年間 6 号発行
ISSN 印刷: 1543-1649
ISSN オンライン: 1940-4352
Indexed in
Inverse Shallow-Water Flow Modeling Using Model Reduction
要約
The idea presented in this paper is variational data assimilation based on model reduction using proper orthogonal decomposition. An ensemble of forward model simulations is used to determine the approximation of the covariance matrix of the model variability, and only the dominant eigenvectors of this matrix are used to define a model subspace. An approximate linear reduced model is obtained by projecting the original model onto this reduced subspace. Compared to the classical variational method, the adjoint of the tangent linear model is replaced by the adjoint of a linear reduced forward model. Thus, it does not require the implementation of the adjoint of the tangent linear model. The minimization process is carried out in reduced subspace and hence reduces the computational cost. Twin experiments using an operational storm surge prediction model in the Netherlands, the Dutch Continental Shelf Model are performed to estimate the water depth, with the findings that the approach with relatively little computational cost and without the burden of implementation of the adjoint model can be used in variational data assimilation.
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Ten-Brummelhuis, P. G. J., Heemink, A.W., and van den Boogard, H. F. P., Identification of shallow sea models. DOI: 10.1002/fld.1650170802
-
Lardner, R.W., Al-Rabeh, A. H., and Gunay, N., Optimal Estimation of Parameters for a Two Dimensional Hydrodynamical Model of the Arabian Gulf. DOI: 10.1029/93JC01411
-
Ulman, D. S., andWilson, R. E., Model Parameter Estimation for Data Assimilation Modeling: Temporal and Spatial Variability of the Bottom Drag Coefficient. DOI: 10.1029/97JC03178
-
Heemink, A. W., Mouthaan, E. E. A., and Roest, M. R. T., Inverse 3D Shallow-Water Flow Modeling of the Continental Shelf. DOI: 10.1016/S0278-4343(01)00071-1
-
Kaminski, T., Giering, R., and Scholze, M., An Example of an Automatic Differentiationbased Modeling System. DOI: 10.1007/3-540-44843-8_11
-
Antoulas, A. C., Approximation of Large-Scale Dynamical Systems.
-
Pearson, K., On Lines and Planes of Closest Fit to Points in Space. DOI: 10.1080/14786440109462720
-
Kepler, G. M., Tran, H. T., and Banks, H. T., Reduced-Order Compensator Control of Species Transport in CVD Reactor.
-
Prabhu, R. D., Scott, C. S., and Changly, Y., The Influence of Control on Proper Orthogonal Decomposition of Wall-Bounded Turbulent Flows. DOI: 10.1063/1.1333038
-
Alfonsi, G., Restanob, C., and Primaveral, L., Coherent Structures of the Flow around a Surface-Mounted Cubic Obstacle in Turbulent Channel Flow. DOI: 10.1016/S0167-6105(02)00429-4
-
Cao, Y., Zhu, J., Luo, Z., and Navon, I. M., Reduced Order Modeling of the Upper Tropical Pacific Ocean Model Using Proper Orthogonal Decomposition. DOI: 10.1016/j.camwa.2006.11.012
-
Gunzburger, M. D., Reduced-Order Modeling, Data Compression and the Design of Experiments.
-
Le Dimet, F. X., and Talagrand, O., Variational Algorithms for Analysis and Assimilation of Meteorological Observations: Theoratical Aspects. DOI: 10.1111/j.1600-0870.1986.tb00459.x
-
Lawless, A. S., Nichols, N. C., Boess, C., and Bunse-Gerstner, A., Using Model Reduction Methods within Incremental 4DVAR. DOI: 10.1175/2007MWR2103.1
-
Daescu, D. N., and Navon, I. M., A Dual Weighted Approach to Order Reduction in 4DVAR Data Assimilation. DOI: 10.1175/2007MWR2102.1
-
Fang, F., Pain, C. C., Navon, I. M., Piggott, D., Gorman, G. J., Farrell, P. E., Allison, P. A., and Goddard, A. J. H., Reduced order modeling of an adaptive mesh ocean model. DOI: 10.1002/fld.1841
-
Fang, F., Pain, C. C., Navon, I. M., Piggott, D., Gorman, G. J., Allison, P. A., and Goddard, A. J. H., A POD Reduced-Order Unstructured Mesh Ocean Modelling Method for Moderate Reynolds Number Flows. DOI: 10.1016/j.ocemod.2008.12.006
-
Delay, F., Buoro, A., and de Marsily, G., Empirical Orthogonal Functions Analysis Applied to the Inverse Problem in Hydrogeology: Evaluation of Uncertainty and Simulation of New Solutions. DOI: 10.1023/A:1012298023051
-
Vermeulen, P. T. M., Heemink, A. W., and Valstar, J. R., Inverse Modeling of Groundwater Flow Using Model Reduction. DOI: 10.1029/2004WR003698
-
Vermeulen, P. T. M., and Heemink, A. W., Model-Reduced Variational Data Assimilation. DOI: 10.1175/MWR3209.1
-
Courant, R., and Hilbert, D., Methods of Mathematical Physics.
-
Sirovich, L., Choatic Dynamics of Coherent Structures. DOI: 10.1016/0167-2789(89)90123-1
-
Cao, Y., Zhu, J., Navon, I. M., and Luo, Z., A Reduced-Order Approach to Fourdimensional Variational Data Assimilation Using Proper Orthogonal Decomposition. DOI: 10.1002/fld.1365
-
Leendertse, J., Aspects of a Computational Model for Long-Period Water Wave Propagation.
-
Stelling, G. S., On the Construction of Computational Methods for ShallowWater Flow Problem.
-
Verboom, G. K., de Ronde, J. G., and van Dijk, R. P., A Fine Grid Tidal Flow and Storm Surge Model of the North Sea. DOI: 10.1016/0278-4343(92)90030-N
-
Mouthaan, E., Heemink, A. W., and Robaczewska, K., Assimilation of ERS-1 Altimeter Data in a Tidal Model of the Continental Shelf. DOI: 10.1007/BF02226308
-
Verlaan, M., Zijderveld, A., Vries, H., and Kroos, J., Operational Storm Surge Forcasting in the Netherlands: Developments in Last Decade. DOI: 10.1098/rsta.2005.1578
-
Verlaan, M., Mouthaan, E., Kuijper, E., and Philippart, M., Parameter Estimation Tools for Shallow Water Flow Models.
-
Verlaan, M., Efficient Kalman Filtering Algorithms for Hydrodynamic Models.
-
Ten-Brummelhuis, P. G. J., Parameter Estimation in Tidal Flow Models with Uncertain Boundary Conditions.
-
Velzen, N., and Verlaan, M., Costa a Problem Solving Environment for Data Assimilation Applied for Hydrodynamical Modeling.
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Kaleta Małgorzata P., Hanea Remus G., Heemink Arnold W., Jansen Jan-Dirk, Model-reduced gradient-based history matching, Computational Geosciences, 15, 1, 2011. Crossref
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Chen X., Navon I. M., Fang F., A dual-weighted trust-region adaptive POD 4D-VAR applied to a finite-element shallow-water equations model, International Journal for Numerical Methods in Fluids, 65, 5, 2011. Crossref
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Chen X., Akella S., Navon I. M., A dual-weighted trust-region adaptive POD 4-D Var applied to a finite-volume shallow water equations model on the sphere, International Journal for Numerical Methods in Fluids, 68, 3, 2012. Crossref
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Altaf Muhammad Umer, Heemink Arnold W., Verlaan Martin, Hoteit Ibrahim, Simultaneous perturbation stochastic approximation for tidal models, Ocean Dynamics, 61, 8, 2011. Crossref
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Du Juan, Navon I.M., Zhu Jiang, Fang Fangxin, Alekseev A.K., Reduced order modeling based on POD of a parabolized Navier–Stokes equations model II: Trust region POD 4D VAR data assimilation, Computers & Mathematics with Applications, 65, 3, 2013. Crossref
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Ştefănescu R., Navon I.M., POD/DEIM nonlinear model order reduction of an ADI implicit shallow water equations model, Journal of Computational Physics, 237, 2013. Crossref
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Altaf M. U., Verlaan M., Heemink A. W., Efficient identification of uncertain parameters in a large-scale tidal model of the European continental shelf by proper orthogonal decomposition, International Journal for Numerical Methods in Fluids, 68, 4, 2012. Crossref
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Pelc Joanna S., Simon Ehouarn, Bertino Laurent, El Serafy Ghada, Heemink Arnold W., Application of model reduced 4D-Var to a 1D ecosystem model, Ocean Modelling, 57-58, 2012. Crossref
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Garcia Ivan D., Serafy Ghada El, Heemink Arnold, Schuttelaars Henk, Towards a data assimilation system for morphodynamic modeling: bathymetric data assimilation for wave property estimation, Ocean Dynamics, 63, 5, 2013. Crossref
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Fang F., Pain C.C., Navon I.M., Cacuci D.G., Chen X., The independent set perturbation method for efficient computation of sensitivities with applications to data assimilation and a finite element shallow water model, Computers & Fluids, 76, 2013. Crossref
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Wahle Kathrin, Staneva Joanna, Guenther Heinz, Data assimilation of ocean wind waves using Neural Networks. A case study for the German Bight, Ocean Modelling, 96, 2015. Crossref
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van Velzen Nils, Altaf Muhammad Umer, Verlaan Martin, OpenDA-NEMO framework for ocean data assimilation, Ocean Dynamics, 66, 5, 2016. Crossref
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Xiao Cong, Leeuwenburgh Olwijn, Lin Hai Xiang, Heemink Arnold, Non-intrusive subdomain POD-TPWL for reservoir history matching, Computational Geosciences, 23, 3, 2019. Crossref
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Xiao Cong, Leeuwenburgh Olwijn, Lin Hai Xiang, Heemink Arnold, Efficient estimation of space varying parameters in numerical models using non-intrusive subdomain reduced order modeling, Journal of Computational Physics, 424, 2021. Crossref
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Xiao Cong, Tian Leng, Surrogate‐Based Joint Estimation of Subsurface Geological and Relative Permeability Parameters for High‐Dimensional Inverse Problem by Use of Smooth Local Parameterization, Water Resources Research, 56, 7, 2020. Crossref
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Xiao Cong, Deng Ya, Wang Guangdong, Deep‐Learning‐Based Adjoint State Method: Methodology and Preliminary Application to Inverse Modeling, Water Resources Research, 57, 2, 2021. Crossref
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Xiao Cong, Zhang Shicheng, Ma Xinfang, Jin Jianbing, Zhou Tong, Model‐Reduced Adjoint‐Based Inversion Using Deep‐Learning: Example of Geological Carbon Sequestration Modeling, Water Resources Research, 58, 1, 2022. Crossref
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Xiao Cong, Lin Hai-Xiang, Leeuwenburgh Olwijn, Heemink Arnold, Surrogate-assisted inversion for large-scale history matching: Comparative study between projection-based reduced-order modeling and deep neural network, Journal of Petroleum Science and Engineering, 208, 2022. Crossref