scholarly journals Some Observing System Simulation Experiments with a Hybrid 3DEnVAR System for Storm-Scale Radar Data Assimilation

2014 ◽  
Vol 142 (9) ◽  
pp. 3326-3346 ◽  
Author(s):  
Jidong Gao ◽  
David J. Stensrud
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Control Variable ◽  
Simulated Data ◽  
Variational Data Assimilation ◽  
Sampling Errors ◽  
Advanced Regional Prediction System ◽  
Sensitivity Experiments ◽  
Variable Approach ◽  
Regional Prediction

A hybrid three-dimensional ensemble–variational data assimilation (3DEnVAR) algorithm is developed based on the 3D variational data assimilation (3DVAR) and ensemble Kalman filter (EnKF) programs with the Advanced Regional Prediction System (ARPS). The method uses the extended control variable approach to combine the static and ensemble-derived flow-dependent forecast error covariances. The method is applied to the assimilation of simulated data from two radars for a supercell storm. Some sensitivity experiments are performed to answer questions about how flow-dependent covariance estimated from the forecast ensemble can be best used in the hybrid 3DEnVAR scheme. When the ensemble size is relatively small (with 5 or 10 ensemble members), it is found that experiments with a weaker weighting value for the ensemble covariance leads to better analysis results. Even when severe sampling errors exist, introducing ensemble-estimated covariances into the variational method still benefits the analysis. For reasonably large ensemble sizes (50–100 members), a stronger relative weighting (>0.8) for the ensemble covariance leads to better analyses from the hybrid 3DEnVAR. In addition, the sensitivity experiments also indicate that the best results are obtained when the number of the augmented control variables is a function of three spatial dimensions and ensemble members, and is the same for all analysis variables.

scholarly journals The Development of a Hybrid EnKF-3DVAR Algorithm for Storm-Scale Data Assimilation

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Jidong Gao ◽  
Ming Xue ◽  
David J. Stensrud
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Control Variable ◽  
Radar Data ◽  
Ensemble Forecasts ◽  
Advanced Regional Prediction System ◽  
Error Covariance ◽  
Variable Approach ◽  
Regional Prediction ◽  
Rms Errors

A hybrid 3DVAR-EnKF data assimilation algorithm is developed based on 3DVAR and ensemble Kalman filter (EnKF) programs within the Advanced Regional Prediction System (ARPS). The hybrid algorithm uses the extended alpha control variable approach to combine the static and ensemble-derived flow-dependent forecast error covariances. The hybrid variational analysis is performed using an equal weighting of static and flow-dependent error covariance as derived from ensemble forecasts. The method is first applied to the assimilation of simulated radar data for a supercell storm. Results obtained using 3DVAR (with static covariance entirely), hybrid 3DVAR-EnKF, and the EnKF are compared. When data from a single radar are used, the EnKF method provides the best results for the model dynamic variables, while the hybrid method provides the best results for hydrometeor related variables in term of rms errors. Although storm structures can be established reasonably well using 3DVAR, the rms errors are generally worse than seen from the other two methods. With two radars, the results from 3DVAR are closer to those from EnKF. Our tests indicate that the hybrid scheme can reduce the storm spin-up time because it fits the observations, especially the reflectivity observations, better than the EnKF and the 3DVAR at the beginning of the assimilation cycles.

A New Approach for Estimating the Observation Impact in Ensemble–Variational Data Assimilation

2018 ◽  
Vol 146 (2) ◽  
pp. 447-465 ◽  
Author(s):  
Mark Buehner ◽  
Ping Du ◽  
Joël Bédard
Keyword(s):  
Data Assimilation ◽  
Forecast Error ◽  
Forecast Model ◽  
Variational Data Assimilation ◽  
Observation Error ◽  
New Approach ◽  
Regional Prediction ◽  
Observation Impact ◽  
Adjoint Approach ◽  
The Impact

Abstract Two types of approaches are commonly used for estimating the impact of arbitrary subsets of observations on short-range forecast error. The first was developed for variational data assimilation systems and requires the adjoint of the forecast model. Comparable approaches were developed for use with the ensemble Kalman filter and rely on ensembles of forecasts. In this study, a new approach for computing observation impact is proposed for ensemble–variational data assimilation (EnVar). Like standard adjoint approaches, the adjoint of the data assimilation procedure is implemented through the iterative minimization of a modified cost function. However, like ensemble approaches, the adjoint of the forecast step is obtained by using an ensemble of forecasts. Numerical experiments were performed to compare the new approach with the standard adjoint approach in the context of operational deterministic NWP. Generally similar results are obtained with both approaches, especially when the new approach uses covariance localization that is horizontally advected between analysis and forecast times. However, large differences in estimated impacts are obtained for some surface observations. Vertical propagation of the observation impact is noticeably restricted with the new approach because of vertical covariance localization. The new approach is used to evaluate changes in observation impact as a result of the use of interchannel observation error correlations for radiance observations. The estimated observation impact in similarly configured global and regional prediction systems is also compared. Overall, the new approach should provide useful estimates of observation impact for data assimilation systems based on EnVar when an adjoint model is not available.

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 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.

Intercomparison of an Ensemble Kalman Filter with Three- and Four-Dimensional Variational Data Assimilation Methods in a Limited-Area Model over the Month of June 2003

2011 ◽  
Vol 139 (2) ◽  
pp. 566-572 ◽  
Author(s):  
Meng Zhang ◽  
Fuqing Zhang ◽  
Xiang-Yu Huang ◽  
Xin Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Wrf Model ◽  
Warm Season ◽  
Variational Data Assimilation ◽  
Lead Times ◽  
Limited Area ◽  
Forecast Errors

Abstract This study compares the performance of an ensemble Kalman filter (EnKF) with both the three-dimensional and four-dimensional variational data assimilation (3DVar and 4DVar) methods of the Weather Research and Forecasting (WRF) model over the contiguous United States in a warm-season month (June) of 2003. The data assimilated every 6 h include conventional sounding and surface observations as well as data from wind profilers, ships and aircraft, and the cloud-tracked winds from satellites. The performances of these methods are evaluated through verifying the 12- to 72-h forecasts initialized twice daily from the analysis of each method against the standard sounding observations. It is found that 4DVar has consistently smaller error than that of 3DVar for winds and temperature at all forecast lead times except at 60 and 72 h when their forecast errors become comparable in amplitude, while the two schemes have similar performance in moisture at all lead times. The forecast error of the EnKF is comparable to that of the 4DVar at 12–36-h lead times, both of which are substantially smaller than that of the 3DVar, despite the fact that 3DVar fits the sounding observations much more closely at the analysis time. The advantage of the EnKF becomes even more evident at 48–72-h lead times; the 72-h forecast error of the EnKF is comparable in magnitude to the 48-h error of 3DVar/4DVar.

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.

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