scholarly journals Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling

2018 ◽  
Vol 25 (4) ◽  
pp. 731-746 ◽  
Author(s):  
Sangeetika Ruchi ◽  
Svetlana Dubinkina
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Particle Filter ◽  
Reservoir Modeling ◽  
Model Parameters ◽  
Uncertain Parameters ◽  
Initial Ensemble ◽  
Leading Mode ◽  
Ensemble Transform

Abstract. Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. The most reliable Markov chain Monte Carlo (MCMC) methods are computationally expensive. Sequential ensemble methods such as ensemble Kalman filters and particle filters provide a favorable alternative. However, ensemble Kalman filter has an assumption of Gaussianity. Ensemble transform particle filter does not have this assumption and has proven to be highly beneficial for an initial condition estimation and a small number of parameter estimations in chaotic dynamical systems with non-Gaussian distributions. In this paper we employ ensemble transform particle filter (ETPF) and ensemble transform Kalman filter (ETKF) for parameter estimation in nonlinear problems with 1, 5, and 2500 uncertain parameters and compare them to importance sampling (IS). The large number of uncertain parameters is of particular interest for subsurface reservoir modeling as it allows us to parameterize permeability on the grid. We prove that the updated parameters obtained by ETPF lie within the range of an initial ensemble, which is not the case for ETKF. We examine the performance of ETPF and ETKF in a twin experiment setup, where observations of pressure are synthetically created based on the known values of parameters. For a small number of uncertain parameters (one and five) ETPF performs comparably to ETKF in terms of the mean estimation. For a large number of uncertain parameters (2500) ETKF is robust with respect to the initial ensemble, while ETPF is sensitive due to sampling error. Moreover, for the high-dimensional test problem ETPF gives an increase in the root mean square error after data assimilation is performed. This is resolved by applying distance-based localization, which however deteriorates a posterior estimation of the leading mode by largely increasing the variance due to a combination of less varying localized weights, not keeping the imposed bounds on the modes via the Karhunen–Loeve expansion, and the main variability explained by the leading mode. A possible remedy is instead of applying localization to use only leading modes that are well estimated by ETPF, which demands knowledge of which mode to truncate.

scholarly journals Application of ensemble transform data assimilation methods for parameter estimation in nonlinear problems

2018 ◽  
Author(s):  
Sangeetika Ruchi ◽  
Svetlana Dubinkina
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Nonlinear Problems ◽  
Model Parameters ◽  
Ensemble Size ◽  
Uncertain Model ◽  
Initial Ensemble ◽  
Non Gaussian ◽  
Posterior Estimation ◽  
Ensemble Transform

Abstract. Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. However, most of these computationally affordable methods have assumptions of Gaussianity, e.g. an Ensemble Kalman Filter. Ensemble Transform Particle Filter does not have the assumption of Gaussianity and has proven to be highly beneficial for an initial condition estimation and a small number of parameter estimation in chaotic dynamical systems with non-Gaussian distributions. In this paper we employ Ensemble Transform Particle Smoother (ETPS) and Ensemble Transform Kalman Smoother (ETKS) for parameter estimation in nonlinear problems with 1, 5, and 2500 uncertain parameters and compare them to importance sampling (IS). We prove that the updated parameters obtained by ETPS lie within the range of an initial ensemble, which is not the case for ETKS. We examine the performance of ETPS and ETKS in a twin experiment setup, where observations of pressure are synthetically created based on the know values of parameters. The numerical experiments demonstrate that the ETKS provides good estimations of the mean parameters but not of the posterior distributions and as the ensemble size increases the posterior does not improve. ETPS provides good approximations of the posterior and as the ensemble size increases the posterior converges to the posterior obtained by IS with a large ensemble. ETKS is very robust while ETPS is very sensitive with respect to the initial ensemble. An issue of an increase in the root mean square error after data assimilation is performed in ETPS for a high-dimensional test problem is resolved by applying distance-based localization, which however deteriorated the posterior estimation.

A Simulation Study Using a Local Ensemble Transform Kalman Filter for Data Assimilation in New York Harbor

2008 ◽  
Vol 25 (9) ◽  
pp. 1638-1656 ◽  
Author(s):  
Ross N. Hoffman ◽  
Rui M. Ponte ◽  
Eric J. Kostelich ◽  
Alan Blumberg ◽  
Istvan Szunyogh ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Standard Deviation ◽  
Data Assimilation ◽  
External Forcing ◽  
Ensemble Spread ◽  
Initial Ensemble ◽  
Error Standard Deviation ◽  
Grid Points ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

Abstract Data assimilation approaches that use ensembles to approximate a Kalman filter have many potential advantages for oceanographic applications. To explore the extent to which this holds, the Estuarine and Coastal Ocean Model (ECOM) is coupled with a modern data assimilation method based on the local ensemble transform Kalman filter (LETKF), and a series of simulation experiments is conducted. In these experiments, a long ECOM “nature” run is taken to be the “truth.” Observations are generated at analysis times by perturbing the nature run at randomly chosen model grid points with errors of known statistics. A diverse collection of model states is used for the initial ensemble. All experiments use the same lateral boundary conditions and external forcing fields as in the nature run. In the data assimilation, the analysis step combines the observations and the ECOM forecasts using the Kalman filter equations. As a control, a free-running forecast (FRF) is made from the initial ensemble mean to check the relative importance of external forcing versus data assimilation on the analysis skill. Results of the assimilation cycle and the FRF are compared to truth to quantify the skill of each. The LETKF performs well for the cases studied here. After just a few assimilation cycles, the analysis errors are smaller than the observation errors and are much smaller than the errors in the FRF. The assimilation quickly eliminates the domain-averaged bias of the initial ensemble. The filter accurately tracks the truth at all data densities examined, from observations at 50% of the model grid points down to 2% of the model grid points. As the data density increases, the ensemble spread, bias, and error standard deviation decrease. As the ensemble size increases, the ensemble spread increases and the error standard deviation decreases. Increases in the size of the observation error lead to a larger ensemble spread but have a small impact on the analysis accuracy.

scholarly journals Parameter Estimation Based on a Local Ensemble Transform Kalman Filter Applied to El Niño–Southern Oscillation Ensemble Prediction

2021 ◽  
Vol 13 (19) ◽  
pp. 3923
Author(s):  
Yanqiu Gao ◽  
Youmin Tang ◽  
Xunshu Song ◽  
Zheqi Shen
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Real World ◽  
El Nino ◽  
Southern Oscillation ◽  
Model Error ◽  
Model Parameters ◽  
Enso Prediction ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

Parameter estimation plays an important role in reducing model error and thus is of great significance to improve the simulation and prediction capabilities of the model. However, due to filtering divergence, parameter estimation by ensemble-based filters still faces great challenges. Previous studies have shown that a covariance inflation scheme could alleviate the filtering divergence problem by increasing the signal-to-noise ratio of the state-parameter covariance. In this study, we proposed a new inflation scheme based on a local ensemble transform Kalman filter (LETKF). With the new scheme, the Zebiak–Cane (Z-C) model parameters were estimated by assimilating the sea surface temperature anomaly (SSTA) data. The effectiveness of the parameter estimation and its influence on El Niño–Southern Oscillation (ENSO) prediction were evaluated in an observation system simulation experiments (OSSE) framework and real-world scenario, respectively. With the utilization of the OSSE framework, the results showed that the model parameters were successfully estimated. Parameter estimation reduced the model error when compared with only state estimation (onlySE); however, multiple parameter estimation (MPE) further improved the ENSO prediction skill by providing better initial conditions and parameter values than the single parameter estimation (SPE). Parameter estimation could thus alleviate the spring prediction barrier (SPB) phenomenon of ENSO to a certain extent. In real-world experiments, the optimized parameters significantly improved the ENSO forecasting skill, primarily in prediction of warm events. This study provides an effective parameter estimation strategy to improve climate models and further climate predictions in the real world.

scholarly journals Gain Form of the Ensemble Transform Kalman Filter and Its Relevance to Satellite Data Assimilation with Model Space Ensemble Covariance Localization

2017 ◽  
Vol 145 (11) ◽  
pp. 4575-4592 ◽  
Author(s):  
Craig H. Bishop ◽  
Jeffrey S. Whitaker ◽  
Lili Lei
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Satellite Data ◽  
Localization Length ◽  
Model Space ◽  
Ensemble Size ◽  
Length Scales ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Expanded Ensemble

To ameliorate suboptimality in ensemble data assimilation, methods have been introduced that involve expanding the ensemble size. Such expansions can incorporate model space covariance localization and/or estimates of climatological or model error covariances. Model space covariance localization in the vertical overcomes problematic aspects of ensemble-based satellite data assimilation. In the case of the ensemble transform Kalman filter (ETKF), the expanded ensemble size associated with vertical covariance localization would also enable the simultaneous update of entire vertical columns of model variables from hyperspectral and multispectral satellite sounders. However, if the original formulation of the ETKF were applied to an expanded ensemble, it would produce an analysis ensemble that was the same size as the expanded forecast ensemble. This article describes a variation on the ETKF called the gain ETKF (GETKF) that takes advantage of covariances from the expanded ensemble, while producing an analysis ensemble that has the required size of the unexpanded forecast ensemble. The approach also yields an inflation factor that depends on the localization length scale that causes the GETKF to perform differently to an ensemble square root filter (EnSRF) using the same expanded ensemble. Experimentation described herein shows that the GETKF outperforms a range of alternative ETKF-based solutions to the aforementioned problems. In cycling data assimilation experiments with a newly developed storm-track version of the Lorenz-96 model, the GETKF analysis root-mean-square error (RMSE) matches the EnSRF RMSE at shorter than optimal localization length scales but is superior in that it yields smaller RMSEs for longer localization length scales.

scholarly journals Genetic Operator-Based Particle Filter Combined with Markov Chain Monte Carlo for Data Assimilation in a Crop Growth Model

Agriculture ◽  
2020 ◽  
Vol 10 (12) ◽  
pp. 606
Author(s):  
Alaa Jamal ◽  
Raphael Linker
Keyword(s):  
Monte Carlo ◽  
Parameter Estimation ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Data Assimilation ◽  
Particle Filter ◽  
Sequential Estimation ◽  
Measurement Noise ◽  
Genetic Operators ◽  
True Value

Particle filter has received increasing attention in data assimilation for estimating model states and parameters in cases of non-linear and non-Gaussian dynamic processes. Various modifications of the original particle filter have been suggested in the literature, including integrating particle filter with Markov Chain Monte Carlo (PF-MCMC) and, later, using genetic algorithm evolutionary operators as part of the state updating process. In this work, a modified genetic-based PF-MCMC approach for estimating the states and parameters simultaneously and without assuming Gaussian distribution for priors is presented. The method was tested on two simulation examples on the basis of the crop model AquaCrop-OS. In the first example, the method was compared to a PF-MCMC method in which states and parameters are updated sequentially and genetic operators are used only for state adjustments. The influence of ensemble size, measurement noise, and mutation and crossover parameters were also investigated. Accurate and stable estimations of the model states were obtained in all cases. Parameter estimation was more challenging than state estimation and not all parameters converged to their true value, especially when the parameter value had little influence on the measured variables. Overall, the proposed method showed more accurate and consistent parameter estimation than the PF-MCMC with sequential estimation, which showed highly conservative behavior. The superiority of the proposed method was more pronounced when the ensemble included a large number of particles and the measurement noise was low.

scholarly journals A particle filter scheme for multivariate data assimilation into a point-scale snowpack model in an Alpine environment

2018 ◽  
Vol 12 (7) ◽  
pp. 2287-2306 ◽  
Author(s):  
Gaia Piazzi ◽  
Guillaume Thirel ◽  
Lorenzo Campo ◽  
Simone Gabellani
Keyword(s):  
Data Assimilation ◽  
Particle Filter ◽  
Multivariate Data ◽  
Model Parameters ◽  
Parameter Perturbation ◽  
Point Scale ◽  
Meteorological Forcing ◽  
System Sensitivity ◽  
Filter Performance ◽  
The Impact

Abstract. The accuracy of hydrological predictions in snow-dominated regions deeply depends on the quality of the snowpack simulations, with dynamics that strongly affect the local hydrological regime, especially during the melting period. With the aim of reducing the modelling uncertainty, data assimilation techniques are increasingly being implemented for operational purposes. This study aims to investigate the performance of a multivariate sequential importance resampling – particle filter scheme, designed to jointly assimilate several ground-based snow observations. The system, which relies on a multilayer energy-balance snow model, has been tested at three Alpine sites: Col de Porte (France), Torgnon (Italy), and Weissfluhjoch (Switzerland). The implementation of a multivariate data assimilation scheme faces several challenging issues, which are here addressed and extensively discussed: (1) the effectiveness of the perturbation of the meteorological forcing data in preventing the sample impoverishment; (2) the impact of the parameter perturbation on the filter updating of the snowpack state; the system sensitivity to (3) the frequency of the assimilated observations, and (4) the ensemble size.The perturbation of the meteorological forcing data generally turns out to be insufficient for preventing the sample impoverishment of the particle sample, which is highly limited when jointly perturbating key model parameters. However, the parameter perturbation sharpens the system sensitivity to the frequency of the assimilated observations, which can be successfully relaxed by introducing indirectly estimated information on snow-mass-related variables. The ensemble size is found not to greatly impact the filter performance in this point-scale application.

scholarly journals Simultaneous state-parameter estimation of rainfall-induced landslide displacement using data assimilation

2019 ◽  
Author(s):  
Jing Wang ◽  
Guigen Nie ◽  
Shengjun Gao ◽  
Changhu Xue
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Prediction Method ◽  
State Parameter ◽  
Joint Estimation ◽  
Model Parameters ◽  
Displacement Estimation ◽  
Landslide Stability ◽  
Landslide Displacement Prediction ◽  
Using Data

Abstract. Landslide displacement prediction has great practical engineering significance to landslide stability evaluation and early warning. The evolution of landslide is a complex dynamic process, applying classical prediction method will result in significant error. Data assimilation method offers a new way to merge multi-source data with the model. However, data assimilation is still deficient in the ability to meet the demand of dynamic landslide system. In this paper, simultaneous state-parameter estimation (SSPE) using particle filter-based data assimilation is applied to predict displacement of the landslide. Landslide SSPE assimilation strategy can make use of time-series displacements and hydrological information for the joint estimation of landslide displacement and model parameters, which can improve the performance considerably. We select Xishan Village, Sichuan province, China as experiment site to test SSPE assimilation strategy. Based on the comparison of actual monitoring data with prediction values, results strongly suggest the effectiveness and feasibility of SSPE assimilation strategy in short-term landslide displacement estimation.

scholarly journals Estimating Surface Carbon Fluxes Based on a Local Ensemble Transform Kalman Filter with a Short Assimilation Window and a Long Observation Window

2017 ◽  
Author(s):  
Yun Liu ◽  
Eugenia Kalnay ◽  
Ning Zeng ◽  
Ghassem Asrar ◽  
Zhaohui Chen ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Grid Point ◽  
Carbon Fluxes ◽  
Transfer Model ◽  
Observation Window ◽  
Surface Carbon ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform ◽  
Assimilation System

Abstract. We developed a Carbon data assimilation system to estimate the surface carbon fluxes using the Local Ensemble Transform Kalman Filter and atmospheric transfer model of GEOS-Chem driven by the MERRA-1 reanalysis of the meteorological fields based on the Goddard Earth Observing System Model, Version 5 (GEOS-5). This assimilation system is inspired by the method of Kang et al. [2011, 2012], who estimated the surface carbon fluxes in an Observing System Simulation Experiment (OSSE) mode, as evolving parameters in the assimilation of the atmospheric CO2, using a short assimilation window of 6 hours. They included the assimilation of the standard meteorological variables, so that the ensemble provided a measure of the uncertainty in the CO2 transport. After introducing new techniques such as variable localization, and increased observation weights near the surface, they obtained accurate carbon fluxes at grid point resolution. We developed a new version of the LETKF related to the Running-in-Place (RIP) method used to accelerate the spin-up of EnKF data assimilation [Kalnay and Yang, 2010; Wang et al., 2013, Yang et al., 2014]. Like RIP, the new assimilation system uses the no-cost smoothing algorithm for the LETKF [Kalnay et al., 2007b], which allows shifting at no cost the Kalman Filter solution forward or backward within an assimilation window. In the new scheme a long observation window (e.g., 7-days or longer) is used to create an LETKF ensemble at 7-days. Then, the RIP smoother is used to obtain an accurate final analysis at 1-day. This analysis has the advantage of being based on a short assimilation window, which makes it more accurate, and of having been exposed to the future 7-days observations, which accelerates the spin up. The assimilation and observation windows are then shifted forward by one day, and the process is repeated. This reduces significantly the analysis error, suggesting that this method could be used in other data assimilation problems.

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