Efficiency of using 4DVar, 3DVar and EnKF data assimilation methods in groundwater contaminant transport modelling

References

• Altaf, M., El Gharamti, M., Heemink, A., & Hoteit, I. (2013). A reduced adjoint approach to variational data assimilation. Computer Methods in Applied Mechanics and Engineering, 254, 1–13.10.1016/j.cma.2012.10.003
   Web of Science ®Google Scholar
• Assumaning, G. A., & Chang, S.-Y. (2012). Use of simulation filters in three-dimensional groundwater contaminant transport modeling. Journal of Environmental Engineering, 138, 1122–1129.10.1061/(ASCE)EE.1943-7870.0000578
   Web of Science ®Google Scholar
• Beale, C. M., Lennon, J. J., Yearsley, J. M., Brewer, M. J., & Elston, D. A. (2010). Regression analysis of spatial data. Ecology Letters, 13, 246–264. doi:10.1111/j.1461-0248.2009.01422.x
   PubMed Web of Science ®Google Scholar
• Bouttier, F., & Courtier, P. (2002). Data assimilation concepts and methods March 1999. Meteorological Training Course Lecture Series. ECMWF.
   Google Scholar
• Chang, S.-Y., & Jin, A. (2011). Dual state-mechanism adjustment adaptive filtering to improve accuracy of subsurface transport models. Journal of Environmental Engineering, 138, 17–26.
   Web of Science ®Google Scholar
• Chang, S.-Y., & Latif, S. M. I. (2009). Extended Kalman filtering to improve the accuracy of a subsurface contaminant transport model. Journal of Environmental Engineering, 136, 466–474.
   Web of Science ®Google Scholar
• Courtier, P., Thépaut, J. N., & Hollingsworth, A. (1994). A strategy for operational implementation of 4D-Var, using an incremental approach. Quarterly Journal of the Royal Meteorological Society, 120, 1367–1387.10.1002/(ISSN)1477-870X
   Web of Science ®Google Scholar
• Daescu, D., & Navon, I. (2008). A dual-weighted approach to order reduction in 4DVAR data assimilation. Monthly Weather Review, 136, 1026–1041.10.1175/2007MWR2102.1
   Web of Science ®Google Scholar
• Evensen, G. (2003). The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dynamics, 53, 343–367.10.1007/s10236-003-0036-9
   Google Scholar
• Gao, J., Xue, M., & Stensrud, D. J. (2013). The development of a hybrid EnKF-3DVAR algorithm for storm-scale data assimilation. Advances in Meteorology. doi:10.1155/2013/512656
   PubMed Web of Science ®Google Scholar
• Gillijns, S., Mendoza, O. B., Chandrasekar, J., De Moor, B., Bernstein, D., & Ridley, A. (2006). What is the ensemble Kalman filter and how well does it work? Paper presented at the American Control Conference, Minneapolis, Minnesota, USA.
   Google Scholar
• Hamill, T. M., & Snyder, C. (2000). A hybrid ensemble Kalman filter–3D variational analysis scheme. Monthly Weather Review, 128, 2905–2919.10.1175/1520-0493(2000)128<2905:AHEKFV>2.0.CO;2
   Web of Science ®Google Scholar
• Johnson, C. (2003). Information content of observations in variational data assimilation. University of Reading.
   Google Scholar
• Kalnay, E., Li, H., Miyoshi, T., Yang, S. C., & Ballabrera-Poy, J. (2007). 4-D-Var or ensemble Kalman filter? Tellus A, 59, 758–773.10.1111/tea.2007.59.issue-5
   Google Scholar
• Latif, S., & Chang, S.-Y. (2014). Ensemble Kalman Filter with regional covariance to improve the accuracy of a three dimensional contaminant transport model. Journal of Civil Engineering and Architecture Research, 1, 87–103.
   Google Scholar
• Lawless, A., Nichols, N., Boess, C., & Bunse-Gerstner, A. (2008). Using model reduction methods within incremental four-dimensional variational data assimilation. Monthly Weather Review, 136, 1511–1522.10.1175/2007MWR2103.1
   Web of Science ®Google Scholar
• Lee, M.-S., Kuo, Y.-H., Barker, D. M., & Lim, E. (2006). Incremental analysis updates initialization technique applied to 10-km MM5 and MM5 3DVAR. Monthly Weather Review, 134, 1389–1404.10.1175/MWR3129.1
   Web of Science ®Google Scholar
• Liu, H., Xue, M., Purser, R. J., & Parrish, D. F. (2007). Retrieval of moisture from simulated GPS slant-path water vapor observations using 3DVAR with anisotropic recursive filters. Monthly Weather Review, 135, 1506–1521. doi:10.1175/MWR3345.1
   Web of Science ®Google Scholar
• Liu, C., Xiao, Q., & Wang, B. (2008). An ensemble-based four-dimensional variational data assimilation scheme. Part I: Technical formulation and preliminary test. Monthly Weather Review, 136, 3363–3373.10.1175/2008MWR2312.1
   Web of Science ®Google Scholar
• Lorenc, A. C., & Rawlins, F. (2005). Why does 4D-Var beat 3D-Var? Quarterly Journal of the Royal Meteorological Society, 131, 3247–3257.10.1256/qj.05.85
   Web of Science ®Google Scholar
• Lorenc, A., Ballard, S., Bell, R., Ingleby, N., Andrews, P., Barker, D., … Li, D. (2000). The Met. Office global three-dimensional variational data assimilation scheme. Quarterly Journal of the Royal Meteorological Society, 126, 2991–3012.10.1002/(ISSN)1477-870X
   Web of Science ®Google Scholar
• Lorenc, A. C., Bowler, N. E., Clayton, A. M., Pring, S. R., & Fairbairn, D. (2015). Comparison of hybrid-4DEnVar and hybrid-4DVar data assimilation methods for global NWP. Monthly Weather Review, 143, 212–229.10.1175/MWR-D-14-00195.1
   Web of Science ®Google Scholar
• Moradkhani, H., Sorooshian, S., Gupta, H. V., & Houser, P. R. (2005). Dual state–parameter estimation of hydrological models using ensemble Kalman filter. Advances in Water Resources, 28, 135–147.10.1016/j.advwatres.2004.09.002
   Web of Science ®Google Scholar
• Nash, J., & Sutcliffe, J. V. (1970). River flow forecasting through conceptual models part I – A discussion of principles. Journal of Hydrology, 10, 282–290.10.1016/0022-1694(70)90255-6
   Google Scholar
• Nowak, W. (2009). Best unbiased ensemble linearization and the quasi-linear Kalman ensemble generator. Water Resources Research, 45. doi:10.1029/2008WR007328
   Web of Science ®Google Scholar
• Papadakis, N., Mémin, É., Cuzol, A., & Gengembre, N. (2010). Data assimilation with the weighted ensemble Kalman filter. Tellus A, 62, 673–697.
   Google Scholar
• Pelc, J. S., Simon, E., Bertino, L., El Serafy, G., & Heemink, A. W. (2012). Application of model reduced 4D-Var to a 1D ecosystem model. Ocean Modelling, 57–58, 43–58.10.1016/j.ocemod.2012.09.003
   Web of Science ®Google Scholar
• Qiu, C., Shao, A., Xu, Q., & Wei, L. (2007). Fitting model fields to observations by using singular value decomposition: An ensemble-based 4DVar approach. Journal of Geophysical Research: Atmospheres (1984–2012), 112.
   Web of Science ®Google Scholar
• Rawlins, F., Ballard, S., Bovis, K., Clayton, A., Li, D., Inverarity, G., … Payne, T. (2007). The Met Office global four-dimensional variational data assimilation scheme. Quarterly Journal of the Royal Meteorological Society, 133, 347–362.10.1002/(ISSN)1477-870X
   Web of Science ®Google Scholar
• Robert, C., Blayo, E., & Verron, J. (2006). Reduced-order 4D-Var: A preconditioner for the Incremental 4D-Var data assimilation method. Geophysical research letters, 33.
   PubMed Web of Science ®Google Scholar
• Schwartz, F., & Domenico, P. A. (1997). Physical and chemical hydrogeology. New York, NY: John Wiley.
   Google Scholar
• Song, H., Edwards, C. A., Moore, A. M., & Fiechter, J. (2012). Incremental four-dimensional variational data assimilation of positive-definite oceanic variables using a logarithm transformation. Ocean Modelling, 54–55, 1–17.10.1016/j.ocemod.2012.06.001
   Web of Science ®Google Scholar
• Tsai, C. W., & Franceschini, S. (2005). Evaluation of probabilistic point estimate methods in uncertainty analysis for environmental engineering applications. Journal of Environmental Engineering, 131, 387–395.10.1061/(ASCE)0733-9372(2005)131:3(387)
   Web of Science ®Google Scholar
• Vermeulen, P., & Heemink, A. (2006). Model-reduced variational data assimilation. Monthly Weather Review, 134, 2888–2899.10.1175/MWR3209.1
   Web of Science ®Google Scholar
• Wackernagel, H., & Bertino, L. (2005). Geostatistics and sequential data assimilation . Geostatistics Banff 2004 (pp. 893–898). Banff, Alberta, Canada. Springer.
   Google Scholar
• Wang, X., & Lei, T. (2014). GSI-based four-dimensional ensemble-variational (4DEnsVar) data assimilation: Formulation and single-resolution experiments with real data for NCEP global forecast system. Monthly Weather Review, 142, 3303–3325.10.1175/MWR-D-13-00303.1
   Web of Science ®Google Scholar
• Wang, X., Barker, D. M., Snyder, C., & Hamill, T. M. (2008). A hybrid ETKF–3DVAR data assimilation scheme for the WRF model. Part I: Observing system simulation experiment. Monthly Weather Review, 136, 5116–5131.10.1175/2008MWR2444.1
   Web of Science ®Google Scholar
• Zhang, F., Zhang, M., & Hansen, J. A. (2009). Coupling ensemble Kalman filter with four-dimensional variational data assimilation. Advances in Atmospheric Sciences, 26(1), 1–8.10.1007/s00376-009-0001-8
   Web of Science ®Google Scholar
• Zhou, H., Li, L., Franssen, H.-J. H., & Gómez-Hernández, J. J. (2012). Pattern recognition in a bimodal aquifer using the normal-score ensemble Kalman filter. Mathematical Geosciences, 44, 169–185.10.1007/s11004-011-9372-3
   Web of Science ®Google Scholar