Inhomogeneous Background Error Modeling for WRF-Var Using the NMC Method

2014 ◽  
Vol 53 (10) ◽  
pp. 2287-2309 ◽  
Author(s):  
Hongli Wang ◽  
Xiang-Yu Huang ◽  
Juanzhen Sun ◽  
Dongmei Xu ◽  
Man Zhang ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Control Variable ◽  
Variational Data Assimilation ◽  
Error Modeling ◽  
Error Statistics ◽  
Background Error ◽  
New Approach ◽  
Data Assimilation System ◽  
Assimilation System

AbstractBackground error modeling plays a key role in a variational data assimilation system. The National Meteorological Center (NMC) method has been widely used in variational data assimilation systems to generate a forecast error ensemble from which the climatological background error covariance can be modeled. In this paper, the characteristics of the background error modeling via the NMC method are investigated for the variational data assimilation system of the Weather Research and Forecasting (WRF-Var) Model. The background error statistics are extracted from short-term 3-km-resolution forecasts in June, July, and August 2012 over a limited-area domain. It is found 1) that background error variances vary from month to month and also have a feature of diurnal variations in the low-level atmosphere and 2) that u- and υ-wind variances are underestimated and their autocorrelation length scales are overestimated when the default control variable option in WRF-Var is used. A new approach of control variable transform (CVT) is proposed to model the background error statistics based on the NMC method. The new approach is capable of extracting inhomogeneous and anisotropic climatological information from the forecast error ensemble obtained via the NMC method. Single observation assimilation experiments show that the proposed method not only has the merit of incorporating geographically dependent covariance information, but also is able to produce a multivariate analysis. The results from the data assimilaton and forecast study of a real convective case show that the use of the new CVT improves synoptic weather system and precipitation forecasts for up to 12 h.

scholarly journals Simulation of Monsoon Depressions Using WRF-VAR: Impact of Different Background Error Statistics and Lateral Boundary Conditions

2014 ◽  
Vol 142 (10) ◽  
pp. 3586-3613 ◽  
Author(s):  
A. Routray ◽  
S. C. Kar ◽  
P. Mali ◽  
K. Sowjanya
Keyword(s):  
Data Assimilation ◽  
Boundary Conditions ◽  
Initial Conditions ◽  
Variational Data Assimilation ◽  
Error Statistics ◽  
Background Error ◽  
Single Observation ◽  
Monsoon Depressions ◽  
Data Assimilation System ◽  
Assimilation System

Abstract In a variational data assimilation system, background error statistics (BES) spread the influence of the observations in space and filter analysis increments through dynamic balance or statistical relationships. In a data-sparse region such as the Bay of Bengal, BES play an important role in defining the location and structure of monsoon depressions (MDs). In this study, the Indian-region-specific BES have been computed for the Weather Research and Forecasting (WRF) three-dimensional variational data assimilation system. A comparative study using single observation tests is carried out using the computed BES and global BES within the WRF system. Both sets of BES are used in the assimilation cycles and forecast runs for simulating the meteorological features associated with the MDs. Numerical experiments have been conducted to assess the relative impact of various BES in the analysis and simulations of the MDs. The results show that use of regional BES in the assimilation cycle has a positive impact on the prediction of the location, propagation, and development of rainbands associated with the MDs. The track errors of MDs are smaller when domain-specific BES are used in the assimilation cycle. Additional experiments have been conducted using data from the Interim European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim) as initial and boundary conditions (IBCs) in the assimilation cycle. The results indicate that the use of domain-dependent BES and high-resolution ERA-I data as IBCs further improved the initial conditions for the model leading to better forecasts of the MDs.

scholarly journals CIRA/CSU Four-Dimensional Variational Data Assimilation System

2005 ◽  
Vol 133 (4) ◽  
pp. 829-843 ◽  
Author(s):  
Milija Zupanski ◽  
Dusanka Zupanski ◽  
Tomislava Vukicevic ◽  
Kenneth Eis ◽  
Thomas Vonder Haar
Keyword(s):  
Data Assimilation ◽  
Initial Conditions ◽  
Control Variable ◽  
Three Dimensional ◽  
Atmospheric Modeling ◽  
Variational Data Assimilation ◽  
Regional Atmospheric Modeling ◽  
The Impact ◽  
Data Assimilation System ◽  
Assimilation System

A new four-dimensional variational data assimilation (4DVAR) system is developed at the Cooperative Institute for Research in the Atmosphere (CIRA)/Colorado State University (CSU). The system is also called the Regional Atmospheric Modeling Data Assimilation System (RAMDAS). In its present form, the 4DVAR system is employing the CSU/Regional Atmospheric Modeling System (RAMS) nonhydrostatic primitive equation model. The Weather Research and Forecasting (WRF) observation operator is used to access the observations, adopted from the WRF three-dimensional variational data assimilation (3DVAR) algorithm. In addition to the initial conditions adjustment, the RAMDAS includes the adjustment of model error (bias) and lateral boundary conditions through an augmented control variable definition. Also, the control variable is defined in terms of the velocity potential and streamfunction instead of the horizontal winds. The RAMDAS is developed after the National Centers for Environmental Prediction (NCEP) Eta 4DVAR system, however with added improvements addressing its use in a research environment. Preliminary results with RAMDAS are presented, focusing on the minimization performance and the impact of vertical correlations in error covariance modeling. A three-dimensional formulation of the background error correlation is introduced and evaluated. The Hessian preconditioning is revisited, and an alternate algebraic formulation is presented. The results indicate a robust minimization performance.

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.

A Flow-dependent Targeted Observation Method

2020 ◽  
Author(s):  
Youmin Tang ◽  
Yaling Wu
Keyword(s):  
Data Assimilation ◽  
Tropical Indian Ocean ◽  
Seasonal Prediction ◽  
Test Bed ◽  
Error Statistics ◽  
Background Error ◽  
Observation Method ◽  
Targeted Observation ◽  
Data Assimilation System ◽  
Assimilation System

<p>In this study, we developed a flow-dependent ensemble-based targeted observation method, by minimizing the analysis error variance under the framework of Ensemble Kalman filter (EnKF) data assimilation system. This method estimates the background error statistics as a flow dependent function. The covariance localization is also introduced for computing efficiency and alleviating the spurious observations.  As a test bed, an  optimal observation array of sea level anomalies (SLA) is designed for its seasonal prediction over the tropical Indian Ocean (TIO) region.  Furthermore, the observing system simulation experiments (OSSEs) is used to verify the resultant optimal observational array using our recently developed coupled data assimilation system. A comparison between this flow-dependent method and the traditional method is also given. ​</p>

Comparison of the Impacts of Momentum Control Variables on High-Resolution Variational Data Assimilation and Precipitation Forecasting

2015 ◽  
Vol 144 (1) ◽  
pp. 149-169 ◽  
Author(s):  
Juanzhen Sun ◽  
Hongli Wang ◽  
Wenxue Tong ◽  
Ying Zhang ◽  
Chung-Yi Lin ◽  
...  
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Control Variable ◽  
Wrf Model ◽  
Variational Data Assimilation ◽  
Error Modeling ◽  
Limited Area ◽  
Control Variables ◽  
Background Error ◽  
Precipitation Prediction

Abstract The momentum variables of streamfunction and velocity potential are used as control variables in a number of operational variational data assimilation systems. However, in this study it is shown that, for limited-area high-resolution data assimilation, the momentum control variables ψ and χ (ψχ) pose potential difficulties in background error modeling and, hence, may result in degraded analysis and forecast when compared with the direct use of x and y components of wind (UV). In this study, the characteristics of the modeled background error statistics, derived from an ensemble generated from Weather Research and Forecasting (WRF) Model real-time forecasts of two summer months, are first compared between the two control variable options. Assimilation and forecast experiments are then conducted with both options for seven convective events in a domain that encompasses the Rocky Mountain Front Range using the three-dimensional variational data assimilation (3DVar) system of the WRF Model. The impacts of the two control variable options are compared in terms of their skills in short-term qualitative precipitation forecasts. Further analysis is performed for one case to examine the impacts when radar observations are included in the 3DVar assimilation. The main findings are as follows: 1) the background error modeling used in WRF 3DVar with the control variables ψχ increases the length scale and decreases the variance for u and υ, which causes negative impact on the analysis of the velocity field and on precipitation prediction; 2) the UV-based 3DVar allows closer fits to radar wind observations; and 3) the use of UV control variables improves the 0–12-h precipitation prediction.

scholarly journals Regional Ensemble–Variational Data Assimilation Using Global Ensemble Forecasts

2017 ◽  
Vol 32 (1) ◽  
pp. 83-96 ◽  
Author(s):  
Wan-Shu Wu ◽  
David F. Parrish ◽  
Eric Rogers ◽  
Ying Lin
Keyword(s):  
Data Assimilation ◽  
Initial Conditions ◽  
Positive Impact ◽  
Relative Weight ◽  
Variational Data Assimilation ◽  
Forecast System ◽  
Ensemble Forecasts ◽  
Background Error ◽  
Data Assimilation System ◽  
Assimilation System

Abstract At the National Centers for Environmental Prediction, the global ensemble forecasts from the ensemble Kalman filter scheme in the Global Forecast System are applied in a regional three-dimensional (3D) and a four dimensional (4D) ensemble–variational (EnVar) data assimilation system. The application is a one-way variational method using hybrid static and ensemble error covariances. To enhance impact, three new features have been added to the existing EnVar system in the Gridpoint Statistical Interpolation (GSI). First, the constant coefficients that assign relative weight between the ensemble and static background error are now allowed to vary in the vertical. Second, a new formulation is introduced for the ensemble contribution to the analysis surface pressure. Finally, in order to make use of the information in the ensemble mean that is disregarded in the existing EnVar in GSI, the trajectory correction, a novel approach, is introduced. Relative to the application of a 3D variational data assimilation algorithm, a clear positive impact on 1–3-day forecasts is realized when applying 3DEnVar analyses in the North American Mesoscale Forecast System (NAM). The 3DEnVar DA system was operationally implemented in the NAM Data Assimilation System in August 2014. Application of a 4DEnVar algorithm is shown to further improve forecast accuracy relative to the 3DEnVar. The approach described in this paper effectively combines contributions from both the regional and the global forecast systems to produce the initial conditions for the regional NAM system.

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 ◽  
Vol 13 (8) ◽  
pp. 3789-3816
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 and 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 current system, and these can, for example, be expanded relatively easily to include operators for Doppler winds. 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, each with special uncorrelated spatial patterns. The software developed performs (amongst other things) model runs, calibration tasks associated with the background error covariance matrix, testing and diagnostic tasks, single data assimilation runs, and multi-cycle assimilation/forecast experiments, and it also 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 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 represented at convective scale. Ideas for further possible developments of ABC-DA are discussed.

scholarly journals Can Wavelets Improve the Representation of Forecast Error Covariances in Variational Data Assimilation?

2007 ◽  
Vol 135 (2) ◽  
pp. 387-408 ◽  
Author(s):  
Ross N. Bannister
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Control Variable ◽  
Variational Data Assimilation ◽  
Covariance Structures ◽  
Spectral Space ◽  
Error Statistics ◽  
Length Scales ◽  
Spectral Bands ◽  
The Right

Abstract Two wavelet-based control variable transform schemes are described and are used to model some important features of forecast error statistics for use in variational data assimilation. The first is a conventional wavelet scheme and the other is an approximation of it. Their ability to capture the position and scale-dependent aspects of covariance structures is tested in a two-dimensional latitude–height context. This is done by comparing the covariance structures implied by the wavelet schemes with those found from the explicit forecast error covariance matrix, and with a non-wavelet-based covariance scheme used currently in an operational assimilation scheme. Qualitatively, the wavelet-based schemes show potential at modeling forecast error statistics well without giving preference to either position or scale-dependent aspects. The degree of spectral representation can be controlled by changing the number of spectral bands in the schemes, and the least number of bands that achieves adequate results is found for the model domain used. Evidence is found of a trade-off between the localization of features in positional and spectral spaces when the number of bands is changed. By examining implied covariance diagnostics, the wavelet-based schemes are found, on the whole, to give results that are closer to diagnostics found from the explicit matrix than from the nonwavelet scheme. Even though the nature of the covariances has the right qualities in spectral space, variances are found to be too low at some wavenumbers and vertical correlation length scales are found to be too long at most scales. The wavelet schemes are found to be good at resolving variations in position and scale-dependent horizontal length scales, although the length scales reproduced are usually too short. The second of the wavelet-based schemes is often found to be better than the first in some important respects, but, unlike the first, it has no exact inverse transform.

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