A probabilistic collocation based iterative Kalman filter for landfill data assimilation

2017 ◽  
Vol 109 ◽  
pp. 170-180 ◽  
Author(s):  
Qiang Zheng ◽  
Wenjie Xu ◽  
Jun Man ◽  
Lingzao Zeng ◽  
Laosheng Wu
SPE Journal ◽  
2011 ◽  
Vol 16 (02) ◽  
pp. 294-306 ◽  
Author(s):  
Lingzao Zeng ◽  
Haibin Chang ◽  
Dongxiao Zhang

Summary The ensemble Kalman filter (EnKF) has been used widely for data assimilation. Because the EnKF is a Monte Carlo-based method, a large ensemble size is required to reduce the sampling errors. In this study, a probabilistic collocation-based Kalman filter (PCKF) is developed to adjust the reservoir parameters to honor the production data. It combines the advantages of the EnKF for dynamic data assimilation and the polynomial chaos expansion (PCE) for efficient uncertainty quantification. In this approach, all the system parameters and states and the production data are approximated by the PCE. The PCE coefficients are solved with the probabilistic collocation method (PCM). Collocation realizations are constructed by choosing collocation point sets in the random space. The simulation for each collocation realization is solved forward in time independently by means of an existing deterministic solver, as in the EnKF method. In the analysis step, the needed covariance is approximated by the PCE coefficients. In this study, a square-root filter is employed to update the PCE coefficients. After the analysis, new collocation realizations are constructed. With the parameter collocation realizations as the inputs and the state collocation realizations as initial conditions, respectively, the simulations are forwarded to the next analysis step. Synthetic 2D water/oil examples are used to demonstrate the applicability of the PCKF in history matching. The results are compared with those from the EnKF on the basis of the same analysis. It is shown that the estimations provided by the PCKF are comparable to those obtained from the EnKF. The biggest improvement of the PCKF comes from the leading PCE approximation, with which the computational burden of the PCKF can be greatly reduced by means of a smaller number of simulation runs, and the PCKF outperforms the EnKF for a similar computational effort. When the correlation ratio is much smaller, the PCKF still provides estimations with a better accuracy for a small computational effort.


Author(s):  
Nicolas Papadakis ◽  
Etienne Mémin ◽  
Anne Cuzol ◽  
Nicolas Gengembre

1997 ◽  
Vol 125 (7) ◽  
pp. 1674-1686 ◽  
Author(s):  
P. M. Lyster ◽  
S. E. Cohn ◽  
R. Ménard ◽  
L-P. Chang ◽  
S-J. Lin ◽  
...  

2016 ◽  
Vol 66 (8) ◽  
pp. 955-971 ◽  
Author(s):  
Stéphanie Ponsar ◽  
Patrick Luyten ◽  
Valérie Dulière

2014 ◽  
Vol 142 (2) ◽  
pp. 716-738 ◽  
Author(s):  
Craig S. Schwartz ◽  
Zhiquan Liu

Abstract Analyses with 20-km horizontal grid spacing were produced from parallel continuously cycling three-dimensional variational (3DVAR), ensemble square root Kalman filter (EnSRF), and “hybrid” variational–ensemble data assimilation (DA) systems between 0000 UTC 6 May and 0000 UTC 21 June 2011 over a domain spanning the contiguous United States. Beginning 9 May, the 0000 UTC analyses initialized 36-h Weather Research and Forecasting Model (WRF) forecasts containing a large convection-permitting 4-km nest. These 4-km 3DVAR-, EnSRF-, and hybrid-initialized forecasts were compared to benchmark WRF forecasts initialized by interpolating 0000 UTC Global Forecast System (GFS) analyses onto the computational domain. While important differences regarding mean state characteristics of the 20-km DA systems were noted, verification efforts focused on the 4-km precipitation forecasts. The 3DVAR-, hybrid-, and EnSRF-initialized 4-km precipitation forecasts performed similarly regarding general precipitation characteristics, such as timing of the diurnal cycle, and all three forecast sets had high precipitation biases at heavier rainfall rates. However, meaningful differences emerged regarding precipitation placement as quantified by the fractions skill score. For most forecast hours, the hybrid-initialized 4-km precipitation forecasts were better than the EnSRF-, 3DVAR-, and GFS-initialized forecasts, and the improvement was often statistically significant at the 95th percentile. These results demonstrate the potential of limited-area continuously cycling hybrid DA configurations and suggest additional hybrid development is warranted.


Icarus ◽  
2010 ◽  
Vol 209 (2) ◽  
pp. 470-481 ◽  
Author(s):  
Matthew J. Hoffman ◽  
Steven J. Greybush ◽  
R. John Wilson ◽  
Gyorgyi Gyarmati ◽  
Ross N. Hoffman ◽  
...  

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