CN110472648B - Cloud classification-based method for constructing error covariance of hydrogel background field - Google Patents
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Abstract
According to the construction scheme of the hydraulic background field error covariance, the hydraulic variable is introduced into the background field error covariance, and after the hydraulic background field error covariance is applied, the assimilation system can realize direct analysis of the hydraulic variable. The beneficial effects are that: the cloud zone classification operator based on the set samples can effectively classify the covariance of the background field errors of the water condensate according to cloud quantity, and the classified covariance of the background field errors of the water condensate can more reasonably represent the characteristics of the background errors of the cloud zone and the clear sky zone.
Description
Technical Field
The invention relates to the technical field of atmospheric science, in particular to a method for constructing a covariance of a hydrogel background field error based on cloud cover classification.
Background
The distribution, the morphology and the change of the cloud represent the condition and the change trend of the atmospheric movement, the relevant information of the cloud has important leading value for carrying out the analysis and the forecast of a weather system, however, the assimilation of the satellite data is mainly carried out under the clear sky condition at present, and a large amount of satellite data influenced by the cloud is always discarded. The effective utilization of satellite data affected by the cloud is an important way for further improving the initial field of numerical forecasting and further improving the accuracy of numerical forecasting. In a variation assimilation system, a background field error covariance matrix (B matrix) is one of key factors influencing the performance of the assimilation system, so that reasonable background field error covariance is a key link for assimilation of materials, and therefore, the construction and understanding of the background field error covariance in a cloud and rain area is one of core work for improving the assimilation performance of the assimilation system in the cloud and rain area.
In most assimilation systems, the background field error covariance only contains conventional control variables such as wind, temperature, surface air pressure and humidity, so that in order to enable the assimilation system to directly give an analysis field of the condensate variable, the condensate is required to be used as the control variable of the assimilation system, and the condensate variable is introduced into the background field error covariance.
In the weather data assimilation, the problem that the ultra-large-scale background field error covariance matrix is difficult to directly express and calculate exists, and the current data assimilation system of each large-value prediction center generally adopts a control variable conversion method (Control Variable Transforms, CVT) for constructing the background field error covariance matrix which can be conveniently operated and is more real and reliable. The control variable transformation implies the background field error covariance matrix in the control variable transformation operator, and no direct representation is needed. By controlling variable transformation, the storage and calculation of the B matrix can be effectively relieved. However, in regional data assimilation research and application, the matrix B is often approximated by adopting a horizontal lattice point averaging manner in the process of controlling variable conversion, so that the structure of B is simplified, but different background error characteristics under different weather backgrounds in the horizontal direction are ignored. This is especially true for the background errors of the hydrogel variables, which are more pronounced in different weather backgrounds, since the hydrogel distribution has spatially discontinuous features.
Disclosure of Invention
The invention aims to overcome the defect that the background field error covariance in most assimilation systems at present does not introduce a condensate control variable and cannot reasonably and directly analyze condensate, and provides a condensate background field error covariance construction method based on cloud classification, which is used for introducing a condensate variable into a newly constructed condensate background field error covariance and simultaneously can more reasonably represent the background error characteristics of a cloud zone and a clear sky zone, and is realized by the following technical scheme:
the method for constructing the error covariance of the hydrogel background field based on cloud cover classification comprises the following steps:
step 1) taking a GEFS global set forecasting product as a numerical mode initial field, and disturbing the mode initial field by different parameterization schemes to obtain a group of set samples, wherein the set samples comprise water condensate variables Q respectively corresponding to cloud water, cloud ice, rainwater, snow and aragonite cloud 、Q ice 、Q rain 、Q snow Q and graupel ；
step 2) reading the set samples by means of set averaging and Q in set members cloud And Q ice Calculating cloud class discrimination criteria according to formula (1), the cloud class discrimination criteria comprising: aggregate average discriminant criterion P ens_ave And set member criterion P ens_mem ，
Wherein top and bot represent the air pressure at the top and bottom of the mode layer, respectively, "-" represents the average of n collection members;
step 3) classifying the set error samples according to a cloud classification discriminant criterion P and a formula (2),
the classified partition operators P are obtained as cloud region operators (P cloudy ) Clear sky region operator (P) clear ) Blend zone operator (P mixed ) The method comprises the steps of carrying out a first treatment on the surface of the Step 4) performing control variable conversion on the partitioned error samples according to the formula (3),
U＝U p U v U h (3)
in the formula (3), U represents control variable conversion, U p Representing physical transformations, U v Representing vertical transformation, U h Representing a horizontal transformation;
the obtained partitioned hydrogel background field error covariance B is correspondingly expressed as:
the method for constructing the error covariance of the hydrogel background field based on cloud cover classification is further designed in that the classification standard of the aggregate error sample in the step 3) is as follows: the collection members and the collection average sample meet that P is more than or equal to 0.01g.kg -1 The grid point of the cloud zone error sample is defined; the collection members and the collection average sample meet that P is less than or equal to 0.01g.kg -1 The grid points of the grid points are defined as clear sky zone error samples; when the classification disagreement occurs between the members of the set and the average same lattice point of the set, the error sample is defined as a mixed region error sample.
The further design of the cloud classification-based method for constructing the covariance of the error of the background field of the water condensate is that the conversion of the control variable in the step 4) comprises the following steps:
step 4-1) performing physical transformation, and dividing the state variables into a balanced part and an unbalanced part according to the balance relation existing between the state variables represented by regression statistics or balance equations;
step 4-2) performing vertical transformation, and decomposing through an empirical orthogonal function to obtain a characteristic value and a characteristic vector of a variable field, wherein the characteristic value and the characteristic vector are used for representing the magnitude of a background error and the vertical structural characteristics;
step 4-3) performing horizontal transformation according to the formula (5), and calculating to obtain a horizontal length scale;
in the formula (5), L is a horizontal length scale, D represents variance,
representing an unbalanced physical quantity field.
The method for constructing the error covariance of the background field of the hydrogel based on cloud cover classification is further designed in that in the step 4-2), an error field of a control variable is projected onto an orthogonal mode in the vertical direction, so that the inside of each diagonal matrix of each block is further diagonalized, and the error covariance matrix of the background field is further decomposed into a characteristic value and a characteristic vector in the vertical direction:
B v ＝E∧E T (6)
in the formula (6), E is a matrix composed of K eigenvectors, B v Is a positive symmetric matrix which is a part of the background field error covariance matrix after vertical transformation and meets the formula (6)
The further design of the method for constructing the error covariance of the hydrogel background field based on cloud cover classification is that in the step 4), the method for acquiring the error covariance of the partitioned hydrogel background field comprises the following steps:
step A) sample the background field error ε b The method is divided into a cloud zone clear, a clear sky zone clear and a mixed zone mixed sum:
ε b ＝P cloudy ε b +P clear ε b +P mixed ε b (8)
in the formula (8), P cloudy Representing cloud partition operators; p (P) clear Representing a clear sky region operator; p (P) mixed Representing a blend region classification operator;
step B) decompose the background field error covariance B into:
in the formula (9), ε b Representing sample error, "-" represents mathematical expectation
B is further decomposed into:
B＝P cloudy B cloudy P cloudy T +P clear B clear P clear T +P mixed B mixed P mixed T (10)
the cloud area classification operator based on the aggregate sample divides the error covariance area of the hydrogel background field into three parts, namely a cloud area, a sunny area and a mixed area.
The method for constructing the covariance of the error of the background field of the water condensate based on cloud classification is further designed in that the equilibrium equation in the step 4-1) is shown as a formula (11),
in the formula (11), a closed b Representing the equilibrium field of the hydrogel variables calculated from the variables, i and j representing the number of lattice points in the horizontal direction, k and l representing the number of sigma layers in the vertical direction, k, l e 0, N K ]Alpha represents the regression coefficient between the variables.
The invention has the following advantages:
according to the construction method of the hydraulic background field error covariance, the hydraulic variable is introduced into the background field error covariance, and after the hydraulic background field error covariance is applied, the assimilation system can realize direct analysis of the hydraulic variable.
On the other hand, the cloud zone classification operator based on the set sample can effectively classify the covariance of the background field errors of the water condensate according to cloud quantity, and the classified covariance of the background field errors of the water condensate can more reasonably represent the characteristics of the background errors of the cloud zone and the clear sky zone.
Drawings
Fig. 1 is a flowchart of acquiring a partition operator P.
FIG. 2 is a flow chart of cloud region background field error covariance calculation using a partitioning operator.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
The method for constructing the error covariance of the hydrogel background field based on cloud cover classification provided by the embodiment comprises the following steps:
as shown in fig. 1, to obtain the partition operator P, the following steps are required:
step 1) taking a GEFS global set forecasting product as a numerical mode initial field, and disturbing the mode initial field by different parameterization schemes to obtain a set of 80 member set samples, wherein the set samples comprise Q cloud (cloud Water), Q ice (Yun Bing), Q rain (rain water), Q snow (snow) and Q graupel (aragonite) five hydraulic variables;
step 2) reading the set samples by means of set averaging and Q in set members cloud And Q ice Calculating cloud classification discriminant criteria according to formula (1), and collecting average discriminant criteria: p (P) ens_ave Set member criterion: p (P) ens_mem ，
Step 3) classifying the set error samples according to cloud classification discrimination criteria P and referring to a formula (2),
the classification standard of the aggregate error sample in the step 3) is as follows: the collection members and the collection average sample meet that P is more than or equal to 0.01g.kg -1 The grid point of the cloud zone error sample is defined; the collection members and the collection average sample satisfy P < 0.01g.kg -1 The grid points of the grid points are defined as clear sky zone error samples; when the classification disagreement occurs between the members of the set and the average same lattice point of the set, the error sample is defined as a mixed region error sample. The classified partition operators P are obtained as cloud region operators (P cloudy ) Clear sky region operator (P) clear ) Blend zone operator (P mixed )；
As shown in fig. 2, the cloud region background field error covariance calculation by using the partition operator includes the following steps:
step 4) performing control variable conversion on the partitioned error samples according to the formula (3),
U＝U p U v U h (3)
in the formula (3), U represents control variable conversion, U p Representing physical transformations, U v Representing vertical transformation, U h Representing a horizontal transformation;
the obtained partitioned hydrogel background field error covariance B is correspondingly expressed as:
the control variable conversion in step 4) includes the steps of:
step 4-1) performing physical transformation, and dividing the state variables into a balanced part and an unbalanced part according to the balance relation existing between the state variables represented by regression statistics or balance equations; for the condensate control variables, the equilibrium equation is as in equation (5),
in the formula (5), a closed b Representing the equilibrium field of the hydrogel variables calculated from the variables, i and j representing the number of lattice points in the horizontal direction, k and l representing the number of sigma layers in the vertical direction, k, l e 0, N K ]Alpha represents the regression coefficient between the variables.
Step 4-2) performing vertical transformation, and decomposing through an empirical orthogonal function to obtain a characteristic value and a characteristic vector of a variable field, wherein the characteristic value and the characteristic vector are used for representing the magnitude of a background error and the vertical structural characteristics; projecting the error field of the control variable to an orthogonal mode in the vertical direction, and continuously diagonalizing the inside of each block diagonal matrix, so as to decompose the background field error covariance matrix into characteristic values and characteristic vectors in the vertical direction:
B v ＝E∧E T (6)
wherein, the liquid crystal display device comprises a liquid crystal display device,e is a matrix of K eigenvectors, B v Is the vertical transformed part of the background field error covariance matrix and is a positive symmetry matrix, satisfying the formula (7)
Step 4-3) performing horizontal transformation according to a formula (8), and calculating to obtain a horizontal length scale;
where L is the horizontal length scale, D is the variance,
representing an unbalanced physical quantity field.
In step 4), the obtaining of the partitioned hydrogel background field error covariance includes the following steps: step A) sample the background field error ε b The method is divided into a cloud zone clear, a clear sky zone clear and a mixed zone mixed sum:
ε b ＝P cloudy ε b +P clear ε b +P mixed ε b (9)
in the formula (9), P cloudy Representing cloud partition operators; p (P) clear Representing a clear sky region operator; p (P) mixed Representing a blend region classification operator;
step B) decompose the background field error covariance B into:
in the formula (10), ε b Representing sample error, "-" represents mathematical expectation
B is further decomposed into:
B＝P cloudy B cloudy P cloudy T +P clear B clear P clear T +P mixed B mixed P mixed T (11)
the cloud area classification operator based on the aggregate sample divides the error covariance area of the hydrogel background field into three parts, namely a cloud area, a sunny area and a mixed area.
According to the construction method of the hydraulic background field error covariance, the hydraulic variable is introduced into the background field error covariance, and after the hydraulic background field error covariance is applied, the assimilation system can realize direct analysis of the hydraulic variable. In addition, the cloud zone classification operator based on the set sample can effectively classify the covariance of the background field errors of the water condensate according to cloud quantity, and the classified covariance of the background field errors of the water condensate can more reasonably represent the characteristics of the background errors of the cloud zone and the clear sky zone.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (6)
1. A method for constructing a covariance of a hydrogel background field error based on cloud cover classification is characterized by comprising the following steps:
step 1) taking a GEFS global set forecasting product as a numerical mode initial field, and disturbing the mode initial field by different parameterization schemes to obtain a group of set samples, wherein the set samples comprise water condensate variables Q respectively corresponding to cloud water, cloud ice, rainwater, snow and aragonite cloud 、Q ice 、Q rain 、Q snow Q and graupel ；
step 2) reading the set samples by means of set averaging and Q in set members cloud And Q ice Calculating cloud class discrimination criteria according to formula (1), the cloud class discrimination criteria comprising: collection setAverage criterion P ens_ave And set member criterion P ens_mem ，
Wherein top and bot represent the air pressure at the top and bottom of the mode layer, respectively, "-" represents the average of n collection members;
step 3) classifying the set error samples according to a cloud classification discriminant criterion P and a formula (2),
obtaining classified partition operators, namely cloud region operator P cloudy Clear sky region operator P clear Blend zone operator P mixed ；
Step 4) performing control variable conversion on the partitioned error samples according to the formula (3),
U＝U p U v U h (3)
in the formula (3), U represents control variable conversion, U p Representing physical transformations, U v Representing vertical transformation, U h Representing a horizontal transformation;
the obtained partitioned hydrogel background field error covariance B is correspondingly expressed as:
2. the method for constructing the error covariance of the background field of the water condensate based on cloud computing as recited in claim 1, wherein the classification criteria of the aggregate error samples in the step 3) are: the collection members and the collection average sample meet that P is more than or equal to 0.01g.kg -1 The grid point of the cloud zone error sample is defined; flattening set membersThe average sample satisfies P less than or equal to 0.01 g.kg -1 The grid points of the grid points are defined as clear sky zone error samples; when the classification disagreement occurs between the members of the set and the average same lattice point of the set, the error sample is defined as a mixed region error sample.
3. The method for constructing the covariance of the background field error of the water condensate based on the cloud cover classification according to claim 1, wherein the controlling variable conversion in the step 4) comprises the following steps:
step 4-1) performing physical transformation, and dividing the state variables into a balanced part and an unbalanced part according to the balance relation existing between the state variables represented by regression statistics or balance equations;
step 4-2) performing vertical transformation, and decomposing through an empirical orthogonal function to obtain a characteristic value and a characteristic vector of a variable field, wherein the characteristic value and the characteristic vector are used for representing the magnitude of a background error and the vertical structural characteristics;
step 4-3) performing horizontal transformation according to the formula (5), and calculating to obtain a horizontal length scale;
in the formula (5), L is a horizontal length scale, D represents variance,
representing an unbalanced physical quantity field.
4. The method for constructing the error covariance of the background field of the hydrogel based on cloud cover classification as recited in claim 3, wherein in the step 4-2), the error field of the control variable is projected onto the orthogonal mode in the vertical direction, so that the diagonalization is further performed in each diagonal matrix of the block, and the error covariance matrix of the background field is decomposed into eigenvalues and eigenvectors in the vertical direction:
B v ＝E∧E T (6)
in the formula (6), E is a matrix composed of K eigenvectors, B v Is a positive symmetric matrix, satisfying the formula (7)
5. The method for constructing a hydraulic background field error covariance based on cloud computing as recited in claim 4), wherein in the step 4), the obtaining of the partitioned hydraulic background field error covariance comprises the following steps: step A) sample the background field error ε b The method is divided into a cloud zone clear, a clear sky zone clear and a mixed zone mixed sum:
step B) decompose the background field error covariance B into:
in the formula (9), ε b Representing sample error, "-" represents mathematical expectation
B is further decomposed into:
B＝P cloudy B cloudy P cloudy T +P clear B clear P clear T +P mixed B mixed P mixed T (10)
the cloud area classification operator based on the aggregate sample divides the error covariance area of the hydrogel background field into three parts, namely a cloud area, a sunny area and a mixed area.
6. The method for constructing the covariance of the background field error of the hydrogel based on cloud cover classification according to claim 3, wherein the equilibrium equation in the step 4-1) is represented by the formula (11),
in the formula (11), a closed b Representing the equilibrium field of the hydrogel variables calculated from the variables, i and j representing the number of lattice points in the horizontal direction, k and l representing the number of sigma layers in the vertical direction, k, l e 0, N K ]Alpha represents the regression coefficient between the variables.
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