CN109840311A - Coupling data assimilation and parameter optimization method based on optimal observation time window - Google Patents
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Abstract
Coupling data assimilation and parameter optimization method based on optimal observation time window, belong to data assimilation, parameter optimization and the Numerical Forecast Technology field of Coupled Climate Models system.For the assimilation of traditional coupling data and the deficiency of the observation utilization of resources and state estimation and parameter optimization precision existing for parameter optimization method, the characteristic time scale of the spectrum information coupled mode state of the free integrating state of present invention combination coupled mode, the time scale according to coupled mode state set up the size of optimal observation time window.Time weighting coefficient in observation window is introduced on the basis of obtaining effective atmosphere and oceanographic observation data based on optimal observation time window, extract effective observation information to the full extent to be fitted the feature variability of coupled mode state and ignore the time varying characteristic of mode internal parameter and introduce the time mean coefficient in time window, it realizes the more accurate estimation and optimization to mode parameter, strengthens the atmosphere of coupled mode and the numerical forecast ability of ocean.
Description
Technical field
The invention belongs to the data assimilation of Coupled Climate Models system, parameter optimization and Numerical Forecast Technology fields, specifically
Be related to it is a kind of based on optimal observation time window coupling data assimilation and parameter optimization method.
Background technique
Currently, each subsystem in the earth systems such as Coupled Climate Models energy feasible simulation atmosphere, ocean, land and sea ice
Interaction process between system, thus simulation climate change procedure.But in coupled mode again often exist various errors with not
Certainty (such as faulty Numerical Implementation and physical parameter process and unreasonable mode internal parameter value etc.), thus
Mode output result is caused to deviate the actual observation data of true climate characteristic and change procedure, to limit coupled mode
Climatic prediction ability.The advantage of traditional coupling data assimilation and parameter optimisation procedure is that observation information can pass through coupled mode
Coupled Dynamics feature transmitted between the subsystems of coupled mode, so that Assured Mode subsystems can obtain
To the characteristic for scale interaction of holding time while consistent and coherent adjustment.Reach the premise of quasi-balanced state in mode state
Under the conditions of, coupled mode parameter Estimation and optimization process utilize effective observation information by mode state and dependence on parameter
It realizes adjustment to mode parameter, realizes and straggling parameter is accurately estimated and compensated brought by the physical parameter process of deviation
It influences.Traditional coupling data assimilation can effectively improve state and Parameter Estimation Precision with parameter optimisation procedure;Defect be by
Design conditions are limited, and the assimilation period is far longer than observation interval, and the observation on assimilation time point is only considered in assimilation process
Information has ignored the observation information on non-assimilation time point, causes the significant wastage of observation information, assimilated to limit
Journey is to the fitting of mode state feature variability and the precision of parameter Estimation.
Observation window commonly used in collecting effective observation information with for each data assimilation and parameter optimization period,
To improve the estimation of each mode state and the observation utilization rate in the parameter optimization period.Observation time window is to ignore sight
Using assimilation time point as the notional effective observation information of center acquisition time under conditions of the time difference opposite sex between survey, one
The big observation time window of aspect can incorporate more observation informations, and on the other hand excessive observation time window can twisted state
Fitting degree of the assimilation process to the feature variability of mode state.Observation information can be maximally utilized and also can by how determining one
The size for minimizing the optimal observation time window for the degreeof tortuosity being fitted to pattern feature variability becomes a problem.It sees simultaneously
The time difference opposite sex surveyed between effectively observing in time window will cause over-evaluating and underestimating to the observation on non-assimilation time point,
To the accuracy of reduction mode state and parameter Estimation.How time difference observation time window in effectively observe between is eliminated
The opposite sex is also the another problem faced when introducing observation time window.
Summary of the invention
The purpose of the present invention is to provide a kind of coupling data assimilation and parameter optimization based on optimal observation time window
Method, for the assimilation of traditional coupling data and the observation utilization of resources present in parameter optimization method and state estimation and parameter
Optimize the deficiency of precision, the present invention combines the spy of the spectrum information coupled mode state of the free integrating state of coupled mode first
Time scale is levied, and the time scale according to coupled mode state sets up the size of optimal observation time window.Based on optimal
Observation time window introduces time weighting coefficient in observation window on the basis of obtaining effective atmosphere and oceanographic observation data, most
Effective observation information is extracted in big degree to be fitted the feature variability of coupled mode state;Ignore mode internal parameter simultaneously
Time varying characteristic simultaneously introduces the time mean coefficient in time window, realizes the more accurate estimation and optimization to mode parameter;
To strengthen the atmosphere of coupled mode and the numerical forecast ability of ocean.
The object of the present invention is achieved like this:
Coupling data assimilation and parameter optimization method based on optimal observation time window, include the following steps:
Step 1: obtaining the characteristic time scale of coupled mode state;Coupling is obtained on the basis of coupled mode freely integrates
The time series of syntype state, and spectral factorization carried out to the time series of state, when feature to obtain different couple states
Between scale;
Step 2: being pre-processed to data are observed in optimal observation time window;It rejects in optimal observation time window
Invalid data and abnormal data will effectively observe dataFormat needed for being converted to assimilation process, whereinEffective observation of observation point k is represented, m indicates effective observation quantity in observation window;
Step 3: solving the observation increment effectively observed in optimal observation window respectively;Coupling is corresponded to based on assimilation time point k
Syntype state set (xK, 1..., xK, N), wherein xK, 1The state variable of lattice point k is represented, N indicates state set number of members,
Corresponding observation increment is solved to effective observations all in optimal observation windowWhereinTable
M-th of observation increment effectively observed to n-th state set member in window on sign lattice point k;By state set (xK, 1...,
xK, N) i-th, i=1:N member, be projected into observation space using Systems with Linear Observation operator, the priori set observedIn conjunction with observation observation increment corresponding with the total calculation of observation a prior set
Step 4: introducing time weighting coefficient in observation window and solve the average observed increment for being directed to mode state;For step
To effective observation increments all in optimal observation window obtained in rapid 3When introducing in observation window
Between weight coefficient Wii:
It wherein include m effectively observations in optimal observation window L, each effectively observes the time difference with assimilation time point
Different is respectively (L1..., Lm);
The observation increment of equalizationAre as follows:
Step 5: solving the average analysis increment for mode state estimation;Observation according to the equalization that step 4 obtains
IncrementAnd observation errorThe corresponding analysis increment of Solution model stateAre as follows:
WhereinIndicate the prior uncertainty covariance of observation with state set, observation errorFor
Step 6: realizing the optimization and update to mode internal parameter;After mode state estimation reaches quasi-balanced state,
Mode internal parameter is estimated and optimized using the observation information in optimal observation window, for the optimal window of parameter Estimation
Mouth setting depends on the corresponding optimal observation time window of observation of Optimal Parameters, and effective observation in window is respectively according to step
3 calculate corresponding observation increment, and equalization seeks average observed increment on the basis of observing increment;Difference is general mould
Formula inner parameter does not have time varying characteristic, and the observation in window and parameter excellent time point do not have the time difference anisotropic, when in observation window
Between weight coefficient be average weight coefficient Wii':
Wii'=1/m;Ii=1:m
The observation increment equalized at this timeAre as follows:
The corresponding observation error of observation increment after equalizationWith aggregate error is tested before observationIt is respectively as follows:
After the observation increment and observation error that are equalized, the analysis of inner parameter is directed to based on solution shown in step 5
Increment Delta PI, j:
WhereinIt indicates parameter to be estimated and observes the error covariance of priori set, it later will analysis
Increment Delta PI, jIt is realized in the corresponding parameter sets that are added to and treats the optimization and update for estimating parameter sets;
Step 7: adaptive distention protocol is used at the end of state estimation procedure and parameter optimisation procedure, based on update
Mode state and inner parameter afterwards, mode continue to integrate and enter next parameter Estimation and parameter optimization period.
Optimal observation time window of corresponding size is arranged in the characteristic time scale that the step 1 obtains coupled mode state
Mouth size realizes the fitting to coupled mode state feature variability while utmostly extracting effective observation information.
Increment is observed in the step 3Are as follows:
Wherein N represents set member's quantity, and m, which is represented, effectively observes quantity in observation window,WithIt respectively represents
The ensemble average and set of set of modes offset on observation lattice point are disturbed when introducing observation;It is observation priori set,Indicate observation priori set member,WithObservation priori ensemble average and disturbance are respectively indicated,Collective standard difference and observation error standard deviation ratio are tested before expression;
Corresponding parameter Estimation is arranged in the corresponding optimal observation time window of the observation based on Optimal Parameters in the step 6
Optimal window, binding pattern state-parameter error covariance, realize utmostly observation information to mode internal parameter carry out
Adjustment and optimization.
The beneficial effects of the invention are that:
Optimal observation time window is arranged on the basis of based on the analysis of coupled mode state characteristic time scale in the present invention
To obtain effective atmosphere and oceanographic observation data and introduce time weighting coefficient in observation window, extract has to the full extent mouth
The observation information of effect is to be fitted the feature variability of coupled mode state;Ignore time varying characteristic and the introducing of mode internal parameter simultaneously
Time mean coefficient in time window realizes the more accurate estimation and optimization to mode parameter;To strengthen coupled mode
The atmosphere of formula and the numerical forecast ability of ocean.
Detailed description of the invention
Fig. 1 is optimal observation time window schematic diagram;
Fig. 2 is the execution flow chart of coupling data assimilation and parameter optimization method based on optimal observation time window.
Specific embodiment
The present invention is further described with reference to the accompanying drawing.
The present invention proposes that a kind of coupling data based on optimal observation time window assimilates with parameter optimization method come maximum
Degree extracts observation confidence and improves state estimation and parameter optimization precision while observation utilization rate to improve, to improve coupling
The atmosphere of mode and the numerical forecast precision of ocean.This method combines the spectrum information of the free integrating state of coupled mode first
The characteristic time scale of coupled mode state, and the time scale according to coupled mode state sets up optimal observation time window
Size.It is introduced in observation window on the basis of obtaining effective atmosphere and oceanographic observation data based on optimal observation time window
Time weighting coefficient extracts effective observation information to the full extent to be fitted the feature variability of coupled mode state;It neglects simultaneously
It omits the time varying characteristic of mode internal parameter and introduces the time mean coefficient in time window, realize to the more smart of mode parameter
True estimation and optimization;To strengthen the atmosphere of coupled mode and the numerical forecast ability of ocean.
Compared to traditional data assimilation and parameter optimisation procedure, the maximum difference of the present invention is according to mode state
Characteristic time scale introduces optimal observation time window of corresponding size utmostly to utilize observation information;It is seen simultaneously to eliminate
The time difference opposite sex observed in window is surveyed, time weighting coefficient in observation window is introduced;State estimation procedure is different from, in mode
Portion's parameter does not have a time varying characteristic, introduces average weight coefficient in the time to reduce the influence of observation error, improve state estimation with
Parameter optimization precision.One aspect of the present invention can greatly improve the utilization efficiency of observation, to utmostly incorporate observation information;
On the other hand more accurate mode state estimation and parameter optimization are realized in the influence that can reduce observation error;The mould of optimization
Formula state and inner parameter can greatly improve the atmosphere of mode and the numerical forecast precision of ocean.
It is optimal observation time window schematic diagram shown in Fig. 1.Technical solution proposed by the present invention will be described in detail below according to process
Specific embodiment, execute process it is as shown in Figure 2.The embodiment mainly includes following key content:
The characteristic time scale of step 1 acquisition coupled mode state: coupling is obtained on the basis of coupled mode freely integrates
The time series of syntype state, and spectral factorization carried out to the time series of state, when feature to obtain different couple states
Between scale.As shown in Fig. 1, the characteristic time scale for choosing 3% is that optimal observation time window is arranged in corresponding couple state
Size (observation window length L).
Step 2 is pre-processed to observing data in optimal observation time window: for the assimilation convenient for measured data, first
It needs to reject the invalid data and abnormal data in optimal observation time window, and will effectively observe data
(whereinEffective observation of observation point k is represented, m indicates effective observation quantity in observation window) it is converted to needed for assimilation process
Format.
Step 3 solves the observation increment effectively observed in optimal observation window respectively: based on the corresponding coupling of assimilation time point k
Mode state set (xK, 1..., xK, N) (wherein xK, 1The state variable of lattice point k is represented, N indicates state set number of members), it is right
All effective observations solve corresponding observation increment in optimal observation window(whereinCharacterization
M-th of observation increment effectively observed to n-th state set member in window on lattice point k);First by state set
(xK, 1..., xK, N) i-th, i=1:N member, observation space is projected into using Systems with Linear Observation operator, to be seen
The priori set of surveyIn conjunction with observation observation increment corresponding with the total calculation of observation a prior set
Wherein N represents set member's quantity, and m, which is represented, effectively observes quantity in observation window,WithIt respectively represents
The ensemble average and set of set of modes offset on observation lattice point are disturbed when introducing observation;It is observation priori set,Indicate observation priori set member,With withRespectively indicate observation priori ensemble average and disturbance.Collective standard difference and observation error standard deviation ratio are tested before representative.
Step 4 introduces time weighting coefficient in observation window and solves the average observed increment for being directed to mode state: for step
Obtained on rapid 3 to effective observation increments all in optimal observation windowWhen introducing in observation window
Between weight coefficient, the time difference on the one hand eliminating observation time point and assimilation time point is anisotropic, on the other hand introduces equalization energy
Effectively reduce observation error.Include m effectively observations, each effectively observation and assimilation time point in optimal observation window L
Time difference is respectively (L1..., Lm), then time weighting coefficient W in time windowiiAre as follows:
The observation increment equalized at this time becomesAre as follows:
The corresponding observation error of observation increment after then equalizingAre as follows:
That is:
Similarly, the standard deviation of set is tested before the observation after equalizationBecome:
Wherein (L1 4+…+Lm 4)/(L1 2+…+Lm 2)2< 1.
Step 5 solves the average analysis increment for mode state estimation: the observation increasing according to the equalization that step 4 obtains
AmountAnd observation errorThe corresponding analysis increment of Solution model state
WhereinIndicate the prior uncertainty covariance of observation with state set.Increase in the state analysis asked
AmountOn the basis of, the upper (x of the mode state set member that is added toK, 1..., xK, N), the posteriority set for the mode state asked is real
Now to the estimation of mode state and update, and initial fields are provided for next mode integral process.
Step 6 realizes the optimization and update to mode internal parameter: after mode state estimation reaches quasi-balanced state, benefit
Mode internal parameter is estimated and optimized with the observation information in optimal observation window;For the optimal window of parameter Estimation
The corresponding optimal observation time window of observation depending on Optimal Parameters is set, and effective observation in window is respectively according to step 3
Corresponding observation increment is calculated, and equalization seeks average observed increment on the basis of observing increment;Difference is general mould
Formula inner parameter does not have time varying characteristic, i.e. observation in window and parameter excellent time point does not have the time difference anisotropic, so observation window
Time weighting coefficient is average weight coefficient W in mouthfulii', it may be assumed that
Wii'=1/m;Ii=1:m
The observation increment equalized at this timeBecome:
The corresponding observation error of observation increment after then equalizingWith aggregate error is tested before observationIt is respectively as follows:
After the observation increment and observation error that are similarly equalized, inner parameter is directed to based on solving shown in step 5
Analysis increment, difference isIt indicates parameter to be estimated and observes the error covariance of priori set.Then
The analysis increment Delta P sought for parameter Estimation and optimization processI, j:
Increment Delta P will be analyzed laterI, jIt is realized in the corresponding parameter sets that are added to and treats the optimization for estimating parameter sets and more
Newly;And the parameter after optimizing can be applied in the mode integral of next step.
Required at the end of step 7 state estimation procedure and parameter optimisation procedure using adaptive distention protocol to avoid
Mode state set is excessively concentrated to cause the set that can not rationally characterize the general of state and parameter with member in parameter sets
Rate Density Distribution.Based on the mode state and inner parameter after update, mode continues to integrate and enters next parameter Estimation
With the parameter optimization period.
Characteristic time scale setting of corresponding size optimal observation time window of the step 1 based on couple state is big
It is small, the fitting to coupled mode state feature variability is realized while utmostly extracting effective observation information.
The step 3 introduces time weighting coefficient in observation window and solves the average observed increment for being directed to mode state,
The time difference opposite sex the over-evaluating to the observation on non-assimilation time point between effectively observing in observation time window can be effectively reduced
With the influence underestimated.
The step 6 is arranged corresponding parameter in the corresponding optimal observation time window of the observation based on Optimal Parameters and estimates
Meter optimal window, binding pattern state-parameter error covariance, realize utmostly observation information to mode internal parameter into
Row adjustment and optimization;Time weighting coefficient in identical observation window is introduced simultaneously, is effectively seen reducing in observation time window
Ignore the time varying characteristic of mode internal parameter while the time difference opposite sex between survey.
Claims (4)
1. coupling data assimilation and parameter optimization method based on optimal observation time window characterized by comprising
Step 1 obtains the characteristic time scale of coupled mode state;Coupling is obtained on the basis of coupled mode freely integrates
The time series of mode state, and spectral factorization is carried out to the time series of state, to obtain the characteristic time of different couple states
Scale;
Step 2 is pre-processed to data are observed in optimal observation time window;Reject the nothing in optimal observation time window
Data and abnormal data are imitated, data will be effectively observedFormat needed for being converted to assimilation process, wherein
Effective observation of observation point k is represented, m indicates effective observation quantity in observation window;
Step 3 solves the observation increment effectively observed in optimal observation window respectively;Coupled mode is corresponded to based on assimilation time point k
Formula state set (xk,1,…,xk,N), wherein xk,1The state variable of lattice point k is represented, N indicates state set number of members, to most
All effective observations solve corresponding observation increment in excellent observation windowWhereinCharacterize lattice
M-th of observation increment effectively observed to n-th state set member in window on point k;By state set (xk,1,…,xk,N)
I-th, i=1:N member, be projected into observation space using Systems with Linear Observation operator, the priori set observedIn conjunction with observation observation increment corresponding with the total calculation of observation a prior set
Step 4 introduces time weighting coefficient in observation window and solves the average observed increment for being directed to mode state;For step 3
Obtained in effective observation increments all in optimal observation windowIntroduce the time in observation window
Weight coefficient Wii:
It wherein include m effectively observations in optimal observation window L, each effectively observes the time difference minute with assimilation time point
It Wei not (L1,…,Lm);
The observation increment of equalizationAre as follows:
Step 5 solves the average analysis increment for mode state estimation;Observation increment according to the equalization that step 4 obtainsAnd observation errorThe corresponding analysis increment of Solution model stateAre as follows:
WhereinIndicate the prior uncertainty covariance of observation with state set, observation errorFor
Step 6 realizes optimization and update to mode internal parameter;After mode state estimation reaches quasi-balanced state, utilize
Observation information in optimal observation window is estimated and is optimized to mode internal parameter, sets for the optimal window of parameter Estimation
The corresponding optimal observation time window of observation depending on Optimal Parameters is set, effective observation in window is counted according to step 3 respectively
Corresponding observation increment is calculated, and equalization seeks average observed increment on the basis of observing increment;The observation increment of equalizationFor
The corresponding observation error of observation increment after equalizationWith aggregate error is tested before observationRespectively
After the observation increment and observation error that are equalized, the analysis increment of inner parameter is directed to based on solution shown in step 5
ΔPi,j
WhereinIt indicates parameter to be estimated and observes the error covariance of priori set, increment will be analyzed later
ΔPi,jIt is realized in the corresponding parameter sets that are added to and treats the optimization and update for estimating parameter sets;
Step 7: using adaptive distention protocol at the end of state estimation procedure and parameter optimisation procedure, after updating
Mode state and inner parameter, mode continues to integrate and enters next parameter Estimation and parameter optimization period.
2. the coupling data assimilation and parameter optimization method according to claim 1 based on optimal observation time window,
Be characterized in that: optimal observation time window of corresponding size is arranged in the characteristic time scale that the step 1 obtains coupled mode state
Mouth size realizes the fitting to coupled mode state feature variability while utmostly extracting effective observation information.
3. the coupling data assimilation and parameter optimization method according to claim 1 based on optimal observation time window,
It is characterized in that: observing increment in the step 3For
Wherein N represents set member's quantity, and m, which is represented, effectively observes quantity in observation window,WithRespectively represent introducing
The ensemble average and set of set of modes offset on observation lattice point are disturbed when observation;It is observation priori set,Table
Show observation priori set member,WithObservation priori ensemble average and disturbance are respectively indicated,It indicates
Before test collective standard difference and observation error standard deviation ratio.
4. the coupling data assimilation and parameter optimization method according to claim 1 based on optimal observation time window,
Be characterized in that: the step 6 is arranged corresponding parameter in the corresponding optimal observation time window of the observation based on Optimal Parameters and estimates
The optimal window of meter, binding pattern state-parameter error covariance realize that utmostly observation information is to mode internal parameter
It is adjusted and optimizes.
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CN111208586A (en) * | 2020-01-20 | 2020-05-29 | 山东超越数控电子股份有限公司 | Weather forecasting method and system based on mesoscale sea air coupling mode |
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CN114841442A (en) * | 2022-05-10 | 2022-08-02 | 中国科学院大气物理研究所 | Strong coupling method and system applied to atmosphere-ocean observation data |
CN114841442B (en) * | 2022-05-10 | 2024-04-26 | 中国科学院大气物理研究所 | Strong coupling method and system applied to atmosphere-ocean observation data |
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