scholarly journals Spectral characteristics of background error covariance and multiscale data assimilation

2016 ◽  
Vol 82 (12) ◽  
pp. 1035-1048 ◽  
Author(s):  
Zhijin Li ◽  
Xiaoping Cheng ◽  
William I. Gustafson Jr. ◽  
Andrew M. Vogelmann
Keyword(s):  
Data Assimilation ◽  
Spectral Characteristics ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance

Reducing TC Position Uncertainty in an Ensemble Data Assimilation and Prediction System: A Case Study of Typhoon Fanapi (2010)

2018 ◽  
Vol 33 (2) ◽  
pp. 561-582 ◽  
Author(s):  
Kuan-Jen Lin ◽  
Shu-Chih Yang ◽  
Shuyi S. Chen
Keyword(s):  
Data Assimilation ◽  
Negative Impact ◽  
Wrf Model ◽  
Track Forecast ◽  
Background Error ◽  
Position Uncertainty ◽  
Background Error Covariance ◽  
Error Covariance ◽  
The Impact

Abstract Ensemble-based data assimilation (EDA) has been used for tropical cyclone (TC) analysis and prediction with some success. However, the TC position spread determines the structure of the TC-related background error covariance and affects the performance of EDA. With an idealized experiment and a real TC case study, it is demonstrated that observations in the core region cannot be optimally assimilated when the TC position spread is large. To minimize the negative impact from large position uncertainty, a TC-centered EDA approach is implemented in the Weather Research and Forecasting (WRF) Model–local ensemble transform Kalman filter (WRF-LETKF) assimilation system. The impact of TC-centered EDA on TC analysis and prediction of Typhoon Fanapi (2010) is evaluated. Using WRF Model nested grids with 4-km grid spacing in the innermost domain, the focus is on EDA using dropsonde data from the Impact of Typhoons on the Ocean in the Pacific field campaign. The results show that the TC structure in the background mean state is improved and that unrealistically large ensemble spread can be alleviated. The characteristic horizontal scale in the background error covariance is smaller and narrower compared to those derived from the conventional EDA approach. Storm-scale corrections are improved using dropsonde data, which is more favorable for TC development. The analysis using the TC-centered EDA is in better agreement with independent observations. The improved analysis ameliorates model shock and improves the track forecast during the first 12 h and landfall at 72 h. The impact on intensity prediction is mixed with a better minimum sea level pressure and overestimated peak winds.

scholarly journals Relationships among Four-Dimensional Hybrid Ensemble–Variational Data Assimilation Algorithms with Full and Approximate Ensemble Covariance Localization

2016 ◽  
Vol 144 (2) ◽  
pp. 591-606 ◽  
Author(s):  
Chengsi Liu ◽  
Ming Xue
Keyword(s):  
Data Assimilation ◽  
Linear Model ◽  
Control Variable ◽  
Adjoint Model ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Covariance Term ◽  
Observation Space ◽  
Static Background

Abstract Ensemble–variational data assimilation algorithms that can incorporate the time dimension (four-dimensional or 4D) and combine static and ensemble-derived background error covariances (hybrid) are formulated in general forms based on the extended control variable and the observation-space-perturbation approaches. The properties and relationships of these algorithms and their approximated formulations are discussed. The main algorithms discussed include the following: 1) the standard ensemble 4DVar (En4DVar) algorithm incorporating ensemble-derived background error covariance through the extended control variable approach, 2) the 4DEnVar neglecting the time propagation of the extended control variable (4DEnVar-NPC), 3) the 4D ensemble–variational algorithm based on observation space perturbation (4DEnVar), and 4) the 4DEnVar with no propagation of covariance localization (4DEnVar-NPL). Without the static background error covariance term, none of the algorithms requires the adjoint model except for En4DVar. Costly applications of the tangent linear model to localized ensemble perturbations can be avoided by making the NPC and NPL approximations. It is proven that En4DVar and 4DEnVar are mathematically equivalent, while 4DEnVar-NPC and 4DEnVar-NPL are mathematically equivalent. Such equivalences are also demonstrated by single-observation assimilation experiments with a 1D linear advection model. The effects of the non-flow-following or stationary localization approximations are also examined through the experiments. All of the above algorithms can include the static background error covariance term to establish a hybrid formulation. When the static term is included, all algorithms will require a tangent linear model and an adjoint model. The first guess at appropriate time (FGAT) approximation is proposed to avoid the tangent linear and adjoint models. Computational costs of the algorithms are also discussed.

scholarly journals Construction of non-diagonal background error covariance matrices for global chemical data assimilation

2010 ◽  
Vol 3 (4) ◽  
pp. 1783-1827 ◽  
Author(s):  
K. Singh ◽  
M. Jardak ◽  
A. Sandu ◽  
K. Bowman ◽  
M. Lee ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Computational Procedure ◽  
Covariance Matrices ◽  
Chemical Data ◽  
Spatial Correlations ◽  
Transport Models ◽  
Background Error ◽  
Spatial Error ◽  
Background Error Covariance ◽  
Error Covariance

Abstract. Chemical data assimilation attempts to optimally use noisy observations along with imperfect model predictions to produce a better estimate of the chemical state of the atmosphere. It is widely accepted that a key ingredient for successful data assimilation is a realistic estimation of the background error distribution. Particularly important is the specification of the background error covariance matrix, which contains information about the magnitude of the background errors and about their correlations. Most models currently use diagonal background covariance matrices. As models evolve toward finer resolutions, the diagonal background covariance matrices become increasingly inaccurate, since they captures less of the spatial error correlations. This paper discusses an efficient computational procedure for constructing non-diagonal background error covariance matrices which account for the spatial correlations of errors. The benefits of using the non-diagonal covariance matrices for variational data assimilation with chemical transport models are illustrated.

Scale-Dependent Background Error Covariance Localization: Evaluation in a Global Deterministic Weather Forecasting System

2018 ◽  
Vol 146 (5) ◽  
pp. 1367-1381 ◽  
Author(s):  
Jean-François Caron ◽  
Mark Buehner
Keyword(s):  
Data Assimilation ◽  
Weather Forecasting ◽  
Spatial Scales ◽  
Winter Period ◽  
Wind Fields ◽  
Horizontal Scale ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Forecasting System

Abstract Scale-dependent localization (SDL) consists of applying the appropriate (i.e., different) amount of localization to different ranges of background error covariance spatial scales while simultaneously assimilating all of the available observations. The SDL method proposed by Buehner and Shlyaeva for ensemble–variational (EnVar) data assimilation was tested in a 3D-EnVar version of the Canadian operational global data assimilation system. It is shown that a horizontal-scale-dependent horizontal localization leads to implicit vertical-level-dependent, variable-dependent, and location-dependent horizontal localization. The results from data assimilation cycles show that horizontal-scale-dependent horizontal covariance localization is able to improve the forecasts up to day 5 in the Northern Hemisphere extratropical summer period and up to day 7 in the Southern Hemisphere extratropical winter period. In the tropics, use of SDL results in improvements similar to what can be obtained by increasing the uniform amount of spatial localization. An investigation of the dynamical balance in the resulting analysis increments demonstrates that SDL does not further harm the balance between the mass and the rotational wind fields, as compared to the traditional localization approach. Potential future applications for the SDL method are also discussed.

scholarly journals Generalized background error covariance matrix model (GEN_BE v2.0)

2015 ◽  
Vol 8 (3) ◽  
pp. 669-696 ◽  
Author(s):  
G. Descombes ◽  
T. Auligné ◽  
F. Vandenberghe ◽  
D. M. Barker ◽  
J. Barré
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Chemical Species ◽  
Variational Data Assimilation ◽  
Control Variables ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
The Impact

Abstract. The specification of state background error statistics is a key component of data assimilation since it affects the impact observations will have on the analysis. In the variational data assimilation approach, applied in geophysical sciences, the dimensions of the background error covariance matrix (B) are usually too large to be explicitly determined and B needs to be modeled. Recent efforts to include new variables in the analysis such as cloud parameters and chemical species have required the development of the code to GENerate the Background Errors (GEN_BE) version 2.0 for the Weather Research and Forecasting (WRF) community model. GEN_BE allows for a simpler, flexible, robust, and community-oriented framework that gathers methods used by some meteorological operational centers and researchers. We present the advantages of this new design for the data assimilation community by performing benchmarks of different modeling of B and showing some of the new features in data assimilation test cases. As data assimilation for clouds remains a challenge, we present a multivariate approach that includes hydrometeors in the control variables and new correlated errors. In addition, the GEN_BE v2.0 code is employed to diagnose error parameter statistics for chemical species, which shows that it is a tool flexible enough to implement new control variables. While the generation of the background errors statistics code was first developed for atmospheric research, the new version (GEN_BE v2.0) can be easily applied to other domains of science and chosen to diagnose and model B. Initially developed for variational data assimilation, the model of the B matrix may be useful for variational ensemble hybrid methods as well.

scholarly journals The “ABC-DA system” (v1.4): a variational data assimilation system for convective scale assimilation research with a study of the impact of a balance constraint

2020 ◽  
Author(s):  
Ross Noel Bannister
Keyword(s):  
Data Assimilation ◽  
Covariance Matrix ◽  
Variational Data Assimilation ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Convective Scale ◽  
Data Assimilation System ◽  
Assimilation System

Abstract. Following the development of the simplified atmospheric convective-scale "toy" model (the ABC model, named after its three key parameters: the pure gravity wave frequency, A, the controller of the acoustic wave speed, B, and the constant of proportionality between pressure and density perturbations, C), this paper introduces its associated variational data assimilation system, ABC-DA. The purpose of ABC-DA is to permit quick and efficient research into data assimilation methods suitable for convective scale systems. The system can also be used as an aid to teach and demonstrate data assimilation principles. ABC-DA is flexible, configurable and is efficient enough to be run on a personal computer. The system can run a number of assimilation methods (currently 3DVar and 3DFGAT have been implemented), with user configurable observation networks. Observation operators for direct observations and wind speeds are part of the system, although these can be expanded relatively easily. A key feature of any data assimilation system is how it specifies the background error covariance matrix. ABC-DA uses a control variable transform method to allow this to be done efficiently. This version of ABC-DA mirrors many operational configurations, by modelling multivariate error covariances with uncorrelated control parameters, and spatial error covariances with special uncorrelated spatial patterns separately for each parameter. The software developed (amongst other things) does model runs, calibration tasks associated with the background error covariance matrix, testing and diagnostic tasks, single data assimilation runs, multi-cycle assimilation/forecast experiments, and has associated visualisation software. As a demonstration, the system is used to tackle a scientific question concerning the role of geostrophic balance (GB) to model background error covariances between mass and wind fields. This question arises because, although GB is a very useful mechanism that is successfully exploited in larger scale assimilation systems, its use is questionable at convective scales due to the typically larger Rossby numbers where GB is not so relevant. A series of identical twin experiments is done in cycled assimilation configurations. One experiment exploits GB to represent mass-wind covariances in a mirror of an operational set-up (with use of an additional vertical regression (VR) step, as used operationally). This experiment performs badly where assimilation error accumulates over time. Two further experiments are done: one that does not use GB, and another that does but without the VR step. Turning off GB impairs the performance, and turning off VR improves the performance in general. It is concluded that there is scope to further improve the way that the background error covariance matrices are calibrated, with some directions discussed.

Ocean spectral data assimilation without background error covariance matrix

2016 ◽  
Vol 66 (9) ◽  
pp. 1143-1163 ◽  
Author(s):  
Peter C. Chu ◽  
Chenwu Fan ◽  
Tetyana Margolina
Keyword(s):  
Data Assimilation ◽  
Spectral Data ◽  
Covariance Matrix ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance
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