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

Satellite data assimilation vertical direction adaptive localization method and integrated Kalman filtering weather assimilation forecasting method Download PDF

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CN111259324A
CN111259324A CN202010013183.6A CN202010013183A CN111259324A CN 111259324 A CN111259324 A CN 111259324A CN 202010013183 A CN202010013183 A CN 202010013183A CN 111259324 A CN111259324 A CN 111259324A
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雷荔傈
谈哲敏
储可宽
王晨
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Abstract

The invention discloses an adaptive localization method for satellite data assimilation in the vertical direction and an integrated Kalman filtering weather assimilation forecasting method. The adaptive localization method calculates the correlation coefficient of observation data and mode variables according to any observation data and mode variables given in the collective Kalman filtering assimilation system; estimating the original localization function of the observation data and the mode variable by using the grouped correlation coefficient; estimating the position p of the satellite observation from the profile of the correlation coefficientoAnd locate the original localization function at poFitting the maximum value of the GC function at the position to obtain the influence range c of satellite observationo. Position poC range of influenceoI.e. the adaptive localization parameters sought by the present invention. Will be provided withThe obtained adaptive localization parameters are used for forecasting typhoon in a regional mode, compared with the forecasting result without the method, the forecasting result has obviously reduced error relative to observation, and meanwhile, the method also obviously improves the forecasting of a typhoon rapid enhancement stage.

Description

Satellite data assimilation vertical direction adaptive localization method and integrated Kalman filtering weather assimilation forecasting method
Technical Field
The invention relates to a weather assimilation forecasting method, in particular to an integrated Kalman filtering weather assimilation forecasting method based on an adaptive localization technology.
Background
Data assimilation is a technique that uses observations to correct pattern variables to obtain the best estimate of the current atmospheric state.
Collective kalman filtering is a common data assimilation method, but collective kalman filtering is affected by sampling errors when applied to a high-dimensional atmospheric mode, and sample errors can be handled by localization. Localization generally assumes that correlations farther from the observation are more likely to be spurious. Commonly used localization functions are Gaspari and Cohn (Gaspari and Cohn1999) functions, abbreviated GC functions. When the localization function is used to assimilate observed data in the collective kalman filter assimilation system, it is a common practice to: the influence of the observation data on the nearby mode variables is reserved, the influence of the observation data on the mode variables far away from the observation data is reduced, and meanwhile, the influence of the observation data outside a certain range on the mode variables is ignored.
However, in non-local observation such as satellite observation, the influence range of the position and the vertical direction of observation is not well defined, and localization cannot be directly performed. Meanwhile, for observation at different time and in different regions, the localization functions of satellite observation should be different, but the prior art cannot adaptively estimate the needed localization functions.
Therefore, there is a need for an adaptive localization scheme that provides adaptive localization functions in the vertical direction for satellite observations at different platforms and channels, different regions, and different times.
Disclosure of Invention
The invention provides an adaptive localization method for assimilating satellite data in a vertical direction aiming at the defects of the prior art. The method uses the correlation coefficient of satellite observation and mode variables in an integrated Kalman filtering assimilation system, estimates the original localization functions of the satellite observation and mode variables at the current time and in the current area by using the grouped correlation coefficient, and fits the original localization functions by a GC function so as to obtain the adaptive localization functions and the relevant parameters. The obtained adaptive localization function and related parameters are applied to an integrated Kalman filtering assimilation system so as to estimate the state of the current atmosphere by more effectively using satellite data, thereby improving the accuracy of weather forecast.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
an adaptive localization method for assimilation of satellite data in a vertical direction, comprising: calculating the correlation coefficient of the satellite observation and the mode variable in the vertical direction according to the satellite observation and the mode variable in any time in any sub-region range given in the collective Kalman filtering assimilation system; then, estimating an original localization function of the satellite observation and mode variable in the vertical direction at the current time and in the current area by using the correlation coefficient; estimating the position p of the satellite observation in the vertical direction according to the correlation coefficient profileoAnd is located at poFitting the maximum value of the GC function at the position to the original localization function to obtain the influence range c of the satellite observation in the vertical directiono(ii) a Estimated position p of satellite observation in vertical directionoThe influence range c of the satellite observation in the vertical directionoI.e. adaptive localization parameters.
Further, the satellite observation and mode variables within a specific sub-region range and at a specific time given in the collective kalman filter assimilation system are respectively:
observation yl,nThe disturbance amount of (2):
Figure BDA0002357887530000021
wherein: observation yl,nAn L-th observation representing an N-th set member of the satellite observations given in the set kalman filter assimilation system, L ∈ { 1.. and L } and N ∈ { 1.. and N }; n is a setThe number of members of a set of the Kalman filtering assimilation system is L, and L is the number of observation numbers of a certain channel observed by a certain satellite;
Figure BDA0002357887530000022
set member y representing satellite observationsl,nAverage value of (d);
disturbance amount of mode variable:
Figure BDA0002357887530000023
wherein: mode variables
Figure BDA0002357887530000024
The mode variable is represented in an aggregate Kalman filtering assimilation system, and an nth aggregate member projected to the position of the l observation variable in the horizontal direction is positioned at the height of a kth layer; l is in the range of {1, …, L }, N is in the range of {1,. eta., N }, and K is in the range of {1,. eta., K }; k is the number of layers of the mode in the vertical direction;
Figure BDA0002357887530000031
representing variables of each mode
Figure BDA0002357887530000032
Average value of (a).
Further, for a given satellite observation of a certain type and a certain mode variable in the collective Kalman filtering assimilation system, the correlation coefficient r of the satellite observation at any height k isl kComprises the following steps:
Figure BDA0002357887530000033
in the formula:
Figure BDA0002357887530000034
representing mode variables
Figure BDA0002357887530000035
The amount of disturbance of; Δ yl,nRepresentative of observation yl,nThe amount of disturbance of;
yl,nan L-th observation representing an N-th set member of the satellite observations given in the set kalman filter assimilation system, L ∈ { 1.. and L } and N ∈ { 1.. and N }; n is the number of set members of the set Kalman filtering assimilation system, and L is the number of observations of a certain channel observed by a certain satellite;
Figure BDA0002357887530000036
representing the mode variable of the nth set member positioned at the kth layer height, which is projected to the position of the l observation variable in the horizontal direction in the set Kalman filtering assimilation system; l is the number of layers of the mode in the vertical direction, wherein L is the { 1.,. L }, N is the { 1.,. N }, and K is the number of layers of the mode in the vertical direction.
Further, the correlation coefficient r between the mode variables observed with an arbitrary satellite and at an arbitrary height k in the vertical directionl kBefore estimating the original localization function of the satellite observation and mode variable in the vertical direction at the current time and in the current area, a correlation coefficient r needs to be obtainedl kGrouping, wherein the grouping mode is as follows: dividing each group of G elements into M groups, and recording any one of the correlation coefficients in each group as
Figure BDA0002357887530000037
Figure BDA0002357887530000038
Further, the original localization function is the parameter αkPerpendicular profile of (A), parameter αkA confidence index representing the correlation coefficient of the mode variable for a certain satellite observation and altitude k;
if each correlation coefficient is looked at
Figure BDA0002357887530000041
All have the same probability as true value, the correlation coefficient after localization
Figure BDA0002357887530000042
Is the objective function J ofkIt should satisfy:
Figure BDA0002357887530000043
when the objective function JkWhen taken at minimum, confidence index αkSatisfies the following conditions:
Figure BDA0002357887530000044
in the formula:
Figure BDA0002357887530000045
represents the correlation coefficient rl kDividing the correlation coefficients into M groups containing G members, and then selecting any one of the correlation coefficients in each group;
coefficient of correlation rl kRepresenting the correlation coefficient at any altitude k for a given class of satellite observations and for a mode variable.
Further, the satellite observes an estimated position p in the vertical directiono: is a correlation coefficient rl kThe air pressure value at the height of the maximum of the profile.
Further, the influence range c of the satellite observation in the vertical directionoThe acquisition mode of (1): first is located at poFitting the GC function maximum value at the position to an original localization function to obtain an adaptive localization function;
then, by comparing the adaptive localization function with the original localization function, the influence range c of the satellite observation in the vertical direction can be obtainedoThe range of influence of the satellite observation in the vertical direction coAs a width value c of the GC functionoIs indicated as being located at poA width parameter of the GC function corresponding to the least root mean square error of both the adaptive localization function and the original localization function at the location.
Further, the localization method comprises the following steps:
(1) selecting proper area and time
Aiming at different weather systems, satellite observation and mode variables in a specific sub-area range and at a specific time are given through a collective Kalman filtering assimilation system;
the specific sub-area comprises a TC area and/or a non-TC area; the TC area is defined as a square area with the position of the tropical cyclone at the current moment as the center and the side length of 20 longitude and latitude;
the specific sub-region range needs to ensure that the total number of observations in all times is not less than O, and O is 102；
The specific time is a representative time in the observation and mode variables of the given satellite or a previous time or two times before the local localization parameter at the current time is estimated;
(2) obtaining observed and mode variables
Observation yl,nThe disturbance amount of (2):
Figure BDA0002357887530000051
wherein: observation yl,nAn L-th observation representing an N-th 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 members of the set Kalman filtering assimilation system, L is the number of observations of a certain channel of certain satellite data;
Figure BDA0002357887530000052
set member y representing satellite observationsl,nAverage value of (d);
mode variables
Figure BDA0002357887530000053
The disturbance amount of (2):
Figure BDA0002357887530000054
wherein: mode variables
Figure BDA0002357887530000055
Representation in collective Kalman Filter assimilation SystemThe model variable of the nth set member at the kth layer height projected to the position of the l observation variable in the horizontal direction; l belongs to { 1.,. L }, N belongs to { 1.,. N }, and K belongs to {1, …, K }; k is the number of layers of the mode in the vertical direction;
Figure BDA0002357887530000056
representing variables of each mode
Figure BDA0002357887530000057
Average value of (d);
(3) calculating a correlation coefficient
First observation ylAnd the l mode variable
Figure BDA0002357887530000058
Is related tol kComprises the following steps:
Figure BDA0002357887530000059
(4) computing original localization functions
For a given satellite observation of a certain type and a certain mode variable, the correlation coefficient r of any altitude k is determinedl kDividing each group of G elements into M groups, and recording any one of the correlation coefficients in each group as
Figure BDA0002357887530000061
If each correlation coefficient is looked at
Figure BDA0002357887530000062
If all the same probability becomes true value, the locally correlated coefficient
Figure BDA0002357887530000063
Is the objective function J ofkSatisfies the following conditions:
Figure BDA0002357887530000064
αka confidence index representing the correlation coefficient for this satellite observation and for a mode variable of height k, when the objective function JkWhen taken at minimum, confidence index αkSatisfies the following conditions:
Figure BDA0002357887530000065
αkthe vertical profile of (a) is an estimated original localization function in the vertical direction;
(5) fitting parameters
Finding the observation position p in the vertical directiono；
At maximum value of poFitting the original localization function by the GC function to obtain an adaptive localization function;
obtaining the estimated GC function width value c through the adaptive localization function and the original localization functionoWidth value c of GC functionoIndicates that is located at poThe least root mean square error of the original localization function and the original localization function corresponds to the width parameter of the GC function, namely the influence range of the satellite observation.
Another technical object of the present invention is to provide an ensemble kalman filter weather assimilation forecast method, including: 1) in the collective Kalman filtering assimilation system, 1 or more variables which can be directly assimilated are selected as mode variables; 2) selecting the characteristic mode variables to estimate the localization parameters by comparing the correlation coefficients between the various types of mode variables and the satellite observations, the estimated localization parameters including the estimated position p of the satellite observations in the vertical directionoAnd estimated range of influence c of satellite observations in the vertical directiono(ii) a 3) And using the estimated localized parameters in a weather assimilation forecast system to obtain a forecast result at the next moment.
Further, the estimated influence range c of the satellite observation in the vertical directionoAs a width value c of the GC functionoDenotes to be located at poRoot mean square error minimization of both the adaptive localization function and the original localization function at a locationWidth parameters of the corresponding GC functions; the adaptive localization function is located at p by a maximumoIs obtained by fitting the original localization function, which is the parameter αkPerpendicular profile of (A), parameter αkConfidence index representing the correlation coefficient between a given satellite observation and a mode variable of height k when the objective function JkWhen taken at minimum, confidence index αkSatisfies the following conditions:
Figure BDA0002357887530000071
objective function JkSatisfies the following conditions:
Figure BDA0002357887530000072
therein
Figure BDA0002357887530000073
A correlation coefficient r for a given satellite observation of a certain type and a certain mode variable at altitude kl kDividing each group of G elements into M groups, and uniformly recording as any one correlation coefficient
Figure BDA0002357887530000074
Figure BDA0002357887530000075
Coefficient of correlation rl kThe expression of (a) is as follows:
Figure BDA0002357887530000076
in the formula:
Figure BDA0002357887530000081
Δyl,nrepresents observation yl,nThe amount of disturbance of; y isl,nLth representing nth set member in satellite observation given in set Kalman Filter assimilation SystemObserving that L belongs to { 1.,. L } and N belongs to { 1.,. N }; n is the number of members of the set Kalman filtering assimilation system, L is the number of observations of a certain channel of certain satellite data;
Figure BDA0002357887530000082
set member y representing satellite observationsl,nAverage value of (d);
Figure BDA0002357887530000083
representing mode variables
Figure BDA0002357887530000084
The disturbance amount of (2):
Figure BDA0002357887530000085
the mode variable is represented in an aggregate Kalman filtering assimilation system, and an nth aggregate member projected to the position of the l observation variable in the horizontal direction is positioned at the height of a kth layer; l is in the range of { 1.,. L }, N is in the range of { 1.,. N }, and K is in the range of { 1.,. K }; k is the number of layers of the mode in the vertical direction;
Figure BDA0002357887530000086
representing variables of each mode
Figure BDA0002357887530000087
Average value of (d);
position p of the estimated observation in the vertical directionoIs a correlation coefficient rl kThe air pressure value at the height of the maximum of the profile.
According to the technical scheme, compared with the prior art, the invention has the following beneficial effects:
the invention obtains the adaptive localization function in the vertical direction in the selected time and space range by utilizing the correlation coefficient of a certain observation variable and a certain mode variable projected to the position of the observation variable. The method is used for forecasting the typhoon in the regional mode, compared with the forecasting result without the method, the forecasting result has obviously reduced error relative to observation, and meanwhile, the forecasting of the typhoon fast enhancement stage is obviously improved by using the method. The invention also reduces the sampling error by grouping the related coefficients, and further reduces the error between the forecast result and the observation.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
FIG. 2 shows the average correlation coefficient, the original localization function and the fitted localization function of the microwave observation instrument AMSU-A channel 6 loaded on a satellite NOAA-15 and the mode variable temperature in the whole mode area when the invention is applied to a typhoon rabbit (2018).
Fig. 3a and 3b show adaptive localization parameters of the microwave observer AMSU-a in the TC region and the non-TC region, where points and lines (the non-TC region uses a circular point and a solid line, and the TC region uses a diamond shape and a dotted line) respectively represent the average value and standard deviation of the localization parameters in each satellite platform, and the mode variable is selected as the temperature.
FIG. 4 is a root mean square error of the 6 hour forecast obtained without the use of the present invention (control experiment) versus the conventional observed (a) temperature, (c) wind speed and (e) specific humidity averaged over the horizontal area and over time, and the difference of the 6 hour forecast error obtained using the adaptive localization function calculated by the present invention versus the control experiment forecast error versus (b) temperature, (d) wind speed and (f) specific humidity.
FIG. 5 is a 6 hour forecast of (a) path, (b) lowest sea level air pressure, and (c) maximum wind speed for a typhoon rabbit (2018) using the adaptive localization parameters (GGF-Domain, GGF-TC, GGF-Time) calculated by the present invention and a control experiment not using the present invention. Wherein the large dots with thick solid lines are observed values.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and 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. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention. Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values.
As shown in fig. 1 to 5, the adaptive localization method for assimilating satellite data in the vertical direction according to the present invention uses correlation coefficients of satellite observation and mode variables in an integrated kalman filter assimilation system, estimates original localization functions of the satellite observation and mode variables at the current time and in the current area by using the grouped correlation coefficients, and fits the original localization functions with GC functions to obtain the adaptive localization functions and the relevant parameters. The adaptive localization function and associated parameters may then be applied in an ensemble kalman filter assimilation system to improve the prediction. The method comprises the following specific steps:
step one, selecting proper area and time
The invention can adaptively estimate the localization function, namely using the localization function which changes along with time in different sub-areas.
1.1. Adaptive localization function for different regions
Lei et al (2015) proposes to use different localization parameters for regions with or without precipitation, while weather systems such as Tropical Cyclone (TC) have multi-scale features, so different localization parameters should be used for sub-regions of different weather systems (e.g. inside and outside the TC region). The sub-regions should not be chosen too small to ensure that the number of observations therein can be controlled by the quality of step (3.1).
1.2. Adaptive localization function for different assimilation moments
The location, intensity, structure, etc. of the weather system changes over time. Thus, adaptive localization parameters that follow changes in the moment of assimilation can be used, and localization parameters at a time can be estimated from observations and mode variables one, some, or more times before it.
Step two, acquiring observation variables and mode variables
Satellite observation and mode variables of all set members are given in the set Kalman filtering assimilation system. The number of layers of the pattern in the vertical direction is marked as K, the number of members of the set is marked as N, and the number of observations of a certain channel of certain satellite data is marked as L.
2.1. Obtaining an observed variable
With yl,nThe l-th observation of the n-th set member of the representation. (L ∈ { 1.,. L } and N ∈ { 1.,. N }). For observation y at the same timelnCan calculate the disturbance quantity
Figure BDA0002357887530000101
In the equation
Figure BDA0002357887530000102
Represents the mean of the members of the set.
2.2. Obtaining a mode variable
For the mode variable, firstly, the model variable is projected to the position of the l observed variable in the horizontal direction, and the variable of the n set member at the k layer height is recorded as
Figure BDA0002357887530000103
The disturbance amount of the mode variable is defined in a similar manner to the observation variable,
Figure BDA0002357887530000111
wherein
Figure BDA0002357887530000112
Representing members of a set
Figure BDA0002357887530000113
Average value of (a).
Step three, calculating correlation coefficient
3.1. Quality control
In order to avoid that the number of observations in the region is too small, the sampling error is difficult to eliminate, and the accuracy of the estimation localization function is affected, the lower limit of the number of observations is set to 100 empirically. When the number of observations in a region is less than 100, the present invention is not applicable and a default GC function configuration is used.
3.2. Calculating a correlation coefficient
First observation ylAnd the l mode variable
Figure BDA0002357887530000114
Is related tol kCan be given by the definition of the correlation coefficient, namely:
Figure BDA0002357887530000115
step four, calculating an original localization function
4.1. Grouping correlation coefficients
For a given satellite observation of a certain type and a certain mode variable, the correlation coefficient r of any altitude k is determinedl kDividing each group of G elements into M groups, i.e. L-M G, rl kCan be rewritten as
Figure BDA0002357887530000116
Empirically G was taken as 4.
4.2. Localized function of a certain height
Each of the m-th group
Figure BDA0002357887530000117
The correlation coefficients marked as 'true' respectively, the correlation coefficients after localization
Figure BDA0002357887530000118
The objective function with the "true value" is
Figure BDA0002357887530000119
α minimizing the objective functionkThe value should be
Figure BDA0002357887530000121
4.3. Computing original localization functions
α in step (3.2)kThe confidence index for this satellite observation and the mode variable correlation coefficient for altitude k is shown, αkThe vertical profile of (K ∈ { 1.,. K }) is the original localization function of the estimated vertical direction.
Step five, fitting parameters
The value of the GC function is usually the largest at the location where the observation is located and decreases as the distance of the observation from the mode variable increases, with the value of the function decreasing to 0 outside a certain range.
5.1. Finding out vertical observation position
The air pressure value of the height of the maximum value of the correlation coefficient profile is taken as the position p of the satellite in the observation vertical directiono。
5.2. Fitting GC function Width (influence Range)
Fitting the original local localization function with GC function to find the GC function width value c which minimizes the root mean square error of the twoo。
For satellite observations, only the adaptive GC-width c is currently usedoAnd an observation position p in the vertical directionoTwo parameters are fitted to the original localization function.
Step six, applying the adaptive localization function in the mode
6.1. Selecting a mode variable
All variables directly assimilated in the collective Kalman filtering assimilation system can be used as mode variables. For observation of a certain channel of a certain satellite, the adaptive localization parameter corresponding to the mode variable with a larger correlation coefficient is selected as the adaptive localization parameter of the observation.
6.2. Applying adaptive localization functions
And (6.1) applying the adaptive localization parameters corresponding to each channel observed by each satellite platform in the (6.1) into an assimilation prediction mode, and detecting the prediction result of the mode.
Examples
The method uses the correlation coefficient of satellite observation and mode variables in the collective Kalman filtering assimilation system, takes the simulation of a typhoon rabbit (2018) in a regional mode WRF as an example, and estimates the localization function and the correlation parameter of certain satellite observation and mode variables according to the correlation coefficient. These correlation coefficients were then put into an assimilation prediction system to observe the 6 hour prediction of the test pattern, comparing the prediction error obtained with and without the present invention. The results of the predictions of the path and intensity (lowest sea level barometric pressure and maximum wind speed) of the typhoon rabbit (2018) with and without the present invention were also examined. Figure 1 shows a flow chart of the present invention.
Step one, determining the area and time of the application of the invention
The WRF-ensemble Kalman filtering cyclic assimilation prediction experiment is carried out from 1200UTC of 19 th month 10 in 2018 to 1200UTC of 2 nd month 11 in 2018, the adaptation time of the mode to the new assimilation method is required, and therefore prediction in two days before the cycle starts is abandoned. The control experiment is a predictive experiment without the use of the invention, and all other settings of the experiment with the invention are the same as the control experiment.
1.1. Determining the region of application of the invention
The first scheme is as follows: for the entire pattern coverage area without distinction, the localization function and the correlation parameters are estimated using the present invention using all samples of the entire area.
Scheme II: taking into account the multiscale characteristics possessed by Tropical Cyclones (TC), TC regions and non-TC regions are distinguished, and the localization function and the relevant parameters are estimated using the present invention for samples of these two regions, respectively. The TC zone is defined as a square area with a side length of 20 longitude and latitude with the position of the TC at the current time as the center.
1.2. Determining the time of assimilation for the application of the invention
The first scheme is as follows: adaptive localization functions were estimated using observation and pattern variables output from some representative times in the control experiment, and the time of use in the rabbit (2018) simulation experiment included four cycles before typhoon fast boost (from 10 months 22 days 0000UTC to 10 months 22 days 1800UTC) and four cycles after fast boost (from 10 months 23 days 1800UTC to 10 months 24 days 1200 UTC).
Scheme II: using the time-varying localization parameters, an adaptive localization function is estimated using the observations and mode variables from the previous time or from the previous two times.
The following four experiments were designed at the time of selection of different regions and assimilation:
Figure BDA0002357887530000141
step two, acquiring observation variables and mode variables
Satellite observation and mode variables of all set members are given in the set Kalman filtering assimilation system. The number of layers of the pattern in the vertical direction is marked as K, the number of members of the set is marked as N, and the number of observations of a certain channel of certain satellite data is marked as L. In the experiment, the set membership is 80, and adaptive localization functions and parameters are calculated for observation of each channel of each satellite instrument in turn. 2.1. Obtaining an observed variable
With yl,nThe l-th observation of the n-th set member of the representation. (L ∈ { 1.,. L } and N ∈ { 1.,. N }). For observation y at the same timel,nCan calculate the disturbance quantity
Figure BDA0002357887530000142
In the equation
Figure BDA0002357887530000143
Represents the mean of the members of the set.
2.2. Obtaining a mode variable
For the mode variable, firstly, the model variable is projected to the position of the l observed variable in the horizontal direction, and the variable of the n set member at the k layer height is recorded as
Figure BDA0002357887530000144
Mode variable disturbance quantity definition mode and observationThe variables are similar in that,
Figure BDA0002357887530000151
wherein
Figure BDA0002357887530000152
Representing members of a set
Figure BDA0002357887530000153
Average value of (a).
Step three, calculating correlation coefficient
3.1. Quality control
In order to avoid that the sampling error which is difficult to eliminate influences the accuracy of the estimation localization function due to too small number of observations in the region, the lower limit of the number of observations is set to be 100 empirically. When the number of observations in a region is less than 100, the present invention is not applicable and a default GC function configuration is used. The number of samples of individual channels in the TC region of the GGF-TC only experiment was insufficient.
3.2. Calculating a correlation coefficient
First observation ylAnd the l mode variable
Figure BDA0002357887530000154
Is related tol kCan be given by the definition of the correlation coefficient, i.e.
Figure BDA0002357887530000155
The dashed lines in FIG. 2 represent the average correlation coefficients observed at each height level for the AMSU-A instrument channel 6 carried by the satellite NOAA-15 in the GGF-Domain emutexperiment.
Step four, calculating an original localization function
4.1. Grouping correlation coefficients
For a given satellite observation of a certain type and a certain mode variable, the correlation coefficient r of any altitude k is determinedl kDividing each group of G elements into M groups, i.e. L-M G, rl kCan be rewritten as
Figure BDA0002357887530000156
Empirically G was taken as 4.
4.2. Localized function of a certain height
Each of the m-th group
Figure BDA0002357887530000157
The correlation coefficients marked as 'true' respectively, the correlation coefficients after localization
Figure BDA0002357887530000158
The objective function with the "true value" is
Figure BDA0002357887530000159
α minimizing the objective functionkThe values should be:
Figure BDA0002357887530000161
4.3. computing original localization functions
α in step (3.2)kThe confidence index for this satellite observation and the mode variable correlation coefficient for altitude k is shown, αkThe vertical profile of (K ∈ { 1.,. K }) is the original localization function of the estimated vertical direction. The dotted line curve in FIG. 2 represents the original localization function observed at each height level for the AMSU-A instrument channel 6 carried by the satellite NOAA-15 in the GGF-Domain emutexperiment.
Step five, fitting parameters
The value of the GC function is usually the largest at the location where the observation is located and decreases as the distance of the observation from the mode variable increases, with the value of the function decreasing to 0 outside a certain range.
5.1. Finding out vertical observation position
The air pressure value of the height of the maximum value of the correlation coefficient profile is taken as the position p of the satellite in the observation vertical directiono。
5.2. Fitting GC function Width (influence Range)
Fitting the original local localization function with GC function to find out the GC function with the minimum root mean square errorWidth value co。
The solid line-shaped curve in FIG. 2 represents the results of the original localization function fit for the observation of the AMSU-A instrument channel 6 carried by the satellite NOAA-15 in the GGF-Domain emutexperiment. As can be seen, the observed position estimated in this experiment is 505.5hPa, and the localization scale is 2.2ln (hPa).
Step six, applying the adaptive localization function in the mode
6.1. Selecting a mode variable
All variables directly assimilated in the collective Kalman filtering assimilation system can be used as mode variables. Two mode variables, temperature and specific humidity, were selected in the emutexperiment, and for observations from the instrument AMSU-a, the correlation coefficient of the observations with the mode variable temperature was greater than the correlation coefficient with the specific humidity, thus using the temperature estimate to adaptively localize the parameters.
Fig. 3a and 3b show the average value (the non-TC region is a dot, and the TC region is a diamond) and a standard deviation (the non-TC region is a solid line, i.e., the lines above and below the dot are solid lines, and the TC region is a dotted line, i.e., the lines above and below the diamond are dotted lines) of the estimated localization parameters in the TC region and the non-TC region respectively in the GGF-TC experiment. The vertical position estimated for the AMSU-a observations is similar for TC and non-TC regions, but the estimated localization width in the TC region is typically larger than the estimated width of the non-TC region. These adaptive localization parameters will be used for cyclic assimilation prognostics to examine the impact of the adaptive localization parameters on the prognostics. Adaptive localization parameters for other experimental and other types of satellite observations may be estimated accordingly.
6.2. Applying adaptive localization functions
6.2.1. Inspecting and forecasting results by using conventional observation
The control experiment and three adaptive localization experiments using the present invention (GGF-Domain, GGF-TC, GGF-Time) were examined for 6 hour prediction error using conventional observations (temperature, wind speed, specific humidity). Fig. 4(a), 4(c) and 4(e) show the root mean square error averaged over time and in the horizontal region of three conventional observation, inspection and control experiments with temperature, wind speed and specific humidity, respectively. FIGS. 4(b), 4(d), and 4(f) show the difference between the error obtained by using the present invention and the error of the control experiment, wherein a negative value indicates that the result of the experiment using the present invention is better than the control experiment, and a positive value indicates that the result is worse after using the present invention; the short solid line above the figure represents the average value in the vertical direction. In general, the prediction error is smaller than that of the control experiment after the method is used, the GGF-TC experiment of the adaptive localization parameter changing along with Time is better than that of the GGF-Domain experiment of the constant adaptive localization parameter, and the GGF-TC experiment of the adaptive localization parameter distinguishing TC and non-TC areas has little advantage compared with the GGF-Time and the GGF-Domain.
6.2.2. Checking and forecasting results by using the path and strength of typhoon
Fig. 5 shows the predicted impact of observation (thick solid large dots), control experiment (thin solid small dots) and three experiments using the present invention on the path (fig. 5a), lowest sea level air pressure (fig. 5b) and maximum wind speed (fig. 5c) of a typhoon rabbit (2018). Both the control experiment and the experiment using the present invention had a path forecast very close to the observation, but the GGF experiment had a slightly better path forecast than the control experiment at the beginning of typhoon (fig. 5 a). For intensity prediction, i.e. lowest sea level barometric pressure and maximum wind speed, the prediction of the GGF experiment is closer to the observed value than the control experiment. The experiments using the present invention captured the rapid enhancement (RI) process better than the control experiments. However, the peak typhoon intensity predicted experimentally using the present invention is still lower than observed, which may be due to insufficient model resolution to resolve the gradients of the mass field and wind field. Three experiments using the invention have similar path and intensity predictions, and their prediction results are all superior to the control experiments.

Claims (10)

1. An adaptive localization method for assimilation of satellite data in a vertical direction, comprising: calculating the correlation coefficient of the satellite observation and the mode variable in the vertical direction according to the satellite observation and the mode variable in any time in any sub-region range given in the collective Kalman filtering assimilation system; then, the original local position of the satellite observation and mode variable in the vertical direction at the current time and in the current area is estimated by using the correlation coefficientA localization function; estimating the position p of the satellite observation in the vertical direction according to the correlation coefficient profileoAnd is located at poFitting the maximum value of the GC function at the position to the original localization function to obtain the influence range c of the satellite observation in the vertical directiono(ii) a Estimated position p of satellite observation in vertical directionoThe influence range c of the satellite observation in the vertical directionoI.e. adaptive localization parameters.
2. The method of claim 1, wherein the satellite observations and mode variables at a particular time within a given sub-region of the collective kalman filter assimilation system are:
observation yl,nThe disturbance amount of (2):
Figure FDA0002357887520000011
wherein: observation yl,nAn L-th observation representing an N-th set member of the satellite observations given in the set kalman filter assimilation system, L ∈ { 1.. and L } and N ∈ { 1.. and N }; n is the number of set members of the set Kalman filtering assimilation system, and L is the number of observations of a certain channel observed by a certain satellite;
Figure FDA0002357887520000012
set member y representing satellite observationsl,nAverage value of (d);
disturbance amount of mode variable:
Figure FDA0002357887520000013
wherein: mode variables
Figure FDA0002357887520000014
Showing the nth set projected to the position of the l observation variable in the horizontal direction in the set Kalman filtering assimilation systemA mode variable with a member at a kth layer height; l is in the range of { 1.,. L }, N is in the range of { 1.,. N }, and K is in the range of { 1.,. K }; k is the number of layers of the mode in the vertical direction;
Figure FDA0002357887520000015
representing variables of each mode
Figure FDA0002357887520000016
Average value of (a).
3. The method of claim 1 or 2, wherein for a given satellite observation of a given type and a mode variable in the collective Kalman Filter assimilation System, its correlation coefficient at any height k, r, is a function of the number of the mode variablesl kComprises the following steps:
Figure FDA0002357887520000021
in the formula:
Figure FDA0002357887520000022
representing mode variables
Figure FDA0002357887520000023
The amount of disturbance of; Δ yl,nRepresentative of observation yl,nThe amount of disturbance of;
yl,nan L-th observation representing an N-th set member of the satellite observations given in the set kalman filter assimilation system, L ∈ { 1.. and L } and N ∈ { 1.. and N }; n is the number of set members of the set Kalman filtering assimilation system, and L is the number of observations of a certain channel observed by a certain satellite;
Figure FDA0002357887520000024
representing the mode variable of the nth set member positioned at the kth layer height, which is projected to the position of the l observation variable in the horizontal direction in the set Kalman filtering assimilation system;l belongs to {1, …, L }, N belongs to {1, …, N }, K belongs to {1, …, K }, and K is the number of layers of the mode in the vertical direction.
4. The method of claim 3, wherein a correlation coefficient r between any observation with a satellite and any mode variable at any height k in the vertical direction is determinedl kBefore estimating the original localization function of the satellite observation and mode variable in the vertical direction at the current time and in the current area, a correlation coefficient r needs to be obtainedl kGrouping, wherein the grouping mode is as follows: dividing each group of G elements into M groups, and recording any one of the correlation coefficients in each group as
Figure FDA0002357887520000025
m∈{1,...,M}，g∈{1,...,G}。
5. The method of adaptive localization of satellite data assimilation in the vertical direction of claim 1 or 2, characterized by that the original localization function is the parameter αkPerpendicular profile of (A), parameter αkA confidence index representing the correlation coefficient of the mode variable for a certain satellite observation and altitude k;
if each correlation coefficient is looked at
Figure FDA0002357887520000031
All have the same probability as true value, the correlation coefficient after localization
Figure FDA0002357887520000032
Is the objective function J ofkIt should satisfy:
Figure FDA0002357887520000033
when the objective function JkWhen taken at minimum, confidence index αkSatisfies the following conditions:
Figure FDA0002357887520000034
in the formula:
Figure FDA0002357887520000035
represents the correlation coefficient rl kDividing the correlation coefficients into M groups containing G members, and then selecting any one of the correlation coefficients in each group;
coefficient of correlation rl kRepresenting the correlation coefficient at any altitude k for a given class of satellite observations and for a mode variable.
6. The method of claim 1, wherein the estimated position p of the satellite observation in the vertical direction iso: is a correlation coefficient rl kThe air pressure value at the height of the maximum of the profile.
7. The method of claim 1, wherein the satellite observation has an impact on the vertical range coThe acquisition mode of (1): first is located at poFitting the GC function maximum value at the position to an original localization function to obtain an adaptive localization function;
then, by comparing the adaptive localization function with the original localization function, the influence range c of the satellite observation in the vertical direction can be obtainedoThe range of influence of the satellite observation in the vertical direction coAs a width value c of the GC functionoIs indicated as being located at poA width parameter of the GC function corresponding to the least root mean square error of both the adaptive localization function and the original localization function at the location.
8. The method of claim 1, comprising the steps of:
(1) selecting proper area and time
Aiming at different weather systems, satellite observation and mode variables in a specific sub-area range and at a specific time are given through a collective Kalman filtering assimilation system;
the specific sub-area comprises a TC area and/or a non-TC area; the TC area is defined as a square area with the position of the tropical cyclone at the current moment as the center and the side length of 20 longitude and latitude;
the specific sub-region range needs to ensure that the total number of observations in all times is not less than O, and O is 102；
The specific time is a representative time in the observation and mode variables of the given satellite or a previous time or two times before the local localization parameter at the current time is estimated;
(2) obtaining observed and mode variables
Observation yl,nThe disturbance amount of (2):
Figure FDA0002357887520000041
wherein: observation yl,nAn L-th observation representing an N-th 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 members of the set Kalman filtering assimilation system, L is the number of observations of a certain channel of certain satellite data;
Figure FDA0002357887520000042
set member y representing satellite observationsl,nAverage value of (d);
mode variables
Figure FDA0002357887520000043
The disturbance amount of (2):
Figure FDA0002357887520000044
wherein: mode variables
Figure FDA0002357887520000045
The mode variable is represented in an aggregate Kalman filtering assimilation system, and an nth aggregate member projected to the position of the l observation variable in the horizontal direction is positioned at the height of a kth layer; l belongs to { 1.,. L }, N belongs to { 1.,. N }, and K belongs to {1, …, K }; k is the number of layers of the mode in the vertical direction;
Figure FDA0002357887520000046
representing variables of each mode
Figure FDA0002357887520000047
Average value of (d);
(3) calculating a correlation coefficient
First observation ylAnd the l mode variable
Figure FDA0002357887520000048
Is related tol kComprises the following steps:
Figure FDA0002357887520000051
(4) computing original localization functions
For a given satellite observation of a certain type and a certain mode variable, the correlation coefficient r of any altitude k is determinedl kDividing each group of G elements into M groups, and recording any one of the correlation coefficients in each group as
Figure FDA0002357887520000052
m∈{1,...,M}，g∈{1,…,G}；
If each correlation coefficient is looked at
Figure FDA0002357887520000053
If all the same probability becomes true value, the locally correlated coefficient
Figure FDA0002357887520000054
Object of (2)Function JkSatisfies the following conditions:
Figure FDA0002357887520000055
αka confidence index representing the correlation coefficient for this satellite observation and for a mode variable of height k, when the objective function JkWhen taken at minimum, confidence index αkSatisfies the following conditions:
Figure FDA0002357887520000056
αkthe vertical profile of (a) is an estimated original localization function in the vertical direction;
(5) fitting parameters
Finding the observation position p in the vertical directiono；
At maximum value of poFitting the original localization function by the GC function to obtain an adaptive localization function;
the influence range c of the estimated satellite observation in the vertical direction can be obtained through the adaptive localization function and the original localization functiono(ii) a Estimated range of influence c of satellite observations in the vertical directionoAs a width value c of the GC functionoDenotes to be located at poA width parameter of the GC function corresponding to the least root mean square error of both the adaptive localization function and the original localization function at the location.
9. An integrated Kalman filtering weather assimilation forecast method is characterized by comprising the following steps: 1) in the collective Kalman filtering assimilation system, 1 or more variables which can be directly assimilated are selected as mode variables; 2) selecting the characteristic mode variables to estimate the localization parameters by comparing the correlation coefficients between the various types of mode variables and the satellite observations, the estimated localization parameters including the estimated position p of the satellite observations in the vertical directionoAnd estimated range of influence c of satellite observations in the vertical directiono(ii) a 3) Office to be estimatedThe geological parameter is used in a weather assimilation forecast system to obtain a forecast result at the next moment.
10. The collective kalman filter weather assimilation forecast method according to claim 9, wherein: estimated range of influence c of satellite observations in the vertical directionoAs a width value c of the GC functionoDenotes to be located at poThe width parameter of the GC function corresponding to the minimum root mean square error of the adaptive localization function and the original localization function at the position; the adaptive localization function is located at p by a maximumoIs obtained by fitting the original localization function, which is the parameter αkPerpendicular profile of (A), parameter αkConfidence index representing the correlation coefficient between a given satellite observation and a mode variable of height k when the objective function JkWhen taken at minimum, confidence index αkSatisfies the following conditions:
Figure FDA0002357887520000061
objective function JkSatisfies the following conditions:
Figure FDA0002357887520000062
therein
Figure FDA0002357887520000071
A correlation coefficient r for a given satellite observation of a certain type and a certain mode variable at altitude kl kDividing each group of G elements into M groups, and uniformly recording as any one correlation coefficient
Figure FDA0002357887520000072
M belongs to {1,. eta., M }, and G belongs to {1,. eta., G }; coefficient of correlation rl kThe expression of (a) is as follows:
Figure FDA0002357887520000073
in the formula:
Figure FDA0002357887520000074
Δyl,nrepresents observation yl,nThe amount of disturbance of; y isl,nAn L-th observation representing an N-th set member of the satellite observations given in the set kalman filter assimilation system, L ∈ { 1.. and L } and N ∈ { 1.. and N }; n is the number of members of the set Kalman filtering assimilation system, L is the number of observations of a certain channel of certain satellite data;
Figure FDA0002357887520000075
set member y representing satellite observationsl,nAverage value of (d);
Figure FDA0002357887520000076
representing mode variables
Figure FDA0002357887520000077
The disturbance amount of (2):
Figure FDA0002357887520000078
the mode variable is represented in an aggregate Kalman filtering assimilation system, and an nth aggregate member projected to the position of the l observation variable in the horizontal direction is positioned at the height of a kth layer; l belongs to {1, …, L }, N belongs to {1, …, N }, and K belongs to {1, …, K }; k is the number of layers of the mode in the vertical direction;
Figure FDA0002357887520000079
representing variables of each mode
Figure FDA00023578875200000710
Average value of (d);
position p of the estimated observation in the vertical directionoIs a correlation coefficient rl kThe air pressure value at the height of the maximum of the profile.
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