scholarly journals A Fuzzy-Logic-Based Covariance Localization Method in Data Assimilation

Atmosphere ◽  
2020 ◽  
Vol 11 (10) ◽  
pp. 1055
Author(s):  
Yulong Bai ◽  
Xiaoyan Ma ◽  
Lin Ding
Keyword(s):  
Fuzzy Logic ◽  
Data Assimilation ◽  
Ensemble Kalman Filter ◽  
Atmospheric Model ◽  
Localization Method ◽  
Error Covariance ◽  
Logic Control ◽  
Power Spectral ◽  
Performance Evaluation Index ◽  
Lorenz 96

In ensemble data assimilation systems, the impracticalities of full sampling and systematic error often lead to spurious correlations between two variables with low actual correlations. To solve these problems, researchers have previously proposed a covariance localization (CL) method, which mainly involves the Schur product between a state error covariance matrix and a distance-based correlation matrix. Although this CL method can reduce spurious correlations to a certain extent, observational data remain difficult to be used effectively, which results in unreasonable assimilation. In this study, we develop a new CL method coupled with a fuzzy logic control algorithm, which we call the covariance fuzzy (CF) method. The proposed CF method is a distance-based localization method with “fuzzy” vanishing correlations in data assimilation (DA) systems. To verify the effectiveness of the new algorithm, we conducted a set of experiments using an ensemble Kalman filter (EnKF) that combines the nonlinear Lorenz-96 model or the quasi-geostrophic (QG) models. First, the performances of the CL and CF methods are discussed with respect to different strength forcings, ensemble sizes, and covariance inflation factors. The experimental results show that the proposed CF method can obtain a more effective observation weight than the CL method and can reduce the errors caused by spurious correlations. Additionally, using power spectral density (PSD) as a performance evaluation index, the robustness of the proposed fuzzy logic localization method is demonstrated. However, the application of the fuzzy logic-based localization methodology to a real atmospheric model remains to be tested.

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 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 Estimating Observation Error Statistics Using a Robust Filter Method for Data Assimilation

2020 ◽  
Author(s):  
Yue Wang ◽  
Yulong Bai
Keyword(s):  
Data Assimilation ◽  
Error Estimation ◽  
Filter Method ◽  
Robust Filtering ◽  
Observation Error ◽  
Error Statistics ◽  
H Infinity ◽  
Error Covariance ◽  
Lorenz 96 ◽  
Data Assimilation System

For the data assimilation algorithms, the observation error covariance plays an important role, because they control the weight that is given to the model forecast and to the observation in the solution, i.e., the analysis. In order to easily calculate, we often assume observation to be a diagonal matrix, however, the observation errors are correlated to the state and have a certain dependence on time, such as certain observing types which are remotely sensed. In this work, we obtain the time-dependent and correlated observation error by the method of observation error estimation in the data assimilation system. We combine the ensemble time-local H-infinity filter (EnTLHF) with an estimate of observation error covariance matrix, named ensemble time-local H-infinity filter with observation error covariance estimation (EnTLHF-R). In the experiment, a classical nonlinear Lorenz-96 model to evaluate the performance of new method is used. The results show that the robust filtering with observation error estimation is more accurate, more robust, and the filtering is more stable.

scholarly journals Mitigating Observation Perturbation Sampling Errors in the Stochastic EnKF

2015 ◽  
Vol 143 (7) ◽  
pp. 2918-2936 ◽  
Author(s):  
I. Hoteit ◽  
D.-T. Pham ◽  
M. E. Gharamti ◽  
X. Luo
Keyword(s):  
Ensemble Kalman Filter ◽  
Forecast Error ◽  
Sampling Errors ◽  
Observational Error ◽  
Error Covariance ◽  
Atmospheric Data ◽  
Observational Errors ◽  
Analysis Error ◽  
Lorenz 96 ◽  
The Impact

Abstract The stochastic ensemble Kalman filter (EnKF) updates its ensemble members with observations perturbed with noise sampled from the distribution of the observational errors. This was shown to introduce noise into the system and may become pronounced when the ensemble size is smaller than the rank of the observational error covariance, which is often the case in real oceanic and atmospheric data assimilation applications. This work introduces an efficient serial scheme to mitigate the impact of observations’ perturbations sampling in the analysis step of the EnKF, which should provide more accurate ensemble estimates of the analysis error covariance matrices. The new scheme is simple to implement within the serial EnKF algorithm, requiring only the approximation of the EnKF sample forecast error covariance matrix by a matrix with one rank less. The new EnKF scheme is implemented and tested with the Lorenz-96 model. Results from numerical experiments are conducted to compare its performance with the EnKF and two standard deterministic EnKFs. This study shows that the new scheme enhances the behavior of the EnKF and may lead to better performance than the deterministic EnKFs even when implemented with relatively small ensembles.

scholarly journals On the Propagation of Information and the Use of Localization in Ensemble Kalman Filtering

2010 ◽  
Vol 67 (12) ◽  
pp. 3823-3834 ◽  
Author(s):  
Young-noh Yoon ◽  
Edward Ott ◽  
Istvan Szunyogh
Keyword(s):  
Correlation Function ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Atmospheric Model ◽  
Spatial Correlation Function ◽  
Wave Dynamics ◽  
Error Covariance ◽  
Principal Tool ◽  
Ensemble Kalman Filtering ◽  
Made In

Abstract Several localized versions of the ensemble Kalman filter have been proposed. Although tests applying such schemes have proven them to be extremely promising, a full basic understanding of the rationale and limitations of localization is currently lacking. It is one of the goals of this paper to contribute toward addressing this issue. The second goal is to elucidate the role played by chaotic wave dynamics in the propagation of information and the resulting impact on forecasts. To accomplish these goals, the principal tool used here will be analysis and interpretation of numerical experiments on a toy atmospheric model introduced by Lorenz in 2005. Propagation of the wave packets of this model is shown. It is found that, when an ensemble Kalman filter scheme is employed, the spatial correlation function obtained at each forecast cycle by averaging over the background ensemble members is short ranged, and this is in strong contrast to the much longer range correlation function obtained by averaging over states from free evolution of the model. Propagation of the effects of observations made in one region on forecasts in other regions is studied. The error covariance matrices from the analyses with localization and without localization are compared. From this study, major characteristics of the localization process and information propagation are extracted and summarized.

scholarly journals Multivariate localization functions for strongly coupled data assimilation in the bivariate Lorenz ’96 system

2021 ◽  
Author(s):  
Zofia Stanley ◽  
Ian Grooms ◽  
William Kleiber
Keyword(s):  
Data Assimilation ◽  
Spatial Scales ◽  
Background Error ◽  
Strongly Coupled ◽  
Localization Function ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Coupled Data Assimilation ◽  
Lorenz 96 ◽  
The Impact

Abstract. Localization is widely used in data assimilation schemes to mitigate the impact of sampling errors on ensemble-derived background error covariance matrices. Strongly coupled data assimilation allows observations in one component of a coupled model to directly impact another component through inclusion of cross-domain terms in the background error covariance matrix. When different components have disparate dominant spatial scales, localization between model domains must properly account for the multiple length scales at play. In this work we develop two new multivariate localization functions, one of which is a multivariate extension of the fifth-order piecewise rational Gaspari-Cohn localization function; the within-component localization functions are standard Gaspari-Cohn with different localization radii while the cross-localization function is newly constructed. The functions produce non-negative definite localization matrices, which are suitable for use in variational data assimilation schemes. We compare the performance of our two new multivariate localization functions to two other multivariate localization functions and to the univariate analogs of all four functions in a simple experiment with the bivariate Lorenz '96 system. In our experiment the multivariate Gaspari-Cohn function leads to better performance than any of the other localization functions.

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.

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.

scholarly journals A Physically Based Empirical Localization Method for Assimilating Synthetic SWOT Observations of a Continental-Scale River: A Case Study in the Congo Basin

Water ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 829 ◽  
Author(s):  
Revel ◽  
Ikeshima ◽  
Yamazaki ◽  
Kanae
Keyword(s):  
Data Assimilation ◽  
Hydrodynamic Modeling ◽  
Congo Basin ◽  
Localization Method ◽  
Continental Scale ◽  
Error Covariance ◽  
Physically Based ◽  
Local Patch ◽  
In Situ Observations

Water resource management has faced challenges in recent decades due to limited in situ observations and the limitations of hydrodynamic modeling. Data assimilation techniques have been proposed to improve hydrodynamic model outputs of local rivers (river length ≤ 1500 km) using synthetic observations of the future Surface Water and Ocean Topography (SWOT) satellite mission to overcome limited in situ observations and the limitations of hydrodynamic modeling. However, large-scale data assimilation schemes require computationally efficient filtering techniques, such as the Local Ensemble Transformation Kalman Filter (LETKF). Expansion of the assimilation domain to maximize observations is limited by error covariance caused by limited ensemble size in complex river networks, such as the Congo River. Therefore, we tested the LETKF algorithm in a continental-scale river (river length > 1500 km) using a physically based empirical localization method to maximize the observations available while filtering error covariance areas. Physically based empirical local patches were derived separately for each river pixel, considering spatial auto-correlations. An observing system simulation experiment (OSSE) was performed using empirical localization parameters to evaluate the potential of our method for estimating discharge. We found our method could improve discharge estimates considerably without affected from error covariance while fully using the available observations. We compared this experiment using empirical localization parameters with conventional fixed-shape local patches of different sizes. The empirical local patch OSSE showed the lowest normalized root mean square error of discharge for the entire Congo basin. Extending the conventional local patch without considering spatial auto-correlation results in very large errors in LETKF assimilation due to error covariance between small tributaries. The empirical local patch method has the potential to overcome the limitations of conventional local patches for continental-scale rivers using SWOT observations.

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