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.

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.

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.

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 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 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.

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 A Comparison between the 4DVAR and the Ensemble Kalman Filter Techniques for Radar Data Assimilation

2005 ◽  
Vol 133 (11) ◽  
pp. 3081-3094 ◽  
Author(s):  
A. Caya ◽  
J. Sun ◽  
C. Snyder
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Forecast Model ◽  
Radar Data ◽  
Forecast Errors ◽  
Error Covariance ◽  
Convective Scale ◽  
Cloud Resolving Model ◽  
Comparable Accuracy

Abstract A four-dimensional variational data assimilation (4DVAR) algorithm is compared to an ensemble Kalman filter (EnKF) for the assimilation of radar data at the convective scale. Using a cloud-resolving model, simulated, imperfect radar observations of a supercell storm are assimilated under the assumption of a perfect forecast model. Overall, both assimilation schemes perform well and are able to recover the supercell with comparable accuracy, given radial-velocity and reflectivity observations where rain was present. 4DVAR produces generally better analyses than the EnKF given observations limited to a period of 10 min (or three volume scans), particularly for the wind components. In contrast, the EnKF typically produces better analyses than 4DVAR after several assimilation cycles, especially for model variables not functionally related to the observations. The advantages of the EnKF in later cycles arise at least in part from the fact that the 4DVAR scheme implemented here does not use a forecast from a previous cycle as background or evolve its error covariance. Possible reasons for the initial advantage of 4DVAR are deficiencies in the initial ensemble used by the EnKF, the temporal smoothness constraint used in 4DVAR, and nonlinearities in the evolution of forecast errors over the assimilation window.

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 Tests of an Ensemble Kalman Filter for Mesoscale and Regional-Scale Data Assimilation. Part III: Comparison with 3DVAR in a Real-Data Case Study

2008 ◽  
Vol 136 (2) ◽  
pp. 522-540 ◽  
Author(s):  
Zhiyong Meng ◽  
Fuqing Zhang
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Regional Scale ◽  
Warm Season ◽  
Real Data ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Scale Data

Abstract The feasibility of using an ensemble Kalman filter (EnKF) for mesoscale and regional-scale data assimilation has been demonstrated in the authors’ recent studies via observing system simulation experiments (OSSEs) both under a perfect-model assumption and in the presence of significant model error. The current study extends the EnKF to assimilate real-data observations for a warm-season mesoscale convective vortex (MCV) event on 10–12 June 2003. Direct comparison between the EnKF and a three-dimensional variational data assimilation (3DVAR) system, both implemented in the Weather Research and Forecasting model (WRF), is carried out. It is found that the EnKF consistently performs better than the 3DVAR method by assimilating either individual or multiple data sources (i.e., sounding, surface, and wind profiler) for this MCV event. Background error covariance plays an important role in the performance of both the EnKF and the 3DVAR system. Proper covariance inflation and the use of different combinations of physical parameterization schemes in different ensemble members (the so-called multischeme ensemble) can significantly improve the EnKF performance. The 3DVAR system can benefit substantially from using short-term ensembles to improve the prior estimate (with the ensemble mean). Noticeable improvement is also achieved by including some flow dependence in the background error covariance of 3DVAR.

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