Seeking an Objective Method of Estimating the Value of Diffusion Coefficient for an Increased Resolution of Model
by
Kyungjeen Park
FSU
Coauthors: X. Zou, and F. X. Le Dimet

A twin experiment was designed to estimate the diffusion coefficient of a 1-D shallow water model using adjoint techniques. Two different resolutions of the model were used for the experiment: a low-resolution model was used to generate ``observations'' and a high-resolution model was used as an assimilation model, with its diffusion coefficient serving as a control variable. In general, the diffusion coefficient should be ufficiently large (low limit) to remove unwanted small-scale noises, but small enough (upper limit) to avoid computational instability. A least-square fit of the high-resolution model solution to ``observations'' (low-resolution model solution) was found to be able to objectively determine an ``optimal'' diffusion coefficient value for the high-resolution model that produced sufficient damping on small-scale noises without generating computational instability in the high-resolution model. It was found that an assimilation window that is too short ( <= 2 hours) may result in an ``optimal'' diffusion coefficient value that fails to ensure there will be no computational instability and no undamped noises generated beyond the assimilation window during the model integration. We notice, however, that the values of the cost function increase very rapidly when the diffusion coefficient slightly exceeds the upper limit due to computational instability. Such an abrupt change of the cost function near the upper limit may cause the minimization to fail to find the true minimum when a more complicated model is used. Methods of improving the conditioning of the cost function are being studied and results will also be presented at the conference.

Date received: February 21, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cads-87.