High-resolution data assimilation through stochastic subgrid tensor and parameter estimation from 4DEnVar

References

• Aksoy, A., Zhang, F. and Nielsen-Gammon, J. W. 2006. Ensemble-based simultaneous state and parameter estimation in a two-dimensional sea-breeze model. Mon. Wea. Rev. 134(10), 2951–2970.
   Web of Science ®Google Scholar
• Anderson, J. L. 2001. An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev. 129(12), 2884–2903.
   Web of Science ®Google Scholar
• Anderson, J. L. and Anderson, S. L. 1999. A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Mon. Wea. Rev. 127(12), 2741–2758.
   Web of Science ®Google Scholar
• Baek, S.-J., Hunt, B. R., Kalnay, E., Ott, E. and Szunyogh, I. 2006. Local ensemble Kalman filtering in the presence of model bias. TellusA 58(3), 293–306.
   Google Scholar
• Bereziat, D. and Herlin, I. 2015. Coupling dynamic equations and satellite images for modeling ocean surface circulation. Commun. Comput. Inf. Sci. 550, 191–205.
   Google Scholar
• Beyou, S., Cuzol, A., Gorthi, S. and Mémin, E. 2013. Weighted ensemble transform kalman filter for image assimilation. Tellus 65A, 18803.
   Google Scholar
• Bocquet, M. 2015. Localization and the iterative ensemble Kalman smoother. Q. J. R. Meteorol. Soc. 142(695), 1075–1089.
   Web of Science ®Google Scholar
• Bocquet, M. and Sakov, P. 2013a. An iterative ensemble Kalman smoother. Q. J. R. Meteorol. Soc. 140(682), 1521–1535.
   Web of Science ®Google Scholar
• Bocquet, M. and Sakov, P. 2013b. Joint state and parameter estimation with an iterative ensemble Kalman smoother. Nonlinear Proc. Geoph. 20(5), 803–818.
   Web of Science ®Google Scholar
• Bradford, S. F. and Sanders, B. F. 2002. Finite-volume model for shallow-water flooding of arbitrary topography. J. Hydraulic Eng. 128, 289–298.
   Web of Science ®Google Scholar
• Buehner, M. 2005. Ensemble-derived stationary and flow-dependent background-error covariances: Evaluation in a quasi-operational NWP setting. Q. J. R. Meteorol. Soc. 131(607), 1013–1043.
   Web of Science ®Google Scholar
• Buehner, M., Houtekamer, P. L., Charette, C., Mitchell, H. L. and He, B. 2010. Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part I: Description and single-observation experiments. Mon. Wea. Rev. 138(5), 1550–1566.
   Web of Science ®Google Scholar
• Buizza, R., Miller, M. and Palmer, T. 1999. Stochastic representation of model uncertainties in the ECMWF ensemble prediction system. Q. J. R. Meteorol. Soc. 125, 2887–2908.
   Web of Science ®Google Scholar
• Cacuci, D., Navon, I. and Ionescu-Bujor, M. 2013. Computational Methods for Data Evaluation and Assimilation. Boca Radon, FL: CRC Press.
   Google Scholar
• Chabot, V., Nodet, M., Papadakis, N. and Vidard, A. 2015. Accounting for observation errors in image data assimilation. Tellus 67A, 23629.
   Google Scholar
• Combes, B., Heitz, D., Guibert, A. and Mémin, E. 2015. A particle filter to reconstruct a free-surface flow from a depth camera. Fluid Dyn. Res. 47(5), 051404.
   Web of Science ®Google Scholar
• Corpetti, T., Héas, P., Mémin, E. and Papadakis, N. 2009. Pressure image assimilation for atmospheric motion estimation. Tellus 61A(1), 160–178.
   Google Scholar
• Courtier, P., Thépaut, J.-N. and Hollingsworth, A. 1994. A strategy for operational implementation of 4d-var, using an incremental approach. Q. J. R. Meteorol. Soc. 120(519), 1367–1387.
   Web of Science ®Google Scholar
• Cuzol, A. and Mémin, E. 2009. A stochastic filtering technique for fluid flow velocity fields tracking. IEEE Trans. Pattern Anal. Mach. Intell. 31(7), 1278–1293.
   Web of Science ®Google Scholar
• Da Prato, G. and Zabczyk, J. 1992. Stochastic Equations in Infinite Dimensions. Cambridge: Cambridge University Press.
   Google Scholar
• Dee, D. P. 2005. Bias and data assimilation. Q. J. R. Meteorol. Soc. 131(613), 3323–3343.
   Web of Science ®Google Scholar
• Evensen, G. 1994. Sequential data assimilation with a non linear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. 99(C5)(10), 143–162.
   Web of Science ®Google Scholar
• Evensen, G. 2003. The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn. 53, 343–367.
   Google Scholar
• Fairbairn, D., Pring, S. R., Lorenc, A. C. and Roulstone, I. 2013. A comparison of 4DVar with ensemble data assimilation methods. Q. J. R. Meteorol. Soc. 140(678), 281–294.
   Web of Science ®Google Scholar
• Frederiksen, J. S., O’Kane, T. J. and Zidikheri, M. J. 1982. Subgrid modelling for geophysical flows. Philo. Trans. A: Math. Phys. Eng. Sci. 2013(371), 20120166.
   Google Scholar
• Gaspari, G. and Cohn, S. E. 1999. Construction of correlation functions in two and three dimensions. Q. J. R. Meteorol. Soc. 125(554), 723–757.
   Web of Science ®Google Scholar
• Gordon, N., Salmond, D. and Smith, A. 1993. Novel approach to non-linear/non-Gaussian bayesian state estimation. IEE Processing-F 140(2), 107–113.
   Google Scholar
• Gottwald, G. A. and Majda, A. 2013. A mechanism for catastrophic filter divergence in data assimilation for sparse observation networks. Nonlinear Proc. Geoph. 20(5), 705–712.
   Web of Science ®Google Scholar
• Greybush, S. J., Kalnay, E., Miyoshi, T., Ide, K. and Hunt, B. R. 2011. Balance and ensemble Kalman filter localization techniques. Mon. Wea. Rev. 139(2), 511–522.
   Web of Science ®Google Scholar
• Gu, Y. and Oliver, D. S. 2007. An iterative ensemble Kalman filter for multiphase fluid flow data assimilation. SPE J. 12(04), 438–446.
   Web of Science ®Google Scholar
• Gustafsson, N. and Bojarova, J. 2014. Four-dimensional ensemble variational (4D-En-Var) data assimilation for the HIgh Resolution Limited Area Model (HIRLAM). Nonlinear Proc. Geoph. 21(4), 745–762.
   Web of Science ®Google Scholar
• Heitz, D., Memin, E. and Schnoerr, C. 2010. Variational fluid flow measurements from image sequences: Synopsis and perspectives. Exp. Fluids 48(3), 369–393.
   Web of Science ®Google Scholar
• Hunt, B. R., Kostelich, E. J. and Szunyogh, I. 2007. Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D 230, 112–126.
   Web of Science ®Google Scholar
• Huot, E., Herlin, I. and Papari, G. 2013. Optimal orthogonal basis and image assimilation: Motion modeling. In: IEEE International Conference on Computer Vision, Sydney, Australia.
   Google Scholar
• Kadri Harouna, S. and Mémin, E. 2016. Stochastic Representation of the Reynolds Transport Theorem: Revisiting Large-scale Modeling. Working Paper or preprint.
   Google Scholar
• Kalnay, E. and Yang, S.-c. 2010. Accelerating the spin-up of ensemble Kalman filtering. Q. J. R. Meteorol. Soc. 136(651), 1644–1651.
   Web of Science ®Google Scholar
• Kang, J.-S., Kalnay, E., Liu, J., Fung, I., Miyoshi, T., co-authors. 2011. “Variable localization” in an ensemble Kalman filter: Application to the carbon cycle data assimilation. J. Geophys. Res. Atmos. 116(D9), 1984–2012.
   Web of Science ®Google Scholar
• Koyama, H. and Watanabe, M. 2010. Reducing forecast errors due to model imperfections using ensemble Kalman filtering. Mon. Wea. Rev. 138(8), 3316–3332.
   Web of Science ®Google Scholar
• Kunita, H. 1990. Stochastic Flows and Stochastic Differential Equations. Cambridge: Cambridge University Press.
   Google Scholar
• Le Dimet, F.-X. and Talagrand, O. 1986. Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects. Tellus 38A, 97–110.
   Google Scholar
• Leith, C. 1990. Stochastic backscatter in a subgrid-scale model: Plane shear mixing layer. Phys. Fluids 2(3), 1521–1530.
   Web of Science ®Google Scholar
• Lions, J. L. 1971. Optimal Control of Systems Governed by PDEs. Springer-Verlag, New York.
   Google Scholar
• Liu, C., Xiao, Q. and Wang, B. 2008. An ensemble-based four-dimensional variational data assimilation scheme. Part I: Technical formulation and preliminary test. Mon. Wea. Rev. 136(9), 3363–3373.
   Web of Science ®Google Scholar
• Mason, P. and Thomson, D. 1992. Stochastic backscatter in large-eddy simulations of boundary layers. J. Fluid Mech. 242, 51–78.
   Web of Science ®Google Scholar
• Mémin, E. 2014. Fluid flow dynamics under location uncertainty. Geophys. Astro. Fluid. 108(2), 119–146.
   Web of Science ®Google Scholar
• Miller, R. N., Carter, E. F. and Blue, S. T. 1999. Data assimilation into nonlinear stochastic models. Tellus 51A(2), 167–194.
   Google Scholar
• Navon, I. 1998. Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography. Dyn. Atmos. Oceans 27(1), 55–79.
   Web of Science ®Google Scholar
• Ott, E., Hunt, B. R., Szunyogh, I., Zimin, A. V., Kostelich, E. J., co-authors. 2004. A local ensemble Kalman filter for atmospheric data assimilation. Tellus 56A, 415–428.
   Google Scholar
• Papadakis, N. and Mémin, E. 2008. Variational assimilation of fluid motion from image sequence. SIAM J. Imaging Sci. 1(4), 343–363.
   Web of Science ®Google Scholar
• Pulido, M. and Thuburn, J. 2005. Gravity wave drag estimation from global analyses using variational data assimilation principles. i: Theory and implementation. Q. J. R. Meteorol. Soc. 131(609), 1821–1840.
   Web of Science ®Google Scholar
• Resseguier, V., Mémin, E. and Chapron, B. in press-a. Geophysical flows under location uncertainty, part I Random transport and general models. Geophys. Astro. Fluid.
   Google Scholar
• Resseguier, V., Mémin, E. and Chapron, B. in press-b. Geophysical flows under location uncertainty, part II Quasigeostrophic models and efficient ensemble spreading. Geophys. Astro. Fluid.
   Google Scholar
• Resseguier, V., Mémin, E. and Chapron, B. in press-c. Geophysical flows under location uncertainty, part III SQG and frontal dynamics under strong turbulence. Geophys. Astro. Fluid.
   Web of Science ®Google Scholar
• Ruiz, J. and Pulido, M. 2015. Parameter estimation using ensemble-based data assimilation in the presence of model error. Mon. Wea. Rev. 143(5), 1568–1582.
   Web of Science ®Google Scholar
• Ruiz, J., Pulido, M. and Miyoshi, T. 2013. Estimating model parameters with ensemble-based data assimilation: Parameter covariance treatment. J. Meteorol. Soc. Jap. 91(4), 453–469.
   Web of Science ®Google Scholar
• Sagaut, P. 2006. Large Eddy Simulation for Incompressible Flows: An Introduction. Berlin: Springer-Verlag.
   Google Scholar
• Sakov, P. and Bertino, L. 2011. Relation between two common localisation methods for the EnKF. Computat. Geosci. 15(2), 225–237.
   Web of Science ®Google Scholar
• Sakov, P. and Oke, P. R. 2008. A deterministic formulation of the ensemble Kalman filter: An alternative to ensemble square root filters. Tellus A 60(2), 361–371.
   Google Scholar
• Sakov, P., Oliver, D. S. and Bertino, L. 2012. An iterative EnKF for strongly nonlinear systems. Mon. Wea. Rev. 140(6), 1988–2004.
   Web of Science ®Google Scholar
• Sawada, M., Sakai, T., Iwasaki, T., Seko, H., Saito, K., co-authors. 2015. Assimilating high-resolution winds from a Doppler lidar using an ensemble Kalman filter with lateral boundary adjustment. Tellus 67A, 1–13.
   Google Scholar
• Shutts, G. 2005. A kinetic energy backscatter algorithm for use in ensemble prediction systems. Q. J. R. Meteorol. Soc. 612, 3079–3012.
   Web of Science ®Google Scholar
• Simon, E., Samuelsen, A., Bertino, L. and Mouysset, S. 2015. Experiences in multiyear combined state-parameter estimation with an ecosystem model of the North Atlantic and Arctic Oceans using the ensemble Kalman filter. J. Marine Syst. 152(C), 1–17.
   Web of Science ®Google Scholar
• Slingo, J. and Palmer, T. 2011. Uncertainty in weather and climate prediction. Philo. Trans. A: Math. Phys. Eng. Sci. 1956(369), 4751–4767.
   Web of Science ®Google Scholar
• Smagorinsky, J. 1963. General circulation experiments with the primitive equations: I. The basic experiment*. Mon. Wea. Rev. 91(3), 99–164.
   Google Scholar
• Talagrand, O. 1997. Assimilation of observations, an introduction. J. Meteorol. Soc. Japan. 75(1), 191-209.
   Web of Science ®Google Scholar
• Tandeo, P., Pulido, M. and Lott, F. 2014. Offline parameter estimation using EnKF and maximum likelihood error covariance estimates: Application to a subgrid-scale orography parametrization. Q. J. R. Meteorol. Soc. 141(687), 383–395.
   Web of Science ®Google Scholar
• Titaud, O., Vidard, A., Souopgui, I. and Le Dimet, F.-X. 2010. Assimilation of image sequences in numerical models. Tellus 62A(1), 30–47.
   Google Scholar
• Tong, M. and Xue, M. 2008. Simultaneous estimation of microphysical parameters and atmospheric state with simulated radar data and ensemble square root Kalman filter. part i: Sensitivity analysis and parameter identifiability. Mon. Wea. Rev. 136(5), 1630–1648.
   Web of Science ®Google Scholar
• Wei, M., Jacobs, G., Rowley, C., Barron, C., Hogan, P., co-authors. 2013. The impact of initial spread calibration on the relo ensemble and its application to lagrangian dynamics. Nonlinear Proc. Geoph. 20(5), 621–641.
   Web of Science ®Google Scholar
• Yang, X. and Delsole, T. 2009. Using the ensemble Kalman filter to estimate multiplicative model parameters. TellusA 61(5), 601–609.
   Google Scholar
• Yang, Y., Robinson, C., Heitz, D. and Mémin, E. 2015. Enhanced ensemble-based 4dvar scheme for data assimilation. Comput. Fluids 115(C), 201–210.
   Web of Science ®Google Scholar
• Zhang, F., Snyder, C. and Sun, J. 2004. Impacts of initial estimate and observation availability on convective-scale data assimilation with an ensemble Kalman filter. Mon. Wea. Rev. 132(5), 1238–1253.
   Web of Science ®Google Scholar
• Zhu, Y. and Navon, I. 1999. Impact of parameter estimation on the performance of the FSU global spectral model using its full-physics adjoint. Mon. Wea. Rev. 127(7), 1497–1517.
   Web of Science ®Google Scholar
• Zupanski, D. and Zupanski, M. 2006. Model error estimation employing an ensemble data assimilation approach. Mon. Wea. Rev. 134(5), 1337–1354.
   Web of Science ®Google Scholar