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1.
The proper orthogonal decomposition (POD) method is used to construct a set of basis functions for spanning the ensemble of
data in a certain least squares optimal sense. Compared with the singular value decomposition (SVD), the POD basis functions
can capture more energy in the forecast ensemble space and can represent its spatial structure and temporal evolution more
effectively. After the analysis variables are expressed by a truncated expansion of the POD basis vectors in the ensemble
space, the control variables appear explicitly in the cost function, so that the adjoint model, which is used to derive the
gradient of the cost function with respect to the control variables, is no longer needed. The application of this new technique
significantly simplifies the data assimilation process. Several assimilation experiments show that this POD-based explicit
four-dimensional variational data assimilation method performs much better than the usual ensemble Kalman filter method on
both enhancing the assimilation precision and reducing the computation cost. It is also better than the SVD-based explicit
four-dimensional assimilation method, especially when the forecast model is not perfect and the forecast error comes from
both the noise of the initial filed and the uncertainty of the forecast model.
Supported by the National Natural Science Foundation of China (Grant No. 40705035), National High Technology Research and
Development Program of China (Grant No. 2007AA12Z144), Knowledge Innovation Project of Chinese Academy of Sciences (Grant
Nos. KZCX2-YW-217 and KZCX2-YW-126-2), and National Basic Research Program of China (Grant No. 2005CB321704) 相似文献
2.
《Journal of Atmospheric and Solar》2000,62(12):1057-1070
Data assimilation combines atmospheric measurements with knowledge of atmospheric behavior as codified in computer models, thus producing a “best” estimate of current conditions that is consistent with both information sources. The four major challenges in data assimilation are: (1) to generate an initial state for a computer forecast that has the same mass-wind balance as the assimilating model, (2) to deal with the common problem of highly non-uniform distribution of observations, (3) to exploit the value of proxy observations (of parameters that are not carried explicitly in the model), and (4) to determine the statistical error properties of observing systems and numerical model alike so as to give each information source the proper weight. Variational data assimilation is practiced at major meteorological centers around the world. It is based upon multivariate linear regression, dating back to Gauss, and variational calculus. At the heart of the method is the minimization of a cost function, which guarantees that the analyzed fields will closely resemble both the background field (a short forecast containing a priori information about the atmospheric state) and current observations. The size of the errors in the background and the observations (the latter, arising from measurement and non-representativeness) determine how close the analysis is to each basic source of information. Three-dimensional variational (3DVAR) assimilation provides a logical framework for incorporating the error information (in the form of variances and spatial covariances) and deals directly with the problem of proxy observations. 4DVAR assimilation is an extension of 3DVAR assimilation that includes the time dimension; it attempts to find an evolution of model states that most closely matches observations taken over a time interval measured in hours. Both 3DVAR and, especially, 4DVAR assimilation require very large computing resources. Researchers are trying to find more efficient numerical solutions to these problems. Variational assimilation is applicable in the upper atmosphere, but practical implementation demands accurate modeling of the physical processes that occur at high altitudes and multiple sources of observations. 相似文献
3.
Three choices of control variables for meteorological variational analysis (3DVAR or 4DVAR) are associated with horizontal
wind: (1) streamfunction and velocity potential, (2) eastward and northward velocity, and (3) vorticity and divergence. This
study shows theoretical and numerical differences of these variables in practical 3DVAR data assimilation through statistical
analysis and numerical experiments. This paper demonstrates that (a) streamfunction and velocity potential could potentially
introduce analysis errors; (b) A 3DVAR using velocity or vorticity and divergence provides a natural scale dependent influence
radius in addition to the covariance; (c) for a regional analysis, streamfunction and velocity potential are retrieved from
the background velocity field with Neumann boundary condition. Improper boundary conditions could result in further analysis
errors; (d) a variational data assimilation or an inverse problem using derivatives as control variables yields smoother analyses,
for example, a 3DVAR using vorticity and divergence as controls yields smoother wind analyses than those analyses obtained
by a 3DVAR using either velocity or streamfunction/velocity potential as control variables; and (e) statistical errors of
higher order derivatives of variables are more independent, e.g., the statistical correlation between U and V is smaller than the one between streamfunction and velocity potential, and thus the variables in higher derivatives are more
appropriate for a variational system when a cross-correlation between variables is neglected for efficiency or other reasons.
In summary, eastward and northward velocity, or vorticity and divergence are preferable control variables for variational
systems and the former is more attractive because of its numerical efficiency. Numerical experiments are presented using analytic
functions and real atmospheric observations. 相似文献
4.
《Advances in water resources》2003,26(2):161-178
The objective of data assimilation is to provide physically consistent estimates of spatially distributed environmental variables. In this study a relatively simple data assimilation method has been implemented in a relatively complex hydrological model. The data assimilation technique is Newtonian relaxation or nudging, in which model variables are driven towards observations by a forcing term added to the model equations. The forcing term is proportional to the difference between simulation and observation (relaxation component) and contains four-dimensional weighting functions that can incorporate prior knowledge about the spatial and temporal variability and characteristic scales of the state variable(s) being assimilated. The numerical model couples a three-dimensional finite element Richards equation solver for variably saturated porous media and a finite difference diffusion wave approximation based on digital elevation data for surface water dynamics. We describe the implementation of the data assimilation algorithm for the coupled model and report on the numerical and hydrological performance of the resulting assimilation scheme. Nudging is shown to be successful in improving the hydrological simulation results, and it introduces little computational cost, in terms of CPU and other numerical aspects of the model’s behavior, in some cases even improving numerical performance compared to model runs without nudging. We also examine the sensitivity of the model to nudging term parameters including the spatio-temporal influence coefficients in the weighting functions. Overall the nudging algorithm is quite flexible, for instance in dealing with concurrent observation datasets, gridded or scattered data, and different state variables, and the implementation presented here can be readily extended to any of these features not already incorporated. Moreover the nudging code and tests can serve as a basis for implementation of more sophisticated data assimilation techniques in a Richards equation-based hydrological model. 相似文献
5.
Alexander Barth Yajing Yan Aida Alvera-Azcárate Jean-Marie Beckers 《Ocean Dynamics》2016,66(12):1651-1664
Ensemble assimilation schemes applied in their original, global formulation respect linear conservation properties if the ensemble perturbations are set up accordingly. For realistic ocean systems, only a relatively small number of ensemble members can be calculated. A localization of the ensemble increment is therefore necessary to filter out spurious long-range correlations. The conservation of the global properties will be lost if the assimilation is performed locally, since the conservation requires a coupling between all model grid points which is removed by the localization. The distribution of ocean observations is often highly inhomogeneous. Systematic errors of the observed parts of the ocean state can lead to spurious adjustment of the non-observed parts via data assimilation and thus to a spurious increase or decrease in long-term simulations of global properties which should be conserved. In this paper, we propose a local assimilation scheme (with different variants and assumptions) which can satisfy global conservation properties. The proposed scheme can also be used for non-local observation operators. Different variants of the proposed scheme are tested in an idealized model and compared to the traditional covariance localization with an ad-hoc step enforcing conservation. It is shown that the inclusion of the conservation property reduces the total RMS error and that the presented stochastic and deterministic schemes avoiding error space rotation provide better results than the traditional covariance localization. 相似文献
6.
The variational method of data assimilation is used to solve an inverse problem in the transport of sediment in river, which
plays an important role in the change of natural environment. The cost function is defined to measure the error between model
predictions and field observations. The adjoint model of IAP river sedimentation model is created to obtain the gradient of
the cost function with respect to control variables. The initial conditions are taken as the control variables; their optimal
values can be retrieved by minimizing the cost function with limited memory quasi-Newton method (LMQN). The results show that
the adjoint method approach can successfully make the model prediction well fit the simulated observations. And it is expected
to use this method to solve other inverse problems of river sedimentation. But some numerical problems need to be discussed
before applying to real river data.
Project partially supported by the State Key Laboratory of Numerical Modelling for Atmospheric Sciences and Geophysical Fluid
Dynamics, Institute of Atmospheric Physics, Chinese Academy of Sciences 相似文献
7.
Nonlinear balance constraints in 3DVAR data assimilation 总被引：7，自引：2，他引：7
Consideration of the so-called balance properties/ constraints is of great importance in the data assimila- tion. First, it is desirable to separate the slow modes (e.g., Rossby waves) from the fast modes (e.g., gravity waves and deep convection). Second, consideration of the balance constraints enables us to infer information about all variables that are balanced with the observed variable and hereby improve the quality of the analy- sis. The balance properties are usually represented by some… 相似文献
8.
Mesoscale eddy plays an important role in the ocean circulation. In order to improve the simulation accuracy of the mesoscale eddies, a three-dimensional variation (3DVAR) data assimilation system called Ocean Variational Analysis System (OVALS) is coupled with a POM model to simulate the mesoscale eddies in the Northwest Pacific Ocean. In this system, the sea surface height anomaly (SSHA) data by satellite altimeters are assimilated and translated into pseudo temperature and salinity (T-S) profile data. Then, these profile data are taken as observation data to be assimilated again and produce the three-dimensional analysis T-S field. According to the characteristics of mesoscale eddy, the most appropriate assimilation parameters are set up and testified in this system. A ten years mesoscale eddies simulation and comparison experiment is made, which includes two schemes: assimilation and non-assimilation. The results of comparison between two schemes and the observation show that the simulation accuracy of the assimilation scheme is much better than that of non-assimilation, which verified that the altimetry data assimilation method can improve the simulation accuracy of the mesoscale dramatically and indicates that it is possible to use this system on the forecast of mesoscale eddies in the future. 相似文献
9.
Ching-Yuang Huang Ying-Hwa Kuo Shu-Ya Chen Anisetty S. K. A. V. Prasad Rao Chien-Ju Wang 《Pure and Applied Geophysics》2007,164(8-9):1577-1591
In this study, the Weather Research and Forecasting (WRF-2.0.3.1) model with three-dimensional variational data assimilation
(3DVAR) was utilized to study a heavy rainfall event along the west coast of India with and without the assimilation of GPS
occultation refractivity soundings in the monsoon period of 2002. The WRF model is a next-generation mesoscale numerical weather
prediction system designed to serve both operational forecasting and atmospheric research communities. The Global Positioning
System (GPS) radio occultation (RO) refractivity data, processed by UCAR, were obtained from the CHAMP and SAC-C missions.
This study investigates the impact of thirteen GPS occultation refractivity soundings only, as assimilated into the WRF model
with 3DVAR, on the rainfall prediction over the western coastal mountain of India. The model simulation, with the finest resolution
of 10 km, was in good agreement with rainfall observations, up to 72-h forecast. There are some subtle but important differences
in predicted rainfalls between the control run CN (without the assimilation of refractivity soundings) and G13 (with the assimilation
of thirteen GPS RO soundings). In general, the assimilation run G13 gives a better prediction in terms of both rainfall locations
and amounts at later times. The moisture increments were analyzed at the initial and forecast times to assess the impact of
GPS RO data assimilation. The results indicate that remote soundings in the forcing region could have significant impacts
on distant downstream regions. It is anticipated, based on this study, that considerably occultation soundings available from
the six-satellite constellation of FORMOSAT-3/COSMIC would have even more significant impacts on weather prediction in this
region. 相似文献
10.
S. Abhilash A. K. Sahai K. Mohankumar John P. George Someshwar Das 《Pure and Applied Geophysics》2012,169(11):2047-2070
In this paper the impact of Doppler weather radar (DWR) reflectivity and radial velocity observations for the short range forecasting of a tropical storm and associated rainfall event have been examined. Doppler radar observations of a tropical storm case that occurred during 29–30 October 2006 from SHARDWR (13.6° N, 80.2° E) are assimilated in the WRF 3DVAR system. The observation operator for radar reflectivity and radial velocity is included within latest version of WRF 3DVAR system. Keeping all model physics the same, three experiments were conducted at a horizontal resolution of 30?km. In the control experiment (CTRL), NCEP Final Analysis (FNL) interpolated to the model grid was used as the initial condition for 48-h free forecast. In the second experiment (NODWR), 6-h assimilation cycles have been carried out using all conventional (radiosonde and surface data) and non-conventional (satellite) observations from the Global Telecommunication System (GTS). The third experiment (DWR) is the same as the second, except Doppler radar radial velocity and reflectivity observations are also used in the assimilation cycle. Continuous 6-h assimilation cycle employed in the WRF-3DVAR system shows positive impact on the rainfall forecast. Assimilation of DWR data creates several small scale features near the storm centre. Additional sensitivity experiments were conducted to study the individual impact of reflectivity and radial velocity in the assimilation cycle. Radar data assimilation with reflectivity alone produced large analysis response on both thermodynamical and dynamical fields. However, radial velocity assimilation impacted only on dynamical fields. Analysis increments with radar reflectivity and radial velocity produce adjustments in both dynamical and thermodynamical fields. Verification of QPF skill shows that radar data assimilation has a considerable impact on the short range precipitation forecast. Improvement of the QPF skill with radar data assimilation is more clearly seen in the heavy rainfall (for thresholds >7?mm) event than light rainfall (for thresholds of 1 and 3?mm). The spatial pattern of rainfall is well simulated by the DWR experiment and is comparable to TRMM observations. 相似文献
11.
V. Yesubabu C. V. Srinivas K. B. R. R. Hariprasad R. Baskaran 《Pure and Applied Geophysics》2014,171(8):2023-2042
In this work, the impact of assimilation of conventional and satellite remote sensing observations (Oceansat-2 winds, MODIS temperature/humidity profiles) is studied on the simulation of two tropical cyclones in the Bay of Bengal region of the Indian Ocean using a three-dimensional variational data assimilation (3DVAR) technique. The Weather Research and Forecasting (WRF)-Advanced Research WRF (ARW) mesoscale model is used to simulate the severe cyclone JAL: 5–8 November 2010 and the very severe cyclone THANE: 27–30 December 2011 with a double nested domain configuration and with a horizontal resolution of 27 × 9 km. Five numerical experiments are conducted for each cyclone. In the control run (CTL) the National Centers for Environmental Prediction global forecast system analysis and forecasts available at 50 km resolution were used for the initial and boundary conditions. In the second (VARAWS), third (VARSCAT), fourth (VARMODIS) and fifth (VARALL) experiments, the conventional surface observations, Oceansat-2 ocean surface wind vectors, temperature and humidity profiles of MODIS, and all observations were respectively used for assimilation. Results indicate meager impact with surface observations, and relatively higher impact with scatterometer wind data in the case of the JAL cyclone, and with MODIS temperature and humidity profiles in the case of THANE for the simulation of intensity and track parameters. These relative impacts are related to the area coverage of scatterometer winds and MODIS profiles in the respective storms, and are confirmed by the overall better results obtained with assimilation of all observations in both the cases. The improvements in track prediction are mainly contributed by the assimilation of scatterometer wind vector data, which reduced errors in the initial position and size of the cyclone vortices. The errors are reduced by 25, 21, 38 % in vector track position, and by 57, 36, 39 % in intensity, at 24, 48, 72 h predictions, respectively, for the two cases using assimilation of all observations. Simulated rainfall estimates indicate that while the assimilation of scatterometer wind data improves the location of the rainfall, the assimilation of MODIS profiles produces a realistic pattern and amount of rainfall, close to the observational estimates. 相似文献
12.
Problems of the variational data assimilation for the primitive equation ocean model constructed at the Institute of Numerical
Mathematics, Russian Academy of Sciences are considered. The model has a flexible computational structure and consists of
two parts: a forward prognostic model, and its adjoint analog. The numerical algorithm for the forward and adjoint models
is constructed based on the method of multicomponent splitting. The method includes splitting with respect to physical processes
and space coordinates. Numerical experiments are performed with the use of the Indian Ocean and the World Ocean as examples.
These numerical examples support the theoretical conclusions and demonstrate the rationality of the approach using an ocean
dynamics model with an observed data assimilation procedure. 相似文献
13.
Ashish Routray U. C. Mohanty Krishna K. Osuri S. Kiran Prasad 《Pure and Applied Geophysics》2013,170(12):2329-2350
An attempt is made to evaluate the impact of Doppler Weather Radar (DWR) radial velocity and reflectivity in Weather Research and Forecasting (WRF)-3D variational data assimilation (3DVAR) system for prediction of Bay of Bengal (BoB) monsoon depressions (MDs). Few numerical experiments are carried out to examine the individual impact of the DWR radial velocity and the reflectivity as well as collectively along with Global Telecommunication System (GTS) observations over the Indian monsoon region. The averaged 12 and 24 h forecast errors for wind, temperature and moisture at different pressure levels are analyzed. This evidently explains that the assimilation of radial velocity and reflectivity collectively enhanced the performance of the WRF-3DVAR system over the Indian region. After identifying the optimal combination of DWR data, this study has also investigated the impact of assimilation of Indian DWR radial velocity and reflectivity data on simulation of the four different summer MDs that occurred over BoB. For this study, three numerical experiments (control no assimilation, with GTS and GTS along with DWR) are carried out to evaluate the impact of DWR data on simulation of MDs. The results of the study indicate that the assimilation of DWR data has a positive impact on the prediction of the location, propagation and development of rain bands associated with the MDs. The simulated meteorological parameters and tracks of the MDs are reasonably improved after assimilation of DWR observations as compared to the other experiments. The root mean square errors (RMSE) of wind fields at different pressure levels, equitable skill score and frequency bias are significantly improved in the assimilation experiments mainly in DWR assimilation experiment for all MD cases. The mean Vector Displacement Errors (VDEs) are significantly decreased due to the assimilation of DWR observations as compared to the CNTL and 3DV_GTS experiments. The study clearly suggests that the performance of the model simulation for the intense convective system which influences the large scale monsoonal flow is significantly improved after assimilation of the Indian DWR data from even one coastal locale within the MDs track. 相似文献
14.
Data assimilation in groundwater modelling: ensemble Kalman filter versus ensemble smoothers 
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下载免费PDF全文 Groundwater modelling calls for an effective and robust data integrating method to fill the gap between the model and observation data. The ensemble Kalman filter (EnKF), a real‐time data assimilation method, has been increasingly applied in multiple disciplines such as petroleum engineering and hydrogeology. In this approach, a groundwater model is updated sequentially with measured data such as hydraulic head and concentration. As an alternative to the EnKF, the ensemble smoother (ES) has been proposed for updating groundwater models using all the data together, with much less computational cost. To further improve the performance of the ES, an iterative ES has been proposed for continuously updating the model by assimilating measurements together. In this work, we compare the performance of the EnKF, the ES, and the iterative ES using a synthetic example in groundwater modelling. Hydraulic head data modelled on the basis of the reference conductivity field are used to inversely estimate conductivities at unsampled locations. Results are evaluated in terms of the characterization of conductivity and groundwater flow predictions. It is concluded that (a) the iterative ES works better than the standard ES because of its continuous updating and (b) the iterative ES could achieve results comparable with those of the EnKF, with less computational cost. These findings show that the iterative ES should be paid much more attention for data assimilation in groundwater modelling. 相似文献
15.
Oleg G. Logutov 《Ocean Dynamics》2008,58(5-6):441-460
This paper presents a rigorous, yet practical, method of multigrid data assimilation into regional structured-grid tidal models. The new inverse tidal nesting scheme, with nesting across multiple grids, is designed to provide a fit of the tidal dynamics to data in areas with highly complex bathymetry and coastline geometry. In these areas, computational constraints make it impractical to fully resolve local topographic and coastal features around all of the observation sites in a stand-alone computation. The proposed strategy consists of increasing the model resolution in multiple limited area domains around the observation locations where a representativeness error is detected in order to improve the representation of the measurements with respect to the dynamics. Multiple high-resolution nested domains are set up and data assimilation is carried out using these embedded nested computations. Every nested domain is coupled to the outer domain through the open boundary conditions (OBCs). Data inversion is carried out in a control space of the outer domain model. A level of generality is retained throughout the presentation with respect to the choice of the control space; however, a specific example of using the outer domain OBCs as the control space is provided, with other sensible choices discussed. In the forward scheme, the computations in the nested domains do not affect the solution in the outer domain. The subsequent inverse computations utilize the observation-minus-model residuals of the forward computations across these multiple nested domains in order to obtain the optimal values of parameters in the control space of the outer domain model. The inversion is carried out by propagating the uncertainty from the control space to model tidal fields at observation locations in the outer and in the nested domains using efficient low-rank error covariance representations. Subsequently, an analysis increment in the control space of the outer domain model is computed and the multigrid system is steered optimally towards observations while preserving a perfect dynamical balance. The method is illustrated using a real-world application in the context of the Philippines Strait Dynamics experiment. 相似文献
16.
《中国科学:地球科学(英文版)》2017,(3)
The Proper Orthogonal Decomposition(POD)-based ensemble four-dimensional variational(4DVar) assimilation method(POD4DEnVar) was proposed to combine the strengths of EnKF(i.e.,the ensemble Kalman filter) and 4DVar assimilation methods.Recently,a POD4DEnVar-based radar data assimilation scheme(PRAS) was built and its effectiveness was demonstrated.POD4 DEnVar is based on the assumption of a linear relationship between the model perturbations(MPs)and the observation perturbations(OPs);however,this assumption is likely to be destroyed by the highly non-linear forecast model or observation operator.To address this issue,using the Gauss-Newton iterative method,the nonlinear least squares enhanced POD4 DEnVar algorithm(referred to as NLS-4DVar) was proposed.Naturally,the PRAS was upgraded to form the NLS-4DVar-based radar data assimilation scheme(NRAS).To evaluate the performance of NRAS against PRAS,observing system simulation experiments(OSSEs) were conducted to assimilate reflectivity and radial velocity individually,with one,two,and three iterations.The results demonstrated that the NRAS outperformed PRAS in improving the initial condition and the forecasting of model variables and rainfall.The NRAS,with a smaller number of iterations,can yield a convergent result.In contrast to the situation when assimilating radial velocity,the advantages of NRAS over PRAS were more obvious when assimilating reflectivity. 相似文献
17.
18.
Amir Safi Troels N. Vilhelmsen Ibrahim Alameddine Majdi Abou Najm Mutasem El-Fadel 《Ground water》2019,57(4):612-631
Groundwater model predictions are often uncertain due to inherent uncertainties in model input data. Monitored field data are commonly used to assess the performance of a model and reduce its prediction uncertainty. Given the high cost of data collection, it is imperative to identify the minimum number of required observation wells and to define the optimal locations of sampling points in space and depth. This study proposes a design methodology to optimize the number and location of additional observation wells that will effectively measure multiple hydrogeological parameters at different depths. For this purpose, we incorporated Bayesian model averaging and genetic algorithms into a linear data-worth analysis in order to conduct a three-dimensional location search for new sampling locations. We evaluated the methodology by applying it along a heterogeneous coastal aquifer with limited hydrogeological data that is experiencing salt water intrusion (SWI). The aim of the model was to identify the best locations for sampling head and salinity data, while reducing uncertainty when predicting multiple variables of SWI. The resulting optimal locations for new observation wells varied with the defined design constraints. The optimal design (OD) depended on the ratio of the start-up cost of the monitoring program and the installation cost of the first observation well. The proposed methodology can contribute toward reducing the uncertainties associated with predicting multiple variables in a groundwater system. 相似文献
19.
富营养化模型是进行湖泊水环境质量预测和管理的重要工具,然而模型客观存在的误差一直是应用者关心的重要问题.数据同化作为连接观测数据与数值模型的重要方法,可以有效提高模型的准确性.集合卡尔曼滤波(En KF)是众多数据同化算法中应用最为广泛的一种,可进行非线性系统的数据同化,并能有效降低数据同化的计算量.本研究以太湖作为具体实例,选择Delft3D-BLOOM作为富营养化模型,在数值实验确定En KF集合数为100、观测误差方差为1%、模拟误差方差为10%的基础上分别进行模型状态变量同化以及状态变量与关键参数同步同化.结果显示,仅同化状态变量时,模型预测精度有所增加;同时同化状态变量和关键参数时,可显著提升模型在湖泊水环境质量预测中的精度.该研究为应用集合卡尔曼滤波以提高复杂的湖库富营养化模型模拟精度提供了有效的方法. 相似文献
20.
A central difference method with low numerical dispersion for solving the scalar wave equation 总被引：4，自引：0，他引：4
In this paper, we propose a nearly‐analytic central difference method, which is an improved version of the central difference method. The new method is fourth‐order accurate with respect to both space and time but uses only three grid points in spatial directions. The stability criteria and numerical dispersion for the new scheme are analysed in detail. We also apply the nearly‐analytic central difference method to 1D and 2D cases to compute synthetic seismograms. For comparison, the fourth‐order Lax‐Wendroff correction scheme and the fourth‐order staggered‐grid finite‐difference method are used to model acoustic wavefields. Numerical results indicate that the nearly‐analytic central difference method can be used to solve large‐scale problems because it effectively suppresses numerical dispersion caused by discretizing the scalar wave equation when too coarse grids are used. Meanwhile, numerical results show that the minimum sampling rate of the nearly‐analytic central difference method is about 2.5 points per minimal wavelength for eliminating numerical dispersion, resulting that the nearly‐analytic central difference method can save greatly both computational costs and storage space as contrasted to other high‐order finite‐difference methods such as the fourth‐order Lax‐Wendroff correction scheme and the fourth‐order staggered‐grid finite‐difference method. 相似文献