10.4122/1.1000000205
Muccino, Julia
Julia
Muccino
jmuccino@asu.edu
Luo, Hao
Hao
Luo
hao.luo@asu.edu
Chua, Boon
Boon
Chua
chua@coas.oregonstate.edu
Muccino, Julia
Julia
Muccino
jmuccino@asu.edu
Adjoint symmetry for Inverse ADCIRC
XVI International Conference on Computational Methods in Water Resources
2006
2006
ADCIRC, a finite element circulation model for shelves, coasts and estuaries, is used
for weak constraint variational data assimilation. That is, data will be smoothed in
space and time using ADCIRC and boundary conditions as a weak constraints; the
smoother is defined in terms of a quadratic penalty functional which is composed of
dynamic, boundary condition and data error terms. The assimilation will be effected
by the Inverse Ocean Modeling system (IOM). This system solves the nonlinear
Euler-Lagrange (EL) problem using the iterated representer algorithm, which makes
large, nonlinear but functionally smooth optimization problems feasible through
Picard iterations on linear approximations of the nonlinear problem and by making
preconditioned searches in the "data subspace" at each iterate. Much of the IOM is
modular; the significant components required by the modeler are an iteration scheme
and an adjoint operator.
The iteration scheme has already been established; the purpose of this paper is to
discuss the derivation and verification of the adjoint. Owing to the scientific
purposes of data assimilation, we define the penalty functional in terms of the
primitive formulation of the shallow water equations, rather than the wave
formulation used by ADCIRC. This fundamental decision leads to a number of
difficulties in the derivation of the adjoint and consequential loss of adjoint
symmetry, and thus to a suboptimal solution. We show that this cannot be avoided
without loss of the scientific objective of the project. We also identify and
quantify the specific characteristics of the ADCIRC wave equation formulation which
preclude computing THE optimal solution, and show that the suboptimal solution we
find is still of scientific value.