The subject of inverse problems in differential equations is of enormous practical
importance, and has also generated substantial mathematical and computational …

The Gauss–Newton algorithm is an iterative method regularly used for solving nonlinear
least squares problems. It is particularly well suited to the treatment of very large scale …

Recent data assimilation developments which have taken place at numerical weather‐
prediction centres are briefly discussed, from the perspectives of both the importance of data …

Four‐dimensional variational data assimilation (4DVAR) is a powerful tool for data
assimilation in meteorology and oceanography. However, a major hurdle in use of 4DVAR …

GSI-Based Four-Dimensional Ensemble–Variational (4DEnsVar) Data Assimilation: Formulation
and Single-Resolution Experiments with Real Data for NCEP Global Forecast System in …

Remote sensing observations often have correlated errors, but the correlations are typically
ignored in data assimilation for numerical weather prediction. The assumption of zero …

Data assimilation provides techniques for combining observations and prior model forecasts
to create initial conditions for numerical weather prediction (NWP). The relative weighting …

The viewpoint taken in this paper is that data assimilation is fundamentally a statistical
problem and that this problem should be cast in a Bayesian framework. In the absence of …

Environmental systems can be realistically described by mathematical and numerical
models of the system dynamics. These models can be used to predict the future behaviour of …

Operational forecasting centres are currently developing data assimilation systems for
coupled atmosphere–ocean models. Strongly coupled assimilation, in which a single …