scholarly journals The Impact of Length-Scale Variation When Diagnosing the Standard Deviations of Background Error in a 4D-Var System and Filtering Method Investigation

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Xiang Xing ◽  
Bainian Liu ◽  
Weimin Zhang ◽  
Xiaoqun Cao ◽  
Hongze Leng
Keyword(s):  
Standard Deviation ◽  
Data Assimilation ◽  
Variational Data Assimilation ◽  
Small Scale ◽  
Model Parameters ◽  
Spatial Averaging ◽  
Background Error ◽  
Operational System ◽  
Filtering Method ◽  
Standard Deviations

The four-dimensional variational data assimilation (4D-Var) method has been widely employed as an operational scheme in mainstream numerical weather prediction (NWP) centers. In addition to the ensemble data assimilation method, the randomization technique is still used to diagnose the standard deviations of background error in variational data assimilation (VAR) systems; however, such randomization techniques induce sampling noise, which may contaminate the quality of the standard deviations. First, this paper studies the properties of the sampling noise induced by the randomization technique. The results show that the sampling noise is on a small scale displaying high-frequency oscillations around the estimate compared with the estimate and this difference motivates the use of filtering techniques to eliminate the sampling noise effects. The characteristics of the standard deviation field of the control variables are also investigated, and the standard deviation fields of different model parameters have different scales and vary with the vertical model levels. To eliminate such sampling noise, the spectral filtering method used widely in the operational system and a modified spatial averaging approach are investigated. Although both methods have splendid performance in eliminating sampling noise, the spatial averaging approach is more efficient and easier to implement in operational systems. In addition, the optimal filtered results from the spatial averaging approach are dependent on model parameters and vertical levels, which is consistent with the variation in the standard deviation field. Finally, the spatial averaging approach is tested on the operational system at the global scale based on the YH4DVAR and the global NWP system, and the results indicate that the spatial averaging approach has positive effects on both analysis and forecast quality.

scholarly journals THE INFLUENCE OF BACKGROUND ERROR COVARIANCE OF GSI THREE-DIMENSIONAL VARIATIONAL DATA ASSIMILATION ON METEOROLOGY AND AEROSOL PREDICTION

2018 ◽  
Vol XLII-3/W5 ◽  
pp. 17-23
Author(s):  
Y. Hu ◽  
M. Zhang ◽  
Y. Liang ◽  
L. Ye ◽  
D. Zhao ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Three Dimensional ◽  
Variational Data Assimilation ◽  
Small Scale ◽  
Length Scale ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Horizontal Length ◽  
Mean Square Errors

<p><strong>Abstract.</strong> Background error covariance (BEC) plays a key role in a variational data assimilation system. It determines variable analysis increments by spreading information from observation points. In order to test the influence of BEC on the GSI data assimilation and prediction of aerosol in Beijing-Tianjin-Hebei, a regional BEC is calculated using one month series of numerical forecast fields of November 2017 based on the National Meteorological Center (NMC) method, and compared with the global BEC.The results show that the standard deviation of stream function of the regional BEC is larger than that of the global BEC. And the horizontal length-scale of the regional BEC is smaller than that of the global BEC, white the vertical length-scale of the regional BEC is similar with that of the global BEC. The increments of the assimilation experiment with the regional BEC present more small scale information than that with the global BEC. The forecast skill of the experiment with the regional BEC is higher than that with the global BEC in the stations of Beijing, Tianjin, Chengde and Taiyuan, and the average root-mean-square errors (RMSE) reduces by over 13.4%.</p>

scholarly journals Investigation of Local Weighting Filtering on Randomization Technique Estimates in a Data Assimilation System

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1563
Author(s):  
Xiang Xing ◽  
Bainian Liu ◽  
Weimin Zhang ◽  
Xiaoqun Cao ◽  
Jingzhe Sun
Keyword(s):  
Data Assimilation ◽  
Weather Prediction ◽  
Computational Cost ◽  
Atmospheric Model ◽  
Small Scale ◽  
State Variables ◽  
Model Framework ◽  
Background Error ◽  
Filtering Method ◽  
Weighted Correlation

Mainstream numerical weather prediction (NWP) centers usually estimate the standard deviations of background error by using a randomization technique to calibrate specific parameters of the background error covariance model in variational data assimilation (VAR) systems. However, the sampling size of the randomization technique is typically several orders of magnitude smaller than that of model state variables, and using finite-sized estimates as a proxy for the truth can lead to sampling noise, which may contaminate the estimation of the standard deviation. The sampling noise is firstly investigated in an atmospheric model to show that the sampling noise has a symmetrical structure oscillating around the truth on a small scale. To alleviate the sampling noise, a heterogeneous local weighting filtering is proposed based on distance-weighted correlation and similarity-weighted correlation. Local weighting filtering is easy to implement in the VAR operational systems and has a low computational cost in the post-processing of reducing the sampling noise. The validity and performance of local weighting filtering method are examined in a realistic model framework to show that the proposed filtering is able to eliminate most of the sampling noise dramatically, the details of the filtered results are more visible, and the accuracy of the filtered results is almost the same as that estimated from the larger sample. The signal-to-noise ratio of the optimal filtered field is improved by nearly 20%. A comparison with the widely used spectral filtering approach in the operational system is considered, showing that the proposed filtering method is more efficient to implement in the filtering procedure and exhibits very good performance in terms of preserving the local anisotropic features of the estimates. These attractive results show the potential efficiency of the local weighting filtering method for solving the noise issue in the randomization technique.

scholarly journals Intercomparison of Variational Data Assimilation and the Ensemble Kalman Filter for Global Deterministic NWP. Part II: One-Month Experiments with Real Observations

2010 ◽  
Vol 138 (5) ◽  
pp. 1567-1586 ◽  
Author(s):  
Mark Buehner ◽  
P. L. Houtekamer ◽  
Cecilien Charette ◽  
Herschel L. Mitchell ◽  
Bin He
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Forecast Model ◽  
Variational Data Assimilation ◽  
Background Error ◽  
Single Observation ◽  
Operational System ◽  
Medium Range ◽  
Forecast Quality

Abstract An intercomparison of the Environment Canada variational and ensemble Kalman filter (EnKF) data assimilation systems is presented in the context of producing global deterministic numerical weather forecasts. Five different variational data assimilation approaches are considered including four-dimensional variational data assimilation (4D-Var) and three-dimensional variational data assimilation (3D-Var) with first guess at the appropriate time (3D-FGAT). Also included among these is a new approach, called Ensemble-4D-Var (En-4D-Var), that uses 4D ensemble background-error covariances from the EnKF. A description of the experimental configurations and results from single-observation experiments are presented in the first part of this two-part paper. The present paper focuses on results from medium-range deterministic forecasts initialized with analyses from the EnKF and the five variational data assimilation approaches for the period of February 2007. All experiments assimilate exactly the same full set of meteorological observations and use the same configuration of the forecast model to produce global deterministic medium-range forecasts. The quality of forecasts in the short (medium) range obtained by using the EnKF ensemble mean analysis is slightly degraded (improved) in the extratropics relative to using the 4D-Var analysis with background-error covariances similar to those used operationally. The use of the EnKF flow-dependent error covariances in the variational system (4D-Var or 3D-FGAT) leads to large (modest) forecast improvements in the southern extratropics (tropics) as compared with using covariances similar to the operational system (a gain of up to 9 h at day 5). The En-4D-Var approach leads to (i) either improved or similar forecast quality when compared with the 4D-Var experiment similar to the currently operational system, (ii) slightly worse forecast quality when compared with the 4D-Var experiment with EnKF error covariances, and (iii) generally similar forecast quality when compared with the EnKF experiment.

Evaluation of Surface Analyses and Forecasts with a Multiscale Ensemble Kalman Filter in Regions of Complex Terrain

2011 ◽  
Vol 139 (6) ◽  
pp. 2008-2024 ◽  
Author(s):  
Brian C. Ancell ◽  
Clifford F. Mass ◽  
Gregory J. Hakim
Keyword(s):  
Kalman Filter ◽  
High Resolution ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Complex Terrain ◽  
Error Variance ◽  
Small Scale ◽  
Observation Error ◽  
Grid Spacing ◽  
Background Error

Abstract Previous research suggests that an ensemble Kalman filter (EnKF) data assimilation and modeling system can produce accurate atmospheric analyses and forecasts at 30–50-km grid spacing. This study examines the ability of a mesoscale EnKF system using multiscale (36/12 km) Weather Research and Forecasting (WRF) model simulations to produce high-resolution, accurate, regional surface analyses, and 6-h forecasts. This study takes place over the complex terrain of the Pacific Northwest, where the small-scale features of the near-surface flow field make the region particularly attractive for testing an EnKF and its flow-dependent background error covariances. A variety of EnKF experiments are performed over a 5-week period to test the impact of decreasing the grid spacing from 36 to 12 km and to evaluate new approaches for dealing with representativeness error, lack of surface background variance, and low-level bias. All verification in this study is performed with independent, unassimilated observations. Significant surface analysis and 6-h forecast improvements are found when EnKF grid spacing is reduced from 36 to 12 km. Forecast improvements appear to be a consequence of increased resolution during model integration, whereas analysis improvements also benefit from high-resolution ensemble covariances during data assimilation. On the 12-km domain, additional analysis improvements are found by reducing observation error variance in order to address representativeness error. Removing model surface biases prior to assimilation significantly enhances the analysis. Inflating surface wind and temperature background error variance has large impacts on analyses, but only produces small improvements in analysis RMS errors. Both surface and upper-air 6-h forecasts are nearly unchanged in the 12-km experiments. Last, 12-km WRF EnKF surface analyses and 6-h forecasts are shown to generally outperform those of the Global Forecast System (GFS), North American Model (NAM), and the Rapid Update Cycle (RUC) by about 10%–30%, although these improvements do not extend above the surface. Based on these results, future improvements in multiscale EnKF are suggested.

scholarly journals Variational data assimilation with superparameterization

2015 ◽  
Vol 2 (2) ◽  
pp. 513-536 ◽  
Author(s):  
I. Grooms ◽  
Y. Lee
Keyword(s):  
Data Assimilation ◽  
Large Scale ◽  
Climate Models ◽  
Low Cost ◽  
Ocean Model ◽  
Variational Data Assimilation ◽  
Scale Model ◽  
Small Scale ◽  
New Applications ◽  
Lorenz 96

Abstract. Superparameterization (SP) is a multiscale computational approach wherein a large scale atmosphere or ocean model is coupled to an array of simulations of small scale dynamics on periodic domains embedded into the computational grid of the large scale model. SP has been successfully developed in global atmosphere and climate models, and is a promising approach for new applications. The authors develop a 3D-Var variational data assimilation framework for use with SP; the relatively low cost and simplicity of 3D-Var in comparison with ensemble approaches makes it a natural fit for relatively expensive multiscale SP models. To demonstrate the assimilation framework in a simple model, the authors develop a new system of ordinary differential equations similar to the two-scale Lorenz-'96 model. The system has one set of variables denoted {Yi}, with large and small scale parts, and the SP approximation to the system is straightforward. With the new assimilation framework the SP model approximates the large scale dynamics of the true system accurately.

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 A radar reflectivity operator with ice-phase hydrometeors for variational data assimilation (version 1.0) and its evaluation with real radar data

2019 ◽  
Vol 12 (9) ◽  
pp. 4031-4051 ◽  
Author(s):  
Shizhang Wang ◽  
Zhiquan Liu
Keyword(s):  
Data Assimilation ◽  
Three Dimensional ◽  
Wrf Model ◽  
Radar Data ◽  
Poor Quality ◽  
Variational Data Assimilation ◽  
Radar Reflectivity ◽  
Background Error ◽  
Background Fields ◽  
Ice Phase

Abstract. A reflectivity forward operator and its associated tangent linear and adjoint operators (together named RadarVar) were developed for variational data assimilation (DA). RadarVar can analyze both rainwater and ice-phase species (snow and graupel) by directly assimilating radar reflectivity observations. The results of three-dimensional variational (3D-Var) DA experiments with a 3 km grid mesh setting of the Weather Research and Forecasting (WRF) model showed that RadarVar was effective at producing an analysis of reflectivity pattern and intensity similar to the observed data. Two to three outer loops with 50–100 iterations in each loop were needed to obtain a converged 3-D analysis of reflectivity, rainwater, snow, and graupel, including the melting layers with mixed-phase hydrometeors. It is shown that the deficiencies in the analysis using this operator, caused by the poor quality of the background fields and the use of the static background error covariance, can be partially resolved by using radar-retrieved hydrometeors in a preprocessing step and tuning the spatial correlation length scales of the background errors. The direct radar reflectivity assimilation using RadarVar also improved the short-term (2–5 h) precipitation forecasts compared to those of the experiment without DA.

scholarly journals Optimal solution error covariance in highly nonlinear problems of variational data assimilation

2012 ◽  
Vol 19 (2) ◽  
pp. 177-184 ◽  
Author(s):  
V. Shutyaev ◽  
I. Gejadze ◽  
G. J. M. Copeland ◽  
F.-X. Le Dimet
Keyword(s):  
Nonlinear Dynamics ◽  
Data Assimilation ◽  
Optimal Solution ◽  
Nonlinear Problems ◽  
Variational Data Assimilation ◽  
Model Parameters ◽  
Efficient Computation ◽  
Viscous Term ◽  
Highly Nonlinear ◽  
The Cost

Abstract. The problem of variational data assimilation (DA) for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition, boundary conditions and/or model parameters. The input data contain observation and background errors, hence there is an error in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can be approximated by the inverse Hessian of the cost function. For problems with strongly nonlinear dynamics, a new statistical method based on the computation of a sample of inverse Hessians is suggested. This method relies on the efficient computation of the inverse Hessian by means of iterative methods (Lanczos and quasi-Newton BFGS) with preconditioning. Numerical examples are presented for the model governed by the Burgers equation with a nonlinear viscous term.

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