scholarly journals Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz 96 system

2021 ◽  
Vol 28 (4) ◽  
pp. 565-583
Author(s):  
Zofia Stanley ◽  
Ian Grooms ◽  
William Kleiber
Keyword(s):  
Data Assimilation ◽  
Spatial Scales ◽  
Background Error ◽  
Strongly Coupled ◽  
Localization Function ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Coupled Data Assimilation ◽  
Lorenz 96 ◽  
The Impact

Abstract. Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through the inclusion of cross-domain terms in the background error covariance matrix. When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work, we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari–Cohn localization function; the within-component localization functions are standard Gaspari–Cohn with different localization radii, while the cross-localization function is newly constructed. The functions produce positive semidefinite localization matrices which are suitable for use in both Kalman filters and variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate and weakly coupled analogs of all four functions in a simple experiment with the bivariate Lorenz 96 system. In our experiments, the multivariate Gaspari–Cohn function leads to better performance than any of the other multivariate localization functions.

scholarly journals Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz ’96 system

2021 ◽  
Author(s):  
Zofia Stanley ◽  
Ian Grooms ◽  
William Kleiber
Keyword(s):  
Data Assimilation ◽  
Spatial Scales ◽  
Background Error ◽  
Strongly Coupled ◽  
Localization Function ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Coupled Data Assimilation ◽  
Lorenz 96 ◽  
The Impact

Abstract. Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through inclusion of cross-domain terms in the background error covariance matrix. When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari-Cohn localization function; the within-component localization functions are standard Gaspari-Cohn with different localization radii while the cross-localization function is newly constructed. The functions produce non-negative definite localization matrices, which are suitable for use in variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate analogs of all four functions in a simple experiment with the bivariate Lorenz '96 system. In our experiment the multivariate Gaspari-Cohn function leads to better performance than any of the other localization functions.

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.

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 A Multiscale Variational Data Assimilation Scheme: Formulation and Illustration

2015 ◽  
Vol 143 (9) ◽  
pp. 3804-3822 ◽  
Author(s):  
Zhijin Li ◽  
James C. McWilliams ◽  
Kayo Ide ◽  
John D. Farrara
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Cost Function ◽  
Spatial Scales ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
The Cost ◽  
Fine Resolution

Abstract A multiscale data assimilation (MS-DA) scheme is formulated for fine-resolution models. A decomposition of the cost function is derived for a set of distinct spatial scales. The decomposed cost function allows for the background error covariance to be estimated separately for the distinct spatial scales, and multi-decorrelation scales to be explicitly incorporated in the background error covariance. MS-DA minimizes the partitioned cost functions sequentially from large to small scales. The multi-decorrelation length scale background error covariance enhances the spreading of sparse observations and prevents fine structures in high-resolution observations from being overly smoothed. The decomposition of the cost function also provides an avenue for mitigating the effects of scale aliasing and representativeness errors that inherently exist in a multiscale system, thus further improving the effectiveness of the assimilation of high-resolution observations. A set of one-dimensional experiments is performed to examine the properties of the MS-DA scheme. Emphasis is placed on the assimilation of patchy high-resolution observations representing radar and satellite measurements, alongside sparse observations representing those from conventional in situ platforms. The results illustrate how MS-DA improves the effectiveness of the assimilation of both these types of observations simultaneously.

scholarly journals Using Temperature–Salinity Relations in a Global Ocean Implementation of a Multivariate Data Assimilation Scheme

2007 ◽  
Vol 135 (11) ◽  
pp. 3785-3807 ◽  
Author(s):  
A. Bellucci ◽  
S. Masina ◽  
P. DiPietro ◽  
A. Navarra
Keyword(s):  
Data Assimilation ◽  
General Circulation ◽  
Circulation Model ◽  
Ocean General Circulation Model ◽  
Global Ocean ◽  
Special Focus ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
The Impact

Abstract In this paper results from the application of an ocean data assimilation (ODA) system, combining a multivariate reduced-order optimal interpolator (OI) scheme with a global ocean general circulation model (OGCM), are described. The present ODA system, designed to assimilate in situ temperature and salinity observations, has been used to produce ocean reanalyses for the 1962–2001 period. The impact of assimilating observed hydrographic data on the ocean mean state and temporal variability is evaluated. A special focus of this work is on the ODA system skill in reproducing a realistic ocean salinity state. Results from a hierarchy of different salinity reanalyses, using varying combinations of assimilated data and background error covariance structures, are described. The impact of the space and time resolution of the background error covariance parameterization on salinity is addressed.

scholarly journals Background error covariance with balance constraints for aerosol species and applications in data assimilation

2015 ◽  
Vol 8 (11) ◽  
pp. 10053-10088
Author(s):  
Z. Zang ◽  
Z. Hao ◽  
Y. Li ◽  
X. Pan ◽  
W. You ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Elemental Carbon ◽  
Statistical Regression ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Balance Analysis ◽  
Forecasting System ◽  
Cross Correlations ◽  
The Impact

Abstract. Balance constraints are important for a background error covariance (BEC) in data assimilation to spread information between different variables and produce balance analysis fields. Using statistical regression, we develop the balance constraint for the BEC of aerosol variables and apply it to a data assimilation and forecasting system for the WRF/Chem model. One-month products from the WRF/Chem model are employed for BEC statistics with the NMC method. The cross-correlations among the original variables are generally high. The highest correlation between elemental carbon and organic carbon without balance constraints is approximately 0.9. However, the correlations for the unbalanced variables are less than 0.2 with the balance constraints. Data assimilation and forecasting experiments for evaluating the impact of balance constraints are performed with the observations of the surface PM2.5 concentrations and speciated concentrations along an aircraft flight track. The speciated increments of the experiment with balance constraints are more coincident than the speciated increments of the experiment without balance constraints, for the observation information can spread across variables by balance constraints in the former experiment. The forecast results of the experiment with balance constraints show significant and durable improvements from the 3rd hour to the 18th hour compared with the forecast results of the experiment without the balance constraints. However, the forecasts of these two experiments are similar during the first 3 h. The results suggest that the balance constraint is significantly positive for the aerosol assimilation and forecasting.

scholarly journals Generalized Background Error covariance matrix model (GEN_BE v2.0)

2014 ◽  
Vol 7 (4) ◽  
pp. 4291-4352
Author(s):  
G. Descombes ◽  
T. Auligné ◽  
F. Vandenberghe ◽  
D. M. Barker
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 to allow for a simpler, flexible, robust, and community-oriented framework that gathers methods used by meteorological operational centers and researchers. We present the advantages of this new design for the data assimilation community by performing benchmarks and showing some of the new features on 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 involve new control variables. While the generation of the background errors statistics code has been first developed for atmospheric research, the new version (GEN_BE v2.0) can be easily extended to other domains of science and be chosen as a testbed for diagnostic and new modeling of 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 Strongly Coupled Data Assimilation Experiments with Linearized Ocean–Atmosphere Balance Relationships

2018 ◽  
Vol 146 (4) ◽  
pp. 1233-1257 ◽  
Author(s):  
Andrea Storto ◽  
Matthew J. Martin ◽  
Bruno Deremble ◽  
Simona Masina
Keyword(s):  
Data Assimilation ◽  
General Circulation ◽  
Circulation Model ◽  
Variational Data Assimilation ◽  
Global Ocean ◽  
Background Error ◽  
Near Surface ◽  
Strongly Coupled ◽  
Coupled Data Assimilation ◽  
The Impact

Coupled data assimilation is emerging as a target approach for Earth system prediction and reanalysis systems. Coupled data assimilation may be indeed able to minimize unbalanced air–sea initialization and maximize the intermedium propagation of observations. Here, we use a simplified framework where a global ocean general circulation model (NEMO) is coupled to an atmospheric boundary layer model [Cheap Atmospheric Mixed Layer (CheapAML)], which includes prognostic prediction of near-surface air temperature and moisture and allows for thermodynamic but not dynamic air–sea coupling. The control vector of an ocean variational data assimilation system is augmented to include 2-m atmospheric parameters. Cross-medium balances are formulated either through statistical cross covariances from monthly anomalies or through the application of linearized air–sea flux relationships derived from the tangent linear approximation of bulk formulas, which represents a novel solution to the coupled assimilation problem. As a proof of concept, the methodology is first applied to study the impact of in situ ocean observing networks on the near-surface atmospheric analyses and later to the complementary study of the impact of 2-m air observations on sea surface parameters, to assess benefits of strongly versus weakly coupled data assimilation. Several forecast experiments have been conducted for the period from June to December 2011. We find that especially after day 2 of the forecasts, strongly coupled data assimilation provides a beneficial impact, particularly in the tropical oceans. In most areas, the use of linearized air–sea balances outperforms the statistical relationships used, providing a motivation for implementing coupled tangent linear trajectories in four-dimensional variational data assimilation systems. Further impacts of strongly coupled data assimilation might be found by retuning the background error covariances.

The role of flow-dependent oceanic background-error covariance information in air-sea coupled data assimilation during tropical cyclones: a case study

2021 ◽  
Author(s):  
Tsz Yan Leung ◽  
Polly J. Smith ◽  
Amos S. Lawless ◽  
Nancy K. Nichols ◽  
Matthew J. Martin
Keyword(s):  
Data Assimilation ◽  
Tropical Cyclones ◽  
Hybrid Approach ◽  
Covariance Structures ◽  
Spatial And Temporal Variability ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Coupled Data Assimilation

<p>In variational data assimilation, background-error covariance structures have the ability to spread information from an observed part of the system to unobserved parts.  Hence an accurate specification of these structures is crucially important for the success of assimilation systems and therefore of forecasts that their outputs initiate.  For oceanic models, background-error covariances have traditionally been modelled by parametrisations which mainly depend on macroscopic properties of the ocean and have limited dependence on local conditions.  This can be problematic during passage of tropical cyclones, when the spatial and temporal variability of the ocean state depart from their characteristic structures.  Furthermore, the traditional method of estimating oceanic background-error covariances could amplify imbalances across the air-sea interface when weakly coupled data assimilation is applied, thereby bringing a detrimental impact to forecasts of cyclones.  Using the case study of Cyclone Titli, which affected the Bay of Bengal in 2018, we explore hybrid methods that combine the traditional modelling strategy with flow-dependent estimates of the ocean's error covariance structures based on the latest-available short-range ensemble forecast.  This hybrid approach is investigated in the idealised context of a single-column model as well as in the UK Met Office’s state-of-the-art system.  The idealised model helps inform how the inclusion of ensemble information can improve coupled forecasts.  Different methods for producing the ensemble are explored, with the goal of generating a limited-sized ensemble that best represents the uncertainty in the ocean fields.  We then demonstrate the power of this hybrid approach in changing the analysed structure of oceanic fields in the Met Office system, and explain the difference between the traditional and hybrid approaches in light of the ways the assimilation systems respond to single synthetic observations.  Finally, we discuss the benefits that the hybrid approach in ocean data assimilation can bring to atmospheric forecasts of the cyclone.</p>

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