonable and effective, but also the water vapor field and temperature field in the background field are adjusted to a certain extent, which is effective Numerical model predictions of precipitation and echoes during convective processes have been significantly improved.

2. Compared with the assimilation of three-dimensional data, the maximum vertical velocity of the two-dimensional assimilation of the present invention reduces the amount of calculation.

Description of drawings

The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

FIG. 1 is a vertical localization function diagram of the mode basic state quantity calculated according to the GGF vertical localization scheme in the present invention. Among them: (u), (v), (w), (prt), (ph), (qv), (qr), (qc), (qg), (qi), (qs) represent the u component wind, respectively , v component wind, vertical velocity, disturbance potential temperature, disturbance potential, water vapor mixing ratio, rain mixing ratio, cloud water mixing ratio, graupel mixing ratio, ice mixing ratio, snow mixing ratio.

FIG. 2 is a schematic diagram of the conversion of lightning into the maximum vertical velocity on the pattern grid in the present invention. where: (a) is the observed total flash within 20 min; (b) is the lightning frequency assigned to the 1 km grid; (c) is the conversion of the lightning frequency to the maximum vertical on the 1 km grid Velocity; (d) is the assignment of the maximum vertical velocity on the 1 km grid to the model simulation grid (3 km).

Figure 3 is the lightning distribution 20 minutes before the assimilation time in the present invention, and the maximum vertical velocity map obtained by conversion. Among them: (a1) is the lightning distribution 20 minutes before 03 UTC on July 6, 2019; (b1) is the lightning distribution 20 minutes before 04 UTC on July 6, 2019; (c1) is July 6, 2019 05 Lightning distribution 20 minutes before UTC; (d1) is the lightning distribution 20 minutes before 06 UTC on July 6, 2019; (a2) is the maximum vertical velocity at 03 UTC on July 6, 2019 converted according to lightning frequency; (b2 ) is the maximum vertical speed on July 6, 2019 04 UTC converted according to the lightning frequency; (c2) is the maximum vertical speed on July 6, 2019 05 UTC converted according to the lightning frequency; (d2) is the maximum vertical speed converted according to the lightning frequency The maximum vertical velocity at 06 UTC on July 6, 2019.

Fig. 4 is a distribution diagram of cumulative precipitation observed and simulated in the present invention. Where: (a1) is the observed cumulative precipitation from 06 UTC to 09 UTC on July 6, 2019; (a2) is the cumulative precipitation simulated by the control experiment (CTL) from 06 UTC to 09 UTC on July 6, 2019; (a3 ) is the cumulative precipitation from 06 UTC to 09 UTC on July 6, 2019 simulated by the assimilation experiment (LDA_GGF); (b1) is the observed cumulative precipitation from 09 UTC to 12 UTC on July 6, 2019; (b2) is the control The experimental (CTL) simulated cumulative precipitation from 09 UTC to 12 UTC on July 6, 2019; (b3) is the simulated cumulative precipitation from the assimilation experiment (LDA_GGF) from 09 UTC to 12 UTC on July 6, 2019.

FIG. 5 is a performance diagram of precipitation forecasting in the present invention. Among them: (a) is the performance map of precipitation forecast when the threshold is 1 mm; (b) is the performance map of precipitation forecast when the threshold is 5 mm.

Detailed ways

A method for improving severe convective forecasting by assimilating lightning data, comprising the following steps:

(1) Since the observation data (frequency) of lightning is not the model variable of the numerical model, the observation operator of lightning and other model variables must be established first when assimilating it.

，而最大垂直速度与云顶高度之间的关系为

，因此，建立闪电频数和最大垂直速度之间的观测算子：

；Existing studies have shown that there is a fifth-power relationship between lightning frequency and cloud top height in convective activity. Ushio et al. (2001) used the data of the precipitation radar and lightning imager on the TRMM satellite to obtain the "instantaneous" lightning frequency and convective cloud cloud. The relationship between the top heights is

, while the relationship between maximum vertical velocity and cloud top height is

, therefore, establish the observation operator between the lightning frequency and the maximum vertical velocity:

;

Where: w _max represents the maximum vertical speed, unit: m/s; F is the lightning frequency per kilometer per minute; Z is the height of the cloud top, unit: km.

This observation operator only works on 1 km grids.

(2) Extract the lightning data 20 minutes before the assimilation time, convert the lightning data into the maximum vertical speed on a 1 km grid according to the observation operator between the lightning frequency and the maximum vertical speed, and then assign the maximum vertical speed of 1 km to the maximum vertical speed. onto the numerical mode grid.

The specific process: the first step assigns the lightning data to a 1 km grid, the second step converts the 1 km lightning frequency into the maximum vertical velocity according to the obtained observation operator, and finally converts the maximum vertical velocity into a pattern grid (3 km), the specific process is shown in Figure 2.

(3) According to the GGF (global group filter) method, the vertical localization function of each variable is calculated by using the background field. The difficulty of using the EnSRF method to assimilate the maximum vertical velocity lies in the setting of the vertical localization scheme. In the present invention, the vertical localization scheme adopts the GGF scheme. The GGF localization scheme observes the disturbance set of state variables and uses the sample correlation calculation to obtain.

The vertical localization function is calculated as follows:

表示来自第n个样本的第m层的第l个观测处的模式状态变量；其中

，

，

；

是

的集合平均；① Let N denote the sample size, L denote the number of observations, and M denote the vertical layer of the pattern,

represents the mode state variable at the lth observation from the mth layer of the nth sample; where

,

,

;

Yes

the ensemble average of ;

，

；式中：

代表来自第n个样本的第l个观测；

是由闪电转换的第l个最大垂直速度；

是计算得到的第n个样本的观测扰动；

是

的平均，其中

是

的平均，

，H'是观测算子；在本研究中H'也就是利用背景场计算最大垂直速度的方法。②There is no observation disturbance in EnSRF. In order to calculate the GGF vertical localization function, it is necessary to construct a set of observation disturbances according to the background field according to the following method:

,

; where:

represents the lth observation from the nth sample;

is the l -th maximum vertical velocity converted by lightning;

is the observed disturbance of the calculated nth sample;

Yes

the average of which

Yes

Average,

, H' is the observation operator; in this study, H' is the method of calculating the maximum vertical velocity using the background field.

③ The correlation coefficient between observations and model variables can be calculated by the following formula:

；

;

为相关系数；

代表

的集合平均；where:

is the correlation coefficient;

represent

the ensemble average of ;

随机地分为G个组，每个组有Q个样本，则相关系数

表示为

，

以及

，所有的G个组中Q个样本的估计相关的均方根（RMS）差

表示为：④Correlation coefficient

Randomly divided into G groups, each group has Q samples, then the correlation coefficient

Expressed as

,

as well as

, the estimated correlated root mean square (RMS) difference of Q samples in all G groups

Expressed as:

；这里的q,i,j没有实际的意义，就是数组算法的表示，求和算法，q从1取到Q，i从1取到G，j从1取到G，其中j不等于i。

; The q, i, j here have no practical meaning, they are the representation of the array algorithm, the summation algorithm, q is taken from 1 to Q, i is taken from 1 to G, and j is taken from 1 to G, where j is not equal to i.

，

是计算得到的自适应的垂直局地化函数，即GGF函数； G取16。Root mean square minimization yields:

,

is the calculated adaptive vertical localization function, namely the GGF function; G takes 16.

The normalized result of the localization function of the calculated basic quantity of the pattern is shown in Fig. 1.

(4) Using the Ensemble Root Mean Square Filtering (EnSRF) method, combined with the vertical localization function to assimilate the maximum vertical velocity of the proxy, and obtain the analysis field after cyclic assimilation four times.

Since the maximum vertical velocity is a special two-dimensional variable, the ensemble root mean square filtering method (EnSRF) is easy to establish a balance constraint between the maximum vertical velocity and other variables. In addition, the EnSRF method avoids the sampling error generated when the perturbed observation is generated. Therefore, in the present invention, the maximum vertical velocity of EnSRF assimilation lightning conversion is selected.

In ^EnSRF , the superscripts a , b , o represent the analysis field, background field and observation, respectively, x ^b is the background field predicted by the model, yo is a series of observations, and the minimum variance of the analysis field x ^a is estimated according to the Kalman filter equation It can be expressed as:

，

,

，

,

），集合平均（

）和第i个集合的偏差（

）可以表示为：Where: H is the linearized form of the observation operator H ' , the observation operator H' is the projection relationship between the state quantity x and the observation y ^o , K is the Kalman gain matrix, P ^b is the background error covariance matrix, R is the Observation error covariance matrix with no observation perturbation in EnSRF (

), the ensemble average (

) and the deviation of the ith set (

)It can be expressed as:

，

,

；

;

称为“简化”卡尔曼增益矩阵，定义如下：in

is called the "simplified" Kalman gain matrix and is defined as:

。

.

In the present invention, the observed variable is the maximum vertical velocity w _max ; the analysis variables include wind field ( u,v,w ), disturbance potential temperature ( prt ), disturbance potential ( ph ), water vapor mixing ratio ( qv ), rainwater mixing ratio ( qr ), ice mixing ratio ( qi ), graupel mixing ratio ( qg ), cloud mixing ratio ( qc ), snow mixing ratio ( qs ).

⑸ Use the analysis field to continue forecasting to obtain the forecast field.

⑹ Carry out forecast inspection.

In order to verify the improvement effect of the present invention on the forecast of strong convection, a case analysis of a strong convection process that occurred in Shandong and Jiangsu regions of my country on July 6, 2019 was selected for analysis. A set of control experiments and a set of loops were designed in this experiment. Assimilation test, the detailed test design is shown in Table 1:

Table 1: Experimental Design Table

The understanding of spin-up in Table 1 is: because the medium and small scale models are all started from the cloud-free initial field, it takes a certain time to generate the corresponding cloud water information at the beginning, and the actual cloud will be generated within a period of time after the cold start. water information, but forecasts for these hours are inaccurate, referring to these hours as "spin-up" time. That is to say, the simulation results during this period are unreliable, so the results of the spin-up period are not analyzed during the analysis.

In the above experiments, experiment I (CTL) is a control experiment, and experiment II (LDA_GGF) is an experiment using the EnSRF method to assimilate lightning. The assimilation time is July 6, 2019 03, 04, 05, 06 UTC. In this study, WRF 3.6.1 version was selected. The ensemble forecast of 21 national ensemble member forecast systems was used to provide the initial field and boundary field for the WRF model. In order to enhance the sample dispersion, the RRTMG and Goddard radiation schemes were used to make the 21 samples become 42 samples. In addition, the selected parameterization schemes include the Thompson microphysics scheme, the Monin-Obukhov near-surface layer scheme, the Mellor-Yamada-Janjic TKE planetary boundary layer scheme, the RUC land surface scheme, and the Tiedtke cumulus parameterization scheme ( Only used in D01). In this study, two nested grids were used, the horizontal resolution of D01 was 9 km, the model grid was 171×151, and the horizontal resolution of D02 was 3 km, the model grid was 391×271, and there were 50 layers in the vertical direction.

In this study, the EnSRF scheme is used to assimilate the maximum vertical velocity, and the vertical localization scheme is the GGF localization scheme. Figure 1 shows the localization function of the mode state quantity calculated according to the GGF localization scheme. This study also established an observation operator between the maximum vertical velocity and the lightning frequency. Figure 2 shows the process of converting lightning observations to the maximum vertical velocity on the model grid. Figure 3 shows the lightning data used in this experiment. Figure 3 (a1-d1) is the accumulated lightning 20 minutes before the assimilation time on the hour, Figure 3 (a2-d2) is the maximum vertical velocity obtained by the conversion of the established observation operator, it can be seen that this convection process occurred After many lightning processes, the 03 UTC lightning was mostly concentrated in the Shandong area, and then the convective process moved southward at a faster speed, and by 06 UTC the lightning was mainly distributed in the northern part of Jiangsu.

Figure 4 is the distribution of the observed and simulated cumulative precipitation, the first row is the cumulative precipitation from 06-09 UTC on July 6, 2019, the second row is the cumulative precipitation from 09-12 UTC, the first column is the observed precipitation, the second The column is the precipitation simulated by the control experiment, and the third column is the precipitation simulated by the assimilation experiment. The observed precipitation from 06-09 UTC is mainly concentrated in northern Jiangsu. The control experiment did not simulate the main rainbands in Jiangsu, while the assimilation experiment improved well. For the precipitation in Jiangsu, the precipitation observed from 09-12 UTC is mainly concentrated in the southern part of Jiangsu, while the simulated precipitation is located in the north.

Figure 5 is the precipitation forecast performance map. Figures (a) and (b) represent the results of selecting 1 mm and 5 mm thresholds, respectively. The forecast performance map can reflect a lot of information, including the forecast deviation (FR, shown by the dotted line in the figure, the more Close to 1 indicates that the forecast deviation is smaller, greater than 1 indicates overestimation, and less than 1 indicates underestimation), hit rate (POD, higher indicates better forecast), critical success index (CSI, as shown by the curve in the figure, the range is 0-1, It is close to 1, the better), the success rate (SR, 1 minus the empty alarm rate, the closer it is to 1, the better). Generally speaking, it is close to the upper right corner in the forecast performance graph, indicating that the forecast effect is more accurate. The light circles in the figure represent the results of the control experiment, and the dark circles represent the results of the assimilation experiment. It can be seen that for a smaller threshold, the assimilation experiment is significantly better than the control experiment at 6 hours. When the threshold is 5 mm, the assimilation experiment is in the front. A 4-hour forecast is better. In general, the prediction effect of the assimilation experiment is significantly better than that of the control experiment.

Claims (2)

1. A method for improving strong convection forecasts by assimilating lightning data, comprising the steps of:

the method comprises the following steps of according to the relation between the lightning frequency and the cloud top height in the convection activity:

and the relationship between the maximum vertical velocity and the height of the cloud top is

Establishing an observation operator between the lightning frequency and the maximum vertical speed:

；

in the formula:w _max represents the maximum vertical velocity, in units: m/s; f is the lightning frequency per kilometer per minute; z is the cloud top height in units: km;

secondly, extracting lightning data 20 minutes before the assimilation moment, converting the lightning data into the maximum vertical speed on a1 km grid according to an observation operator between the lightning frequency and the maximum vertical speed, and then distributing the 1 km maximum vertical speed to a numerical mode grid;

thirdly, according to the GGF method, calculating by using a background field to obtain a vertical localization function of each variable; the vertical localization function is calculated as follows:

let N denote the sample size,Lrepresenting the number of observations, M represents the vertical layer of the mode,

is indicated from the firstnA first sample ofmFirst of the layerlMode state variables at each observation; wherein

，

，

；

Is that

(ii) ensemble averaging;

secondly, a group of observation disturbances is constructed according to the background field by the following method:

，

(ii) a In the formula:

represents from the firstnA first sample ofl(ii) an observation;

is converted by lightninglA maximum vertical velocity;

is calculated to ben(ii) observed perturbations of individual samples;

is that

Wherein, on average

Is that

Is calculated based on the average of (a) and (b),

，

is an observation operator;

③ the correlation coefficient between the observation and the mode variables can be calculated by the following formula:

；

in the formula:

is a correlation coefficient;

represents

(ii) ensemble averaging;

correlation coefficient

Is randomly divided intoGGroups, each group havingQSample by sample, correlation coefficient

Is shown as

，

And

all ofGIn a groupQRoot mean square deviation of estimated correlations of individual samples

Expressed as:

；

root mean square minimization yields:

，

is a self-adaptive vertical localization function obtained by calculation, namely a GGF function; Gtaking 16;

fourthly, utilizing an ensemble root mean square filtering method, assimilating the maximum vertical speed of the agent by combining the vertical localization function, and circularly assimilating for four times to obtain an analysis field;

in EnSRF, superscripta，b，oRespectively representing the analysis field, the background field and the observation,x ^b is the background field of the mode forecast,y ^o analyzing the field for a series of observationsx ^a The minimum variance estimate of (c) can be expressed as:

，

，

wherein: h is an observation operatorH'Of the linearized form, observation operatorH'Is a state quantityxTo observey ^o K is a kalman gain matrix,P^bis the background error covariance matrix, R is the observation error covariance matrix, and there is no observed perturbation in EnSRF: (

) Ensemble averaging (A)

) And a firstiDeviation of a set (

) Can be expressed as:

，

；

wherein

Referred to as a "simplified" kalman gain matrix, defined as follows:

；

fifthly, continuously forecasting by utilizing the analysis field to obtain a forecasting field;

sixthly, forecasting and checking.

2. A method of improving a strong convection forecast by assimilating lightning data according to claim 1, characterized by: fourth step of collecting observation variable in root mean square filtering method as maximum sagStraight speedw _max (ii) a The analysis variables include wind field, disturbance potential temperature, disturbance potential, water-vapor mixing ratio, rainwater mixing ratio, ice mixing ratio, aragonite mixing ratio, cloud mixing ratio, snow mixing ratio.

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