Abstract
The adequacy of observations to locate the minimum of the standard cost function for variational data assimilation under strong constraint has been investigated. A simplified yet meaningful Lagrangian air/sea interaction model that captures key aspects of air mass modification over the Gulf of Mexico in wintertime is the dynamical tool used to examine this question of adequacy. Two mathematically different yet equivalent variational schemes are used in numerical experiments with a fixed number of observations along a prior known trajectory over the Gulf. Research clearly indicates that sensitivity of model output to elements of control (initial condition, boundary condition, and physical parameter) is key to placement of observations in order to minimize the cost function and determine optimal corrections to control.
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Acknowledgements
The authors thank Carlisle Thacker for a copy of his notes on variational data assimilation associated with his 1989 invited lectures at the Forschungscentrum in Hamburg, Germany. His discussion of adequacy/inadequacy of observations in variational analysis was especially lucid. We also thank research meteorologists Geoff Manikin and Zavisa Janjic of NCEP/EMC (National Center for Environmental Prediction/Environmental Modeling Center) for valued discussions related to the possible sources of bias in forecasts of return flow over the Gulf of Mexico.
We thank Joan O’Bannon, former graphics specialist at National Severe Storms Laboratory, for drafting Fig. 5.1, and we thank the National Geographic Society, particularly Eric Lindstrom, the Society’s senior map editor and map library director, for permission to reproduce the bathymetric chart of the Gulf of Mexico that has been used as backdrop for the trajectory in Fig. 5.2. S. Lakshmivarahan’s efforts are supported in part by two grants: NSF EPSCOR Track 2 grant 105-155900 and NSF grant 105-15400.
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Lewis, J.M., Lakshmivarahan, S. (2013). A Question of Adequacy of Observations in Variational Data Assimilation. In: Park, S., Xu, L. (eds) Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol. II). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35088-7_5
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