ABSTRACT
The objective of four-dimensional variational data assimilation (4-D VAR) is
to find a model solution which best fits observational data distributed over
some space and time intervals. A popular measure of the lack of fit between
model forecast and observations is a cost function, J , mathematically describ-
ing a weighted least-square norm. Assuming that the observations are given
by analyzed fields, such a cost function can be represented in the form
J(~X(t0)) = 1
[ X(tr)−Xobs(tr)
]T W(tr)
[ X(tr)−Xobs(tr)
] , (5.1)
where: X(tr) is a vector of dimension N containing all model variables over
all grid points at time tr; R is the number of time levels for the analyzed fields
Evaluation and
in the assimilation window; Xobs(tr) is the observational counterpart of the
model variable X(tr); W (tr) is an N ×N diagonal matrix of weighting coefficients, usually taken to be the inverse covariance matrix of the observations
errors.
