scholarly journals A New Data Assimilation Scheme: The Space-Expanded Ensemble Localization Kalman Filter

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Hongze Leng ◽  
Junqiang Song ◽  
Fengshun Lu ◽  
Xiaoqun Cao
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Forecast Error ◽  
Three Dimensional ◽  
Full Rank ◽  
Observation Error ◽  
Model Framework ◽  
Background Error ◽  
Error Covariance ◽  
Expanded Ensemble

This study considers a new hybrid three-dimensional variational (3D-Var) and ensemble Kalman filter (EnKF) data assimilation (DA) method in a non-perfect-model framework, named space-expanded ensemble localization Kalman filter (SELKF). In this method, the localization operation is directly applied to the ensemble anomalies with a Schur Product, rather than to the full error covariance of the state in the EnKF. Meanwhile, the correction space of analysis increment is expanded to a space with larger dimension, and the rank of the forecast error covariance is significantly increased. This scheme can reduce the spurious correlations in the covariance and approximate the full-rank background error covariance well. Furthermore, a deterministic scheme is used to generate the analysis anomalies. The results show that the SELKF outperforms the perturbed EnKF given a relatively small ensemble size, especially when the length scale is relatively long or the observation error covariance is relatively small.

scholarly journals Assimilation of Stratospheric Temperature and Ozone with an Ensemble Kalman Filter in a Chemistry–Climate Model

2011 ◽  
Vol 139 (11) ◽  
pp. 3389-3404 ◽  
Author(s):  
Thomas Milewski ◽  
Michel S. Bourqui
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Climate Model ◽  
Observation Error ◽  
Background Error ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Analysis Error

Abstract A new stratospheric chemical–dynamical data assimilation system was developed, based upon an ensemble Kalman filter coupled with a Chemistry–Climate Model [i.e., the intermediate-complexity general circulation model Fast Stratospheric Ozone Chemistry (IGCM-FASTOC)], with the aim to explore the potential of chemical–dynamical coupling in stratospheric data assimilation. The system is introduced here in a context of a perfect-model, Observing System Simulation Experiment. The system is found to be sensitive to localization parameters, and in the case of temperature (ozone), assimilation yields its best performance with horizontal and vertical decorrelation lengths of 14 000 km (5600 km) and 70 km (14 km). With these localization parameters, the observation space background-error covariance matrix is underinflated by only 5.9% (overinflated by 2.1%) and the observation-error covariance matrix by only 1.6% (0.5%), which makes artificial inflation unnecessary. Using optimal localization parameters, the skills of the system in constraining the ensemble-average analysis error with respect to the true state is tested when assimilating synthetic Michelson Interferometer for Passive Atmospheric Sounding (MIPAS) retrievals of temperature alone and ozone alone. It is found that in most cases background-error covariances produced from ensemble statistics are able to usefully propagate information from the observed variable to other ones. Chemical–dynamical covariances, and in particular ozone–wind covariances, are essential in constraining the dynamical fields when assimilating ozone only, as the radiation in the stratosphere is too slow to transfer ozone analysis increments to the temperature field over the 24-h forecast window. Conversely, when assimilating temperature, the chemical–dynamical covariances are also found to help constrain the ozone field, though to a much lower extent. The uncertainty in forecast/analysis, as defined by the variability in the ensemble, is large compared to the analysis error, which likely indicates some amount of noise in the covariance terms, while also reducing the risk of filter divergence.

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.

Theoretical Application of Ensemble Kalman Filter to Adsorptive Solute Cr(VI) Transfer from Soil into Surface Runoff

2014 ◽  
Vol 919-921 ◽  
pp. 1257-1261
Author(s):  
Chao Qun Tan ◽  
Ju Xiu Tong ◽  
Bill X. Hu ◽  
Jin Zhong Yang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Surface Runoff ◽  
Amplification Factor ◽  
Forecast Error ◽  
Assimilation Effect ◽  
Solute Transfer ◽  
Error Covariance ◽  
Theoretical Application

This paper mainly discusses some details when applying data assimilation method via an ensemble Kalman filter (EnKF) to improve prediction of adsorptive solute Cr(VI) transfer from soil into runoff. Based on this work, we could make better use of our theoretical model to predict adsorptive solute transfer from soil into surface runoff in practice. The results show that the ensemble number of 100 is reasonable, considering assimilation effect and efficiency after selecting its number from 25 to 225 at an interval of 25. While the initial ensemble value makes little difference to data assimilation (DA) results. Besides, DA results could be improved by multiplying an amplification factor to forecast error covariance matrix due to underestimation of forecast error.

scholarly journals Efficient Adaptive Error Parameterizations for Square Root or Ensemble Kalman Filters: Application to the Control of Ocean Mesoscale Signals

2010 ◽  
Vol 138 (3) ◽  
pp. 932-950 ◽  
Author(s):  
Jean-Michel Brankart ◽  
Emmanuel Cosme ◽  
Charles-Emmanuel Testut ◽  
Pierre Brasseur ◽  
Jacques Verron
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Error Estimates ◽  
Forecast Error ◽  
Observation Error ◽  
Square Root ◽  
Error Statistics ◽  
Error Covariance Matrix ◽  
Error Covariance ◽  
Optimal Estimates

Abstract In Kalman filter applications, an adaptive parameterization of the error statistics is often necessary to avoid filter divergence, and prevent error estimates from becoming grossly inconsistent with the real error. With the classic formulation of the Kalman filter observational update, optimal estimates of general adaptive parameters can only be obtained at a numerical cost that is several times larger than the cost of the state observational update. In this paper, it is shown that there exists a few types of important parameters for which optimal estimates can be computed at a negligible numerical cost, as soon as the computation is performed using a transformed algorithm that works in the reduced control space defined by the square root or ensemble representation of the forecast error covariance matrix. The set of parameters that can be efficiently controlled includes scaling factors for the forecast error covariance matrix, scaling factors for the observation error covariance matrix, or even a scaling factor for the observation error correlation length scale. As an application, the resulting adaptive filter is used to estimate the time evolution of ocean mesoscale signals using observations of the ocean dynamic topography. To check the behavior of the adaptive mechanism, this is done in the context of idealized experiments, in which model error and observation error statistics are known. This ideal framework is particularly appropriate to explore the ill-conditioned situations (inadequate prior assumptions or uncontrollability of the parameters) in which adaptivity can be misleading. Overall, the experiments show that, if used correctly, the efficient optimal adaptive algorithm proposed in this paper introduces useful supplementary degrees of freedom in the estimation problem, and that the direct control of these statistical parameters by the observations increases the robustness of the error estimates and thus the optimality of the resulting Kalman filter.

Evaluating Ensemble Kalman Filter Analyses of Severe Hailstorms on 8 May 2017 in Colorado: Effects of State Variable Updating and Multimoment Microphysics Schemes on State Variable Cross Covariances

2020 ◽  
Vol 148 (6) ◽  
pp. 2365-2389
Author(s):  
Jonathan Labriola ◽  
Nathan Snook ◽  
Youngsun Jung ◽  
Ming Xue
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Variable Cross ◽  
Background Error ◽  
Mixing Ratios ◽  
State Variable ◽  
Error Covariance ◽  
Thermodynamic Variables ◽  
The Impact

Abstract Ensemble Kalman filter (EnKF) analyses of the storms associated with the 8 May 2017 Colorado severe hail event using either the Milbrandt and Yau (MY) or the NSSL double-moment bulk microphysics scheme in the forecast model are evaluated. With each scheme, two experiments are conducted in which the reflectivity (Z) observations update in addition to dynamic and thermodynamic variables: 1) only the hydrometeor mixing ratios or 2) all microphysical variables. With fewer microphysical variables directly constrained by the Z observations, only updating hydrometeor mixing ratios causes the forecast error covariance structure to become unreliable, and results in larger errors in the analysis. Experiments that update all microphysical variables produce analyses with the lowest Z root-mean-square innovations; however, comparing the estimated hail size against hydrometeor classification algorithm output suggests that further constraint from observations is needed to more accurately estimate surface hail size. Ensemble correlation analyses are performed to determine the impact of hail growth assumptions in the MY and NSSL schemes on the forecast error covariance between microphysical and thermodynamic variables. In the MY scheme, Z is negatively correlated with updraft intensity because the strong updrafts produce abundant small hail aloft. The NSSL scheme predicts the growth of large hail aloft; consequently, Z is positively correlated with storm updraft intensity and hail state variables. Hail production processes are also shown to alter the background error covariance for liquid and frozen hydrometeor species. Results in this study suggest that EnKF analyses are sensitive to the choice of MP scheme (e.g., the treatment of hail growth processes).

scholarly journals An Examination of the Incremental Balance in a Global Ensemble-Based 3D-Var Data Assimilation System

2010 ◽  
Vol 138 (10) ◽  
pp. 3946-3966 ◽  
Author(s):  
Jean-François Caron ◽  
Luc Fillion
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Three Dimensional ◽  
Vertical Motion ◽  
Variational Data Assimilation ◽  
Spatial Covariance ◽  
Background Error ◽  
Localization Technique ◽  
Vertical Localization

Abstract This study examines the modification to the balance properties of the analysis increments in a global three-dimensional variational data assimilation scheme when using flow-dependent background-error covariances derived from an operational ensemble Kalman filter instead of static homogenous and isotropic background-error covariances based on lagged forecast differences. It is shown that the degree of balance in the analysis increments is degraded when the former method is used. This change can be attributed in part to the reduced degree of rotational balance found in short-term ensemble Kalman filter perturbations as compared to lagged forecast differences based on longer-range forecasts. However, the use of a horizontal and vertical localization technique to increase the rank of the ensemble-based covariances are found to have a significant deleterious effect on the rotational balance with the largest detrimental impact coming from the vertical localization and affecting particularly the upper levels. The examination of the vertical motion part of the analysis increments revealed that the spatial covariance localization technique also produces unrealistic vertical structure of vertical motion increments with abnormally large increments near the surface. A comparison between the analysis increments from the ensemble Kalman filter and from the ensemble-based three-dimensional variational data assimilation (3D-Var) scheme showed that the balance characteristics of the analysis increments resulting from the two systems are very similar.

scholarly journals A Comparison of Multiscale GSI-Based EnKF and 3DVar Data Assimilation Using Radar and Conventional Observations for Midlatitude Convective-Scale Precipitation Forecasts

2015 ◽  
Vol 143 (8) ◽  
pp. 3087-3108 ◽  
Author(s):  
Aaron Johnson ◽  
Xuguang Wang ◽  
Jacob R. Carley ◽  
Louis J. Wicker ◽  
Christopher Karstens
Keyword(s):  
Data Assimilation ◽  
Multiscale Analysis ◽  
Multiple Scales ◽  
Three Dimensional ◽  
Forecast Period ◽  
Background Error ◽  
Cold Pools ◽  
Error Covariance ◽  
Convective Scale

Abstract A GSI-based data assimilation (DA) system, including three-dimensional variational assimilation (3DVar) and ensemble Kalman filter (EnKF), is extended to the multiscale assimilation of both meso- and synoptic-scale observation networks and convective-scale radar reflectivity and velocity observations. EnKF and 3DVar are systematically compared in this multiscale context to better understand the impacts of differences between the DA techniques on the analyses at multiple scales and the subsequent convective-scale precipitation forecasts. Averaged over 10 diverse cases, 8-h precipitation forecasts initialized using GSI-based EnKF are more skillful than those using GSI-based 3DVar, both with and without storm-scale radar DA. The advantage from radar DA persists for ~5 h using EnKF, but only ~1 h using 3DVar. A case study of an upscale growing MCS is also examined. The better EnKF-initialized forecast is attributed to more accurate analyses of both the mesoscale environment and the storm-scale features. The mesoscale location and structure of a warm front is more accurately analyzed using EnKF than 3DVar. Furthermore, storms in the EnKF multiscale analysis are maintained during the subsequent forecast period. However, storms in the 3DVar multiscale analysis are not maintained and generate excessive cold pools. Therefore, while the EnKF forecast with radar DA remains better than the forecast without radar DA throughout the forecast period, the 3DVar forecast quality is degraded by radar DA after the first hour. Diagnostics revealed that the inferior analysis at mesoscales and storm scales for the 3DVar is primarily attributed to the lack of flow dependence and cross-variable correlation, respectively, in the 3DVar static background error covariance.

scholarly journals Forecast Sensitivity Observation Impact in the 4DVAR and Hybrid-4DVAR Data Assimilation Systems

2019 ◽  
Vol 36 (8) ◽  
pp. 1563-1575 ◽  
Author(s):  
Sung-Min Kim ◽  
Hyun Mee Kim
Keyword(s):  
Data Assimilation ◽  
East Asia ◽  
Forecast Error ◽  
Integration Time ◽  
Ensemble Forecasts ◽  
Background Error ◽  
Error Covariance ◽  
Atmospheric Motion ◽  
Observation Impact ◽  
Atmospheric Motion Vectors

AbstractIn this study, the observation impacts on 24-h forecast error reduction (FER), based on the adjoint method in the four-dimensional variational (4DVAR) data assimilation (DA) and hybrid-4DVAR DA systems coupled with the Unified Model, were evaluated from 0000 UTC 5 August to 1800 UTC 26 August 2014. The nonlinear FER in hybrid-4DVAR was 12.2% greater than that in 4DVAR due to the use of flow-dependent background error covariance (BEC), which was a weighted combination of the static BEC and the ensemble BEC based on ensemble forecasts. In hybrid-4DVAR, the observation impacts (i.e., the approximated nonlinear FER) for most observation types increase compared to those in 4DVAR. The increased observation impact from using hybrid-4DVAR instead of 4DVAR changes depending on the analysis time and regions. To calculate the ensemble BEC in hybrid-4DVAR, analyses at 0600 and 1800 UTC (0000 and 1200 UTC) used 3-h (9-h) ensemble forecasts. Greater observation impact was obtained when 3-h ensemble forecasts were used for the ensemble BEC at 0600 and 1800 UTC, than with 9-h ensemble forecasts at 0000 and 1200 UTC. Different from other observations, the atmospheric motion vectors (AMVs) deduced from geostationary satellite are more frequently observed in the same area. When the ensemble forecasts with longer integration times were used for the ensemble BEC in hybrid-4DVAR, the observation impact of the AMVs decreased the most in East Asia. This implies that the observation impact of AMVs in East Asia shows the highest sensitivity to the integration time of the ensemble members used for deducing the flow-dependent BEC in hybrid-4DVAR.

scholarly journals The impacts of uncertainties in emissions on aerosol data assimilation and short-term PM<sub>2.5</sub> predictions in CMAQ v5.2.1 over East Asia

2020 ◽  
Author(s):  
Sojin Lee ◽  
Chul Han Song ◽  
Kyung Man Han ◽  
Daven K. Henze ◽  
Kyunghwa Lee ◽  
...  
Keyword(s):  
Air Quality ◽  
Data Assimilation ◽  
East Asia ◽  
Conventional Method ◽  
Meteorological Data ◽  
Three Dimensional ◽  
Short Term ◽  
Background Error ◽  
Multi Scale ◽  
Error Covariance

Abstract. For the purpose of improving PM prediction skills in East Asia, we estimated a new background error covariance matrix (BEC) for aerosol data assimilation using surface PM2.5 observations that accounts for the uncertainties in anthropogenic emissions. In contrast to the conventional method to estimate the BEC that uses perturbations in meteorological data, this method additionally considered the perturbations using two different emission inventories. The impacts of the new BEC were then tested for the prediction of surface PM2.5 over East Asia using Community Multi-scale Air Quality (CMAQ) initialized by three-dimensional variational method (3D-VAR). The surface PM2.5 data measured at 154 sites in South Korea and 1,535 sites in China were assimilated every six hours during the Korea-United States Air Quality Study (KORUS-AQ) campaign period (1 May–14 June 2016). Data assimilation with our new BEC showed better agreement with the surface PM2.5 observations than that with the conventional method. Our method also showed closer agreement with the observations in 24-hour PM2.5 predictions with ~ 44 % fewer negative biases than the conventional method. We conclude that increased standard deviations, together with horizontal and vertical length scales in the new BEC, tend to improve the data assimilation and short-term predictions for the surface PM2.5. This paper also suggests further research efforts devoted to estimating the BEC to improve PM2.5 predictions.

Comparisons of Hybrid En3DVar with 3DVar and EnKF for Radar Data Assimilation: Tests with the 10 May 2010 Oklahoma Tornado Outbreak

2021 ◽  
Vol 149 (1) ◽  
pp. 21-40
Author(s):  
Rong Kong ◽  
Ming Xue ◽  
Chengsi Liu ◽  
Youngsun Jung
Keyword(s):  
Data Assimilation ◽  
Radial Velocity ◽  
Forecast Error ◽  
Radar Data ◽  
Separate Analysis ◽  
Background Error ◽  
Mixing Ratios ◽  
Error Covariance ◽  
Radial Velocity Data ◽  
Made In

AbstractIn this study, a hybrid En3DVar data assimilation (DA) scheme is compared with 3DVar, EnKF, and pure En3DVar for the assimilation of radar data in a real tornadic storm case. Results using hydrometeor mixing ratios (CVq) or logarithmic mixing ratios (CVlogq) as the control variables are compared in the variational DA framework. To address the lack of radial velocity impact issues when using CVq, a procedure that assimilates reflectivity and radial velocity data in two separate analysis passes is adopted. Comparisons are made in terms of the root-mean-square innovations (RMSIs) as well as the intensity and structure of the analyzed and forecast storms. For pure En3DVar that uses 100% ensemble covariance, CVlogq and CVq have similar RMSIs in the velocity analyses, but errors grow faster during forecasts when using CVlogq. Introducing static background error covariance at 5% in hybrid En3DVar (with CVlogq) significantly reduces the forecast error growth. Pure En3DVar produces more intense reflectivity analyses than EnKF that more closely match the observations. Hybrid En3DVar with 50% outperforms other weights in terms of the RMSIs and forecasts of updraft helicity and is thus used in the final comparison with 3DVar and EnKF. The hybrid En3DVar is found to outperform EnKF in better capturing the intensity and structure of the analyzed and forecast storms and outperform 3DVAR in better capturing the intensity and evolution of the rotating updraft.

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