Statistics – Computation
Scientific paper
Aug 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978dyato...2..341f&link_type=abstract
Dynamics of Atmospheres and Oceans, Volume 2, Issue 4, p. 341-381.
Statistics
Computation
38
Scientific paper
Methods of calibration layer models (choosing the adjustable parameters defifining the layer depths and density steps) are presented. The radii of deformation, the surface and bottom amplitudes of the vertical normal modes and the depth-averaged triple products of the modes are the important functionals of the stratification which determine the behavior of the system. We show how these can be matched to the equivalent two-layer model functions of the density step ɛ and upper-layer depth H1 in three different physical situations: time-dependent wind forcing, bottom slope or friction influences, and nonlinear interactions. In each physical situation we illustrate two different choices of which characteristics of the behavior to match and make quantitative comparisons with a continuously stratified model with the stratification derived from oceanic data. These examples show that the optimal calibrations are very different in the three physical situations; i.e., any single choice of ɛ and H1 will inevitably lead to serious errors in predicting the behavior in at least two of the three physical situations. This inaccuracy may lead to serious qualitative misbehavior of a two-layer model in a situation where two or more physical processes are competing (e.g., bottom topography and nonlinearity). We propose a two-mode model (of the same computational simplicity) which does not suffer from this problem, but is optimally calibrated in all three physical situations without changes in the parameters. In addition, it offers the advantages of being automatically calibrated by the specification of the mean continuous density profile and being readily applied to oceanic data of all kinds.
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