CN111259324A - Satellite data assimilation vertical direction adaptive localization method and integrated Kalman filtering weather assimilation forecasting method - Google Patents

Abstract

The invention discloses an adaptive localization method of satellite data assimilation in the vertical direction and an ensemble Kalman filter weather assimilation forecast method. The adaptive localization method calculates the correlation coefficient between the observation data and the model variable according to the arbitrary observation data and model variables given in the ensemble Kalman filter assimilation system; The original localization function; according to the profile of the correlation coefficient, the position p ^o of the satellite observation is estimated, and the original localization function is fitted with the maximum value of the GC function located at the position p ^o to obtain the influence range c of the satellite observation ^o . The position p ^o and the influence range c ^o are the adaptive localization parameters required by the present invention. The obtained adaptive localization parameters are used to forecast typhoons in regional models. Compared with the forecast results without the use of the present invention, the error of the forecast results relative to the observations is significantly reduced, and at the same time, the use of the present invention also significantly improves the rapidity of typhoons. Enhancement phase forecast.

Description

Adaptive localization method of satellite data assimilation in vertical direction and ensemble Kaman filter weather assimilation forecast method

technical field

The invention relates to a weather assimilation forecasting method, in particular to an ensemble Kalman filter weather assimilation forecasting method based on adaptive localization technology, which uses adaptive localization technology to correct the existing ensemble Kalman filter assimilation system, to improve weather forecast results.

Background technique

Data assimilation is a technique that uses observations to correct model variables to obtain the best estimate of the current state of the atmosphere.

Ensemble Kalman filtering is a commonly used method for data assimilation, but it is affected by sampling errors when applied to high-dimensional atmospheric models, and localization can deal with sampling errors. Localization generally assumes that correlations farther away from observations are more likely to be spurious. The commonly used localization function is the Gaspari and Cohn (Gaspari and Cohn1999) function, referred to as the GC function. When using the localization function to assimilate the observational data in the ensemble Kalman filter assimilation system, the usual practice is to retain the influence of the observational data on the nearby model variables, and reduce the influence of the observational data on the distant model variables. At the same time, the influence of observation data outside a certain range on the model variables is ignored.

However, for non-local observations such as satellite observations, the location of the observations and the influence range in the vertical direction are not well defined and cannot be directly localized. At the same time, for observations at different times and in different regions, the localization functions of satellite observations should also be different, but the existing technology cannot adaptively estimate the required localization functions.

Therefore, an adaptive localization scheme is required to provide an adaptive localization function in the vertical direction for satellite observations of different platforms and channels, different regions, and different times.

SUMMARY OF THE INVENTION

Aiming at the deficiencies of the prior art, the present invention provides an adaptive localization method for satellite data assimilation in the vertical direction. The method uses the ensemble Kalman filter to assimilate the correlation coefficients of satellite observations and model variables in the system, and uses the grouped correlation coefficients to estimate the original localization functions of the satellite observations and model variables at the current moment and current area, and then converts these The original localization function is fitted with the GC function to obtain the adaptive localization function and related parameters. The obtained adaptive localization functions and related parameters are applied in an ensemble Kalman filter assimilation system to estimate the current state of the atmosphere by using satellite data more efficiently, thereby improving the accuracy of weather forecasting.

For realizing the above-mentioned technical purpose, the present invention will take the following technical scheme:

An adaptive localization method for satellite data assimilation in the vertical direction, which is characterized in that: according to the satellite observations and model variables in any sub-region given in the ensemble Kalman filter assimilation system at any time, calculate The correlation coefficient between satellite observations and model variables in the vertical direction; then use the correlation coefficient to estimate the original localization function of the satellite observations and model variables in the vertical direction at the current moment and in the current area; estimate the satellite according to the correlation coefficient profile. Observe the position p ^o in the vertical direction, and fit the above original localization function with the maximum value of the GC function at the position p ^o to obtain the influence range c ^o of the satellite observation in the vertical direction; The estimated position p ^o and the influence range c ^o of satellite observations in the vertical direction are the adaptive localization parameters.

Further, the satellite observations and model variables within a specific sub-region given in the ensemble Kalman filter assimilation system at a specific time are:

Observe the disturbance of y _l,n :

代表卫星观测的集合成员y_l,n的平均值；where: observation y _l,n denotes the lth observation of the nth set member in the satellite observations given in the set Kalman filter assimilation system, l∈{1,...,L} and n∈{1, ...,N}; N is the number of ensemble members of the ensemble Kalman filter assimilation system, and L is the number of observations of a certain channel observed by a certain satellite;

represents the mean value of ensemble members y _l,n of satellite observations;

The amount of disturbance of the mode variable:

表示在集合卡曼滤波同化系统中，在水平方向投影至第l个观测变量所在位置的第n个集合成员位于第k层高度的模式变量；l∈{1,…,L},n∈{1,...,N},k∈{1,...,K}；K为模式在垂直方向的层数；

代表各模式变量

的平均值。where: pattern variable

In the ensemble Kalman filter assimilation system, the nth ensemble member projected in the horizontal direction to the position of the lth observation variable is the pattern variable at the height of the kth layer; l∈{1,…,L},n∈{ 1,...,N},k∈{1,...,K}; K is the number of layers in the vertical direction;

represents each model variable

average of.

Further, for a given type of satellite observation and a certain model variable in the ensemble Kalman filter assimilation system, the correlation coefficient r _l ^k at any height k is:

代表模式变量

的扰动量；Δy_l,n代表观测y_l,n的扰动量；where:

represents the pattern variable

Δy _l,n represents the disturbance of observed y _l,n ;

y _l,n denotes the lth observation of the nth set member in the satellite observations given in the set Kalman filter assimilation system, l∈{1,...,L} and n∈{1,... ,N}; N is the number of ensemble members of the ensemble Kalman filter assimilation system, and L is the number of observations of a certain channel observed by a satellite;

代表模式变量在集合卡曼滤波同化系统中，在水平方向投影至第l个观测变量所在位置的第n个集合成员位于第k层高度的模式变量；l∈{1,...,L},n∈{1,...,N},k∈{1,...,K}，K为模式在垂直方向的层数。

In the ensemble Kalman filter assimilation system, the representative pattern variable is the pattern variable of the nth ensemble member at the height of the kth layer projected in the horizontal direction to the position of the lth observation variable; l∈{1,...,L} ,n∈{1,...,N},k∈{1,...,K}, where K is the number of layers in the vertical direction.

Further, use the correlation coefficient _r ^k between any satellite observation and the model variable at any height k in the vertical direction to estimate the original local position of the satellite observation and the model variable in the vertical direction at the current moment and the current area. Before transforming the function, it is necessary to group the correlation coefficients r _l ^k . The grouping method is as follows: each group of G elements is divided into M groups, and any correlation coefficient in each group of correlation coefficients is recorded as

Further, the original localization function is the vertical profile of the parameter α ^k ; the parameter α ^k represents the confidence index of the correlation coefficient between a certain satellite observation and the model variable with an altitude of k;

都有相同的概率为真值，则局地化后的相关系数

的目标函数J^k应满足：If considering each correlation coefficient

have the same probability as the true value, then the localized correlation coefficient

The objective function J ^k should satisfy:

When the objective function J ^k takes the minimum value, the confidence index α ^k satisfies:

代表相关系数r_l ^k分为每组包含有G个成员的M组后，每组相关系数中的任意一个相关系数；where:

After the representative correlation coefficient r _l ^k is divided into M groups containing G members in each group, any correlation coefficient in each group of correlation coefficients;

The correlation coefficient r _l ^k represents the correlation coefficient at any height k for a given type of satellite observation and a certain model variable.

Further, the estimated position p ^o of the satellite observation in the vertical direction: is the air pressure value at the height where the correlation coefficient r _l ^k is the maximum value of the profile.

Further, the acquisition method of the influence range c ^o of the satellite observation in the vertical direction: firstly fit the original localization function with the maximum value of the GC function located at the position p ^o to obtain the adaptive localization function;

Then, by comparing the adaptive localization function and the original localization function, the influence range c ^o of the satellite observation in the vertical direction can be obtained, and the influence range c ^o of the satellite observation in the vertical direction is the GC function width value c ^o , indicating The width parameter of the GC function corresponding to the minimum root mean square error of both the adaptive localization function and the original localization function at the p ^o position.

Further, the above-mentioned localization method includes the following steps:

(1) Select the appropriate area and time

For different weather systems, the satellite observations and model variables in a specific sub-region and at a specific time are given through the ensemble Kalman filter assimilation system;

The specific sub-area includes TC area and/or non-TC area; TC area is defined as a square area with the location of the tropical cyclone at the current moment as the center and a side length of 20 longitude and latitude;

It is necessary to ensure that the total number of observations at all times in a specific sub-region is not less than O, O=10 ² ;

The specific time is a representative time in the given satellite observation and model variables or the previous time or the previous two time when the localization parameter is estimated at the current time;

(2) Obtain observation variables and model variables

Observe the disturbance of y _l,n :

代表卫星观测的集合成员y_l,n的平均值；where: observation y _l,n denotes the lth observation of the nth set member of satellite observations given in the set Kalman filter assimilation system, l∈{1,...,L} and n∈{1,. ..,N}; N is the number of ensemble members of the ensemble Kalman filter assimilation system, and L is the number of observations of a certain channel of satellite data;

represents the mean value of ensemble members y _l,n of satellite observations;

的扰动量：pattern variable

The amount of disturbance:

表示在集合卡曼滤波同化系统中，在水平方向投影至第l个观测变量所在位置的第n个集合成员位于第k层高度的模式变量；l∈{1,...,L},n∈{1,...,N},k∈{1,…,K}；K为模式在垂直方向的层数；

代表各模式变量

的平均值；where: pattern variable

In the ensemble Kalman filter assimilation system, the nth ensemble member projected to the position of the lth observation variable in the horizontal direction is the pattern variable at the height of the kth layer; l∈{1,...,L},n ∈{1,...,N},k∈{1,...,K}; K is the number of layers of the pattern in the vertical direction;

represents each model variable

average of;

(3) Calculate the correlation coefficient

的相关系数r_l ^k为：The lth observation y _l and the lth pattern variable

The correlation coefficient r _l ^k of is:

(4) Calculate the original localization function

For a given type of satellite observation and a certain model variable, the correlation coefficient r _l ^k of any height k is divided into M groups according to each group of G elements, and any correlation coefficient in each group of correlation coefficients is recorded as

都有相同的概率成为真值，则局地化后的相关系数

的目标函数J^k满足：If considering each correlation coefficient

have the same probability to become the true value, then the localized correlation coefficient

The objective function J ^k satisfies:

α ^k represents the confidence index of the correlation coefficient between this kind of satellite observation and the model variable with height k. When the objective function J ^k takes the minimum value, the confidence index α ^k satisfies:

The vertical profile of α ^k is the estimated original localization function in the vertical direction;

(5) Fitting parameters

Find out the observation position p ^o in the vertical direction;

Fit the original localization function with the GC function whose maximum value is at p ^o , and the obtained result is the adaptive localization function;

Through the adaptive localization function and the original localization function, the estimated GC function width value c ^o can be obtained, and the GC function width value c ^o indicates that the adaptive localization function and the original localization function located at p ^o The width parameter of the GC function corresponding to the minimum root mean square error of the two is the influence range of satellite observations.

Another technical purpose of the present invention is to provide an ensemble Kalman filter weather assimilation forecasting method, including: 1) in the ensemble Kalman filter assimilation system, selecting one or more variables that can be directly assimilated as model variables; 2 ) By comparing the correlation coefficients between various model variables and satellite observations, select the representative model variables to estimate the localization parameters, the estimated localization parameters include the estimated satellite observations in the vertical direction of the position p ^o and The estimated influence range c ^o of the satellite observation in the vertical direction; 3) The estimated localization parameters are used in the weather assimilation forecast system to obtain the forecast result of the next moment.

Further, the influence range c ^o of the estimated satellite observation in the vertical direction is the GC function width value c ^o , which represents the root mean square error of both the adaptive localization function and the original localization function located at the position p ^o The width parameter of the GC function corresponding to the minimum; the adaptive localization function is obtained by fitting the GC function with the maximum value at p ^o to the original localization function, and the original localization function is the vertical profile of the parameter α ^k ; The parameter α ^k represents the confidence index of the correlation coefficient between a given satellite observation and a model variable with a height of k. When the objective function J ^k takes the minimum value, the confidence index α ^k satisfies:

The objective function J ^k satisfies:

均为某一类给定的卫星观测和某一种位于高度k的模式变量的相关系数r_l ^k按每组G个元素分为M组后的任意一个相关系数，统一记为

相关系数r_l ^k的表达式如下：one of them

are the correlation coefficients of a given type of satellite observation and a certain type of model variable located at height k r _l ^k is any one of the correlation coefficients after each group of G elements is divided into M groups, and is uniformly recorded as

The expression of the correlation coefficient r _l ^k is as follows:

where:

代表卫星观测的集合成员y_l,n的平均值；Δy _l,n denotes the disturbance of the observation y _l,n ; y _l,n denotes the lth observation of the nth ensemble member in the satellite observations given in the ensemble Kalman filter assimilation system, l∈{1,. ..,L} and n∈{1,...,N}; N is the number of ensemble members of the ensemble Kalman filter assimilation system, and L is the number of observations of a certain channel of satellite data;

represents the mean value of ensemble members y _l,n of satellite observations;

表示模式变量

的扰动量：

表示在集合卡曼滤波同化系统中，在水平方向投影至第l个观测变量所在位置的第n个集合成员位于第k层高度的模式变量；l∈{1,...,L},n∈{1,...,N},k∈{1,...,K}；K为模式在垂直方向的层数；

代表各模式变量

的平均值；

Represents a pattern variable

The amount of disturbance:

In the ensemble Kalman filter assimilation system, the nth ensemble member projected to the position of the lth observation variable in the horizontal direction is the pattern variable at the height of the kth layer; l∈{1,...,L},n ∈{1,...,N},k∈{1,...,K}; K is the number of layers of the pattern in the vertical direction;

represents each model variable

average of;

The position p ^o of the estimated observation in the vertical direction is the barometric pressure value at the height where the correlation coefficient r _l ^k is the maximum of the profile.

According to the above-mentioned technical scheme, with respect to the prior art, the present invention has the following beneficial effects:

The present invention obtains an adaptive localization function in the vertical direction within a selected time and space range by using the correlation coefficient between a certain observation variable and a certain mode variable that has been projected to the position of the observation variable. When the present invention is used for forecasting typhoon in regional models, the error of the forecast result compared with the forecast result without the present invention is obviously reduced relative to the observation, and meanwhile, the forecast of the typhoon rapidly intensifying stage is obviously improved by using the present invention. The invention also reduces the sampling error by grouping the correlation coefficients, and further reduces the error between the prediction result and the observation.

Description of drawings

FIG. 1 is a schematic flow chart of the present invention.

Fig. 2 shows the average correlation coefficient, original localization function and simulated temperature between the microwave observation meter AMSU-A channel 6 of NOAA-15 satellite and the model variable temperature over the entire model area when the present invention is applied to Typhoon Yutu (2018). combined localization function.

Figure 3a, Figure 3b are the adaptive localization parameters of the microwave observation meter AMSU-A in the TC area and the non-TC area, the dots and lines in the figure (the non-TC area uses the dots and solid lines, the TC area uses the diamonds and dotted lines) They represent the mean and standard deviation of the localization parameters on each satellite platform, respectively, and the model variable is selected as temperature.

Fig. 4 is the 6-hour forecast relative to conventional observations (a) temperature, (c) wind speed and (e) specific humidity averaged over time in the horizontal region and the root mean square error of the 6-hour forecast without the use of the present invention (control experiment). , and the 6-hour forecast error relative to the control experimental forecast error for (b) temperature, (d) wind speed, and (f) specific humidity using the adaptive localization function computed in the present invention.

Fig. 5 is the (a) path, (b) of the adaptive localization parameters (GGF-Domain, GGF-TC, GGF-Time) calculated using the present invention and the control experiment without using the present invention for Typhoon Yutu (2018) 6-hour forecast of minimum sea level pressure and (c) maximum wind speed. The large dots with thick solid lines are the observed values.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention. Meanwhile, it should be understood that, for the convenience of description, the dimensions of various parts shown in the accompanying drawings are not drawn in an actual proportional relationship. Techniques, methods, and devices known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, such techniques, methods, and devices should be considered part of the authorized description. In all examples shown and discussed herein, any specific value should be construed as illustrative only and not as limiting. Accordingly, other examples of exemplary embodiments may have different values.

As shown in Figures 1 to 5, the adaptive localization method of satellite data assimilation in the vertical direction of the present invention uses the ensemble Kalman filter to assimilate the correlation coefficient between satellite observations and model variables in the system, and uses the grouped correlation coefficient Estimate the original localization functions of the satellite observations and model variables at the current moment and in the current area, and fit these original localization functions with GC functions to obtain adaptive localization functions and related parameters. The adaptive localization function and related parameters can then be applied in the ensemble Kalman filter assimilation system to improve the forecast. Specific steps are as follows:

Step 1. Select the appropriate area and time

The present invention can adaptively estimate the localization function, that is, use the time-varying localization function in different sub-regions.

1.1. Adaptive localization function for different regions

Lei et al. (2015) proposed that different localization parameters should be used for areas with or without precipitation. At the same time, weather systems such as tropical cyclones (TC) have multi-scale characteristics. Therefore, for sub-regions of different weather systems (such as inside and outside the TC area) ) should use different localization parameters. The sub-region should not be selected too small to ensure that the number of observations in it can pass the quality control of step (3.1).

1.2. Adaptive localization function for different assimilation times

The location, strength, structure, and other characteristics of weather systems change over time. Therefore, adaptive localization parameters that follow assimilation epochs can be used, and the localization parameters at a certain time can be estimated from observations and model variables at one, one or more epochs preceding it.

Step 2. Obtain the observed variables and model variables

The satellite observations and model variables of each ensemble member are given in the ensemble Kalman filter assimilation system. The number of layers in the vertical direction of the model is denoted as K, the number of set members is denoted as N, and the number of observations of a certain channel of satellite data is denoted as L.

2.1. Obtaining observed variables

等式中

代表集合成员的平均值。The lth observation of the nth set member denoted by y _l,n . (l∈{1,...,L} and n∈{1,...,N}). At the same time, the disturbance amount can be calculated for the observation y _ln

in the equation

Represents the mean of the set members.

2.2. Get pattern variables

模式变量扰动量的定义方式与观测变量相似，

其中

代表集合成员

的平均值。For the mode variable, firstly project to the position of the lth observed variable in the horizontal direction, and record the variable with the nth set member at the height of the kth layer as

The model variable disturbance is defined in a similar way to the observed variable,

in

Represents set members

average of.

Step 3. Calculate the correlation coefficient

3.1. Quality Control

In order to avoid that the number of observations in the region is too small, it is difficult to eliminate sampling errors and affect the accuracy of the estimated localization function, the lower limit of the number of observations is empirically set to 100. When the number of observations in the area is less than 100, the present invention is not applicable, and the default GC function configuration is used.

3.2. Calculate the correlation coefficient

的相关系数r_l ^k可以由相关系数的定义给出，即：The lth observation y _l and the lth pattern variable

The correlation coefficient r _l ^k of can be given by the definition of correlation coefficient, namely:

Step 4. Calculate the original localization function

4.1. Grouping the correlation coefficients

经验上G取为4。For a given type of satellite observation and a certain model variable, the correlation coefficient r _l ^k of any height k is divided into M groups according to each group of G elements, that is, L=M*G, r _l ^k can be rewritten as

In experience, G is taken as 4.

4.2. Localization function value at a certain height

分别记为“真实”的相关系数，则局地化后的相关系数

与“真值”的目标函数为each of the mth group

are recorded as "true" correlation coefficients, then the localized correlation coefficients

The objective function with "truth value" is

The value of α ^k that minimizes the objective function should be

4.3. Calculate the original localization function

α ^k in step (3.2) represents the confidence index of the correlation coefficient between this kind of satellite observation and the model variable with height k, and the vertical profile of α ^k (k∈{1,...,K}) is Estimated vertical raw localization function.

Step 5. Fitting parameters

The value of the GC function is usually the largest at the location of the observation, and decreases as the distance between the observation and the model variable increases, and the function value decreases to 0 outside a certain range.

5.1. Find the vertical observation position

The barometric pressure value at the height of the maximum correlation coefficient profile is taken as the position p ^o in the vertical direction of this satellite observation.

5.2. Fitting GC function width (range of influence)

Fit the original localization function with the GC function, and find the GC function width value c ^o that minimizes the root mean square error of both.

For satellite observations, currently only two parameters, the adaptive GC width c ^o and the observation position p ^o in the vertical direction are used to fit the original localization function.

Step 6. Apply the adaptive localization function to the pattern

6.1. Selecting Mode Variables

The variables directly assimilated in the ensemble Kalman filter assimilation system can be used as model variables. For the observation of a certain channel of a certain satellite, the adaptive localization parameter corresponding to the model variable with a larger correlation coefficient is selected as the adaptive localization parameter of this observation.

6.2. Applying an adaptive localization function

Apply the adaptive localization parameter corresponding to each channel of each observation of each satellite platform in (6.1) to the assimilation prediction model, check the prediction result of the model, and use the adaptive localization parameter of the present invention. Results have improved.

Example

The present invention uses the correlation coefficient of satellite observations and model variables in the ensemble Kalman filter assimilation system, taking the simulation of typhoon Yutu (2018) in the regional model WRF as an example, and estimates the localization function of a certain satellite observation and model variables according to the correlation coefficient. and related parameters. These correlation coefficients are then put into the assimilation forecast system, and the 6-hour forecast of the model is observed and verified, and the forecast errors obtained with and without the present invention are compared. The forecast results of the path and intensity (minimum sea level pressure and maximum wind speed) of Typhoon Yutu (2018) with and without the use of the present invention were also examined. Figure 1 shows a flow chart of the present invention.

Step 1. Determine the area and time of application of the present invention

The WRF-ensemble Kalman filter cycle assimilation forecast experiment was carried out from 1200UTC on October 19, 2018 to 1200UTC on November 2, 2018. It takes time for the model to adapt to the new assimilation method, so the forecast two days before the start of the cycle is discarded. The control experiment was a prediction experiment without the use of the present invention, and all other settings of the experiment using the present invention were the same as the control experiment.

1.1. Determine the area of application of the present invention

Scheme 1: The entire pattern coverage area is not differentiated, and all samples in the entire area are used to estimate the localization function and related parameters using the present invention.

Option 2: Considering the multi-scale characteristics of tropical cyclones (TC), distinguish the TC area and the non-TC area, and use the present invention to estimate the localization function and related parameters for the samples of these two areas respectively. The TC area is defined as a square area with the position of the TC at the current moment as the center and a side length of 20 latitude and longitude.

1.2. Determine the assimilation time for the application of the present invention

Option 1: Estimate the adaptive localization function using observations and model variables from some representative times in the control experiment. The times used in the Yutu (2018) simulation experiment include the four periods before the rapid intensification of the typhoon (from 10 0000UTC on 22 October to 1800 UTC on 22 October) and four periods after the rapid intensification (from 1800 UTC on 23 October to 1200 UTC on 24 October).

Option 2: Use the time-varying localization parameters to estimate the adaptive localization function using observations and model variables from the previous moment or two.

Four experiments were designed with different regions and assimilation times as follows:

Step 2. Obtain the observed variables and model variables

The satellite observations and model variables of each ensemble member are given in the ensemble Kalman filter assimilation system. The number of layers in the vertical direction of the model is denoted as K, the number of set members is denoted as N, and the number of observations of a certain channel of satellite data is denoted as L. In the experiment, the number of ensemble members is 80, and the adaptive localization functions and parameters are calculated for the observations of each channel of each satellite instrument in turn. 2.1. Obtaining observed variables

等式中

代表集合成员的平均值。The lth observation of the nth set member denoted by y _l,n . (l∈{1,...,L} and n∈{1,...,N}). At the same time, the disturbance amount can be calculated for the observation y _l,n

in the equation

Represents the mean of the set members.

2.2. Get pattern variables

模式变量扰动量的定义方式与观测变量相似，

其中

代表集合成员

的平均值。For the mode variable, firstly project to the position of the lth observed variable in the horizontal direction, and record the variable with the nth set member at the height of the kth layer as

The model variable disturbance is defined in a similar way to the observed variable,

in

Represents set members

average of.

Step 3. Calculate the correlation coefficient

3.1. Quality Control

In order to avoid that the number of observations in the region is too small, the sampling error that is difficult to eliminate affects the accuracy of the estimated localization function, the lower limit of the number of observations is empirically set to 100. When the number of observations in the area is less than 100, the present invention is not applicable, and the default GC function configuration is used. The number of samples of individual channels within the TC region of the GGF-TC-only experiment was insufficient in the experiments.

3.2. Calculate the correlation coefficient

的相关系数r_l ^k可以由相关系数的定义给出，即

The lth observation y _l and the lth pattern variable

The correlation coefficient r _l ^k of can be given by the definition of the correlation coefficient, namely

The dotted line in Fig. 2 represents the average correlation coefficient at each altitude of the observations of the AMSU-A instrument channel 6 carried on the satellite NOAA-15 in the GGF-Domain experiment.

Step 4. Calculate the original localization function

4.1. Grouping the correlation coefficients

经验上G取为4。For a given type of satellite observation and a certain model variable, the correlation coefficient r _l ^k of any height k is divided into M groups according to each group of G elements, that is, L=M*G, r _l ^k can be rewritten as

In experience, G is taken as 4.

4.2. Localization function value at a certain height

分别记为“真实”的相关系数，则局地化后的相关系数

与“真值”的目标函数为

each of the mth group

are recorded as "true" correlation coefficients, then the localized correlation coefficients

The objective function with "truth value" is

The value of α ^k that minimizes the objective function should be:

4.3. Calculate the original localization function

α ^k in step (3.2) represents the confidence index of the correlation coefficient between this kind of satellite observation and the model variable with height k, and the vertical profile of α ^k (k∈{1,...,K}) is Estimated vertical raw localization function. The dotted-line curve in Fig. 2 represents the original localization function at each altitude level observed by the AMSU-A instrument channel 6 carried by the satellite NOAA-15 in the GGF-Domain experiment.

Step 5. Fitting parameters

The value of the GC function is usually the largest at the location of the observation, and decreases as the distance between the observation and the model variable increases, and the value of the function decreases to 0 outside a certain range.

5.1. Find the vertical observation position

The barometric pressure value at the height of the maximum correlation coefficient profile is taken as the position p ^o in the vertical direction of this satellite observation.

5.2. Fitting GC function width (range of influence)

Fit the original localization function with the GC function, and find the GC function width value c ^o that minimizes the root mean square error of both.

The solid line curve in Figure 2 represents the result of fitting the original localization function to the observation of the AMSU-A instrument channel 6 carried on the satellite NOAA-15 in the GGF-Domain experiment. According to the figure, the estimated observation position of this observation in this experiment is 505.5hPa, and the localization scale is 2.2ln(hPa).

Step 6. Apply the adaptive localization function to the pattern

6.1. Selecting Mode Variables

The variables directly assimilated in the ensemble Kalman filter assimilation system can be used as model variables. Two model variables, temperature and specific humidity, were selected in the experiment. For the observations from the instrument AMSU-A, the correlation coefficient between the observation and the model variable temperature is greater than the correlation coefficient with the specific humidity, so temperature was used to estimate the adaptive localization parameter.

Figure 3a and Figure 3b show the average values of localization parameters estimated in the TC area and the non-TC area on different satellite platforms in the GGF-TC experiment (the non-TC area is a circle and the TC area is a diamond) and a standard Difference (the non-TC area is a solid line, that is, the line above and below the dot is a solid line, and the TC area is a dashed line, that is, the line above and below the diamond is a dashed line). The vertical positions estimated for AMSU-A observations are similar for TC and non-TC regions, but the estimated localized widths in TC regions are generally larger than those estimated in non-TC regions. These adaptive localization parameters will be used in cyclic assimilation forecasts to examine the effects of adaptive localization parameters on forecasts. Adaptive localization parameters for other experiments and other kinds of satellite observations can also be estimated accordingly.

6.2. Applying an adaptive localization function

6.2.1. Using routine observations to check forecast results

The control experiments and three adaptive localization experiments using the present invention (GGF-Domain, GGF-TC, GGF-Time) were used to examine the 6-hour forecast errors using conventional observations (temperature, wind speed, specific humidity). Fig. 4(a), Fig. 4(c), Fig. 4(e) respectively show the average root mean square error of the control experiment in time and in the horizontal area by three kinds of routine observation test of temperature, wind speed and specific humidity. Fig. 4(b), Fig. 4(d), Fig. 4(f) show the difference between the error obtained after using the present invention and the error of the control experiment, the negative value in the figure indicates that the experimental result using the present invention is better than the control experiment, Positive values indicate worse results after using the present invention; the short solid line above the graph represents the average value in the vertical direction. In general, the error of the prediction results after using the present invention is smaller than that of the control experiment, and the GGF-Time experiment with the adaptive localization parameter changing with time is better than the GGF-Domain experiment with constant adaptive localization parameters, distinguishing TC and non-TC. The GGF-TC experiment of the adaptive localization parameters of the region has a slight advantage over GGF-Time and GGF-Domain.

6.2.2. Use the track and intensity of the typhoon to check the forecast results

Figure 5 shows the path (Figure 5a), minimum sea level pressure ( Fig. 5b) and forecast effects of maximum wind speed (Fig. 5c). The track predictions of both the control experiment and the experiment using the present invention are very close to the observations, but the track prediction of the GGF experiment is slightly better than that of the control experiment at the onset of the typhoon (Fig. 5a). For intensity forecasts, i.e. minimum sea level pressure and maximum wind speed, the predictions from the GGF experiments were much closer to the observations than the control experiments. Experiments using the present invention capture the rapid enhancement (RI) process better than control experiments. However, the typhoon peak intensity predicted by the experiments of the present invention is still lower than the observed value, which may be due to insufficient model resolution to resolve the gradients of the mass field and wind field. The three experiments using the present invention have similar path and intensity predictions, and their prediction results are better than the control experiments.

Claims (10)

1. an adaptive localization method of satellite data assimilation in vertical direction, it is characterized in that: according to the arbitrary sub-region scope that provides in the set Kalman filter assimilation system, be in the satellite observation and model variable of arbitrary time, Calculate the correlation coefficient between satellite observations and model variables in the vertical direction; then use the correlation coefficient to estimate the original localization function of the satellite observations and model variables in the vertical direction at the current moment and in the current area; estimate according to the correlation coefficient profile Get the position p ^{o of the satellite observation in the vertical direction, and fit the above original localization function with the maximum value of the GC function at the position p o to} obtain the influence range c ^o of the satellite observation in the vertical direction; The estimated position p ^o of the direction and the influence range c ^o of the satellite observation in the vertical direction are the adaptive localization parameters. 2. The adaptive localization method of satellite data assimilation in vertical direction according to claim 1, it is characterized in that, in the specific sub-region range given in the set Kalman filter assimilation system, in the satellite observation of specific time times and mode variables are: Observe the disturbance of y _l,n :

where: observation y _l,n denotes the lth observation of the nth set member in the satellite observations given in the set Kalman filter assimilation system, l∈{1,...,L} and n∈{1, ...,N}; N is the number of ensemble members of the ensemble Kalman filter assimilation system, and L is the number of observations of a certain channel observed by a certain satellite;

Represents the mean value of ensemble members y _l,n of satellite observations; The amount of disturbance of the mode variable:

where: pattern variable

In the ensemble Kalman filter assimilation system, the nth ensemble member projected to the position of the lth observation variable in the horizontal direction is the pattern variable at the height of the kth layer; l∈{1,...,L},n ∈{1,...,N},k∈{1,...,K}; K is the number of layers of the pattern in the vertical direction;

represents each model variable

average of. 3. The adaptive localization method of satellite data assimilation in vertical direction according to claim 1 or 2, characterized in that, for a certain type of given satellite observation and a certain pattern in the set Kalman filter assimilation system variable, and its correlation coefficient r _l ^k at any height k is:

where:

represents the pattern variable

Δy _l,n represents the disturbance of observed y _l,n ; y _l,n denotes the lth observation of the nth set member in the satellite observations given in the set Kalman filter assimilation system, l∈{1,...,L} and n∈{1,... ,N}; N is the number of ensemble members of the ensemble Kalman filter assimilation system, and L is the number of observations of a certain channel observed by a satellite;

In the ensemble Kalman filter assimilation system, the representative pattern variable is the pattern variable of the nth ensemble member at the height of the kth layer that is projected in the horizontal direction to the position of the lth observation variable; l∈{1,…,L},n ∈{1,…,N},k∈{1,…,K}, where K is the number of layers of the pattern in the vertical direction. 4. The adaptive localization method of satellite data assimilation in vertical direction according to claim 3, is characterized in that, the correlation between using any satellite observation and any mode variable at any height k in the vertical direction Before estimating the original localization function of this kind of satellite observation and model variable in the vertical direction at the current moment and the current area, the coefficient r _l ^k needs to be grouped by the correlation coefficient r _l ^k . is M groups, and any one of the correlation coefficients in each group is recorded as

m∈{1,...,M}, g∈{1,...,G}. 5. The adaptive localization method in vertical direction of satellite data assimilation according to claim 1 or 2, wherein the original localization function is the vertical profile of parameter α ^k ; parameter α ^k represents that for a certain The confidence index of the correlation coefficient between the satellite observations and the model variable of altitude k; If considering each correlation coefficient

have the same probability as the true value, then the localized correlation coefficient

The objective function J ^k should satisfy:

When the objective function J ^k takes the minimum value, the confidence index α ^k satisfies:

where:

After the representative correlation coefficient r _l ^k is divided into M groups containing G members in each group, any correlation coefficient in each group of correlation coefficients; The correlation coefficient r _l ^k represents the correlation coefficient at any height k for a given type of satellite observation and a certain model variable. 6. the adaptive localization method of satellite data assimilation according to claim 1 in vertical direction, is characterized in that, the estimated position p ^o of satellite observation in vertical direction: is the height where correlation coefficient _r ^k profile maximum value is located air pressure value. 7. The adaptive localization method of satellite data assimilation in vertical direction according to claim 1, is characterized in that, the acquisition mode of the influence range c ^o of satellite observation in vertical direction: first with the GC located at p ^o position The function maximum fits the original localization function to obtain the adaptive localization function; Then, by comparing the adaptive localization function and the original localization function, the influence range c ^o of the satellite observation in the vertical direction can be obtained, and the influence range c ^o of the satellite observation in the vertical direction is the GC function width value c ^o , indicating The width parameter of the GC function corresponding to the minimum root mean square error of both the adaptive localization function and the original localization function at the p ^o position. 8. The adaptive localization method of satellite data assimilation in vertical direction according to claim 1, is characterized in that, comprises the following steps: (1) Select the appropriate area and time For different weather systems, the satellite observations and model variables in a specific sub-region and at a specific time are given through the ensemble Kalman filter assimilation system; The specific sub-area includes TC area and/or non-TC area; TC area is defined as a square area with the location of the tropical cyclone at the current moment as the center and a side length of 20 longitude and latitude; It is necessary to ensure that the total number of observations at all times in a specific sub-region is not less than O, O=10 ² ; The specific time is a representative time in the given satellite observation and model variables or the previous time or the previous two time when the localization parameter is estimated at the current time; (2) Obtain observation variables and model variables Observe the disturbance of y _l,n :

where: observation y _l,n denotes the lth observation of the nth set member of satellite observations given in the set Kalman filter assimilation system, l∈{1,...,L} and n∈{1,. ..,N}; N is the number of ensemble members of the ensemble Kalman filter assimilation system, and L is the number of observations of a certain channel of satellite data;

represents the mean value of ensemble members y _l,n of satellite observations; pattern variable

The amount of disturbance:

where: pattern variable

In the ensemble Kalman filter assimilation system, the nth ensemble member projected to the position of the lth observation variable in the horizontal direction is the pattern variable at the height of the kth layer; l∈{1,...,L},n ∈{1,...,N},k∈{1,...,K}; K is the number of layers of the pattern in the vertical direction;

represents each model variable

average of; (3) Calculate the correlation coefficient The lth observation y _l and the lth pattern variable

The correlation coefficient r _l ^k of is:

(4) Calculate the original localization function For a given type of satellite observation and a certain model variable, the correlation coefficient r _l ^k of any height k is divided into M groups according to each group of G elements, and any correlation coefficient in each group of correlation coefficients is recorded as

m∈{1,...,M}, g∈{1,...,G}; If considering each correlation coefficient

have the same probability to become the true value, then the localized correlation coefficient

The objective function J ^k satisfies:

α ^k represents the confidence index of the correlation coefficient between this kind of satellite observation and the model variable with height k. When the objective function J ^k takes the minimum value, the confidence index α ^k satisfies:

The vertical profile of α ^k is the estimated original localization function in the vertical direction; (5) Fitting parameters Find out the observation position p ^o in the vertical direction; Fit the original localization function with the GC function whose maximum value is at p ^o , and the obtained result is the adaptive localization function; Through the adaptive localization function and the original localization function, the estimated influence range c ^o of the satellite observation in the vertical direction can be obtained; the estimated influence range c ^o of the satellite observation in the vertical direction is the GC function width value c ^o , Represents the width parameter of the GC function that minimizes the root mean square error of both the adaptive localization function and the original localization function at position p ^o . 9. An ensemble Kalman filter weather assimilation forecasting method is characterized in that, comprising the following steps: 1) in the ensemble Kalman filter assimilation system, select 1 and more variables that can be directly assimilated as model variables; 2) By comparing the correlation coefficients between various model variables and satellite observations, the representative model variables are selected to estimate the localization parameters. The estimated ^localization parameters include the estimated position of the satellite observations in the vertical direction and 3) The estimated ^localization parameters are used in the weather assimilation forecast system to obtain the forecast result of the next moment. 10. The ensemble Kalman filter weather assimilation forecasting method according to claim 9, characterized in that: the influence range c ^o of the estimated satellite observation in the vertical direction is the GC function width value c ^o , which means that the estimated satellite observation is located at the position p ^o . The width parameter of the GC function corresponding to the minimum root mean square error of both the adaptive localization function and the original localization function; the adaptive localization function fits the original localization by the GC function with the maximum value at p ^o function, and the original localization function is the vertical profile of the parameter α ^k ; the parameter α ^k represents the confidence index of the correlation coefficient between the given satellite observation and the model variable of height k, when the objective function J ^k When the value is the smallest, the confidence index α ^k satisfies:

The objective function J ^k satisfies:

one of them

are the correlation coefficients of a given type of satellite observation and a certain type of model variable located at height k r _l ^k is any one of the correlation coefficients after each group of G elements is divided into M groups, and is uniformly recorded as

m∈{1,...,M}, g∈{1,...,G}; the expression of the correlation coefficient r _l ^k is as follows:

where:

Δy _l,n denotes the disturbance of the observation y _l,n ; y _l,n denotes the lth observation of the nth ensemble member in the satellite observations given in the ensemble Kalman filter assimilation system, l∈{1,. ..,L} and n∈{1,...,N}; N is the number of ensemble members of the ensemble Kalman filter assimilation system, and L is the number of observations of a certain channel of satellite data;

represents the mean value of ensemble members y _l,n of satellite observations;

Represents a pattern variable

The amount of disturbance:

In the ensemble Kalman filter assimilation system, the nth ensemble member projected in the horizontal direction to the position of the lth observation variable is the pattern variable at the height of the kth layer; l∈{1,…,L},n∈{ 1,…,N},k∈{1,…,K}; K is the number of layers in the vertical direction;

represents each model variable

average of; The position p ^o of the estimated observation in the vertical direction is the barometric pressure value at the height where the correlation coefficient r _l ^k is the maximum of the profile.

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