A method is suggested for estimating unknown velocities by combining their sparse measurements with observations of a tracer on a fine grid advected by the underlined velocity field. The dependence of the estimation error on a coarseness parameter and parameters of the flow in question is investigated numerically using synthetic velocity fields typical for real oceanic circulation. In an advanced version of the estimation procedure uncertainty in the transport equation forcing is modeled via a fuzzy sets approach. We also compare the method with a traditional interpolation which is in contrast to the developed procedure unable to capture the flow details.
Cite this paper
L. Piterbarg and L. Ivanov, "Estimating Circulation Patterns by Combining Velocity and Tracer Observations," Open Journal of Applied Sciences, Vol. 3 No. 1, 2013, pp. 8-14. doi: 10.4236/ojapps.2013.31002.
 C. Wunsch, “The North Atlantic General Circulation West of 50W Determined by Inverse Methods,” Reviews of Geophysics, Vol. 16, No. 4, 1978, pp. 583-620.
 M. E. Fiadeiro and G. Veronis, “Obtaining Velocities from Tracer Distributions,” Journal of Physical Oceanography, Vol. 14, No. 11, 1984, pp. 1734-1746.
 C. Wunsch, “Can a Tracer Field Be Inverted for Veloci ty?” Journal of Physical Oceanography, Vol. 15, No. 11, 1985, pp. 1521-1531.
 K. A. Kelly, “An Inverse Model for Near-Surface Veloci ty from Infrared Images,” Journal of Physical Oceanography, Vol. 19, No. 12, 1989, pp. 1845-1864.
 C. Frankignoul and R. W. Reynolds, “Testing a Dynami cal Model for Mid-Latitude Sea Surface Temperature Anomalies,” Journal of Physical Oceanography, Vol. 13, No. 7, 1983, pp. 1131-1145.
 A. G. Ostrovskii and L. I. Piterbarg, “Inversion for the Heat Anomaly Transport from SST Time Series,” Journal of Geophysical Research: Oceans, Vol. 100, No. C3, 1995, pp. 4845-4865. doi:10.1029/94JC03041
 A. G. Ostrovskii and L. I. Piterbarg, “A New Method for Obtaining Velocity and Mixing Coefficients from Time Dependent Distributions of Tracer,” Journal of Computational Physics, Vol. 133, No. 2, 1997, pp. 340-360.
 A. G. Ostrovskii and L. I. Piterbarg, “Inversion of Upper Ocean Temperature Time Series for Entrainment, Advection, and Diffusivity,” Journal of Physical Oceanography, Vol. 72, No. 1, 2000, pp. 301-315.
 W. J. Emery, A. C. Thomas, M. J. Collins,W. R. Craw ford and D. L. Mackas, “An Objective Procedure to Compute Surface Advective Velocities from Sequential Infrared Satellite Images,” Journal of Geophysical Research, Vol. 91, No. 12, 1986, pp. 12865-12879.
 W. J. Emery, C. W. Fowler and C. A. Clayson, “Satellite Image Derived Gulf Stream Currents,” Journal of Atmospheric and Oceanic Technology, Vol. 9, No. 3, 1992, pp. 285-304.
 I. Crocker, D. Matthews, W. J. Emery and D. Baldwin, “Computing Ocean Surface Currents from Infrared and Ocean Color Imagery,” IEEE Transactions on Geoscience and Remote Sensing, Vol. 45, No. 2, 2007, pp. 435-447. doi:10.1109/TGRS.2006.883461
 A. Turiel, J. Sol, V. Nieves, J. Ballabrera-Poy and E. Gar ca-Ladona, “Tracking Oceanic Currents by Singularity Analysis of Microwave Sea Surface Temperature Images,” Remote Sensing of Environment, Vol. 112, No. 5, 2008, pp. 2246-2260. doi:10.1016/j.rse.2007.10.007
 A. F. Bennett, “Inverse Methods in Physical Oceanogra phy,” Cambridge University Press, Cambridge, 1992.
 E. Huot, T. Isambert, I. Herlin, J.-P. Berroir and G. Korotaev, “Data Assimilation of Satellite Images within an Oceanographic Circulation Model,” Acoustics, Speech and Signal Processing, Vol. 2, No. 3, 2006, pp. 265-268.
 W. Chen, “Nonlinear Inverse Model for Velocity Estimation from Infrared Image Sequences,” International Archives of the Photogrammetry, Remote Sensing and Spatial Information Science, Vol. 8, No. 10, 2010, pp. 958-963.
 A. Mercatini, A. Griffa, L. Piterbarg, E. Zambianchi and M. G. Magaldi, “Estimating Surface Velocities from Satellite Data and Numerical Models: Implementation and Testing of a New Simple Method,” Ocean Modeling, Vol. 33, No. , 2010, pp. 190-203.
 L. I. Piterbarg, “A Simple Method for Computing Velocities from Tracer Observations and a Model Output,” Applied Mathematical Modeling, Vol. 33, No. 1-2, 2009, pp. 3693-3704. doi:10.1016/j.apm.2008.12.006
 L. I. Piterbarg and L. Ivanov, “Fuzzy-logic Based Algorithm for Estimating Circulation Patterns,” Current Applied Mathematics, Vol. 1, No. 1, 2011, pp. 17-39.
 D. Dubious and H. Prade, “Possibility Theory,” Plenum Press, New York and London, 1986.
 G. Shafer, “A Mathematical Theory of Evidence,” Prince ton University Press, Princeton, 1976.
 K. Deb, “Multi-Objective Optimization Using Evolutionary Algorithms,” Willey, Hoboken, 2001.