scholarly journals Background error covariance functions for vector wind analyses using Doppler-radar radial-velocity observations

2006 ◽  
Vol 132 (621C) ◽  
pp. 2887-2904 ◽  
Author(s):  
Qin Xu ◽  
Shun Liu ◽  
Ming Xue
Keyword(s):  
Radial Velocity ◽  
Doppler Radar ◽  
Background Error ◽  
Background Error Covariance ◽  
Covariance Functions ◽  
Error Covariance ◽  
Vector Wind

scholarly journals Emulation of an ensemble Kalman filter algorithm on a flood wave propagation model

2013 ◽  
Vol 10 (6) ◽  
pp. 6963-7001
Author(s):  
S. Barthélémy ◽  
S. Ricci ◽  
O. Pannekoucke ◽  
O. Thual ◽  
P. O. Malaterre
Keyword(s):  
Correlation Length ◽  
Computational Cost ◽  
Error Variance ◽  
Observation Point ◽  
Propagation Model ◽  
Length Scale ◽  
Background Error ◽  
Background Error Covariance ◽  
Covariance Functions ◽  
Error Covariance

Abstract. This study describes the emulation of an Ensemble Kalman Filter (EnKF) algorithm on a 1-D flood wave propagation model. This model is forced at the upstream boundary with a random variable with gaussian statistics and a correlation function in time with gaussian shape. This allows for, in the case without assimilation, the analytical study of the covariance functions of the propagated signal anomaly. This study is validated numerically with an ensemble method. In the case with assimilation with one observation point, where synthetical observations are generated by adding an error to a true state, the dynamic of the background error covariance functions is not straightforward and a numerical approach using an EnKF algorithm is prefered. First, those numerical experiments show that both background error variance and correlation length scale are reduced at the observation point. This reduction of variance and correlation length scale is propagated downstream by the dynamics of the model. Then, it is shown that the application of a Best Linear Unbiased Estimator (BLUE) algorithm using the background error covariance matrix converged from the EnKF algorithm, provides the same results as the EnKF but with a cheaper computational cost, thus allowing for the use of data assimilation in the context of real time flood forecasting. Moreover it was demonstrated that the reduction of background error correlation length scale and variance at the observation point depends on the error observation statistics. This feature is quantified by abacus built from linear regressions over a limited set of EnKF experiments. These abacus that describe the background error variance and the correlation length scale in the neighboring of the observation point combined with analytical expressions that describe the background error variance and the correlation length scale away from the observation point provide parametrized models for the variance and the correlation length scale. Using this parametrized variance and correlation length scale with a diffusion operator makes it possible to model the converged background error covariance matrix from the EnKF without actually integrating the EnKF algorithm. This method was finally applied to a case with two different observation point with different error statistics. It was shown that the results of this emulated EnKF (EEnKF) in terms of background error variance, correlation length scale and analyzed water level is close to those of the EnKF but with a significantly reduced computational cost.

scholarly journals Influence of the Self-Consistent Regional Ensemble Background Error Covariance on Hurricane Inner-Core Data Assimilation with the GSI-Based Hybrid System for HWRF

2016 ◽  
Vol 73 (12) ◽  
pp. 4911-4925 ◽  
Author(s):  
Zhaoxia Pu ◽  
Shixuan Zhang ◽  
Mingjing Tong ◽  
Vijay Tallapragada
Keyword(s):  
Data Assimilation ◽  
Inner Core ◽  
Doppler Radar ◽  
Three Dimensional ◽  
The Self ◽  
Background Error ◽  
Core Data ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Self Consistent

Abstract An initial vortex spindown, or strong adjustment to the structure and intensity of a hurricane’s initial vortex, presents a significant problem in hurricane forecasting, as with the NCEP Hurricane Weather Research and Forecasting Model (HWRF), because it can cause significantly degraded intensity forecasts. In this study, the influence of the self-consistent regional ensemble background error covariance on assimilating hurricane inner-core tail Doppler radar (TDR) observations in HWRF is examined with the NCEP gridpoint statistical interpolation (GSI)-based ensemble–three-dimensional variational (3DVAR) hybrid data assimilation system. It is found that the resolution of the background error covariance term, coming from the ensemble forecasts, has notable influence on the assimilation of hurricane inner-core observations and subsequent forecasting results. Specifically, the use of ensemble forecasting at high-resolution native grids results in significant reduction of the vortex spindown problem and thus leads to improved hurricane intensity forecasting. Further diagnoses are conducted to examine the spindown problem with a gradient wind balance. It is found that artificial vortex initialization, performed before data assimilation, can cause strong supergradient winds or imbalance in the vortex inner-core region. Assimilation of hurricane inner-core TDR data can significantly mitigate this imbalance by reducing the supergradient effects. Compared with the use of a global ensemble background error term, application of the self-consistent regional ensemble background covariance to inner-core data assimilation leads to better representation of the mesoscale hurricane inner-core structures. It can also result in more realistic vortex structures in data assimilation even when the observational data are unevenly distributed.

Impact of AMSU-A Radiances in a Column Ensemble Kalman Filter

2018 ◽  
Vol 146 (12) ◽  
pp. 3949-3976 ◽  
Author(s):  
Herschel L. Mitchell ◽  
P. L. Houtekamer ◽  
Sylvain Heilliette
Keyword(s):  
Covariance Matrix ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Microwave Sounding Unit ◽  
The Matrix ◽  
Microwave Sounding ◽  
Background Temperature ◽  
The Difference

Abstract A column EnKF, based on the Canadian global EnKF and using the RTTOV radiative transfer (RT) model, is employed to investigate issues relating to the EnKF assimilation of Advanced Microwave Sounding Unit-A (AMSU-A) radiance measurements. Experiments are performed with large and small ensembles, with and without localization. Three different descriptions of background temperature error are considered: 1) using analytical vertical modes and hypothetical spectra, 2) using the vertical modes and spectrum of a covariance matrix obtained from the global EnKF after 2 weeks of cycling, and 3) using the vertical modes and spectrum of the static background error covariance matrix employed to initiate a global data assimilation cycle. It is found that the EnKF performs well in some of the experiments with background error description 1, and yields modest error reductions with background error description 3. However, the EnKF is virtually unable to reduce the background error (even when using a large ensemble) with background error description 2. To analyze these results, the different background error descriptions are viewed through the prism of the RT model by comparing the trace of the matrix , where is the RT model and is the background error covariance matrix. Indeed, this comparison is found to explain the difference in the results obtained, which relates to the degree to which deep modes are, or are not, present in the different background error covariances. The results suggest that, after 2 weeks of cycling, the global EnKF has virtually eliminated all background error structures that can be “seen” by the AMSU-A radiances.

Development of Convective-Scale Static Background Error Covariance within GSI-Based Hybrid EnVar System for Direct Radar Reflectivity Data Assimilation

2021 ◽  
Author(s):  
Yongming Wang ◽  
Xuguang Wang
Keyword(s):  
Sampling Errors ◽  
Background Error ◽  
3 Dimensional ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Convective Scale ◽  
Cross Correlations ◽  
Horizontal Momentum ◽  
Reflectivity Data ◽  
Static Background

AbstractA convective-scale static background-error covariance (BEC) matrix is further developed to include the capability of direct reflectivity assimilation and evaluated within the GSI-based 3-dimensional variational (3DVar) and hybrid ensemble-variational (EnVar) methods. Specific developments are summarized as follows: 1) Control variables (CVs) are extended to include reflectivity, vertical velocity, and all hydrometeor types. Various horizontal momentum and moisture CV options are included. 2) Cross-correlations between all CVs are established. 3) A storm intensity-dependent binning method is adopted to separately calculate static error matrices for clear-air and storms with varying intensities. The resultant static BEC matrices are simultaneously applied at proper locations guided by the observed reflectivity. 4) The EnVar is extended to adaptively incorporate static BECs based on the quality of ensemble covariances.Evaluation and examination of the new static BECs are first performed on the 8 May 2003 Oklahoma City supercell. Detailed diagnostics and 3DVar examinations suggest zonal/meridian winds and pseudo-relative humidity are selected horizontal momentum and moisture CVs for direct reflectivity assimilation, respectively; inclusion of cross-correlations favors to spinup and maintain the analyzed storms; application of binning improves characteristics and persistence of the simulated storm. Relative to an experiment using the full ensemble BECs (Exp-PureEnVar), incorporating static BECs in hybrid EnVar reduces spinup time and better analyzes reflectivity distributions while the background ensemble is deficient in sampling errors. Compared to both pure 3DVar and Exp-PureEnVar, hybrid EnVar better predicts reflectivity distributions and better maintains strong mesocyclone. Further examination through the 20 May 2013 Oklahoma supercells confirms these results and additionally demonstrates the effectiveness of adaptive hybridization.

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 A Comparison of HWRF Six-Hourly 4DEnVar and Hourly 3DEnVar Assimilation of Inner Core Tail Dopper Radar Observations for the Prediction of Hurricane Edouard (2014)

Atmosphere ◽  
2021 ◽  
Vol 12 (8) ◽  
pp. 942
Author(s):  
Benjamin Davis ◽  
Xuguang Wang ◽  
Xu Lu
Keyword(s):  
Inner Core ◽  
Doppler Radar ◽  
Three Dimensional ◽  
Weather Research And Forecasting ◽  
Location Error ◽  
Background Error ◽  
Error Covariance ◽  
Storm Center ◽  
The One ◽  
Better Than

Six-hourly three-dimensional ensemble variational (3DEnVar) (6H-3DEnVar) data assimilation (DA) assumes constant background error covariance (BEC) during a six-hour DA window and is, therefore, unable to account for temporal evolution of the BEC. This study evaluates the one-hourly 3DEnVar (1H-3DEnVar) and six-hourly 4DEnVar (6H-4DEnVar) DA methods for the analyses and forecasts of hurricanes with rapidly evolving BEC. Both methods account for evolving BEC in a hybrid EnVar DA system. In order to compare these methods, experiments are conducted by assimilating inner core Tail Doppler Radar (TDR) wind for Hurricane Edouard (2014) and by running the Hurricane Weather Research and Forecasting (HWRF) model. In most metrics, 1H-3DEnVar and 6H-4DEnVar analyses and forecasts verify better than 6H-3DEnVar. 6H-4DEnVar produces better thermodynamic analyses than 1H-3DEnVar. Radar reflectivity shows that 1H-3DEnVar produces better structure forecasts. For the first 24–48 h of the intensity forecast, 6H-4DEnVar forecast performs better than 1H-3DEnVar verified against the best track. Degraded 1H-3DEnVar forecasts are found to be associated with background storm center location error as a result of underdispersive ensemble storm center spread. Removing location error in the background improves intensity forecasts of 1H-3DEnVar.

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