Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient methods for computing observation impact in 4D-Var data
  assimilation   This paper presents a practical computational approach to quantify the effect
of individual observations in estimating the state of a system. Such an
analysis can be used for pruning redundant measurements, and for designing
future sensor networks. The mathematical approach is based on computing the
sensitivity of the reanalysis (unconstrained optimization solution) with
respect to the data. The computational cost is dominated by the solution of a
linear system, whose matrix is the Hessian of the cost function, and is only
available in operator form. The right hand side is the gradient of a scalar
cost function that quantifies the forecast error of the numerical model. The
use of adjoint models to obtain the necessary first and second order
derivatives is discussed. We study various strategies to accelerate the
computation, including matrix-free iterative solvers, preconditioners, and an
in-house multigrid solver. Experiments are conducted on both a small-size
shallow-water equations model, and on a large-scale numerical weather
prediction model, in order to illustrate the capabilities of the new
methodology.

10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ