#### Date of Award

1998

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### First Advisor

Lawrence J. Rouse, Jr

#### Abstract

Oceanic surface velocity fields are objectively estimated from time-sequential satellite images of sea-surface temperature from the Advanced Very High Resolution Radiometey on board the National Oceanic and Atmospheric Administration's polar orbiters. The hierarchical technique uses the concept of image pyramids and multi-resolution grids for increased computational efficiency. Images are Gaussian filtered and sub-sampled from fine to coarse grid scales. The number of pyramid levels is selected such that the maximum expected velocity in the image results in a displacement of less than one pixel at the coarsest spatial scale. Maximum Cross-Correlation at the sub-pixel level with orthogonal polynomial approximation is used to compute a velocity field at each level of the pyramid which is then iterated assuming a locally linear velocity field. The first image at the next finer level of the pyramid is warped towards the second image by the calculated velocity field. At each succeeding finer grid scale, the velocity field is updated and the process repeated. The final result is an estimated velocity at each pixel at the finest resolution of the imagery. There are no free parameters as used in some gradient-based approaches and the only assumption is that the velocity field is locally linear. Test cases are shown using both simulated and real images with numerically simulated velocity fields which demonstrate the accuracy of the technique. Results are compared to gradient-based techniques using concepts of optical flow and projection onto convex sets and to the standard Maximum Cross-Correlation technique. The hierarchical computations for a real satellite image numerically advected by a rotational sheared flow recover the original field with a rms speed error of 12.6% and direction error of 4.9$\sp\circ.$ Hierarchically-estimated velocity fields from real image pairs are compared to ground-truth estimates of the velocity from satellite-tracked drifters in the eastern Gulf of Mexico. Results indicate the technique underestimates daily mean buoy vector speeds, but with reasonably good direction. The problems of ground truth relations to hierarchically computed flows are discussed with regard to mismatches of time and space scales of measurement.

#### Recommended Citation

Leming, Thomas Dean, "Hierarchical Estimation of Oceanic Surface Velocity Fields From Satellite Imagery." (1998). *LSU Historical Dissertations and Theses*. 6786.

https://digitalcommons.lsu.edu/gradschool_disstheses/6786

#### ISBN

9780599081772

#### Pages

219

#### DOI

10.31390/gradschool_disstheses.6786