Abstract
We apply the recently proposed hybrid particle-ensemble Kalman filter to assimilate Lagrangian data into a non-linear, high-dimensional quasi-geostrophic ocean model. Effectively the hybrid filter applies a particle filter to the highly nonlinear, low-dimensional Lagrangian instrument variables while applying an ensemble Kalman type update to the high-dimensional Eulerian flow field. We present some initial results from this hybrid filter and compare those to results from a standard ensemble Kalman filter and an ensemble run without assimilation.
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Notes
- 1.
We will use the term drifter going forward to refer to any Lagrangian instrument.
- 2.
We use a modified version of the codes due to Guillaume Roullet. [13].
References
Apte, A., Jones, C.: The effect of nonlinearity on Lagrangian data assimilation. Nonlin. Process. Geophys. 20, 329–341 (2013)
Beskos, A., Crisan, D., Jasra, A.: On the stability of sequential Monte Carlo methods in high dimensions. Ann. Appl. Probab. 24(4), 1396–1445 (2014). http://arxiv.org/abs/1103.3965
Beskos, A., Crisan., D., Jasra., A., Whiteley., N.: Error bounds and normalizing constants for sequential Monte Carlo in high dimensions. Adv. Appl. Probab. (To appear). http://arxiv.org/abs/1112.1544
Cotter, S., Dashti, M., Robinson, J., Stuart, A.: Bayesian inverse problems for functions and applications to fluid mechanics. Inverse Prob. 25, 115008 (2009)
Doucet, A., De Freitas, N., Murphy, K., Russell, S.: Rao-blackwellised particle filtering for dynamic bayesian networks. In: Proceedings of the Sixteenth Conference on Uncertainty in Artificial Intelligence, Morgan Kaufmann Publishers Inc., pp. 176–183 (2000)
Ide, K., Kuznetsov, L., Jones, C.K.R.T.: Lagrangian data assimilation for point vortex systems. J. Turbul. 3, 053 (2002)
Kantas, N., Beskos, A., Jasra, A.: Sequential Monte Carlo methods for high-dimensional inverse problems: a case study for the Navier-Stokes equations. SIAM/ASA J. Uncertain. Quantif. 2(1), 464–489 (2014). http://arxiv.org/abs/1307.6127
Kuznetsov, L., Ide, K., Jones, C.K.R.T.: A method for assimilation of Lagrangian data. Mon. Wea. Rev. 131, 2247–2260 (2003)
Molcard, A., Piterbarg, L., Griffa, A., Özgökmen, T., Mariano, A.: Assimilation of drifter positions for the reconstruction of the Eulerian circulation field. J. Geophys. Res. 108, 3056 (2003)
Özgökmen, T., Molcard, A., Chin, T., Piterbarg, L., Griffa, A.: Assimilation of drifter positions in primitive equation models of midlatitude ocean circulation. J. Geophys. Res. 108, 3238 (2003)
Pedlosky, J.: Geophysical Fluid Dynamics. Springer, New York (1986)
Robert, C., Casella, G.: Monte Carlo Statistical Methods. Springer, New York (1999)
Roullet, G.: 2d versatile model - multimod (2013). http://stockage.univ-brest.fr/roullet/codes.html
Salman, H.: A hybrid grid/particle filter for lagrangian data assimilation. i: formulating the passive scalar approximation. Q. J. Roy. Meteor. Soc. 134, 1539–1550 (2008a)
Salman, H.: A hybrid grid/particle filter for lagrangian data assimilation. ii: application to a model vortex flow. Q. J. Roy. Meteor. Soc. 134, 1539–1550 (2008b)
Salman, H., Kuznetsov, L., Jones, C.K.R.T., Ide, K.: A method for assimilating Lagrangian data into a shallow-water equation ocean model. Mon. Wea. Rev. 134, 1081–1101 (2006)
Cotter, S.L., Roberts, G.O., Stuart, A., White, D.: MCMC methods for functions: modifying old algorithms to make them faster. Stat. Sci. 28, 424–446 (2013)
Slivinski, L., Spiller, E., Apte, A., Sanstede, B.: A hybrid particle-ensemble Kalman filter for Lagrangian data assimilation. Mon. Wea. Rev. 143, 195–211 (2014). http://www.whoi.edu/cms/files/hybrid_MWR_2col_194185.pdf
Snyder, C., Bengtsson, T., Bickel, P., Anderson, J.: Obstacles to high-dimensional particle filtering. Mon. Wea. Rev. 136, 4629–4640 (2008)
Spiller, E., Budhiraja, A., Ide, K., Jones, C.: Modified particle filter methods for assimilating Lagrangian data into a point-vortex model. Physica D 237, 1498–1506 (2008)
Acknowledgments
The authors would like to acknowledge the use of the numerical implementation of the QG model by Guillaume Roullet (see http://stockage.univ-brest.fr/~roullet/codes.html). The authors would like to thank Chris Jones for initially suggesting this collaboration and the Mathematics and Climate Research Network (NSF grant DMS-0940363) for enabling this collaboration. Apte would like to thank the EADS/Airbus Chair in ‘Mathematics of Complex Systems’ at TIFR for partial support for this work. Spiller would like to acknowledge support by NSF grant DMS-1228265 and ONR grant N00014-11-1-0087.
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Slivinski, L., Spiller, E., Apte, A. (2015). A Hybrid Particle-Ensemble Kalman Filter for High Dimensional Lagrangian Data Assimilation. In: Ravela, S., Sandu, A. (eds) Dynamic Data-Driven Environmental Systems Science. DyDESS 2014. Lecture Notes in Computer Science(), vol 8964. Springer, Cham. https://doi.org/10.1007/978-3-319-25138-7_24
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DOI: https://doi.org/10.1007/978-3-319-25138-7_24
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