Adaptive Observations And Multilevel Optimization
In Data Assimilation
S. Gratton, M. M. Rincon-Camacho and Ph. L. Toint
Report NAXYS-05-2013 21 May 2013
Abstract.
We propose to use a decomposition of large-scale incremental four
dimensional (4D-Var) data assimilation problems in order to make their
numerical solution more efficient. This decomposition is based on exploiting
an adaptive hierarchy of the observations. Starting with a low-cardinality
set and the solution of its corresponding optimization problem, observations
are adaptively added based on a posteriori error estimates. The
particular structure of the sequence of associated linear systems allows the
use of a variant of the conjugate gradient algorithm which effectively
exploits the fact that the number of observations is smaller than the size
of the vector state in the 4D-Var model. The method proposed is justified by
deriving the relevant error estimates at different levels of the hierarchy
and a practical computational technique is then derived. The new algorithm
is tested on a 1D-wave equation and on the Lorenz-96 system, the latter one
being of special interest because of its similarity with Numerical Weather
Prediction (NWP) systems.