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 Chinese Science Bulletin , 2008, DOI: 10.1007/s11434-008-0419-x Abstract: Variational method is capable of dealing with observations that have a complicated nonlinear relation with model variables representative of the atmospheric state, and so make it possible to directly assimilate such measured variables as satellite radiance, which have a nonlinear relation with the model variables. Assimilation of any type of observations requires a corresponding observation operator, which establishes a specific mapping from the space of the model state to the space of observation. This paper presents in detail how the direct assimilation of real satellite radiance data is implemented in the GRAPES-3DVar analysis system. It focuses on all the components of the observation operator for direct assimilation of real satellite radiance data, including a spatial interpolation operator that transforms variables from model grid points to observation locations, a physical transformation from model variables to observed elements with different choices of model variables, and a data quality control. Assimilation experiments, using satellite radiances such as NOAA17 AMSU-A and AMSU-B (Advanced Microwave Sounding Unit), are carried out with two different schemes. The results from these experiments can be physically understood and clearly reflect a rational effect of direct assimilation of satellite radiance data in GRAPES-3DVar analysis system.
 Chinese Science Bulletin , 2008, DOI: 10.1007/s11434-008-0494-z Abstract: A new generation of numerical prediction system GRAPES (a short form of Global/Regional Assimilation and PrEdiction System) was set up in China Meteorological Administration (CMA). This paper focuses on the scientific design and preliminary results of the numerical prediction model in GRAPES, including basic idea and strategy of the general scientific design, multi-scale dynamic core, physical package configuration, architecture and parallelization of the codes. A series of numerical experiments using the real data with horizontal resolutions from 10 to 280 km and idealized experiments with very high resolution up to 100 m are conducted, giving encouraging results supporting the multi-scale application of GRAPES. The results of operational implementation of GRAPES model in some NWP centers are also presented with stress at evaluations of the capability to predict the main features of precipitation in China. Finally the issues to be dealt with for further development are discussed.
 大气科学进展 , 2007, Abstract: This paper summarizes the recent progress of numerical weather prediction(NWP)research since the last review Was published.The new generation NWP system named GRAPES (the Global and Regional Assimilation and Prediction System),which consists of variational or sequential data assimilation and nonhydrostatic prediction model with options of configuration for either global or regional domains,is briefly introduced,with stress on their scientific design and preliminary results during pre-operational implementation.In addition to the development of GRAPES.the achievements in new methodologies of data assimilation,new improvements of model physics such as parameterization of clouds and planetary boundary layer,mesoscale ensemble prediction system and numerical prediction of air quality are presented.The scientific issues which should be emphasized for the future are discussed finally.
 气候与环境研究 , 2009, Abstract: Data assimilation has been successfully applied in atmospheric,oceanic,and land surface models.However,the four-dimensional variational(4DVar)assimilation system demands great computational costs.The authors introduced a new Historical-Sample-Projection data assimilation scheme(HSP-4DVar),and accomplished the HSP-4DVar land surface data assimilation system based on the Common Land Model(CoLM).As a scheme which requires no adjoint models,HSP-4DVar can be directly solved and easily realized,therefore avoids h...
 大气科学进展 , 2012, Abstract: Constructing β-mesoscale weather systems in initial fields remains a challenging problem in a mesoscale numerical weather prediction (NWP) model. Without vertical velocity matching the β-mesoscale weather system, convection activities would be suppressed by downdraft and cooling caused by precipitating hydrometeors. In this study, a method, basing on the three-dimensional variational (3DVAR) assimilation technique, was developed to obtain reasonable structures of β-mesoscale weather systems by assimilating radar data in a next-generation NWP system named GRAPES (the Global and Regional Assimilation and Prediction System) of China. Single-point testing indicated that assimilating radial wind significantly improved the horizontal wind but had little effect on the vertical velocity, while assimilating the retrieved vertical velocity (taking Richardson’s equation as the observational operator) can greatly improve the vertical motion. Experiments on a typhoon show that assimilation of the radial wind data can greatly improve the prediction of the typhoon track, and can ameliorate precipitation to some extent. Assimilating the retrieved vertical velocity and rainwater mixing ratio, and adjusting water vapor and cloud water mixing ratio in the initial fields simultaneously, can significantly improve the tropical cyclone rainfall forecast but has little effect on typhoon path. Joint assimilating these three kinds of radar data gets the best results. Taking into account the scale of different weather systems and representation of observational data, data quality control, error setting of background field and observation data are still requiring further in-depth study.
 Jochen Br？cker Physics , 2010, DOI: 10.1002/qj.695 Abstract: Variational data assimilation in continuous time is revisited. The central techniques applied in this paper are in part adopted from the theory of optimal nonlinear control. Alternatively, the investigated approach can be considered as a continuous time generalisation of what is known as weakly constrained four dimensional variational assimilation (WC--4DVAR) in the geosciences. The technique allows to assimilate trajectories in the case of partial observations and in the presence of model error. Several mathematical aspects of the approach are studied. Computationally, it amounts to solving a two point boundary value problem. For imperfect models, the trade off between small dynamical error (i.e. the trajectory obeys the model dynamics) and small observational error (i.e. the trajectory closely follows the observations) is investigated. For (nearly) perfect models, this trade off turns out to be (nearly) trivial in some sense, yet allowing for some dynamical error is shown to have positive effects even in this situation. The presented formalism is dynamical in character; no assumptions need to be made about the presence (or absence) of dynamical or observational noise, let alone about their statistics.
 Physics , 2012, Abstract: The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general derivation of this approach and extend the method to particle smoothing as well as to data assimilation for perfect models. We show that the minimizations required by implicit particle methods are similar to the ones one encounters in variational data assimilation and explore the connection of implicit particle methods with variational data assimilation. In particular, we argue that existing variational codes can be converted into implicit particle methods at a low cost, often yielding better estimates, that are also equipped with quantitative measures of the uncertainty. A detailed example is presented.
 Physics , 2013, DOI: 10.3402/tellusa.v66.21789 Abstract: This paper studies the role of sparse regularization in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable of interest exhibits sparsity in the real or transformed domain. We show that in the presence of sparsity, the $\ell_{1}$-norm regularization produces more accurate and stable solutions than the classic data assimilation methods. To motivate further developments of the proposed methodology, assimilation experiments are conducted in the wavelet and spectral domain using the linear advection-diffusion equation.
 Ma？lle Nodet Mathematics , 2008, DOI: 10.1088/0266-5611/22/1/014 Abstract: We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional space-time circulation of the ocean. This problem is solved using the four-dimensional variational technique and the adjoint method. In this problem the control vector is chosen as being the initial state of the dynamical system. The observed variables, namely the positions of the floats, are expressed as a function of the control vector via a nonlinear observation operator. This method has been implemented and has the ability to reconstruct the main patterns of the oceanic circulation. Moreover it is very robust with respect to increase of time-sampling period of observations. We have run many twin experiments in order to analyze the sensitivity of our method to the number of floats, the time-sampling period and the vertical drift level. We compare also the performances of the Lagrangian method to that of the classical Eulerian one. Finally we study the impact of errors on observations.
 Eugene Kazantsev Mathematics , 2009, DOI: 10.1016/j.jcp.2009.09.018 Abstract: Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows us to discuss in detail as the development of the adjoint model and assimilation results. It is shown what kind of errors can be corrected by this control and how these errors are corrected. This study is carried out in view of using this control to identify optimal numerical schemes in coastal regions of ocean models.
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