CN109033029A - Method and system for generating deterministic analysis set based on reverse localization - Google Patents

Method and system for generating deterministic analysis set based on reverse localization Download PDF

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CN109033029A
CN109033029A CN201810697284.2A CN201810697284A CN109033029A CN 109033029 A CN109033029 A CN 109033029A CN 201810697284 A CN201810697284 A CN 201810697284A CN 109033029 A CN109033029 A CN 109033029A
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冷洪泽
宋君强
曹小群
赵军
张卫民
任开军
吴建平
银福康
杨锦辉
刘柏年
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National University of Defense Technology
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Abstract

The invention discloses a deterministic analysis set generation method and a system based on reverse localization, wherein the method comprises the steps of calculating an analysis state mean value based on a control variable analysis value, a prediction set state mean value and a localized prediction error covariance square root matrix, constructing a square root matrix of the state variable analysis error covariance matrix and calculating an analysis increment for each set member; and summing the analysis state mean value and the analysis increment of each set member to obtain a final analysis state set of each set member as an initial state set. By improving the localization scheme and the analysis set generation mode, the method can better remove sampling errors and long-distance pseudo correlation on one hand, and can generate a set with analysis dispersion more tending to the analysis errors on the other hand, so that the data assimilation performance is obviously improved, and the more accurate and reliable initial state of the numerical prediction problem is obtained.

Description

Deterministic parsing set generation method and system based on reverse localization
Technical field
The present invention relates to numerical forecast or prediction fields, and in particular to a kind of deterministic parsing collection based on reverse localization Symphysis is at method and system.
Background technique
For the fields such as numerical weather forecast, numerical value marine forecasting, the shape of simulation system in these application fields Very high (the O (10 of state dimension8)~O (109)), calculation amount itself is huge, when using collection approach processing, the increase of number of members It will lead to being doubled and redoubled for calculation amount again, set member's number used in practical application will be substantially less that system mode dimension.Numerical value Forecast or forecasting problem are an initial-value problems, namely: an original state is given, the known system development law the case where Under, it can forecast or predict the state at the following a certain moment.Therefore, whether original state will accurately directly affect the value of forecasting Quality.
By taking numerical weather forecast as an example, equation group shown in formula (1) indicates Earth Atmosphere System development law, namely forecast mould After given initial value condition, by time integral, the forecast state after a period of time is can be obtained in formula.
In formula (1), V is velocity vector, and t is the time, and ρ is density,Indicating gradient, Ω is rotational-angular velocity of the earth vector, G is acceleration of gravity, and F is frictional force acceleration, and p is air pressure, and T is temperature, cpFor specific heat at constant pressure, R is specific gas constant, q For than wet, F is condensation function, δ is 0-1 function, RdFor dry air specific gas constant.
Data Assimilation method has exactly been organically blended all available observation informations by Numerical Prediction Models Come, provides reported as precisely as possible and dynamic compatibility original state (alternatively referred to as analysis state) for Forecast Mode.Mainstream at present A kind of Data Assimilation method is pooling information assimilation method, and this method runs Forecast Mode using multiple set members, then adopts The error co-variance matrix that there is stream to rely on background error information is generated with monte carlo method, is had and is simply easily realized and be convenient for The advantages of parallel processing etc..But limited set member's number will lead to very important sampling error.Reduce sampling error And an important way for removing remote spurious correlation is exactly covariance localization.However, the introducing of covariance localization will again So that the exact configuration of analysis set member (the initial fields set member obtained after Data Assimilation step) becomes a big difficulty.
After carrying out the operation of covariance localization, current analysis set member's generation method is mainly that random perturbation is seen Survey document method.Really qualitative observation only has one to observation space, and forecast ensemble member have it is multiple therefore same in the data of progress Need to generate multiple corresponding observations when change.Randomized method basic principle is as follows: given observation error variance and covariance, According to Gaussian Profile random perturbation observational data, forecast ensemble member is merged using Ensemble Kalman Filter method, is ultimately produced Corresponding analysis set member, shown in mathematical formulae such as formula (2)；
In formula (2),Indicate i-th of analysis set member's vector,Indicate that i-th of forecast ensemble member vectors, P indicate Prediction error conariance matrix, R indicate that observation error covariance matrix, y indicate observation vector, εiIndicate that i-th of observation is random Disturbance, H indicate state space projection to the non-linear Observation Operators of observation space, the tangent linear matrix of H expression operator H, ()T ()-1Respectively indicate the transposition and inverse of a matrix of matrix.
As shown in Figure 1, including: using the step of random perturbation observational data method analysis set member's generation method at present
Step1: using the analysis state set member in a upper stage, the N number of Forecast Mode of independent operating is obtained N number of pre- Report set member
Step2: using shown in forecast ensemble construction prediction error conariance matrix such as formula (3)；
In formula (3),Indicate that forecast state average value, N indicate set member's number,Indicate _ i-th forecast member, Indicate i-th of forecast ensemble bias vector, δ XbIndicate forecast ensemble deviation matrix, PbExpression _ forecast ensemble error covariance square Battle array.
Step3: introducing correlation matrix C, shown in the prediction error conariance matrix such as formula (4) after obtaining localization；
P=PbοC (4)
In formula (4), P indicates the prediction error conariance matrix after localization, PbIndicate original prediction error conariance square Battle array, ο indicate Schur product (multiplication of matrix corresponding element), and C is correlation matrix.Wherein, correlation matrix C is by the tight Zhi Quanchong of 5 ranks The symmetrical matrix that function generates (diagonal element 1, when remoter from diagonal distance, element value is smaller).
Step4: the tangent linear matrix of calculating observation operator calculates gain matrix such as in conjunction with observation error covariance matrix Shown in formula (5)；
K=PHT(HPHT+R)-1 (5)
In formula (5), K is gain matrix, and P indicates that the prediction error conariance matrix after localization, H indicate Observation Operators Tangent linear matrix, R indicate observation error covariance matrix；
Step5: projection of the CALCULATING PREDICTION state in observation space
Step6: according to the observation error regularity of distribution, observation error is constructed for each set member and disturbs εi；
Step7: it is calculated shown in renewal vector such as formula (6) for each member；
In formula (6), y indicates observation vector, εiIndicate the corresponding random observation disturbance of i-th of forecast member, H indicates observation Operator (or observation function),Indicate i-th of forecast ensemble member；
Step8: it is calculated shown in analysis increment such as formula (7) for each member；
In formula (7), K is gain matrix, and P indicates that the prediction error conariance matrix after localization, H indicate Observation Operators Tangent linear matrix, R indicate observation error covariance matrix；Y indicates observation vector, εiIndicate i-th of forecast member it is corresponding with Machine observation disturbance, H indicate Observation Operators,Indicate i-th of forecast ensemble member；
Step9: in conjunction with forecast state set, final analysis state set is obtained
But there are following disadvantages for the program: (1) in step Step6, the program uses observation random perturbation Method, due to observation error statistic itself be it is devious, randomized method would be possible to cause bigger system deviation and Sampling error；(2) in step step8, the information of ambient field covariance localization cannot be well in observation random perturbation mistake It is preserved in journey, the effect for causing sampling error to be eliminated is undesirable, so that gathering, dispersion is less than normal to eventually lead to set System is not restrained and is finally dissipated.In pooling information assimilation method, limited set member's number will introduce sampling error and association Remote spurious correlation in variance matrix, therefore need to be eliminated using covariance localization technology.But localization technology It uses and the generation for analyzing set member is become difficult, be often used random perturbation observational data method at present and handled. But due to observation error statistic itself be it is devious, randomized method would be possible to cause bigger system deviation and adopt Sample error, meanwhile, filtering degeneration makes set dispersion less than normal, so as to cause aggregation system diverging.Therefore, how preferably Removal sampling error generates dispersion and suitably analyzes set, has become a key technical problem urgently to be resolved.
Summary of the invention
The technical problem to be solved in the present invention: it in view of the above problems in the prior art, provides a kind of based on reverse localization Deterministic parsing set generation method and system.The present invention closes generating mode by improving localization scheme and analytic set, and one Aspect can preferably remove sampling error and remote spurious correlation, on the other hand can be generated an analysis dispersion more towards In the set of analytical error, it is obviously improved the performance of Data Assimilation, it is pre- to obtain more accurate reliable numerical value The original state of report problem.
In order to solve the above-mentioned technical problem, the technical solution adopted by the present invention are as follows:
A kind of deterministic parsing set generation method based on reverse localization, implementation steps include:
1) using the N number of Forecast Mode of analysis state set member's independent operating in a upper stage, N number of forecast ensemble was obtained MemberAccording to N number of forecast ensemble member CALCULATING PREDICTION Set Status average value
2) by N number of forecast ensemble memberForecast ensemble state average value is individually subtractedObtained forecast ensemble deviation square On Square-Rooting Matrices of the battle array as prediction error conariance matrixWhereinFor i-th of forecast collection Synthesis personSubtract forecast ensemble state average valueI-th obtained of forecast departure vector,It is average for forecast ensemble state Value；
3) using the On Square-Rooting Matrices C of the tight branch weighting function construction correlation matrix of 5 ranks1/2, then calculate the forecast of localization Error covariance On Square-Rooting Matrices Zb；
4) Observation Operators are combined, the localization background error covariance On Square-Rooting Matrices Y for projecting to observation space is calculatedb:
5) based on the localization background error covariance On Square-Rooting Matrices Y for projecting to observation spaceb, observation error covariance Matrix, R calculate gain matrix (Yb)TR-1Using as observation renewal vector weight matrix:
6) CALCULATING PREDICTION Set Status average valueIn the projection of observation spaceWhereinTo see Survey the projection function in space；
7) based on observation state observation space projection yoWith forecast ensemble state average valueIn the throwing of observation space ShadowObtain renewal vector
8) it is based on gain matrix (Yb)TR-1Calculate the analytical error covariance matrix P of control variablew,a；
9) based on observation renewal vector (Yb)TR-1, renewal vectorControl the analytical error covariance matrix of variable Pw,aThree calculates control variable analysis value
10) based on control variable analysis valueForecast ensemble state average valueThe prediction error conariance of localization On Square-Rooting Matrices ZbThree calculates analysis state mean value
11) the prediction error conariance On Square-Rooting Matrices Z based on localizationb, control variable analytical error covariance square Battle array Pw,aCalculate the State variable analysis error co-variance matrix P with localization informationa；
12) the On Square-Rooting Matrices Z of structural regime variable analysis error co-variance matrixa；
13) according to the On Square-Rooting Matrices Z of State variable analysis error co-variance matrixa, correlation matrix On Square-Rooting Matrices C1/2, analysis increment is calculated for each set member
14) it is directed to each set member, state mean value will be analyzedWith analysis incrementSummation, obtains each assemble The final analysis state of member, set are used as original state set
Preferably, the prediction error conariance On Square-Rooting Matrices Z of localization is calculated in step 3)bAs shown in formula (10)；
In formula (10),For the prediction error conariance On Square-Rooting Matrices Z of localizationbIn i-th of submatrix, i ∈ 1, 2 ..., N }, N is forecast ensemble number of members, and diag () indicates vector carrying out diagonal matrix, obtained diagonal matrix The diagonal element of every row is the element of the correspondence row of vector,Indicate diagonal matrix and On Square-Rooting Matrices C1/2Phase Multiply, C1/2Indicate the On Square-Rooting Matrices using the tight branch weighting function construction correlation matrix of 5 ranks.
Preferably, the localization background error covariance On Square-Rooting Matrices Y for projecting to observation space is calculated in step 4)b's Shown in function expression such as formula (11)；
In formula (11), N is forecast ensemble number of members, and diag () indicates vector carrying out diagonal matrix,Table Show i-th of forecast ensemble member in the projection of observation space,Indicate forecast ensemble state average value in the throwing of observation space Shadow,Indicate project to observation space correlation matrix On Square-Rooting Matrices, i ∈ { 1,2 ..., N },Indicate the difference diagonal matrix that forecast ensemble member and state average value project in observation space Afterwards with the product of the On Square-Rooting Matrices of correlation matrix.
Preferably, the analytical error covariance matrix P of control variable is calculated in step 8)w,aFunction expression such as formula (12) shown in；
In formula (12), N is forecast ensemble number of members, and K indicates the time step number of assimilation time window, and subscript j is indicated j-th Time step, Yb,jIndicate that j-th of time step projects to the localization background error covariance On Square-Rooting Matrices of observation space, RjTable Show the observation error covariance matrix of j-th of time step.
Preferably, control variable analysis value is calculated in step 9)Function expression such as formula (13) shown in；
In formula (13), Pw,aFor the analytical error covariance matrix for controlling variable, K indicates the time step number of assimilation time window, Subscript j indicates j-th of time step, Yb,jIndicate j-th of time step project to observation space localization background error covariance it is flat Sqrtm, RjIndicate the observation error covariance matrix of j-th of time step,Indicate the update of j-th of time step Vector.
Preferably, step 10) fall into a trap point counting analysis state mean valueFunction expression such as formula (14) shown in；
In formula (14),Expression control variable analysis value,Indicate forecast ensemble state average value, ZbIndicate localization Prediction error conariance On Square-Rooting Matrices Zb。
Preferably, the State variable analysis error co-variance matrix P with localization information is calculated in step 11)aFunction Shown in expression formula such as formula (15)；
Pa=ZbPw,a(Zb)T (15)
In formula (15), ZbIndicate prediction error conariance On Square-Rooting Matrices, the P of localizationw,aIndicate the analysis of control variable Error co-variance matrix.
Preferably, the On Square-Rooting Matrices Z of step 12) structural regime variable analysis error co-variance matrixaFunction representation Shown in formula such as formula (16)；
In formula (16),For the On Square-Rooting Matrices Z of State variable analysis error co-variance matrixaIn i-th of submatrix,For p × r matrix, i ∈ { 1,2 ..., N },It indicatesWithDifference, N be forecast ensemble number of members；Indicate square Battle array C1/2Jth row kth column element, j ∈ { 1,2 ..., p }, k ∈ { 1,2 ..., r }, p be system mode dimension, r is Correlation Moment The truncation dimension of battle array On Square-Rooting Matrices.
It preferably, is that each set member calculates analysis increment in step 13)Function expression such as formula (17) institute Show；
In formula (17),Indicate that i-th of element of k-th of analysis increment, mean are function of averaging,Table Show submatrixThe i-th row jth column element,Representing matrix C1/2The i-th row jth column element, i ∈ { 1,2 ..., p }, j ∈ { 1,2 ..., r }, p are system mode dimension, and r is the truncation dimension of correlation matrix On Square-Rooting Matrices.
The present invention also provides a kind of deterministic parsing set based on reverse localization to generate system, including department of computer science System, the computer system are programmed to perform the aforementioned deterministic parsing set generation method based on reverse localization of the present invention The step of.
Compared to the prior art, the present invention have it is following the utility model has the advantages that
In pooling information assimilation method, limited set member's number will be introduced into remote in sampling error and covariance matrix Apart from spurious correlation, therefore need to be eliminated using covariance localization technology.But localization technology uses and to analyze The generation of set member becomes difficult, and is often used random perturbation observational data method at present and is handled.But due to observation error Statistic itself be it is devious, randomized method would be possible to lead to bigger system deviation and sampling error, meanwhile, filter Wave degeneration makes set dispersion less than normal, so as to cause aggregation system diverging.Therefore, in order to preferably remove sampling error, It generates dispersion and suitably analyzes set, the present invention is based on the deterministic parsing set generation methods of reverse localization to pass through improvement Localization scheme and analytic set close generating mode, and one aspect of the present invention can preferably remove sampling error and remote pseudo- phase It closes, the set that an analysis dispersion tends to analytical error on the other hand can be generated, finally make the property of Data Assimilation It can be obviously improved, obtain the original state of more accurate reliable numerical forecast problem.
Detailed description of the invention
Fig. 1 is that the analytic set of existing random perturbation observational data closes the flow chart of generation method.
Fig. 2 is the flow chart of deterministic parsing of embodiment of the present invention set generation method.
Specific embodiment
As shown in Fig. 2, the implementation steps packet of deterministic parsing set generation method of the present embodiment based on reverse localization It includes:
1) using the N number of Forecast Mode of analysis state set member's independent operating in a upper stage, N number of forecast ensemble was obtained MemberAccording to N number of forecast ensemble member CALCULATING PREDICTION Set Status average value
2) by N number of forecast ensemble memberForecast ensemble state average value is individually subtractedObtained forecast ensemble deviation square Battle array, the On Square-Rooting Matrices as prediction error conariance matrixWhereinIt is forecast for i-th Set memberSubtract forecast ensemble state average valueI-th obtained of forecast departure vector,It is flat for forecast ensemble state Mean value；
3) using the On Square-Rooting Matrices C of the tight branch weighting function construction correlation matrix of 5 ranks1/2, then calculate the forecast of localization Error covariance On Square-Rooting Matrices Zb；
4) Observation Operators are combined, the localization background error covariance On Square-Rooting Matrices Y for projecting to observation space is calculatedb:
5) based on the localization background error covariance On Square-Rooting Matrices Y for projecting to observation spaceb, observation error covariance Matrix R calculates gain matrix (Yb)TR-1Using as observation renewal vector weight matrix:
6) CALCULATING PREDICTION Set Status average valueIn the projection of observation spaceWhereinTo see Survey the projection function in space；
7) based on observation state observation space projection yoWith forecast ensemble state average valueIn the throwing of observation space ShadowObtain renewal vector
8) it is based on gain matrix (Yb)TR-1Calculate the analytical error covariance matrix P of control variablew,a；
9) based on observation renewal vector (Yb)TR-1, renewal vectorControl the analytical error covariance matrix of variable Pw,aThree calculates control variable analysis value
10) based on control variable analysis valueForecast ensemble state average valueThe prediction error conariance of localization On Square-Rooting Matrices ZbThree calculates analysis state mean value
11) the prediction error conariance On Square-Rooting Matrices Z based on localizationb, control variable analytical error covariance square Battle array Pw,a, calculate the State variable analysis error co-variance matrix P with localization informationa；
12) the On Square-Rooting Matrices Z of structural regime variable analysis error co-variance matrixa；
13) according to the On Square-Rooting Matrices Z of State variable analysis error co-variance matrixa, correlation matrix On Square-Rooting Matrices C1/2, analysis increment is calculated for each set member
14) it is directed to each set member, state mean value will be analyzedWith analysis incrementSummation, obtains each assemble The final analysis state of member, set are used as original state set
In the present embodiment, according to N number of forecast ensemble member in step 1)CALCULATING PREDICTION Set Status average valueLetter Shown in number expression formula such as formula (8)；
In formula (8),For i-th of forecast ensemble member in forecast ensemble member, N is forecast ensemble number of members.
In the present embodiment, shown in forecast ensemble deviation matrix such as formula (9) obtained in step 2)；
In formula (9), δ XbFor obtained forecast ensemble deviation matrix,For i-th of forecast ensemble memberSubtract forecast Set Status average valueI-th obtained of forecast departure vector,For forecast ensemble state average value.
In the present embodiment, the prediction error conariance On Square-Rooting Matrices Z of localization is calculated in step 3)bSuch as formula (10) institute Show；
In formula (10),For the prediction error conariance On Square-Rooting Matrices Z of localizationbIn i-th of submatrix, i ∈ 1, 2 ..., N }, N is forecast ensemble number of members, and diag () indicates vector carrying out diagonal matrix, obtained diagonal matrix The diagonal element of every row is the element of the correspondence row of vector,Indicate diagonal matrix and On Square-Rooting Matrices C1/2Phase Multiply, C1/2Indicate the On Square-Rooting Matrices using the tight branch weighting function construction correlation matrix of 5 ranks.
In the present embodiment, the localization background error covariance On Square-Rooting Matrices for projecting to observation space are calculated in step 4) YbFunction expression such as formula (11) shown in；
In formula (11), N is forecast ensemble number of members, and diag () indicates vector carrying out diagonal matrix,Table Show i-th of forecast ensemble member in the projection of observation space,Indicate forecast ensemble state average value in the throwing of observation space Shadow,Indicate project to observation space correlation matrix On Square-Rooting Matrices, i ∈ { 1,2 ..., N },Indicate the difference diagonal matrix that forecast ensemble member and state average value project in observation space Afterwards with the product of the On Square-Rooting Matrices of correlation matrix.
In the present embodiment, the analytical error covariance matrix P of control variable is calculated in step 8)w,aFunction expression such as Shown in formula (12)；
In formula (12), N is forecast ensemble number of members, and K indicates the time step number of assimilation time window, and subscript j is indicated j-th Time step, Yb,jIndicate that j-th of time step projects to the localization background error covariance On Square-Rooting Matrices of observation space, RjTable Show the observation error covariance matrix of j-th of time step.
Control variable analysis value is calculated in the present embodiment, in step 9)Function expression such as formula (13) shown in；
In formula (13), Pw,aFor the analytical error covariance matrix for controlling variable, K indicates the time step number of assimilation time window, Subscript j indicates j-th of time step, Yb,jIndicate j-th of time step project to observation space localization background error covariance it is flat Sqrtm, RjIndicate the observation error covariance matrix of j-th of time step,Indicate the update of j-th of time step Vector.
In the present embodiment, step 10) fall into a trap point counting analysis state mean valueFunction expression such as formula (14) shown in；
In formula (14),Expression control variable analysis value,Indicate forecast ensemble state average value, ZbIndicate localization Prediction error conariance On Square-Rooting Matrices.
In the present embodiment, the State variable analysis error co-variance matrix P with localization information is calculated in step 11)a's Shown in function expression such as formula (15)；
Pa=ZbPw,a(Zb)T (15)
In formula (15), ZbIndicate prediction error conariance On Square-Rooting Matrices, the P of localizationw,aIndicate the analysis of control variable Error co-variance matrix.
In the present embodiment, the On Square-Rooting Matrices Z of step 12) structural regime variable analysis error co-variance matrixaFunction Shown in expression formula such as formula (16)；
In formula (16),For the On Square-Rooting Matrices Z of State variable analysis error co-variance matrixaIn i-th of submatrix,For p × r matrix, i ∈ { 1,2 ..., N },It indicatesWithDifference (the corresponding analysis of also referred to as i-th of set member Increment), N is forecast ensemble number of members；Representing matrix C1/2Jth row kth column element, j ∈ { 1,2 ..., p }, k ∈ { 1,2 ..., r }, p are system mode dimension, and r is the truncation dimension of correlation matrix On Square-Rooting Matrices.
It is that each set member calculates analysis increment in the present embodiment, in step 13)Function expression such as formula (17) It is shown；
In formula (17),Indicate that i-th of element of k-th of analysis increment, mean are function of averaging,Table Show submatrixThe i-th row jth column element,Representing matrix C1/2The i-th row jth column element, i ∈ { 1,2 ..., p }, j ∈ { 1,2 ..., r }, p are system mode dimension, and r is the truncation dimension of correlation matrix On Square-Rooting Matrices.
In the present embodiment, step 14) is directed to each set member, will analyze state mean valueWith analysis incrementSummation, The final analysis state of each set member is obtained, set is used as original state set
The present embodiment also provides a kind of deterministic parsing set generation system based on reverse localization, including department of computer science System, the computer system are programmed to perform the aforementioned deterministic parsing set generation method based on reverse localization of the present embodiment The step of.
The above is only a preferred embodiment of the present invention, protection scope of the present invention is not limited merely to above-mentioned implementation Example, all technical solutions belonged under thinking of the present invention all belong to the scope of protection of the present invention.It should be pointed out that for the art Those of ordinary skill for, several improvements and modifications without departing from the principles of the present invention, these improvements and modifications It should be regarded as protection scope of the present invention.

Claims (10)

1. a kind of deterministic parsing set generation method based on reverse localization, it is characterised in that implementation steps include:
1) using the N number of Forecast Mode of analysis state set member's independent operating in a upper stage, N number of forecast ensemble member was obtainedAccording to N number of forecast ensemble member CALCULATING PREDICTION Set Status average value
2) by N number of forecast ensemble memberForecast ensemble state average value is individually subtractedObtained forecast ensemble deviation matrix is made For the On Square-Rooting Matrices of prediction error conariance matrixWhereinFor i-th of forecast ensemble at MemberSubtract forecast ensemble state average valueI-th obtained of forecast departure vector,For forecast ensemble state average value；
3) using the On Square-Rooting Matrices C of the tight branch weighting function construction correlation matrix of 5 ranks1/2, then calculate the prediction error of localization Covariance square root matrix Zb；
4) Observation Operators are combined, the localization background error covariance On Square-Rooting Matrices Y for projecting to observation space is calculatedb:
5) based on the localization background error covariance On Square-Rooting Matrices Y for projecting to observation spaceb, observation error covariance matrix R calculates gain matrix (Yb)TR-1Using as observation renewal vector weight matrix:
6) CALCULATING PREDICTION Set Status average valueIn the projection of observation spaceWherein H () is in observation space Projection function；
7) based on observation state observation space projection yoWith forecast ensemble state average valueIn the projection of observation space Obtain renewal vector
8) it is based on gain matrix (Yb)TR-1Calculate the analytical error covariance matrix P of control variablew,a；
9) it is based on gain matrix (Yb)TR-1, renewal vectorControl the analytical error covariance matrix P of variablew,aThree, Calculate control variable analysis value
10) based on control variable analysis valueForecast ensemble state average valueThe prediction error conariance square of localization Root matrix ZbThree calculates analysis state mean value
11) the prediction error conariance On Square-Rooting Matrices Z based on localizationb, control variable analytical error covariance matrix Pw,a, Calculate the State variable analysis error co-variance matrix P with localization informationa；
12) the On Square-Rooting Matrices Z of structural regime variable analysis error co-variance matrixa；
13) according to the On Square-Rooting Matrices Z of State variable analysis error co-variance matrixa, correlation matrix On Square-Rooting Matrices C1/2, it is Each set member calculates analysis increment
14) it is directed to each set member, state mean value will be analyzedWith analysis incrementSummation, obtains each set member's Final analysis state, set are used as original state set
2. the deterministic parsing set generation method according to claim 1 based on reverse localization, which is characterized in that step Rapid 3) the middle prediction error conariance On Square-Rooting Matrices Z for calculating localizationbAs shown in formula (10)；
In formula (10),For the prediction error conariance On Square-Rooting Matrices Z of localizationbIn i-th of submatrix, i ∈ 1, 2 ..., N }, N is forecast ensemble number of members, and diag () indicates vector carrying out diagonal matrix, obtained diagonal matrix The diagonal element of every row is the element of the correspondence row of vector,Indicate diagonal matrix and On Square-Rooting Matrices C1/2Phase Multiply, C1/2Indicate the On Square-Rooting Matrices of the correlation matrix using the tight branch weighting function construction of 5 ranks.
3. the deterministic parsing set generation method according to claim 1 based on reverse localization, which is characterized in that step Rapid 4) middle calculating projects to the localization background error covariance On Square-Rooting Matrices Y of observation spacebFunction expression such as formula (11) shown in；
In formula (11), N is forecast ensemble number of members, and diag () indicates vector carrying out diagonal matrix,Indicate the I forecast ensemble member observation space projection,Indicate forecast ensemble state average value observation space projection,Indicate project to observation space correlation matrix On Square-Rooting Matrices, i ∈ { 1,2 ..., N },Indicate the difference diagonal matrix that forecast ensemble member and state average value project in observation space Afterwards with the product of correlation matrix On Square-Rooting Matrices.
4. the deterministic parsing set generation method according to claim 1 based on reverse localization, which is characterized in that step Rapid 8) the middle analytical error covariance matrix P for calculating control variablew,aFunction expression such as formula (12) shown in；
In formula (12), N is forecast ensemble number of members, and K indicates the time step number of assimilation time window, and subscript j indicates j-th of time Step, Yb,jIndicate that j-th of time step projects to the localization background error covariance On Square-Rooting Matrices of observation space, RjIndicate jth The observation error covariance matrix of a time step.
5. the deterministic parsing set generation method according to claim 1 based on reverse localization, which is characterized in that step Rapid 9) middle calculate controls variable analysis valueFunction expression such as formula (13) shown in；
In formula (13), Pw,aFor the analytical error covariance matrix for controlling variable, K indicates the time step number of assimilation time window, subscript J indicates j-th of time step, Yb,jIndicate that j-th of time step projects to the localization background error covariance square root of observation space Matrix, RjIndicate the observation error covariance matrix of j-th of time step,Indicate the renewal vector of j-th of time step.
6. the deterministic parsing set generation method according to claim 1 based on reverse localization, which is characterized in that step Rapid point counting analysis state mean value of 10) falling into a trapFunction expression such as formula (14) shown in；
In formula (14),Expression control variable analysis value,Indicate forecast ensemble state average value, ZbIndicate the forecast of localization Error covariance On Square-Rooting Matrices Zb。
7. the deterministic parsing set generation method according to claim 1 based on reverse localization, which is characterized in that step Rapid 11) middle State variable analysis error co-variance matrix P of the calculating with localization informationaFunction expression such as formula (15) institute Show；
Pa=ZbPw,a(Zb)T (15)
In formula (15), ZbIndicate prediction error conariance On Square-Rooting Matrices, the P of localizationw,aIndicate the analytical error of control variable Covariance matrix.
8. the deterministic parsing set generation method according to claim 1 based on reverse localization, which is characterized in that step The On Square-Rooting Matrices Z of rapid 12) structural regime variable analysis error co-variance matrixaFunction expression such as formula (16) shown in；
In formula (16),For the On Square-Rooting Matrices Z of State variable analysis error co-variance matrixaIn i-th of submatrix,For P × r matrix, i ∈ { 1,2 ..., N },It indicatesWithDifference, N be forecast ensemble number of members；Representing matrix C1/2 Jth row kth column element, j ∈ { 1,2 ..., p }, k ∈ { 1,2 ..., r }, p are system mode dimension, and r is flat for correlation matrix The truncation dimension of sqrtm.
9. the deterministic parsing set generation method according to claim 1 based on reverse localization, which is characterized in that step It is rapid 13) in be that each set member calculates analysis incrementFunction expression such as formula (17) shown in；
In formula (17),Indicate that i-th of element of k-th of analysis increment, mean are function of averaging,Indicate son MatrixThe i-th row jth column element,Representing matrix C1/2The i-th row jth column element, i ∈ { 1,2 ..., p }, j ∈ 1, 2 ..., r }, p is system mode dimension, and r is the truncation dimension of correlation matrix On Square-Rooting Matrices.
10. a kind of deterministic parsing set based on reverse localization generates system, including computer system, it is characterised in that: The computer system is programmed to perform the certainty point based on reverse localization described in any one of claim 1~9 The step of analysis set generation method.
CN201810697284.2A 2018-06-29 2018-06-29 Method and system for generating deterministic analysis set based on reverse localization Pending CN109033029A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110555616A (en) * 2019-09-05 2019-12-10 中国气象局广州热带海洋气象研究所 Dense observation data optimization scheduling method of numerical weather mode assimilation system
CN113360854A (en) * 2021-08-10 2021-09-07 中国人民解放军国防科技大学 Data assimilation method based on adaptive covariance expansion

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN110555616A (en) * 2019-09-05 2019-12-10 中国气象局广州热带海洋气象研究所 Dense observation data optimization scheduling method of numerical weather mode assimilation system
CN110555616B (en) * 2019-09-05 2021-12-14 中国气象局广州热带海洋气象研究所 Dense observation data optimization scheduling method of numerical weather mode assimilation system
CN113360854A (en) * 2021-08-10 2021-09-07 中国人民解放军国防科技大学 Data assimilation method based on adaptive covariance expansion
CN113360854B (en) * 2021-08-10 2021-11-05 中国人民解放军国防科技大学 Data assimilation method based on adaptive covariance expansion

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