Four-dimensional data assimilation method based on SVD: Theoretical aspect

Qiu, Chongjian; Jifan, Chou

doi:10.1007/s00704-005-0162-z

Cited by 23 publications

(26 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Tian and Xie [11] proposed a new explicit 4DVAR method by merging the Monte Carlo method and the proper orthogonal decomposition (POD) technique into 4DVAR in order to transform an implicit optimization problem into an explicit one. Qiu et al [9,10] proposed another new method for 4DVAR using the singular value decomposition (SVD) technique based on the theory of the atmospheric attractors. Like the I4DVAR, the POD-E4DVAR also needs to choose an assimilation time window.…”

Section: Two Ensemble-based Explicit 4dvar Methodsmentioning

confidence: 99%

“…These methods generally focus on how to produce the flow-dependent background error variance statistics by ensemble forecasts; however, the tangent linear operator or adjoint model is still necessary in these methods. Recently, Qiu et al [9,10] proposed a new method (referred to as SVD-E4VAR) for the 4DVar using a singular value decomposition (SVD) technique based on the theory of the atmospheric attractors to simplify the assimilation process considerably. Tian and Xie [11] developed another explicit 4DVAR method (referred to as POD-E4DVAR) by merging the Monte-Carol method and proper orthogonal decomposition (POD) [12,13] technique.…”

mentioning

confidence: 99%

See 1 more Smart Citation

Effects of sample density on the assimilation performance of an explicit four-dimensional variational data assimilation method

Tian

Xie

2009

Sci. China Ser. D-Earth Sci.

View full text Add to dashboard Cite

The concepts of sample sphere radius and sample density are proposed in this paper to help illustrate that different vector transformations result in diverse sample density with the same sample ensemble, which finally affects their assimilation performance. Several numerical experiments using a onedimensional (1-D) soil water equation and synthetic observations are conducted to evaluate this new theory in land data assimilation.POD/SVD-E4DVAR, data assimilation, sample densityThe four-dimensional variational data assimilation (4DVar) method [1,2] and the ensemble Kalman filter [3][4][5][6] (EnKF) are probably the two most popular assimilation methods in the data assimilation community. They both have their own attractive features. Essentially, the 4DVAR method transforms the data assimilation problem into an optimization one, whose advantages mainly embody on the followings: 1) the physical model provides a strong dynamical constraint; 2) it has the ability to assimilate the observational data at multiple times. However, the control variables (or initial states) are expressed implicitly in the cost function. In order to compute the gradient of the cost function with respect to the control variables, one has to integrate the adjoint model, whose development and maintenance require significant resources. Moreover, the background error covariance applied in the 4DVAR is usually flow-independent, which is obviously inappropriate for forward integration of the weather or climate models. On the other hand, EnKF has become an increasingly popular method because of its simple conceptual formulation and relative of implementation. For example, it requires no derivation of a tangent linear operator or adjoint equations, and no integration backward in time. By forecasting the statistical characteristics, the EnKF can provide flowdependent error estimates of the background errors using the Monte-Carol method. Nevertheless, there are still some deficiencies in the EnKF: the usual EnKF can neither assimilate the observational data at multiple times nor take the physical model as a strong dynamical constraint over an assimilation time window. Although many encouraging research results of the EnKF have been obtained in either global data assimilation or regional mescoscale data assimilation, not much evidence indicates that the EnKF outperforms variational data assimilation system in operational applications. Since variational data assimilation has been practically proved to be a very successful technique in operational numerical weather prediction, application of ensemble based background error covariance statistics to variatioanl data assimilation should be a good choice, which can extract the flow-dependent error covariance from ensemble forecasts to the analysis [7,8] . Lorenc [7] proposed that the control variable was preconditioned upon perturbation of background ensemble forecast so that the background error in variational system is flow-dependent. Buehnerm [8] adopted a similar hybrid ensemble 3DVar (En3DVar) scheme, and...

show abstract

Section: Two Ensemble-based Explicit 4dvar Methodsmentioning

confidence: 99%

mentioning

confidence: 99%

Effects of sample density on the assimilation performance of an explicit four-dimensional variational data assimilation method

Tian

Xie

2009

Sci. China Ser. D-Earth Sci.

View full text Add to dashboard Cite

show abstract

“…However, it is a fact that operational use of 4DVar in most NWP centers is still limited by high computational cost. Thus, there has been a lot of effort to reduce computational cost or develop new methodology regarding 4DVar, e.g., 3-dimensional variational data assimilation of mapped observation (3DVM; Wang and Zhao 2006) and ensemble-based variational data assimilation (EVDA) approaches (e.g., Lorenc 2003;Qiu and Chou 2006;Liu et al 2008;Tian et al 2008;Wang and Li 2008;Wang et al 2010). …”

Section: Introductionmentioning

confidence: 99%

A Four-Dimensional Variational Data Assimilation Approach with Analysis at the End of Assimilation Window. Part I: Methodology and Preliminary Tests

Wang

Cheng

Xu³

et al. 2011

Journal of the Meteorological Society of Japan

View full text Add to dashboard Cite

In this paper, we propose a new approach to four-dimensional variational data assimilation (4DVar) with analysis of the initial condition (IC) at the end of assimilation window. The new approach is referred to as "backward 4DVar (B-4DVar)." The minimization of its cost function is fulfilled through an ensemble of historical prediction samples.B-4DVar is computationally efficient because it does not use tangent linear or adjoint models. To prepare it for numerical weather prediction, a B-4DVar assimilation system is developed based on an operational regional prediction model, the Advanced Regional Eta Model (AREM). Two single observation experiments (SOEs) and an observing system simulation experiment (OSSE) are conducted to evaluate the system. The SOEs reveal a characteristic of flow dependence in B-4DVar, which is consistent with statistical estimation of the background error covariance matrix (simply B-matrix) using a group of IC-reliant historical prediction samples. The OSSE suggests that the B-4DVar approach improves the analytic quality of IC by effectively incorporating conventional observations, thereby outperforming the 3DVar.The time-saving feature, flow dependence in B-matrix, and good performance in assimilating conventional observations indicate the potential and feasibility of B-4DVar in operational use.

show abstract

“…However, like the traditional four-dimensional data assimilation, the adjoint model is still required because it remains the basic characteristics of the 4DVAR. Recently, Qiu and Chou [16] proposed a new method for four-dimensional data assimilation. They pointed out that the solution of the data assimilation should be restricted to the attractors of atmosphere dynamic equations in the phase space in order to reduce the degree of underdetermined problem.…”

mentioning

confidence: 99%

An explicit four-dimensional variational data assimilation method

2007

View full text Add to dashboard Cite

A new data assimilation method called the explicit four-dimensional variational (4DVAR) method is proposed. In this method, the singular value decomposition (SVD) is used to construct the orthogonal basis vectors from a forecast ensemble in a 4D space. The basis vectors represent not only the spatial structure of the analysis variables but also the temporal evolution. After the analysis variables are expressed by a truncated expansion of the basis vectors in the 4D space, the control variables in the cost function appear explicitly, so that the adjoint model, which is used to derive the gradient of cost function with respect to the control variables, is no longer needed. The new technique significantly simplifies the data assimilation process. The advantage of the proposed method is demonstrated by several experiments using a shallow water numerical model and the results are compared with those of the conventional 4DVAR. It is shown that when the observation points are very dense, the conventional 4DVAR is better than the proposed method. However, when the observation points are sparse, the proposed method performs better. The sensitivity of the proposed method with respect to errors in the observations and the numerical model is lower than that of the conventional method. data assimilation, four-dimensional variation, explicit method, singular value decomposition, shallow water equationThe four-dimensional variational data assimilation (4DVAR) has been a very successful technique and used in operational numerical weather prediction (NWP) of some weather forecast centers [1,2] . In this method the optimal estimate of initial condition of a forecast model is obtained by fitting the forecasts to observations within a time window. The attractive features of 4DVAR include: (1) the full-model is set as a strong dynamical constraint, and (2) it has the ability to assimilate the data at multiple time. However, the control variables (initial state) are expressed implicitly in the cost function. In order to compute gradient of the cost function with respect to the control variables, one has to integrate the adjoint model of the forecast model. But coding the adjoint for the 4DVAR and maintaining the adjoint, updated with the model upgrading, are extremely labor-intensive, especially when the forecast model is nonlinear and the model physics contain parameterized discontinuities [3,4] . Some researchers try to avoid integrating the adjoint model or reducing the expensive computation [5][6][7] . But the linear or adjoint model is still required in the methods mentioned above. So the three-dimensional variational data assimilation (3DVAR) becomes the common practice in many numerical weather forecast centers. The 3DVAR can be considered as a simplification of the 4DVAR, but it has lost the two advantages of the 4DVAR mentioned above. In general, the analysis results rely heavily on the information from the background field. However, as we know, in 3DVAR the background error covariance matrix is usually simplified and not flo...

show abstract

Four-dimensional data assimilation method based on SVD: Theoretical aspect

Cited by 23 publications

References 23 publications

Effects of sample density on the assimilation performance of an explicit four-dimensional variational data assimilation method

Effects of sample density on the assimilation performance of an explicit four-dimensional variational data assimilation method

A Four-Dimensional Variational Data Assimilation Approach with Analysis at the End of Assimilation Window. Part I: Methodology and Preliminary Tests

An explicit four-dimensional variational data assimilation method

Contact Info

Product

Resources

About