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).

Impact of Removing Covariance Localization in an Ensemble Kalman Filter: Experiments with 10 240 Members Using an Intermediate AGCM

2016 ◽  
Vol 144 (12) ◽  
pp. 4849-4865 ◽  
Author(s):  
Keiichi Kondo ◽  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
Long Range ◽  
Ensemble Kalman Filter ◽  
Sampling Error ◽  
Forecast Error ◽  
Forecast Accuracy ◽  
Large Sample Size ◽  
Background Error ◽  
Error Covariance ◽  
The Impact

Abstract The ensemble Kalman filter (EnKF) with high-dimensional geophysical systems usually employs up to 100 ensemble members and requires covariance localization to reduce the sampling error in the forecast error covariance between distant locations. The authors’ previous work pioneered implementation of an EnKF with a large ensemble of up to 10 240 members, but this method required application of a relatively broad covariance localization to avoid memory overflow. This study modified the EnKF code to save memory and enabled for the first time the removal of completely covariance localization with an intermediate AGCM. Using the large sample size, this study aims to investigate the analysis and forecast accuracy, as well as the impact of covariance localization when the sampling error is small. A series of 60-day data assimilation cycle experiments with different localization scales are performed under the perfect model scenario to investigate the pure impact of covariance localization. The results show that the analysis and 7-day forecasts are much improved by removing covariance localization and that the long-range covariance between distant locations plays a key role. The eigenvectors of the background error covariance matrix based on the 10 240 ensemble members are explicitly computed and reveal long-range structures.

scholarly journals Including Uncertainties of Sea Surface Temperature in an Ensemble Kalman Filter: A Case Study of Typhoon Sinlaku (2008)

2012 ◽  
Vol 27 (6) ◽  
pp. 1586-1597 ◽  
Author(s):  
Masaru Kunii ◽  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
Surface Temperature ◽  
Sea Surface Temperature ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Ocean Model ◽  
Sea Surface ◽  
Ensemble Spread ◽  
Error Covariance ◽  
The Impact

Abstract Sea surface temperature (SST) plays an important role in tropical cyclone (TC) life cycle evolution, but often the uncertainties in SST estimates are not considered in the ensemble Kalman filter (EnKF). The lack of uncertainties in SST generally results in the lack of ensemble spread in the atmospheric states near the sea surface, particularly for temperature and moisture. In this study, the uncertainties of SST are included by adding ensemble perturbations to the SST field, and the impact of the SST perturbations is investigated using the local ensemble transform Kalman filter (LETKF) with the Weather Research and Forecasting Model (WRF) in the case of Typhoon Sinlaku (2008). In addition to the experiment with the perturbed SST, another experiment with manually inflated ensemble perturbations near the sea surface is performed for comparison. The results indicate that the SST perturbations within EnKF generally improve analyses and their subsequent forecasts, although manually inflating the ensemble spread instead of perturbing SST does not help. Investigations of the ensemble-based forecast error covariance indicate larger scales for low-level temperature and moisture from the SST perturbations, although manual inflation of ensemble spread does not produce such structural effects on the forecast error covariance. This study suggests the importance of considering SST perturbations within ensemble-based data assimilation and promotes further studies with more sophisticated methods of perturbing SST fields such as using a fully coupled atmosphere–ocean model.

scholarly journals Examination of Situation-Dependent Background Error Covariances at the Convective Scale in the Context of the Ensemble Kalman Filter

2013 ◽  
Vol 141 (10) ◽  
pp. 3369-3387 ◽  
Author(s):  
Kao-Shen Chung ◽  
Weiguang Chang ◽  
Luc Fillion ◽  
Monique Tanguay
Keyword(s):  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Early Stage ◽  
Forecast Error ◽  
Radar Data ◽  
Physical Processes ◽  
Background Error ◽  
Time To Build ◽  
Convective Scale ◽  
Thermodynamic Variables

Abstract A high-resolution ensemble Kalman filter (HREnKF) system at the convective scale has been developed based on the Canadian Meteorological Center's operational global ensemble Kalman filter (EnKF) system. This study focuses on the very early stage of transition from purely homogeneous isotropic background error correlations to situation-dependent correlations. It has been found that forecast error structures can develop situation-dependent features in as little as 15 min. Furthermore, the dynamic and thermodynamic variables require different periods of time to build up their own forecast error structures. Differences in these structures between regions with and without precipitation are also investigated. An examination of temperature tendencies revealed that physical processes are as important as dynamical forcing in determining the structure of convective-scale errors structures, and that once physical processes become active, these structures change rapidly before the onset of precipitation. This study is intended to be the basis for a systematic exploration in the near future of the usefulness of the HREnKF system in assimilating high-density observations such as radar data.

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.

Using analysis state to construct a forecast error covariance matrix in ensemble Kalman filter assimilation

2013 ◽  
Vol 30 (5) ◽  
pp. 1303-1312 ◽  
Author(s):  
Xiaogu Zheng ◽  
Guocan Wu ◽  
Shupeng Zhang ◽  
Xiao Liang ◽  
Yongjiu Dai ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Error Covariance Matrix ◽  
Error Covariance

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.

scholarly journals An estimate of the inflation factor and analysis sensitivity in the ensemble Kalman filter

2017 ◽  
Vol 24 (3) ◽  
pp. 329-341 ◽  
Author(s):  
Guocan Wu ◽  
Xiaogu Zheng
Keyword(s):  
Kalman Filter ◽  
Covariance Matrix ◽  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Model Errors ◽  
Error Covariance Matrix ◽  
Spatially Correlated ◽  
Error Covariance ◽  
Inflation Factor ◽  
Analysis Error

Abstract. The ensemble Kalman filter (EnKF) is a widely used ensemble-based assimilation method, which estimates the forecast error covariance matrix using a Monte Carlo approach that involves an ensemble of short-term forecasts. While the accuracy of the forecast error covariance matrix is crucial for achieving accurate forecasts, the estimate given by the EnKF needs to be improved using inflation techniques. Otherwise, the sampling covariance matrix of perturbed forecast states will underestimate the true forecast error covariance matrix because of the limited ensemble size and large model errors, which may eventually result in the divergence of the filter. In this study, the forecast error covariance inflation factor is estimated using a generalized cross-validation technique. The improved EnKF assimilation scheme is tested on the atmosphere-like Lorenz-96 model with spatially correlated observations, and is shown to reduce the analysis error and increase its sensitivity to the observations.

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.

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 Accelerating the EnKF Spinup for Typhoon Assimilation and Prediction

2012 ◽  
Vol 27 (4) ◽  
pp. 878-897 ◽  
Author(s):  
Shu-Chih Yang ◽  
Eugenia Kalnay ◽  
Takemasa Miyoshi
Keyword(s):  
Kalman Filter ◽  
Inner Core ◽  
Global Analysis ◽  
Three Dimensional ◽  
Weather Research And Forecasting ◽  
Background Error ◽  
Error Covariance ◽  
Ensemble Transform Kalman Filter ◽  
The Impact ◽  
Analysis Quality

Abstract A mesoscale ensemble Kalman filter (EnKF) for a regional model is often initialized from global analysis products and with initial ensemble perturbations constructed based on the background error covariance used in the three-dimensional variational data assimilation (3DVar) system. Because of the lack of proper mesoscale information, a long spinup period of typically a few days is required for the regional EnKF to reach its asymptotic level of accuracy, and thus, the impact of observations is limited during the EnKF spinup. For the case of typhoon assimilation, such spinup usually corresponds to the stages of generation and development of tropical cyclones, when observations are important but limited over open waters. To improve the analysis quality during the spinup, the “running in place” (RIP) method is implemented within the framework of the local ensemble transform Kalman filter (LETKF) coupled with the Weather Research and Forecasting model (WRF). Results from observing system simulation experiments (OSSEs) for a specific typhoon show that the RIP method is able to accelerate the analysis adjustment of the dynamical structures of the typhoon during the LETKF spinup, and improves both the accuracy of the mean state and the structure of the ensemble-based error covariance. These advantages of the RIP method are found not only in the inner-core structure of the typhoon but also identified in the environmental conditions. As a result, the LETKF-RIP analysis leads to better typhoon prediction, particularly in terms of both track and intensity.

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