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 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 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 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.

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.

Improving Background Error Covariances in a 3D Ensemble–Variational Data Assimilation System for Regional NWP

2019 ◽  
Vol 147 (1) ◽  
pp. 135-151 ◽  
Author(s):  
Jean-François Caron ◽  
Yann Michel ◽  
Thibaut Montmerle ◽  
Étienne Arbogast
Keyword(s):  
Data Assimilation ◽  
Spatial Scales ◽  
Three Dimensional ◽  
Winter Period ◽  
Ensemble Size ◽  
Ensemble Forecasts ◽  
Background Error ◽  
Error Covariance ◽  
Time Lagged ◽  
Recent Formulation

Following the recent development of a three-dimensional ensemble–variational (3DEnVar) data assimilation algorithm for the AROME-France NWP system, this paper examines different approaches to reduce the sampling noise in the ensemble-derived background error covariances in this new scheme without modifying the background ensemble generation strategy. We first examine two variants of scale-dependent localization: one method consists of applying different amounts of localization to different ranges of background error covariance spatial scales, while simultaneously assimilating all of the available observations. Another separate approach uses time-lagged forecasts in order to increase the effective ensemble size, up to a factor of 3 here. This approach of time-lagged forecasts is considered both on its own and together with scale-dependent localization. When the background error covariances are derived from the most recent 25-member ensemble forecasts, the results from data assimilation cycles over a 33-day winter period show that avoiding cross covariances between scales in the scale-dependent localization formulation first proposed by Buehner performs better than the more recent formulation of Buehner and Shlyaeva. However, when increasing the effective ensemble size to 75 members with time-lagged forecasts, the two scale-dependent formulations provide similar forecast improvements overall. It is also found that the lagged-members approach outperforms scale-dependent localization on its own. The largest forecast improvements are obtained when combining the two approaches.

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.

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