A data assimilation method for a modal information optimization process model

Abstract

The present invention relates to a data assimilation method for a modal information optimization process model, and the steps include: 1) performing modal signal decomposition on the set of observed vector time series and the mapped observed vector time series set of the process model simulated state vector time series; 2) calculating the modal set optimization quantity by using the modal signal decomposition of the set of observed vector time series and the modal signal decomposition of the mapped observed vector time series set of the process model simulated state vector time series; 3) calculating the optimization quantity of the process model state vector by using the modal set optimization quantity and optimizing the state vector; 4) optimizing the process model simulation by using the process model state vector optimized by the modal information. The present invention extends the traditional time-domain assimilation method to the modal domain, and realizes the optimization of the process model by using the time series modal information of the observed vector and the process model simulation.

Description

Technical Field

[0001] The present invention relates to a data assimilation method for optimizing a process model, and particularly to a data assimilation method for optimizing a process model by using modal information. Background Art

[0002] Process models are important methods for studying complex processes such as energy, momentum, mass, hydrology, and ecology that occur on the land surface, in the atmosphere, and in the ocean, as well as their interactions with the atmosphere. Through the kinetic mechanisms of each process and the physical and chemical control equations, the land surface state, the atmospheric state, the land-atmosphere flux interaction, and the performance laws of matter and energy at different spatio-temporal scales can be described. It is also possible to simulate the feedback mechanisms at various spatio-temporal scales among the above processes on the land surface, in the atmosphere, and in the ocean.

[0003] The simulation of process models requires characteristic datasets such as land surface soil, vegetation, terrain, land use, ocean salinity, ocean temperature, and atmospheric composition, as well as regional high spatio-temporal resolution forcing datasets. Up to now, the preparation of these data has been based on reanalysis products processed from sparse observations, and it is difficult to substantially improve the quality of the datasets. The simulation results obtained by these data-driven process models usually have low accuracy, and large errors will occur when they are subsequently used to analyze the states, laws, and mutual feedbacks of the surface hydrological cycle, radiation process, material cycle, energy cycle, and biogeochemical cycle at different spatio-temporal scales. The data assimilation method uses the high spatial resolution of ground observation data and / or remotely sensed inversion products of surface parameters to optimize the process model simulation, providing a new way to improve the simulation quality of the process model.

[0004] Currently, data assimilation methods are divided into sequential data assimilation, continuous data assimilation, and sequential variational methods. Sequential data assimilation is when observations are introduced into the process model simulation, and the process model simulation is optimized by weighting the observations and the simulation according to the observation error and the simulation error, so as to sequentially obtain the posterior optimized estimate of the process model state. Sequential data assimilation methods have evolved from the initial Kalman filter for linear systems, through the extended Kalman filter for nonlinear systems, to the introduction of nonlinear particle filters, unscented Kalman filters, ensemble Kalman filters, central difference Kalman filters, unscented particle filters, etc., and have been widely used in fields such as the ocean, land surface, and atmosphere. Although sequential data assimilation methods are highly operable and easy to use, the assumption of linear requirements for the process model and the observation model makes them less effective in optimizing nonlinear process models.

[0005] Continuous data assimilation is to continuously adjust the state field of the process model within an assimilation window of the process model by using iterative optimization, so that the process model simulation matches all the observations within the assimilation window. Continuous data assimilation methods are divided into variational methods represented by three-dimensional variational and four-dimensional variational methods, and global optimization methods represented by heuristic optimization algorithms, which can handle the nonlinear problems of the dynamic model and the observation model in the process system. When optimizing the process model, continuous data assimilation methods assume that the state field error and the observation field error are spatio-temporally uniform and isotropic, and cannot describe the errors that vary with the process model simulation, thus reducing the optimization effect of continuous data assimilation methods.

[0006] The sequential variational method is developed by combining the advantages of continuous assimilation and sequential assimilation. Through the ensemble strategy of sequential assimilation, the state field of continuous variational assimilation has flow dependence. The flow-dependent schemes include covariance linear combination and adding control variables, and the flow-dependent reconstruction methods include Monte Carlo, breeding vectors, singular vectors, grid noise, perturbed observations, ensemble adjustment, etc. The sequential variational method uses white noise with a normal distribution to describe the state field error. For the optimization of high-dimensional nonlinear process models, this is only a compromise, and the performance of the sequential variational method in optimizing nonlinear process models still needs to be improved.

[0007] One of the common characteristics of the above three data assimilation methods is that the optimization of the process model is realized in the time domain. This characteristic leads to the fact that these three data assimilation methods cannot optimize the process model based on the modal information in the time series of the observation vector and the state vector. The time series of surface temperature, soil temperature, soil moisture and various fluxes involved in process models such as the ocean, atmosphere, and land surface all contain modal information at different time scales, and the time-domain process model optimization methods cannot optimize the modal information of these variables in the process model. The modal information in the time series of surface variables is an eigenmode function different from frequency information and is an important feature of the nonlinear and non-stationary time series signal of surface variables, playing an important role in analyzing the spatio-temporal variation laws of each process. Therefore, there is an urgent need to develop a data assimilation method that uses observation modal information to optimize the process model. Summary of the Invention

[0008] In view of the above technical deficiencies, a data assimilation method for optimizing a process model with modal information is provided.

[0009] To achieve the above object, the technical solution of the present invention is as follows:

[0010] A data assimilation method for optimizing a process model with modal information includes the following steps:

[0011] S1: Perform modal signal decomposition on the set of observation vector time series and the set of mapped observation vector time series of the process model simulation state vector time series;

[0012] S2: Calculate the modal set optimization quantity by using the modal signal decomposition of the observation vector time series set and mapping the observation vector time series set of the process model simulation state vector time series set;

[0013] S3: Calculate the optimization quantity of the process model state vector by using the modal set optimization quantity and optimize the state vector;

[0014] S4: Optimize the process model simulation by using the process model state vector optimized by the modal information.

[0015] The data assimilation method for optimizing the process model by modal information, wherein the S1 includes:

[0016] Perform modal signal decomposition on the observation vector time series set, specifically:

[0017]

[0018] In the formula, represents the observation vector time series set, represents the result after i - 1 times of modal decomposition, the subscript O represents the dimension of the observation vector, N represents the set size of represents the modal signal set after i - 1 times of modal decomposition;

[0019] Perform modal signal decomposition on the mapped observation vector time series set of the process model simulation state vector time series set, specifically:

[0020]

[0021] In the formula, represents the mapped observation vector time series set of the process model simulation state vector time series set, represents the result after i - 1 times of modal decomposition, represents the modal signal set after i - 1 times of modal decomposition.

[0022] The data assimilation method for optimizing the process model by modal information, wherein the S2 includes:

[0023] Calculate the first part of the modal set optimization quantity, specifically:

[0024]

[0025] In the formula, T represents or The time length of each matrix element, where I represents the number of layers of modal decomposition. denotes the covariance matrix of, where T represents matrix transpose.

[0026] Calculate the second part of the optimized modal set quantity, specifically:

[0027]

[0028] In the formula, Ι represents the N×N identity matrix.

[0029] For the data assimilation method of the modal information optimization process model described above, where the S3 is specifically:

[0030]

[0031] In the formula, β N×N is the optimized modal set quantity, X L is the process model state vector, L is the dimension of the process model state vector, X L×N is X L perturbation set of, is the optimized quantity set of X N×N calculated using β L is the nth (1≤n≤N) column of, is the column mean of, that is, the optimized quantity of X L is the optimized process model state vector.

[0032]

[0033] For the data assimilation method of the modal information optimization process model described above, where the S4 is specifically:

[0033]

[0034] In the formula, M represents the process model, FP is the forcing dataset and surface parameter dataset at the same time as represents the result of the next moment state vector of the optimized simulation of the process model.

[0035] Compared with the existing data assimilation technology, the beneficial effects of the present invention are:

[0036] The present invention provides a data assimilation method for optimizing a process model with modal information. Compared with the traditional time-domain data assimilation method for optimizing a process model, while getting rid of the limitations of the traditional data assimilation method that is confined to the limitations of observational and simulated time series information, the present invention further considers the contributions of different modal information in the observational and simulated time series signals to optimize the process model. Modal information represents the local characteristics of different durations in the original signal, while the time-domain data assimilation method cannot utilize this modal information to optimize the process model. This method extends the data assimilation method for optimizing the process model to the modal domain through modal decomposition, realizing the double approximation of the temporal variation of the simulated trajectory of the process model and the intrinsic mode function to the observational signal. Description of the Drawings

[0037] Figure 1 It is a flowchart of the method in the embodiment provided by the present invention; Detailed Embodiments

[0038] To introduce the purpose, principle and technical features of the present invention more clearly, the following will combine the drawings and embodiments to detail the present invention. The representative embodiments cited are only used to explain the present invention and should not be regarded as a limitation of the present invention.

[0039] As Figure 1 shown, a data assimilation method for optimizing a process model with modal information includes the following steps:

[0040] Step S1: Determine the study area, study period, assimilation window length, and prepare the process model and its driving data set, parameter data set, observation model, and observation vector product;

[0041] Step S2: Perturb the state field of the process model and the observation vector product within the assimilation window to generate a state field set and a time series set of the observation vector product within the assimilation window, respectively;

[0042] Step S3: Use the state field set combined with the driving data set and parameter data set to drive the process model and the observation model to obtain a mapped observation vector time series set of the time series set of the simulated state vector of the process model within the assimilation window;

[0043] Step S4: Perform modal signal decomposition on the observation vector time series set and the mapped observation vector time series set of the time series set of the simulated state vector of the process model;

[0044] Step S5: Calculate the modal set optimization quantity using the modal signal decomposition of the observation vector time series set and the modal signal decomposition of the mapped observation vector time series set of the time series set of the simulated state vector of the process model;

[0045] Step S6: Calculate the optimization quantity of the state vector of the process model using the modal set optimization quantity and optimize the state vector.

[0046] Step S7: Optimize the process model simulation using the process model state vector optimized by the modal information.

[0047] Step S8: Execute the optimization of the process model for the subsequent research period according to Steps 2 - 7.

[0048] In an exemplary embodiment, in Step S1, one of the selected process models for preparation may be a land surface process model. Representative land surface process models include CLM4.0, VIC, SWAT, NOAH, etc.; the driving dataset for the prepared process model can be selected as a global meteorological forcing dataset with a global coverage from January 1, 1948 to December 31, 2000 at a 3 - hourly interval and a spatial resolution of 0.25°, or a global data assimilation system forcing dataset with a global coverage from January 1, 1948 to December 31, 2021 at a 3 - hourly interval and a spatial resolution of 0.25°, or a Chinese meteorological forcing driving data with a time span from 1979 to 2018 at a 3 - hourly interval and a spatial resolution of 0.1°; the parameter dataset can be selected as a global hydrological soil database, a vegetation dataset; the observation model can be composed of a land surface temperature inversion model and a land surface evapotranspiration estimation model; the observation vector product can be composed of a land surface temperature product and a land surface evapotranspiration product.

[0049] In an exemplary embodiment, in Step S2, the state field of the perturbed process model generates a state field set, specifically:

[0050] X L×N ={X L1 ,…,X Ln ,…,X LN}

[0051] X Ln =X L +υ Ln

[0052] In the formula, X L is the process model state field, L is the dimension of the state vector that composes the state field in the process model. The state vector is composed of multiple state variables, and the state variables include but are not limited to land surface temperature, 0 - 5 cm soil temperature, and soil moisture, etc. υ Ln represents the nth L - dimensional random vector that follows a generalized Gaussian distribution with a mean of 0, 1 ≤ n ≤ N, N is the size of the perturbation set, X Ln is the nth perturbed state field of X L , and X L×N is the set of perturbed state fields with N as the set member of X L ;

[0053] The observation vector products within the perturbation assimilation window generate a set of time series of observation vector products within the assimilation window, specifically as follows:

[0054] Y O×N ={Θ O1 ,…,Θ On ,…,Θ ON}

[0055] Θ On =[O 1On ,…,O tOn ,…,O TOn ′

[0056] O tOn =O tO +v tOn

[0057] In the formula, Y O×N represents the set of time series of the observation field products, Θ On represents the nth set member of Y O×N , the subscript O represents the dimension of the observation vector that makes up the observation field, O tOn represents the nth perturbation result of the observation field at the simulation time t within the assimilation window, O tO represents the observation field at the simulation time t within the assimilation window, v tOn represents the nth O-dimensional random vector that follows a generalized Gaussian distribution with a zero mean at the simulation time t.

[0058] In an exemplary embodiment, in step S3, the step of obtaining the mapped observation vector time series set of the process model simulation state vector time series set within the assimilation window by using the state field set in combination with the driving data set, the parameter data set to drive the process model and the observation model includes the following steps:

[0059] Using each set member X L×N of X Ln in combination with the driving data set and the parameter data set to drive the process model for simulation within the assimilation window, specifically as follows:

[0060]

[0061] In the formula, t represents the simulation time within the assimilation window, 1 ≤ t ≤ T, T is the length of the assimilation window, M represents the process model, FP t represents the sum of the driving data set and the parameter data set at time t within the assimilation window, X tLn represents the state field of the process model running forward for t steps of simulation;

[0062] Using the set of process model simulation state vector time series within the assimilation window to drive the observation model to obtain the mapped observation vector time series set, specifically as follows:

[0063] τ tOn = H(χ tLn )

[0064] Γ On = [τ 1On ,…,τ tOn ,…,τ TOn

[0065]

[0066] wherein, H represents an observation model, represents the set of mapped observation vector time series of the set of process model simulated state vector time series, and τ tOn represents the mapped observation field at time t when χ tLn is mapped by H to the observation space, and Γ On represents the set of mapped observation field time series when the state field simulated by the process model within the assimilation window of the nth perturbation state field is mapped to the observation space by H.

[0067] In an exemplary embodiment, in step S4, the modal signal decomposition of the set of observation vector time series and the set of mapped observation vector time series of the set of process model simulated state vector time series includes:

[0068] Performing modal signal decomposition on the set of observation vector time series, specifically:

[0069]

[0070] wherein, represents the set of observation vector product time series, represents the result after i - 1 times of modal decomposition, the subscript O represents the dimension of the observation vector, N represents the set size of represents the set of modal signals after i - 1 times of modal decomposition;

[0071] Performing modal signal decomposition on the set of mapped observation vector time series of the set of process model simulated state vector time series, specifically:

[0072]

[0073] wherein, represents the set of mapped observation vector time series of the set of process model simulated state vector time series, represents the result after i - 1 times of modal decomposition, represents​ The set of modal signals after (i - 1) times of modal decomposition;

[0074] In an exemplary embodiment, in step S5, the calculating the modal set optimization quantity by using the modal signal decomposition of the set of observation vector time series and mapping the set of observation vector time series by simulating the state vector time series of the process model includes:

[0075] Calculating the first part of the modal set optimization quantity, specifically:

[0076]

[0077] In the formula, T represents or The time length of each matrix element in, I represents the number of layers of modal decomposition, Represents The covariance matrix of, T represents matrix transpose;

[0078] Calculating the second part of the modal set optimization quantity, specifically:

[0079]

[0080] In the formula, Ι represents the N×N identity matrix.

[0081] In an exemplary embodiment, in step S6, the calculating the optimization quantity of the process model state vector by using the modal set optimization quantity and optimizing the state vector is specifically:

[0082]

[0083] In the formula, β N×N Is the modal set optimization quantity, X L Is the process model state field, X L×N Is X L The perturbation set of, Is the optimization quantity set of X N×N Calculated by using β L , Is The nth (1 ≤ n ≤ N) column of, Is The column mean of, that is, the optimization quantity of X L , Is the optimized process model state vector.

[0084] In an exemplary embodiment, in step S7, the optimizing the process model simulation by using the process model state vector optimized with modal information is specifically:

[0085]

[0086] In the formula, M represents the process model, and FP is the forcing data set and surface parameter data set at the same time, indicating the result of the state vector at the next moment simulated by the process model.

[0087] The above exemplary embodiments are only used to illustrate the representative implementation manners of the present invention, rather than to limit the implementation of the present invention. Those of ordinary skill in the art can improve the technical solutions of the present invention according to the idea of the present invention, and these improvements are within the protection scope of the appended claims of the present invention.

Claims

1. A data assimilation method for a modal information optimization process model, characterized in that Including the following steps: S1: Perform modal signal decomposition on the mapping observation vector time series set of the observation vector time series set and the process model simulation state vector time series set; S2: Calculate the modal set optimization quantity by using the modal signal decomposition of the observation vector time series set and the modal signal decomposition of the mapping observation vector time series set of the process model simulation state vector time series set, including: Calculate the first part of the composition of the modal set optimization quantity, specifically: where T represents or the time length of each matrix element, I represents the number of layers of modal decomposition, represents the covariance matrix of, T represents matrix transpose; Calculate the second part of the composition of the modal set optimization quantity, specifically: In the formula, Ι represents the N×N identity matrix; S3: Calculate the optimization quantity of the process model state vector by using the modal set optimization quantity and optimize the state vector; S4: Optimize the process model simulation by using the process model state vector optimized by the modal information, specifically: Where M represents the process model, and FP is the forcing data set and surface parameter data set at the same time, indicating the result of the state vector at the next moment optimized and simulated by the process model.

2. The data assimilation method for a modal information optimization process model according to claim 1, characterized in that, The S1 includes: Perform modal signal decomposition on the observation vector time series set, specifically: In the formula, represents the set of time series of observation vector products, represents the result after (i - 1) times of mode decomposition. The subscript O represents the dimension of the observation vector, and N represents the set size of represents the set of mode signals after (i - 1) times of mode decomposition; Perform modal signal decomposition on the mapping observation vector time series set of the process model simulation state vector time series set, specifically: In the formula, denotes the set of mapped observation vector time series of the process model simulation state vector time series set, denotes the result after (i - 1) times of mode decomposition, denotes the set of mode signals after (i - 1) times of mode decomposition.

3. The data assimilation method for a modal information optimization process model according to claim 1, characterized in that The S3 is specifically: where β N×N is the optimized quantity of the modal set, X L is the process model state vector, L is the dimension of the process model state vector, X L×N is the perturbation set of X L , is the optimized quantity set of X L calculated by using β N×N , is the nth (1 ≤ n ≤ N) column of , is the column mean of , that is, the optimized quantity of X L , is the optimized process model state vector.

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