Passive tracer reconstruction as a least-squares problem with a semi-Lagrangian constraint: An application to fish eggs and larvae
A variational, data assimilation, algorithm was developed for reconstruction of a two-dimensional, nonstationary, passive tracer field in the ocean with open boundaries and a known velocity field. The observations, spatial smoothing terms and passive tracer conservation equation were included as weak constraints. The algorithm was tested with simulated, nonstationary, pseudo-oceanographic data integrated for a 7-day period. Simulations were run to determine the robustness of the algorithm and the effect of theoretical, simulated 'sampling events,' mimicking the standard oceanographic survey. We explored the sensitivity of the reconstructed tracer fields to the distribution of the pseudo-oceanographic sampling strategy, essentially an antenna problem, and to errors in the velocity field and the observations. The algorithm was applied to observations of silver hake ( Merluccius bilinearis) eggs and larvae obtained in August 1998 on the Scotian Shelf. Finally, the evolution of fish eggs and larvae concentration was found. The corresponding mortality rate of fish eggs and larvae was determined to be 0.28 day-1, with errors of 0.03 day-1. The approach, which is quite general and could be applied to many different problems requiring minimization subject to constraints, allows for error analysis of the results.
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Document Type: Research Article
Publication date: November 1, 2004
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