Using flow geometry for drifter deployment in Lagrangian data assimilation

Methods of Lagrangian data assimilation (LaDA) require carefully chosen sites for optimal drifter deployments. In this work, we investigate a directed drifter deployment strategy with a recently developed LaDA method employing an augmented state vector formulation for an Ensemble Kalman filter. We test our directed drifter deployment strategy by targeting Lagrangian coherent flow structures of an unsteady double gyre flow to analyse how different release sites influence the performance of the method.We consider four different launch methods; a uniform launch, a saddle launch in which hyperbolic trajectories are targeted, a vortex centre launch, and a mixed launch targeting both saddles and centres. We show that global errors in the flow field require good dispersion of the drifters which can be realized with the saddle launch. Local errors on the other hand are effectively reduced by targeting specific flow features. In general, we conclude that it is best to target the strongest hyperbolic trajectories for shorter forecasts although vortex centres can produce good drifter dispersion upon bifurcating on longer time-scales.

[1]  木村 竜治,et al.  J. Pedlosky: Geophysical Fluid Dynamics, Springer-Verlag, New York and Heidelberg, 1979, xii+624ページ, 23.5×15.5cm, $39.8. , 1981 .

[2]  J. Holton Geophysical fluid dynamics. , 1983, Science.

[3]  H. Aref Stirring by chaotic advection , 1984, Journal of Fluid Mechanics.

[4]  E. F. Carter,et al.  Assimilation of Lagrangian data into a numerical model , 1989 .

[5]  A. Bower A Simple Kinematic Mechanism for Mixing Fluid Parcels across a Meandering Jet , 1991 .

[6]  C. Schär,et al.  Shallow-water flow past isolated topography. Part I: Vorticity production and wake formation , 1993 .

[7]  C. Schär,et al.  Shallow-Water Flow past Isolated Topography. Part II: Transition to Vortex Shedding , 1993 .

[8]  Peter R. Gent,et al.  The energetically consistent shallow-water equations , 1993 .

[9]  G. Evensen Sequential data assimilation with a nonlinear quasi‐geostrophic model using Monte Carlo methods to forecast error statistics , 1994 .

[10]  B. Cushman-Roisin Introduction to Geophysical Fluid Dynamics , 1994 .

[11]  J. O'Brien,et al.  Continuous data assimilation of drifting buoy trajectory into an equatorial Pacific Ocean model , 1995 .

[12]  Hassan Aref,et al.  Chaos applied to fluid mixing , 1995 .

[13]  Alexander F. Shchepetkin,et al.  A Physically Consistent Formulation of Lateral Friction in Shallow-Water Equation Ocean Models , 1996 .

[14]  Stephen Wiggins,et al.  Geometric Structures, Lobe Dynamics, and Lagrangian Transport in Flows with Aperiodic Time-Dependence, with Applications to Rossby Wave Flow , 1998 .

[15]  George Haller,et al.  Finite time transport in aperiodic flows , 1998 .

[16]  George Haller,et al.  Geometry of Cross-Stream Mixing in a Double-Gyre Ocean Model , 1999 .

[17]  Stephen Wiggins,et al.  Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics , 2000 .

[18]  S. Cohn,et al.  Ooce Note Series on Global Modeling and Data Assimilation Construction of Correlation Functions in Two and Three Dimensions and Convolution Covariance Functions , 2022 .

[19]  Annalisa Griffa,et al.  On the Predictability of Lagrangian Trajectories in the Ocean , 2000 .

[20]  Stephen Wiggins,et al.  Intergyre transport in a wind-driven, quasigeostrophic double gyre: An application of lobe dynamics , 2000 .

[21]  G. Haller Distinguished material surfaces and coherent structures in three-dimensional fluid flows , 2001 .

[22]  J. Whitaker,et al.  Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter , 2001 .

[23]  Christopher K. R. T. Jones,et al.  Drifter Launch Strategies Based on Lagrangian Templates , 2002 .

[24]  G. Haller Lagrangian coherent structures from approximate velocity data , 2002 .

[25]  Christopher K. R. T. Jones,et al.  Chapter 2 – Invariant Manifolds and Lagrangian Dynamics in the Ocean and Atmosphere , 2002 .

[26]  Christopher K. R. T. Jones,et al.  The Loop Current and adjacent rings delineated by Lagrangian analysis of the near-surface flow , 2002 .

[27]  K. Ide,et al.  Lagrangian data assimilation for point vortex systems , 2002 .

[28]  K. Ide,et al.  A Method for Assimilation of Lagrangian Data , 2003 .

[29]  A. Mariano,et al.  Assimilation of drifter observations for the reconstruction of the Eulerian circulation field , 2003 .

[30]  T. M. Chin,et al.  Assimilation of drifter observations in primitive equation models of midlatitude ocean circulation , 2003 .

[31]  Geir Evensen,et al.  The Ensemble Kalman Filter: theoretical formulation and practical implementation , 2003 .

[32]  Andrew C. Poje,et al.  Nonlinear Processes in Geophysics Lagrangian Velocity Statistics of Directed Launch Strategies in a Gulf of Mexico Model , 2022 .

[33]  Stephen Wiggins,et al.  Computation of hyperbolic trajectories and their stable and unstable manifolds for oceanographic flows represented as data sets , 2004 .

[34]  Stephen Wiggins,et al.  The dynamical systems approach to lagrangian transport in oceanic flows , 2005 .

[35]  George Haller,et al.  Predicting transport by Lagrangian coherent structures with a high-order method , 2006 .

[36]  Tamay M. Özgökmen,et al.  Directed drifter launch strategies for Lagrangian data assimilation using hyperbolic trajectories , 2006 .

[37]  K. Ide,et al.  A Method for Assimilating Lagrangian Data into a Shallow-Water-Equation Ocean Model , 2006 .

[38]  Pierre F. J. Lermusiaux,et al.  Quantifying Uncertainties in Ocean Predictions , 2006 .

[39]  William E. Johns,et al.  Product water mass formation by turbulent density currents from a high-order nonhydrostatic spectral element model , 2006 .