scholarly journals Towards the use of conservative thermodynamic variables in data assimilation: preliminary results using ground-based microwave radiometer measurements

2021 ◽  
Author(s):  
Pascal Marquet ◽  
Pauline Martinet ◽  
Jean-François Mahfouf ◽  
Alina Lavinia Barbu ◽  
Benjamin Ménétrier
Keyword(s):  
Data Assimilation ◽  
Water Vapour ◽  
Diurnal Cycle ◽  
Liquid Water ◽  
Covariance Matrices ◽  
Background Error ◽  
Background Error Covariance ◽  
Brightness Temperatures ◽  
Error Covariance ◽  
Thermodynamic Variables

Abstract. This study aims at introducing two conservative thermodynamic variables (moist-air entropy potential temperature and total water content) into a one-dimensional variational data assimilation system (1D-Var) to demonstrate the benefit for future operational assimilation schemes. This system is assessed using microwave brightness temperatures from a ground-based radiometer installed during the field campaign SOFGO3D dedicated to fog forecast improvement. An underlying objective is to ease the specification of background error covariance matrices that are currently highly dependent on weather conditions making difficult the optimal retrievals of cloud and thermodynamic properties during fog conditions. Background error covariance matrices for these new conservative variables have thus been computed by an ensemble approach based on the French convective scale model AROME, for both all-weather and fog conditions. A first result shows that the use of these matrices for the new variables reduces some dependencies to the meteorological conditions (diurnal cycle, presence or not of clouds) compared to usual variables (temperature, specific humidity). Then, two 1D-Var experiments (classical vs. conservative variables) are evaluated over a full diurnal cycle characterized by a stratus-evolving radiative fog situation, using hourly brightness temperatures. Results show, as expected, that analysed brightness temperatures by the 1D-Var are much closer to the observed ones than background values for both variable choices. This is especially the case for channels sensitive to water vapour and liquid water. On the other hand, analysis increments in model space (water vapour, liquid water) show significant differences between the two sets of variables.

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.

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

2011 ◽  
Vol 4 (2) ◽  
pp. 299-316 ◽  
Author(s):  
K. Singh ◽  
M. Jardak ◽  
A. Sandu ◽  
K. Bowman ◽  
M. Lee ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Computational Procedure ◽  
Correct Choice ◽  
Covariance Matrices ◽  
Chemical Data ◽  
Spatial Correlations ◽  
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. As models evolve toward finer resolutions, the use of diagonal background covariance matrices is increasingly inaccurate, as 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 correlation length scales are specified by the user; a correct choice of correlation lengths is important for a good performance of the data assimilation system. The benefits of using the non-diagonal covariance matrices for variational data assimilation with chemical transport models are illustrated.

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 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

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.

Sign in / Sign up

Export Citation Format

Share Document