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Four-dimensional variational data assimilation for a limited area model
Nils Gustafsson,Xiang-Yu Huang,Xiaohua Yang,Kristian Mogensen
Tellus A , 2012, DOI: 10.3402/tellusa.v64i0.14985
Abstract: A 4-dimensional variational data assimilation (4D-Var) scheme for the HIgh Resolution Limited Area Model (HIRLAM) forecasting system is described in this article. The innovative approaches to the multi-incremental formulation, the weak digital filter constraint and the semi-Lagrangian time integration are highlighted with some details. The implicit dynamical structure functions are discussed using single observation experiments, and the sensitivity to various parameters of the 4D-Var formulation is illustrated. To assess the meteorological impact of HIRLAM 4D-Var, data assimilation experiments for five periods of 1 month each were performed, using HIRLAM 3D-Var as a reference. It is shown that the HIRLAM 4D-Var consistently out-performs the HIRLAM 3D-Var, in particular for cases with strong mesoscale storm developments. The computational performance of the HIRLAM 4D-Var is also discussed.The review process was handled by Subject Editor Abdel Hannachi
An Economical Approach to Four-dimensional Variational Data Assimilation

WANG Bin,LIU Juanjuan,WANG Shudong,CHENG Wei,LIU Juan,LIU Chengsi,Qingnong XIAO,Ying-Hwa KUO,

大气科学进展 , 2010,
Abstract: Four-dimensional variational data assimilation (4DVar) is one of the most promising methods to provide optimal analysis for numerical weather prediction (NWP). Five national NWP centers in the world have successfully applied 4DVar methods in their global NWPs, thanks to the increment method and adjoint technique. However, the application of 4DVar is still limited by the computer resources available at many NWP centers and research institutes. It is essential, therefore, to further reduce the computational cost of 4DVar. Here, an economical approach to implement 4DVar is proposed, using the technique of dimension-reduced projection (DRP), which is called ``DRP-4DVar." The proposed approach is based on dimension reduction using an ensemble of historical samples to define a subspace. It directly obtains an optimal solution in the reduced space by fitting observations with historical time series generated by the model to form consistent forecast states, and therefore does not require implementation of the adjoint of tangent linear approximation. To evaluate the performance of the DRP-4DVar on assimilating different types of mesoscale observations, some observing system simulation experiments are conducted using MM5 and a comparison is made between adjoint-based 4DVar and DRP-4DVar using a 6-hour assimilation window.
On the 4D Variational Data Assimilation with Constraint Conditions

Zhu Keyun,

大气科学进展 , 2001,
Abstract: An investigation is carried out on the problem involved in 4D variational data assimilation (VDA) with constraint conditions based on a finite-element shallow-water equation model. In the investigation, the adjoint technology, penalty method and augmented Lagrangian method are used in constraint optimization field to minimize the defined constraint objective functions. The results of the numerical experiments show that the optimal solutions are obtained if the functions reach the minima. VDA with constraint conditions controlling the growth of gravity oscillations is efficient to eliminate perturbation and produces optimal initial field. It seems that this method can also be applied to the problem in numerical weather prediction.
Parallel Computing of a Variational Data Assimilation Model for GPS/MET Observation Using the Ray-Tracing Method
Parallel Computing of a Variational Data Assimilation Model for GPS/MET Observation Using the Ray-Tracing Method

ZHANG Xin,LIU Yuewei,WANG Bin,JI Zhongzhen,
,LIU Yuewei,WANG Bin,JI Zhongzhen

大气科学进展 , 2004,
Abstract: The Spectral Statistical Interpolation (SSI) analysis system of NCEP is used to assimilate meteorological data from the Global Positioning Satellite System (GPS/MET) refraction angles with the variational technique. Verified by radiosonde, including GPS/MET observations into the analysis makes an overall improvement to the analysis variables of temperature, winds, and water vapor. However, the variational model with the ray-tracing method is quite expensive for numerical weather prediction and climate research. For example, about 4 000 GPS/MET refraction angles need to be assimilated to produce an ideal global analysis. Just one iteration of minimization will take more than 24 hours CPU time on the NCEP's Gray C90 computer. Although efforts have been taken to reduce the computational cost, it is still prohibitive for operational data assimilation. In this paper, a parallel version of the three-dimensional variational data assimilation model of GPS/MET occultation measurement suitable for massive parallel processors architectures is developed. The divide-and-conquer strategy is used to achieve parallelism and is implemented by message passing. The authors present the principles for the code's design and examine the performance on the state-of-the-art parallel computers in China. The results show that this parallel model scales favorably as the number of processors is increased. With the Memory-IO technique implemented by the author, the wall clock time per iteration used for assimilating 1420 refraction angles is reduced from 45 s to 12 s using 1420 processors. This suggests that the new parallelized code has the potential to be useful in numerical weather prediction (NWP) and climate studies.
Control of lateral boundary conditions in four-dimensional variational data assimilation for a limited area model
Nils Gustafsson
Tellus A , 2012, DOI: 10.3402/tellusa.v64i0.17518
Abstract: The limited area model forecasting problem is a lateral boundary condition (LBC) problem in addition to the initial condition problem. The data assimilation has traditionally been considered as a process for estimation of the initial condition only, while for the limited area data assimilation this estimation may be extended to include also the LBCs, at least during the data assimilation time window when observations are available. A procedure for such a control of the LBCs has been included in the four-dimensional variational data assimilation (4D-Var) scheme for the HIgh Resolution Limited Area Model (HIRLAM) forecasting system. A description of this procedure is provided together with results from idealised as well as real data experiments. The results indicate that control of LBCs may be important with small forecast domains and in particular for weather disturbances moving quickly into and through the forecast domain.
Coupling Ensemble Kalman Filter with Four-dimensional Variational Data Assimilation


大气科学进展 , 2009,
Abstract: This study examines the performance of coupling the deterministic four-dimensional variational assimilation system (4DVAR) with an ensemble Kalman filter (EnKF) to produce a superior hybrid approach for data assimilation. The coupled assimilation scheme (E4DVAR) benefits from using the state-dependent uncertainty provided by EnKF while taking advantage of 4DVAR in preventing filter divergence: the 4DVAR analysis produces posterior maximum likelihood solutions through minimization of a cost function about which the ensemble perturbations are transformed, and the resulting ensemble analysis can be propagated forward both for the next assimilation cycle and as a basis for ensemble forecasting. The feasibility and effectiveness of this coupled approach are demonstrated in an idealized model with simulated observations. It is found that the E4DVAR is capable of outperforming both 4DVAR and the EnKF under both perfect- and imperfect-model scenarios. The performance of the coupled scheme is also less sensitive to either the ensemble size or the assimilation window length than those for standard EnKF or 4DVAR implementations.
POD/DEIM Reduced-Order Strategies for Efficient Four Dimensional Variational Data Assimilation  [PDF]
R?zvan ?tef?nescu,Adrian Sandu,Ionel Michael Navon
Computer Science , 2014, DOI: 10.1016/j.jcp.2015.04.030
Abstract: This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order solution is that reduced order Karush-Kuhn-Tucker conditions accurately represent their full order counterparts. In particular, accurate reduced order approximations are needed for the forward and adjoint dynamical models, as well as for the reduced gradient. New strategies to construct reduced order based are developed for Proper Orthogonal Decomposition (POD) ROM data assimilation using both Galerkin and Petrov-Galerkin projections. For the first time POD, tensorial POD, and discrete empirical interpolation method (DEIM) are employed to develop reduced data assimilation systems for a geophysical flow model, namely, the two dimensional shallow water equations. Numerical experiments confirm the theoretical framework for Galerkin projection. In the case of Petrov-Galerkin projection, stabilization strategies must be considered for the reduced order models. The new reduced order shallow water data assimilation system provides analyses similar to those produced by the full resolution data assimilation system in one tenth of the computational time.
A New Global Four-Dimensional Variational Ocean Data Assimilation System and Its Application
LIU Juan,WANG Bin,LIU Hailong,YU Yongqiang,
LIU Juan
,WANG Bin,LIU Hailong,YU Yongqiang

大气科学进展 , 2008,
Abstract: A four-dimensional variational data assimilation (4DVar) system of the LASG/IAP Climate Ocean Model, version 1.0 (LICOM1.0), named LICOM-3DVM, has been developed using the three-dimensional variational data assimilation of mapped observation (3DVM), a 4DVar method newly proposed in the past two years. Two experiments with 12-year model integrations were designed to validate it. One is the as- similation run, called ASSM, which incorporated the analyzed weekly sea surface temperature (SST) fields from Reynolds and Smith (OISST) between 1990 and 2001 once a week by the LICOM-3DVM. The other is the control run without any assimilation, named CTL. ASSM shows that the simulated temperatures of the upper ocean (above 50 meters), especially the SST of equatorial Pacific, coincide with the Tropic Atmo- sphere Ocean (TAO) mooring data, the World Ocean Atlas 2001 (WOA01) data and the Met Office Hadley Centre's sea ice and sea surface temperature (HadISST) data. It decreased the cold bias existing in CTL in the eastern Pacific and produced a Nino index that agrees with observation well. The validation results suggest that the LICOM-3DVM is able to effectively adjust the model results of the ocean temperature, although it's hard to correct the subsurface results and it even makes them worse in some areas due to the incorporation of only surface data. Future development of the LICOM-3DVM is to include subsurface in situ observations and satellite observations to further improve model simulations.
Four-Dimensional Variational Data Assimilation Experiments for a Heavy Rain Case During the 2002 IOP in China
ZHANG Lin,NI Yunqi,
,NI Yunqi

大气科学进展 , 2005,
Abstract: A heavy rainfall event along the mei-yu front during 22-23 June 2002 was chosen for this study. To assess the impact of the routine and additional IOP (intensive observation period) radiosonde observations on the mesoscale heavy rainfall forecast, a series of four-dimensional variational (4DVAR) data assimilation and model simulation experiments was conducted using nonhydrostatic mesoscale model MM5 and the MM5 4DVAR system. The effects of the intensive observations in the different areas on the heavy rainfall forecast were also investigated. The results showed that improvement of the forecast skill for mesoscale heavy rainfall intensity was possible from the assimilation of the IOP radiosonde observations. However,the impact of the IOP observations on the forecast of the rainfall pattern was not significant. Initial conditions obtained through the 4DVAR experiments with a 12-h assimilation window were capable of improving the 24-h forecast. The simulated results after the assimilation showed that it would be best to perform the intensive radiosonde observations in the upstream of the rainfall area and in the moisture passageway area at the same time. Initial conditions created by the 4DVAR led to the low-level moisture convergence over the rainfall area, enhanced frontogenesis and upward motion within the mei-yu front,and intensified middle- and high-level unstable stratification in front of the mei-yu front. Consequently,the heavy rainfall forecast was improved.
Four-dimensional variational assimilation in the unstable subspace (4DVar-AUS) and the optimal subspace dimension  [PDF]
Anna Trevisan,Massimo D'Isidoro,Olivier Talagrand
Physics , 2009,
Abstract: A key a priori information used in 4DVar is the knowledge of the system's evolution equations. In this paper we propose a method for taking full advantage of the knowledge of the system's dynamical instabilities in order to improve the quality of the analysis. We present an algorithm, four-dimensional variational assimilation in the unstable subspace (4DVar-AUS), that consists in confining in this subspace the increment of the control variable. The existence of an optimal subspace dimension for this confinement is hypothesized. Theoretical arguments in favor of the present approach are supported by numerical experiments in a simple perfect non-linear model scenario. It is found that the RMS analysis error is a function of the dimension N of the subspace where the analysis is confined and is minimum for N approximately equal to the dimension of the unstable and neutral manifold. For all assimilation windows, from 1 to 5 days, 4DVar-AUS performs better than standard 4DVar. In the presence of observational noise, the 4DVar solution, while being closer to the observations, if farther away from the truth. The implementation of 4DVar-AUS does not require the adjoint integration.
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