CN116912459A - Variable-grid multi-scale mixed data assimilation method - Google Patents
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Abstract
The invention discloses a variable-grid multi-scale mixed data assimilation method, which belongs to the technical field of data assimilation, adopts a self-adaptive meshing strategy, uses multiple stages of continuous grids from thick to thin to respectively adjust sea state fields with different space scales from large to small, and effectively reduces the calculation requirement for completing remote related assimilation; the method is assisted by an aggregate optimal interpolation method, so that an assimilation module provides extremely fine resolution support consistent with a mode, in addition, the four-sub-field superposition solution is innovated, and grid division logic is simpler on the premise of ensuring reliable data assimilation; the method can support very high calculation parallelism, has high calculation efficiency, can well solve the problem of optimizing subdomains, effectively realizes data assimilation under different scales in ultrahigh resolution large-area calculation, and has wide popularization and practical values.
Description
Technical Field
The invention belongs to the technical field of data assimilation, and particularly relates to a variable-grid multi-scale mixed data assimilation method which is used for data assimilation under different scales in ultrahigh-resolution large-area calculation.
Background
The observed information is scattered in time and space compared with the world of transient universal change, and can not present and represent the real three-dimensional continuously evolving ocean environment state. Data assimilation has now been developed as a novel technique capable of effectively utilizing large amounts of multi-source, non-conventional data, a method capable of organically combining numerical patterns and observing the basic means of the two marine studies. The marine numerical mode for marine data assimilation continuously absorbs and digests the observation information, so that the mode state is more and more similar to the real state.
By introducing data assimilation, the method not only can effectively improve the ocean simulation effect and reduce the uncertainty of the ocean and weather forecast initial conditions, but also can provide analysis data for deep sea and marginal sea lacking ocean observation and design basis for ocean observation plans, physical quantity and parameters of a numerical forecast mode and the like. Marine data assimilation therefore occupies a very important place in the research of modern physical oceanography. In the last decade, data assimilation technology has been rapidly developed, from early relatively simple objective analysis to four-dimensional variation and ensemble Kalman filtering, etc. capable of assimilating a large amount of unconventional data.
Due to the rise of high-resolution and ultra-high resolution marine numerical modes, multi-scale marine assimilation is becoming one of the important research directions in this field. The multi-scale assimilation is an assimilation method which is developed based on the multi-scale property of fluid movement and respectively extracts observation information on space-time scale modes with different sizes, and the information fusion precision of numerical simulation and the mode forecasting skill can be improved through multi-scale coordination correction. The advent of ultra-high resolution has also presented new challenges to the field of data assimilation: one is that the requirement for the improvement of the computational efficiency of assimilation reaches a new height, and the other is that the incomplete observation conditions cause problems in the mutual coordination between new multi-scale interactions.
In order to meet the requirements of higher and higher resolution model data processing, a new data assimilation method needs to be provided, the assimilation effect is ensured, the calculation efficiency of marine data assimilation in ultrahigh resolution large-area calculation is optimized, and the multi-scale scientific division problem under the current experience condition and the problem of how observation data sets under different scales should be selected are further improved.
Disclosure of Invention
The invention provides a variable-grid multi-scale mixed data assimilation method for solving the problems of low calculation efficiency, poor multi-scale interaction coordination and the like of the existing ultrahigh-resolution mode assimilation method.
The invention is realized by adopting the following technical scheme: a variable grid multi-scale mixed data assimilation method comprises the following steps:
step A, the mode state is setThe original mode grid is contracted to the scale grid C, which is marked as +.>And constructs the following cost function:
, in the formula ,/>Representing jacobian->The scale is represented by a scale and,Mis of a scalelNumber of->Indicates the mode status +_>，/>，/>，/> and />The respective corresponding representation dimensions->State increment of (2), a spatial filter operator, background error covariance, observation error and observation update residual error, and H represents a difference operator; the principle of variable grid multi-scale mixed data assimilation is as follows: by->=1 to->=M Sequentially performing minimization solution on the created cost function by using a spatial filtering operator +.>Collecting observation update residual +.>And spatially filtering, and feeding back the result to the state increment->At the lattice point, the cost function is minimized and solved by spatial filter operator +.>Performing calculation on a scale grid; />Is composed of elements->Composition, each element representing the firstjThe observed updated difference value is corresponding toiWeights of individual states; />，
Wherein omega represents a localized function,for the scale->The following observation response feature distance is defined as the scale feature a, < >>For the distance between the j-th observation point and the i-th pattern lattice point,Kis the total number of observations;
step B, according to the characteristics of different scalesaSelecting different transformation grid computing state incrementsTwo transformation grids, respectively called a scale grid C and a subdomain grid S, are created; the dimension of the scale grid C is [ C, v]The dimensions of the subdomain grid S are [ S, c]V represents the length of the original mesh state vector, +.>，/> and />The average crossing distance of the original grid coverage area in the weft direction and the warp direction is respectively determined by the parallel computing capability of the super computing platform;
step B1, judging the size of the scale feature a: when the scale feature a is large enough to ensure that the assimilation work can be completed on one process, selecting a scale grid C for data assimilation, for example, according to the current computing capacity, the grid point number of the C grid is generally 160×160, and when the scale feature a is large enough to be characterized by 160×160 grid points, the assimilation can be completed in one process at the moment, and selecting the grid C for assimilation at the moment; when the scale characteristic a is too small and the scaled C grid cannot be put on a process to finish, further dividing the grid into subdomain grids S, and at the moment, selecting the subdomain grids S for data assimilation and executing the step B3;
step B2, carrying out state assimilation under the scale grid C:
assimilating the states of all the observation data with the distance from the observation point to the state point being less than 2a under the scale grid C, and observing and updating residual errorsThe expression is as follows:
，
wherein ,representing observation data->Representing the dimension +.>Difference operator of>Representation->Mode state of =1, bring it into cost function calculation state increment +.>；
Step B3, carrying out state assimilation under the subdomain grid S:
carrying out sub-domain subdivision solution based on a four-superposition method, carrying out four similar sub-domain subdivision on the scale grid C, staggering the sub-domain subdivision by half the length of the sub-domain grid S, and carrying out observation updating residual errors on the simulation point state under the sub-domain grid SFurther bringing it into the cost function calculation state increment +.>；
Step C, increasing the stateTransformation to +.>；
(1) Status of modeFidelity transformation from original grid to scale grid (+)> <=N) Or first to scale grid C and then further to subdomain grid ()>>N) When->After determination, the observation update residual is calculated>；
Here, the state is incremented by step BAfter solving on the scale grid C and the subdomain grid S, the multi-scale mode state is required to be +.>And (3) optimizing, wherein an optimization formula is as follows:
，
，
，
wherein , representing the dimension +.>Grid C scaling operator of +.>Represents a grid S-scaling operator, superscript t represents different processes,/for>Original grid state +.>Representing the mode state when collapsing to grid C or S, superscript +.>、/> ,*PEtc. all represent the current scale, N represents the different scale, x represents the four-fold method on the S-grid.
(2) Performing observation updating residual errorSolving and cost function minimizing solving, resulting state increment +.>On a scale grid or a subdomain grid, the mode state increment under the current scale is obtained by inverting the mode state increment back to the original mode grid>The next-scale optimization is restartedA chemical process;
(3) After three-dimensional variation solving is completed on different scales in sequence, final optimal interpolation assimilation is carried out once under the mode original resolution, the optimal interpolation result is the assimilation result of the final scale, and the final simulation state updating quantity is as follows:
and (3) finishing the update of the current state, and repeating the steps A-C when the mode is operated to a certain moment and the data is required to be assimilated again, so as to finish the mode state data assimilation at the moment.
Compared with the prior art, the invention has the advantages and positive effects that:
the scheme can process multiple types of observation data to generate coherent multi-spatial scale analysis increment; the self-adaptive meshing strategy is adopted, and the multi-stage continuous coarse-to-fine grids are used for respectively adjusting sea state fields with different space scales from large to small, so that the calculation requirement for completing remote correlation assimilation is effectively reduced; and is aided by a collective optimal interpolation method so that the assimilation module provides extremely fine resolution support consistent with the mode. The four sub-domain superposition solution is innovated, so that the grid division logic is simpler on the premise of ensuring the reliable assimilation of the data; the method can support high calculation parallelism, has high calculation efficiency and can well solve the problem of optimizing subdomains.
Drawings
FIG. 1 is a schematic flow chart of a data assimilation method according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a sub-domain four-overlap method according to an embodiment of the present invention, a is a state correction amount after an optimization solution is performed by using a double sub-domain division, b is a state correction amount synthesized by a central region after the optimization solution is performed by using a double sub-domain division, and c, d, e, f is a double different sub-domain division of the same scale grid;
FIG. 3 is a diagram showing the comparison of the calculated amounts of the four-overlap method and the circular conventional buffer boundary method according to the embodiment of the present invention.
Detailed Description
In order that the above objects, features and advantages of the invention will be more readily understood, a further description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings. In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced otherwise than as described herein, and therefore the present invention is not limited to the specific embodiments disclosed below.
Aiming at the objective demands on the calculation parallelism brought by the higher and higher resolution of ocean modes and the heterogeneous trend of the novel supercomputer many-core, the mode space is divided into small blocks for assimilation treatment to improve the parallelism, but the ocean field is an autocorrelation field, and large-scale remote correlation exists among different space points. If only small area blocks are subjected to data assimilation respectively, the collaborative optimization between points not in the same block cannot be implemented, and if the collaborative optimization is performed on the whole field, the collaborative optimization is not bearable in terms of speed due to the mode resolution requirement.
The embodiment provides a variable-grid multi-scale mixed data assimilation method (Mesh-varying, multiscale, hybrid Data Assimilation, MMH-DA), which divides an original mode state vector according to spatial scales, respectively optimizes the original mode state vector, synthesizes optimized results, and details the data assimilation principle thereof with reference to fig. 1.
For example, in the running process of a specific ocean mode, the simulated ocean state continuously changes along with the time step, when the time step comes to a certain moment and the moment just has observation data, the data assimilation can be carried out on the ocean state at the moment, so that the simulated ocean state is closer to the real situation. In the process of data assimilation, large-scale remote correlation among different space points needs to be considered, so that in the MMH-DA process, the specific steps comprise:
step A, setting the state of the ocean or atmosphere mode of the backgroundThe original mode grid is contracted to a scale grid C, which is recorded as；
MMH-DA main body is multi-scale three-dimensional variation assimilation, and is formed by large spatial scale=1 to small spatial scale-> =M And sequentially carrying out minimization solution on the created cost function:
(1)
in the formula ,is a mathematical operator, representing the jacobian ++>The scale is represented by a scale and,Mfor the scale->Number of->Indicates the mode status +_>，/>，/>，/> and />Respectively corresponding to the dimensions oflState increment of (a), spatial filter operatorBackground error covariance, observation error and observation update residual (residual difference between the observation and the current state), H represents the difference operator.
MMH-DA passes through spatial filtering operatorCollecting observation update residual +.>And spatially filtering, and feeding back the result to the state increment->The lattice point where it is located. The minimization solution to the cost function is by +.>The computation is performed on the pattern mesh (actually the addition of the variational mesh technique is performed on the scale mesh converted from the pattern mesh, which is the contracted state of the original pattern mesh). />Is composed of elements->Composition, each element representing the firstjThe observed updated difference value is corresponding toiWeights of individual states, derived from localization functions Ω designed by gasari and Cohn in 1999,/>And Ω are calculated as follows:
(2)
(3)
wherein ,for the scale->The following observed response feature distance, which in this embodiment is defined as the scale feature a,bfor the distance between the observation point and the pattern lattice point,Kis the total number of observations.
Step B, according to the characteristics of different dimensions of ocean or atmosphereaSelecting different scale grid computing state increments；
The present embodiment creates two transformation grids to computationally decompose the original problem, called scale grid C and subdomain grid S, respectively. As shown in connection with fig. 2, scale grids C and S are different at each scale, but for scale grids C and S at a uniform scale, there is always a higher resolution of S than C. The dimension of the scale grid C is [ C, v]The dimensions of the subdomain grid S are [ S, c]. v is the length of the original trellis state vector,，/> and />The average crossing distance of the original grid coverage in the weft direction and the warp direction are respectively the scale characteristicsaIn one direction, 4 points are contained, so that the scale grid C can distinguish that the wavelength is larger than 1/2 at the current scaleaThe above wave. s=32 2 The base number can be smaller as the system speed ratio is higher, but is generally between 8 and 64. When (when)aWhen the resolution is very large, the resolution of C is far lower than that of the original grid, and the whole simulation range is covered; when (when)aAt very small, the C resolution approaches that of the original grid, but differentiates into 32 2 A small S region is solved, and the remote correlation characteristic of the state field is in the rough C and largeaThe optimization of the corresponding scale is solved, so that the results of S can be spliced into the super-domainAnd optimizing the result with high resolution. The use of the grid-changing technology ensures the direct optimization of the simulation state, ensures that the whole variation solving process can keep very high parallelism, is suitable for the development trend of ultra-high parallelism many-core isomerism of the current super-computing system, is very efficient in calculation, and can meet the practical requirements of sub-mesoscale ocean simulation and corresponding business prediction on ultra-high resolution.
Step B1, judging scale characteristicsaSize of the material;
mode state under traditional three-dimensional variational assimilation versus original mode gridOptimizing, wherein the mode state vector consists of multiple variables such as temperature, salt, vorticity and the like, and the vector length is 10 7 Above, the corresponding background error covariance is more of the order of magnitude of 10 14 This is objectively not addressed by conventional three-dimensional variational methods.
Scale featuresaThe method is the most important core parameter under the MMH-DA method, not only determines the scale of the multi-scale method, but also determines the reduction ratio of each scale grid to the original mode grid when the grid is changed. As can be seen from equations (2) and (3), since at each level of scaleaDifferent, each state point in a large scale can collect a larger range of observation updating residuals, and the observation updating residuals are subjected to spatial filtering processing according to a localization function omega.
This embodiment is based on features of different dimensionsaSelecting different scale grids for calculation, wherein two transformation grids, namely a scale grid C and a subdomain grid S, are created, and for the scale grids C and S under uniform scale, the resolution of S is higher than that of C; when the scale feature a is large enough that the assimilation work can be done in one process, step B2 is performed, e.g. the number of lattice points of the C-grid is typically 160X, depending on the current computing power160，When the scale feature a can be characterized by 160×160 lattice points, the assimilation can be completed in one process, and the lattice C is selected for assimilation; when the scale feature a is too small and the scaled C grid cannot be put on one process to finish, namely the grid number of the C grid is 160×160, when the scale feature a cannot be described, further dividing the grids into sub-field grids S, at this time, selecting to assimilate the data by using the sub-field grids S, and executing step B3, specifically:
and B2, carrying out state assimilation under the scale grid C.
All distances to the state point to be updated are less than 2aIs considered to assimilate the simulated dot state under scale grid C. Observing the update residualDetermined by the following equation when solving for the first scale (+.> =1)，/>The difference between the observed and background simulation results is:
(4)
then calculate the state increment using equation (1)。
Step B3, carrying out state assimilation under the subdomain grid S;
(1) First, the mode state on the scale grid CFurther decomposing to four sub-domain grids S for solving, wherein each sub-domain grid is responsible for by a single program. Decomposed ofc l() Observation update residuals of each sub-domain including only very small regions are determined>. The points at the borders of adjacent subfields are now collected during assimilation by the filter operator L +.>Quite differently, this can lead to very severe optimization solution bias (e.g., a in fig. 2). As shown in c in fig. 2, each subdomain S grid point number is 32' 32, and the scale feature distance is equal to the scale feature distanceaAcross 4 grid points.
Each subfield divided in a black solid line in c, d, e, f of fig. 2 may be divided into a central area of a square type and an edge area surrounding the central area. Taking the C in fig. 2 alone, the diagram is a subdomain grid, it can be understood that C in fig. 2 is a C grid, then the C is divided into 24 small grids (S becomes subdomain grid) by thin lines, then the four different subdomain grids of cdef are each divided by shifting the length of one half subdomain grid (the grid dividing lines in the cdef diagram are carefully observed, and the black grid lines in each diagram are different), and cdef is a state that forms four subdomains by different dividing modes. The grid points of the central area can collect all required observation updating residual errorsWhereas the lattice points of the edge area can only collect part of the required +.>The method comprises the steps of carrying out a first treatment on the surface of the For two adjacent lattice points belonging to different subfields (e.g. two black points circled in c), completely different and incomplete +_ respectively belonging to two subfields are used in the optimization process>The discontinuity evident in figure a on the final optimization results is created. To solve this problem, a width of 2 may be added to the periphery of each subfieldaBut because the calculation process of assimilation solution is different from methods such as finite difference used by ordinary mode dynamics integration, a brand new four-overlap method is innovatively developed in MMH-DA to carry out subdomain subdivision solution.
(2) The concrete principle of carrying out subdomain subdivision solution by using the four-fold superposition method is as follows:
to make four similar sub-domain subdivisions of the scale grid, the four sub-domain subdivisions are each staggered by half a sub-domain length, with the result that the entire central region under the four sub-domain subdivision can just be stitched into a complete scale grid (c, d, e, f in fig. 2). The four-overlap method maintains high computational parallelism (does not increase the size of a single-process subdomain), and the obtained solving result can well overcome the problem in one-fold subdomain optimization (b in fig. 2). Moreover, in the case of smaller subfields, the four-fold method is lower in calculation consumption than the buffer boundary method, and as shown in fig. 3, when the unidirectional length of the subfields is about <9a, the four-fold method is superior to the conventional buffer boundary method.
Observing and updating residual errors of simulation point states under subdomain grid SThe calculation formula of (2) is also represented by formula (4). Then calculate the state increment +.>。
In the embodiment, when the large-scale remote correlation problem is optimized, the original grid is 'shrunk' so as to reduce the grid number, and when the small-scale detail problem is optimized, slicing assimilation is performed so as to improve the parallelism (at this time, the remote correlation problem is solved under the large scale). Thus, whether the large scale telecorrelation problem or the small scale local problem is optimized, the matrix size calculated by each calculation unit is similar finally. The grid-changing mode has the same target (reducing the calculated amount) as the traditional method of carrying out modal decomposition first and then assimilating the modes, but the specific implementation principle is different, and the generation of the large-scale shrinkage grid has more freedom.
Step C, status incrementTransformation to +.>。
State increment in equation (1)Solving on a scale grid C and a subdomain grid S, which is not directly equivalent to the state increment +.>. The multiscale mode state to be optimized in this embodiment +.>The result of each round of assimilation needs to be taken into account and then contracted to either scale grid C or scale grid S (i.e. in doing +.>In the assimilation process when n+1, consideration must be given to +.>The assimilation result of =1, 2,3 … N), determined by the following formula:
，
， (5)
at the beginning of the optimization process for each scale, the current mode stateWill be transformed from the original mesh fidelity to the scale mesh (+.> <=N) Or first to the scale grid and then further to the subdomain grid ()> >N). Through the formula (1) and the formula (4)After calculation, the status increment obtained>On the scale grid or subdomain grid, the mode state increment of the current scale is obtained by inverting the mode state increment back to the original mode grid through the formula (5)>（/>The S term on the right of the equal sign in the formula (5) is adopted, and the optimization process of the next scale is started.
After three-dimensional variational solving is sequentially performed on all scales, one-time set optimal interpolation assimilation (Ensemble Optimal Interpolation, enOI) is performed finally under the mode original resolution (no grid transformation). And (3) collecting optimal interpolation assimilation areas, wherein 180km of ring overlapping areas are reserved at the periphery of each area. And collecting the optimal interpolation result as an assimilation result of a final scale. Synthesizing the simulation result with other multi-scale assimilation results to obtain the final simulation state updating quantity as follows:
(6)
and then finishing the update of the current state, repeating the steps A-C when the mode is operated to a certain moment and the data is required to be assimilated again, and finishing the data assimilation of the mode state.
In this embodiment, the MMH-DA is also a hybrid assimilation method, and the three-dimensional variational method is used to assimilate data under a larger scale, and the data is converted into an aggregate optimal interpolation method in a very small scale so as to utilize the mode background error obtained by the aggregate and preserve the microscopic peak intensity of the state field as much as possible. In the optimization solving process of each scale, the mode original grid is respectively transformed into two new grids of a scale grid (thick) and a subdomain grid (thin). In assimilation under large scale, changing an original mode grid into a scale grid with thicker resolution, and carrying out wide-area optimization solution to obtain a mode state vector correction value considering remote correlation of a physical field under sparse observation, thereby improving the bullseye problem caused by local observation loss; the original mode grid is changed into the scale grid with finer resolution in the assimilation of the small scale, and then the fine scale grid is decomposed into small sub-field blocks which are mutually overlapped to solve so as to reduce the assimilation state vector size of the unit area and greatly improve the calculation efficiency. The calculation parallelism of the multi-scale data assimilation system can be greatly improved through the decomposition and superposition of the two new grids, and the method is better suitable for the development trend of high parallelism and many-core isomerism of a super-computing platform due to the continuous improvement of the resolution of ocean modes.
The present invention is not limited to the above-mentioned embodiments, and any equivalent embodiments which can be changed or modified by the technical content disclosed above can be applied to other fields, but any simple modification, equivalent changes and modification made to the above-mentioned embodiments according to the technical substance of the present invention without departing from the technical content of the present invention still belong to the protection scope of the technical solution of the present invention.
Claims (6)
1. A method for assimilating variable-grid multi-scale mixed data, which is characterized by comprising the following steps:
step A, the mode state is setThe original mode grid is contracted to the scale grid C, which is marked as +.>And constructs the following cost function:
，
in the method, in the process of the invention,representing jacobian->The scale is represented by a scale and,Mis of a scalelNumber of->Indicates the mode status +_>，/>，，/>And->The respective corresponding representation dimensions->State increment of (2), a spatial filter operator, background error covariance, observation error and observation update residual error, and H represents a difference operator;
step B, defining different scalesThe following observation response feature distance is a scale featureaAccording to features of different scalesaSelecting different transformation grids to calculate state increment +.>；
Two transformation grids, namely a scale grid C and a subdomain grid S, are created, and for the scale grids C and S under uniform scale, the resolution of S is higher than that of C; judging the scale a, and selecting a scale grid C for data assimilation when the number of grid points divided by the scale characteristic a can be ensured and assimilated on one process; when the number of grid points divided by the scale feature a can not enable assimilation work to be completed on one process, selecting a subdomain grid S for data assimilation;
step C, increasing the stateTransformation to +.>；
(1) Three-dimensional variation solving: status of modeFidelity transformation from original grid to scale grid, or first to scale grid C and then further to subdomain grid, when +.>After the determination, the observation update residual error corresponding to the moment is calculated>And performing cost function minimization solution to obtain state increment +.>On the scale grid C or the subdomain grid S, the mode state increment +.>Then starting the optimization process of the next scale;
(2) After three-dimensional variation solving is completed on different scales in sequence, final optimal interpolation assimilation is carried out once under the mode original resolution, the optimal interpolation result is the assimilation result of the final scale, and the final simulation state updating quantity is as follows:
completion timeAnd (3) updating the pre-state, repeating the steps A-C when the mode is operated to a certain moment and the data is required to be assimilated again, and completing the mode state data assimilation at the moment.
2. The method for assimilating variable-grid multi-scale mixed data according to claim 1, wherein: the cost function constructed in the step A is the key of data assimilation, and the principle of variable-grid multi-scale mixed data assimilation is as follows: from the following components=1 to=M Sequentially performing minimization solution on the created cost function by using a spatial filtering operator +.>Collecting observation update residualsAnd spatially filtering, and feeding back the result to the state increment->The lattice point;
the minimized solution to the cost function is through a spatial filtering operatorPerforming calculation on a scale grid; />Is composed of elements->Composition, each element representing the firstjThe observed updated difference value is corresponding toiWeights of individual states;
wherein Ω represents a localization function, +.>For the scale->The following observation response feature distance is marked as scale feature a +.>For the distance between the j-th observation point and the i-th pattern lattice point,Kis the total number of observations.
3. The method for assimilating variable-grid multi-scale mixed data according to claim 1, wherein: in the step B, when the scale feature a is larger than the resolution of the scale grid C, carrying out state assimilation under the scale grid C on the observation data with the distance from all the observation points to the state points smaller than 2a, and observing and updating residual errorsThe expression is as follows:
，
wherein,representing observation data->Representing the dimension +.>Difference operator of>Representation->Mode state of=1, bring it into cost function calculation state increment in step a +.>。
4. The method for assimilating variable-grid multi-scale mixed data according to claim 3, wherein: in the step B, when the state assimilation is carried out under the subdomain grid S, the subdomain subdivision solution is carried out based on a four-overlap method, the scale grid C is firstly subjected to four similar subdomain subdivision, the four subdomain subdivision is staggered by half the length of the subdomain grid S, and the observation updating residual error of the simulation point state is carried out under the subdomain grid SAnd then brings it into the cost function calculation state increment +.>。
5. The method for assimilating variable-grid multi-scale mixed data according to claim 1, wherein: in the step B, the dimension of the scale grid C is [ C, v ]]The dimensions of the subdomain grid S are [ S, c]V denotes the length of the original trellis state vector,，/>and->The average spanning distance of the original grid coverage in the weft direction and the warp direction is determined by the parallel computing capacity of the super computing platform.
6. According to claimThe variable grid multi-scale mixed data assimilation method of claim 1, which is characterized in that: in the step C, the state increment is performed in the step BAfter solving on the scale grid C and the subdomain grid S, the state of the multi-scale mode is neededc l() And (3) optimizing, wherein an optimization formula is as follows:
，
，
，
wherein,representing the dimension +.>Grid C scaling operator of +.>Representing a grid S-reduction operator,>original grid state +.>Representing the mode state when collapsing to grid C or S, superscript +.> ，/> ,*PAll represent the current scale, N represents the different scale, x represents the four-fold method on the S-grid.
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